Research Collection

Doctoral Thesis

Within-host population dynamics and the evolution of drugresistance in bacterial infections

Author(s): Cadosch, Dominique Richard

Publication Date: 2016

Permanent Link: https://doi.org/10.3929/ethz-a-010795126

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ETH Library

DISS. ETH NO. 23499

W I T H I N - H O S T P O P U L AT I O N D Y N A M I C S A N D T H E E V O L U T I O NO F D R U G R E S I S TA N C E I N B A C T E R I A L I N F E C T I O N S

A thesis submitted to attain the degree of

DOCTOR OF SCIENCES of ETH ZÜRICH

(Dr. sc. ETH Zürich)

presented by

D O M I N I Q U E R I C H A R D C A D O S C H

M.Sc. ETH Zürich, Switzerland

born on 30.05.1984

citizen of Vaz/Obervaz GR, Switzerland

accepted on the recommendation by

Prof. Dr. Sebastian Bonhoeffer, examinerProf. Dr. Theodore H. Cohen, co-examiner

PD Dr. Roland Regoes, co-examiner

2016

To my parents, Ruth and Edgar Cadosch,for their sedulous support and guidance.

“I have a friend who’s an artist and has sometimes taken a view which I don’tagree with very well. He’ll hold up a flower and say "look how beautiful it is,"and I’ll agree. Then he says "I as an artist can see how beautiful this is but youas a scientist take this all apart and it becomes a dull thing," and I think thathe’s kind of nutty. First of all, the beauty that he sees is available to other peopleand to me too, I believe. Although I may not be quite as refined aestheticallyas he is ... I can appreciate the beauty of a flower. At the same time, I seemuch more about the flower than he sees. I could imagine the cells in there, thecomplicated actions inside, which also have a beauty. I mean it’s not just beautyat this dimension, at one centimeter; there’s also beauty at smaller dimensions,the inner structure, also the processes. The fact that the colors in the flowerevolved in order to attract insects to pollinate it is interesting; it means thatinsects can see the color. It adds a question: does this aesthetic sense also existin the lower forms? Why is it aesthetic? All kinds of interesting questionswhich the science knowledge only adds to the excitement, the mystery and theawe of a flower. It only adds. I don’t understand how it subtracts.”

Richard Feynman

v

C O N T E N T S

summary 1

zusammenfassung 3

1 general introduction 5

2 the role of adherence and retreatment in de novo emer-gence of mdr-tb 11

3 alternative treatment strategies for tuberculosis 39

4 considering antibiotic stress-induced mutagenesis 61

5 general discussion 77

acknowledgements 103

curriculum vitae 105

vii

S U M M A RY

This thesis investigates the influence of population dynamics of bacterial infectionsand their treatment on the probability of the emergence of drug resistance. In partic-ular the study of the effects of suboptimal patient compliance, various treatment reg-imens and the possibility of antibiotic stress-induced mutagenesis call for a deeperunderstanding of the mechanisms at play. The work presented in this study usesmathematical models that incorporate pharmacokinetics and -dynamics, as well asthe effect of bacterial traits to make predictions about the evolution of drug resistance.All dynamics are being simulated at the within-host level.

Chapter 1 is a general introduction of the central themes of this thesis. It givesa short overview over the advent of the study of population dynamics as a field ofresearch. The global significance of tuberculosis and the problems that arise due tothe frequent occurrence of drug resistance are being explained. I also address theissue of suboptimal treatment adherence and rationalize the value of mathematicalmodeling to tackle the questions in the following chapters.

In Chapter 2, we investigate how adherence to the treatment regimen and theuse of a standard retreatment regimen are involved in the emergence of multidrug-resistant tuberculosis (MDR-TB). MDR-TB is characterized by its resistance againstisoniazid and rifampicin, two important first-line drugs. To answer the questionwhether there is a considerable probability for the de novo emergence of MDR-TB wesimulate patients with various degrees of adherence to a standard treatment regimencontaining a combination of four drugs. Patients who do not achieve complete clear-ance of the infection undergo a prolonged retreatment regimen with an additionalfifth drug.

Chapter 3 explores proposed alternative strategies for the treatment of pulmonarytuberculosis. We extend the previously established model and introduce more de-tailed absorption pharmacokinetics. This extension of the model enables us to inves-tigate the potential benefit and effects of extended-release formulations of rifampicin.Extended-release formulations show a much lower absorption and thus exhibit alower but longer time-concentration profile. Such formulations are compared indaily or intermittent treatment regimens with conventional rifampicin formulationsand their influence on the probability of treatment failure and the emergence ofdrug resistance are recorded. Furthermore, we also tested the advantage and risksinvolved with increased rifampicin doses.

Chapter 4 then deals with the concept of antibiotic stress-induced mutagenesis(ASIM). The concept of stress-induced mutagenesis describes the increase of thebacterial mutation rate in response to a stress, such as the exposure to certain an-tibiotics. We propose a model to simulate the increase of the mutation rate in adrug concentration-dependent manner. With this ASIM model we then investigatehow much a model with a fixed mutation rate would underestimate the risk for theemergence of a drug resistance mutation. Lastly, we study whether the regimen ofadministering a stress-inducing drug and a non-stress-inducing drug has an influ-ence on the emergence of resistance if we consider ASIM.

1

2 summary

Finally, in Chapter 5 I put the results and conclusions from the preceding chaptersin a bigger perspective. Furthermore, I present some future directions that could beexplored with further research.

Z U S A M M E N FA S S U N G

Diese Dissertation untersucht den Einfluss von Populationsdynamik in bakteriel-len Infektionen und deren Behandlung auf die Wahrscheinlichkeit des Auftretensvon Medikamentenresistenz. Im Besonderen die Analyse der Effekte suboptimalerPatienten-Adhärenz, die Anwendung unterschiedlicher Behandlungsstrategien unddie Möglichkeit stress-bedingter Mutagenese durch Antibiotika verlangen nach ei-nem tiefgreifenderem Verständnis für die zugrundeliegenden Wirkmechanismen. DieArbeit, welche in dieser Dissertation vorgestellt wird nutzt mathematische Model-le, welche Pharmakokinetik und Pharmakodynamik, sowie Effekte von bakteriellenMerkmalen beinhalten, um Prognosen in Bezug auf die Evolution von Medikamen-tenresistenz aufstellen zu können. Alle Dynamiken werden dabei jeweils auf derEbene eines einzelnen Patienten simuliert.

Kapitel 1 ist eine allgemeine Einführung in die zentralen Themen dieser Disserta-tion. Das Kapitel gibt einen kurzen Überblick über die Ursprünge der Erforschungvon Populationsdynamiken. Die globale Bedeutung von Tuberkulose sowie die Pro-bleme, welche durch das häufige Auftreten von Medikamentenresistenz entstehen,werden erklärt. Ich spreche auch die Thematik von suboptimaler Adhärenz an sowieden Wert von mathematischer Modellierung, um die Fragestellungen der folgendenKapitel anzupacken.

In Kapitel 2 untersuchen wir, wie Adhärenz während der Behandlung und die An-wendung einer standardisierten Nachbehandlung involviert sind in das Auftretenvon multiresistenter Tuberkulose (engl. multi-drugresistant tuberculosis; MDR-TB).MDR-TB ist gekennzeichnet durch die Resistenz gegenüber Isoniazid und Rifampi-cin, zwei wichtigen standardmässig eingesetzten Antibiotika. Um die Frage zu beant-worten, ob es eine nennenswerte Wahrscheinlichkeit gibt für das Auftreten de novoMDR-TB, simulieren wir Patienten mit unterschiedlichen Adhärenzen gegenüber ei-ner Behandlungsstrategie mit einer Kombination von vier Medikamenten. Patienten,in denen die Infektion nicht vollständig sterilisiert wurde, werden einer längerenNachbehandlung mit einem zusätzlichen fünften Medikament unterzogen.

Kapitel 3 erforscht alternative Behandlungsvorschläge für Lungentuberkulose. Wirerweitern das zuvor etablierte Modell und führen eine detailiertere Absorptions-Pharmakokinetik ein. Diese Erweiterung des Modells ermöglicht es uns, die poten-tiellen Vorteile und Auswirkungen eines Retard-Präparats von Rifampicin zu un-tersuchen. Retardarzneiformen zeichnen sich durch eine verlangsamte Absorptionaus und weisen deshalb eine niedrigeres aber gestrecktes Konzentrationsprofil. Sol-che Arzeneiformen werden in täglichen und intermittierenden Behandlungsregimesverglichen mit konventionellen Rifampicin-Präparaten und die Wahrscheinlichkeitenfür ein Behandlungsversagen sowie das Auftreten von Medikamentenresistenz wer-den ermittelt. Des Weiteren testen wir ebenfalls die Vorteile und Risiken die miterhöhten Rifampicindosen verbunden sind.

Kapitel 4 behandelt das Konzept von stressbedingter Mutagenese durch Antibio-tika (engl. antibiotic stress-induced mutagenesis; ASIM). Das Konzept von stressbe-dingter Mutagenese beschreibt den Anstieg der bakteriellen Mutationsrate als Reakti-

3

4 zusammenfassung

on auf einen äusseren Stressreiz, wie die Exposition gegenüber gewissen Antibiotika.Wir stellen ein Modell vor, um den Anstieg der Mutationsrate in Abhängigkeit zurMedikamentenkonzentration zu simulieren. Mit diesem ASIM-Modell untersuchenwir dann, wie stark ein Modell mit einer festen Mutationsrate das Risiko für dasAuftreten von einer Mutation, die zu Medikamentenresistenz führt, unterschätzenwürde. Schliesslich studieren wir ob ein Behandlungsregime, in dem ein stressauslö-sendes mit einem nicht-stressauslösenden Medikament kombiniert wird, einen Ein-fluss auf die Auftrittswahrscheinlichkeit von Medikamentenresistenz hat, wenn wirASIM in Betracht ziehen.

Zuletzt stelle ich in Kapitel 5 die Resultate und Schlussfolgerungen der voran-gegangenen Kapitel in einen grösseren Kontext. Des Weiteren stelle ich möglicheRichtungen vor, welche zukünftige Studien erforschen könnten.

1G E N E R A L I N T R O D U C T I O N

The advent of the scientific discussion of population dynamics is probably An Es-say on the Principle of Population [1] by Thomas Robert Malthus. In this book Malthusintroduces the Malthusian growth model, which describes the exponential growth ofa population over time. This growth is governed by the population growth rate r,sometimes called Malthusian parameter. While this model may seem rather simpleit is still a basic component for most population dynamics models today. It is appli-cable to all scales of life - from large animals and plants down to tumor cells andbacteria.

Since Thomas Robert Malthus the modeling of populations evolved further to reflectmore complex relationships. The influence of density dependence on populationgrowth can be achieved by introducing a carrying capacity parameter that turns theexponential growth model into a logistic function [2]. Further one could considerthe mutual influence of two distinct populations that are either competing over thesame resource or that are in a predator-prey relationship [3]. The complexity mayincrease even more if we consider migration and mutation as well as temporal andspatial dependencies of parameters.

Particularly in the case of infectious diseases the study of population dynamicscan be of great value. Historically this has been done predominantly on an epidemi-ological scale but scientific progress provided a more detailed picture of intra-hostdynamics, which enables the development of models dealing with viral and bacterialpopulations. Among pathogens viruses represent a special case because they dependon the replication machinery of other living cells to proliferate. Bacteria on the otherhand usually reproduce through binary fission.

The study of population dynamics is of particular interest when we try to under-stand the underlying mechanisms of the emergence of drug resistance in bacterialinfections. Here we can examine on an epidemiological scale the population dy-namics of patients who are at risk of being infected, actually infected or who haverecovered from an infection [4] or we can study the population dynamics of bacte-ria (or viruses) inside a patient. In the first case we are interested in the relativespread of susceptible and resistant pathogens in a host population and in the latercase we focus on the spread of individual bacteria and the evolution of drug resistantsubgroups of the overall bacterial population within a single host.

This thesis concentrates on the study of the within-host population dynamics ofa bacterial infection with a particular interest in the corresponding mechanisms thatmay lead to drug resistance. These studies are performed with the help of stochas-tic computer simulations. Two chapters of this thesis deal with the influence oftreatment and retreatment strategies on the emergence of drug resistance in pul-monary tuberculosis infections. The last chapter is a more conceptual work thatinvestigates the impact of antibiotic stress-induced mutagenesis in any bacterial in-fection in which this may occur.

5

6 general introduction

1.1 tuberculosis

Two chapters of this thesis focus on the population dynamics and the treatment ofpulmonary tuberculosis. For years the research funding for tuberculosis has onlybeen a fraction of what is spent on HIV/AIDS [5]. Concerns about tuberculosismay be often less acute due to a reduced awareness among the population in de-veloped countries where incidence rates of TB are mostly rather low [6]. However,there are still about 2 billion people worldwide who are latently infected with TB[7], 9.6 million people have fallen ill and 1.5 million people died in 2014 due to aTB infection [6]. When in the middle of the 20th century effective antibiotics likestreptomycin, isoniazid and rifampicin were discovered tuberculosis was thought tobe under control [8]. Today we have to acknowledge that TB remains a global healthproblem. Even though the global incidence rates of TB started to decline the fre-quency of multidrug-resistant TB (MDR-TB) cases did not decline despite increasedefforts for specialized MDR-TB treatments [6]. MDR-TB is characterized by its resis-tance against at least isoniazid and rifampicin, two important first-line drugs [6]. Insome countries MDR-TB and extensively drug-resistant TB (XDR-TB) have becomea growing epidemic [9; 10; 11]. Besides resistance against isoniazid and rifampicinXDR-TB is also resistant against at least one fluoroquinolone and either kanamycin,amikacin or capreomycin [12].

The standard short-course therapy for TB lasts six months. During the intensivephase of the first two months isoniazid, rifampicin, pyrazinamide and ethambutolare administered as a combination therapy. In the following two months of the con-tinuation phase only isoniazid and rifampicin are given [13]. The reasoning behindthe application of a combination therapy is based on concerns regarding the loss ofefficacy due to the pre-existence or de novo emergence of mono-resistant subpopula-tions [13]. During monotherapy it could be possible for bacteria that already carry acorresponding resistance mutation to gain a selective advantage, eventually replacethe susceptible bacteria and render the therapy ineffective. In combination therapythere should always be another drug against which mono-resistant bacteria are stillsusceptible and are subsequently eradicated.

1.2 adherence

Non-adherence to treatment has always been considered a major risk factor for theemergence of de novo drug resistance [14; 15]. One of the main goals of the directlyobserved treatment, short course strategy (DOTS) by the WHO is to ensure a suffi-ciently high level of adherence to ensure treatment success [16]. The actual monitor-ing of DOTS in resource-limited settings is often provided by community members[17]. However, the actual degree of adherence by patients under such community-base programs has not been assessed [17] and these programs are often beyond directcontrol of health care providers. It is generally often difficult to obtain accurate es-timates of patient adherence. Patients may not truthfully answer in a survey andmore sophisticated measures like a Medication Event Monitoring System (MEMS)[17] may only be conducted on a small scale. It is also imaginable that it not nec-essarily patient compliance that jeopardizes treatment success, discontinuous drug

1.3 methodology 7

supply or other factors that may occasionally prevent physical access to drugs (e.g.unreliable means of transport, armed conflicts etc.) and influence overall adherencenegatively.

Problems that may arise due to suboptimal patient adherence can be relativelyconveniently examined with the help of mathematical models. Mathematical modelsallow us to assess the implications of reduced adherence. We are able to gatherestimates about what levels of adherence are still reasonably safe and when do weface serious consequences. When we assume suboptimal adherence and simulatethe corresponding population dynamics we get predictions about possible negativetreatment outcomes like treatment failure and the emergence of resistance and wealso gather estimates about the strength of association between different adherencelevels and those outcomes.

1.3 methodology

In all chapters of this thesis we are applying mathematical models that are beingsimulated in silico. Mathematical models in evolutionary biology serve generally twopurposes that are also relevant for the conclusions of this thesis. Firstly, mathematicalmodels can be used to do "proof-of-concept" tests [18]. Verbal or theoretical conceptscan be translated into a mathematical model and it can be assessed whether thehypothesized results of the theory coincide with the predictions of the model. Thisis particularly useful for concepts that are difficult to prove in vivo or in vitro becauseof experimental constraints or because of ethical reasons.

The second purpose of mathematical models becomes evident when their validityhas been confirmed by real-life observations. Then they can be used to explore newdirections and make predictions about the natural world. The two purposes of com-putational modeling therefore engage in an ideally mutually stimulating interactionwith empirical sciences: The theory about empirical observations can be tested incomputational models, which then again may extend the currently existing theoryand inspire new empirical investigations.

A crucial point of contact between empiricism and modeling are assumptions. Ahypothesis that is verbalized to explain an empirically observed phenomenon con-tains specific assumptions. These assumptions also have to be the foundation of amathematical model. If the model is then not able to corroborate the hypothesis with-out violating the basic assumptions the hypothesis may have to be reconsidered orreformulated. The reformulation of the hypothesis may be supported by the modelbecause the model allows to test whether changing one or a few assumptions mightbe sufficient to explain the observed phenomenon.

In this thesis we use computational modeling for both scopes. On one hand, themathematical model with which we simulate the course of infection and treatmentof pulmonary tuberculosis is able to replicate patient outcomes that other studiesobserved previously. It is further able to confirm hypotheses about the progression tohigher levels of drug resistance and the risks and chances involved with suboptimaland alternative treatment strategies. On the other hand, our mathematical modelallows us to make qualitative predictions about the potential benefits of retreatment

8 general introduction

regimens and alternative treatment strategies. These results hopefully fuel furtherresearch in these directions.

1.4 overview of chapters

This thesis contains three studies that I conducted during my doctoral studies (Chap-ters 2–4). Chapters 2 and 3 explore how treatment of a pulmonary tuberculosisinfection affects the probabilities for the emergence of drug resistance. Chapter 4 isa more conceptual work and examines how increased mutation rates due to stresselicited by the exposure to antibiotics changes the risk for the emergence of drugresistance. The thesis then concludes with a general Discussion (Chapter 5).

In Chapter 2 we present a model framework that simulates the intra-host pathogen-esis during an acute pulmonary tuberculosis (TB) infection and its treatment. Thepopulation dynamics of M. tuberculosis is modeled in three distinct compartmentswithin the lung: macrophages, granulomas and open cavities [19]. The treatmentthat we apply and the retreatment, in case the first treatment is not able to clearthe infection, correspond to standard regimens recommended by the WHO [20; 21].The stochastic model simulates patient that differ in several pharmacodynamic andpharmacokinetic parameters and they adhere to the treatment regimen to variousdegrees. Eventually after treatment and retreatment, patients are diagnosed as eithersuccessfully treated, if they do not harbor any M. tuberculosis bacteria anymore, failedpatients, if there are any bacteria left, failed patients with multi-drug resistant TB, if10% or more of the remaining bacteria are at least resistant against isoniazid andrifampicin, or failed patients with fully resistant TB, if 10% or more of the remainingbacterial population is resistant against all drugs that have been applied.

Chapter 3 considers alternative treatment strategies for pulmonary tuberculosis.To study these strategies we extend the model framework that we used in Chapter2 with a more detailed pharmacokinetic model. Besides the elimination of the drugin the patient due to excretion the pharmacokinetics model now also simulates theabsorption of the drugs after administration. This enables us to test the efficacy ofdrug formulations that have lower absorption rate constants. Low absorption rateconstants are a characteristic feature of extended-release formulations [22]. In pa-tient simulations we examine how combinations of intermittent and daily treatmentregimens with and without the use of extended-release formulations of rifampicininfluence the probabilities for a successful treatment outcome and for the emergenceof resistance. Lastly, we also test what the effect of a net increase of the rifampicindosage yields for the patient [23].

In Chapter 4 we then explore the influence of antibiotic stress-induced mutagene-sis (ASIM) on the probability for the emergence of resistance. In the model that wepresent the mutation rate of bacteria increases in a concentration-dependent mannerwhen the bacteria are exposed to a drug that triggers a specific stress response [24].We compare the ASIM model with a model that does not consider a change of themutation rate and show the relative differences regarding the probabilities for theoccurrence of resistance mutations. We also show the relative dependence of theobserved effects on the underlying parameters. Eventually, we test whether the in-

1.4 overview of chapters 9

clusion of ASIM causes a difference in the effectiveness of combination therapy or acycling regimen for a single patient.

Chapter 5 is a general discussion of this thesis. There I explore possible futuredirections in which research could expand. I also put the results and observationsthat have been made in this thesis in a bigger perspective.

2T H E R O L E O F A D H E R E N C E A N D R E T R E AT M E N T I N D E N O V OE M E R G E N C E O F M D R - T B

Published as:D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (2016). The Role of Ad-herence and Retreatment in De Novo Emergence of MDR-TB. PLOS ComputationalBiology 12(3):e1004749.

abstract

Treatment failure after therapy of pulmonary tuberculosis (TB) infections is an impor-tant challenge, especially when it coincides with de novo emergence of multi-drug-resistant TB (MDR-TB).We seek to explore possible causes why MDR-TB has beenfound to occur much more often in patients with a history of previous treatment.Wedevelop a mathematical model of the replication of Mycobacterium tuberculosis withina patient reflecting the compartments of macrophages, granulomas, and open cavi-ties as well as parameterizing the effects of drugs on the pathogen dynamics in thesecompartments. We use this model to study the influence of patient adherence to ther-apy and of common retreatment regimens on treatment outcome. As expected, thesimulations show that treatment success increases with increasing adherence. How-ever, treatment occasionally fails even under perfect adherence due to interpatientvariability in pharmacological parameters. The risk of generating MDR de novo ishighest between 40% and 80% adherence. Importantly, our simulations highlight thedouble-edged effect of retreatment: On the one hand, the recommended retreatmentregimen increases the overall success rate compared to re-treating with the initialregimen. On the other hand, it increases the probability to accumulate more resis-tant genotypes. We conclude that treatment adherence is a key factor for a positiveoutcome, and that screening for resistant strains is advisable after treatment failureor relapse.

11

12 the role of adherence and retreatment in de novo emergence of mdr-tb

2.1 author summary

Our ability to treat and control acute pulmonary tuberculosis (TB) is threatened bythe increasing occurrence of multi-drug-resistant tuberculosis (MDR-TB) in manycountries around the globe. It is not clear whether MDR-TB occurs predominantlydue to transmission, or whether there is a substantial contribution due to de novoemergence during treatment. Understanding the underlying mechanisms that areinvolved in the emergence of MDR-TB is important to develop countermeasures. Weuse a computational model of within-host TB infection and its subsequent treatmentto qualitatively assess the risks of treatment failure and resistance emergence undervarious standard therapy regimes. The results show that especially patients with ahistory of previous TB treatment are at risk of developing MDR-TB. We conclude thatde novo emergence of MDR-TB is a considerable risk during treatment. Based on ourfindings, we strongly recommend widespread implementation of drug sensitivitytests prior to the initiation of TB treatment.

2.2 introduction

Tuberculosis (TB) is a key challenge for global health [25; 26]. At present aboutone third of the global population is latently infected [27] and every year about 1.7million people die of tuberculosis. A large number of patients live in resource-limitedsettings with restricted access to health-care. It is imperative that standard treatmentmeasures are assessed for their efficacy and reliability.

Understanding the driving forces behind therapy failures is challenging. This is toa large extent the case because of the complex life cycle and population structure ofTB: The typical sequence of events leading to acute pulmonary tuberculosis occursas follows [25; 28; 19; 29; 30]. Upon inhalation, TB bacilli reach the pulmonary alveoliof the lung. There they are assimilated by phagocytic macrophages. In most casesthe bacteria are being killed continuously by phagocytosis while the cell-mediatedimmunity develops. More rarely, they may persist in an inactive state, which isconsidered a latent infection. Infected macrophages may aggregate and form gran-ulomas by recruiting more macrophages and other cell types. Inside granulomas,increased necrosis of macrophages can lead to the formation of a caseous core. In la-tently infected hosts, an equilibrium establishes where the immune system preventsfurther growth but the bacteria persist in a dormant state [31; 32]. However, espe-cially in patients with a compromised immune system, the bacteria may continueor resume growth [28; 29]. In this case, the bacterial population steadily increasesuntil the granuloma bursts into the bronchus forming an open cavity. Mycobacteriumtuberculosis is an aerobic organism and depends on the availability of oxygen to pro-mote its growth. Because the oxygen levels inside macrophages and granulomas arelow, the growth rate is reduced [29; 32; 33; 34; 35]. In open cavities, oxygen supplyis not limiting anymore and the population size increases rapidly. The extracellularbacteria in the cavities may also spread to other locations in the lung where they areagain combated by the dendritic cells of the immune system. Some bacteria can beexpelled with sputum and be transmitted to other individuals or they may enter ablood vessel and cause lesions in other organs.

2.2 introduction 13

The standard treatment is a six-month short-course regimen [25; 36; 37; 38; 13],consisting of two months of combination therapy with isoniazid, rifampicin, pyrazi-namide and ethambutol followed by a continuation phase of four months with iso-niazid and rifampicin only [39]. According to tuberculosis treatment guidelines alldrugs are taken daily during the first two months. During the following four monthsisoniazid and rifampicin are administered three times a week with a 3-fold increasedisoniazid dose [37]. For patients with previous TB treatments the WHO recommendsa 8-month retreatment regimen containing additionally streptomycin [13].

In recent years, the problem of drug resistance has increased in severity due to theemergence and spread of multi-drug-resistant tuberculosis (MDR-TB) [40; 41; 42],where MDR-TB is defined as infection by M. tuberculosis strains conferring resistanceto at least isoniazid and rifampicin. Resistant TB is assumed to emerge at leastin part due to inappropriate treatment or suboptimal adherence to the treatmentregimen [43]. Poor compliance has been associated with treatment failure and theemergence of resistance in previous studies [44; 45; 46; 47; 48]. Multi-drug-resistanceusually develops in a step-wise manner. These steps are thought to include func-tional monotherapy; either due to different drug efficacies among certain bacterialpopulations or due to different pharmacokinetics [49; 50]. Prevalence data of MDR-TB in Europe (see Fig 2.1) show that patients who have previously received treatmentare on average six times more likely to suffer from MDR-TB than patients who arenewly diagnosed. There are several possible explanations for this observation. Indi-viduals who are infected with MDR-TB are more likely to have a treatment failure ora later relapse [51; 20; 52; 53], especially if they are not properly diagnosed. These pa-tients could then come under more accurate scrutiny and eventually be reported asMDR-TB patients with previous treatment history. Another more direct possibility isthat a considerable fraction of patients who have contracted susceptible TB developde novo MDR-TB during the first therapy [54].

The goal of this study is to assess the factors that determine the de novo acquisitionof drug resistance and to get a better insight in the underlying dynamics. Specif-ically, we want to study the contribution of imperfect compliance and retreatmentregimens. In some areas, second-line drugs are not easily accessible. Moreover,drug-susceptibility tests may not be performed due to the lack of required infrastruc-ture or questionable reliability of patient treatment history [55]. Hence, we assess theimpact of a retreatment that is identical to the first therapy as well as a retreatmentthat follows the WHO recommendation [13]. To achieve this goal we develop a com-putational model of a within-host TB infection and its consecutive treatment withcurrently recommended first-line regimens. The model framework encompasses thepopulation dynamics of various M. tuberculosis genotypes with different resistancepatterns in three pulmonary compartments as well as the pharmacodynamics andthe pharmacokinetics of the drugs that are used for treatment. The aim is to providequalitative insights into the infection dynamics of tuberculosis. The parameterizationis based on the most recent concepts and individual experimental results found inthe literature. Given the current lack of a good animal or in vitro model for TB, acomputational model,may help to bridge the gaps arising from the inaccessibility ofTB in experimental model systems and allow the hypothetical assessment of treat-ment scenarios, which would be otherwise ethically inadmissible in patient trials.

14 the role of adherence and retreatment in de novo emergence of mdr-tb

Figure 2.1: The prevalence of multidrug-resistant tuberculosis (MDR-TB) in most Euro-pean countries is higher among previously treated patients than among newlydiagnosed patients. The data on the percentage of newly diagnosed and previ-ously treated patients with MDR-TB where taken from reference [56] for 2009 andfrom reference [57] for 2010. Countries with incomplete data were omitted.

In particular, problems resulting from imperfect therapy adherence can be usefullyaddressed with a computational model.

2.3 methods

In the following section we present the basic framework of the computational model,the parameterization and key aspects of our simulations. In essence, our modelconsists of coupled logistic-growth models that are connected such that they capturethe basic population structure (compartments) of TB (see Fig 2.2). The action of TB-drugs is included in this model via realistic pharmacokinetics / pharmacodynamicsfunctions. Resistance to these drugs is modelled by distinguishing between up to 32

genotypes (all combinations of 5 mutations) with varying resistance patterns. Sincemutations are generated at low frequencies and numbers (due to the low bacterialmutation rate), chance events are essential in the dynamics of this system and hencewe consider a stochastic version of the model. In the following we provide a detailed

2.3 methods 15

description of the model; the model equations and further details can be found in S1

Text.

2.3.1 Model

Our model describes pulmonary tuberculosis and assesses the emergence of resis-tance during multi-drug therapy. A graphical illustration of the model is providedin Fig 2.2. The model reflects the compartmentalization of the bacteria into threedistinct subpopulations as described by Grosset [19] intracellular bacteria withinmacrophages (M), bacteria within the caseating tissue of granulomas (G) and ex-tracellular bacteria which mostly reside in open cavities (OC). The compartmentsdiffer in their maximum population sizes as well as the bacterial replication ratesthat they allow. The base replication rate r is modified by a factor γ, which reflectsthe compartment specific conditions that influence the replication rate. Bacteria havea natural density-dependent death rate in each compartment. The constant replica-tion rate and the density-dependent death rate constitute a logistic growth modelthat was assumed to describe the basic population dynamics. Bacteria also migrateunidirectionally at a rate m from one compartment to another. Offspring bacteriahave a certain chance to acquire or lose a mutation that confers resistance to oneout of up to five drugs that may be administered during treatment. Every resistancemutation confers a fitness cost which affects the reproductive success of its carrier.This means that the bacterial population inside a compartment comprises of up to32 genotypes, which differ in their drug resistance pattern as well as their relativefitness.

To outline the population dynamics within a single compartment we describe themfirst in the form of a deterministic differential equation. The dynamical equation isgiven by

dNc,g

dt= r ·γc ·ωg ·Nc,g−mc ·

Nc

Kc·Nc,g+mc ′ ·

Nc ′

Kc ′·Nc ′,g− (dc+ κc,g) ·Nc,g (2.1)

Here Nc,g is the number of bacteria of a specific genotype g in a specific compart-ment c. The parameter r is the base replication rate of M. tuberculosis and γc is a factor,which modifies the replication rate according to the different metabolic activities ineach compartment. ωg represents the relative fitness of the specific genotype. mc isthe rate with which bacteria migrate to the subsequent compartment. The migrationrate is multiplied by the ratio between the total population size Nc and the carryingcapacity Kc. This reflects the increased migratory activity that takes place duringan acute infection. Nc ′ , Kc ′ and mc ′ correspond to the overall bacterial populationincluding all genotypes of the supplying compartment, its carrying capacity and itsmigration rate, respectively. The last term reflects the density-dependent death ratedc and the drug induced genotype specific killing rate κc,g. The bactericidal effectsof the drugs contribute additively to the killing rate κc,g (see 2.A for further details).

The dynamics of the bacterial population in the model are actually simulated asstochastic processes. For this reason we translated the underlying deterministic dif-ferential equations into a corresponding stochastic framework by applying Gillespie'sτ -leap method [58].

16 the role of adherence and retreatment in de novo emergence of mdr-tb

Figure 2.2: Diagram of model for the pathogenesis during acute pulmonary tuberculosisinfection. We consider three different physiological compartments for the loca-tion of TB bacteria: host macrophages (M), granulomas (G) and open cavities(OC). The base replication rate r of the bacteria is modified by a compartment spe-cific parameter γ. The bacteria die with a density-dependent rate d and migratefrom one compartment to another at a rate m.

2.3 methods 17

2.3.2 Parameterization

The parameter estimates used in this model are whenever possible drawn or derivedfrom experimental results in the literature. To account for the diversity of infectionand treatment courses in different patients we allow some parameters to vary withina certain range. Parameters are summarized in Table 2.1.

The basic growth dynamics rest upon the replication rate and the carrying capac-ity of the compartments. Based on recent studies [59; 60; 61] we assume a maximumbacterial load between 10

5 and 107 bacteria each for the macrophage and the granu-

loma compartment and 108 to 10

10 bacteria for the extracellular compartment. Underoptimal conditions M. tuberculosis has a replication time of 20 h, hence we set themaximum replication rate in the model to 0.8 d−1 [19].

Every new bacteria cell has at birth the chance to acquire or lose one or multi-ple resistance mutations and therefore get a genotype, which is different from themother cell. The frequency of specific resistance mutations and therefore the mu-tation rate for the main first-line drugs have been first estimated by David in 1970

[62] to be around 10−7–10

−10. However, more recent observations suggest consid-erably higher frequencies in the order of 10

−6 to 10−8 [29; 63]. A possible reason

for this discrepancy between these estimates are varying mutation rates in in vitroexperiments compared to the conditions encountered in vivo due to stress-inducedmutagenesis mechanisms or variations among strains [64; 65; 66]. Furthermore, weassume that mutations only occur during proliferation while mutations during thestationary phase could serve as an additional source of resistance mutations [67].Therefore, we choose to allow for patients with the more recent higher mutationrates because this will yield more conservative estimates (see 2.2). Our model incor-porates backwards mutations from the resistant to the sensitive phenotype, whichalso restore the reproductive fitness. However, we consider a reversion to be tentimes less likely than the original forward mutation because the occurrence of anyadditional mutation within a gene to be an exact reversion is more infrequent.

When assessing the prevalence of certain genotypes, fitness costs that come withresistance mutations have to be considered. The cost of resistance against anti-tuberculosis drugs appears generally to be low [88; 84; 85; 86]. Drug-resistant mu-tants isolated in patients have even been found to be on par with susceptible wildtype strains regarding their infectivity and replicative potential. Since cost-free resis-tance mutations are rather rare, the high fitness of resistant strains that have beenfound in clinical isolates [48,49] is assumed to arise due to the acquisition of sec-ondary site mutations which minimize the fitness costs (so-called compensatory mu-tations) [85]. However, there is evidence that at least initially newly acquired drugresistance confers some physiological cost [89]. Because our model simulates thede novo acquisition of resistance mutations and because the time frame of a singlepatient treatment is rather short we assign a small fitness cost to every possible mu-tation and neglect the counterbalance of fitness costs by compensatory mutations.

The effect of administered drugs depends on the pharmacokinetics and pharma-codynamics of these drugs (see Table 1). Both influence the killing rate κc,g at anygiven time point during treatment. While pharmacokinetic parameters describe thecourse of the drug concentration in the target tissue, pharmacodynamic parame-

18 the role of adherence and retreatment in de novo emergence of mdr-tb

Table 2.1: Compartment characteristics

Macrophages Granulomas Open cavities

Compartmental characteristicsCarrying capacity (Kc) 10

5–107

105–10

7108–10

10

Growth modifier (γc) 0.5 0.1 1

Migration rate (mc,m’,d−1) 0–0.1 a0–0.1 a

0–0.1 a

Relative drug efficaciesIsoniazid 0–1 [68; 69; 70] 0.01 [71] 1

Rifampicin 0.01 [69] 0.01 [29] 1

Pyrazinamide 0 [72; 73] 1 [29] 0 [74]Ethambutol 1 [69] 0–1 [29; 75; 76] 1

Streptomycin 0.1 [77; 68] 0.01 [29] 1

The provided references support the order of magnitude of the parameters,not the exact value.a estimation

ters characterize the effect the drugs have at a given concentration. The minimalinhibitory concentration (MIC) describes the minimal drug concentration at whichbacterial growth is reduced by at least 99%. Additionally, the EC50 describes at whichdrug concentration the half-maximal effect (commonly, bacterial killing) is observed,while the Emax indicates the maximal effect of the drug. These pharmacodynamicparameters are obtained by fitting the drug action model to killing curves found inthe literature [90; 82] (see S1 Text). The specific efficacy of most drugs in the differ-ent compartments is typically not quantified. There are several studies that tried toassess the bactericidal activity inside macro- phages [77; 68; 72; 69]. Unfortunately,these estimates are highly variable and sometimes even contradictory [91; 72]. Inaddition to these experimental difficulties, it is possible that the pharmacodynamicsof anti-tuberculosis drugs are again different in the human body [92; 93; 94; 95; 96].To reflect this uncertainty we assign compartment efficacies from a range of valueswhich cor- responds to the most recent estimates [77; 68; 72; 69; 75; 73; 74; 70; 71; 76].

2.3.3 Simulations

To investigate the role of treatment adherence on patient outcome, we followed dis-ease progression starting with the infection of macrophages until all compartmentsapproximately reached their maximum bacterial load. For each parameter set, wesimulate the outcome of 10,000 patients who vary both in their pharmacokinetic and-dynamic characteristics as well as compartmental attributes. Parameters are gener-ally picked from a normal distribution. If only a range is known the parameters arechosen from a uniform distribution. To measure the actual treatment efficacy we letevery patient develop an acute tuberculosis infection during 360 days. This allows

2.3 methods 19

Tabl

e2

.2:M

odel

para

met

ers

Ison

iazo

dR

ifam

pici

nPy

razi

nam

ide

Etha

mbu

tol

Stre

ptom

ycin

Hal

f-lif

e(h

−1)

FAa

:1.5

4±

0.3

0[7

8]

SAa

:3.6

8±

0.5

9[7

8]

2.4

6[7

8]

9.6±

1.8

[78]

2.6

[79]

3[8

0;8

1]

Dos

e(m

g/L)

FAa

:2.8

0±

0.7

1b

[81]

SAa

:4.2

6±

0.9

4b

[81

]13.6

1±

3.9

6[8

1]

29.2

1±

4.3

5[8

1]

5.0

[79]

35

–45

[36;8

1]

MIC

(mg/

L)0.0

25

[68

]0.4

[68]

28

[74]

1.0

[68]

0.5

[82;7

7]

EC50

(mg/

L)0.0

33d

0.5

1d

40d

0.2

0d

0.3

2d

E max

1.8

6d

1.8

2d

1.9

4d

0.9

6d

1.3

1d

CELF/CSerum(ρ)e

FAa

:1.7

4–5

.88

[83]

SAa

:1.3

7–5

.69

[83]

0.3

4[8

3]

13.6

0–2

4.7

6[8

3]

0.9

2–1

.13

[83]

1c

Res

ista

nce

freq

uenc

y2.5

6·1

0−8–1

0−7

[62;6

3]

2.2

5·1

0−10–1

0−8

[62;6

3]

10−9–1

0−8

10−7

[62

]2.9

5·1

0−8–1

0−7

[62],c

Res

ista

nce

cost

0.1

[84

]0

.1[8

5;8

6]

0.1

[84]

0.1c

0.1

[84

;85

]

Som

eof

the

prov

ided

refe

renc

essu

ppor

tth

eor

der

ofm

agni

tude

ofth

epa

ram

eter

s,no

tth

eex

act

valu

e.a

FA=

fast

acet

ylat

ors,

SA=

fast

acet

ylat

ors

bIf

ison

iazi

dis

adm

inis

tere

dth

ree

tim

esa

wee

kin

stea

dof

daily

the

dosa

geis

thre

eti

mes

high

er[3

6;8

7]

ces

tim

atio

nd

see

text

eEL

F=

epit

helia

llin

ing

fluid

20 the role of adherence and retreatment in de novo emergence of mdr-tb

for the emergence of mutants prior to treatment initiation and provides enough timefor the establishment of an equilibrium in the bacterial population composition. Af-ter this period we start the standard short course therapy regimen with four drugsbeing taken daily for two months followed by four months in which just isoniazidand rifampicin are taken three times per week. If the infection is not completely ster-ilized after the first treatment we schedule a retreatment. Since the model does notcover the possibility of dormant bacteria the population recovers rather quickly afteran unsuccessful treatment. Hence, we begin the retreatment 30 days after completionof the previous treatment. After such a time span the population reaches a bacterialload where acute symptoms would be again suspected. If not stated otherwise theretreatment corresponds to the WHO recommendation for retreatments [20; 21]. TheWHO recommendations include streptomycin, which is used together with the origi-nal four first-line drugs during the first two months. Afterwards the therapy is beingcontinued for another month without streptomycin and during the last five monthsonly isoniazid, rifampicin and ethambutol are administered. All drugs are beingtaken daily during the whole retreatment.

The 95% confidence intervals (CI) of patient outcomes in the figures is calculatedby picking the value for a two-sided 95% confidence limit with n − 1 degrees offreedom from a t-distribution table where n is the number of patients. This valueis then multiplied with the standard deviation σ and divided by the square root ofn. The resulting value is then added and subtracted from the mean to get the actualconfidence interval.

CI =t95%n−1 · σ√

n(2.2)

2.4 results

2.4.1 Treatment efficacy in single compartments against wild-type TB and MDR-TB

The impact of treatment on the net growth rate of wild-type or MDR bacteria dif-fers strongly between compartments (Fig 2.3): Before treatment starts, the growthrates in macrophages and granulomas are lower than in the open lung cavities dueto hypoxia and a generally adverse environment for bacterial growth in these com-partments. Since we assume that the drug concentration immediately reaches themaximum the impact of combination therapy on growth rate is immediately appar-ent after the administration of the first dose of drugs. In all compartments the drugsare able to keep the wild-type populations from regrowth during the following days.Especially in granulomas pyrazinamide is able to diminish the population over along period due to its relatively long half-life. MDR-TB is substantially less affectedby the combination therapy because only pyrazinamide and ethambutol are effec-tive. This means that in macrophages or open lung cavities the multi-drug-resistantpopulation remains constant at best or is even able to slowly grow. Only in the gran-ulomas where mostly pyrazinamide is active (see Table 1) the loss of effectiveness ofisoniazid and rifampicin is less prominent.

2.4 results 21

wild typeMDR−TB−6

−4

−2

0

0.0 1.0 2.0 3.0

Gro

wth

ra

te [d

−1]

Days

wild typeMDR−TB

2

4

6

8

10

0.0 1.0 2.0 3.0

Lo

g C

FU

Days

wild typeMDR−TB−6

−4

−2

0

0.0 1.0 2.0 3.0

Gro

wth

ra

te [d

−1]

Days

wild typeMDR−TB

2

4

6

8

10

0.0 1.0 2.0 3.0

Lo

g C

FU

Days

wild typeMDR−TB−6

−4

−2

0

0.0 1.0 2.0 3.0

Gro

wth

ra

te [d

−1]

Days

wild typeMDR−TB

2

4

6

8

10

0.0 1.0 2.0 3.0

Lo

g C

FU

Days

Macrophages

Granulomas

Open cavities

Figure 2.3: Net growth rates and population dynamics of wild-type and MDR bacteria inthe modeled compartments after two days of treatment with the four first linedrugs. All parameters for which a range of values exist have been set to themedian value. On day 1 and day 2 all four drugs are applied simultaneously.

22 the role of adherence and retreatment in de novo emergence of mdr-tb

2.4.2 The role of adherence

The compliance of a patient with the prescribed drug regimen is a key factor fora successful treatment outcome. For the assessment of treatment success we mon-itor for every patient three different nested treatment outcomes. Firstly, we definetreatment failure as the incomplete sterilization of the lung at the end of the ther-apy. Secondly, the emergence of MDR-TB is defined in our simulations as 10% ormore [97] of the remaining bacterial population after treatment failure being resis-tant against at least isoniazid and rifampicin. Finally, emergence of full resistance(FR) is defined as 10% or more of the population being resistant against all drugsthat were used in the treatment regimen (either 4 drugs for first treatment or up to 5

drugs for retreatment).Adherence in our simulations refers to the probability with which the patient takes

the prescribed drugs at any given day. We assume that failure to take drugs on agiven day always affects all drugs of the prescribed regimen.

In our simulations, the level of adherence has a strong but complex impact ontreatment success (Fig 2.4 A). Under perfect adherence the model shows a very lowfailure rate. However, if adherence decreases the probability for treatment failureincreases rapidly. Between 40% and 80% adherence there is also a small fraction ofpatients that fail treatment due to the emergence of MDR-TB. Furthermore, at theseadherence levels the model also shows only limited treatment success. Thus, failuredecreases monotonically with adherence while MDR is maximized at intermediatelevels. Patients who fail on the first treatment and who undergo retreatment (Fig2.4 B) have a failure rate of 20% at 80% adherence. However, the probability fortreatment failure increases to about 50% under perfect adherence. Patients who failthe first treatment despite high adherence may often have disadvantageous combina-tions of PK/PD parameters, which also decrease their success probabilities duringthe retreatment. In Fig 2.4 B, 2.4C and 2.4 D the number of patients per adherencelevel undergoing retreatment decreases strongly as can be seen from the frequencyof treatment failure in Fig 2.4 A. When comparing Fig 2.4 A and 2.4 E, which showsthe combined outcome probabilities for both treatments, we see that the retreatmentreduces the probability of failure over the upper half of the adherence spectrum.

2.4.3 The role of retreatment

The additional treatment success of retreatment regimens depends on adherenceand the addition of streptomycin to the regimen (Fig 2.4 B). In our model, evenunder perfect adherence the chance of treatment failure remains substantial, andin the majority of patients who fail under retreatment MDR-TB emerged de novo.Furthermore, at suboptimal adherence levels a considerable proportion of patientseven carry strains that are not susceptible to any of the five administered drugs. Theoutcome of retreatment depends crucially on whether MDR was acquired duringinitial treatment: Because the majority of patients who fail the first treatment do notcarry MDR-TB their outcome probabilities for the retreatment are almost identicalto the overall cohort of failed patients (Fig 2.4 C). Even though the vast majority ofpatients who failed the first treatment did not develop MDR-TB, a substantial fraction

2.5 discussion 23

of patients who also failed the second treatment harbor MDR or FR strains. Thisoccurs due to increased subpopulations of monoresistant bacteria that accumulateduring the first treatment and that are by itself not sufficient to be diagnosed asMDR-TB. When comparing patients who are diagnosed with MDR-TB after the firsttreatment (Fig 2.4 D) and those who are not (Fig 2.4 C) we see that patients whodevelop MDR-TB are very likely to fail the retreatment as well. At higher adherencelevels the majority of those patients develops full resistance against all five drugs(Fig 2.4 D). When considering the outcome for both treatments combined (Fig 2.4E) it becomes more evident that the addition of streptomycin and the more intenseretreatment has a beneficial effect on the overall success rate but patients who alsofail the retreatment are more likely to carry multi-drug-resistant TB strains.

When second-line drugs are not available or susceptibility test are not performed,it may occur frequently that a previously treated patient is retreated with the first linetreatment. Our results in Fig 2.5 show that such a retreatment with the first line drugshas almost no additional treatment success beyond the initial treatment. Patients allacross the spectrum of adherence experience treatment failure. The identical first-line retreament only increases the chances for the bacteria to accumulate resistancemutations and leads between 50% to 100% adherence to nearly all uncleared patientsharboring MDR-TB or worse. This outcome is standing out when comparing thecumulative treatment success in Fig 2.5 D with the results after the first treatment.While the overall success curve did not change the fraction of MDR-TB patients overa large adherence range increased substantially.

2.5 discussion

The aim of this study is to elucidate the effects of treatment adherence and retreat-ment on the emergence of resistance in TB. The model explicitly incorporates thepharmacodynamics and pharmacokinetics of all drugs that are used for standardtherapy and the WHO retreatment recommendation. Depending on the compart-ment in the lung in which the bacteria reside (macrophages, caseous centers ofgranulomas or open cavities), M. tuberculosis has different stages of infection anddrug-susceptibilities. Therefore, we explicitly include these different compartmentsto be able capture the effect of heterogeneous selection pressure. Because not allof the parameters used in our model have been quantified with high accuracy, wedo not claim that the model has quantitative predictive power. Rather, it aims toqualitatively demonstrate the underlying dynamics of a tuberculosis infection.

Our results suggest that poor adherence is a major cause for treatment failure.Whenconsidering the predicted rates of treatment failure one also has to take into accountthat our definition of treatment failure is probably rather conservative. We do notinclude the possibility of remaining dormant bacteria, which might increase the like-lihood of treatment failure or relapse. On the other hand, we also neglect the pos-sibility of the infection being contained at a later time point by the immune system,thus probably underestimating the chance of success. It is also noteworthy that evenat perfect adherence some patientsmay have a negative treatment outcome. This ismost likely due to a random aggregation of very adverse pharmacokinetic param-eters and unfavorable infection attributes in some patients. Such outcomes due to

24 the role of adherence and retreatment in de novo emergence of mdr-tb

Treatment outcome after

first treatment

Adherence

Pro

ba

bili

ty

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Emergence of FREmergence of MDRTreatment failure

A Treatment outcome after retreatment

among failed patients

Adherence

Pro

ba

bili

ty

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

B

Treatment outcome after retreatment

among failed patients without MDR

Adherence

Pro

ba

bili

ty

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

C Treatment outcome after retreatment

among failed patients with MDR

Adherence

Pro

ba

bili

ty0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

no

da

ta

D

Treatment outcome for

both treatments combined

Adherence

Pro

ba

bili

ty

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

E

Figure 2.4: Probabilities for treatment failure (blue), emergence of MDR-TB (green) andthe emergence of a fully resistant strain (FR, red). (A) Treatment outcome prob-abilities based on the assessment of 10,000 simulated patients undergoing sixmonth short course therapy at different levels of adherence. (B) Outcome proba-bilities of the standard retreatment regimen containing streptomycin for patientsfailing the previous treatment. (C and D) Retreatment outcome probabilities forpatients failing the first treatment without or with MDR-TB respectively. (E) Theoverall probabilities for treatment outcome when both treatment regimens areconsidered. The width of the dark colored areas indicate the 95% confidence in-terval. Please note that the colored areas overlap and share a common baseline.Therefore, FR is a subcategory of MDR and FR and MDR are subcategories oftreatment failure. The confidence intervals for the retreatment tend to widen athigher adherence levels due to the lower number of patients failing the previoustreatment. The area with no data in panel (D) arises because patients with lowadherence do not harbor MDR-TB after the first treatment.

2.5 discussion 25

Treatment outcome after retreatment

among failed patients

Adherence

Pro

ba

bili

ty

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

A

Emergence of FREmergence of MDRTreatment failure

Treatment outcome after retreatment

among failed patients without MDR

AdherenceP

rob

ab

ility

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

B

Treatment outcome after retreatment

among failed patients with MDR

Adherence

Pro

ba

bili

ty

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

no

da

ta

C Treatment outcome for

both treatments combined

Adherence

Pro

ba

bili

ty

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

D

Figure 2.5: Corresponding treatment outcomes after two rounds of identical six-monthshort course therapy. (A) Treatment outcome probabilities after two rounds ofidentical first line therapy for treatment failure (blue), the emergence of MDR-TB(green) and the emergence of a fully resistant strain (FR, red). (B) Probabilities forpatients who did not complete the first therapy successfully but who also did notharbor MDR-TB. (C) Treatment outcome probabilities for patients who failed thefirst treatment with MDR-TB. (D) The overall probabilities for treatment outcomewhen both treatment regimens are considered. There is no data available in panel(C) for patients with a lower adherence than 25% because such patients did notharbor MDR-TB after the first treatment.

26 the role of adherence and retreatment in de novo emergence of mdr-tb

pharmacokinetic variability and despite good adherence have been predicted in anin vitro study [98]. Furthermore, our results show that over a certain range of ad-herence a small fraction of patients develop MDR-TB. At intermediate adherencethese patients also have a low likelihood of being treated successfully. Thus, goodadherence to therapy is crucial: Not only does it increase treatment success, it alsodecreases the probability for the emergence of MDR-TB.

According to our model, the WHO recommendation for retreatment is somewhatof a double-edged sword. While at high adherence levels the recommended treat-ment is able to cure the majority of patients who failed the first line therapy, it alsoincreases the fraction of patients harboring drug resistant strains across almost thewhole spectrum of adherence. Previous studies already raised concerns about thepossible amplification of resistance [21; 99; 100; 101; 102]. In the WHO treatmentguidelines it is recommended that drug susceptibility test results should be takeninto account when deciding upon the retreatment regimen [17]. However, the vastmajority of patients in our model would probably not have been diagnosed withMDR-TB after the first regimen even though they may still harbor increased subpop-ulations of monoresistant bacteria. Therefore it is conceivable that many would havebeen treated with the WHO recommended regimen. A large fraction of patients whofailed this retreatment eventually developed MDR-TB. Considering the results fromour model further clinical studies are needed which analyze the treatment successrates and the accompanying risks of the standard retreatment regimen.

Retreating failed patients with an identical short course therapy leads to poor out-come in our simulations. A lower success rate for MDR-TB patients treated with thestandard short- course therapy has been confirmed in a large cohort study [55]. Inour simulations it is rare that patients who failed the previous treatment are cured af-ter undergoing the same therapy again provided that adherence remains unchanged.Retreatment with the same regimen only generates more opportunities for singleresistant mutants that emerged during the first treatment to accumulate further mu-tations, thus minimizing the number of future treatment options.

These findings are in accordance with previous studies which found a positivecorrelation between previous treatment and the occurrence of resistance [103; 104;105; 106]. This might be an indicator that de novo resistance on an epidemiologicalscale occurs at a significant frequency and that the main contributor to the frequencyof MDR-TB is not necessarily the mere transmission of such strains.

In summary our data show that patient adherence is a crucial component of treat-ment success. The probably cheapest and most effective way to ensure a positivetreatment outcome while also minimizing the risk for the emergence of MDR-TB isto maintain proper patient compliance with the treatment. This supports the DirectlyObserved Treatment, Short-Course (DOTS) strategy of the WHO, which includeshealthcare workers or community health workers who directly monitor patient med-ication. If treatment fails, thorough tests of drug susceptibility of the remaininginfecting population, would be of considerable value. According to our results aretreatment regimen including streptomycin has the potential to increase the overallcure rate, but also increases the fraction of patients who carry drug-resistant strains.A common principle of physicians is to “never add a single drug to a failing regime”[107] this principle is often not followed in retreatment. A preceding drug sensitiv-

2.6 acknowledgments 27

ity test might show existing drug resistances and the retreatment regimen could beadapted accordingly. Nonetheless the standard retreatment regimen is still superiorto a retreatment with the identical first-line drugs. Such a retreatment is unlikelyto achieve a higher overall cure rate and dramatically increases the probability forthe emergence of MDR-TB, which reduces further treatment options. This showsthat a dependable patient treatment history that is available to the responsible healthprofessional is also important before initiating a treatment regimen.

2.6 acknowledgments

We thank Florian Marx and Ted Cohen for reviewing the manuscript and stimulatingdiscussions.

2.7 author contributions

Conceived and designed the experiments: DC PAzW RK SB. Performed the experi-ments: DC. Analyzed the data: DC PAzW. Contributed reagents/materials/analysistools: SB. Wrote the paper: DC PAzW RK SB.

A P P E N D I X

2.a supplementary material

2.a.1 Model equations

The following descriptions contain further details about the model mechanics andspecifications of the equations that comprise the mathematical basis in addition tothe explanations in the main article (see 2.3.1).

The model is based on the τ-leap approximation [58]. In our case we do the simu-lations with a temporal resolution of 10

−2 d. If in a time step a new bacterium is bornit mutates and gains or loses resistance to one or several drugs with a likelihood thatis equal to the corresponding mutation rate. For every patient and every drug weinitially randomly pick a rate from a uniform distribution with the indicated mini-mum and maximum values in Table 2.1. The probability for a backward mutation isten times lower than the corresponding picked rate.

We assume that (uncompensated) resistance alleles confer a fitness disadvantagein the absence of drugs. In our model we restrict the effect of resistance costs cl to thereduction of the reproductive success. If multiple alleles involve a cost, the fitness ofthe corresponding genotype is given by

wg =

n∏l=1

(1− cl) (2.3)

where cl is the cost of a resistance allele at the locus l and n is the number ofresistance loci. The susceptible wild-type alleles have no cost and therefore the fullysusceptible strain has a fitness of 1. The death rate dc of the bacterial populationdepends on the population density in the compartment among all genotypes.

dc = r · γcNc

Kc(2.4)

where r is the maximal replication rate of M. tuberculosis and γc is a factor, whichmodifies the maximal growth rate according to the different metabolic activities ineach compartment. Nc is the combined population size of all genotypes in the com-partment and Kc is the carrying capacity of that specific compartment. The higherthe population density is, the more increases the death rate. Together with the basicgrowth function this results in the conventional model for logistic growth:

dNc,g

dt= r ·Nc,g ·

(1−

Nc

Kc

)(2.5)

The bactericidal activity of the antituberculosis drugs is accounted for by the sig-moid Emax model [108]. This leads to an adapted version of the enhanced death model

29

30 the role of adherence and retreatment in de novo emergence of mdr-tb

by Czock et al. [108] which we extend to reflect the use of multiple distinct drugs .The bactericidal effects of the drugs in a compartment are reflected in the killing ratevariable κc,g.

κc,g =

n∑d=1

Emax,d ·

1− 1Cd·δc,d·ρdEC50,d

+ 1· νg,d

(2.6)

The killing rate depends on the genotype. Here we assume that a resistant mutantallele confers full resistance to the bactericidal activity of the corresponding drug.The resistance of a given genotype against an antibiotic drug is represented by theboolean variable νg,d with νg,d = 0 indicating resistance.

For simplicity we assumed that the drug effects are additive. n is the number ofdrugs and EC50,d describes the concentration at which the half-maximal kill rate ofa specific drug is reached. Emax is the maximal death rate. Together with the MICand the EC50 it determines the antibacterial potency of a drug. Cd is the currentdrug concentration while δc,d and ρd are the efficacy of the drug in the specificcompartment and the ratio between plasma and epithelial lining fluid concentration,respectively.

We assume that immediately after the uptake of a drug the concentration increasesinstantaneously by an amount Cmax,d, followed by a exponential decay according tothe following function,

Cd(t) = Cd(t0) · e−a(t−t0) (2.7)

where t0 is the last time point where the drug has been taken and

a =ln(2)

td1/2

(2.8)

where td1/2 is the half-life of drug d within the patient.For simplicity we assume that if the patient is non-adherent on a specific day

all due drugs are missed simultaneously. Allowing the drugs to be missed inde-pendently caused only a marginally lower chance of a treatment failure (data notshown).

2.a.2 Fitting of anti-tuberculosis drug action

The Emax and EC50 values as we use them in our model were not readily available inthe literature. In order to obtain them we use again an equation from the enhanced-death constant-replication model [108].

dN

dt= r ·N− Emax ·

C

EC50 +C·N (2.9)

2.A supplementary material 31

If we assume that the population has no net growth and therefore the drug con-centration C is equal to the MIC we get the following relation

Emax =r · (MIC+ EC50)

MIC(2.10)

The different Emax and EC50 values are collected by fitting equation 2.10 to the killcurves that were recorded in vitro by de Steenwinkel et al. and Marcel et al. [90; 82].These papers report the in vitro effects of constant drug concentrations of isoniazid, ri-fampicin, ethambutol and streptomycin on the density of a M. tuberculosis suspensionover the course of six or seven days, respectively. In Figure 2.6 we show simulationsof this experimental setup using our model by assuming a single compartment inwhich all four available drugs have unimpaired efficacy. The data points were ex-tracted from the original figures as far as the data points were distinguishable. Inorder to prevent the unpredictable stochastic influence of rescue mutations we re-move the possibility of emerging resistance from the model. From the growth curvesin the absence of any drug we estimate the average growth rate to be 1.95. Thiscomparably high growth rate is likely due to the adapted phenotypes of regular labstrains of M. tuberculosis. The carrying capacity in the assays of de Steenwinkel et al.[90] we estimated to be 10

8.5 and 1013 in the assay of Marcel et al. [82].

The MIC concentrations from the literature [82; 77; 68] which are also confirmed inthe experimental kill curves serve as reference points at which the bacterial growthand the bactericidal activity of the drug would cancel each other out and the pop-ulation would stay constant. The EC50 concentrations and the interdependent Emaxvalues are derived by linear least-square fitting. The best fit values are calculated byaveraging over all the available concentrations. The experimental data for isoniazidshows a recovery of population growth after day 2. The authors claim that this effectappears due to the development of a isoniazid-resistant subpopulation [90]. Becausewe do not consider such rescue mutations we decide to include only the first twodays for the fitting of the bactericidal activity of isoniazid.

To validate the quality of the fitting we calculate the average coefficient of determi-nation R2 for every drug. Isoniazid and ethambutol show a satisfactory R2 of 0.67 and0.70 respectively and a very good 0.90 for streptomycin. The coefficient of determi-nation for the fitting of rifampicin is rather low with 0.36. Our model overestimatesthe bactericidal activity of rifampicin at high concentrations and underestimates theactivity at low concentrations. Apparently a single drug action model as we use itdoes not provide the same descriptive quality for every first line drug. No kill curveswere available for pyrazinamide hence we estimate an appropriate EC50 value fromother studies [74; 109].

2.a.3 Robustness analysis

In order to obtain a better understanding of the influences of different parameter es-timates in the model we performed a robustness analysis in which we vary them andlooked at their impact on the treatment outcome. In the following results we moni-tor the likelihood of treatment failure and the emergence of MDR-TB after a single

32 the role of adherence and retreatment in de novo emergence of mdr-tb

treatment with the four standard first-line drugs. As in the main text treatment fail-ure is again defined as incomplete sterilization after the completion of therapy andemergence of MDR-TB is defined as 10% or more [97] of the remaining populationbeing resistant against at least isoniazid and rifampicin.

2.a.3.1 Carrying capacity

There is a large variance in reports about the maximum population size of M. tuber-culosis in a human lung during acute infection. This is also based on the fact thatthis number depends on the host immune defense and the course of infection. Manystudies report 10

9 bacilli per open cavity and therefore an overall population size of1010 or above. Thus, to study the effect of varying carrying capacity we ran simu-

lations with compartmental carrying capacities that are 10-fold higher or lower forevery compartment (see Figure 2.7 A and B). With 10-fold higher carrying capacitiesthe probability for treatment failure increases substantially. The increased numberof bacilli in each compartment also increases the standing variation in the bacterialpopulation. This means that there are more bacteria that carry single or even dou-ble resistance mutations. Therefore, an increased carrying capacity also favors theemergence of MDR-TB.

2.a.3.2 Resistance costs

The cost of resistance in M. tuberculosis is generally assumed to be low [88; 84; 85; 86].However, those estimates are mostly based on observations of clinically isolatedstrains. It is possible that these fitness costs are alleviated by compensatory mu-tations, which occur later during a chronic infection or during the chain of transmis-sion events. Since we assumed de novo emergence of resistance we assigned a 10%fitness cost on reproductive success for every mutation.

We ran simulations in which we increased as well as decreased the fitness costs perresistance mutations. As we can see in Figure 2.7 C and D the results with slightlylower fitness costs still provide reasonable results. Although, if the costs are lowerthan 5% the probability of treatment failure and the likelihood of MDR emergenceare unrealistically high. Thus, we conclude that resistance mutations are do verylikely carry some fitness costs. Otherwise treatment outcomes would be expectedto be much worse than what is generally observed in studies. This conclusion ispartially confirmed in a previous study [89].

2.a.3.3 Migration rates

The rate with which M. tuberculosis migrates among the three compartments has toour knowledge not been quantified. We follow the assumptions made by Lipsitchand Levin [50]. The migration has only a pronounced influence if it increases (seeFigure 2.7 C and D). This is most likely due to the increased density-dependentbacterial killing in the small compartments of macrophages and granulomas. Withhigher migration rates these compartments are flooded with bacteria from the opencavities. However, the influence on the emergence of MDR-TB is still small. Eventhough our estimates for the migration rate are not well established and we consider

2.A supplementary material 33

them to be already rather high we think that its minor influence does not severelyaffect the validity of our model.

2.a.3.4 EC50

We also investigate the influence of the EC50 parameter, i.e. the efficiency of thedrug. In Figure 2.7 G and H we vary the EC50 values of every drug simultaneouslybetween 1/10, 5/10 and the five- and tenfold of the standard parameter setting. Anincreased EC50 is predicted to cause a guaranteed treatment failure even at perfectadherence. On the other hand a decreased EC50 may dramatically improve the likeli-hood of a successful treatment at adherence levels, which are far below the optimum.Figure 7 F indicates that an elevated EC50 only promotes the selection of MDR-TB atintermediate levels of adherence, i.e. if the drugs are able to exert a certain selectivepressure.

2.a.3.5 Missing drugs

In resource-limited settings, the drug supply is not always guaranteed, such thattherapy might only comprise a subset of the four drugs. To investigate the impactof a missing drug, we test all four possible standard treatments that each lack one ofthe first-line drugs and assess the effect (see Figure 2.7 I and J). The lack of isoniazid,rifampicin or ethambutol always leads to treatment failure irrespective of the levelof adherence. The explanation for this is as follows: The extracellular compartmentharbors the largest number of bacteria. Here, isoniazid rifampicin and ethambutolmost efficiently reduce bacterial load. Because of the high bacterial load we wouldexpect that mutants resistant to either of these drugs pre-exist at treatment initiation.However, double-resistant mutants that could evade two drugs are expected to pre-exist only in a small fraction of drug-naive patients. If one of these main drugs ismissing the mutants that are resistant against the remaining drug immediately takeover and spread. Compared to isoniazid, rifampicin and ethambutol pyrazinamideis less essential for treatment success. This is probably because it does not affect thelarge extracellular compartment. However, it is important for clearing bacteria resid-ing in the caseous centers of granulomas, where it is the most active drug. Therefore,its usage favors a positive treatment outcome. However, its absence does not affectthe outcome as much as the other drugs.

Because the lack of isoniazid and rifampicin does not select for resistance againstthese drugs it is also unlikely that MDR occurs at a substantial frequency. The pre-viously observed minor influence of pyrazinamide is also evident as its absencedoes not substantially increase the risk of MDR emergence. Only a regimen with-out ethambutol drastically increases the probability for MDR to occur. This showshow important the role of ethambutol as a third extensively effective bactericidaldrug is. Ethambutol is needed to prevent widespread treatment failure due to thedevelopment of MDR-TB.

2.a.3.6 Transmitted resistance

In Figure 2.8 we examine the possible effect of an infection with an M. tuberculosisstrain that is already resistant at transmission. To model this, we exchange the bacte-

34 the role of adherence and retreatment in de novo emergence of mdr-tb

rial inoculum at the beginning of the infection with a strain that is resistant to one ortwo drugs. It is known that patients with active TB are highly infectious and even asmall inoculum of one hundred bacilli or less that comprises primarily resistant mu-tants might establish an infection in a susceptible host. As in every simulation theinfection is simulated for one year to reach its full potential and equilibrate. Duringthis year random reversion mutations may occur which give rise to sensitive strains.These strains may slowly outcompete resistant strains and become more frequentdue to their higher fitness in absence of drugs.

The pre-existence of rifampicin or isoniazid resistance increases the risk of treat-ment failure the most among the single mutants at perfect adherence. This could bedue to the potency of these drugs and the competitive advantage that such resistancemutations grant. Not surprisingly, a isoniazid- or rifampicin-resistant inoculum alsoincreases the risk of MDR-TB. Pre-existing pyrazinamide or ethambutol-resistancehas almost no effect on treatment outcome. Most likely due to their minor bacteri-cidal effectivity during the therapy. A double-resistant inoculum as in Figure 2.8 Cand D has a fatal impact. Treatment failure is almost inevitable and MDR-TB occursespecially at higher levels of adherence.

2.A supplementary material 35

Isoniazid

Time (days)

Lo

g C

FU

/ml

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6

Control0.015 mg/L0.031 mg/L0.062 mg/L0.125 mg/L0.25 mg/L0.5 mg/L1 mg/L2 mg/L4 mg/L8 mg/L16 mg/L32 mg/L64 mg/L128 mg/L256 mg/L

Experimental data

Time (days)

Lo

g C

FU

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6

Isoniazid

R2: 0.67

Control0.015 mg/L0.031 mg/L0.062 mg/L0.125 mg/L0.25 mg/L0.5 mg/L1 mg/L2 mg/L4 mg/L8 mg/L16 mg/L32 mg/L64 mg/L128 mg/L256 mg/L

Fitted model

Rifampicin

Time (days)

Lo

g C

FU

/ml

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6

Control0.0005 mg/L0.001 mg/L0.0019 mg/L0.0038 mg/L0.0075 mg/L0.015 mg/L0.031 mg/L0.062 mg/L0.25 mg/L0.5 mg/L1 mg/L2 mg/L8 mg/L16 mg/L32 mg/L64 mg/L128 mg/L256 mg/L

Rifampicin

R2: 0.36

Time (days)

Lo

g C

FU

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6

Control0.0005 mg/L0.001 mg/L0.0019 mg/L0.0038 mg/L0.0075 mg/L0.015 mg/L0.031 mg/L0.062 mg/L0.25 mg/L0.5 mg/L1 mg/L2 mg/L8 mg/L16 mg/L32 mg/L64 mg/L128 mg/L256 mg/L

Ethambutol

Time (days)

Lo

g C

FU

/ml

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6

Control0.125 mg/L0.25 mg/L0.5 mg/L1 mg/L2 mg/L4 mg/L8 mg/L16 mg/L32 mg/L64 mg/L128 mg/L256 mg/L

Ethambutol

R2: 0.70

Time (days)

Lo

g C

FU

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6

Control0.125 mg/L0.25 mg/L0.5 mg/L1 mg/L2 mg/L4 mg/L8 mg/L16 mg/L32 mg/L64 mg/L128 mg/L256 mg/L

Streptomycin

Time (days)

Lo

g C

FU

/ml

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 60 1 2 3 4 5 6 7

0

1

2

3

4

5

6

7

8

9

10

11

0.01 mg/L0.125 mg/L0.25 mg/L0.5 mg/L1 mg/L2 mg/L4 mg/L8 mg/L16 mg/L32 mg/L

Streptomycin

R2: 0.90

Time (days)

Lo

g C

FU

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 60 1 2 3 4 5 6 7

0

1

2

3

4

5

6

7

8

9

10

11

0.01 mg/L0.125 mg/L0.25 mg/L0.5 mg/L1 mg/L2 mg/L4 mg/L8 mg/L16 mg/L32 mg/L

Figure 2.6: Comparison of the concentration- and time-dependent effects of isoniazid, ri-fampicin, ethambutol and streptomycin on sensitive M. tuberculosis. The plotsin the left column are experimentally obtained killing curves for anti-tuberculosisdrugs by de Steenwinkel et al. [90] and Marcel et al. [82] and originate from ametabolically highly active strain of Mtb H37Rv cultured in vitro at 37°C [90]. Theplots on the right show the simulated killing curves that were calculated by fittingthe pharmacodynamic model to the experimental data. The fitting was done byminimizing the sum of least squares over all curves. The coefficient of determi-nation (R2) indicates the average goodness of fit for each drug. Greyed out lineswere not used for fitting. Modified from [90].

36 the role of adherence and retreatment in de novo emergence of mdr-tb

0.0 0.2 0.4 0.6 0.8 1.00

.00

.20

.40

.60

.81

.0

Adherence

Pro

ba

bili

ty o

f Tre

atm

en

t F

ailu

re

Carrying Capacity

Standard10−fold decreased10−fold increased

A

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f M

DR

Str

ain

B

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f Tre

atm

en

t F

ailu

re

Resistance Costs

0.000.020.050.080.100.15

C

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f M

DR

Str

ain

D

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f Tre

atm

en

t F

ailu

re

Migration Rates

10%50%100%500%1000%

E

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f M

DR

Str

ain

F

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f Tre

atm

en

t F

ailu

re

EC50

10%50%100%500%1000%

G

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f M

DR

Str

ain

H

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f Tre

atm

en

t F

ailu

re

Missing Drug

no drug missingIsoniazidRifampicinPyrazinamideEthambutol

I

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f M

DR

Str

ain

J

Figure 2.7: Sensitivity analysis of the probability of treatment failure and emergence ofresistance. In the left column are the plots for the probability of treatment failuredue to incomplete clearance and in the right column are the plots for the proba-bility of the emergence of an MDR-TB strain, which accounts for at least 10% ofthe overall population. (A and B) Effect of different carrying capacities. (C andD) Effect of different fitness costs per resistance mutation. (E and F) Effect of dif-ferent migration rates among compartments. (G and H) Effect of lower or higherEC50 values. (I and J) Effect of treatment consisting of only three drugs.

2.A supplementary material 37

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f Tre

atm

en

t F

ailu

re

Single Mutants

wtINHRMPPZMEMB

A

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty o

f M

DR

Str

ain

B

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty o

f Tre

atm

en

t F

ailu

re

Double Mutants

wtINH + RMPINH + PZMRMP + PZMINH + EMBRMP + EMBPZM + EMB

C

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty o

f M

DR

Str

ain

D

Figure 2.8: Influence of pre-existing resistance mutations on treatment outcome after a reg-ular six-month therapy. In the left column are the plots for the probability oftreatment failure due to incomplete clearance and in the right column are theplots for the probability of the emergence of an MDR-TB strain, which accountsfor at least 10% of the overall population. (A and B) Effect of a homogeneousinoculum consisting of genotypes resistant to one drug. (C and D) Effect of ahomogeneous inoculum consisting of genotypes resistant to two drugs.

3A LT E R N AT I V E T R E AT M E N T S T R AT E G I E S F O R T U B E R C U L O S I S

D Cadosch, P Abel zur Wiesch, S Bonhoeffer

abstract

The standard six-month short-course therapy for pulmonary tuberculosis has beenestablished in the 1970s. Since then there have not been major changes in the reg-imen that still requires considerable effort and dedication from the patient as wellas from the health care system. In this study we explore the potential benefits anddisadvantages of intermittent therapy as well as extended-release formulations anddose escalations of rifampicin. These alternative treatment strategies are tested forvarying levels of patient adherence. Intermittent therapy is shown to have a reducedprobability for a positive treatment outcome as well as a lower risk for the emer-gence of de novo MDR-TB. Extended-release formulations of rifampicin can mitigatethe lower chances of successful treatment associated with intermittency but they alsoincrease the probability for the emergence of resistance at suboptimal adherence lev-els. In contrast to the other strategies the absolute drug exposure is increased whenwe test for the effects of dose escalation of rifampicin. Dose escalation of rifampicinshows the same or lower probabilities for treatment failure at equal adherence levelsbut the probability of de novo MDR-TB increases for intermediate levels of adher-ence. We conclude that intermittent regimens could potentially lower the time andorganizational burden for patients and the health care system but they show lowersuccess rates. Extended-release formulations of rifampicin are a feasible strategy tomitigate the potential weaknesses of intermittent regimens. Dose escalation is also apromising alternative strategy. However, dose escalation as well as extended-releaseformulations of rifampicin depend on a very good patient compliance to be effective,otherwise the risks associated with the stronger selection for resistant genotypes mayoutweigh the benefits.

39

40 alternative treatment strategies for tuberculosis

3.1 introduction

The treatment of pulmonary tuberculosis (TB) with a six-month short-course che-motherapy was developed in the 1970s by the British Medical Research Counciland its partners [110; 111]. This treatment regimen containing four antituberculo-sis drugs is still the current standard recommended by the WHO [13]. Adherenceto the treatment regimen is considered to be a crucial factor influencing the success-ful completion of treatment and for preventing emergence of drug-resistant TB. Theimprovement of adherence was one of the goals of the directly observed treatment,short course (DOTS) strategy launched in the mid-90s. Since then, the case detec-tion increased and case prevalence decreased in countries where DOTS was applied[27]. However, the effort and organization that is needed to maintain a successfulTB control program is substantial. TB patients are usually administered their drugson a daily basis by a local health care worker during at least the first two months ofthe treatment. Also the long treatment period and the effort of the patient who insome countries has to travel long distances to see his supervising health worker mayprevent him or her from uninterrupted attendance [13]. Another reason for patientsto discontinue therapy may be the high pill burden or uncomfortable side effects[13; 112].

Given the difficulties with the current treatment strategy possible improvementsof the standards could be of interest. In this study we are discussing three al-ternative strategies that address the problems outlined above: intermittent treat-ment, extended-release drug formulations and dose escalation. Intermittent regi-mens could facilitate the task of treatment supervision. Some studies found intermit-tent regimens to have equally good success rates when compared to daily treatment[21; 38]. Large-scale tuberculosis control programs that used simplified intermittenttreatment regimes were considered to be sufficiently successful [113; 114]. However,intermittent treatment has also been found to be associated with a greater risk ofacquired drug resistance [21] and with higher incidence rates of side effects fromisoniazid and rifampicin [13; 38; 115; 116], the two most important first-line drugs.Another possible concern in intermittent treatment regimens is the possible phar-macokinetic mismatch that could lead to prolonged phases of mono-therapy [117].Because the concerns of intermittent therapy are thought to outweigh the potentialbenefits the WHO recommends daily administration of antituberculosis drugs if pos-sible [13].

However, some of the issues mentioned with intermittent regimens could be al-leviated with the use of extended-release formulations. Such formulations cause aslower absorption of the drug and consequentially provide a more steady suppres-sive drug concentration over time [22]. Intermittently extended-release formulationsshould keep the antibiotic concentration above the minimum inhibitory concentra-tion (MIC) long enough to prevent a substantial regrowth of the bacterial population.The more long-lasting presence of rifampicin for example could decrease the prob-ability for side effects such as flu-like symptoms. These symptoms are assumed tobe at least partially caused by the formation of anti-rifampicin antibodies and thedevelopment of a more potent immune reaction which may be triggered during al-ternating prolonged phases of high and low rifampicin concentrations that occur

3.2 methods 41

with intermittent therapy and standard rifampicin formulations [115; 116; 81; 92].The benefits of an intermittent regimen with extended release drugs could prove tobe at least as successful as daily treatment, decrease the work effort and operatingexpenses for monitoring programs as well as lower the pill burden and incidence ofside effects for the patient and hence increase adherence and herewith the probabilityfor a positive treatment outcome.

Another point of improvement of the conventional treatment strategy would be theincrease of the rifampicin dose (dose escalation). An increase of the rifampicin dosehas been considered a promising direction because rifampicin is known to cause sideeffects less frequently than other first-line drugs [115; 63]. Furthermore, higher dosesare more likely to prevent sub-target plasma concentrations due to malabsorption orreduced bioavailability in certain patients [115; 118; 119]. A study looked at theearly bactericidal activity of an increased rifampicin dose in 14 patients and foundpromising results but concluded that further studies are warranted [120]. A moreextensive clinical study that looked at increasing rifampicin doses found that higherdoses were well tolerated and had a stronger bactericidal effect while also reducingresistance [23].

In this study we investigate the possible benefits of extended-release formulationsin a daily or intermittent treatment regimen by means of extending a mathematicalmodel used in a previous study [121]. We further test how big the impact of increasedrifampicin doses is on treatment outcome. We evaluate the effects of these regimensover a range of patient adherence. We focus here exclusively on rifampicin since itis considered to have the biggest untapped potential in terms of sterilizing capacity[115; 63].

3.2 methods

3.2.1 Model

Our model is based on the extension of a framework of an acute pulmonary TBinfection from an earlier study [121]. The mathematical model of the populationdynamics of Mycobacterium tuberculosis considers three different compartments:macrophages, granulomas and open cavities. The compartments differ in their size,which limits the maximal population size and in the growth rate at which bacteriamay replicate. Bacteria may migrate from macrophages to granulomas, from gran-ulomas to open cavities and from there again to macrophages. This represents anabstraction of the pathogenic cycle during an acute pulmonary TB outbreak in a pa-tient. The bacterial populations are assumed to consist of up to 16 genotypes, whichrepresent all possible combinations of the four considered resistance mutations – onefor each first-line drug. During replication bacteria may acquire resistance mutationswith a certain probability. To reflect variations in the phenotype of bacteria as well asin the physiology of patients parameters are picked randomly from a specified rangeof values. Bacteria differ in their migration rates, maximal population densities andmutation rates for resistances against each drug. Patients may absorb and excretedrugs at variable rates, vary in their efficacy to absorb drugs, have different ratiosbetween the blood serum drug concentration and the concentration in the epithelial

42 alternative treatment strategies for tuberculosis

lining fluid inside the lungs as well as varying drug penetrations for the three com-partments. The precise description of the model as well as its parametrization canbe found in the previous study by Cadosch et al. [121]. Newly introduced parametersand parameter values that differ from the previous study are in Table 3.1. Beyondthe previously established model framework we extended the pharmacokinetics toalso include a first order absorption reaction. All simulations are stochastic and usethe τ-leap method by Gillespie [58].

3.2.2 Pharmacokinetics

In the model the blood serum drug concentration in a patient is governed by a firstorder absorption reaction and a first-order excretion reaction. The first order absorp-tion reaction in our case reflects the uptake of drug from the digestive tract to theblood stream while the first order excretion reaction reflects the elimination of drugprimarily by the kidneys or the biliary tract [126]. Upon drug administration theamount of unabsorbed drug U in the digestive tract instantaneously increases by theadministered dose D. The amount of unabsorbed drug U then decreases accordingto the following differential equation:

dU

dt= −ka ·U (3.1)

where ka is absorption rate constant. Besides the absorption rate constant the drugconcentration in the blood serum C is also influenced by the excretion rate constantke.

dC

dt= ka ·U− ke ·C (3.2)

The absorption rate constant ka is related to the time tmax until the peak bloodserum concentration is reached on the absorption and excretion rate constant as

tmax =ln(ka) − ln(ke)

ka − ke(3.3)

By transforming equation 3.3 we can calculate the absorption rate constant ka forknown tmax and ke.

ka = −W−1(−e

−ke·tmax · ke · tmax)tmax

(3.4)

Here W−1 denotes the lower branch of the Lambert function. The excretion rateconstant depends on the concentration half-life t1/2.

ke =ln(2)

t1/2(3.5)

3.2 methods 43

Tabl

e3.1

:Dru

gpa

ram

eter

izat

ion

Ison

iazi

dR

ifam

pici

nPy

razi

nam

ide

Etha

mbu

tol

Hal

f-lif

e(h

−1)

1.5

–4[1

15;1

22;1

23;7

8;7

9]

1.6

–3[1

15;1

22;1

23;7

8;7

9]

5.5

–9.6

[115;1

22;1

23;7

8;7

9]

2–4

[115;1

24]

Cmax

(mg/

l)1.9

–7.1

[115;1

22;1

23;7

9;1

25]

6.1

–9.9

[23;1

22;1

23]

20–5

0[1

15;1

22;1

23;7

8;1

25]

1.0

–5.5

[115;1

23;7

9;1

24]

t max

(h)

0.7

5–2

[115;1

22;1

23;7

9;1

25]

1.3

–3[1

15;1

22;1

23;7

9;1

25]

1–2

[115;1

22;1

23;7

9;1

25]

1.5

–3[1

15;1

23;7

9;1

24]

MIC

(mg/

L)0.0

25

[68

]0

.4[6

8]

12.5

[95

;98]

1.0

[68]

Som

eof

the

prov

ided

refe

renc

essu

ppor

tth

eor

der

ofm

agni

tude

ofth

epa

ram

eter

s,no

tth

eex

act

valu

e.

44 alternative treatment strategies for tuberculosis

To calculate the required dose D that has to be administered in order to achievea maximum blood serum concentration Cmax after a time tmax we can look at theBateman equation [127; 128], which is used to calculate the drug concentration C attime t depending on the underlying absorption and excretion rate constants.

C(t) =D · kaka − ke

· (e−ke·t − e−ka·t) (3.6)

From equation 3.6 we can then derive a formula with which we can calculate thedose D that is needed to reach the specified concentration Cmax.

D =Cmax · (ka − ke)

ka · (e−ke·tmax − e−ka·tmax)(3.7)

The different concentration-time curves of rifampicin between the standard absorp-tion rate constant of 16.3 d−1 and a fixed absorption rate constant of 1 d−1, represent-ing an extended-release formulation, can be seen in Figure 3.1. Both curves are basedon a half-life of 2.3 h [115; 122; 123; 78; 79] and the same amount of drug is adminis-tered but the fast standard absorption rate constant results from a tmax that is set to2.15 h [10,26,27,29,30]. In the simulations involving extended-release formulations ofrifampicin the standard fast absorption rifampicin formulation with an absorptionrate constant ka that is dependent on tmax and ke is compared to an extended-releaseformulation of rifampicin that has a fixed slow absorption rate constant of 1 d−1 oran intermediate absorption rate constant of 5 d−1.

3.2.3 Patient simulations

In order to capture a wide range of combinations of bacterial and patient parameterswe simulate every treatment scenario for 1000 independent patients. Every patientis initially inoculated with 1000 wild-type bacteria. Because we assume that the pa-tients are immunocompromised, we allow bacteria to replicate and mutate freelyfor 360 days. During this time all three compartments harbor bacteria up to theircarrying capacity and in the compartment of open cavities small subpopulations ofmonoresistant bacteria emerge and reach equilibrium sizes. The compartment ofopen cavities is the only compartment that is large enough for such low frequencygenotypes to establish. The size of these subpopulations in the absence of any drug isdetermined by the carrying capacity, the mutation rate and the fitness cost, which isimposed by the de novo mutations. After the first 360 days a six months short-coursetherapy starts. The treatment involves the four standard first-line drugs isoniazid,rifampicin, pyrazinamide and ethambutol. In our standard regimen all drugs areadministered daily during the first two months (intensive phase) and during the lastfour months isoniazid and rifampicin are administered three times a week (contin-uation phase) [13]. If the simulation involves intermittent therapy then rifampicinis administered every second or third day during the intensive phase and 1.5 timesor once per week during the continuation phase respectively. To ensure compara-ble drug exposure the rifampicin doses are doubled or tripled in an intermittentregimen.

3.2 methods 45

0.0 1.0 2.0 3.0

0

2

4

6

8

Time [days]

Co

nce

ntr

atio

n [

mg

/l]

0.0 1.0 2.0 3.0

0

2

4

6

8

Time [days]

Co

nce

ntr

atio

n [

mg

/l]

Rifampicin

Figure 3.1: Comparison of serum concentration profiles of rifampicin between the stan-dard absorption rate constant and the extended-release formulation. In the leftpanel are the pharmacokinetic profiles for a single administration of a rifampicindose with the midpoint standard absorption rate constant of 16.3 d−1 (solid line)and with an absorption rate constant of 1 d−1 representing the extended-releaseformulation (dashed red line). The dotted line is the MIC of rifampicin for M.tuberculosis (see Table 3.1) [68]. The right panel shows the profiles for three con-secutive daily administrations with the standard absorption rate constant (solidline) or a single three-fold higher dose with the extended-release pharmacokinet-ics. The drug concentration profiles in each panel have within the computationalaccuracy the same AUC.

46 alternative treatment strategies for tuberculosis

At the end of the six months of therapy a patient is diagnosed with treatmentfailure if there are any Mtb bacteria left in any compartment. Among treatmentfailures besides patients with predominantly drug susceptible bacteria we furtherdifferentiate between patients with bacterial populations of which 10% or more [97]are resistant against at least isoniazid, resistant against at least rifampicin or thosethat are resistant against at least both isoniazid and rifampicin, which is the defini-tion of MDR-TB [99; 107]. Please note that MDR-TB is a subset of our definitionsof isoniazid or rifampicin resistance and that it is the exact intersection of these tworesistance definitions.

3.2.4 Pharmacodynamics simulations

In the pharmacodynamics simulations we have four genotypically distinct subpop-ulations: a fully susceptible wild-type, two populations that are either isoniazid- orrifampicin-resistant and a multidrug-resistant population that is resistant to isoni-azid and rifampicin. As we are interested in the relative population dynamics ofthe four genotypes, we start all populations from an arbitrary initial size that doesnot necessarily reflect their size in any patient at any time point. All drugs areadministered only every second time that they are prescribed which correspondsto an enforced adherence level of exactly 50%, which has for all considered treat-ment regimens a high relative probability to favor the emergence of MDR-TB (seeResults). The growth conditions and the drug efficacies are identical to the ones weattribute to the open cavities compartment, which we consider due to its size to bethe most influential. In contrast to other simulations all patient-specific parametersare based on the midpoint of the parameter intervals (see Table 3.1 and [121]). Forthe pharmacodynamic simulations of intermittent therapy rifampicin is prescribedto be administered every three days in a triple-dose — but effectively it is taken onlyevery six days due to the lowered adherence.

3.3 results

3.3.1 Treatment efficacy of an extended-release formulation of rifampicin in a daily or inter-mittent treatment regimen

The comparison between treatment regimens of different intermittencies with andwithout extended-release rifampicin formulations reveals that intermittency gener-ally has a negative effect on the probability of treatment failure while extended-release formulations have a positive effect (see Figure 3.2). We perform this compari-son over the full range of patient adherence. The standard daily administration of alldrugs with rifampicin that has the standard fast absorption rate constant achieves asuccessful treatment outcome in almost all patients under perfect adherence (Figure3.2 A). The success rate drops substantially below 90% adherence and at less than40% adherence we find that the infection is not cleared in almost all patients. If anextended-release formulation of rifampicin is administered the curve shifts furtherto the left the slower the absorption is, indicating that such formulations providea similar or higher likelihood of treatment success at the same adherence level. If

3.3 results 47

rifampicin with the standard absorption rate constant is administered at intervalsof two or even three days in a double or triple-dose respectively, a positive treat-ment outcome at the same adherence level becomes less likely. However, the treat-ment success rate of high-dose intermittent administration of rifampicin increases ifrifampicin is given as an extended-release formulation with lower absorption rateconstants. The relative increase of benefit of the extended-release formulations ishigher in high-dose intermittent regimens as is shown by the spread of the treatmentfailure curves within a group of equal absorption rate constants. While the treatmentfailure curves in the upper half of the adherence range between treatments with thesame standard absorption rate constant but varying intermittency differ substantiallyfrom each other, the curves for the lowest absorption rate constant are rather closetogether.

When we look at the probability for the emergence of MDR-TB we see that thereis a substantial increase in the middle of the adherence spectrum for daily treatmentregimens if we lower the absorption rate constant (Figure 3.2 B). For the intermit-tent regimens the probability of MDR-TB emergence is almost zero if we administerrifampicin with the standard absorption rate. The probability of MDR emergencewhen we intermittently use a rifampicin formulation with an intermediate absorp-tion rate constant is equal or lower than the daily administration of the fast absorp-tion formulation. When we use rifampicin formulations with the lowest absorptionrate constant the risk of MDR-TB increases substantially for both intermittent thera-pies.

We also compare the probabilities for the occurrence of genotypes that are at leastresistant against against isoniazid or rifampicin for the different treatment regimens(see Figure 3.2 C and D). The slopes of all curves for isoniazid-resistance betweenabout 30% and 100% adherence are almost identical to the curves indicating the prob-ability of treatment failure (Figure 3.2 C). This implies that at adherence levels above30% treatment failure is generally due to the remaining bacterial population beingresistant to at least isoniazid. The frequency of isoniazid-resistance decreases rapidlybelow 30% adherence. The probability for the occurrence of rifampicin-resistance onthe other hand almost exactly mirrors the probability for the emergence of MDR-TBover the whole adherence spectrum (Figure 3.2 D). This indicates that rifampicin-resistance almost exclusively occurs in the context of MDR-TB. These results areconfirmed when we exclusively consider isoniazid- or rifampicin-monoresistance.The probabilities for the emergence of isoniazid-monoresistance (Figure 3.2 E) arealmost identical to Figure 3.2 C. Only when the adherence levels are low enough forMDR-TB to occur in regimens with slowly absorbed extended-release formulationsof rifampicin does the probability for isoniazid-resistance decrease more than in Fig-ure 3.2 C. The low probability for the emergence of rifampicin-monoresistance for allregimens along the whole spectrum of adherence except for a narrow band between10% and 40% adherence supports the prior observation that rifampicin-resistance isalmost exclusively associated with MDR-TB (Figure 3.2 F).

48 alternative treatment strategies for tuberculosis

Probability of treatment failure

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty

A Probability of MDR−TB emergence

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty

B

Probability of isoniazid−

resistance emergence

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty

C Probability of rifampicin−

resistance emergence

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty

D

Probability of isoniazid−

monoresistance emergence

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty

E Probability of rifampicin−

monoresistance emergence

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty

F

Figure 3.2: Probabilities of treatment failure and the emergence of MDR-TB, isoniazid-and rifampicin-resistance with 10% fitness costs per resistance mutation fordifferent treatment intervals and varying absorption rate constants. We distin-guish the risk of incomplete infection clearance (A), the emergence of MDR-TB(B), the emergence of any isoniazid-resistant genotype (C), the emergence of anyrifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E)and the risk of the emergence of rifampicin-monoresistance (F). In every panel arethe probabilities for a regime with the standard dose daily administration of alldrugs (black lines), a regime where a double-dose of rifampicin is administeredonly on every second occasion (blue lines) and a regime in which rifampicin isgiven every third time in a triple-dose (red lines). Within a regime the pharma-cokinetics of rifampicin have a standard fast absorption rate constant (solid lines),a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixedlow absorption rate constant of 1 d−1 (dashed lines). The intermediate and lowabsorption rate constants represent two different extended-release formulationsof rifampicin. Emergence of resistance is defined as at least 10% of the bacterialpopulation in the open cavities compartment being resistant.

3.3 results 49

3.3.2 Pharmacodynamics of an extended-release formulation of rifampicin in a daily or in-termittent treatment regimen at intermediate adherence

To better understand the underlying population dynamics during daily or intermit-tent treatment regimens with slowly absorbed extended-release formulations of ri-fampicin we performed additional pharmacodynamics simulations shown in Figure3.3. Under the daily treatment regimen with the standard formulation of rifampicin(see Figure 3.3 A) we observe that the wild-type population declines rapidly everytime after the antibiotics are being taken but the decline slows down and the popu-lation is even able to recover somewhat before the next administration every otherday. The time until extinction for this initial population size is approximately 12

days. The isoniazid-resistant subpopulation also declines after every drug adminis-tration but the regrowth of the population after the drug concentrations declined tosub-MIC is more pronounced than the initial decline and the population is thereforeable to persist and even increases over time. The rifampicin-resistant subpopulationon the other hand is more strongly affected by the remainder of effective drugs anddeclines similar to the wild-type population — just with a slightly slower rate. Sincepyrazinamide is not expected to be effective in the pH-neutral environment of opencavities the MDR-TB population is only influenced by ethambutol. Ethambutol isnot potent enough to control the MDR-TB population, which equally increases in allshown scenarios.

If we administer rifampicin intermittently and in a triple-dose the picture lookssimilar (see Figure 3.3 B). The rifampicin-resistant population declines at the samerate here as well as in every other situation because the only difference betweenregimens is the formulation and frequency of rifampicin administrations. The wild-type population declines at a slower rate than if it is administered daily which maypartially explain the lower success rates of intermittent therapies with standard ri-fampicin formulations. Isoniazid-resistant bacteria as well as the wild-type show amore distinct drop of their population size every sixth day when rifampicin is ad-ministered. These rare events as well as the smaller declines in population size inbetween rifampicin administrations are however not strong enough to diminish thepopulation size in the long term. The overall growth rate is even higher than withthe daily regimen.

The extended-release formulation with a lower absorption rate constant in Fig-ure 3.3 C and D is able to suppress the isoniazid-resistant subpopulation in a dailyregimen and in an intermittent regimen with a higher dosage. Extended-release ri-fampicin also seems to be more effective against wild-type TB as the population goesextinct after approximately 8 days in contrast to 12 or 15 days with the standard ri-fampicin formulation.

The influence of different assumptions of fitness costs for resistance mutations onthese results is described in the Supplementary Material 3.A.

3.3.3 Treatment efficacy of a regimen with increased rifampicin doses

A dose escalation of rifampicin decreases the probability for treatment failure butincreases the risk of MDR-TB (see Figure 3.4). In the clinical study [23] that we re-

50 alternative treatment strategies for tuberculosis

0 5 10 15 20

time [days]

CF

U

101

102

103

104

105

106

A

wild typerINH

rRMP

MDR−TB

0 5 10 15 20

time [days]

CF

U

101

102

103

104

105

106

B

0 5 10 15 20

time [days]

CF

U

101

102

103

104

105

106

C

0 5 10 15 20

time [days]

CF

U

101

102

103

104

105

106

D

Figure 3.3: Pharmacodynamics at 50% adherence of four subpopulations with differentdrug susceptibilities under treatment regimens with different rifampicin ad-ministrations. The four panels all show the bactericidal effect of the standardregimen on four different M. tuberculosis subpopulations. The subpopulations areeither fully susceptible to all drugs (wild type), fully resistant to isoniazid (rINH),fully resistant to rifampicin (rRMP) or resistant to both isoniazid and rifampicin(MDR-TB). The environmental conditions correspond to the extracellular compart-ment in a patient. All patient-specific variable parameters are set to their midpointvalue. The initial population sizes are arbitrarily chosen and do not necessarilyreflect the population composition in any patient at any time point. The absorp-tion rate constant for rifampicin in the panels A and B is at the standard midpointvalue of 16.3 d−1. In the panels C and D rifampicin is given as an extended-release formulation with a slow absorption rate constant of 1 d−1. The treatmentregimen for the panels A and C prescribes all drugs to be administered daily. Theregimen for the panels B and D prescribes a three-fold higher rifampicin doseevery third day under perfect adherence. In all panels every second prescribeddrug administration is missed corresponding to an enforced adherence level of50%.

3.4 discussion 51

Probability of treatment failure

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty

Rifampicin

10 mg/kg

20 mg/kg

25 mg/kg

30 mg/kg

35 mg/kg

Probability of MDR−TB emergence

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

ba

bili

ty

Figure 3.4: Probabilities of treatment failure and the emergence of MDR for increasingdoses of rifampicin. The parametrization of the increased rifampicin doses isderived from a clinical study [23].

produce in our model the 10 mg/kg dose that we use as our standard dose and whichis the recommended dosage by the WHO [13] reaches a mean Cmax concentrationof 8 mg/l. For the 20 mg/kg rifampicin dose the clinical study we get a mean Cmaxof 23.95 mg/l. Therefore, unsurprisingly we find that the 20 mg/kg dose achievesa substantially higher treatment success rate than 10 mg/kg at least for adherencelevels between 40% and 100%. The mean Cmax concentration correlates well withthe applied dosage. However, the additional benefit of an increased rifampicin dosebecomes smaller with higher doses. When we look at the probability for MDR emer-gence we see that 10 mg/kg bears the lowest risk at any level of adherence. This riskincreases for intermediate adherence levels with higher rifampicin dosages.

3.4 discussion

In this study we investigated the feasibility of applying extended-release formula-tions of rifampicin in daily or intermittent treatment regimens as well as increasingthe rifampicin dosing to improve TB therapies. We tested these alternative treatmentstrategies in a previously established mathematical model [121]. The mathematicalmodel simulates the population dynamics of various genotypes with different drugsusceptibilities during an acute pulmonary tuberculosis infection within a patient.Furthermore, the model also encompasses the pharmacodynamics and pharmacoki-netics during the treatment with first-line drugs. Many parameter values that arebeing used in our model have been established in in vitro studies or are based onestimates with limited accuracy. Because of the intrinsic uncertainty with these pa-rameter values we have to stress that the results we are presenting are of a qualitativekind and do not provide accurate quantitative predictions.

From our results we see that in general the application of extended-release formu-lations increases or maintains the probability of a successful treatment for the samedosing regimen. This is most probably attributed to the fact that slowly absorbedextended-release formulations keep the rifampicin concentration above the growthsuppression threshold for a longer time (see Figure 3.1). Furthermore, extended-release formulations may maintain suppressive concentrations even if the drug is

52 alternative treatment strategies for tuberculosis

occasionally not taken. On the other hand, according to our results intermittencyis expected to work less well if formulations are used that are given at higherdoses but with the standard absorption kinetics. An intuition for this observationcan be found if we consider that the half-life of rifampicin is between 1.6 and 3 h[115; 122; 123; 78; 79] and the bactericidal activity does not necessarily linearly cor-relate with the concentration [121; 90]. Therefore, even if we double or triple thedose the rifampicin concentration stays above the MIC for only a few more hourswhich is too small of a benefit if the administration interval is two or three days.However, if we combine an intermittent treatment regimen with extended-releaseformulations the negative consequences are somewhat mitigated and we see com-parable or even better results than with the daily administration of the standardrifampicin formulation. Thus, the application of extended-release formulations hasthe potential to decrease the possible negative aspects of intermittent treatment andmake it a more promising strategy. An intermittent dosing strategy is attractive be-cause it is expected to be less time-consuming for the responsible health care workerand therefore less costly. It also decreases the pill burden for the patient and es-pecially in combination with extended-release formulations, that induce lower peakconcentrations, may cause fewer side effects. These patient-specific benefits may in-crease compliance and decrease the likelihood of defaulting, which in turn makesthe whole control program more effective.

Extended-release formulations potentially have a negative effect if adherence issuboptimal. At intermediate adherence levels our simulations showed a higher like-lihood for the emergence of MDR-TB in regimens that use extended-release formu-lations especially for formulations with the lower absorption rate constant. To un-derstand this phenomenon we have to look at the prevalence of subpopulations thatare resistant against either isoniazid or rifampicin. We notice that treatment failureexcept for very low adherence levels (between 0% and 30%) almost always coincideswith the presence of isoniazid-resistance. The association of isoniazid-resistance anda lower probability for a positive treatment outcome has been described previouslyin epidemiological studies [55; 53]. In our simulations rifampicin-resistance is lesscommon and predominantly occurs in the context of MDR-TB. This confirms therationale for the GeneXpert MTB/RIF assay to be used to diagnose the presenceof MDR-TB [129]. The answer to the question why in our simulations isoniazid-resistance correlates with treatment failure and why extended-release formulationsof rifampicin may increase the likelihood of MDR-TB to emerge can be found in thepharmacodynamics. There we see that in regimens that do not use extended-releaseformulations the isoniazid-resistant subpopulation is not sufficiently suppressed atsuboptimal adherence and can grow. In comparison a rifampicin-resistant subpopu-lation is expected to go extinct. The pre-existence of isoniazid-resistance even beforethe treatment starts is expected in a small fraction of the overall bacterial population.This population would be strongly selected for its competitive advantage over thewild-type and rifampicin-resistant populations during treatment and would even-tually dominate the composition of the overall population. Besides the higher fre-quency of isoniazid-resistance mutations relative to rifampicin-resistance mutations[63; 62] this may also contribute to the higher prevalence of clinical isoniazid-resistantsamples among all clinically diagnosed first-line drug monoresistances [130; 105]. An

3.4 discussion 53

MDR subpopulation would be even less suppressed than the isoniazid-resistant one.However, MDR-TB is not expected to be initially present in a treatment-naïve patientwho gets infected with wild-type TB. It most probably emerges from an isoniazid-resistant bacterium at a later stage of treatment and due to the rather low repro-ductive rate of Mycobacterium tuberculosis it would need some time before it couldreach a detectable frequency. If we would continue an unsuccessful treatment thatis not able to suppress the infection but still exerts a sufficiently high selection pres-sure we would expect MDR-TB to eventually dominate the overall population. Thishas been suggested previously in a computational model, in which unsuccessfullytreated patients underwent again the standard first-line therapy and accumulatedfurther resistance mutations [121]. This step-wise accumulation of resistance hasalso been confirmed by clinical studies [100; 48; 131]. If we use extended-release for-mulations of rifampicin the isoniazid-resistant subpopulation is most probably notable to grow even if we miss half of all prescribed doses. It will decline while MDR-TB on the other hand is now at a clear competitive advantage, which means that itwill outcompete all other monoresistant subpopulations rather quickly if it can arisein the first place. There are currently technical means developed that are able toreduce the absorption rate constant for drugs (unpublished data). In the example ofrifampicin we see that such extended-release formulations are expected to be moreeffective in treating TB patients, and it is conceivable that the extension of this toall first-line drugs could increase the positive effects even more. However, if patientcompliance drops low enough that more resistant genotypes have sufficient time andopportunity to arise they are more strongly selected.

The relative order of the results in terms of treatment efficacy and risk of resis-tance emergence is rather robust to changes of the fitness of resistant genotypes (seeSupplementary Material 3.A). Because the competitive advantage conferred by drugresistance is so strong the comparably low imposed fitness costs of 10% per mutationdo not substantially influence the relative pharmacodynamics between genotypes.

In contrast to the previous simulations in which the total amount of drug exposureremained constant we also tested treatment regimens in which we simply increasedthe amount of rifampicin that is being administered. Unsurprisingly, this strategyimproves the success rate of treatment for intermediate to high adherence levels.However, according to our results an increased rifampicin dose is also more likelyto promote the emergence of MDR-TB at intermediate adherence levels. This find-ing seems to contradict the results from a previous in vitro study [93]. In this studyGumbo et al. discovered that suppression of resistance was associated with a higherCmax-to-MIC ratio. This makes sense if resistance is not absolute as in our model butvariable. If we have in a population a diversity of genotypes that vary in their extentof resistance for a particular drug, e.g. their MIC, then it follows that higher dosesare more likely to exceed the MIC of these moderately resistant subpopulations andare able to suppress them. For simplicity our model only considers absolute suscep-tibility or resistance and the level of resistance is not concentration dependent. Wealso do not simulate the emergence of higher resistance through step-wise acquisi-tion of intermediate resistance mutations for a single drug. Our model is thereforenot able to capture this aspect of partial resistance emergence or suppression andmay thus overestimate the occurrence of de novo MDR-TB. However, there are single

54 alternative treatment strategies for tuberculosis

point mutations that confer resistance that is high enough to enable its carrier to bevirtually unaffected by clinically achievable rifampicin concentrations [132]. Hence,such genotypes may account for only a small fraction within the rifampicin-resistantsubpopulation but they would be more strongly selected if they could arise.

We can see that intermittent treatment could be a more feasible regimen option ifextended-release formulations of rifampicin would be available. Intermittency itselfhas a number of benefits for care providers as well as for patients. Also higherrifampicin doses are a promising alternative treatment strategy. However, those moreeffective hypothetical treatment regimens might also bear an increased risk if theyare suboptimally applied. If a potentially more effective regimen is inappropriatelyapplied it could backfire due to its stronger selective pressure for drug resistance.We conclude that the guideline of ’hitting hard’ does yield a positive effect in that itis able to eradicate the infection more reliably. However, if a hard-hitting strategyis compromised by low enough adherence so that monoresistant genotypes maythrive it may actually increase the selective pressure on these genotypes and causean amplification of resistance [133; 134].

3.5 acknowledgments

We thank Balázs Bogos for reviewing the manuscript.

A P P E N D I X

3.a supplementary material

In order to investigate the influence of fitness costs on the probabilities for treatmentfailure and the emergence of drug resistance when testing daily and intermittentregimens with and without extended-release formulations of rifampicin we ran ad-ditional simulations in which we varied the relative fitness of genotypes. With ourstandard assumptions every mutation rate confers a fitness cost of 10% and the costsstack in a multiplicative manner with every additional mutation. That means thatMDR-TB usually is assumed to have a relative fitness of 81% ((1− 0.1)2) if it does notcarry any more resistance mutations.

Instead of 10% fitness costs per mutation we assumed 5% fitness costs and repeatthe simulation of 1’000 patients (see Figure 3.5). In comparison with Figure 3.2 weobserve slightly increased probabilities for treatment failure above 50% adherence forall treatment regimens (Figure 3.5 A). The probability for the emergence of MDR-TBincreased substantially relative to the simulations with 10% fitness costs per mutation(Figure 3.5 B). Even the daily treatment regimen with the standard formulations ofrifampicin now bears a considerable risk for the emergence of MDR-TB from 20%up to 100% adherence. The occurrence of isoniazid- and rifampicin-resistance arecomparable to the pattern observed in Figure 3.2. For the upper half of the adherencespectrum isoniazid-resistance (Figure 3.5 C) coincides with treatment failure andrifampicin-resistance almost exclusively occurs in the context of MDR-TB (Figure 3.5D).

If we completely neglect the any fitness costs inferred by resistance mutations thesituation appears even more serious (see Figure 3.6). There is now a substantialchance for treatment failure even at perfect adherence and under the most effectivetreatment regimen (Figure 3.6 A). The comparison of Figure 3.6 A and B showsthat treatment failure in regimens with extended-release formulations of rifampicinoccurs almost always due to the emergence of MDR-TB at adherence levels of 75%and higher. The prevalence of isoniazid- and rifampicin-resistance are again verysimilar to the previous patterns.

When we keep the fitness cost for monoresistance at 10% but increase the fitnessof MDR-TB to the same level as the fully susceptible wild type the situation changessomewhat (see Figure 3.7). The probabilities for treatment failure are almost thesame as with the original assumptions (Figure 3.7 A). However, treatment failurefor patients with an adherence above 40% ensues almost always due to MDR-TB(Figure 3.7 B). Monoresistances of isoniazid an rifampicin are more rare than in anyprevious scenario (Figure 3.7 E and F) indicating that MDR-TB is outcompeting themonoresistant subpopulations.

When we look at the pharmacodynamics with and without fitness costs we observeslight increases in growth rates if we neglect the costs inferred by resistance muta-tions (see Figure 3.8). However, neglecting the fitness costs does not affect the relative

55

56 alternative treatment strategies for tuberculosis

selective advantage of the different genotypes granted by the resistance mutations.Therefore, it is not surprising that we do not observe much of a change betweenthe order of regimens in the Figures 3.2 and 3.5 – 3.7 in regard to the probability oftreatment failure or the emergence of MDR-TB.

3.A supplementary material 57

Probability of treatment failure

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty

A Probability of MDR−TB emergence

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Adherence

Pro

babili

ty

B

Probability of isoniazid−

resistance emergence

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0.0

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babili

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Figure 3.5: Probabilities of treatment failure and the emergence of MDR-TB, isoniazid-and rifampicin-resistance with fitness costs of 5% per resistance mutation fordifferent treatment intervals and varying absorption rate constants. We distin-guish the risk of incomplete infection clearance (A), the emergence of MDR-TB(B), the emergence of any isoniazid-resistant genotype (C), the emergence of anyrifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E)and the risk of the emergence of rifampicin-monoresistance (F). In every panelare the probabilities for a regime with the standard daily administration of alldrugs (black lines), a regime where a double-dose of rifampicin is administeredonly on every second occasion (blue lines) and a regime in which rifampicin isgiven every third time in a triple-dose (red lines). Within a regime the pharma-cokinetics of rifampicin have a standard fast absorption rate constant (solid lines),a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixedlow absorption rate constant of 1 d−1 (dashed lines). The intermediate and lowabsorption rate constants represent two different extended-release formulationsof rifampicin. Emergence of resistance is defined as at least 10% of the bacterialpopulation in the open cavities compartment being resistant.

58 alternative treatment strategies for tuberculosis

Probability of treatment failure

0.0 0.2 0.4 0.6 0.8 1.0

0.0

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babili

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A Probability of MDR−TB emergence

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ty

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0.0

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Figure 3.6: Probabilities of treatment failure and the emergence of MDR-TB, isoniazid-and rifampicin-resistance with no fitness costs for any resistance mutation fordifferent treatment intervals and varying absorption rate constants. We distin-guish the risk of incomplete infection clearance (A), the emergence of MDR-TB(B), the emergence of any isoniazid-resistant genotype (C), the emergence of anyrifampicin-resistant genotype (D), the emergence of isoniazid-monoresistance (E)and the risk of the emergence of rifampicin-monoresistance (F). In every panelare the probabilities for a regime with the standard daily administration of alldrugs (black lines), a regime where a double-dose of rifampicin is administeredonly on every second occasion (blue lines) and a regime in which rifampicin isgiven every third time in a triple-dose (red lines). Within a regime the pharma-cokinetics of rifampicin have a standard fast absorption rate constant (solid lines),a fixed intermediate absorption rate constant of 5 d−1 (dotted lines) or a fixedlow absorption rate constant of 1 d−1 (dashed lines). The intermediate and lowabsorption rate constants represent two different extended-release formulationsof rifampicin. Emergence of resistance is defined as at least 10% of the bacterialpopulation in the open cavities compartment being resistant.

3.A supplementary material 59

Probability of treatment failure

0.0 0.2 0.4 0.6 0.8 1.0

0.0

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babili

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A Probability of MDR−TB emergence

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Figure 3.7: Probabilities of treatment failure and the emergence of MDR-TB, isoniazid-and rifampicin-resistance with monoresistance conferring normal 10% fitnesscost and MDR-TB with the same fitness as the wild type for different treatmentintervals and varying absorption rate constants. We distinguish the risk of in-complete infection clearance (A), the emergence of MDR-TB (B), the emergenceof any isoniazid-resistant genotype (C), the emergence of any rifampicin-resistantgenotype (D), the emergence of isoniazid-monoresistance (E) and the risk of theemergence of rifampicin-monoresistance (F). In every panel are the probabilitiesfor a regime with the standard daily administration of all drugs (black lines), aregime where a double-dose of rifampicin is administered only on every secondoccasion (blue lines) and a regime in which rifampicin is given every third timein a triple-dose (red lines). Within a regime the pharmacokinetics of rifampicinhave a standard fast absorption rate constant (solid lines), a fixed intermediateabsorption rate constant of 5 d−1 (dotted lines) or a fixed low absorption rate con-stant of 1 d−1 (dashed lines). The intermediate and low absorption rate constantsrepresent two different extended-release formulations of rifampicin. Emergenceof resistance is defined as at least 10% of the bacterial population in the opencavities compartment being resistant.

60 alternative treatment strategies for tuberculosis

0 5 10 15 20

time [days]

CF

U

101

102

103

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106

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rRMP

MDR−TB

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time [days]

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time [days]

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Figure 3.8: Pharmacodynamics at 50% adherence of four subpopulations with differentdrug susceptibilities, with and without fitness costs under treatment regimenswith different rifampicin administrations. The four panels all show the bacte-ricidal effect of the standard regimen on four different M. tuberculosis subpopu-lations. The subpopulations are either fully susceptible to all drugs (wild type),fully resistant to isoniazid (rINH), fully resistant to rifampicin (rRMP) or resistantto both isoniazid and rifampicin (MDR-TB). Fitness costs are either 10% per re-sistance mutation (dashed lines) or resistance mutations do not confer any costsat all (solid lines). The environmental conditions correspond to the extracellularcompartment in a patient. All patient-specific variable parameters are set to theirmidpoint value. The initial population sizes are arbitrarily chosen and do notnecessarily reflect the population composition in any patient at any time point.The absorption rate constant for rifampicin in the panels A and B is at the stan-dard midpoint value of 16.3 d−1. In the panels C and D rifampicin is given asan extended-release formulation with a slow absorption rate constant of 1 d−1.The treatment regimen for the panels A and C prescribes all drugs to be admin-istered daily. The regimen for the panels B and D prescribes a three-fold higherrifampicin dose every third day under perfect adherence. In all panels everysecond prescribed drug administration is missed corresponding to an enforcedadherence level of 50%.

4C O N S I D E R I N G A N T I B I O T I C S T R E S S - I N D U C E D M U TA G E N E S I S

D Cadosch, P Abel zur Wiesch, S Bonhoeffer

abstract

The mutation rate is a key parameter in the assessment of the risk of drug resistance.Mutation rates of resistance mutations are usually measured in absence of antibioticsand are assumed to be constant rates. Environmental stress elicited by antibiotic ex-posure has been shown to transiently increase the mutation rate in pathogenic bac-teria. In this study we explore the implications for the emergence of drug resistancethat arise due to antibiotic stress-induced mutagenesis (ASIM). With a computationalmodel we simulate the effect of ASIM on bacterial population dynamics. We showthe magnitude by which models with a constant mutation rate underestimate theprobability for the emergence of drug resistance. In a within-host model that alsoincorporates pharmacokinetics we further demonstrate that a cycling regimen of twodrugs is less likely to cause multidrug-resistance compared to a combination regi-men if ASIM is taken into account. We conclude that ASIM is likely to substantiallyincrease the risk of drug resistance and reveals drug interaction dynamics that couldimprove treatment efficacy. Our study shows that the measurement of parametersinvolved in ASIM is crucial for reliable estimates about the occurrence of drug resis-tance.

61

62 considering antibiotic stress-induced mutagenesis

4.1 introduction

Resistance to antibiotics has been a concern for almost as long as the history of an-tibiotic usage and will likely continue to be a major threat to public health in theforeseeable future [135; 136; 137; 138]. A large body of literature describes the un-derlying factors that lead to drug resistance in many pathogen/drug combinations.One of the key factors for the emergence of antibiotic resistance is the mutation rate[139; 140; 141]. The mutation rate is typically measured by culturing bacteria in theabsence of drugs and then measuring the frequency of spontaneously emerged re-sistant mutants in this population on selective media [142; 143]. However, in recentyears there has been mounting evidence that phenotypic mutation rates in bacteriaare influenced by various stresses [24]. Importantly, these stresses include many an-tibiotics [144]. Most of the stresses are directly or indirectly linked to an increasedabundance of reactive oxygen species (ROS) [24; 145]. Higher ROS concentrations,which can also be caused by certain antibiotics, may inflict DNA damage and lead toa change in the regulation of genes that are involved in DNA repair and replication.These genes control the induction of the SOS stress response, the methyl-directedmismatch repair pathway, the activation of double-strand break repair proteins orthe expression of error-prone DNA polymerases [24; 146]. All of these responsesincrease the probability of introducing mutations. It has been argued that the abil-ity to transiently increase the mutation rate is a trait that has been established inmany bacteria due to a second-order selection for increased mutability under ad-verse circumstances [24; 147; 148]. The existence of stress-induced mutagenesis hasbeen controversially discussed [149; 150]. However, it may be still worth investigat-ing how a phenotypic alteration of mutation rates in response to antibiotic exposureaffects resistance evolution.

Here, we focus on the transient mutagenic effect of antibiotic exposure. We ex-pect that the resulting stress response has a positive feedback on the emergence ofresistance mutations against the drug that is mutagenic as well as other drugs. Mostmathematical models investigating the emergence of drug resistance assume stablemutation rates [151; 152; 153; 154]. By not taking into account the possibility of chang-ing mutation rates they may fail to describe a possible effect of pharmacokinetics onmutation rate and misjudge the overall likelihood of the emergence of resistance, es-pecially when more than one antibiotic is used. The aim of this study is to assess theinfluence of antibiotic stress-induced mutagenesis (ASIM) on the emergence of drugresistance. We find that ASIM does not only alter the expected frequency of de novoemergence of resistance, but also changes our expectations regarding the success ofdifferent treatment strategies.

4.2 methods

4.2.1 Mathematical model

The detailed description of the mathematical model is available in the SupplementaryMaterial 4.A. In brief, we model bacterial population biology by assuming logisticgrowth and adding a drug-dependent death rate (Suppl Mat 4.A.1). The relationship

4.2 methods 63

between drug concentration and antibiotic-induced killing is described by a sigmoidEmax model [108] extended to multiple drugs (Suppl Mat 4.A.2). Additionally, wemodel the emergence of resistance mutations and assume that the mutation rate de-pends on the drug concentration (Suppl Mat 4.A.3). Pharmacokinetics are describedby translating the values of the maximally achievable peak concentration, Cmax, thetime until the peak concentration is reached, tmax, and the excretion half-life, t1/2,from the literature to a time-dependent concentration profile in patients (Suppl Mat4.A.5). The bacterial population dynamics are simulated as stochastic processes byapplying the Gillespie τ-leap method [58].

4.2.2 Assumptions and parameterization

4.2.2.1 Bacterial growth

The modeling of the bacterial growth is described in detail in Suppl Mat 4.A.1. Weassume that the bacteria have a growth rate of 2 d−1, corresponding to a doublingtime of approximately 15.1 h. The initial population size for the simulations withconstant drug concentrations is assumed to be 10

7 fully susceptible bacteria. Themaximum population size (carrying capacity) is 10

9 bacteria.

4.2.2.2 Resistance mutations

The model assumptions for the emergence of resistance are described in detail inSuppl Mat 4.A.4. The central part of this study is the introduction of a drug concen-tration dependent mutation rate. We assume that bacterial mutation rates increasewith drug concentration in a sigmoidal fashion [155]. We make this assumption be-cause the mutagenic effect of antibiotics has been argued to arise due to the increasedexpression of more error prone DNA polymerases and repair proteins [144; 156; 157].The expression levels of such polymerases and repair proteins are likely to eventuallysaturate and their error rate is expected to be constant at high drug concentrations.The sigmoidal curve is defined by three parameters: a minimum corresponding tothe base mutation rate in absence of drugs, a maximum corresponding to the satura-tion of the mutation rate at high drug concentration, and a parameter termed mut50,which corresponds to the drug concentration at which the mutation rate reaches thehalf-point between minimum and maximum. As an estimate for the minimum mu-tation rate to become resistant to a single drug we conservatively assumed a rateof 10

−9 per cell doubling [62]. The maximum mutation rate varies widely betweenstudies [158; 159; 160; 161; 162; 163; 164; 165; 166]. The differences are probably dueto both differences between combinations of bacteria and drugs and differences in ex-perimental designs and measuring methods. Here we assume a maximum ten-foldincrease of the mutation rate for high drug concentrations. Most of the aforemen-tioned studies did not look at the concentration-dependent increase of the mutationrate. The few studies that measured the increase of the mutation rate at more thanone drug concentration did this mostly at sub-MIC concentrations [158; 162; 165; 166].Therefore, it is difficult to estimate whether and how far ASIM extends beyond theMIC. In our default parameter setting, we assume that the turning point of the mut50parameter coincides with the MIC.

64 considering antibiotic stress-induced mutagenesis

Furthermore we assume that if a resistance mutation is acquired, it grants absoluteresistance and the drug becomes completely ineffective. For every drug we assumethat there is on such resistance mutation and the corresponding allele confers a fit-ness cost of 10% on the growth rate. Multiple resistance mutations are assumed tocontribute multiplicatively to the overall fitness costs.

4.2.2.3 Pharmacokinetics

During the simulations the drug concentrations are either kept constant or they in-crease and decrease according to a pharmacokinetic model that is described in detailin Suppl Mat 4.A.5. Firstly, we investigate the effect of ASIM in a situation wherea patient is treated with two equally bactericidal drugs, only one of which elicitsASIM. Secondly, we explore the dosing regime and compare situations where pa-tients are taking the two drugs combined every day (combination) and situationswhere patients alternate between the drugs every day (cycling). In order to be ableto compare the two regimens the efficacy of the two regimens is equalized by ad-justing the dosage of the drugs in both cases so that patient clearance is achieved onaverage after 28 days. The exact dosages can be found in the Suppl Mat. Before treat-ment starts every patient harbors 5 × 10

7 fully susceptible wild-type bacteria andthe simulation is repeated 1’000 times for every treatment scenario and drug type inFigures 4.1 and 4.2. In order to decrease the confidence intervals in the Figures 4.3and 4.4 we performed these simulations 10’000 times each.

4.3 results

To get an overview over the basic parameters and their effects we first study a ba-sic model of ASIM. In Figure 4.1 a homogeneous population of sensitive bacteria isexposed to various constant drug concentrations. The net growth rate (red line), i.e.the difference of the natural replication rate and the drug-induced bactericidal killingrate, declines with increasing drug concentrations in a sigmoidal manner. In additionto the drug concentration, the net growth rate is affected by the replication rate, theKC50, the Emax value and the MIC of the drug (see Equations 4.4–4.4 and Table 4.1).At the MIC the drug-induced killing and the replication rate cancel each other outand the net growth rate is zero. The mutation rate (black line) without consideringASIM stays constant and is independent of the drug concentration (grey line). WhenASIM is taken into account the mutation rate increases sigmoidally with higher drugconcentrations (black line). The mutation rate increase depends on the mut50 andthe maximum fold change Md. Here, mut50 is set to the MIC. These parameters areassumed constant during the simulations shown in Figure 4.1. We get three possibletreatment outcomes: (i) complete sterilization, i.e. the drug concentration is suffi-cient to eradicate the bacterial population and the treatment is deemed successful;(ii) treatment failure, here defined as the treatment being unable to clear the bacterialpopulation after 20 days (green line); (iii) emergence of resistance, defined here asthe population containing at least 50 resistant bacteria after 20 days (dark blue line).Emergence of resistance implies treatment failure and is therefore a subset of the pre-vious category. We show the emergence of resistance with ASIM (dark blue line) andwithout ASIM (light blue line). Unsurprisingly, the risk for treatment failure drops

4.3 results 65

Table 4.1: Compartment characteristics

Replication rate (r) 2 d−1

Initial population size (N0) 5 × 107 CFU

Carrying capacity (K) 109 CFU

Drug half-life (t1/2) a 3 hAbsorption time (tmax) a 1 hDosage (D0) 3.18 / 8.80

c

MIC a1b

KC50 a 5b

Base mutation rate (md) a 10−9 per replication

mut50 d 0.25b

Maximum fold increase of mutation rate (Md) 10

Resistance cost (cl) a 0.1 b

a for all used drugsb arbitrary concentration unitc combination / cyclingd only for mutagenic drug

from 100% at sub-inhibitory drug concentrations rapidly if the drug concentrationsare above the MIC. Beyond the MIC in about 5% of all simulations the bacterial pop-ulation is rescued by the emergence of a resistant mutant under ASIM. Below theMIC resistant genotypes occur in up to 60% of all populations. This is substantiallymore frequent than in a model without ASIM.

Next we assess how the emergence of resistance depends on mut50 (see Figure4.2). To do so we repeat the simulations shown above for a wide range of drugconcentrations and additionally vary the mut50 concentration. For each pair of drugconcentration and mut50 value we count the frequency of the emergence of resistantmutants. The remaining parameters and the criteria for scoring the outcome of thesimulations are the same as above. Resistant genotypes emerge rarely if the mut50value is high and the drug concentration is either very low or very high. The risk forthe emergence of resistance generally increases with lower mut50. It is highest at thelowest mut50 that we tested and at a drug concentration of 1/4 × MIC. Interestingly,1/4 × MIC is the drug concentration at which the frequency of drug resistance ishighest for every mut50. We conclude that the mut50 concentration has a substantialinfluence on the probability of emergence of resistance.

To estimate the influence of ASIM on the emergence of resistance we repeated theabove simulations 10’000 times for each parameter set with and without ASIM (seeFigure 4.3). At low drug concentrations the frequency of emergence of resistance onlydiffers marginally. However, at the MIC the risk of emergence of resistance increasesabout five-fold increasing to an about ten-fold risk at high drug concentrations. InFigure 4.1 we see that a considerable fraction of bacterial populations are rescued

66 considering antibiotic stress-induced mutagenesis

Concentration

10

−92

×10

−9

4×

10

−9

6×

10

−9

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10

−9

10

−8

Muta

tio

n r

ate

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−4

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t gro

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sitiv

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1

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0.0

0.1

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0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

Tre

atm

ent fa

ilure

ra

teFigure 4.1: Antibiotic stress-induced mutagenesis (ASIM) increases the risk of drug resis-

tance over a large concentration range. A population of 107 bacteria is exposed

to a range of constant drug concentrations. The outcome of 1000 simulations oftreatment per parameter set is collected and the lines show the average. Treat-ment failure (green line) is defined as incomplete clearance after 20 days. Thefrequency of resistance emergence under ASIM is given in dark blue and withoutASIM in light blue. At least 50 drug resistant bacteria have to be present in thepopulation for a strain to be classified as resistant. Without considering ASIMresistance evolves in fewer populations. The mutation rate per generation in pres-ence of ASIM is given in black and increases in a sigmoidal manner with higherdrug concentrations. The base mutation rate (without ASIM) is given in grey. Theinflection point where the mutation rate reaches the half maximal increase (mut50)is at the MIC. The net growth rate (red line) is composed of the natural growthrate and the killing due to the bactericidal drug activity.

4.3 results 67

mut 5

0

0.2

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Concentration

Pro

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ty o

f em

erg

ence o

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ce

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×M

IC

132

×M

IC

116

×M

IC

1/

8×M

IC

1/

4×M

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1/

2×M

IC

1

×M

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×M

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×M

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×M

IC

1

6×M

IC

3

2×M

IC

0.0625

0.125

0.25

0.5

1

2

4

8

Figure 4.2: Emergence of drug resistance depends on drug concentration and mutation rate.The mut50 concentration is the antibiotic concentration at which the half maximalmutation rate is reached. To predict the influence of the mut50 value on theprobability of resistance emergence 10

7 bacteria with varying mut50 values areexposed to a wide range of drug concentrations. The color scale indicates thefraction of 1000 simulations per parameter set in which at least 50 drug resistantbacteria evolved after 20 days.

68 considering antibiotic stress-induced mutagenesis

due to the emergence of resistance even at very high drug concentrations. This isa much higher fraction than with a constant mutation rate. The simulations thussuggest that the underestimation of the risk of emergence of resistance due to AISMincreases with higher drug concentrations.

Next we investigate the implications of ASIM for the treatment of patients. To thisend we are introducing a model that incorporates the pharmacokinetics as would beobserved in a human patient treated with two bactericidal drugs simultaneously (seeFigure 4.4). Four cases are studied: Patients receive both drugs either simultaneouslyor alternatingly every day and the drugs either do not elicit ASIM or only one of themelicits ASIM. The dosage of the drugs is adjusted to achieve complete clearance after28 days on average if no double-resistance emerges. The simulation is stopped after50 days and the frequency of patients harboring double-resistant bacteria is counted.Thus, if the bacterial population is not eradicated after 50 days, it is always dueto the emergence of resistance. In accordance with the previous results the risk ofemergence of double-resistant genotype is substantially lower if both drugs are notmutagenic. The two treatment strategies also do not differ from each other if no drugelicits ASIM. However, if one drug is mutagenic combination treatment seems to besignificantly worse than an alternating regimen. The advantage of the alternatingtreatment is a direct consequence of ASIM.

4.4 discussion

Mathematical models are a useful tool to investigate the expected outcome of antibi-otic treatment strategies before costly and time consuming experimental and clinicalstudies are performed. Moreover, they aid in identifying gaps in our current knowl-edge that preclude quantitative predictions of treatment success and resistance evolu-tion. It is well known that at least some antibiotics increase bacterial mutation ratesand thereby the rate of resistance evolution in a dose-dependent fashion. In thisstudy we present a population dynamic model that addresses how dose-dependentantibiotic stress induced mutagenesis (ASIM) affects the probability of emergence ofdrug resistance in a single patient.

Our study indicates that ASIM changes both our quantitative expectations regard-ing the frequency of resistance emergence as well as our qualitative expectationswhich treatment strategy is least likely to lead to treatment failure due to resis-tance. This is in agreement with previous expectations and results from other studies[160; 162; 167; 168]. Previous models, which do not take ASIM into account, under-estimate the probability for the emergence of resistance. The degree to which thosemodels underestimate resistance evolution depends on the drug concentration towhich the bacteria are exposed. High drug concentrations do not necessarily reducethe risk of drug resistance if fully resistant mutants rescue the bacterial populationbefore it is completely eradicated. We find that the probability of resistance emer-gence peaks at approximately 1/4 ×MIC independent from the exact relationship ofdrug concentration and mutation rates. Sub-MIC concentrations have been demon-strated to be associated with elevated occurrences of drug resistance [164; 166]. Thereare several factors which we would expect to drive resistance evolution: i) the size ofthe susceptible population that gives rise to resistant mutants, ii) the number of gen-

4.4 discussion 69

0

1

5

10

15

164

×M

IC

132

×M

IC

116

×M

IC

18

×M

IC

14

×M

IC

12

×M

IC

1×M

IC

2×M

IC

4×M

IC

8×M

IC

16×M

IC

32×M

IC

drug concentration

fold

change o

f re

sis

tance e

merg

ence w

ith A

SIM

Figure 4.3: ASIM increases the emergence of drug resistance at higher drug concentrations.A population is classified as resistant when at least 50 bacteria became drug re-sistant after 20 days of treatment. The panel shows the fold change in emergenceof drug resistance with ASIM compared to a model with a fixed mutation rate.In the ASIM model the mutation rate increases with higher drug concentrationsassuming mut50 equals the MIC. The fixed mutation rate model assumes a mu-tation rate that is equal to that of the ASIM model at drug concentration zero.Each data point summarizes 10’000 simulations. The error bars indicate the 95%confidence interval. The increasing size of the confidence intervals is due to theincreasingly rare occurrence of drug resistant bacteria at high drug concentrationswithout ASIM.

70 considering antibiotic stress-induced mutagenesis

Figure 4.4: ASIM changes theoretical predictions for optimal drug therapy. This graphshows the emergence of drug resistance within single patients that are treatedwith two bactericidal drugs, either administered every day simultaneously (com-bination, red bars) or given alternately on consecutive days (cycling, blue bars)Patients harbor a homogeneous population of 5 × 10

7 wild-type bacteria. For thesimulations assuming fixed mutation rates neither drug is mutagenic (i.e. resis-tance mutations arise irrespective of the applied drug concentration), while withASIM one of the two drugs induces mutagenesis. The mut50 concentration forthe ASIM drug is 1/4 × MIC. Every parameter set is simulated 10’000 times andthe fraction of patients that developed multidrug-resistance is given. The drugdosages are adjusted to achieve complete clearance after 28 days of treatment as-suming no emergence of multidrug-resistant strains. The error bars indicate the95% confidence interval. In this case, the emergence of resistance is equivalentto treatment failure, i.e. patients who develop resistance are still infected after 28

days and all patients who fail treatment do so because of resistance evolution.

4.5 acknowledgments 71

erations before the population is eradicated, iii) the rate per replication with whichresistance mutations emerge and iv) the fitness difference between susceptible andresistant bacteria. When keeping the initial population size constant, there seems tobe an optimum for the last three factors to favor a high frequency of populationscontaining drug resistant bacteria.

Patients who are treated with a mixture of drugs usually receive them in com-bination [169; 170]. Our results show that this strategy might not be optimal inpreventing the emergence of resistance if one of the drugs elicits ASIM. This effectprobably arises due to the lower number of drug applications that is compensatedby higher doses. If a drug is less often administered the drug concentration is less of-ten at subinhibitory concentrations, which have previously been shown to favor theemergence of drug resistance. The advantage of a cycling regimen over combinationtherapy on an epidemiological scale has previously been shown to be advantageousin a hospital setting [168].

To the best of our knowledge, this study is the first that addresses the effects ofdose-dependent ASIM. Our main limitation is the scarcity of experimentally obtainedparameters. Depending on the study the increase of mutation rates varies widely,from 2-fold [164; 166] up to 10’000-fold [160]. Most studies report increases in theorder of a few- up to 100-fold [158; 159; 161; 162; 163; 165]. Furthermore, most stud-ies showed an increase of the mutation rate only qualitatively, but did not establisha quantitative relationship between the drug concentration and the increase of themutation rate. Due to the insufficient data from the literature we apply conservativeparameter estimates. This also means that we are potentially over- or underestimat-ing the magnitude of the effects that we found. We therefore have to point out thatthe focus should be on the qualitative aspects of our results. We further have to pointout that we look specifically at the influence of changing probabilities on the emer-gence of de novo rescue mutations [171]. That means, mutations that are involvedin preventing the population from eradication and which appear when the stress isalready present. We assume that none of these mutations occur in the populationbefore the introduction of antibiotics and that the population is therefore geneticallyhomogeneous.

Here, we show that that ASIM has a profound effect on resistance evolution. Oneof the main messages of this work is therefore that dose-dependent ASIM shouldbe investigated experimentally in more detail, especially at antibiotic concentrationsabove the MIC. The negative consequences of ASIM could be prevented by the intro-duction of drugs that specifically inhibit the intracellular mechanisms that increasethe mutation rate of bacteria. Such drugs have been proposed previously as an ef-fective instrument to reduce the evolvability of pathogens [161; 172; 173; 174]. Wefind that ASIM increases the probability of treatment failure by up to 10-fold. Thus,drugs that prevent stress-induced mutagenesis might have a major impact on treat-ment outcome and warrant further investigation.

4.5 acknowledgments

We thank Antoine Frénoy for reviewing the manuscript.

A P P E N D I X

4.a supplementary material

4.a.1 General model

The bacterial population dynamics are simulated as stochastic processes by applyingthe Gillespie τ-leap method [58] with a temporal resolution of 10

−2 d. The underlyingprocesses can be described in differential equations that are explained below.

4.a.2 Bacterial growth and death

The general population dynamics are based on a classic logistic growth model.

dNg

dt= r ·ωg ·Ng − (dg + κg) ·Ng (4.1)

Here Ng is the number of bacteria of a specific genotype. r is the replication rateof the bacteria, which is modified by the fitness ωg of the strain. The population isreduced by the natural death rate dg and the drug-induced killing κg.

The fitness of a specific genotype is influenced by the fitness costs that are imposedby resistance mutations.

ωg =

n∏l=1

(1− cl) (4.2)

cl is the cost of a resistance allele at the locus l and n is the number of resistanceloci. Susceptible wild-type alleles do not confer any costs.

The death rate dg depends on the overall population density that is influenced bybacteria of every genotype.

dg = r ·N

K(4.3)

Here K is the carrying capacity.

4.a.3 Pharmacodynamics

The killing rate κg is calculated by using the sigmoid Emax model by Czock et al. [108].We extend it to include the effects of multiple drugs.

κg =

n∑d=1

Emax,d ·

1− 1Cd

KC50,d+ 1

· νg,d (4.4)

73

74 considering antibiotic stress-induced mutagenesis

The killing rate depends on the additive effects of all drugs to which the specificbacterial strain is susceptible. The potency of a drug is governed by Emax,d, which isthe maximal death rate. It is modified by the drug concentration Cd and the KC50,dconcentration, which represents the concentration at which the drug exerts its half-maximal bactericidal potential. The Boolean parameter νg,d determines whether thedrug is effective or whether the bacteria strain is resistant against the drug. Drugresistance is assumed to be absolute.

The Emax value is obtained by adopting the equation from the enhanced-death con-stant replication model [108].

dN

dt= r ·N− Emax ·N ·

C

KC50 +C(4.5)

When the drug concentration C is equal to the minimum inhibitory concentration(MIC) growth and killing cancel each other out and we get the following equationthat determines the Emax value.

Emax =r · (MIC+KC50)

MIC(4.6)

4.a.4 Resistance mutations

The increase of the mutation rate m by a stress-inducing drug follows a curve that isdefined by a sigmoid function [155].

m(t) =

n∏d=1

m ·

(Md −

(Md − 1Cd

mut50+ 1

))(4.7)

If we assume that resistance to a drug is granted by the mutation of a single allele,then the number of drugs n is the number of resistance loci. m is the base mutationrate and M is the maximum increase of this rate that is achievable by a drug. Theturning point of the sigmoid curve is defined by the mut50 concentration.

4.a.5 Pharmacokinetics

If the drug concentration in the simulation is not kept constant, classic absorptionand excretion kinetics are applied to the drug concentration.

Two drug compartments are simulated in the model: At the time point of drug ad-ministration, the whole dosage is instantly added to the compartment of unabsorbeddrug D. From the first compartment D the drug is absorbed into the compartment Cof the pharmacodynamically effective drug. From compartment C the drug concen-tration constantly decays due to excretion. The decrease of the drug concentration incompartment D is calculated according to the following equation:

dD

dt= −ka ·D (4.8)

4.A supplementary material 75

ka here is the absorption rate constant. The dynamics in compartment C are gov-erned accordingly:

dC

dt= ka ·D− ke ·C (4.9)

ke is the excretion constant of the drug. To calculate the absorption rate constantka we use the following equation that describes the relationship between the absorp-tion rate constant, the excretion rate constant ke and the time until the maximumconcentration peak is reached tmax:

tmax =ln(ka) − ln(ke)

ka − ke(4.10)

From this we can derive an equation that enables us to calculate the absorptionrate constant for a known tmax and ke.

ka = −W−1(−e

−ka·tmax · ke · tmax)tmax

(4.11)

W−1 denotes the lower branch of the Lambert function. The excretion rate constantke is derived by from the concentration half-life t1/2.

ke =ln(2)

t1/2(4.12)

To calculate the initial amount of drug D0 that has to be administered in order toreach a predefined peak concentration Cmax, we use the Bateman equation [127; 128],which is also the solution to equation 4.9 to calculate the drug concentration at anygiven time point considering drug absorption and excretion:

C(t) =D · kaka − ke

· (e−ke·t − e−ka·t) (4.13)

From this we derive a formula that calculates the required D0.

D0 =Cmax · (ka − ke)

ka · (e−ke·tmax − e−ka·tmax)(4.14)

5G E N E R A L D I S C U S S I O N

5.1 conclusions

5.1.1 Treatment of pulmonary tuberculosis

The initiation of the directly observed treatment, short course (DOTS) strategy im-plemented by the WHO had five main components: increasing government commit-ment, case detection by sputum smear microscopy, the standardization of treatmentby the application of a short course treatment regimen under professional supervi-sion, providing sufficient drug supply and a standardized recording and reportingsystem [16]. While DOTS was reported to be very successful [27] there were alsostudies that showed the inadequacy of DOTS in areas with a high prevalence of drugresistance [175; 55]. It was argued that the incautious application of treatment reg-imens within the DOTS program could lead to an amplification of drug resistanceamong patients due to the undetected preexistence of mono- or multi-drug resistance[176; 177].

In Chapter 3 we see that there is a substantial likelihood that treatment failurecoincides frequently with at least mono-resistance against isoniazid. Even if drugsusceptibility testing with a GeneXPert MTB/RIF test [129] would be performedsuch patients would probably not be diagnosed as harboring MDR-TB (M. tuberculo-sis that is resistance against at least isoniazid and rifampicin). In Chapter 2 we findthat the retreatment of patients with a treatment history indeed bears the risk of ac-cumulating additional resistance mutations if patients also fail the retreatment. Thisconfirms the concerns mentioned above that the application of standard treatmentfor patients who are suspected to harbor Mtb with low resistance could lead to anamplification of the resistance.

The DOTS-Plus strategy aims specifically at the diagnosis and optimal treatmentof MDR-TB patients [178]. Based on our results we argue that this might aim toolow. A thorough drug susceptibility testing that also screens for isoniazid-resistancecould help to prevent a potentially detrimental administration of ineffective drugs.Not only is the patient more likely to fail the treatment if not all drugs are effective,he or she could also be forced to suffer later through retreatment regimens that havea lower success rate and are associated with more severe side-effects. Besides the per-sonal disadvantages for the patient, MDR-TB or XDR-TB (extensively drug-resistantTB: resistance against at least isonazid and rifampicin, a fluoroquinolone, and eitheramikacin, kanamycin or capreomycin [179]) treatments are also considerably moretime-consuming and expensive [180; 181].

77

78 general discussion

5.1.2 Antibiotic stress-induced mutagenesis

Mutation rates are commonly assessed under ideal growth conditions for bacteria[62]. When any other influences can be excluded the mutation rate for a specificlocus can be assumed to be dependent solely on the fidelity of the DNA replicationmachinery. However, in different environments there exist factors that may changemutation rates. The concept that mutation rates are not constant but can vary undercertain circumstances has not been discussed in the literature for a long time. It istherefore not surprising that it is not customarily incorporated into within-host mod-els that deal with mutation rates. Mutation rates are a key parameter for modelsabout the probability for the emergence of resistance [151; 182]. Several environmen-tal stresses have been shown to increase mutation rates in bacteria. Among thosestresses is also the exposure to certain antibiotics [144]. In Chapter 4 we conceptuallyshow what the implications of antibiotic stress-induced mutagenesis (ASIM) may befor the evolution of drug resistance in bacteria. When we compare the probabilitiesfor the emergence of resistance between a model that assumes a static mutation rateand a model in which the antibiotic increases the mutation rate in a concentration-dependent manner, we observe a substantial increase of the probability for the emer-gence of drug resistance. This leads us to the conclusion that the concept of ASIMshould at least be considered in future models that attempt to quantify the probabil-ities for the emergence of mutations.

When we take ASIM into account we are also able to discover novel implicationsfor combination therapy. In a scenario in which a patient is treated with two drugsagainst a bacterial infection we observe that it could be beneficial to administer thedrugs alternately rather than simultaneously if one of the drugs increases mutage-nesis and the other does not. To my knowledge this study is the first to assess thepotential benefits of a cycling drug administration regimen for an individual regard-ing the emergence of resistance.

5.2 future directions

When one is engaged in the business of modeling one has to accept the intrinsicshortcomings of models. Models try to represent actual systems in an abstract andsimplified form. The human mind constantly constructs models to get a grasp on thereality around it and they help it to see and understand relationships and causalities.Because models are a simplification of reality they are also never absolutely truebecause they cannot fully capture the nature of reality. However, models are notmeant to replicate the real world. Their task is to show whether certain assumptionsare sufficient or necessary to give a reasonably accurate representation of the naturalworld. Still, one has to constantly answer the question whether a model reflectsreality accurately enough to provide a sufficiently trustworthy answer to the specificquestion one is trying to tackle.

In this section I would like to talk about aspects that we could not implement inour projects. There are various reasons for why we did not include certain things butit generally left me behind with some unrest. For the aforementioned reasons I haveto constantly question my confidence in my models and their predictions because

5.2 future directions 79

not considering some aspects of the disease dynamics may open up the door forunjust conclusions. At the same time this attitude also helps me to maintain a criticaleye on my own work and that of my colleagues and to think about possibilities forimprovements of current models and future directions to explore.

5.2.1 Pharmacodynamics

Antibacterial drugs are commonly divided in two main classes: bacteriocidal drugsand bacteriostatic drugs. Bacteriocidal drugs are characterized by their ability to killbacteria while bacteriostatic drugs merely inhibit the proliferation of bacteria. If youtry to put an antimicrobial drug in one of these two categories you may discover thatthis is not always a straightforward task. Many antibiotics have a predominantly bac-teriostatic effect at low concentrations but may actually exhibit bacteriocidal activityat higher concentrations. It could even be taken into question whether a drug is bac-teriostatic at low concentrations if one could just observe that a colony does not growanymore. The classification of bacteriostatic and bacteriocidal drugs is usually doneat a population level. Hence, if one would examine the drug efficacy at a cellularlevel it is conceivable that the bacteriocidal activity of a drug and the bacterial pro-liferation just about cancel each other out and therefore no net growth of the colonyis observed. Therefore, a bacteriocidal drug could at low concentrations be mistakenfor being bacteriostatic.

In fact one of the simplifications that we did in all chapters of this thesis is toassume that the activity of antimicrobial drugs is exclusively bacteriocidal. Thissimplification may lead to an overestimation of the probability of resistance emer-gence. If a drug is also at least partially bacteriostatic it would reduce the numberof cell divisions and thereby the number of opportunities for mutations to arise. Inearly stages of the development we experimented with a pharmacodynamic modelthat also incorporated bacteriostatic activity. When we tried to fit this model to invitro time-kill curves of anti-tuberculosis drugs [90] we observed negative growthinhibition at some concentrations (data not shown) and other unrealistic behavior.Eventually we settled for a pharmacodynamic model that only considered the bacte-riocidal effect of drugs. This simplified model allowed us to achieve reasonably goodfits to the in vitro time-kill curves for most drugs (see Supplementary Material 2.A).However the effects of rifampicin, at least for higher concentrations, could not be fitvery well. This is an indication that a single pharmacodynamic model is probablynot sufficient to capture the activity of all drugs accurately. To further improve thepharmacodynamic model it would be desirable if drug actions could be experimen-tally observed at the cellular level. Eventually, we would be able develop a tailoredfunction for every drug that describe their action more accurately.

Another simplification of our pharmacodynamic model is the omission of the post-antibiotic effect [183]. The post-antibiotic effect inhibits growth for a certain timeperiod even when the drug is not present anymore [184; 80]. The presence of thepost-antibiotic effect has been reported in in vitro studies for most first-line drugsagainst M. tuberculosis [111]. It is reasonable to assume that it may last for severalhours [185]. Neglecting the post-antibiotic effect may overestimate the risks in con-

80 general discussion

nection to intermittent therapy (see Chapter 3) and the risk for the emergence ofdrug resistance.

5.2.2 Pharmacokinetics

One factor that may be highly influential in the transferability of in vitro experimentsto in vivo models is bioavailability. I am using here the pharmacological definitionof bioavailability, which states that the bioavailability is a measurement of the rateand extent to which a drug reaches the site of action [186]. In this thesis the conceptof bioavailability is embodied in the TB model as the ratio between the serum drugconcentration and the concentration in the epithelial lining fluid within the lung [83]and it also influenced the relative drug efficacy parameters. For example, the relativedrug efficacy parameters were assumed to be lower in macrophages if the drugs werereported to have a low cell-penetration [69; 68; 70; 77]. The ratio between the serumconcentration and the epithelial lining fluid on the other hand is a global parameterbecause it changes the drug exposure in all simulated compartments.

While in vitro data suggests that isoniazid and rifampicin have comparable bacte-riocidal activity at clinically relevant serum concentrations [90] the picture changeswhen we also consider the amount of drug that actually reaches the bacteria. Be-cause the rifampicin concentration in the epithelial lining fluid is only about a thirdas high as in the serum [83] it loses a substantial amount of its potency relative toisoniazid that actually is more concentrated in the epithelial lining fluid than in theblood serum [83]. This phenomenon also partially explains the strong survival bene-fit of isoniazid-resistance for M. tuberculosis relative to rifampicin-resistance that weobserved in the results of Chapter 3.

Somewhat related to that issue is the limited certitude about the conditions insidegranulomas. Because the pathogenesis of a tuberculosis infection is different fromthe progression in animal models [187; 188] the knowledge about processes insidegranulomas remains vague. The population growth dynamics inside granulomas aswell as the pharmacokinetics and pharmacodynamics are largely based on assump-tions, less on actual measurements. It is not known whether the bioavailability ofdrugs is similar to the one in the epithelial lining fluid, and the premises about theefficacy of drugs is largely based on the assumptions of low bacterial growth and alow pH [19]. Furthermore, it is debatable whether all granulomas develop similarlyand progress into open cavities during an acute infection. It is possible that the bac-terial populations in single granulomas remain dormant and are mostly unaffectedby a treatment. Such granulomas could then at a later time point cause a relapse —probably with fully susceptible bacteria. Although, one has to keep in mind that thepossibility of relapse, caused either by the regrowth of previously dormant bacteriaor by reinfection, is anyway excluded in our model. If we included these possibilitiesthey would decrease our net treatment success rate.

5.2.3 Immune system and life history traits

In our TB model apart from the role of macrophages as a compartment we do not ex-plicitly simulate the effect of the immune system on the progression of the infection.

5.2 future directions 81

We assume that the immune system of the patients is weak enough for the infectionto become acute and are therefore neglecting any contributions of it to contain theinfection. This is a reasonable assumption for an untreated infection, however, it ispossible that after the initiation of treatment the infection is suppressed well enoughthat the immune system becomes less overwhelmed and is able to suppress the lastremains of an infection even if patient adherence is suboptimal. This would implythat the treatment success rate could be underestimated.

A classic simplification in our model is the absence of a natural death rate ofbacteria. Bacteria may only die because of the limited population density inside thecompartments or because of bacteriocidal drug actions. Such an assumption is aclassical logistic growth model [2]. If we assumed a natural unconditional death rateand a correspondingly increased birth rate we could achieve the same net growthrate that we originally assumed. The difference would be that we would have ahigher turnover of bacteria. With a higher turnover we would get more birth eventsand therefore more opportunities for resistance mutations to emerge. This meansthat our model may underestimate the probability for the emergence of resistance.Unfortunately, the growth rate of M. tuberculosis in vivo can only be estimated withlimited certainty [189] and measurements of the natural birth and death rate in vitrodo not exist in the literature.

The definition of drug resistance that we apply in the models of this thesis is ratherabsolute. We assume that a particular mutation in a locus confers complete resistanceto the corresponding drug. This definition is more strict than the common concep-tion that states that drug resistance is characterized by a reduction in effectiveness ofa drug [190]. Measurements of the mutation frequency usually determine the ratioof bacteria that are able to grow or at least persist at drug concentrations above theMIC [62; 93; 191]. Such measurements are at risk to also include bacteria that arephenotypically drug tolerant. Drug tolerance has been described in M. tuberculosisand attributed to a slow down of metabolism [192] or an increased expression ofefflux pumps [96]. Drug tolerance may serve as a stepping stone for the evolutionof higher genetic drug resistance [192]. Genotypes with low levels of drug resistancemay then accumulate further mutations that grant higher levels of drug mutation. Inour model we do not simulate the stepwise acquisition of resistance mutations thatrender their carrier increasingly more drug resistant because currently available datadoes not allow for more accurate modeling. A more detailed model may also notprovide much additional benefit because resistance mutations that grant low levelsof resistance or that infer high fitness costs are not particularly relevant for the evo-lution of resistance. In a previous study it has been found that of several rifampicinresistance mutations the one that conferred the least fitness costs is predominantlyfound in clinical isolates [193]. It could therefore be justified to not consider theemergence of all resistance mutations but only the ones that provide a sufficientprotection from drug actions without affecting the fitness too much.

The mutation rate for drug resistance mutations itself is also less certain thanwhat would be desirable to improve the predictions of models. There has been adebate about whether there are M. tuberculosis strains (e.g. Beijing strain) that havea genotypically higher mutation rate than other strains [131; 194; 66]. Furthermore,there are even discussions whether mutation rates could change transiently due to

82 general discussion

environmental influences. While some excluded the possibility for the inductionof mutations by oxidative stress [195; 196] others still consider this as a possibleexplanation for the the observation of high mutation frequencies during latency [197;189]. It has also been observed that genes for DNA repair and DNA stability weredown regulated in clinical multi-drug resistant isolates of M. tuberculosis [192]. Thiscould be an indication that M. tuberculosis is able under the influence of stress toincrease its mutation rate and faster adapt to averse conditions.

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A C K N O W L E D G E M E N T S

I would like to thank here all the people who contributed to my thesis and those whomade my years here in the group of Theoretical Biology a great experience. First ofall I am immensely grateful for having Sebastian Bonhoeffer as my supervisor. Icould not wish for a more accommodating doctoral father. He provided a stimulat-ing environment and granted me the freedom to pursue the studies that interestedme. By granting me the personal freedom to explore various directions and alsooccasionally divert from an originally chosen path I sometimes may have gotten lostbut it also allowed me through introspection to learn to keep the bigger picture inperspective. At the same time he provided me always the support when I requestedit. With this attitude and by his example he cultivated an environment that fostereda way of independent and critical thinking.

It would be difficult to exaggerate the influence that Pia Abel zur Wiesch hadon my doctoral studies. She is probably the single most responsible person for mechoosing to pursue my doctoral studies. From my master’s thesis throughout myPh.D. she fulfilled the role of my supervisor at least as much as Sebastian did. Ithink the mere fact that she was involved in every study in this thesis as well as aprevious publication speaks volumes. I am forever grateful for all the knowledgeand experience that she shared with me. It is a privilege to have collaborated withsomeone for whom I foresee an outstanding scientific career.

Many thanks also go to Roger Kouyos who introduced me to the field of infectiousdisease modeling. He was my first mentor in the group of Theoretical Biology andmuch of what he taught me is still at the roots of all my mathematical models. I amalways amazed by his capability to almost instantly capture concepts of rather com-plex issues that he is being confronted with. This was frequently highly appreciatedwhen I called for his support or opinion.

Special thanks go to Ted Cohen and Roland Regoes who kindly agreed to be inmy examination committee. It humbles me to know that my work is being judgedby people whose expertise I value greatly.

Unfortunately, it would exceed the appropriate length of an acknowledgementsection if I would express my heartfelt gratitude towards every former or currentmember in the group of Theoretical Biology, Experimental Ecology, Microbial Molec-ular Biology, Evolutionary Biology and Pathogen Ecology. I just want to state that Iconsider myself incredibly lucky to have been allowed to not only share office spacebut also share many stories and beers during countless hours of stimulating dis-cussions with people, none of which I would not consider a friend. Thanks for allthe exhaustive runs up to the Waldhüsli, the beer brewing, hikes, skiing weekendsand parties! I sincerely hope that we will stay in touch and that the procrastinatingdiscussions continue.

I definitely have to thank my sister, Eliane, with whom I shared a home for manyyears. Thank you for your patience and your leniency when I did not fully adhere tothe house cleaning schedule!

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104 Bibliography

Last but certainly not least I thank my parents, Ruth and Edgar. They spurredmy ambition to always progress and develop further. Even when I diverted frommy original path and they may have struggled initially to embrace my new goalsI was absolutely sure that they would support me. Thank you very much for yourconfidence and your encouragement!

C U R R I C U L U M V I TA E

Dominique Richard Cadosch

Institute of Integrative BiologyCHN H76.1Universitätstrasse 16

8092 ZürichSwitzerland

Phone: +41 44 632 89 22

Email: dominique.cadosch@env.ethz.churl: http://www.tb.ethz.ch/people/person-detail.html?persid=130634

Birth date: 30 May, 1984

Nationality: Swiss

Language skills: German (native), English (full professional proficiency), French(limited working proficiency), Japanese (elementary proficiency)

education

Mar. 2012 – May. 2016

Doctoral student in Theoretical BiologyThesis Title: Within-host population dynamics and the evolution of drug resistancein bacterial infectionsSupervisor: Prof. Sebastian BonhoefferInstitute of Integrative Biology, D-USYS, ETH ZürichZürich, Switzerland

Mar. 2010 – Nov. 2011

M.Sc. ETH in Ecology and EvolutionThesis Title: Modelling the within-host infection and therapy of pulmonary tubercu-losisSupervisor: Prof. Sebastian BonhoefferInstitute of Integrative Biology, D-USYS, ETH ZürichZürich, Switzerland

Sep. 2005 – Feb. 2010

B.Sc. ETH in BiologyETH ZürichZürich, Switzerland

105

106 curriculum vitae

Jul. 2004 – May. 2005

Military serviceMechanized infantry of the Swiss ArmySwitzerland

Aug. 2000 – Jun. 2004

Gymnasial MaturaAlte Kantonsschule AarauAarau, Switzerland

other research experience

Jan. 2014

Participation in the Swiss Epidemiological Winter SchoolCourse: Applied Bayesian Statistics in Medical Research University of BernWengen, Switzerland

Sep. 2010 – Jun. 2011

Research project in Theoretical Biology at the ETH ZürichTitle: Assessing the impact of adherence to anti-retroviral therapy on treatmentfailure and resistance evolution in HIVSupervisors: Roger Kouyos and Sebastian BonhoefferETH ZürichZürich, Switzerland

Sep. 2009 – Oct. 2011

Research project in the AI Lab of the University of ZürichTitle: Attempt on Plant-Machine Interface: Towards Self-monitoring Plant SystemsSupervisors: Dana Damian, Shuhei Miyashita, Rolf Pfeifer AI Lab, University ofZürichZürich, Switzerland

teaching and supervisory experience

Sep. 2015 – Feb. 2016

Supervised seminar paper of a Master studentTheoretical Biology group, ETH Zürich

Sep. 2014 – Apr. 2015

Supervised term paper of a Master studentTheoretical Biology group, ETH Zürich

other professional activities

Referee or co-referee for: Nature Genetics, PLOS ONE, Infectious Diseases - Drug Targets.

curriculum vitae 107

publications

D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (2016) The role of adherenceand retreatment in de novo emergence of MDR-TB. PLOS Computational Biology 12(3):e1004749. doi: 10.1371/journal.pcbi.1004749

DD Damian, S Miyashita, S Aoyama, D Cadosch, PT Huang, M Ammann, R Pfeifer(2014) Automated physiological recovery of avocado plants for plant-based adaptivemachines. Adaptive Behaviour 22(2): 109-122. doi:10.1177/1059712313511919

D Cadosch, S Bonhoeffer, R Kouyos (2012) Assessing the impact of adherence toanti-retroviral therapy on treatment failure and resistance evolution in HIV. Journalof the Royal Society Interface 9(74), 2309-2320. doi:10.1098/rsif.2012.0127

D Cadosch, HP Huang, DD Damian, S Miyashita, S Aoyama, R Pfeifer (2011)Attempt on Plant Machine Interface: Towards Self-monitoring Plant Systems.IEEE International Conference on Systems, Man and Cybernetics pp. 791-796. IEEE.doi:10.1109/ICSMC.2011.6083749

oral presentations

Sep. 2011

Attempt on Plant Machine Interface: Towards Self-monitoring Plant Systems.IEEE International Conference on Systems, Man and CyberneticsAnchorage AK, USA

poster presentations

D Cadosch, S Bonhoeffer (Aug. 2015) Antibiotic stress-induced mutagenesis and theimplications for the emergence of drug resistance.Gordon Research Conference on Microbial Population BiologyAndover NH, USAD Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (Aug. 2014) The role ofadherence, retreatment and fitness costs for the emergence of MDR-TB.Gordon Research Conference on Drug ResistanceNewry ME, USA

D Cadosch, P Abel zur Wiesch, R Kouyos, S Bonhoeffer (Aug. 2013) Modelling thewithin-host infection and therapy of pulmonary tuberculosis.Gordon Research Conference on Drug ResistanceEaston MA, USAD Cadosch, HP Huang, DD Damian, S Miyashita, S Aoyama, R Pfeifer (Sep. 2011)Attempt on Plant Machine Interface: Towards Self-monitoring Plant Systems.IEEE International Conference on Systems, Man, and CyberneticsAnchorage AK, USA

108 curriculum vitae

D Cadosch, M Böller, M Ammann, DD Damian, S Miyashita, R Pfeifer (Jan. 2010)Attempt towards the cyborg-plant – Robotic response to water stress in avocados.4th International Conference on Cognitive Systems, CogSys 2010Zürich, Switzerland

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