Blanchard et al. BMC Systems Biology 2014, 8:23http://www.biomedcentral.com/1752-0509/8/23
RESEARCH ARTICLE Open Access
Extinction, coexistence, and localizedpatterns of a bacterial population withcontact-dependent inhibitionAndrew E Blanchard1, Venhar Celik2 and Ting Lu1,2,3*
Background: Contact-dependent inhibition (CDI) has been recently revealed as an intriguing but ubiquitousmechanism for bacterial competition in which a species injects toxins into its competitors through direct physicalcontact for growth suppression. Although the molecular and genetic aspects of CDI systems are being increasinglyexplored, a quantitative and systematic picture of how CDI systems benefit population competition and hence altercorresponding competition outcomes is not well elucidated.
Results: By constructing a mathematical model for a population consisting of CDI+ and CDI- species, we havesystematically investigated the dynamics and possible outcomes of population competition. In the well-mixed case,we found that the two species are mutually exclusive: Competition always results in extinction for one of the twospecies, with the winner determined by the tradeoff between the competitive benefit of the CDI+ species and itsgrowth disadvantage from increased metabolic burden. Initial conditions in certain circumstances can also alter theoutcome of competition. In the spatial case, in addition to exclusive extinction, coexistence and localized patternsmay emerge from population competition. For spatial coexistence, population diffusion is also important ininfluencing the outcome. Using a set of illustrative examples, we further showed that our results hold true when thecompetition of the population is extended from one to two dimensional space.
Conclusions: We have revealed that the competition of a population with CDI can produce diverse patterns,including extinction, coexistence, and localized aggregation. The emergence, relative abundance, and characteristicfeatures of these patterns are collectively determined by the competitive benefit of CDI and its growth disadvantagefor a given rate of population diffusion. Thus, this study provides a systematic and statistical view of CDI-basedbacterial population competition, expanding the spectrum of our knowledge about CDI systems and possiblyfacilitating new experimental tests for a deeper understanding of bacterial interactions.
Keywords: Contact dependent inhibition, Bacterial population, Competition, Extinction and coexistence, Spatialaggregation
BackgroundBacteria are highly social and present dominantly inthe form of complex communities where they interactthrough a variety of fashions [1-3]. Among all types ofbacterial interactions discovered, competition has been
*Correspondence: firstname.lastname@example.orgDepartment of Physics, University of Illinois at Urbana-Champaign, 1110 WestGreen Street, 61801 Urbana, USA2Department of Bioengineering, University of Illinois at Urbana-Champaign,1304 West Springfield Avenue, Urbana IL 61801, USAFull list of author information is available at the end of the article
identified as the most prevalent by recent studies [4-6].The ubiquity of competition has been mainly attributed tothe limited space and resources of natural environments.To maximize their survival and reproduction, bacteriahave indeed developed numerous competition strate-gies, including interference competition where a speciesdirectly harms another via active production of toxin andother effectors [4,6-8].Interference competition was initially shown to be
mediated by diffusible soluble factors, such as antibi-otics and bacteriocins. These effector molecules serve to
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potently decrease survival and reproduction of neighbor-ing bacteria at a long range spatial scale [2,9-11]. Forinstance, Lactococcus lactis produces and secretes nisin,a small antimicrobial peptide, into the extracellular mil-ium (e.g., milk) to efficiently inhibit other bacterial speciesfor lactose competition . A set of recent studies, how-ever, have illustrated that interference competition canalso occur through direct physical contact between cells,revealing a new class of competition with an interactionscale restricted to nearest neighbors [13-17].Furthermore, studies have uncovered a surprisingly high
degree of diversity among these contactdependent inhi-bitions (CDIs). They occur across a wide range of organ-isms including both Gram- negative and positive bacteria[17-21], use different toxins similar to nuclease, tRNAseand DNase, and further exploit various delivery machiner-ies spanning Type III, IV, V, and VI secretion systems[13-15,22,23]. Moreover, it has been shown that certainstrains even have multiple CDI modules and multipletoxins for competition [17,24].Despite their structural and compositional diversity, all
of the CDI systems possess a common mode of action inwhich growth inhibition toxins are deployed into competi-tor cells via direct cell to cell physical contact. A repre-sentative example is the CdiBAI system discovered in theenterobacterium E. coli EC93 : The system consistsof three functional components: CdiA, the toxin effector,CdiB, the -barrel protein localized to the outer mem-brane for effector export, and CdiI, the immunity protein.Upon contact with a neighboring cell, a CDI equipped cellemploys CdiB to inject toxin CdiA into the target cell toinhibit its growth while expressing the immunity proteinCdiI to prevent autoinhibition.The intriguing functionality and characteristics of CDI
motivate us to ask the following questions: How doesCDI impact the competition between a CDI equipped(CDI+) and deficient (CDI-) species? Can the two speciescoexist, or does extinction always occur for one of thespecies? Due to the intrinsic association of protein expres-sion and metabolic load, will the growth disadvantage ofCDI+ species counteract its competition advantage fromtoxin production? How does cell motility alter the compe-tition outcome in different environmental settings, suchas liquid or solid agar?Although current experimental efforts [13,23-26] have
started to address some of the above questions, a system-atic and quantitative understanding of CDI-based bacte-rial competition has not been achieved. In particular, itis not clear how the competition outcome is influencedby the inhibition advantage of CDI-based competitionand the growth disadvantage associated with metabolicload. Moreover, most experimental efforts have primar-ily focused on liquid culture settings where populationsare well mixed [14,24,25] but little has been elucidated
when competitions occur in space. There is hence a clearneed for a systematic investigation of CDI-based bacterialcompetition that integrates the tradeoff between com-petitor inhibition and metabolic cost with spatiotemporaldynamics.Here, we present a mathematical model to describe a
bacterial population with CDI+ and CDI- species thatcompete through both contact-dependent inhibition andnutrient utilization. With this model, we studied the com-position of the competing population in the well-mixedcase, showing that the outcome is always extinction forone of the species depending on initial conditions as wellas the tradeoff between inhibition strength and metaboliccost.We then continued to investigate the dynamics of thepopulation in one dimensional space, revealing possiblespatial coexistence of the species through aggregation. Toacquire a statistical understanding of the coexistence pat-terns, we further conducted a systematic survey into thespatial structure of the competing populations by alteringthe interplay between inhibition strength and metabolicgrowth disadvantage. A set of illustrating tests in twodimensional space was also implemented to demonstratethe generality of our results. We finally conclude bysummarizing our findings and discussing possible futuredevelopments.
ResultsAmathematical model of bacterial competition with CDIBacterial competition has been modeled through cou-pled systems of ordinary differential equations, datingback to the work of Lotka and Volterra [27,28]. Laterdevelopments of the original Lotka-Volterra model haveincorporated the effects of nutrient limitation andspecies diffusion [29-36]. Typically, these models incor-porated only on-site interactions (i.e. the interactionrange for competing species is taken to be infinites-imally small). For bacteria competing through CDI,however, it is natural to explicitly include a finiteinteraction range in order to account for the intrin-sic nearest-neighbor effects of toxin injection in thesystem.Previous studies on competition with a finite interac-
tion range have shown that spatial aggregation is possi-ble in the long time limit [37-43]. For instance, a singlespecies with nonlocal interactions has unstable homoge-neous states for certain functional forms of its growth rate,leading to a spatial distribution of the population withclumps of high species concentration separated by regionswith low density [41,44-47]. For two species systems, ithas been shown that systems with specific features, suchas syste