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A model for simulating cognate recognition and response in the immune system

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A model for simulating cognate recognition and response in the immune system
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  J. theor. BioL (1992) 158, 329-357 Model for Simulating Cognate Recognition and Response in the Immune System PHILIP E. SELDEN AND FRANCO CELADA~ t IBM T. J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598 and ~ Hospital for Joint Diseases, 301 E. 17th St., New York, NY 10003, U.S.A. Received on 5 October 1991, Accepted in revised form on 25 March 1992) We have constructed a model of the immune system that focuses on the clonotypic cell types and their interactions with other cells, and with antigens and antibodies. We carry out simulations of the humoral immune system based on a generalized cellular automaton implementation of the model. We propose using computer simu- lation as a tool for doing experiments in machina, in the computer, as an adjunct to the usual in oioo and in oitro techniques. These experiments would not be intended to replace the usual biological experiments since, in the foreseeable future, a complete enough computer model capable of reliably simulating the whole immune would not be possible. However a model simulating areas of interest could be used for exten- sively testing ideas to help in the design of the critical biological experiments. Our present model concentrates on the cellular interactions and is quite adept at testing the importance and effects of cellular interactions with other cells, antigens and antibodies. The implementation is quite general and unrestricted allowing most other immune system components to be added with relative ease when desired. I Introduction A scientific discipline in rapid expansion, immunology has built up a body of observa- tions, proven facts, theories tested and confirmed experimentally, that we shall call the hard core. This body is today large and solid enough to offer a rather credible picture of the immune system s structure and functions. This picture will probably not change drastically in the future, although the perspective of it in the context of biology could very well undergo significant modifications. Beyond the core is a large area of soft material that awaits confirmation in order to produce an advancement that could expand the core. Examples are, confirmed facts that cannot be interpreted unambiguously or on the relevance of which there is no consensus, and ideas and hypotheses that have not yet been confirmed by experiments because the necessary technology is not yet available. Hypotheses that tend to undermine traditional views are the most stimulating but may also be the most difficult to test and the least likely to survive. Experimenters are known to hesitate before engaging in high risk experiments: this is only natural but leaves many wild and perhaps important experiments undone. One reason for hesitation is that biological experiments, both in vivo and in vitro, are labor intensive and expensive. 329 0022-5193/92/190329 + 29 08.00/0 © 1992 Academic Press Limited  330 P E SEIDEN AND F CELADA We thought that it would be useful to build a system where critical experiments on the immune system can be performed in a computer in order to predict the effects of experimental modifications on the immune system, and thus offer a criterion for the selection of the most likely meaningful biological experiments. That is, in m chin experiments may precede, guide, help interpret--but obviously not substitute for-- the in vitro or in vivo experiments. These experiments will have two advantages. Firstly, they will be relatively cheap and easy to do. Secondly, in contrast to the usual biological experiments, everything about the experiment can be measured in all its detail. Often one believes that a certain property of an element of the immune system is responsible for the results observed but finds that it is difficult or impossible to measure with the tools at hand. This is not true in a computer. Every aspect of the system is measurable so that any idea can be tested. The purpose of the present modeling is to create a system in which the hypotheses about interactions between system elements can be probed and tested. In order to do this we want the system to incorporate the principal core facts of today s immunological knowledge, in particular those concerning the interaction of the cells with internal (self) and external (non-self) entities and the mode and language of cell-cell communication within the immune system. Since it is clear that cell-cell communication is critical for the cellular immune response, we want to be able to change the various interactions and test the results of such changes. In addition we wish to look for co-operative effects and perhaps even phase transitions, effects which are known to exist in other m ny body systems. Most attempts at modeling the immune system, as well as other biological phenom- ena, have involved setting up a system of differential equations that are believed to represent the behavior of the system and then try to solve the equations (Perelson, 1990). In general the equations are too complicated to solve as they stand so many mathematical approximations must be made to allow solutions to be obtained. One major difficulty is non-linearities; non-linear equations are difficult to solve but non- linearities are essential to the system. We have chosen a different approach, that of a simulation using a cellul r utom ton (Wolfram, 1986). The advantage of such a technique is two-fold. Firstly, we are able to represent the components and processes of interest in biological language so that the approximations we make in allowing the simulation to be carried out are usually more biological in character than mathe- matical. We would hope that this would allow a better assessment of the applicability of the results. Secondly, it is easy to modify the complexity of the interactions without introducing any new qualitative difficulties in solving the model; non-linearities are not intrinsically difficult to handle. However, there are penalties to be paid for this. Firstly, we will always be dealing with a finite system. In reality the immune system is gigantic, in humans involving 10 2 cells of perhaps 109 specificities. The simulations will always be much smaller and we must pay constant attention to whether the results we see are artifacts due to our restricted size. Secondly, it will sometimes be harder to extract the essence of what is happening. Three hundred years of experience with differential equations gives us a feel for the significance of the various terms in the differential equations we write down. The field of cellular automata is much younger and much less is  SIMULATING THE IMMUNE SYSTEM 331 known about them, so our intuition is less well developed. Nevertheless, we feel that the ability to be closer to biology and biological thinking and to be able to make biological approximations rather than mathematical ones greatly outweighs this problem. In the event we will be able to also use differential equations where conveni- ent and have the advantage of looking at the same problem in complementary ways. There are many questions immunologists would like to ask if they had a working model where experiments could be performed by introducing various changes in the starting elements or in the rules. Typical questions that may be asked of such a model are the following: --Is the idiotypic network concept central to the development/function of the immune system, or an inevitable consequence of self recognition? --Can massive autoimmunity be avoided without B-cell tolerance and without suppression? --What is the impact of immune complexes on the patterns of the secondary response? --Can the quality of the immune response be altered if the paratope of the processing B-cell influences the presentation of peptides to T cells? --What is the effect of exposure to multiple antigens on the rheumatoid factor formation if the antigen moiety of an immune complex can be processed and presented by rheumatoid factor B cells? --Is direct recognition of polymorphic MHC by the T-cell receptor necessary for the generation of the T-cell repertoire? 2 The Model Obviously, we cannot contemplate including the entire immune system in our model, it is much too big for that. Our model focuses on those components which are essential for the initiation and regulation of the humoral immune response, and constitute the effect of this response on the body fluids. 2.1. THE CELLS A central feature of the model is the inclusion of two sets of lonotypi elements, B cells and T cells. Each cell possesses a receptor which is represented as a binary string of N bits with a fixed, directional reading framer. Each cell will then have a receptor diversity of 2 ~. A T cell has only the single N-bit receptor. The B cell also has an N-bit receptor but in addition possesses N-bit major histocompatibility complex molecules MHCs). In addition to the two clonotypic cells we also include non-specific antigen presenting t The idea of a binary receptor was introduced by Farmer et a 1986). In their model they allowed a sliding interaction between entities. For example, for an N-bit antigen and an M-bit receptor, with M< N they would look for the best M-bit fit available along the N-bit antigen. We insist that the antigen and receptor be in register and be of the same length. An antigen may consist of P segments but each segment consists of N bits and each segment is presented to a receptor in the same alignment.  332 P. E. SEIDEN AND F. CELADA cells such as macrophages). We call these APCs or A cells) and although they do not have a specific antigen receptor, they do possess the same MHCs as the B cells. Examples of B cells, T cells and A cells are shown in Fig. 1. The use of identical elements to depict all structures with diversity is made possible by setting the rules of the system to allow only certain interactions to take place e.g. antigen/B cell, MHC-peptide, etc). That is, although the B-cell and T-cell receptors are formally the same molecule as explained below, we allow bare antigen to interact only with the B-cell receptor and the MHCs to interact only with the T-cell receptor. The B cells exist in two forms. One is the active antigen binding B cell virgin or memory) and the second is the plasma cell. The plasma cell is created during the clonal division of stimulated B cells, as described in section 2.3, and their role is to create antibodies that are released into the body fluids. 2.2. THE MOLECULES Antigens Ag) are represented by a number of N-bit segments representing epitopes and peptides. Epitopes are defined as the portion of an antigen that is recognized by a B-cell receptor. Peptides are defined as the portion of the antigen that can be bound by an MHC molecule and be recognized by an appropriate T cell. The epitopes and peptides are specified separately since an epitope corresponds to a fully folded three- dimensional structure while the peptides are the pieces of the antigen broken down by endocytosis and do not necessarily have a simple relationship to the epitope. Therefore, an antigen is denoted by a number of segments, some representing epi- topes and others peptides. Some examples are shown see Fig. 2). The epitopes are represented by the exposed segments, it is to these segments that B cells and antibod- ies may bind. The boxed segments are the peptides, the segments which can be Receptor 57 MHC 37 MHC 37 Receptor 186 T FIG. i. Examples of an APC B ceil and T cell for the case of N= : The integer names of the 8-bit segments re the decimal values of the binary strings.  SIMULATING THE IMMUNE SYSTEM 333 presented on the MHC molecules of the B cells and A cells that have bound the antigen by means of an epitope. Model antibodies Ab) are taken to have the same form as antigens and have a paratope which is identical to the receptor of the B cell plasma cell) that secretes them. Besides the paratope the antibody can contain both foreign arising from the variable regions) and self arising from the constant regions) peptides. Lastly, it contains the Fc portion, an epitope identical for all antibodies. A cartoon of an antibody is shown in Fig. 3. Our representation is shown as the bottom diagram of Fig. 2. It is not necessary to explicitly show the Fc epitope since it is the same for all antibodies just as we did not explicitly show the A-cell receptor). The Fc portion Antigen 8 2 8 Antigen 198 8 67 23 145 Antigen I U-H I 38 72 173 245 _H_H I H I Antigen 48 27 203 FIG. 2. Examples of antigens for N= 8: The epitopes are shown as exposed segments and the peptides as boxed segments. The integer names of the 8 bit segments are the decimal values of the binary strings.
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