In silico simulations suggest that Th-cell development is regulated by both selective and instructive mechanisms

Theoretical Article

In silico simulations suggest that Th-cell development is regulated by

both selective and instructive mechanisms

ANDREAS JANSSON , 1,2 MAGNUS FAGERL IND, 1,2 D IANA KARLSSON , 2,3

PATR IC N ILSSON 2 and MARGARET COOLEY 1

1School of Biotechnology and Biomolecular Sciences, The University of New South Wales, Sydney, New South Wales,

Australia; 2Systems Biology, School of Life Sciences, University of Skovde, Skovde and 3Swedish Institute for

Infectious Disease Control, Microbiology and Tumor Biology Center, Karolinska Institutet, Stockholm, Sweden

Summary Th-cell differentiation is highly influenced by the local cytokine environment. Although cytokines such as

IL-12 and IL-4 are known to polarize the Th-cell response towards Th1 or Th2, respectively, it is not known whether

these cytokines instruct the developmental fate of uncommitted Th cells or select cells that have already been

committed through a stochastic process. We present an individual based model that accommodates both stochastic

and deterministic processes to simulate the dynamic behaviour of selective versus instructive Th-cell development. The

predictions made by each model show distinct behaviours, which are compared with experimental observations. The

simulations show that the instructive model generates an exclusive Th1 or Th2 response in the absence of an external

cytokine source, whereas the selective model favours coexistence of the phenotypes. A hybrid model, including both

instructive and selective development, shows behaviour similar to either the selective or the instructive model depend-

ent on the strength of activation. The hybrid model shows the closest qualitative agreement with a number of well-

established experimental observations. The predictions by each model suggest that neither pure selective nor instructive

Th development is likely to be functional as exclusive mechanisms in Th1/Th2 development.

Key words: cellular automata (CA), individual based modelling (IBM), Th1 cell, Th2 cell.

Introduction

The use of mathematical modelling has been increasingly

applied to help understand the complex dynamics of T-cell acti-

vation and development. Several models of T-cell recognition

and activation have been established with great success.1,2

Individual based modelling, which has become feasible with

modern computer power, has made significant advances in

simulating the immune system. For example, Segovia-Juarez

et al.3 simulated granuloma formation by treating macro-

phages and T cells as discrete agents, whereas Chao et al.4

used a stage-structure approach to model CTL response to

antigens. We have previously established a theoretical frame-

work for the molecular basis of costimulation based on a sys-

tem of ordinary differential equations.5 The model was based

on rigorous biophysical and experimental data, allowing for

quantitative analysis of the molecular interactions.

However, modelling Th1/Th2 differentiation has been diffi-

cult for two reasons. First, the basic biology is not completely

understood, and the numerous components that are involved in

the process make it difficult to propose a detailed schematic

model. Second, the lack of well-defined kinetic data, such as

the influence of different cytokines on Th-cell differentiation,

makes it difficult to predict the response even if an appropriate

model were established.6 The theoretical field of Th1/Th2 dif-

ferentiation is still struggling to model the basic dynamics

to help understand the role of the key players involved in the

differentiation process. The majority of the previous models

assume a well-mixed population of cells, using a mean-field

approach with a system of deterministic ordinary differential

equations.7–12 For example, Fishman and Perelson8 studied the

role of cross-regulatory cytokines on Th-cell differentiation,

whereas Yates et al.9 investigated the effect of Fas-mediated

activation-induced cell death on this process. The consistent

finding of these studies is that the relative strength of Th-

cell activation and the nature of the cytokine environment are

critical determinants of Th-cell polarization. By using cellular

automata, which are discrete in both time and space, Brass

et al.13 and Tome and Drugowich de Felicio14 could study

behaviour at a single cell level and showed that the local dens-

ities of Th1/Th2 cells profoundly affect Th-cell development.

The development of Th1 and Th2 effector cells starts with the

activation of uncommitted naive Th cells. After the activated Th

cell enters the cell cycle, it may differentiate into either a Th1 or

a Th2 cell,15 dependent on a number of influences in its local

environment. One crucial influencing factor is the cytokine

environment in which the Th cells differentiate. IL-12 and

IFN-g promote Th1 development, whereas IL-4 promotes Th2

development.16 Because Th1 cells produce IFN-g, which pro-

motes the production of IL-12 by macrophages, and Th2 cells

produce IL-4, these cytokines act in positive feedback loops by

enhancing their characteristic responses. These cytokines have

Correspondence: Andreas Jansson, Systems Biology, School of

Life Sciences, University of Skovde, Box 408, 54128 Skovde, Sweden.

Email: [email protected]

Received 4 October 2005; accepted 30 November 2005.

Immunology and Cell Biology (2006) 84, 218–226 doi:10.1111/j.1440-1711.2006.01425.x

� 2006 The Authors

Journal compilation � 2006 Australasian Society for Immunology Inc.

recently been shown to act locally, by being released between

cells that are interacting.17 However, it is not clear whether the

cytokines act during the differentiation process or act as growth

factors by selectively expanding already differentiated Th1 or

Th2 cells. Evidence for both stochastic and instructive Th1/Th2

differentiation mechanisms has been published18–21 and has

provided strong arguments for both theories.22–24 Coffman and

Reiner proposed two possible mechanisms for Th-cell develop-

ment, the instructive and the selective models, each in principle

compatible with the observed influences cytokines have on Th1

and Th2 development (Fig. 1).25 The instructive model sug-

gests that uncommitted Th cells adopt one of the two develop-

mental states determined by the presence or absence of Th1 and

Th2 cytokines. The selective model implies that Th1 and Th2

cells adopt their Th fate based on a stochastic process with no

bias towards either extreme and that the cytokines act as growth

factors to selectively expand Th1 or Th2 populations. Coffman

and Reiner also proposed a hybrid mechanism, including both

instructive and selective development.25 These schematic mod-

els are an appealing target to simulate as they attempt to explain

the most fundamental process of Th-cell development and their

simple structures can easily be accommodated within a theo-

retical framework. Modelling provides a tool to evaluate and

simulate the behaviour of an immune response and to predict

the outcome of changes to important parameters.

In this study we present a model, by using a minimum set of

parameters that can be related to experimentally derived data, to

predict the outcome of selective and instructive mechanisms in

Th-cell development. This is the first time that an attempt has

been made to directly characterize the behavioural differences

between the selective and instructive models for Th-cell devel-

opment. In addition, it is the first study that compares stochastic

and deterministic processes of Th1/Th2 differentiation.We have

therefore used individual based modelling as it is adaptable to

include both deterministic and/or stochastic events, accom-

modating both the responses of individual cells with unique

characteristics and their interactions in space and time. The

simulations of the selective and instructivemodels show distinct

behaviours, which are discussed in the context of experimental

observations.

The models

In this section we present a theoretical framework that was

developed to investigate the simple schematic models proposed

by Coffman and Reiner (Fig. 1).25 Thus, we leave out the

details of the early events that trigger Th-cell activation, which

are beyond the scope of the present study, and focus only on

the dynamics of activated Th cells. In our model, activated Th

cells can take the form of either uncommitted precursor Th

cells (pTh), primary differentiated Th1/Th2 cells (Th1¢, Th2¢)or memory Th1/Th2 cells (Th1

m, Th2m). We extend the already

existing cellular automata models established by Brass et al.13

and Tome and Drugowich de Felicio14 by including cell move-

ment and proliferation, and modify their structures to mimic

the schematic models proposed by Coffman and Reiner.25 In

addition, we include memory Th1/Th2 cells and treat Th cells

as discrete individuals by using an individual based modelling

approach. We consider a constant recruitment rate of pTh

cells, simulating a chronic infection with a continuous antigen

exposure, and assume that the number of pTh cells reflects the

concentration of a particular antigen, an assumption similar to

that used previously.9,11 We thereby model the antigen dose

implicitly by varying the frequency of pTh cells that can be

committed to Th1 or Th2. The timescales of the cytokine

dynamics are relatively short compared with the cell pop-

ulation dynamics.11 We therefore make a steady-state assump-

tion and relate the local Th1 and Th2 cytokine environment

directly to the local density of Th1 and Th2 cells, respectively.

The system

The environment simulated is a Th-cell-enriched area such as

that in a lymph node. We represent Th cells as discrete individ-

uals in a cellular automata environment, corresponding to a 2-D

square matrix with 1002 sites. To avoid edge effects we use

periodic boundary conditions, where the opposing edges of

the lattice are joined. Each site in the lattice represents

a square with dimensions 11 mm ´ 11 mm, large enough to

contain an activated Th cell, and each site can hold at most

one Th cell at any time. Every site in the lattice is defined as

having eight neighbours.

Movement

The movement of each individual Th cell in the model is based

on recent two-photon microscopy studies of a mouse lymph

node in vivo, showing that T cells move in a manner analo-

gous to a random walk, with a mean velocity of approximately

11 mm/min.26,27 We therefore assume random walk of cells in

the lattice where each Th cell can move from one site to a ran-

domly selected neighbouring site every minute. If the selected

site is occupied by another Th cell, the Th cell remains in its

position. With this approach we account for crowding effects

where the movement is reduced as a result of increased cell

density.

Recruitment and memory Th cell

Uncommitted pTh cells are recruited to empty sites in the lattice

with probability h, where they are assigned a lifespan ran-

domly selected between 0 and b hours. The age of the cell is

updated every hour and the cell is removed from the lattices if

its age reaches its lifespan, representing death or migration.

Selective Instructive

pTh Random

Th1

Th2

Th1

Th2

pTh

Figure 1 Schematic models of Th-cell development, similar to

the ones proposed by Coffman and Reiner.25 In the selective

model, the fate of the uncommitted precursor Th cell (pTh) is

determined by a random process where cytokines produced by

Th1 and Th2 cells regulate proliferation of committed cells. In

the instructive model, differentiation of Th1 and Th2 cells is

determined by the presence of Th1 and Th2 cytokines, and com-

mitted Th cells proliferate independently of Th cytokines.

Modelling Th-cell differentiation 219

� 2006 The Authors. Journal compilation � 2006 Australasian Society for Immunology Inc.

To model the contribution of cytokines from bystander acti-

vated memory Th1/Th2 cells, we place a certain fraction of

Th1m and Th2

m cells initially in the lattice and make a steady-

state approximation so that the inflow and outflow of memory

cells is assumed to be constant. Thus, a given number of

memory cells stay in the lattice throughout the simulation.

These cells are allowed to move and influence the fate of pTh

cells and induce proliferation of Th1¢ and Th2¢ cells.

Differentiation and proliferation

Uncommitted pTh cells develop into either Th1¢ or Th2¢ cellswith the probability d1 or d2, respectively. The proliferation

rate of Th1¢ or Th2¢ cells (r) is based on the observation that

they have a doubling time of approximately 12 h.28–30 The

daughter cells inherit the same cell state and age as their par-

ent, and they are assigned a new random lifespan between its

current age and b hours to allow for variability in lifespans

within the clone. However, a cell can only proliferate if there

is at least one unoccupied site in its neighbourhood, where

one of the daughter cells is randomly placed in one of the

empty neighbouring sites.

Rules for instructive and selective development

In the instructive model, a pTh cell develops into a Th1¢ or Th2¢cell depending on the state of its neighbours, based on the

observation that cytokines are released between interacting

cells.17,31 If the majority of its neighbours are of type Th1, we

assume that the pTh cell is exposed to mostly Th1 cytokines

that instruct the cell to become a Th1¢ cell and vice versa for

Th2 differentiation. When the number of Th1 and Th2 in the

neighbourhood is the same, pTh cells differentiate to either

Th1 or Th2 by a stochastic process. However, if there are no

Th1/Th2 neighbours, the pTh cell remains uncommitted. In

the selective model, differentiation of a pTh occurs indepen-

dently of its neighbours in a stochastic process. The clonal

proliferation is, however, dependent on the state of its neigh-

bours. If the majority of the cell’s neighbours and the cell

itself are of the same phenotype, we assume that the Th cell is

exposed to mostly those cytokines that induce that phenotype

to proliferate. This means, for example, that Th1 cells pro-

mote Th1¢ cell proliferation and consequently inhibit the

proliferation of Th2¢ cells.

Implementation

The individual based model was implemented in an object-

oriented programming language (C11), where the lattice

represents a square matrix. A site can either be empty or include

an object. Each object contains information describing its cell

state (pTh, Th1¢ or Th2¢), position, age and lifespan. The status

of each object in the lattice is updated in a random order. Each

iteration or time-step corresponds to 1 min in real time be-

cause of the cell movement, which is the fastest process in this

system. On a longer timescale (every hour) the age of each

object is updated by 1 h and new pTh cells are introduced into

empty sites in the lattice at probability h. If the age of the

object equals the designated lifespan, the object is removed,

leaving an empty site. If the age of a Th1¢ or a Th2¢ cell corre-sponds to the designated time for proliferation (every r hour)

and it fulfils the proliferation rules, the object is copied to the

selected position where the daughter cells are given a new ran-

dom lifespan between their current age and b hours. If the

state of the object is of type pTh, it may change its state to

Th1¢ or Th2¢ according to the differentiation rules at probabil-

ity di. The number of memory Th1 and Th2 cells is treated as

constant during the simulation and is thus only updated during

the cell movement process. The coding for the simulations

and instructions on how to run them can be made available by

request to the corresponding author.

Simulations and interpretations

The instructive model

We first study the behavioural properties of the instructive

model with the default values given in Table 1. Thus, we

begin by ignoring the contribution of memory Th1/Th2 cells

ðThim = 0Þ and consider the simplest case where parameter

values for Th1¢ and Th2¢ are taken to be equal, which implies

that both Th1¢ and Th2¢ cells have the same capacity to

develop. In this model, there must be an initial contribution of

committed Th1/Th2 cells to instruct the fate of pTh cells in

order for the system to induce a primary Th1 or Th2 response.

We therefore introduce a small equal fraction of Th1¢ and Th2¢cells, randomly distributed, that initially covers 0.2% of the

sites in the lattice. Simulations show that both primary Th1

and Th2 cells coexist at the early response, which shifts

towards either an exclusive Th1 or Th2 response during a

constant exposure to antigen (constant influx of pTh cells).

The given parameter values were tested with 100 simulation

runs in which 53 simulations generated an exclusive Th1¢response, whereas 47 evolved into a pure Th2¢ response. Elim-

ination of one of the phenotypes was observed between 10

and 25 days. Figure 2A shows an example from one typical

simulation, where the response evolves into an exclusive Th2¢

Table 1 Parameter definitions and values

Name Definition Default value Range explored Units References

di Probability of an individual pTh cellto differentiate to Th1 or Th2

0.05 (0.001–0.1) 1/h 32

r Doubling time of Th1 and Th2 cells 12 (6–24) h 28–30b Th-cell lifespan 72 (48–144) h 3, 33h Probability of pTh-cell recruitment

into empty sites in the lattice0.01 (0.001–0.1) 1/h Estimated

Thmi Fraction of sites in the lattice coveredby memory Th1/Th2 cells, initially

0 (0–50) % Estimated

A Jansson et al.220


response. Of the 100 simulations, the equilibrium levels of the

dominating phenotype showed only marginal variations

(insets show the variation among the first 10 simulation runs).

Exclusive Th1 or Th2 response outcomes were observed with

all parameter values in the test range (Table 1) in the absence

of memory Th1 and Th2 cells ðThim = 0Þ:The total number of

Th1¢ or Th2¢ cells in the system increases with a faster dou-

bling time (r), recruitment rate (h), differentiation rate (di) or

with a longer lifespan (b), which is biologically reasonable. In

the case of biased differentiation towards Th1 (d1 = 0.055,

d2 = 0.050), assuming that a given antigen favours a Th1 over

a Th2 response, 95 simulations out of 100 resulted in a pure

Th1¢ response, whereas five simulations evolved into an

exclusive Th2¢ response.We next included a significant number of memory Th1 and

Th2 cells ðThim = 5Þ; by inserting an equal fraction of Th1m

and Th2m cells into random sites in the lattice initially. The

simulations show that under these conditions the response

evolves into a dominant, but not exclusive, Th1¢ or Th2¢response (49 simulations generated a dominant Th1 pop-

ulation, whereas 51 simulations evolved into a dominant Th2

population). This implies that, in the presence of memory Th1

and Th2 cells, the responses are no longer exclusive Th1¢ orTh2¢ cells. Figure 2B shows an example from one simulation,

where the response evolves into a dominant Th1¢ response. Inthe case of a greater number of memory Th1 than Th2 cells

ðTh1m = 5:5, Th2m = 5Þ, the Th-cell differentiation is biased

towards Th1¢ differentiation: 83 out of 100 simulations gener-

ated a dominant Th1¢ response and 17 a dominant Th2¢response.

Biological interpretations

The main property of the instructive model, irrespective of the

parameter settings, is that it evolves into exclusive primary Th1

or Th2 responses in the absence of activated memory cells

(Fig. 2A). This is a consequence of the deterministic fate of

the uncommitted Th cell. Because of the random nature of cell

movement in the model, cells will form temporary clusters,

which will continually dissolve and reform, thus keeping the

ratio between Th1 and Th2 cells in the environment fluctuat-

ing. The fate of newly arrived uncommitted Th cells will be

biased towards the extreme that presently is dominating, thus,

enhancing the most abundant extreme. If the response is sus-

tained, then either Th1¢ or Th2¢ cells will persist by out com-

peting the other. Even during conditions with a relatively high

contribution of memory cells (20% of the total cell numbers),

there is a clear dominant Th1¢ or Th2¢ response (Fig. 2B). Themodel predictions are in agreement with experimental systems

where addition of external Th1 or Th2 cytokines (simulated

by including activated memory cells into the system) favours

either a Th1 or Th2 response, respectively, and where a partic-

ular antigen may favour either a Th1 or Th2 response (d1 6¼d2).34–36 However, the model cannot display coexistence of

Th1 and Th2 cells unless external cytokine sources, such as

the contribution of activated memory cells in this model,

inhibit the elimination of the suppressed Th1 or Th2 response.

Exclusive Th1 and Th2 responses are rarely observed in

nature.32,37 In addition, the model does not change its behav-

iour if the antigen dose is varied, which is not consistent with

the observations in several experimental systems.34–36,38–40

Taken together, these findings predict that Th-cell develop-

ment is unlikely to be deterministically regulated by the cyto-

kine environment.

Simulations of the selective model

In this sectionwe study the dynamics of the selectivemodel.As in

the previous section, we begin by analysing the model in the

absence of memory Th cells ðThim = 0Þ and where the two

phenotypes have the same capacity to develop. The simulations

start with an initial configuration of 2% of sites containing pTh

cells and the use of the default values in Table 1. Simulations

show that the primary response evolves into a coexisting state,

which is independent of the initial configuration, where the

two phenotypes are expressed at equivalent levels (Fig. 3A).

Including equal numbers of memory Th1 and Th2 cells

ðThim > 0Þ during these conditions only alters the total num-

ber of cells at the mixed state. Imposing a bias towards Th1

differentiation (d1 = 0.06, d2 = 0.05) induces a dominant Th1¢response in 100/100 simulation runs (Fig. 3B illustrates a typi-

cal simulation under such conditions). The same behaviour is

observed if the number of Th1 memory cells is greater than

that of Th2 ðTh1m = 10; Th2m = 5Þ: In the case where the

doubling time (r) is varied within a biologically reasonable

A B

Th2’

Th1’

0 20 40 60 80 1000

10

20

30

40

50

Num

ber o

f cel

ls

Days0 20 40 60 80 100

Days

x102

Th1’

Th2’

Figure 2 The population dynamics of the instructive model, showing the number of primary Th1 and Th2 cells over time. (A) An exam-

ple from one simulation run with the default parameter values in Table 1. (B) A simulation run with the default parameter values in

Table 1, but in the presence of memory Th1 and Th2 cells (Thim= 5). Insets, the variation among the first 10 simulation runs.



range (6–24 h), we find interesting dynamic behaviours. Sim-

ulations with a cell doubling time greater than 12 h always

favour a mixed Th1¢/Th2¢ response. In contrast, a faster dou-

bling time (r < 11 h) polarizes the phenotypes in which either

a dominant Th1 or Th2 response is observed (53 out of 100

simulations evolved into a dominant Th1 response and 47 into

a dominant Th2 response). Figure 3C illustrates an example

from one simulation with a doubling time of 9 h, where the

response evolves into a dominant Th1 state after approxi-

mately 15 days. The same phenomenon is observed by

increasing the cell lifespan above 90 h, which has the conse-

quence that each Th1¢/Th2¢ cell generates more daughter cells

during its time in the system. The polarized state attained by

a faster doubling time (r = 9) could be reversed into a mixed

state by increasing the recruitment rate (h > 0.1) or by the

presence of a significant number of memory cells ðThim > 10Þ:

Biological interpretations

The selective model studied in this section displays a behaviour

that is consistent with a number of experiments. First, it predicts

that the Th1 and Th2 phenotypes can coexist, which has been

observed in most experimental systems.32,37 The reason for this

property is that the differentiation process is stochastic, which

makes sure that both phenotypes are present as long as there is

a recruitment of activated uncommitted Th cells. Second, it

predicts that a dominant primary Th1 or Th2 state can be

achieved by the influence of a relevant cytokine source (simu-

lated by imposing bystander memory cells) or by a particular

antigen (d1 6¼ d2) that may favour either Th1 or Th2 differenti-

ation (Fig. 3B). Such behaviours are consistent with experi-

mental observations.34–36,39 Third, the behaviour of the model

is sensitive to antigen dose and to the extent of Th-cell pro-

liferation, which has been observed in several experimental

systems (Fig. 3A,C).34,38–41 Th1 or Th2 dominance was ob-

served at high proliferation rate during a low dose of antigen

(low recruitment rate), whereas a mixed state was obtained at

a low proliferation rate. The reason for this behaviour is sim-

ply because of the nature of the selective model. Recruitment

of pTh cells will always favour a mixed state because of the

purely stochastic fate of pTh cells in this model, whereas

proliferation promotes polarization because the committed

Th cells inhibit the growth of the opposing phenotype. Thus,

polarization is obtained when the selection process (pro-

liferation) is dominant over the stochastic differentiation pro-

cess (recruitment). A fast pTh-cell recruitment therefore

inhibits Th1 or Th2 dominance. This is not consistent with the

experimental findings that a high level of activation promotes

polarization34,39 and that cytokines can, to some extent, alter

the probability of the fate of pTh cells.36

Alternative models

Because neither the instructive nor the selective model can fully

accommodate the experimental observations, we propose two

alternative models. In the first instance we refine the instructive

model from being deterministic to account for more stochastic

processes. Herein, the influence of cytokines alters the proba-

bility of pTh cells becoming Th1¢ or Th2¢, instead of absolutelydetermining the pTh-cell fate (refined instructive model). The

probability ratio for Th1/Th2 differentiation (p) of a particular

pTh cell is therefore determined by the relative numbers of

Th1 and Th2 neighbours that surround it:

pðTh1 j pThÞ =P

Th1neigh�P

Th2neigh

8´1

21

1

2ð1Þ

pðTh2 j pThÞ = 1� pðTh1 j pThÞ: ð2Þ

Thus, the probability for a pTh to become a Th1 (Eqn 1) or

a Th2 cell (Eqn 2) is dependent on the state of its eight neigh-

bouring sites. If there are no Th1 or Th2 neighbours or if there

are equal numbers of Th1 and Th2 neighbours, p(Th1jpTh) andp(Th2jpTh) equals 0.5. In the second instance we extend this

model to include the fact that the cytokines also influence the

proliferation of Th1¢ or Th2¢ cells, as modelled in the selective

model (hybrid model). Thus, the hybrid model includes both

instructive and selective mechanisms.

Simulations of the alternative models

As before, we begin by giving the two phenotypes equal par-

ameter values (default values in Table 1) in the absence of

Num

ber o

f cel

ls

Days Days

A B Cx102

Th2’ Th2’

Th1’Th1’

0 20 40 60 80 100 0 20 40 60 80 100

Days0 20 40 60 80 100

0

10

20

30

40

Figure 3 The population dynamics of the selective model, illustrating the number of primary Th1 and Th2 cells over time. (A) An

example from one simulation run with the default parameter values in Table 1. (B) Imposing a bias towards Th1 differentiation

(d1 = 0.06, d2 = 0.05). (C) An example from one simulation run with the default parameter values in Table 1, but with a faster doubling

time (r = 9). Insets, the variation among the first 10 simulation runs.

A Jansson et al.222


memory Th cells with an initial configuration of 2% of sites

containing pTh cells. Simulations with the refined instructive

model show that only a mixed state exists when the pheno-

types have the same capacity to develop, despite varying

parameter values or initial conditions (data not shown). Thus,

the model cannot result in polarization to the extremes unless

it is set to directly favour Th1 or Th2 development. Simu-

lations with the hybrid model show that two typical states

exist depending on the parameter values. In the first, the pheno-

types are expressed at equivalent levels that are independent

of the initial configuration (Fig. 4A). This state was obtained

using a low level of activation, such as at low proliferation

rate (r > 18), low recruitment rate (h < 0.007) or a short life-

span (b < 60), compared with the default values in Table 1.

Imposing a bias towards Th1 differentiation (d1 = 0.06,

d2 = 0.05) during a low recruitment rate (h = 0.006) generates

a dominant Th1 response in 100/100 simulations (Fig. 4B). In

the second state, obtained by a high level of activation (e.g.

h > 0.01, r < 12 or b > 72), domination of either Th1¢ or Th2¢cells was observed in which 51 simulations evolved into

a dominant Th1 response and 49 into a dominant Th2

response. Figure 4C shows an example from one simulation

during high recruitment rate (h = 0.05). At the early stage,

both Th1¢ and Th2¢ cells are expressed at equivalent levels, but

the response evolves into a dominant primary Th2 response

after approximately 10 days. In the case of differentiation

biased towards Th1 (d1 = 0.06, d2 = 0.05), during a high

recruitment rate (h = 0.05), 100/100 simulations resulted in

a dominant primary Th1 response. The same type of behav-

iour is observed if the number of Th1 memory cells is set to

be greater than that of Th2 ðTh1m = 12; Th2m = 10Þ:

Biological interpretation

The refined instructive model displays a behaviour in which

both extremes are expressed at equivalent levels, unless param-

eters are set to directly favour one of the phenotypes, indicating

that the selectivemechanism is required for polarization to occur

during stochastic differentiation. The hybrid model, that in-

cludes a selective mechanism, displays essentially the same

behaviour as the selective model in that it allows the two pheno-

types to coexist either as a mixed state (Fig. 4A) or as a domi-

nating Th1/Th2 state (Fig. 4C). Thus, the predictions of the

hybrid model are in agreement with experimental observations

in which altering the antigen dose or the extent of Th-cell pro-

liferation changes the behaviour of Th-cell development and

that external cytokines or a particular antigen can indeed

influence Th1/Th2 differentiation.34–36,38–41 However, although

the dominant Th1/Th2 state in the purely selective model was

inhibited by recruitment of uncommitted cells, the hybrid

model generated Th1 or Th2 dominance for all parameter val-

ues associated with a high level of T-cell activation. This is

a result of the fact that a high level of activation will promote

a high density of committed Th cells, in which an uncommit-

ted Th cell will always be in close proximity to either Th1 or

Th2 effector cells. A high concentration of effector cells there-

fore imposes a more instructive mechanism on the fate of

uncommitted Th cells and, thus, promotes polarization. In

contrast, low cell concentrations isolate the uncommitted Th

cells from being exposed to high levels of cytokines from

nearby Th1/Th2 cells. The developmental fate under these

conditions is thus determined by a more stochastic process,

promoting a mixed response.

Discussion

The debate about the relative merits of the selective and the

instructive models of Th-cell development has been extensive,

with strong evidence for both models having been reported.18–25

We have taken an initial step towards understanding the

dynamics of the selective and instructive models by con-

structing a theoretical framework, based on the simple sche-

matic models proposed by Coffman and Reiner.25 Thus, the

full complexity of Th-cell differentiation could be set aside

in our study, which simplified the comparison between the

models.

The simulations carried out offer new insights into the fun-

damental properties of the instructive and selective models and

predict that neither is likely to be functional as exclusive mech-

anisms of Th-cell development. Imposing a deterministic role of

the cytokines (instructive model) tends to generate exclusive

0

15

30

45

60

Num

ber o

f cel

ls

Days Days Days

A B C

0 20 40 60 80 100 0 20 40 60 80 100 0 20 40 60 80 1000

5

10

15

20

25x102 x102 x102

0

10

20

30

40

Th1’Th2’

Th1’

Th2’

Figure 4 The population dynamics of the hybrid model, showing the number of primary Th1 and Th2 cells over time. (A) An example

from one simulation run with the default parameter values in Table 1, but with a low recruitment rate (h = 0.006). (B) Imposing a bias

towards Th1 differentiation (d1 = 0.06, d2 = 0.05) during a low recruitment rate (h = 0.006). (C) A simulation run with the default param-

eters in Table 1, but with a high recruitment rate (h = 0.05). Insets, the variation among the first 10 simulation runs.



Th1 or Th2 responses, which is insufficient to account for the

observed coexistence of Th1 and Th2 in most immune

responses (Fig. 2A).34,39,42 Merely allowing the cytokines to

alter the probability of Th1/Th2 differentiation (refined

instructive model), instead of being deterministic, does not

improve the biological ‘fit’ of the instructive model because it

was unable to display a polarized coexisting state unless

parameters were set to directly favour Th1 or Th2 develop-

ment. Hence, pure instructive mechanisms seem to be insuffi-

cient to explain the polarized coexistent state observed in

most experimental systems.32,37 In contrast, the selective

model displayed a behaviour that was consistent with a num-

ber of experimental observations. However, the selective

model is inconsistent with experiments that have excluded

selection as the only mechanism21 and data from limiting dilu-

tion assays that indicate that the fate of uncommitted Th cells

is not completely stochastic.36 Grakoui et al. showed that Th

fate was a stochastic process in the absence of cytokines, but

the presence of exogenous IL-4 or IL-12 influences the devel-

opment towards a Th2 or a Th1 phenotype, respectively, indi-

cating that cytokines alter the probability of uncommitted

cells becoming Th1 or Th2 cells.36 The same phenomenon has

been observed in B-cell differentiation, where IL-4 alters the

probability of the differentiation event in a dose-dependent

manner.43 However, these experimental observations are in

agreement with the simulations of the hybrid model. At a low

density of Th1/Th2 cells the pTh cells are isolated from effec-

tor cells, which allows for a stochastic differentiation, whereas

a higher density of Th1/Th2 cells will expose the pTh cells to

high levels of cytokines and thus promote instructive differen-

tiation. The hybrid model is further supported by several stud-

ies that have observed both selective and instructive roles of

cytokines.20–25

The behaviour of the hybrid model was also shown to be

sensitive to parameter values associated to the strength of acti-

vation. The model displayed a coexistent mixed state at low

activation level, whereas polarization was observed during

a higher activation level (Fig. 4). These predictions are in

agreement with a large body of evidence showing that differ-

ent antigen doses and manipulation of Th-cell proliferation

have a dramatic effect on the relative outcomes of the Th1/

Th2 response.34–36,38–41 They are also consistent with predic-

tions made by earlier theoretical works by Brass et al.13 and

Tome and Drugowich de Felicio.14 Using simple cellular

automata, without accommodating for cell movement and Th-

cell proliferation, these authors both concluded that a low

level of infection/antigen simulation generated coexistence of

Th1 and Th2 cells at equivalent levels, whereas increasing the

infection level polarized the immune response into either a

dominating Th1 or Th2 response. These predictions were sup-

ported by experimental studies in chronic Trichuris muris

infected mice in which a high level of infection induces a

dominating Th1 or Th2 response, whereas mice were found to

be unable to mount a full protective response during a low level

of infection.44 Such behaviour is further supported by in vivo

studies using varying doses of peptides with different affini-

ties to MHC class II and to the T-cell antigen receptor. A high

affinity peptide was shown to give a strong Th1 response at

high dose, whereas a mixed Th1 and Th2 response was

observed at low doses and with low affinity peptides.39 It is

interesting that in these experiments, the Th2 level was not

decreased at high antigen dose when the Th1 response was

dominating. This is in excellent agreement with the hybrid

model where a high antigen dose (simulated by a high recruit-

ment rate of uncommitted Th cells) generates a dominating

Th1 or Th2 response, but where the level of the suppressed

phenotype stays relatively constant (Fig. 4C). Thus, of our four

models, the behaviour of the hybrid model showed the best

qualitative agreement with many features of Th-cell polariza-

tion seen in both in vivo and in vitro experimental systems. The

hybrid model predicts that during an infection, both Th1 and

Th2 cells will develop initially by stochastic processes because

of the low concentration of effector cells. Development of

numerous Th1 and Th2 cells will influence the stochastic fate

of uncommitted Th cells because of high local levels of

cytokines. Hence, the final polarization is determined once

the two branches have developed and not at the initial

response.

The models presented in this report include, however, only

the fundamental characteristics of Th-cell development thus

providing an initial step towards more comprehensive model-

ling, which will be dependent on good experimental data

defining values for a range of additional parameters. First,

the models assume a continuous recruitment of activated Th

cells, whereas in reality recruitment rate is likely to vary over

time during a chronic infection because of elimination or rep-

lication of the pathogen. Second, the models rely on the local

Th-cell cytokine dynamic within a small area and not on dis-

tant cytokine secretion from bystander immune cells. Third,

the movement of Th1 and Th2 cells might be influenced by

chemokines, rather a than follow random walk as assumed in

the present models. Such factors can be included in our model

once quantitative data become available. In addition, most data

support the concept that Th1 cells dominate in response to high

dose/affinity of antigen, whereas Th2 dominates with low

dose/affinity of antigen,34–36,38,39 which in turn indicates that

the probabilities of Th1 or Th2 development are not equal in

nature. There is also some evidence, although not quantita-

tive data, suggesting that Th2 development is cell cycle

dependent,45,46 in contrast to Th1 development, and that Th2

cells are much less susceptible to dying than Th1 cells.47,48

This may provide an opportunity in future to further refine

the hybrid model to predict under what circumstances Th1 or

Th2 response will be dominant and to elucidate the underly-

ing processes that favour either Th1 or Th2 development.

Finally, our observations with the hybrid model raise an

important question: How much does the cytokine environ-

ment alter the stochastic fate of uncommitted Th cells? It

seems likely that the cytokines alter the probability of

uncommitted Th cells becoming Th1 or Th2 in a dose-

dependent manner, as observed in B-cell differentiation.43

Further experiments that can answer this question may pro-

vide essential data, valuable for further modelling and

advances in our understanding.

Acknowledgements

We are grateful to Stefan Karlsson, Mikael Harlen and Erik

Gustafsson (University of Skovde) for helpful comments on

the manuscript.

A Jansson et al.224


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Documents

In silico simulations suggest that Th-cell development is regulated by both selective and instructive mechanisms