Overview of IMMSIM

We have created a computer simulation of an immune system with the idea of establishing a new experimental technique, called in machina. Our primary motivation is to understand interactions between the entities of the immune system. We presently have a running simulation that includes B-cells, T-cells, macrophages, antigens, antibodies, and lymphokines. Other entities can easily be added as desired. The model, called IMMSIM, attempts to incorporate a realistic description of the humoral side of the immune system and to examine questions concerned with clonal selection. Newer versions of IMMSIM also include the cellular response.

We chose a cellular automaton implementation for this model. Its advantages are two-fold: it allows inclusion of the intrinsic complexity of the system without great difficulty, and the description of the various entities and interactions is made in biological rather than mathematical terms. The usual rules for cellular automata are the following:

• They consist of a discrete lattice of sites.
• They evolve in discrete time steps.
• Each site takes on a finite set of possible values.
• The value of each site evolves according to the same deterministic rules.
• The rules for the evolution of a site depend only on a local neighborhood of sites around it.

The system used for IMMSIM has been called a generalized or hyper cellular automaton. The modifications involve the italicized portions of the rules above. They are changed as follows:

• Deterministic is replaced by probabilistic.
• Local neighborhood of sites around it is replaced by the site itself.

And we add a sixth rule:

• Entities can move from site to site.

The IMMSIM model uses a 2-dimensional grid to represent a small portion the body. Each site, rather than being binary as in the game of life, can be populated with a number of distinct entities of several types. The entities involved consist of B cells, T cells, non-specific antigen presenting cells (APC), antigens, antibodies and antigen/antibody complexes. They are endowed with binary receptors, epitopes and peptides. Schematics of the three types of cells are shown in Fig.~1 for the case of 8-bit receptors. The segment labeled receptor is the specific clonotypic receptor which T and B cells possess. In addition B cells and APCs possess class II major histocompatibility molecules. An APC is nonspecific so it does not have a specific receptor but it will have the same MHC molecules as possessed by the B cell. In addition an APC possesses an Fc receptor. It is not specifically denoted on the cell since it is the same for all APCs. However, it is allowed to bind to the Fc region of an antibody when the antibody is complexed to an antigen.

Antigens are represented by a number of segments representing epitopes and peptides. The epitopes are the segments to which the B and A cells can bind. A B cell will bind if its receptor matches the antigen in a complementary fashion, i.e., zero binds to one and vice-versa. The peptides are the segments of the endocytosed antigen that are presented on the MHC molecule. In reality they are obtained by breaking down the antigen. However, since no biochemistry is done in the model the peptides must be specified along with the epitopes when defining the antigen. Examples of antigens are shown in Fig.~2. Under the proper conditions, as described below, B cells produce antibodies. These antibodies will contain an epitope, identical to the receptor of the B cell producing it, and a peptide. They also contain an Fc epitope which need not be explicitly noted since it is the same for all antibodies.

The core of the model is concerned with the capturing and processing of antigen and how that processing affects the population and activity of the cellular components. A cartoon of the steps in antigen processing by B cells is shown in Fig.~3. Antigen capture and processing are performed by B cells that bear a receptor specific for the antigen. To begin a B cell attempts to bind to the epitopes of the antigen. This binding depends on the number of matching bits. Typically the binding strength decreases with the number of mismatching bits.

The binding and processing of antigens can also be carried out non specifically by APCs in a two ways: directly with a low interaction strength or in an antibody facilitated fashion (by means of an Fc receptor) with intermediate interaction strength. Once the antigen is bound by either a B or A cell the peptides are processed for presentation by the MHC. The MHC molecule is divided in half. The left-hand four bits represent the bare part of the MHC to which the T-cell receptor will bind. The right-hand four bits represents the MHC groove onto which the peptide binds. Binding takes place between the MHC groove and one half of the peptide. The other half of the peptide is presented to the T cell. Therefore, as shown in the right hand side of Fig.~3, the T cell sees an eight bit segment consisting of the left-hand four bits of the MHC and the four bits of the peptide which did not bind to the MHC. The T cell receptor is then allowed to bind to this MHC/peptide complex with the same rules as a B cell receptor binding to an epitope.

When a successful T-cell binding takes place both the T cell and B cell are allowed to divide to establish clones of their own type (if presentation takes place by an A cell only the T cell divides). Some of the daughter B cells become plasma cells and produce antibodies. In the model self-nonself discrimination is obtained by pre-selection of one of the two lymphoid populations. The B cells are chosen randomly with complete diversity (i.e., 2ⁿ types, where n is the number of receptor bits). The T cells are also chosen in the same way but then they are passed through the thymus. In the model thymus they are exposed to self-peptides presented on APCs and if they bind they are eliminated proportional to the strength with which they bind. Since the thymus is a dense organ we can allow the same T cell to be exposed to all the MHC/peptide combinations many times. If the number of times is great enough the thymus will be very efficient and most of the self-reactive T cells will be eliminated.

A typical experiment is set up as follows. First the system is populated with the desired number of APCs and B and T cells. Second a schedule of injections of antigen is chosen. Third the simulation itself begins. In each site all possible interactions are considered. Interactions, which are restricted as to the type of the entities involved, can take place only between entities in the same compartment of the grid. If a single entity is capable of having more than one successful interaction the one that actually happens is determined stochastically. After all interactions are decided upon they are implemented together. Then the birth of new cells occurs, both clonal growth and the birth of new virgin cells. Cells are also allowed to die with a given half life. Then all entities are given an opportunity to diffuse into the neighboring sites. This constitutes a time step. The process can be repeated for as many time steps as desired.

The above is only an abbreviated description intended to let the reader understand the nature of the approach. A fuller more detailed description can be found in Seiden and Celada [1992].

The following images are frames from a video of an experiment simulated with the cellular automaton model of the immune system. The two images are views of the system at the same elapsed time after a primary (left) and secondary injection (right) of antigen:

Left: Since this is the initial exposure to antigen, there are few B cells with a high affinity for the antigen, and most B cells in the system have low affinity. As clonal selection begins the number of high-affinity cells, both B and T, increase. Here, the T cells have gotten a head start, because they are presented with the antigen first by the macrophages, while the high-affinity B-cell population has not yet begun to grow.

Right: In this frame, the same antigen has been introduced but the immune system, having been previously exposed, has produced memory B and T cells specific to that antigen. The proportion of high-affinity cells increases relative to the low-affinity ones, because the former have a greater chance of binding to antigen and thus initiating the cloning process. The response is so strong that the invading antigen will be eliminated long before it has a chance to do any damage.

Key B cells (high affinity) Dark Blue Circles B cells (low affinity) Light Blue Circles T cells (high affinity) Red Diamonds T cells (low affinity) Pink Diamonds Macrophages Green Circles Antigens Small White Circles

The larger B cells superimposed with a T cell upon them are the cells that are in the midst of dividing (the larger size is created just to distinguish them).

Designed & built by: Steven Kleinstein with Philip E. Seiden