Agent-based Simulations of the Human Immune System - CiteSeerX

Immunity through Swarms: Agent-based Simulations of the Human Immune System Christian Jacob1,2 , Julius Litorco1 , and Leo Lee1 University of Calgary, Calgary, Alberta, Canada T2N 1N4 1

2

Department of Computer Science, Faculty of Science Dept. of Biochemistry and Molecular Biology, Faculty of Medicine {jacob, litorcoj}@cpsc.ucalgary.ca http://www.cpsc.ucalgary.ca/∼jacob/ESD/

Abstract. We present a swarm-based, 3-dimensional model of the human immune system and its response to first and second viral antigen exposure. Our model utilizes a decentralized swarm approach with multiple agents acting independently—following local interaction rules—to exhibit complex emergent behaviours, which constitute externally observable and measurable immune reactions. The two main functional branches of the human immune system, humoral and cell-mediated immunity, are simulated. We model the production of antibodies in response to a viral population; antibody-antigen complexes are formed, which are removed by macrophages; virally infected cells are lysed by cytotoxic T cells. Our system also demonstrates reinforced reaction to a previously encountered pathogen, thus exhibiting realistic memory response.

1

Introduction

Major advances in systems biology will increasingly be enabled by the utilization of computers as an integral research tool, leading to new interdisciplinary fields within bioinformatics, computational biology, and biological computing. Innovations in agent-based modelling, computer graphics and specialized visualization technology, such as the CAVEr Automated Virtual Environment, provide biologists with unprecedented tools for research in ‘virtual laboratories’ [4,8,13]. However, current models of cellular and biomolecular systems have major shortcomings regarding their usability for biological and medical research. Most models do not explicitly take into account that the measurable and observable dynamics of cellular/biomolecular systems result from the interaction of a (usually large) number of ‘agents’, such as cytokines, antibodies, lymphocites, or macrophages. With our agent-based models [10,17], simulations and visualizations that introduce swarm intelligence algorithms [2,5] into biomolecular and cellular systems, we develop highly visual, adaptive and user-friendly innovative research tools, which, we think, will gain a much broader acceptance in the biological and life sciences research community—thus complementing most of the

current, more abstract and computationally more challenging3 mathematical and computational models [14,3]. We propose a model of the human immune system, as a highly sophisticated network of orchestrated interactions, based on relatively simple rules for each type of immune system agent. Giving these agents the freedom to interact within a confined, 3-dimensional space results in emergent behaviour patterns that resemble the cascades and feedback loops of immune system reactions. This paper is organized as follows. In section 2, we present a brief synopsis of 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-step description of both simulated humoral and cell-mediated immunity in response to a viral antigen. Memory response, which we analyze in more detail in Section 5, 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-based immune system modelling environment.

2

The Immune System: A Biological Perspective

The human body must defend itself against a myriad of intruders. These intruders include potentially dangerous viruses, bacteria, and other pathogens it encounters in the air and in food and water. It must also deal with abnormal cells that have the capability to develop into cancer. Consequently, the human body has evolved two cooperative defense systems that act to counter these threats: (1) a nonspecific defense mechanism, and (2) a specific defense mechanism. The nonspecific defense mechanism does not distinguish one infectious agent from another. This nonspecific system includes two lines of defense which an invader encounters in sequence. The first line of defense is external and is comprised of epithelial tissues that cover and line our bodies (e.g., skin and mucous membranes) and their respective secretions. The second line of nonspecific defense is internal and is triggered by chemical signals. Antimicrobial proteins and phagocytic cells act as effector molecules that indiscriminately attack any invader that penetrates the body’s outer barrier. Inflammation is a symptom that can result from 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 line of defense against intruders and comes into play simultaneously with the second line of nonspecific defense. The characteristic that defines this defense mechanism is that it responds specifically to a particular type of invader. This immune response includes the production of antibodies as specific defensive proteins. It also involves the participation of white blood cell derivatives (lymphocytes). 3

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

While invaders are attacked by the inflammatory response, antimicrobial agents, and phagocytes, they inevitably come into contact with cells of the immune system, which mount a defense against specific invaders by developing a particular response against each type of foreign microbe, toxin, or transplanted tissue.

Antigen (1st exposure) engulfed by

Free antigens directly activate

Antigens displayed by infected cells activate

Macrophage becomes Antigen-presenting cell stimulates

B cell

Cytotoxic T cell

Helper T cell regulates

regulates Memory Helper T cell stimulates

gives rise to stimulates

stimulates

gives rise to

Antigen (2nd exposure) stimulates Plasma cells

Memory T cells

Memory B cells

Active Cytotoxic T cells

secrete Antibodies

Defend against extracellular pathogens by binding to antigens and making them easier targets for phagocytes and complement

HUMORAL IMMUNITY

CELL-MEDIATED IMMUNITY

Defend against intracellular pathogens and cancer by binding to and lysing the infected cells or cancer cells

Fig. 1. Schematic summary of immune system agents and their interactions in response to a first and second antigen exposure. The humoral and cell-mediated immunity interaction networks are shown on the left and right, respectively. Both immunity responses are 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 results in the production of antibodies through plasma cells. The antibodies circulate as soluble proteins in blood plasma and lymph. Cell-mediated immunity depends upon 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 the cell-mediated response are active against bacteria and viruses inside the host’s

cells. Cell-mediated immunity is also involved in attacks on transplanted tissue and 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 the humoral immune response, and T cells, which are involved in the cell-mediated immune response. Lymphocytes, like all blood cells, originate from pluripotent stem cells in the bone marrow. Initially, all lymphocytes are alike but eventually differentiate into the T cells or B cells. Lymphocytes that mature in the bone marrow become B cells, while those that migrate to the thymus develop into T cells. Mature B and T cells are concentrated in the lymph nodes, spleen and other lymphatic organs where the lymphocytes are most likely to encounter antigens. Both B and T cells are equipped with antigen receptors on their plasma membranes. When an antigen binds to a receptor on the surface of a lymphocyte, the lymphocyte is activated and begins to divide and differentiate. This gives rise to effector cells, the cells that actually defend the body in an immune response. With respect to the humoral response, B cells activated by antigen binding give rise to plasma cells that secrete antibodies, which help eliminate a particular antigen (Fig. 1, left side). Cell-mediated response, however, involves cytotoxic T cells (killer T cells) and helper T cells. Cytotoxic T cells kill infected cells and cancer cells. Helper T cells, on the other hand, secrete protein factors (cytokines), which are regulatory molecules that affect neighbouring cells. More specifically, through helper T cells cytokines regulate the reproduction and actions of both B cells and T cells and therefore play a pivotal role in both humoral and cell-mediated responses. Our immune system model incorporates most of these antibody-antigen and cell-cell interactions.

2.3

Antigen-Antibody Interaction

Antigens are mostly composed of proteins or large polysaccharides. These molecules are often outer components of the coats of viruses, and the capsules and cell walls of bacteria. Antibodies do not generally recognize an antigen as a whole molecule. Rather, they identify a localized region on the surface of an antigen called an antigenic determinant or epitope. A single antigen may have several effective epitopes thereby stimulating several different B cells to make distinct antibodies against it. Antibodies constitute a class of proteins called immunoglobulins. An antibody does not usually destroy an antigen directly. The binding of antibodies to antigens to form an antigen-antibody complex is the basis of several effector mechanisms. Neutralization is the most common and simplest form of inactivation because the antibody blocks viral binding sites. The antibody will neutralize 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-antibody complex. This effector mechanism is part of our simulation.4 One of the most important effector mechanisms of the humoral responses is the activation of the complement system by antigen-antibody complexes. The complement system is a group of proteins that acts cooperatively with elements of the nonspecific and specific defense systems. Antibodies often combine with complement proteins, activating the complement proteins to produce lesions in the antigenic membrane, thereby causing lysis of the cell. Opsonization is a variation on this scheme whereby complement proteins or antibodies will attach to foreign cells and thereby stimulate phagocytes to ingest those cells. Cooperation between antibodies and complement proteins with phagocytes, opsonization, and activation of the complement system is simulated in our IS model. Another important cooperative process occurs with macrophages. Macrophages do not specifically target an antigen but are directly involved in the humoral process which produces the antibodies that will act upon a specific antigen. A macrophage that has engulfed an antigen will present it to a helper T cell. This activates the helper T cell which in turn causes B cells to divide and differentiate through cytokines. A clone of memory B cells, plasma cells, and secreted antibodies will be produced as a result (Fig. 1, bottom left). These aspects are also part of our IS model, which is described in the following section.

3

A Biomolecular Swarm Model

Our computer implementation5 of the immune system and its visualization incorporates a swarm-based approach with a 3D visualization (Fig. 2a), where we use modeling techniques similar to our other agent-based simulations of bacterial chemotaxis, the lambda switch, and the lactose operon [9,8,13,4]. Each individual element in the IS simulation is represented as an independent agent governed by (usually simple) rules of interaction. While executing specific actions when colliding with or getting close to other agents, the dynamic elements in the system move randomly in continuous, 3-dimensional space. This is different to other IS simulation counter parts, such as the discrete, 2D cellular automaton-based versions of IMMSIM [11,6]. As illustrated in Figure 3, we represent immune system agents as spheres of different sizes and colours. Each agent keeps track of other agents in the vicinity of its neighbourhood space, which is defined as a sphere with a specific radius. Each agent’s next-action step is triggered depending on the 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 account that the actual immune system is spread out through a complicated network 4

5

Another effector mechanism is the agglutination or clumping of antigens by antibodies. The clumps are easier for phagocytic cells to engulf than are single bacteria. A similar mechanism is precipitation of soluble antigens through the cross-linking of numerous antigens to form immobile precipitates that are captured by phagocytes. This aspect is not yet built into our current IS model. 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 immune system agents are simulated in a confined 3-dimensional space. (b) Actions for each agent are triggered either by direct collision among agents or by the agent concentrations within an agent’s spherical neighbourhood space. Lines illustrate which cells are considered neighbours with respect to the highlighted cell.

Tissue cells Virus

B cell (plasma & memory)

Macrophage

Helper T cell

Killer T cell

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), plasma and memory B cells (green).

within the human body, including tonsils, spleen, lymph nodes, and bone marrow; neither do we currently—for the sake of keeping our model computationally manageable—incorporate the exchange of particles between the lymphatic vessels, blood capillaries, intestinal fluids, and tissue cells. Each agent follows a set of rules that define its actions within the system. As an example, we show the (much simplified) behaviours of macrophages and B cells in Table 1. The simulation system provides each agent with basic services, such as the ability to move, rotate, and determine the presence and position of other agents. A scheduler implements time slicing by invoking each agent’s Iterate method, which executes a specific, context-dependent action. These actions are based on the agent’s current state, and the state of other agents in its vicinity. Consequently, our simulated agents work in a decentralized fashion with no central control unit to govern the interactions of the agents.

Macrophage

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.

B Cell

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 as examples 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 the system is exposed to a viral antigen. Figure 4 illustrates key stages during the simulation. The simulation starts with 80 tissue cells (light blue), two killer T cells (dark blue), a macrophage (yellow), a helper T cell (purple), and a naive B cell (light green). In order to trigger the immune system responses, five viruses (red) are introduced into the simulation space (Fig. 4b). The viruses start 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 infected cells, 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 of viral 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 then stimulates 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 B cell in the center. Viruses that collide with antibodies are opsonized by forming antigen-antibody complexes (white; Fig. 4h), which labels viruses for elimination by macrophages and prevents them from infecting tissue cells. Eventually, all viruses and infected cells have been eliminated (Fig. 5a), with a large number of helper and cytotoxic T cells, macrophages, and antibodies remaining. As all IS agents are assigned a specific life time, the immune system will eventually restore to its initial state, but now with a reservoir of antibodies, which are prepared to fight a second exposure to the now ‘memorized’ viral antigen (Fig. 5b). The described interactions among the immune system agents are summarized in Figure 8a, which shows the number of viruses and antibodies as they evolve during the simulated humoral and cell-mediated immune response. This graph is the standard way of characterizing specificity and memory in adaptive immunity [7,15,12,1]. After the first antigen exposure the viruses are starting to get eliminated around iteration time = 50, and have vanished from the system at time = 100. The number of antibodies decreases between time step 50 and 100 due to the forming of antigen-antibody complexes, which are eliminated by macrophages. Infected tissue cells are lysed by cytotoxic T cells, which delete all cell-internal viruses. After all viruses have been fought off, a small amount of antibodies remains in the system, which will help to trigger a more intense and faster immune response after a second exposure to the same antigen, which is described in the following section.

5

Immune System Response after Second Exposure to Antigen

The selective proliferation of lymphocytes to form clones of effector cells upon first exposure to an antigen constitutes the primary immune response. Between initial exposure to an antigen and maximum production of effector cells, there is a lag period. During this time, the lymphocytes selected by the antigen are differentiating into effector T cells and antibody-producing plasma cells. If the body is exposed to the same antigen at some later time, the response is faster and more prolonged than the primary response. This phenomenon is called the secondary immune response, which we will demonstrate through our simulated immune system model (Fig. 8b).

Killer T

Helper T

Viruses

Macrophage

Tissue

Naïve B

(a)

Step 0

(b)

Step 3

Step 20

(d)

Step 42

Infected Cells

(c) Macrophages

Killer T

Plasma B

Helper T

(e)

Step 58

(f)

Step 61 AA complexes

Antibodies

(g)

Step 63

(h)

Step 74

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

Memory B

Antibodies

(a)

Step 94

(b)

Step 136

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

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

Time: 0

(a)

Step 145

Time: 40

(b)

Time: 55

(c)

Step 200

Step 185

Time: 130

(d)

Step 270

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 first exposure (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 antibodies are released compared to the first exposure. (d) After 130 time steps the system falls back into a resting state, now with a 10- to 12-fold higher level of antibodies (compare Fig. 8) and newly formed memory B cells. The time steps in the top right corners make it easier to see the increased progression speed of the immune response as compared to the first viral exposure in Figure 4.

Virus Count Vs. Antibody Count - Sampling Every 2 Seconds 300

250

Population Count

200

150 Antibody Count Virus Count 100

50

0 0

50

100

150

200

250

300

-50 Time (Seconds)

(a)

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Fig. 8. Immunological Memory: The graph shows the simulated humoral immunity response reflected in the number of viruses and antibodies after a first and second exposure to a viral antigen. (a) During the viral antigen exposure the virus is starting to get eliminated around iteration time = 70, and has vanished from the system at time = 90. The number of antibodies decreases between time step 70 and 125 due to the 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 exposure to the viral antigen at t = 145, the antibody production is increased in less than 50 time steps. Consequently, the virus is eliminated more quickly. About 13 times more antibodies (130) remain in the system after this second exposure.

The immune system’s ability to recognize a previously encountered antigen is called immunological memory. This ability is contingent upon long-lived memory cells. These cells are produced along with the relatively short-lived effector cells of the primary immune response. During the primary response, these memory cells are not active. They do, however, survive for long periods of time and proliferate rapidly when exposed to the same antigen again. The secondary immune response 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 Figure 5b. About 10 time steps later, we introduce five copies of the same virus the system encountered previously. Each virus, which is introduced into the system, receives a random signature s ∈ [0, 10]. We keep track of all viruses inserted into the system and can thus reinsert any previous virus, for which antibodies have been formed. Once memory B cells collide with a virus, they produce antibodies with the same signature, so that those antibodies will only respond to this specific virus. Consequently, after a second exposure to the same viral antigen at t = 145, the highest concentration of antibodies is increased by five times (to about 250), only after a lag time of 25 steps (Fig. 8b). Consequently, the virus is eliminated much faster, as more antigen-antibody complexes are formed, which get eliminated quickly by the also increased number of macrophages. Additionally, an increased number of helper and killer T cells contributes to a more effective removal of infected cells (Fig. 7). Not even half the number of viruses can now proliferate through the system, compared to the virus count during the first exposure. After the complete elimination of all viruses, ten to fifteen times more antibodies (about 130) remain in the system after this second exposure. This demonstrates that our agent-based model—through emergent behaviour resulting from agent-specific, local interaction rules—is capable of simulating key aspects of both humoral and cell mediated immune responses.

6

Conclusions and Future Research

From our collaborations with biological and medical researchers, we are more and more convinced that a decentralized swarm approach to modelling the immune system closely approximates the way in which biologists view and think about living systems. Although our simulations have so far only been tested for a relatively small number of (hundreds of) interacting agents, the system is currently being expanded to handle a much larger number of immune system agents and other biomolecular entities (such as cytokines), thus getting closer to more accurate simulations of massively-parallel interaction processes among cells that involve hundreds of thousands of particles. Our visualizations, developed as a 2D projection on a normal computer screen are further enhanced through stereoscopic 3D in a CAVEr immersive environment, as we have already done for a simulation 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 and cell agents actually affect the emergent behaviour patterns, which we observe in our simulations and can be measured in vivo in wet-lab experiments.

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

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