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1986 | Buch

The Structure of Mathematical Immunology Kapitel lesen Erstes Kapitel lesen

Immunology and Epidemiology

Proceedings of an International Conference held in Mogilany, Poland, February 18–25, 1985

herausgegeben von: Geoffrey W. Hoffmann, Tomáš Hraba

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Biomathematics

Enthalten in: Professional Book Archive

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Über dieses Buch

In February 1985 a small international meeting of scientists took place at the recreation resort of the Polish Academy of Sci­ ences in Mogilany, near Cracow, Poland. The initiative for holding the workshop came from a working meeting on mathematical immunology and related topics at the International Institute for Applied Sys­ tems Analysis in Laxenburg, Austria, in November 1983. In addition to representatives of IIASA, delegates of the IIASA National Member Organizations (NMO) of Czechoslovakia, Italy, and the soviet Union took part in that working meeting. The participants came to the conclusion that IIASA could play an important role in facilitating the development of research in this field. The first step that they recommended to I IASA was to organize a workshop on mathematical immunology. The purpose of the workshop was to review the progress that has been made in applying mathematics to problems in immunology and to explore ways in which further progress might be achieved, especially by more efficient interactions between scientists working in mathematical and experimental immunology. Some National Member Organizations contributed to the success of the workshop by nominat­ ing further participants working in this or related fields. For instance, thanks to a suggestion of the British NMO, the meeting also included analyses of the interactions between the immune state of a population and epidemiological phenomena. There were 33 participants at Mogilany from 11 countries, namely Canada, Czechoslovakia, Federal Republic of Germany, Hungary, Japan, Netherlands, Poland, Sweden, united Kingdom, USA, and USSR.

Inhaltsverzeichnis

Frontmatter

Overview

Frontmatter
The Structure of Mathematical Immunology
Abstract
Mathematical immunology is a young (some might even say immature) but nevertheless wide-ranging discipline. In order to put the papers of this book into a broader context, we here give a brief, necessarily sketchy, overview of some of the main areas of mathematical immunology, not all of which were represented at the Mogilany conference. A more comprehensive overview of the range of the subject may be gained from the collective contents of several monographs and collections of papers on mathematical immunology (1–6).
G. W. Hoffmann, T. Hraba

Regulation

Frontmatter
Some Notes on Mathematical Modelling of the Immune Response
Abstract
“Although the majority of theories in immunology have been non-mathematical, there are a variety of quantitative questions whose solutions require mathematical analysis and mathematically formulated models” (Bell and Perelson 1978). It is necessary to subjoin that not only quantitative but many qualitative questions, too, require appropriate mathematical solutions (e. g., by the use of kinetic logic — see Přikrylová and Kůrka 1984).
Miloš Jílek, Daniela Přikrylová
On Paradoxes and Progress in Theoretical Immunology, and Evidence for a New Symmetry
Abstract
A view is offered on how we might collectively and perhaps objectively judge which of a variety of theories of regulation are the best, and thus decide which theories should be adopted as standard models for more detailed work. A new theoretical symmetry relationship is then presented for pairs of anti-sera of the type A anti-B and B anti-A, together with experimental evidence validating the relationship. The evidence includes a new phenomenon relevant to transplantation immunology, that we call “reverse enhancement”.
Geoffrey W. Hoffmann, Anwyl Cooper-Willis, Michael Chow
Antigen recognition by T cells.-Towards a Mathematical Description of the T Cell Specificity Repertoire
Abstract
The usefullness of mathematical equations as an adequate description for certain immunological phenomena is occasionally recognized even by experimentalists (see 1, 2). A well known example is the mathematical treatment of antigen-antibody interactions and a more recent example is the paper by Matis et al. (3). Some theoretical implications of this and several related papers shall be discussed in this commentary. These considerations lead to a mathematical description of the T cell specificity repertoire.
Wulf Dröge
Mathematical Modelling of the Immune Response: A Model of The Proliferation Control
Abstract
The successful immune response to given antigen is manifested by elimination of antigen; generation of antibody forming cells and production of antibody (if humoral response) or cytotoxic cells (if cellular immunity); and generation of memory cells. Memory cells remain in the organism after primary response, and they prove that the secondary response is more efficient. Such a process is the result of an intricate interaction within the multicomponent immune system. Although at the present time all major components (cell populations) which take part in the immune response are probably known, the question how these components interact during the course of the immune response has not been solved satisfactorily yet. In our model we have tried to formulate the relations between cell populations taking part in the immune response, which seemed to be substantial for its proper function.
Daniela Přikrylová
Further Development of the Mathematical Model of Immunological Tolerance
Abstract
Our mathematical model of immunological tolerance to human serum albumin (HSA) in chickens [1, 2] was formulated on experimental evidence suggesting that the major mechanism underlying the inhibition of anti-HSA antibody production in tolerant chickens was Β cell tolerance [3, 4]. The relevant experiments were carried out in chickens of homogeneous inbred lines and that made possible lymphoid cell transfers among the syngeneic experimental birds. The existence of suppressor cells induced in tolerant chickens was not proved by these cell transfers. This finding suggested a direct inhibition of immunocompetent cells (ICC) by the tolerizing administration of antigen. The inhibition was apparently irreversible, as escape from tolerance was not observed in the spleen cells of tolerant birds transferred to non-reactive recipients. In contrast to the situation in mammals tolerant to xenogeneic serum proteins, neonatal thymectomy did not detectably influence tolerance to HSA in chickens. On the other side, neonatal bursectomy increased and prolonged substantially the tolerance in chickens. From these and other findings we concluded that Τ cells do not play any substantial role in this tolerant state and that the major mechanism operating there is clonal deletion or irreversible inactiva-tion of Β lymphocytes.
T. Hraba, J. Doležal

Infectious Disease Immunity, Tumor Immunity

Frontmatter
Mathematical Modelling of Infectious Diseases
Abstract
At present the problems of immunity attract steady attention of the scientists from many countries. Such interest is not occasional. The proper functioning of the immune system is one of the necessary conditions of the viability of man. The functions of this system are numerous. It defends the organism from various infectious agents like bacteria and viruses, provides the destruction of mutant, in particular, cancer cells. Disturbances in the functioning of the immune system lead to various pathologies, for instance, the autoimmune and allergic diseases. It is also a well-known fact that immunity is one of the basic obstacles on the way of successful solution of the transplantation of the organs and tissues.
G. I. Marchuk, A. L. Asachenkov, L. N. Belykh, S. M. Zuev
Comparison of Stochastic Models for Tumor Escape
Abstract
In a previous presentation (Michelson, 1983), a stochastic compartment model describing antigenic modulation as an intragenerational tumor escape route was developed. In order to distinguish that model from a Darwinian selection mechanism, a second, intergenerational model has been developed.
Seth Michelson
Implications of Macrophage T-Lymphocyte Interactions for Tumor Rejectability
Abstract
A relatively detailed model of experimentally described macrophage T-lymphocyte interactions has been developed. In this model we investigate the immune response to tumors that differ in antigenicity and/or in initial size. Having deliberately omitted from the model tumor escape mechanisms (e.g. suppression, antigenic modulation or heterogeneity), we study the circumstances that nevertheless lead to progressive tumor growth.
The model behavior shows that: (1) tumor antigenicity can best be defined in terms of helper T cell reactivity; (2) small differences in the availability of HTL (*) markedly influence tumor rejectability; (3) compared with the impact of macrophages, the impact of CTL increases more with increasing tumor antigenicity; and (4) sneaking through and tolerance are intrinsic to this model.
HTL have a large impact on the model behavior (i.e. the immune response) because there are self-reinforcements in the HTL activation and proliferation process. Interestingly, unresponsiveness (tolerance) evolves in this model, despite the presence of these self-reinforcements and the absence of negative interactions (e.g. suppression). Tolerance is caused by a proliferation threshold that comes into existence when T-lymphocyte effectors are made short-lived. We discuss the advantages of using numerical integration combined with numerical phase state analysis. Stable steady states in this model do exist but are of minor importance.
Rob J. de Boer, Pauline Hogeweg

Epidemiology and the Immune System

Frontmatter
Models of the Dynamics of Acquired Immunity to Helminth Infection in Man
Abstract
Upon invading a host organism, parasitic species invariably trigger the defence mechanisms of the immune system. In vertebrate hosts, the system comprises of cells, antibodies, amplification factors and specialized organs. The immune system sometimes enables the host to regulate parasitic abundance and to build up a degree of acquired resistance to reinfection. However, in the case of most parasitic protozoa and helminths, the degree of acquired immunity illicited by infection is variable, and not so solid as that induced by many viruses or bacteria. In endemic areas of the world parasitic infections therefore tend to be persistent in character, where the human inhabitants are repeatedly exposed to reinfection and may harbour parasites for the majority of their lives. The major helminth infections of man (the intestinal nemotodes, the schistosome flukes and the filarial worms) are particularly remarkable in this sense, since man appears unable to develop fully protective immunity, despite repeated exposure to high levels of infection. In part, this is thought to be a consequence of the antigenic complexity of parasitic worms, and their often complex developmental cycles within the human host. Each developmental stage may express different surface or excretory antigens.
Roy M. Anderson
Dynamics of Childhood Infections in High Birthrate Countries
Abstract
The majority of the mathematical literature concerned with disease dynamics is concerned with transmission in populations of fixed size where net births balance net deaths. The current generation of models do not take account of case fatalities nor of positive population growth rates and are therefore of limited use to aid in data interpretation or for the design of optimal control policies in developing areas. A deterministic model for the epidemiology of an infectious disease which induces lifelong immunity is described. The model allows for age dependent case fatality rates and for population growth. Both equilibrium and dynamical results are discussed; the former in connection with the estimation of disease parameters from published data, and the latter with reference to the investigation of the possible effects of different vaccination strategies. Measles is used as an example throughout, and reference is made to the available data on the epidemiology of measles in tropical regions.
Angela McLean
Measurement and Estimation in Heterogeneous Populations
Abstract
Individuals differ in their susceptibility to various causes of morbidity and mortality. Epidemiologists are accustomed to thinking about this heterogeneity in terms of “risk factors” and “relative risks”. Some of the heterogeneity among individuals is genetic in origin and some is acquired as a result of individual behaviour (like cigarette smoking) or environmental exposure (to, say, water pollution). The levels of the risks faced by an individual change over time as the individual ages, changes his behaviour and is exposed to different conditions.
A. I. Yashin, J. W. Vaupel

Diverse Topics

Frontmatter
On Migratory Lymphocyte Models
Abstract
Linear time-delay models are developed and compared to other models for the circulation of lymphocytes throughout the immune system. A building-block synthesis of the lymphatic system is presented. The models mimick experimental tracer data for rats, but more extensive data is needed to do a good job of parameter estimation.
R. R. Mohler, Z. Farooqi, T. Heilig
Procedure for Evaluation of a Liquid Phase Radioimmunoassay Determining Immune Complexes in Sera
Abstract
Employment of the optimal mathematical procedure for determining a standard curve is essential for a proper evaluation of laboratory tests. These test results are then frequently calculated with the use of a standard curve, which expresses the relationship between the dose and response. This approach is also used in a liquid phase radioimmunoassay which employes binding of iodinated (125I) Clq as a measure of the presence of immunological complexes in serum samples. The present work describes our approach for calculation of the predicted variance — which is a rational for giving weights to empirical points composing the standard curve.
C. Łaba, H. Haas, J. T. Jodkowski, A. Lange
Application of Mathematical Models in the Membrane Electrophysiology of Macrophages
Abstract
In most cells there is a transmembrane potential difference, called a resting membrane potential (about -70 mV) arising from the unequal distributions of ions across the cell membrane and the selective permeability of the cell membrane for the various ion species. In nerve and muscle cells a sudden change in the ionic permeability of the membrane causes a rapid all-or-nothing change in membrane potential called an action potential. In nerve cells the action potential forms the basic information-carrying signal and in muscles cells it evokes cell contraction (27).
Can Ince
Metadaten
Titel
Immunology and Epidemiology
herausgegeben von
Geoffrey W. Hoffmann
Tomáš Hraba
Copyright-Jahr
1986
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-642-51691-7
Print ISBN
978-3-540-16431-9
DOI
https://doi.org/10.1007/978-3-642-51691-7