Swarms and Genes: Exploring !-Switch Gene Regulation throughSwarm Intelligence

Christian Jacob, Member, IEEE, Anna Barbasiewicz, and Glorious Tsui

Abstract— We demonstrate a 3-dimensional, agent-basedmodel of the !-switch gene regulatory system, which simulatesthe interactions of proteins, promoters and operators during thephases of lysogenic and lytic growth in the phage ! infectedbacterium Escherichia coli. Following a decentralized approach,all regulatory mechanisms result from local interactions ofthe biomolecular agents within a simulated 3D cytoplasm.We show that our model displays the regulatory ! switchbehavior observed in E. coli, where proteins regulate their ownproduction. Our ! switch simulations provide a versatile testbedfor studying gene regulation in silico, complementing in vitroexperiments.

I. INTRODUCTION

Major advances in systems biology will increasingly beenabled by the utilization of computers as an integral re-search tool, leading to new interdisciplinary fields withinbioinformatics, computational biology, and biological com-puting. Nowadays, in an effort to reduce costs for expensiveexperiments and minimize the time spent in the laboratory,model building, simulation, data gathering and analysis canbe done primarily in silico. Furthermore, innovations inagent-based modeling, computer graphics and specializedvisualization technology, such as the CAVE c! AutomatedVirtual Environment, provide biologists with unprecedentedtools for research in virtual laboratories [1], [2], [3].

However, current mathematical and computer models ofcellular and biomolecular systems have major shortcomingsregarding their usability for biological and medical research.Most models do not explicitly take into account that the mea-surable and observable dynamics of cellular/biomolecularsystems result from the interaction of a (usually large)number of ‘agents’, such as viruses with cells, proteins withproteins, or proteins with promoter and operator regions onthe DNA. With our agent-based models [4], [5], simulationsand visualizations that introduce swarm intelligence algo-rithms [6], [7] into biomolecular and cellular systems, wedevelop highly visual, adaptive and user-friendly innovativeresearch tools, which, we think, will play a more and moredominant role in the biological and life sciences researchcommunity—thus complementing most of the current, moreabstract and computationally more challenging mathematicaland computational modeling approaches [8], [9]. For exam-ple, many differential equation models of biological systems,such as gene regulatory networks, are very sensitive to initialconditions, result in a large number of equations, and usuallyrequire control parameters that have no direct correspondenceto measurable quantities within biological systems [9].

We propose a model of the gene regulatory system utilizedby the bacterial Escherichia coli (E. coli) virus lambda (!), as

a highly sophisticated network of orchestrated interactions,based on relatively simple rules for each of the biomolecularagents involved. Giving these agents the freedom to interactwithin a confined, 3-dimensional space results in emergentbehavior patterns that resemble the regulatory reactions ofthe E. coli genome and proteome in response to a ! phageinfection.

This paper is organized as follows. Section II gives abrief description of the bacterial genomic and proteomiccontrol systems involved in the ! switch. In Section III weprovide a more indepth discussion of the biomolecular agentsthat act as the regulatory units through interactions withpromoter and operator regions on the E. coli genome. Thekey switching mechanism of regulated recruitment amongregulatory proteins is outlined in Section IV. Section Vintroduces our agent-based, 3D model and related work inSection VI. In Section VII a typical simulation run of ourmodel illustrates the actual switching behavior emergingfrom the interactions among the biomolecular agents. Amore detailed analysis of the simulation is provided inSection VIII. The paper concludes with future directions forour ! switch model and the potential of 3D, agent-basedsimulations for computational biology in general.

II. PHAGE ! AND ITS REPLICATION

The bacterium E. coli is one of the most studied modelorganisms in biological and medical research [10], [11], [12].As a procaryotic microorganism it provides an ideal platformto study genomic and proteomic regulatory networks, bothin vitro and in silico. The relative ease of manipulation ofE. coli in wet lab experiments makes it a strong candidatefor building increasingly detailed (hence, more realistic andpredictive) mathematical and computer models, which conse-quently allow us to study gene regulatory systems in a moregeneral context.

Phage !, as all viruses, utilizes the replication machineryof its E. coli host. However, rapid replication of the virusdoes not start immediately after the host’s infection; the! genome is integrated into the bacterial genome and thusresides dormant within its host. In this phase of lysogeny, theviral genome is replicated along with the host chromosome(Fig. 1). During its dormant residency in the lysogen, onlyone phage gene (cI) is active, which expresses the phage !repressor. This repressor ensures that all other phage genesare switched off. Only a socalled induction event will ‘flipthe ! switch.’ For example, after exposure to UV light, therepressor looses its functionality, is in fact switched off, andthe rest of the phage genes (lytic genes) gets activated. As

WCCI 2006, World Congress on Computational Intelligence, Vancouver, BC CEC 2006, Congress on Evolutionary Computation

a consequence, the cell will eventually lyse and release newbacterial phages (Fig. 1).

Fig. 1. Schematic illustration of the lysogenic and lytic growth phasesafter infection of a bacterium by phage !.

III. THE ! SWITCH

After this high-level description of the bacterial switchingbehavior from lysogenic to lytic growth, we have to have acloser look at the actual biomolecular ‘agents’ involved inthese regulatory processes. The two genes cI and cro playa key role in the switch, together with the socalled rightoperator (OR) regulatory region (Fig. 2). The gene cI encodesfor the ! repressor and is switched on in a lysogen, whereasthe gene encoding for the Cro protein is inactive (andvice versa during lysogeny). How this switching behavioris maintained, becomes clear after a closer inspection of theOR regulatory region. There are two aspects to note. First, theoperator is subdivided into three binding sites (OR1, OR2, andOR3). Secondly, the binding sites overlap the two opposingpromoters PRM and PR, which initiate transcription of cI andthe lytic genes (including cro), respectively.

Fig. 2. Sections of the bacterial genome that partake in the ! switch.

IV. REGULATED RECRUITMENT

Looking at the agents involved in the regulatory scheme,we have the following situation (Fig. 3). In a lysogen, the! repressors, which form dimers, bind to two adjacent sites,OR1 and OR2. This binding usually occurs sequentially, withOR1 being occupied first, which then increases the probability

of another repressor dimer to attach to OR2 (Fig. 3a). Thiscooperative binding has two effects. First, the regulatedrecruitment results in a much higher frequency of RNApolymerase binding at PRM, which, in turn, produces morerepressors to stabilize the switch through a positive feedbackloop. Secondly, the PR promoter, which partly overlaps withOR1 and OR2, is blocked, so that RNA polymerase cannotinitiate transcription of cro and other lytic genes.

It is important to note that repressor is not constantlybound to the operator; repressors frequently fall off theoperator and either rebind or are replaced by another nearbyrepressor. Consequently, during these agent-based regulatoryinteractions the concentration of repressors has to be kepthigh enough to ensure that OR1 and OR2 are occupied almostall the time, which self-stabilizes the lysogenic state.

The stable state of the lysogen can only be disturbed byan induction event—with dramatic consequences. Inducers,such as UV light, primarily damage DNA, which changesthe behavior of the bacterial protein RecA, that normallyacts as a catalyzer for recombination of DNA molecules.1After induction, RecA assumes the function of a proteaseand cleaves ! repressor monomers, which prevents furtherformation of repressor dimers and hence disables repressorsfrom binding to the operators. Eventually, OR1 and OR2

become vacant, so that RNA polymerase can now initiatetranscription of the cro gene and other genes, which encodefor proteins necessary in the early stages of lytic growth(Fig. 3b). The Cro protein has a high affinity for bindingto OR3, where it facilitates recruitment of RNA polymeraseto express more of the cro gene. Through this positivefeedback loop, Cro concentration is rising until OR1 and OR2

are also occupied by Cro, which eventually prevents RNApolymerase from further binding to the PR promoter and thusautomatically turns off expression of cro and other early lyticgenes. It is particularly interesting that the binding sequenceof Cros (OR3, OR2, OR1) is reverse to the order in whichrepressors bind onto the operators (OR1, OR2, OR3), which isthe core mechanism for the switch and its bi-stable state.

V. THE AGENT-BASED MODEL

What should be clear at this point is that the wholeswitching behavior can be defined through the interactionsof a number of biomolecular agents of different types:

• Repressor monomers which form dimers;• Repressor dimers, which bind to the operator sites;• Cro monomers, which form dimers;• Cro dimers, which bind to the operator sites;• RecA, which cleaves repressor;• RNA polymerase, which docks onto promoters and

initiates the expression of proteins (repressor and Cro);and

• promoter and operator sites on the DNA.Given these agents and a set of interaction rules, we have

implemented a computational model of the ! switch, whichincorporates a swarm-based approach with a 3D visualization

1How this change occurs is still not fully understood [11].

(a) Schematic of the regulated recruitment of repressor dimers andRNA polymerases, leading to a regulatory, self-stabilizing interac-tion network.

(b) Schematic of the regulated recruitment of Cro dimers and RNApolymerases, leading to a regulatory, self-stabilizing interactionnetwork.

(c) Regulated recruitment of repressor dimers and RNA polymerasesas visualized in our agent-based simulation.

(d) Regulated recruitment of Cro dimers and RNA polymerases asvisualized in our agent-based simulation.

Fig. 3. The key biomolecular entities of the ! switch and their interaction during lysogeny and lytic growth.

Fig. 4. An overview of the ! switch agents included in our current model. (1) Repressor monomer; (2) Repressor dimer; (3) Cro monomer; (4) Crodimer; (5) RNA polymerase; and (6) RecA. The window at the bottom-left corner allows direct observation of the operator sites.

(Fig. 4). We use modeling techniques similar to our otheragent-based simulations of bacterial chemotaxis [3], [2], thehuman immune system [13], and the lactose operon [14],[1]. Each individual element in the ! switch simulation isrepresented as an independent agent governed by (usuallysimple) rules of interaction, for which we use the BREVEphysics-based, multi-agent simulation engine [15]. Whileexecuting specific actions when colliding with or gettingclose to other agents, the dynamic elements in the systemmove randomly in continuous, 3-dimensional space, whichrepresents the bacterial cytoplasm.

As illustrated in Figure 4, we represent ! switch agents asthree-dimensional, abstract shapes, which have been modeledafter illustrations found in the literature [11], [12] (comparealso Fig. 3). The simulation system provides each agent withbasic services, such as the ability to move, rotate, and deter-mine the presence and position of other agents. A schedulerimplements time slicing by invoking each agent’s Iteratemethod, which executes a specific, context-dependent action.These actions are based on the agent’s current state, and thestate of other agents in its vicinity. Each agent keeps trackof other agents in the vicinity of its neighbourhood space,which is defined as a sphere with a specific radius. Eachagent’s next-action step is triggered depending on the typesand numbers of agents within its local interaction space.Consequently, our simulated agents work in a decentralizedfashion with no central control unit to govern the interactionsof the agents.

VI. RELATED WORK

One of the early successful thermodynamic models isdescribed in [16], which accounts for cooperative interactionsof ! repressor with the right operator, based on rate equationsthat capture the probabilities of microscopic configurationsof repressor–operator site bindings. However, this modeldoes not include Cro monomers. An extended version ofthis model by Shea and Ackers incorporates the kineticsfor coupling events, including synthesis of cI and cro [17].Hasty et al. [18] give a good overview of further modelingapproaches using rate equations or stochastic kinetics.

A qualitative simulation model of ! phage growth [19]utilizes qualitative reasoning, which could be used to extractrelations and interactions of biological entities from genomicdatabases. As this mining of interaction rules cannot beperformed automatically at the present time, and a manualcomposition of qualitative constraints is still tedious, wefollow an intermediate approach, where interaction rulesamong biomolecular entities in 3-dimensional cell space areformulated. As it turns out, these rules of interaction can—initially—be rather crude to approximate a given regulatorysystem, as we demonstrate here with the ! switch. Repeatedfine tuning of control parameters for the interaction rules canthen be achieved automatically using evolutionary algorithmsto match data from in vitro experiments with the in silicomodel.

Fig. 5. Graphical user interface to set agent parameters: affinity strengthfor the repressors and operator binding sites 1 through 3; RNA polymerasetranscription speed; cleavage duration.

VII. THE ! SWITCH MODEL IN ACTION

The simulated cell cytoplasm only contains the DNAsection that is important for the switching behavior. Inparticular, we exclude any other genes, such as the earlylytic genes. The DNA, modeled as a stationary ‘beam’ inthe centre of the cell (Fig. 4), contains the two promoters,PRM (left of the centre) and PR (to the right of the centre),as well as the three operator binding sites, OR1, OR2, andOR3 (Fig. 3c,d). The strands for the cI and cro genes arerepresented by the left and right sections, respectively.2

1) Key Switching Stages: In Figure 6 we show some of thekey stages of our ! switch model for the lysogenic and lyticgrowth phase. The simulation is initialized with ! repressormonomers and RNA polymerases only (Fig. 6a). In general,all agents perform a random walk within the designatedcell space. However, when agents enter specific regions theprobability distributions for their movements can change. Forexample, repressor monomers form dimers whenever theyget close to each other and then, as pairs, have an increasedtendency to move towards the operator sites. Whenever adimer gets close to any of the binding sites, the affinityfor each operator determines whether docking occurs withOR1, OR2, or OR3. These affinities can be changed duringthe simulation (Fig. 5) and are set so that repressor dockingoccurs in the desired order OR1–OR2–OR3. Any repressordocked onto one of the operators increases the affinity for itsadjacent operator, which results in the recruitment of furtherrepressors (Fig. 6b). A similar recruitment process applies toRNA polymerases, which have a higher tendency to movetowards and dock onto promoter PRM, once OR1 and OR2 are

2It should be noted that ‘left’ and ‘right’ only refers to this particularfigure. The visualization can be freely rotated and zoomed in 3D space.

(a) Repressors start docking onto OR1. (b) Repressors collectively bind to OR1 and OR2.

(c) RNA polymerase gets increasingly recruited to PRM

and expresses more repressors.

(d) After induction, RecA proteins (blue) are intro-duced into the cell environment, which start cleavingRepressor monomers.

(e) Operator sites OR1 and OR2 become vacant andCro starts docking onto OR3.

(f) Cro is now mainly occupying OR1 during the lyticphase, which keeps repressor production turned off.

Fig. 6. Selected snapshots from the ! switch simulation.

occupied by repressors. As in the real bacterial cell, repres-sors bind to an operator site only for a certain time period!tbind. Therefore, it is not until a certain concentration ofrepressors has been reached, that the operator sites, OR1 andOR2 are occupied most of the time (Fig. 6c).

2) Induction: We simulate an induction event by introduc-ing a large number of RecA proteins into the simulation space(Fig. 6d). RecA cleaves any repressor monomer it encounters.Any RecA that collides with a repressor dimer cleaves one of

its monomers, which also splits the dimer. After some time,almost no dimers exist and most monomers are split into theiramino and carboxyl domains. Consequently, the operatorbinding sites are now vacant, so that RNA polymerases startdocking onto the PR promoter, producing Cro protein. Crothen follows a similar binding and recruitment process asthe repressors, but in reverse order of binding, starting atOR3 and increasingly recruiting RNA polymerases to the crogene (Fig. 6e). As this, again, acts as a positive feedback

Fig. 7. Diagrammatic representation of docking events at the three operator sites over 10, 000 iterations.

loop, the concentration of Cro rises. Eventually, with moreCro in the system—and around the operator binding sites—all three operators tend to be occupied most of the time,which prevents RNA polymerase from producing more Cro.Hence, the concentration of Cro is stabilized (Fig. 6f).

VIII. ANALYSIS OF SIMULATION DATA

As the agent-based system exhibits implicit noise, we willexplain an example of a typical simulation run. The followingexperiment was performed over 10, 000 iteration steps, whereone step is associated with the smallest integration timestep for the physics simulation engine that determines eachparticle’s direction, velocity, and acceleration. Within each ofthese time steps, collision detection (important for bindingevents to the operator sites or for forming dimers frommonomers) and resolution takes place.

Focusing on docking events on the three operator sitesfirst, Figure 7 shows a time plot of the bindings that occurat OR1, OR2, and OR3 over 10, 000 iterations. Each columnrepresents one site, where each horizontal line marks a

docking event at a particular point in time. In each columnplot, time progresses from top to bottom. Repressor dimerbindings are marked by grey lines, whereas Cro dockingsare represented by black lines. During the first 2, 000 timesteps, it is primarily repressors that occupy the OR1 andOR2 sites. Very rarely, when OR2 becomes vacant, Cro docksonto it. Cro never docks onto OR1 during this initial period,as repressors have a much higher affinity for this site thanCro, and Cro itself prefers to dock onto OR3 first. Duringthe intervals where OR3 is vacant RNA polymerases havethe chance to dock onto the PRM promoter in order tostart transcription, translation, and final expression of a newrepressor monomer.3

Shortly before iteration 2, 000 induction agents in the formof RecA are introduced into the system. These cleavageagents separate the amino and the carboxyl part of each

3In our model, we do not explicitly distinguish between transcription,translation, and expression; these are simulated as a single process, as thisdoes not have a direct influence on the overall switching behavior.

Fig. 8. Concentrations of repressor dimers (black) and Cro dimers (grey) over 10, 000 iteration steps. The ’noisy’ repressor numbers are due to continuousdissociation of repressor dimers into monomers and vice versa. Induction agents (RecA) are introduced shortly before time step 2, 000, after which thenumber of repressor dimers declines rapidly due to repressor monomer cleavage by RecA.

(a) Lysogenic Growth: Repressors. (b) Lytic Growth: Repressors.

(c) Lysogenic Growth: Cros. (d) Lytic Growth: Cros.

Fig. 9. Docking frequencies of Cro and Repressor dimers.

repressor monomer (Fig. 6d). This has the consequencethat repressors can no longer form dimers, hence they areno longer able to dock onto any of the operator sites.Consequently, as can be seen in Figure 7, shortly aftertime step 2, 000 no more repressors are bound to operatorsites OR1 or OR2. Instead, operator OR3 is now increasinglyoccupied by Cro, which—in combination with Cro bound tosite OR2—almost completely blocks RNA polymerases fromdocking onto PRM. Therefore, expression of repressors comesto a halt, as illustrated in Figure 8. Also, because OR1 isnow vacant all the time (Cro has a very low affinity for thissite), polymerases can dock onto promoter PR, which leadsto an increased rate of Cro expression. Note in Figure 8 thatafter time step 2, 000 the slope of the Cro concentration curveincreases. Once the concentration of Cro is high enough, Crowill start to also occupy OR1, which then switches off Croexpression in the same way as repressor expression levelsoff, as seen in the left-most section of Figure 8.

Figure 9 gives a more detailed overview of the dockingfrequencies during this experiment. For repressors and Crowe summarize how many docking events occurred bothduring the lysogenic (before induction) and during the lyticphase (after induction). We have extracted each dockingcombination separately, in order to show the cooperativityeffects that are so crucial for the !-switch. Figure 9a showsthat OR1 and OR2 are the sites most occupied by repressors inthe lysogen. The OR2 bar is higher than OR1 as it combinesboth the single dockings at OR2 and the combined OR1-OR2

dockings. Obviously, as the fourth bar illustrates, cooper-ative docking at OR1 and OR2 prevails. All other dockingcombinations occur rather infrequently. During lytic growth,repressor numbers decrease rapidly and therefore the numberof operator bindings by repressor dimers is greatly reduced(Fig. 9b).

Of course, looking at the Cro docking frequencies, thepicture should be exactly reversed. Cro numbers are kept to aminimum during lysogeny, as shown in Figure 9c. However,the dominant number of OR3 dockings reflects Cro’s highaffinity for OR3. On the other hand, during the lytic phaseCro thrives, with bindings at OR3 being most dominant.

IX. CONCLUSION AND FUTURE WORK

We have presented an agent-based (or individual-based)model of the gene regulatory events that occur in the E.coli bacterium after infection by phage lambda. The modelimplements the major biomolecular players involved in theregulatory processes in a lysogen and during lytic growth.The model also replicates the key features of the switch,which is triggered by induction agents.

In our future work with this model we will investigate thefollowing aspects:

• A sensitivity analysis of the agent parameters will beundertaken.

• We will utilize evolutionary algorithms to adjust affinitysettings and other parameters with respect to a certainfitness criterion (e.g., switching speed, robustness).

• We will explore the effects of noise (introduced throughagent velocities and other spatial parameters) on therobustness of the overall switching behavior.

Up to date details about this !-switch model and otheragent-based simulation examples, which are investigated inour Evolutionary & and Swarm Design Lab can be found at:www.swarm-design.org.

ACKNOWLEDGMENT

Financial support for this research was provided by theNatural Sciences and Engineering Research Council ofCanada.

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