Immunity through Swarms: Agent-basedSimulations of the Human Immune System

Christian Jacob1,2, Julius Litorco1, and Leo Lee1

University of Calgary, Calgary, Alberta, Canada T2N 1N4

1 Department of Computer Science, Faculty of Science2 Dept. of Biochemistry and Molecular Biology, Faculty of Medicine

{jacob, litorcoj}@cpsc.ucalgary.cahttp://www.cpsc.ucalgary.ca/∼jacob/ESD/

Abstract. We present a swarm-based, 3-dimensional model of the hu-man immune system and its response to first and second viral antigenexposure. Our model utilizes a decentralized swarm approach with mul-tiple agents acting independently—following local interaction rules—toexhibit complex emergent behaviours, which constitute externally ob-servable and measurable immune reactions. The two main functionalbranches of the human immune system, humoral and cell-mediated im-munity, are simulated. We model the production of antibodies in responseto a viral population; antibody-antigen complexes are formed, which areremoved by macrophages; virally infected cells are lysed by cytotoxic Tcells. Our system also demonstrates reinforced reaction to a previouslyencountered pathogen, thus exhibiting realistic memory response. 3

1 Introduction

Major advances in systems biology will increasingly be enabled by the utilizationof computers as an integral research tool, leading to new interdisciplinary fieldswithin bioinformatics, computational biology, and biological computing. Innova-tions in agent-based modelling, computer graphics and specialized visualizationtechnology, such as the CAVEr Automated Virtual Environment, provide bio-logists with unprecedented tools for research in ‘virtual laboratories’ [4,8,13].

However, current models of cellular and biomolecular systems have majorshortcomings regarding their usability for biological and medical research. Mostmodels do not explicitly take into account that the measurable and observabledynamics of cellular/biomolecular systems result from the interaction of a (usu-ally large) number of ‘agents’, such as cytokines, antibodies, lymphocites, ormacrophages. With our agent-based models [10,17], simulations and visualiza-tions that introduce swarm intelligence algorithms [2,5] into biomolecular and3 in G. Nicosia, V. Cutello, P. Bentley, and J. Timmis (Eds.), Artificial Immune Sys-

tems, ICARIS 2004, Lecture Notes in Computer Science 3239, Springer-Verlag, 2004,pp. 400-412.

cellular systems, we develop highly visual, adaptive and user-friendly innovativeresearch tools, which, we think, will gain a much broader acceptance in the bio-logical and life sciences research community—thus complementing most of thecurrent, more abstract and computationally more challenging4 mathematical andcomputational models [14,3]. We propose a model of the human immune system,as a highly sophisticated network of orchestrated interactions, based on relat-ively simple rules for each type of immune system agent. Giving these agents thefreedom to interact within a confined, 3-dimensional space results in emergentbehaviour patterns that resemble the cascades and feedback loops of immunesystem reactions.

This paper is organized as follows. In section 2, we present a brief synopsisof the immune system as it is currently understood in biology. In section 3,we discuss our agent- or swarm-based implementation of the immune system,highlighting the modelled processes and structures. Section 4 gives a step-by-stepdescription of both simulated humoral and cell-mediated immunity in responseto a viral antigen. Memory response, which we analyze in more detail in Section5, shows the validity of our model in reaction to a second exposure to a virus.We conclude with a brief discussion of future applications of our agent-basedimmune system modelling environment.

2 The Immune System: A Biological Perspective

The human body must defend itself against a myriad of intruders. These in-truders include potentially dangerous viruses, bacteria, and other pathogens itencounters in the air and in food and water. It must also deal with abnormal cellsthat have the capability to develop into cancer. Consequently, the human bodyhas evolved two cooperative defense systems that act to counter these threats:(1) a nonspecific defense mechanism, and (2) a specific defense mechanism. Thenonspecific defense mechanism does not distinguish one infectious agent fromanother. This nonspecific system includes two lines of defense which an invaderencounters in sequence. The first line of defense is external and is comprised ofepithelial tissues that cover and line our bodies (e.g., skin and mucous mem-branes) and their respective secretions. The second line of nonspecific defense isinternal and is triggered by chemical signals. Antimicrobial proteins and phago-cytic cells act as effector molecules that indiscriminately attack any invader thatpenetrates the body’s outer barrier. Inflammation is a symptom that can resultfrom deployment of this second line of defense.

The specific defense mechanism is better known as the immune system (IS),and is the key subject of our simulations. This represents the body’s third lineof defense against intruders and comes into play simultaneously with the second

4 For example, many differential equation models of biological systems, such as generegulatory networks, are very sensitive to initial conditions, result in a large numberof equations, and usually require control parameters that have no direct correspond-ence to measurable quantities within biological systems [3].

line of nonspecific defense. The characteristic that defines this defense mechan-ism is that it responds specifically to a particular type of invader. This immuneresponse includes the production of antibodies as specific defensive proteins.It also involves the participation of white blood cell derivatives (lymphocytes).While invaders are attacked by the inflammatory response, antimicrobial agents,and phagocytes, they inevitably come into contact with cells of the immune sys-tem, which mount a defense against specific invaders by developing a particularresponse against each type of foreign microbe, toxin, or transplanted tissue.

Antigen-presenting cell

Helper T cell

Memory HelperT cell

B cell CytotoxicT cell

Plasma cells Memory B cells Memory T cells Active CytotoxicT cells

Antibodies

Antigen (1st exposure)

Antigen (2nd exposure)

Macrophage

engulfed by

becomes

regulates

stimulates

stimulates

stimulates

stimulates

regulates

stimulates

Free antigensdirectly activate

Antigens displayed byinfected cells activate

gives rise to gives rise to

secrete

Defend against extracellularpathogens by binding to antigens

and making them easier targets forphagocytes and complement

Defend against intracellularpathogens and cancer bybinding to and lysing the

infected cells or cancer cells

HUMORAL IMMUNITY

CELL-MEDIATED IMMUNITY

Fig. 1. Schematic summary of immune system agents and their interactions in responseto a first and second antigen exposure. The humoral and cell-mediated immunity inter-action networks are shown on the left and right, respectively. Both immunity responsesare mostly mediated and regulated by macrophages and helper T cells.

2.1 Humoral Immunity and Cell-Mediated Immunity

The immune system mounts two different types of responses to antigens —humoral response and cell-mediated response (Fig. 1). Humoral immunity resultsin the production of antibodies through plasma cells. The antibodies circulate assoluble proteins in blood plasma and lymph. Cell-mediated immunity dependsupon the direct action of certain types of lymphocytes rather than antibodies.

The circulating antibodies of the humoral response defend mainly against toxins,free bacteria, and viruses present in body fluids. In contrast, lymphocytes of thecell-mediated response are active against bacteria and viruses inside the host’scells. Cell-mediated immunity is also involved in attacks on transplanted tissueand cancer cells, both of which are perceived as non-self.

2.2 Cells of the Immune System

There are two main classes of lymphocytes: B cells, which are involved in thehumoral immune response, and T cells, which are involved in the cell-mediatedimmune response. Lymphocytes, like all blood cells, originate from pluripotentstem cells in the bone marrow. Initially, all lymphocytes are alike but eventuallydifferentiate into the T cells or B cells. Lymphocytes that mature in the bonemarrow become B cells, while those that migrate to the thymus develop intoT cells. Mature B and T cells are concentrated in the lymph nodes, spleen andother lymphatic organs where the lymphocytes are most likely to encounter an-tigens. Both B and T cells are equipped with antigen receptors on their plasmamembranes. When an antigen binds to a receptor on the surface of a lympho-cyte, the lymphocyte is activated and begins to divide and differentiate. Thisgives rise to effector cells, the cells that actually defend the body in an immuneresponse. With respect to the humoral response, B cells activated by antigenbinding give rise to plasma cells that secrete antibodies, which help eliminate aparticular antigen (Fig. 1, left side). Cell-mediated response, however, involvescytotoxic T cells (killer T cells) and helper T cells. Cytotoxic T cells kill infectedcells and cancer cells. Helper T cells, on the other hand, secrete protein factors(cytokines), which are regulatory molecules that affect neighbouring cells. Morespecifically, through helper T cells cytokines regulate the reproduction and ac-tions of both B cells and T cells and therefore play a pivotal role in both humoraland cell-mediated responses. Our immune system model incorporates most ofthese antibody-antigen and cell-cell interactions.

2.3 Antigen-Antibody Interaction

Antigens are mostly composed of proteins or large polysaccharides. These mo-lecules are often outer components of the coats of viruses, and the capsules andcell walls of bacteria. Antibodies do not generally recognize an antigen as awhole molecule. Rather, they identify a localized region on the surface of anantigen called an antigenic determinant or epitope. A single antigen may haveseveral effective epitopes thereby stimulating several different B cells to makedistinct antibodies against it. Antibodies constitute a class of proteins calledimmunoglobulins.

An antibody does not usually destroy an antigen directly. The binding ofantibodies to antigens to form an antigen-antibody complex is the basis of severaleffector mechanisms. Neutralization is the most common and simplest form ofinactivation because the antibody blocks viral binding sites. The antibody willneutralize a virus by attaching to the sites that the virus requires in order to

bind to its host cell. Eventually, phagocytic cells destroy the antigen-antibodycomplex. This effector mechanism is part of our simulation.5

One of the most important effector mechanisms of the humoral responses isthe activation of the complement system by antigen-antibody complexes. Thecomplement system is a group of proteins that acts cooperatively with elementsof the nonspecific and specific defense systems. Antibodies often combine withcomplement proteins, activating the complement proteins to produce lesions inthe antigenic membrane, thereby causing lysis of the cell. Opsonization is a vari-ation on this scheme whereby complement proteins or antibodies will attach toforeign cells and thereby stimulate phagocytes to ingest those cells. Cooperationbetween antibodies and complement proteins with phagocytes, opsonization, andactivation of the complement system is simulated in our IS model.

Another important cooperative process occurs with macrophages. Macro-phages do not specifically target an antigen but are directly involved in thehumoral process which produces the antibodies that will act upon a specific an-tigen. A macrophage that has engulfed an antigen will present it to a helperT cell. This activates the helper T cell which in turn causes B cells to divideand differentiate through cytokines. A clone of memory B cells, plasma cells,and secreted antibodies will be produced as a result (Fig. 1, bottom left). Theseaspects are also part of our IS model, which is described in the following section.

3 A Biomolecular Swarm Model

Our computer implementation6 of the immune system and its visualization in-corporates a swarm-based approach with a 3D visualization (Fig. 2a), where weuse modeling techniques similar to our other agent-based simulations of bacterialchemotaxis, the lambda switch, and the lactose operon [9,8,13,4]. Each individualelement in the IS simulation is represented as an independent agent governed by(usually simple) rules of interaction. While executing specific actions when col-liding with or getting close to other agents, the dynamic elements in the systemmove randomly in continuous, 3-dimensional space. This is different to other ISsimulation counter parts, such as the discrete, 2D cellular automaton-based ver-sions of IMMSIM [11,6]. As illustrated in Figure 3, we represent immune systemagents as spheres of different sizes and colours. Each agent keeps track of otheragents in the vicinity of its neighbourhood space, which is defined as a spherewith a specific radius. Each agent’s next-action step is triggered depending onthe types and numbers of agents within this local interaction space (Fig. 2b).

Confining all IS agents within a volume does, of course, not take into accountthat the actual immune system is spread out through a complicated network5 Another effector mechanism is the agglutination or clumping of antigens by antibod-

ies. The clumps are easier for phagocytic cells to engulf than are single bacteria. Asimilar mechanism is precipitation of soluble antigens through the cross-linking ofnumerous antigens to form immobile precipitates that are captured by phagocytes.This aspect is not yet built into our current IS model.

6 We use the BREVE physics-based, multi-agent simulation engine [16].

(a) (b)

Fig. 2. Interaction space for immune system agents: (a) All interactions between im-mune system agents are simulated in a confined 3-dimensional space. (b) Actions foreach agent are triggered either by direct collision among agents or by the agent concen-trations within an agent’s spherical neighbourhood space. Lines illustrate which cellsare considered neighbours with respect to the highlighted cell.

Macrophage Helper T cell

Tissue cells

Killer T cell

B cell(plasma & memory)

Virus

Fig. 3. The immune system agents as simulated in 3D space: tissue cells (light blue),viruses (red), macrophages (yellow), killer T cells (blue), helper T cells (purple), plasmaand memory B cells (green).

within the human body, including tonsils, spleen, lymph nodes, and bone mar-row; neither do we currently—for the sake of keeping our model computationallymanageable—incorporate the exchange of particles between the lymphatic ves-sels, blood capillaries, intestinal fluids, and tissue cells.

Each agent follows a set of rules that define its actions within the system. Asan example, we show the (much simplified) behaviours of macrophages and Bcells in Table 1. The simulation system provides each agent with basic services,such as the ability to move, rotate, and determine the presence and positionof other agents. A scheduler implements time slicing by invoking each agent’sIterate method, which executes a specific, context-dependent action. Theseactions are based on the agent’s current state, and the state of other agents inits vicinity. Consequently, our simulated agents work in a decentralized fashionwith no central control unit to govern the interactions of the agents.

Macrophage B Cell

if collision with virus:

if virus is opsonized:

Kill virus.

else:

Kill virus with prob. p.

Create new macrophage.

if collision with tissue cell:

if cell is infected:

if sufficient macrophages:

Create new B cell.

Create new macrophage.

state = passive.

if collision with virus:

state = active.

if collision with virus & active:

Increment vir-collision counter.

if vir-collision counter > TH:

if enough helper T cells:

Secrete antibodies.

Create new B cell.

Table 1. Simplified rules governing the behaviours of macrophages and B cells asexamples of immune system agents.

4 Immune Response after Exposure to a Viral Antigen

We will now describe the evolution of our simulated immune response after thesystem is exposed to a viral antigen. Figure 4 illustrates key stages during thesimulation. The simulation starts with 80 tissue cells (light blue), two killerT cells (dark blue), a macrophage (yellow), a helper T cell (purple), and anaive B cell (light green). In order to trigger the immune system responses,five viruses (red) are introduced into the simulation space (Fig. 4b). The virusesstart infecting tissue cells, which turn red and signal their state of infection by

going from light to dark red (Fig. 4c). The viruses replicate inside the infectedcells, which eventually lyse and release new copies of the viruses, which, in turn,infect more and more of the tissue cells (Fig. 4d). The increasing concentration ofviral antigens and infected tissue cells triggers the reproduction of macrophages(yellow), which consequently stimulate helper T cells (purple) to divide faster(Fig. 4e; also compare Fig. 1). The higher concentration of helper T cells thenstimulates more B cells (green) and cytotoxic T cells (killer T cells; dark blue)to become active (Fig. 4f). Whenever active B cells collide with a viral antigen,they produce plasma and memory B cells (dark green) and release antibodies(small green; Fig. 4g). Figure 6 shows a closeup with an antibody-releasing Bcell in the center. Viruses that collide with antibodies are opsonized by formingantigen-antibody complexes (white; Fig. 4h), which labels viruses for eliminationby macrophages and prevents them from infecting tissue cells. Eventually, allviruses and infected cells have been eliminated (Fig. 5a), with a large number ofhelper and cytotoxic T cells, macrophages, and antibodies remaining. As all ISagents are assigned a specific life time, the immune system will eventually restoreto its initial state, but now with a reservoir of antibodies, which are prepared tofight a second exposure to the now ‘memorized’ viral antigen (Fig. 5b).

The described interactions among the immune system agents are summar-ized in Figure 8a, which shows the number of viruses and antibodies as theyevolve during the simulated humoral and cell-mediated immune response. Thisgraph is the standard way of characterizing specificity and memory in adaptiveimmunity [7,15,12,1]. After the first antigen exposure the viruses are starting toget eliminated around iteration time = 50, and have vanished from the systemat time = 100. The number of antibodies decreases between time step 50 and100 due to the forming of antigen-antibody complexes, which are eliminated bymacrophages. Infected tissue cells are lysed by cytotoxic T cells, which deleteall cell-internal viruses. After all viruses have been fought off, a small amount ofantibodies remains in the system, which will help to trigger a more intense andfaster immune response after a second exposure to the same antigen, which isdescribed in the following section.

5 Immune System Response after Second Exposure toAntigen

The selective proliferation of lymphocytes to form clones of effector cells uponfirst exposure to an antigen constitutes the primary immune response. Betweeninitial exposure to an antigen and maximum production of effector cells, thereis a lag period. During this time, the lymphocytes selected by the antigen aredifferentiating into effector T cells and antibody-producing plasma cells. If thebody is exposed to the same antigen at some later time, the response is fasterand more prolonged than the primary response. This phenomenon is called thesecondary immune response, which we will demonstrate through our simulatedimmune system model (Fig. 8b).

(a) Step 0

Tissue

Killer T Helper T

Macrophage

Naïve B

(b) Step 3

Viruses

(c) Step 20

Infected Cells

(d) Step 42

(e) Step 58

Macrophages

Helper T

(f) Step 61

Killer T

Plasma B

(g) Step 63

Antibodies

(h) Step 74

AA complexes

Fig. 4. Simulated immune system response after first exposure to a viral antigen.

(a) Step 94 (b) Step 136

Antibodies

Memory B

Fig. 5. Simulated immune system response after first exposure to a viral antigen (con-tinued from Fig. 4).

Fig. 6. Release of antibodies after collision of an activated B cell with a viral antigen.

(a) Step 145

Time: 0

(b) Step 185

Time: 40

(c) Step 200

Time: 55

(d) Step 270

Time: 130

Fig. 7. Faster and more intense response after second exposure to viral antigens. (a)Five viruses are inserted into the system, continuing from Step 136 after the firstexposure (Fig. 5b). (b) The production of antibodies now starts earlier (at time = 40,instead of time = 60 for the first antigen exposure). (c) Five times more antibodiesare released compared to the first exposure. (d) After 130 time steps the system fallsback into a resting state, now with a 10- to 12-fold higher level of antibodies (compareFig. 8) and newly formed memory B cells. The time steps in the top right corners makeit easier to see the increased progression speed of the immune response as comparedto the first viral exposure in Figure 4.

Virus Count Vs. Antibody Count - Sampling Every 2 Seconds

-50

0

50

100

150

200

250

300

0 50 100 150 200 250 300

Time (Seconds)

Po

pu

lati

on

Co

un

t

Antibody CountVirus Count

(a) (b)

Fig. 8. Immunological Memory: The graph shows the simulated humoral immunityresponse reflected in the number of viruses and antibodies after a first and secondexposure to a viral antigen. (a) During the viral antigen exposure the virus is startingto get eliminated around iteration time = 70, and has vanished from the system attime = 90. The number of antibodies decreases between time step 70 and 125 due tothe forming of antigen-antibody complexes, which are then eliminated by macrophages.A small amount of antibodies (10) remains in the system. (b) After a second exposureto the viral antigen at t = 145, the antibody production is increased in less than 50time steps. Consequently, the virus is eliminated more quickly. About 13 times moreantibodies (130) remain in the system after this second exposure.

The immune system’s ability to recognize a previously encountered antigen iscalled immunological memory. This ability is contingent upon long-lived memorycells. These cells are produced along with the relatively short-lived effector cellsof the primary immune response. During the primary response, these memorycells are not active. They do, however, survive for long periods of time and pro-liferate rapidly when exposed to the same antigen again. The secondary immuneresponse gives rise to a new clone of memory cells as well as to new effector cells.

Figure 7 shows a continuation of the immune response simulation of Fig-ure 5b. About 10 time steps later, we introduce five copies of the same virus thesystem encountered previously. Each virus, which is introduced into the system,receives a random signature s ∈ [0, 10]. We keep track of all viruses inserted intothe system and can thus reinsert any previous virus, for which antibodies havebeen formed. Once memory B cells collide with a virus, they produce antibod-ies with the same signature, so that those antibodies will only respond to thisspecific virus. Consequently, after a second exposure to the same viral antigenat t = 145, the highest concentration of antibodies is increased by five times (toabout 250), only after a lag time of 25 steps (Fig. 8b). Consequently, the virus iseliminated much faster, as more antigen-antibody complexes are formed, whichget eliminated quickly by the also increased number of macrophages. Addition-ally, an increased number of helper and killer T cells contributes to a moreeffective removal of infected cells (Fig. 7). Not even half the number of virusescan now proliferate through the system, compared to the virus count during thefirst exposure. After the complete elimination of all viruses, ten to fifteen timesmore antibodies (about 130) remain in the system after this second exposure.This demonstrates that our agent-based model—through emergent behaviourresulting from agent-specific, local interaction rules—is capable of simulatingkey aspects of both humoral and cell mediated immune responses.

6 Conclusions and Future Research

From our collaborations with biological and medical researchers, we are moreand more convinced that a decentralized swarm approach to modelling the im-mune system closely approximates the way in which biologists view and thinkabout living systems. Although our simulations have so far only been tested fora relatively small number of (hundreds of) interacting agents, the system is cur-rently being expanded to handle a much larger number of immune system agentsand other biomolecular entities (such as cytokines), thus getting closer to moreaccurate simulations of massively-parallel interaction processes among cells thatinvolve hundreds of thousands of particles. Our visualizations, developed as a2D projection on a normal computer screen are further enhanced through ste-reoscopic 3D in a CAVEr immersive environment, as we have already done for asimulation of the lactose operon gene regulatory system [4]. On the other hand,we are also investigating in how far noise and the number of biomolecular andcell agents actually affect the emergent behaviour patterns, which we observe inour simulations and can be measured in vivo in wet-lab experiments.

A swarm-based approach affords a measure of modularity, as agents can beadded and removed from the system. In addition, completely new agents can beintroduced into the simulation. This allows for further aspects of the immunesystem to be modelled, such as effects of immunization through antibiotics orstudies of proviruses (HIV), which are invisible to other IS agents.

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