Modeling The Immune System

Shlomo Ta'asan
Carnegie Mellon University



The immune system is one of the most complex and exciting systems consisting of a variety of agents which exhibit behavior which ranges on disparate spatial and temporal scales. Its complexity is probably second only to that of the nervous system. Its functioning results from a sophisticated interplay of the subsystems, each of a great complexity by itself. Extensive studies of the subsystems have been done both experimentally (1-5,7-9,16,29,36-43,46-51,54,56-57,60-63,70,71,83,85,90) as well as by modeling (6,9-15,17-28,30,32-35,43-46,52,53,55,58-59,64-69,72-82,84,86-89,91). However, the integrated behavior of the full system is still a major challenge. The need for global modeling of the system is clearly a necessity for an understanding its dynamics and its complex response patterns. The importance of such efforts has recently been expressed by two leaders in the field of immunology, A.K. Abbas and C. Janeway [90]: "The impressive advances in immunology are largely a triumph of reductionist approaches .... The greatest gap in our knowledge is where the reductionist approaches fail. For instance we know relatively little about the development of adaptive immune response in vivo, and even less about the largely neglected area of innate immunity, particularly its role in inducing the interplay between innate and adaptive immunity." The resolution of the system complexity may come only by the multidisciplinary effort of immunologists, modelers, mathematicians, software engineers and probably other participants.

The immune system interacts with the environment which is an abundant source of different pathogens including toxins, bacteria, viruses and parasites. Environmental conditions influence the dynamics of the immune system and sometimes the challenges posed by the environment are too big to be met by the immune system. The dynamics of the two is tightly connected.

There are several major challenges in modeling the full immune system. First, the disparate spatial and temporal scales that need to be treated simultaneously; cell-cell interaction, cell-cytokines interaction, disparity of cell and molecular sizes. Second, the limitation on the possible measurements in the system; some aspects of the system are not measurable directly (without killing the animal involved). Third, the complex interaction of several subsystems which cannot be separated. Fourth, the nonlinear aspects involving bifurcation, possible chaotic behavior in some responses, ``phase'' transition and more. Quantitative modeling is a necessity.

Our study of the system aims at some of the major issues by using: 1) a model involving all the subsystems (innate and adaptive); 2) a multiscale representation of the system; 3) a hybrid discrete-continuous modeling; 4) parameter estimation methodology for quantitative prediction capabilities. The goal is toward a quantitative model of the full system, since only this approach can guarantee a true understanding of the system. The development requires the resolution of different mathematical questions as well as certain computer science challenges for fast computations, as well as immunological questions that can be answered only by use of modeling.

One of the main functions of the immune system is to protect the organism from invading pathogens. The system has evolved to consist of a wide range of distinct cell types, each with important roles, and a set of different strategies that allow successful elimination of a wide variety of pathogens, including viruses, bacteria and parasites. Primitive immune system mechanisms, such as lysis via the complement cascade, are very rapid but not very discriminatory on their own and are relatively easily evaded by potential pathogens. Phagocytosis and killing of invading organisms by polymorphonuclear (PMN) and mononuclear leukocytes is a significant improvement in both the range of effector mechanisms and the detection of foreign agents. The antigen-specific mechanisms of lymphocytes ( T cells and B cells) are the most advanced and most precise mechanism of host defense. Yet none of these facets of host defense successfully protects the host independent of the others. Since the host defense function of phagocytes has evolved in the presence of the complement system, the cells are highly dependent on the complement cascade for activating and discriminating signals. Adaptive immunity has evolved in the presence of both of these systems, and thus is highly dependent on complement and phagocytes for antigen recognition as well as effector functions. Moreover, antibodies produced by the specific immune system are used to augment the function of underlying defense systems, such as in antibody-mediated complement activation and antibody-dependent phagocytosis. Although it is often convenient to examine the contribution of individual cells and systems in isolation, the components of host defense, tissue repair, and homeostasis systems are highly integrated. These observations serve us as a main guidance in our research which deals with putting together all the subsystems and their interactions for accurately modeling the immune system and unfolding its complexity.

We describe next in some details the main components of the immune system since all appear later in the formulation of the proposed model, which serves as the basis for this project. However, due the complexity of the interactions in the system we take the liberty of simplifying certain aspects in order to present a clear picture. The full model description cannot fit within the page limitation of this proposal. The different mechanisms that the immune system employs to protect the body include: lysis, opsonization, cytotoxicity, phagocytosis and specific responses by B cells and T cells.

The complement serves as an auxiliary system in immunity, both on its own and by interaction with humoral immunity. On its own, it represents a primitive surveillance for microbes, independent of antibodies or T cells. During evolution, it became tightly coupled to the humoral immune system at multiple levels and now represents a major effector system for antibodies. The complement system comprises more than 30 plasma or membrane proteins. Three different pathways of activation have been recognized, triggered by either target-bound antibody (the classical pathway), by polysaccharide structures of microbes (the MBLectin pathway) or by recognition of foreign surface structures by complement itself (the alternative pathway). All three merge into the activation of the protein C3 and, subsequently, to that of the protein C5. In the common terminal pathway, further complement components are activated and assembled into the membrane attack complex (MAC), which can directly bring about lysis of a microbe. The ability of the complement to eliminate foreign invaders is limited, as many pathogens have evolved to by pass the complement mechanism.

While most bacteria activate the complement system, an infection by a virus causes a different pattern of immune response. Infected cells release certain soluble molecules that slow down the replication of the virus and at the same time attracts NK (natural killer) cells, that are specialized in killing infected cells. These cells upon activation by infection, release certain molecular agents that attract macrophages to the site of infection. These recruited cells then perform the cleaning of tissue by phagocytosis of the dead cells. In addition they release some other molecular agents that promote tissue repair.

Toxins released by bacteria may cause tissue damage which initiates a response by causing a series of molecular events, resulting in the production of soluble pro-inflammatory mediators. These cause several effects including increased blood flow and vascular permeability, migration of leukocytes from the peripheral blood into the tissues, accumulation of these leukocytes at the inflammatory focus, and activation of the leukocytes to destroy and (if possible) eliminate the foreign substance. Neutrophils that migrate into the tissue ingest pathogenic material by phagocytosis, and detoxify and digest this material by the actions of endogenous oxidant and proteolytic enzymes. As the foreign threat is eliminated, anti-inflammatory mediators permit the process to wind down, so as to avoid unnecessary and excessive damage to the tissues surrounding the inflammatory focus. If this acute process results in only incomplete destruction and/or elimination of the foreign substance, the inflammatory process persists and expands its repertoire of soluble mediators and cellular components. The way in which the inflammatory process is initiated depends in part on the nature and portal of entry of the foreign substance and, to some degree, the nature and circumstances of a particular individual.

The efficient response of the immune system has to do with a special mechanism of communication which is facilitated by a large set of molecular mediators. They are classified into several categories, and the most significant ones are cytokines and chemokines. The cytokines functions are numerous and include cell activation, proliferation, effector functions and more. Chemokines, on the other hand, serve for attracting specific cells into areas where they are needed. Also cell-cell interaction is promoted by the secretion of specific chemokines that attract the proper cell required for a given interaction. Probably not all of these chemokine facilitators are understood, but it seems that the immune system uses this mechanism extensively.

The lymphocytes (T cells and B cells) occupy central stage in the immune system because they are the cells that determine the specificity of immunity. The B and T lymphocytes of the immune system express specific receptors that have a high degree of specificity and sensitivity for foreign antigen. It is their response that orchestrates the effector limbs of the immune system. These cells are also responsible for the development of immunological memory, a hallmark of the adaptive immune response. Cells that interact with lymphocytes play critical parts both in the presentation of antigen and in the mediation of immunologic functions. These cells include the monocyte/macrophages, dendritic cells, and the closely related Langerhans cells, as well as natural killer (NK) cells, mast cells, basophils, and other members of the myeloid lineage of cells.

Recognition of a pathogenic infection leads to the development of killing/inactivation mechanisms tailored to individual pathogens, which may be carried out by specific T cells (cytotoxic T cells), antibodies or phagocytic cells (macrophages). It has become apparent that different effector mechanisms are required to eliminate individual pathogens. Thus, an important challenge for the immune system lies not only in the recognition of foreign invaders, but also in the initiation of the appropriate effector response. There are numerous examples in which an inappropriate effector response will lead to overwhelming infection and death, whereas a different response efficiently controls and eliminates the pathogen. In addition, these responses are highly regulated in order to avoid problems with autoimmunity and to control responses that can, if left unchecked, have grave immunopathological consequences.

 Modeling Issues