Page 1

Large Scale Agent-Based Modeling of the

Humoral and Cellular Immune Response

Giovanni Stracquadanio1, Renato Umeton2, Jole Costanza3, Viviana Annibali4,

Rosella Mechelli4, Mario Pavone3, Luca Zammataro5, and Giuseppe Nicosia3

1Department of Biomedical Engineering

Johns Hopkins University

217 Clark Hall, Baltimore, MD 21218, USA

stracquadanio@jhu.edu

2Department of Biological Engineering

Massachusetts Institute of Technology

77 Massachusetts Avenue, Cambridge, MA 02139, USA

umeton@mit.edu

3Department of Mathematics and Computer Science

University of Catania

Viale A. Doria 6, 95125, Catania, Italy

{costanza,mpavone,nicosia}@dmi.unict.it

4Neurology and Centre for Experimental Neurological Therapies (CENTERS),

S. Andrea Hospital Site, Sapienza University of Rome

Via di Grottarossa 1035, 00189, Roma, Italy

{viviana.annibali,rosella.mechelli}@uniroma1.it

5Humanitas, University of Milan

Via Manzoni 56, 20089, Rozzano, Milan, Italy

luca.zammataro@humanitasresearch.it

Abstract. The Immune System is, together with Central Nervous

System, one of the most important and complex unit of our organism.

Despite great advances in recent years that shed light on its understand-

ing and in the unraveling of key mechanisms behind its functions, there

are still many areas of the Immune System that remain object of ac-

tive research. The development of in-silico models, bridged with proper

biological considerations, have recently improved the understanding of

important complex systems [1,2]. In this paper, after introducing major

role players and principal functions of the mammalian Immune System,

we present two computational approaches to its modeling; i.e., two in-

silico Immune Systems. (i) A large-scale model, with a complexity of

representation of 106− 108cells (e.g., APC, T, B and Plasma cells) and

molecules (e.g., immunocomplexes), is here presented, and its evolution

in time is shown to be mimicking an important region of a real im-

mune response. (ii) Additionally, a viral infection model, stochastic and

light-weight, is here presented as well: its seamless design from biological

considerations, its modularity and its fast simulation times are strength

points when compared to (i). Finally we report, with the intent of mov-

ing towards the virtual lymph note, a cost-benefits comparison among

Immune System models presented in this paper.

P. Li` o, G. Nicosia, and T. Stibor (Eds.): ICARIS 2011, LNCS 6825, pp. 15–29, 2011.

c ? Springer-Verlag Berlin Heidelberg 2011

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16G. Stracquadanio et al.

1Introduction

The theory of clonal selection, formalized by Nobel Laureate F. M. Burnet (1959,

whose foundation are in common with D. Talmage’s idea (1957) of a cellular se-

lection as the basis of the immune response), suggests that among all possible

cells, B and T lymphocytes, with different receptors circulating in the host or-

ganism, only those who are actually able to recognize the antigen will start to

proliferate by duplication (cloning). Hence, when a B cell is activated by binding

an antigen, it produces many clones, in a process called clonal expansion. The

resulting cells can undergo somatic hypermutation, and then they can give rise

to offspring B cells with mutated receptors. During the immune activity, antigens

compete with these new B cells, with their parents and with other clones. The

higher the affinity of a B cell to bind to available antigens, the more likely it will

clone. This results in a Darwinian process of variation and selection, called affin-

ity maturation. By increasing the size of those cell populations through clonal

expansion, and through the production of cells with longer lifetime expecta-

tion, and then establishing a defense over time (immune memory), the immune

system (IS) assures the organism a higher specific responsiveness to recognized

antigenic attacks. In particular, on recognition, memory lymphocytes are pro-

duced. Plasma B cells, deriving from stimulated B lymphocytes, are in charge of

the production of antibodies targeting the antigen. This mechanism is usually

observed in population of lymphocytes in two subsequent antigenic infections.

More in detail, the first exposition to the antigen triggers the primary response;

in this phase the antigen is recognized and the memory is developed. During the

second response, that occurs when the same antigen is found again, as a result

of the stimulation of the cells already specialized and present as memory cells, a

rapid and more abundant production of antibodies is observed. The secondary

response can be elicited from any antigen, which is similar, although not neces-

sarily identical, to the original one, which established the memory. This is known

as cross-reactivity.

In this article we present two new computational models capable of capturing

fundamental aspects of the IS, at two different complexity levels. A high-complex

model, large scale agent-based, that embeds all of the entities and all of the

interaction detailed above; thanks to this computational model we have success-

fully reproduced many IS processes and behaviors. In a second, low-complexity

model, we show how a stochastic model based on Gillespie algorithm, captures

major behaviors of the IS during a viral infection, even if we are borderline with

the definition of “well-mixed” solution. The paper is structured as follows: next

Section (S2) details the high-complexity agent-based model; it spans from the

introduction of role-playing entities in the model, to real simulations and discus-

sion. Section 3 details the low-complexity IS model; there, after the introduction

of process algebra concepts adopted, it is presented a viral infection model based

on π-calculus. Conclusions (S4) end the paper and give a cost-benefit comparison

of the two models in order to pave the way for the whole lymph node simulation.

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Large Scale Agent-Based Modeling of the Humoral17

2Agent-Based Modeling

Research on the IS dynamics, in the last two decades, has produced several

mathematical and computational models. Different approaches include differen-

tial equation based models [3,4,5], cellular automata models [6,7], classifier sys-

tems [8], genetic algorithms [9], network/computational models [10,11,12] and

agent-based models [13,14,15,16], which seem to be the best suited abstraction

to handle the great complexity of IS reality.

The first model here presented is based on the deterministic agent-based

paradigm; the high-complexity of this model comes from the fact that it can

be considered a large scale model and it is extremely realistic; indeed, there

are totally 106− 108cells (e.g., APC, T, B and Plasma cells) and molecules

(e.g., immunocomplexes) involved in this model: all of the major role-players

of the IS are embedded and represented in our model. It is worth remarking

the centrality of the scale problem, as choosing a proper model scale have re-

cently allowed for important improvements in the IS simulation [17,18,19,20].

Much like the nervous system, the IS performs pattern recognition tasks and,

additionally, it retains memory of the antigens to which it has been exposed. To

detect an antigen, the IS activates a particular recognition process that involves

many role-players. An overall view of IS role-players includes: antigens (Ag),

B lymphocytes (B), plasma B cells (PLB), antigen presenting cells (APC), T

helper lymphocytes (Th), immunocomplexes (IC) and antibodies (Ab). The Ag

is the target of the immune response. Th and B lymphocytes are responsible

for the discrimination of the self-nonself, while PLBs produce antibodies able

to label the Ags to be taken by the APCs, which represent the wide class of

macrophages. Their function is to present the phagocytised antigens to T helper

cells for activation. The ICs are Ab–Ag ties ready to be phagocytised by the

macrophages. All of the role-playing entities here described are encoded in our

model: each agent has a type (i.e.: Ag, B, PLB, etc.) and those typical features

that characterize the type (e.g., the Ag has a unique code, or bit string, that

will determine whether there will be a bind with a complementary entity); each

agent belongs to a population (e.g., the Ags, Bs, etc.) whose size is plotted in

order to quantify group presence, affinity driven interactions, mutations, clonal

selection and all of the processes detailed above.

2.1Immuno Responses

The IS mounts two different responses against pathogenic entities: the humoral

response, mediated by antibodies, and the cellular one, mediated by cells. Along

with the aforementioned entities, the IS includes the T killer cells, the Epithelial

cells or generic virus-target cells, and various lymphokines. These components

are necessary to activate the cellular response. One can, from an abstract point

of view, envision two types of precise interaction rules: specific interactions, that

occur when an entity binds to another by means of receptors; and, non-specific

interactions, that occur when two entities interact without any specific recog-

nition process. Only a specific subset of mature lymphocytes will respond to a

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18G. Stracquadanio et al.

0

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Concentration

Time Steps

Antigen Dynamics

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70000

0 20 40 60 80 100 120 140 160 180 200

Concentration

Time Steps

Antibody Dynamics

131020

245709

261828

262126

229340

253388

Fig.1. Immunization - Antigen and Antibody dynamics. Injections of antigens at time

steps 0 and 120.

0

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Concentration

Time Steps

B Cell Dynamics

131020

245709

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262126

229340

249804

0

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Concentration

Time Steps

Plasma Cell Dynamics

131020

245709

261828

262126

229340

262100

Fig.2. Immunization - B Cell and Plasma cell dynamics

given Ag, specifically those bearing the receptors that will bind the Ag. Binding

usually occurs on a small patch on the Ag (receptor or antigenic determinant

or epitope), and the antigen-binding sites on T cell receptors and antibodies

(paratopes or idiotypes). Thus, immune recognition of Ags comes from the spe-

cific binding of antigen-to-antigen receptors on B and T cells. Hence, the immune

response derives its specificity from the fact that Ags select the clones. A non-

active B or T cell that has never responded to an Ag before is called virgin or

naive. When a naive, mature lymphocyte bearing receptors of the appropriate

affinity, binds an Ag (in combination with other signals, usually cytokines), it

responds by: proliferating, i.e., cloning itself and, in turn, expanding the popu-

lation of cells bearing those receptors; the produced clones will differentiate into

effector cells that will produce an appropriate response (antibody production for

a B cell; cytotoxic responses or help responses for a T cell), and memory cells

that will be ready (somewhat like the naive cell) to encounter the Ag in the

future and respond in the same way (but this time with many more cells).

Switching from theory right to simulations, we present the results of our agent-

based encoding with 18 bits; its representation capability is of the order of 106

cells/molecules. Fig. 1 shows time track of antigen, and antibody population

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Large Scale Agent-Based Modeling of the Humoral19

0

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Time Steps

T cell Dynamics

252900

253932

251620

253412

253668

251884

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6000

8000

10000

12000

0 50 100 150 200

Concentration

Time Steps

Immuno Complex Dynamics

Fig.3. Immunization - T cell and Immunocomplexes dynamics

of a system injected with the antigen at time steps 0 and 120. Figure 2 shows

primary and secondary immune responses of B lymphocyte and Plasma cell

population. Figure 3 reports T cell population and Immunocomplexes. We have

three main immune response types to a given antigen: immune response by T

killer (cytotoxic) lymphocyte; by T helper lymphocyte; and, by B lymphocyte.

In Figure 2, we can see the immune response performed by lymphocytes of class

B: the free Ag selects a B lymphocyte, whose receptors match its own. These two

entities bind together. A B lymphocyte, which has -internalized- and transformed

the Ag, shows on its surface fragments of Ags bound to a protein coded by MHC

molecule of class II. The mature T helper lymphocyte can, now, bind to the

complex antigen-protein, visible on the B lymphocyte. Such a binding frees the

interleukin IL2, which in turn allows the B lymphocyte to clone and differentiate.

The cellular cloning goes on as long as the B lymphocytes are stimulated by T

helper lymphocytes. Mature PLBs free their receptors, Abs, which bind free

Ags, creating ICs. In turn, they will be phagocytised by APCs (the “garbage

collectors” of the IS). Other mature B lymphocytes stay in the system as B

memory cells. Lastly, the IS comprises the hypermutation phenomena observed

during the immune responses: the DNA portion coding for Abs is subjected to

mutation during the proliferation of the B lymphocytes. This gives the IS the

ability to generate diversity. We should underline that, even if the knowledge on

the various mechanisms of the immune system is quite advanced, the relative

importance of its components with respect to each specific task is not deeply

understood.

2.2Cross-Reactivity and Epithelial Cell Signaling

Now we show the molecular and cellular population dynamics correlated with

two further events involved in the clonal selection principle: cross-reactivity and

epithelial cell signaling. Cell concentrations give us a clear picture of the learning

and immunization processes that occurred during immune responses. To do this,

we need some recollection about a model extended by our agent-based model:

the Celada-Seiden model [7]; the manner is a robust computational model based

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20G. Stracquadanio et al.

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Cross-reactivity - Antigen Dynamics

0011011111101111

1011011101101111

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Cross-reactivity - Antibody Dynamics

262140

262044

261612

262110

261960

262093

Fig.4. Cross-Reactivity, Antigen and Antibody dynamics

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Time Steps

Cross-reactivity - T cell Dynamics

253668

251620

188388

253925

249828

253860

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Time Steps

Cross-reactivity - Immuno Complex Dynamics

0

1

Fig.5. Cross-Reactivity, T cell and Immunocomplexes dynamics

on the cellular automata paradigm that has been validated with in vitro and

in vivo experiments. In particular, it has been shown that Celada-Seiden model

can reproduce real phenomena of the immune response. The model includes

the following seven entities: Ags, B cells, PLB, APC, T-helper cells, IC, and

Ab. The chemical interactions between receptors (the bindings) are mimicked as

stochastic events. The probability that two receptors interact is determined by

a bit-to-bit matching over the bit strings representing them. Every cell can be

in one of the allowed states (e.g., a B cell can be Active, Internalized, Exposing,

Stimulated or Memory according to whether it has bound an antigen or not, if it

expose the MHC/peptide complex, if it duplicates or if it is considered a memory

B cell) and successful interactions between two entities produce a cell-state-

change. The cellular automata of the Celada-Seiden’s model has an underlying

regular, hexagonal, two-dimensional lattice. Each site incorporates many entities,

which interact in loci and diffuse to adjacent sites and then move randomly.

Every site of the automaton includes a large number of bit strings accounting

for the definition of the various entities and for their states (i.e., both receptors

and cell-states). In our agent-based simulation, initially there are neither PLBs

nor Abs, nor ICs in the Host, given a specific class of antigens. The plot of Fig.

4 (left plot) shows the three injections of antigens. In the first two injections,

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Large Scale Agent-Based Modeling of the Humoral21

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Concentration

Time Steps

Cross-reactivity - B cell Dynamics

262140

262044

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262110

261960

262093

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Cross-reactivity - Plasma Cell Dynamics

262140

262044

261612

262110

261960

262093

Fig.6. Cross-Reactivity, B Cell and Plasma cell dynamics

we insert the same antigen, namely the binary string (0011011111101111). The

third time we inject a - mutated - antigen (two bits underwent a simulated flip

mutation), namely the binary string (1011011101101111). It is of note how the

cross-reactivity, observed in nature is here reproduced: Fig. 4 (right plot), Fig.

5 and Fig. 6 present the dynamics of cell populations under control, presenting

important similarities with real immunological responses.

Moving towards larger and then more complex (but closer to the reality)

systems, we have enriched our IS simulation scenario: we indeed simulated a 20

bit encoded IS. With such an encoding, we have been able to simulate more

than 108cells and molecules. We have simulated such an environment for 400

time steps. Fig. 7(a) presents those Ags introduced in the system, while Fig.

7(b) shows the Interferon response released by lymphocytes, a countermeasure

that the IS has dynamically adopted. It is of note how the Interferon response

is triggered rightly after the introduction of Ags, with a diversified intensity.

Such intensity variation is motivated by the primary and secondary responses

and cross-reactivity reaction.

0

500000

1e+06

1.5e+06

2e+06

2.5e+06

3e+06

0 50 100 150 200 250 300 350 400

Concentration

Time Steps

Antigen Dynamics

Antigen type 1

Antigen type 2

0

1e+07

2e+07

3e+07

4e+07

5e+07

6e+07

0 50 100 150 200 250 300 350 400

Concentration

Time Steps

Interferon Dynamics

Fig.7. (a) Antigen Dynamics, as observed after its introduction in the 20 bits simula-

tion environment. (b) Interferon response, dynamically triggered after the Ag detection.

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22G. Stracquadanio et al.

930000

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970000

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990000

1e+06

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Concentration

Time Steps

Epithelial Cell Dynamics

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4e+06

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Concentration

Time Steps

D-Signal

Fig.8. (a) Epithelial cells in the IS; the change in time of this cell population is a key

component in the natural IS. (b) D-signal propagated by epithelial cells to warn other

IS components thought a signaling mechanism.

In Fig. 8(a) it is presented how the number of epithelial cells changes in time:

these cells are part of our natural IS. It has been validated that these cells

represent not only a mechanical barrier in our IS, but they are also enabled to

communicate the infection through an ad-hoc signal as described in [21,22]; in

fact a “warning signal”, namely the D-signal is used to propagate the information

that something uncommon is taking place. Fig. 8(b) presents the D-signal in

object, as observed within this 20 bit simulation.

3Modeling and Simulation by Stochastic π-Calculus

Biological entities, such as proteins or cells, are social entities (i.e., they act as an

organized group), and life depends on their interactions. We can then reduce a

biological system to a network of entities interacting among each others in a par-

ticular way, i.e., a way in which each elementary process is coded and controlled.

The stochastic π-calculus has been recently used to model and simulate a range

of biological systems; in particular, stochastic-based models [23] and more in

general statistics-based models [24], have recently improved our understanding

of key components of the immune system. In this section we want to show the

new features of this approach, the pros and cons, and finally the results obtained

in simulating HBV infections.

In recent years, there has been considerable research on designing program-

ming languages for complex parallel computational tasks. Interestingly, some of

this research is also applicable to biological systems, which are typically highly

complex and massively parallel systems. In particular, a mathematical program-

ming language known as the stochastic π-calculus [25] has been recently used

to model and simulate many biological systems. One of the main benefits of

this calculus is its ability to model large systems incrementally, by composing

simpler models of subsystems in an intuitive way (i.e., modularity). Such in sil-

ico experiments can be used to formulate testable hypotheses on the behavior

of biological systems, as a guide to future experiments in vivo. Currently avail-

able simulators for the stochastic π-calculus are implemented based on standard

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Large Scale Agent-Based Modeling of the Humoral23

theory of chemical kinetics, using an adaptation of the Gillespie algorithm [26].

There has already been substantial research on efficient implementation tech-

niques for variants of the π-calculus, in the context of programming languages

for parallel computer systems. However, this research does not take into account

some specific properties of biological systems, which differ from most computer

systems in fundamental ways. A key difference is that biological systems are

often composed of large numbers of processes with identical (or equivalent) be-

havior, such as thousands of proteins of the same type. Another difference is

that the scope (the environment where the interaction can actually take place)

of private interaction channels is often limited to a relatively small number of

processes, usually to represent the formation of complexes. In general two fun-

damental intuitions are shared by all of these proposals: 1. molecules (individual

biological agents, in general) can be abstracted as processes; 2. molecular inter-

actions can be modeled as communications. Here we introduce SPiM [27], the

calculus simulator used in our experiments, and our simulation of infection, i.e.,

the HBV virus, based on the Perelson’s model [28].

3.1

SPiM

Proceeding from the concept that molecules are represented as processes and

interactions are communications, we can see that the syntax of processes and

environments in SPiM is a subset of the syntax of the stochastic π-calculus (SPi)

with the additional constraint that each choice of action is defined separately in

the environment. Stochastic behavior is incorporated into the system by associ-

ating to each channel x its corresponding interaction rate given by ρ(x), and by

associating each delay τr with a corresponding rate r. Each rate characterizes

an exponential distribution, such that the probability of a reaction with rate r

occurring within the time t is given by F(t) = 1 − e−rt. The average duration

of the reaction is given by the mean 1/r of this distribution. A machine term

V consists of a set of private channels Z, a store S and a heap H. The heap

keeps track of the number of copies of identical species, while the store records

the activity of all the reactions in the heap. The system is executed according

to the reduction rules of the stochastic π-machine [25]. The rules rely on a con-

struction operator V?P , which adds a machine process P to a machine term

For the calculus dialect implemented by SPiM, Phillips et al. proved a formal

equivalence between an ad-hoc graphical notation and a SPiM program [29].

This is very interesting because people without programming background can

formalize a complete and correct model in π-calculus without knowing SPiM:

for instance, biologists can detail a biological system using this graphical nota-

tion and, SPiM is particularly suited to simulate a complete biological system

without building a full mathematical model of the interactions. Together with

good features there are also some drawbacks; in particular, SPiM is suitable

when all rates are known, and they do not change at running time: this is a very

strict hypothesis, because many biological systems have entities that change their

rate of interaction at running time or in some particular situations. E.g., in the

V (cf. Table 1 for detail).

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24G. Stracquadanio et al.

Table 1. Syntax of processes and environments in SPiM. The syntax is a normal form

for the stochastic π-calculus, in which each choice of actions can only occur at the top

level of a definition. For convenience, C is used to denote a restricted choice νnM and

D is used to denote the body of a definition. For each definition of the form X(m) = D

it is assumed that fn(D) ⊂ m.

P,Q ::= 0Null

Instance

Parallel

Restriction

E::=Empty

ProcessX(n)

P — Q

νxP

E,X(m)=P

E,X(m)=νnM Choice

π::= ?x(m)

!x(n)

τr

Input

Output

Delay

M::=0

π.P + M Action

Null

immune system, the rate of interaction, the affinity, between B-cell and Antigen

can change over the time because a B-cell can undergo hypermutations and then

altering its receptor and so its affinity with the Antigen [30].

3.2Modeling HBV Infection with SPiM

Here we present a stochastic pi-calculus model of infection caused by hepatitis

B virus (HBV). The simulation is based on the basic model of virus infection

proposed in [28], from which we report Fig. 9. The choice of the Perelson model

is justified by the fact that this model was tested in vivo and found a broad

consensus where HBV is concerned [31]. The model considers a set of cells sus-

ceptible to infection (i.e., target cells), T which, through interactions with a virus

V , become infected. Infected cells I are assumed to produce new virus particles

at a constant average rate p and to die at rate δ, per cell. The average lifespan of

a productively infected cell is 1/δ, and so if an infected cell produces a total of N

virions during its lifetime, the average rate of virus production per cell, p = Nδ.

Newly produced virus particles, V , can either infect new cells or be cleared from

the Host at rate c per virion. HBV infection was modeled with these Ordinary

Differential Equations (ODE):

dT/dt = s − dT − βV T

dI/dt = βV T − δI

dV/dt = pI − cV

(1)

(2)

(3)

Target cells become infected at a rate taken proportional to both the virions

concentration and the uninfected cell concentration (βV T); while infected cells

(I) are produced at the same rate (βV T) and it is assumed that they are depleted

at rate δ per cell. Finally, it is assumed that free virions are produced at a

constant rate, p, per cell and cleared at constant rate, c. We have simulated

an HBV infection with a high number of virions in blood; we have set virions

at 20% of target cells as we used a population of 5 × 103target cells and 103

virions. This ratio corresponds to the scenario in which the infection is growing,

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Large Scale Agent-Based Modeling of the Humoral25

??

?????????????????

??

?

?

????

?

???????????????????????????????????????????????????

??????

?

????

Fig.9. Perelson’s model for infection

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Target Cells

Infected Cells

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Target Cell

Virions

(a)(b)

Fig.10. Simulation of HBV infection using a stochastic π-calculus model. In (a), we

report the variation over time (x-axis) of the number of target and infected cells (y-

axis); in (b), we present the variation over time (x-axis) of the number of target cells

and virions (y-axis).

rapidly, possibly degenerating in a chronic status. We have set the infection rate

at a relatively low rate, but from the analysis of the plot in Fig. 10, we can see

that the number of virions is big enough to kill target cells. Moreover, infected

cells rapidly grow with respect to healthy ones; it is clear that after a first

phase where initial virions infect target cells, thanks to the growth of infected

cells, the growth in terms of number of virions comes along. This observation

is confirmed by Perelson studies, where, after an initial steady state, virions

grow proportionally to the number of infected cells. As in Perelson model, the

immune system response is implicitly considered by setting the rate of death

for virions and infected cells; although there is an in-vivo assessment of this

model, in general, fine-grained simulation should take into account several other

boundary conditions, like cell type and pharmacological treatment.

4 Conclusions

In this paper we have given a broad understanding of the Immune System and

we have presented two models for its simulation (i.e., a large-scale agent-based

model, and a simpler stochastic one), each model has been introduced together

with its strength key points, and with its pertinence context. It is worth men-

tioning in our conclusions, which are the modeling factors that have to be taken

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26 G. Stracquadanio et al.

into account in the choice of a modeling approach for the IS. If the choice is

between a more complex agent-based model versus a stochastic simpler model,

there are three factors that play a major role in the modeling outcome: (i) simula-

tion time, (ii) model precision and accuracy, and (iii) model applicability. Where

simulation time is concerned, stochastic models have surely to be preferred; in

fact, models here outlined base their evolution process on the evaluation of a

stochastic function; e.g., the Gillespie algorithm used in SPiM, guarantees light

binaries and execution times in the order of seconds on a desktop computer for a

small model, such as the one we presented on HBV. As far as agent-based mod-

els are concerned, execution times are generally larger of at least one order of

magnitude, moving towards minutes and, according to the number of molecules

involved in the simulations, maybe towards hours. It is also interesting how, for

agent-based and cellular automata models, there is a direct mapping (through an

opportune scaling factor) between simulated time steps and real-world timing;

the latter, can provide interesting insights about the reliability of an IS simula-

tion and its biological plausibility (e.g., a model where humoral immune response

is seen within the same day of the infection has to be preferred when compared

to another model where the same response can be observed only after a simula-

tion time that corresponds to one year in real-world timing). The second factor

that has to be considered in the modeling is the precision and the accuracy: if

stochastic models provide faster answers, with agent-based models we can track

the behavior of the single cell/molecule involved in the system and then we have

a significantly higher precision in the model controlling. This means, for instance,

that we can operate single element alterations at run-time (e.g., an unexpected

mutation), without the need of hard-coding this event in our model specification

(as one has to do in π-calculus and in process algebra in general). Moreover,

in agent-based models, we can tune affinity and the equivalent of reaction rate

constants at run-time. Finally, we can track the behavior of a family of agents

involved in the system and then study how different cell populations interact one

versus the other. These interesting features of agent-based models, come with

a price, that is the longer execution time discussed above. The last factor here

discussed, is the model applicability and its pertinence: with this argument we

want to highlight the fact that not all the modeling approaches can be really

extended towards the perfect virtual simulation that has a 1:1 mapping with re-

ality. With respect to this, it is worth noting that when the spatial characteristic

of the IS has to be simulated, stochastic models based on the Gillespie algorithm

loose one of their theoretical axes, that is the fact that all of the molecules in

the simulation are in a “well-mixed” context. Recent extensions of the Gillespie

algorithm have been proposed to account for the spatial information [32]; in

an example in which there are areas where Antigens are the majority and the

immune response begins, then there are regions where almost nothing happens,

and finally there are other regions where naive lymphocytes are the majority, it

seems clear that the spatial information has an important role.

In conclusion, where SPiM based modeling of the IS is concerned, its features

are definitely preferable when either light computation or system modularity are

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Large Scale Agent-Based Modeling of the Humoral27

more important than model precision and accuracy and when the spatial as-

pect of the system does not play an important role. Finally, moving towards

the virtual lymph node, agent-based models, and in particular the 20 bit model

here presented, seems a valuable approach for the simulation of this (very)large

scale system, made of a number of cells/molecules in the order of 108, that can

interact among eachothers in a spatially aware context where different regions

are devoted to different functions. In the following we give some insights about

possible applications of such a system. Biological transferability and applicability

of a very-large scale system are important and wide; where prevention therapies

are concerned, a verified computational model could be employed in the develop-

ment of new vaccines. The idea would be to perform a simulation on a number of

new molecules (e.g., molecule [A] and molecule [B]) and study how they interact

with the Host, i.e.: f(newmolecule) and among eachothers, as the effect could be

additive (f([A] + [B]) = f([A]) + f([B])), neutral, i.e.: molecules designed for a

competing aim ignore eachothers resulting in f([A]+[B]) = f([A]) = f([B]), or

even disruptive. With a verified IS computational model, we could even study

time-series of the simulated response – a practical application would be (i) to

modulate vaccine injection schedule in order to have and enhanced immuniza-

tion; (ii) drug resistance could be studied in terms of time-series as well. To

move towards such beautiful scenarios, we are currently considering the conver-

sion of the Binary epitope into a realistic one, built on top of the amino acid

alphabet; with respect to the latter point we are investigating an alternative

epitope library employing an accepted framework [33] for the (i) Single- and (ii)

Multi-Objective modeling approach aimed at a design of the antibody comple-

mentary determining regions that is (iii) extended with the notion of functional

Robustness [34] at the epitope binding task.

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