Download Immunity through Swarms: Agent-based Simulations of the Human

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. 3
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
3
in G. Nicosia, V. Cutello, P. Bentley, and J. Timmis (Eds.), Artificial Immune Systems, ICARIS 2004, Lecture Notes in Computer Science 3239, Springer-Verlag, 2004,
pp. 400-412.
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 challenging4 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
4
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].
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).
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.5
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 implementation6 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
5
6
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)
(b)
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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