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In this paper, a cell-colony based formalism for the healing of superficial wounds is presented. The paper incorporates the migration, proliferation, and death of constituent cells, in the context of wound healing. The present study considers wound healing under ischemic conditions where a bacterial infection develops, which impairs the motility of the constituent cells. In this work, the performance of the immune response system is incorporated in the sense that migrating leukocyte are modelled which engulf the infectious pathogens. The model is based on both deterministic and stochastic principles. Simulation results are discussed in a biological context.

This paper is based on a new model of the immune network which explicitly incorporates B-T cell co-operation. A major feature of this model is the simplifying assumption that inhibition by anti-TCR soluble Ig is the only possible down-regulatory influence on activated T-cells. This model is capable of coupling with antigens in both an “immune response” mode and a “tolerant” mode. In the present paper, we simulate the ontogenesis of the immune system by metadynamical recruitment of T- and B-cell clones from the thymus and the bone marrow, seeking to identify the conditions under which each of these modes of antigen coupling occurs. Achieving the tolerant mode depends principally on four parameters: a high value of S B , the rate of bone-marrow production of B-cells; a relatively high efficiency of T-help through mIg-TCR recognition compared with (MHC + peptide)-TCR interaction; and a relatively high value of the product P R .N A , where P R is the average probability that an Ig recognizes another molecule and N A is the number of antigens which are present throughout ontogeny. Analysis of the conditions under which these two modes can coexist, shows that this is possible when a sufficiently numerous set of founder antigens couple in a tolerant mode, whereas isolated antigens first presented once development is completed couple in an immune response mode. The present model thus provides a possible mechanism for the distinction (hitherto purely descriptive) between a Central Immune System organized as a network and responsible for tolerance, and a Peripheral Immune System responsible for immune responses.

Onset and development of autoimmunity have been attributed to a number of factors, including genetic predisposition, age and different environmental factors. In this paper we discuss mathematical models of autoimmunity with an emphasis on two particular aspects of immune dynamics: breakdown of immune tolerance in response to an infection with a pathogen, and interactions between T cells with different activation thresholds. We illustrate how the explicit account of T cells with different activation thresholds provides a viable model of immune dynamics able to reproduce several types of immune behaviour, including normal clearance of infection, emergence of a chronic state, and development of a recurrent infection with autoimmunity. We discuss a number of open research problems that can be addressed within the same modelling framework.

Pancreatic cancer is one of the most deadly types of cancer and has extremely poor prognosis. This malignancy typically induces only limited cellular immune responses, the magnitude of which can increase with the number of encountered cancer cells. On the other hand, pancreatic cancer is highly effective at evading immune responses by inducing polarization of pro-inflammatory M1 macrophages into anti-inflammatory M2 macrophages, and promoting expansion of myeloid derived suppressor cells, which block the killing of cancer cells by cytotoxic T cells. These factors allow immune evasion to predominate, promoting metastasis and poor responsiveness to chemotherapies and immunotherapies. In this paper we develop a mathematical model of pancreatic cancer, and use it to qualitatively explain a variety of biomedical and clinical data. The model shows that drugs aimed at suppressing cancer growth are effective only if the immune induced cancer cell death lies within a specific range, that is, the immune system has a specific window of opportunity to effectively suppress cancer under treatment. The model results suggest that tumor growth rate is affected by complex feedback loops between the tumor cells, endothelial cells and the immune response. The relative strength of the different loops determines the cancer growth rate and its response to immunotherapy. The model could serve as a starting point to identify optimal nodes for intervention against pancreatic cancer.

Leishmaniasis is a disease caused by the Leishmania parasites. The two common forms of leishmaniasis are cutaneous leishmaniasis (CL) and visceral leishmaniasis (VL). VL is the more severe of the two and, if untreated, may become fatal. The hallmark of VL is the formation of granuloma in the liver or the spleen. In this paper, we develop a mathematical model of the evolution of granuloma in the liver. The model is represented by a system of partial differential equations and it includes migration of cells from the adaptive immune system into the granuloma; the rate of the influx is determined by the strength of the immune response of the infected individual. It is shown that parasite load decreases as the strength of the immune system increases. Furthermore, the efficacy of a commonly used drug, which increases T cells proliferation, increases in an individual with stronger immune response. The model also provides an explanation why, in contrast to humans, mice recover naturally from VL in the liver.

It has been known for some time that human autoimmune diseases can be triggered by viral infections. Several possible mechanisms of interactions between a virus and immune system have been analysed, with a prevailing opinion being that the onset of autoimmunity can in many cases be attributed to ‘‘molecular mimicry’’, where linear peptide epitopes, processed from viral proteins, mimic normal host self-proteins, thus leading to a cross-reaction of immune response against virus with host cells. In this paper we present a mathematical model for the dynamics of an immune response to a viral infection and autoimmunity, which takes into account T cells with different activation thresholds. We show how the infection can be cleared by the immune system, as well as how it can lead to a chronic infection or recurrent infection with relapses and remissions. Numerical simulations of the model are performed to illustrate various dynamical regimes, as well as to analyse the potential impact of treatment of autoimmune disease in the chronic and recurrent states. The results provide good qualitative agreement with available data on immune responses to viral infections and progression of autoimmune diseases.

Through careful mapping of the physiology of the T-zone and GC B-blast dynamics to a mathematical representation of the cell processes including proliferation, migration, differentiation, and cell death, a mathematical model is constructed to capture the dominant nominal primary, late follicular, and secondary humoral response toHaemophilus influenzaeType b. This model explicitly incorporates the dynamics of memory B-cells, T-zone and GC B-dynamics, IgM and IgG antibodies, avidity maturation, and IC presentation by FDCs into a coherent framework. This paper describes the relevant immunology, the pertinent physiological assumptions, the developed model, and the parameter identification procedure. The model parameters were found using a parameter identification procedure that capitalizes on the timing and interactions of certain dominant physiological attributes. Simulation results and validation tests indicate that the model reflects not only a nominal primary and secondary humoral immune response but also the tertiary and T-independent responses. The model shows robustness to variations in infection dosage, bacterial growth rate (virulence of the strain), and onset-timing of the secondary response. The utility of this model in studying the humoral immune response is demonstrated through suggested physiological assumptions, mechanisms, and rates to be eventually clinically evaluated as well as insights into vaccination design. The model and parameter identification techniques are easily adapted to other diseases which primarily evoke a humoral immune response.

Somatic cells, including immune cells such as T-cells have a limited capacity for proliferation and can only replicate for a finite number of generations (known as the Hayflick limit) before dying. In this paper we use mathematical models to investigate the consequences of introducing a Hayflick limit on the dynamics of T-cells stimulated with specific antigen. We show that while the Hayflick limit does not alter the dynamics of T-cell response to antigen over the short term, it may have a profound effect on the long-term immune response. In particular we show that over the long term the Hayflick limit may be important in determining whether an immune response can be maintained to a persistent antigen (or parasite). The eventual outcome is determined by the magnitude of the Hayflick limit, the extent to which antigen reduces the input of T-cells from the thymus, and the rate of antigen-induced proliferation of T-cells. Counter to what might be expected we show that the persistence of an immune response (immune memory) requires the density of persistent antigen to be less than a defined threshold value. If the amount of persistent antigen (or parasite) is greater than this threshold value then immune memory will be relatively short lived. The consequences of this threshold for persistent mycobacterial and HIV infections and for the generation of vaccines are discussed.

International audience; The occurrence of metastasis is an important feature in cancer development. In order to have a one-site model taking into account the interactions between host, effector immune and tumor cells which is not only valid for the early stages of tumor growth, we developed in this paper a new model where are incorporated interactions of these three cell populations with endothelial cells. These latter cells are responsible for the neo-vascularization of the tumor site which allows the migration of tumor cells to distant sites. It is then shown that, for some parameter values, the resulting model for the four cell populations reproduces the angiogenic switch, that is, the transition from avascular to vascular tumor.

In this paper we propose a model of tumor immunity in terms of discrete automata where each automation describes the concentration of one particular type of cell involved in immune response. In contrast to the earlier models of normal immune response, there is more than one type of cell surface antigen in this model. As a consequence, the tumor can evade destruction through humoral response by changing its identity. However, the tumor can be killed by the killer cells through cell-mediated response unless protected by a high concentration of the suppressor T cells.

The present approach to the mathematical modelling of infectious diseases is based upon the idea that specific immune mechanisms play a leading role in development, course, and outcome of infectious disease. The model describing the reaction of the immune system to infectious agent invasion is constructed on the bases of Burnet's clonal selection theory and the co-recognition principle. The mathematical model of antiviral immune response is formulated by a system of ten non-linear delay-differential equations. The delayed argument terms in the right-hand part are used for the description of lymphocyte division, multiplication and differentiation processes into effector cells. The analysis of clinical and experimental data allows one to construct the generalized picture of the acute form of viral hepatitis B. The concept of the generalized picture includes a quantitative description of dynamics of the principal immunological, virological and clinical characteristics of the disease. Data of immunological experiments in vitro and experiments on animals are used to obtain estimates of permissible values of model parameters. This analysis forms the bases for the solution of the parameter identification problem for the mathematical model of antiviral immune response which will be the topic of the following paper (Marchuk et al., 1991, J. theor. Biol. 15).

In this paper we propose a unified model of immune response in terms of discrete automata describing the concentrations of the cells constituting the immune network. The model of normal immune response proposed by Kaufman, Urbain and Thomas and that of auto-immune response proposed by Weisbuch, Atlan and Cohen are special cases of this unified model. Moreover, this model also describes the immune response in patients infected by the human immunodeficiency virus (HIV), the virus that is known to cause Acquired Immune Deficiency Syndrome (AIDS).

In this paper, a chronic viral infection model with cell-mediated immunity and immune impairment is proposed and studied, under the assumption that the presence of the antigen can both stimulate and impair immunity. It is shown that the virus persists in the host if the basic reproductive ratio of the virus is greater than 1. The immune cells persist when there is only one positive equilibrium. The system can exhibit two positive equilibria if the basic reproductive ratio of the virus is above a threshold. This allows a bistable behavior, and the immune cells persist or die out, i.e., infection will result in disease or immune control outcome, depending on the initial conditions. By theoretical analysis and numerical simulations, we show that therapy could shift the patient from a disease progression to an immune control outcome, despite that the therapy is not necessarily lifelong. This would allow the immune response to control the virus in the long term even in the absence of continued therapy.

The use of simple mathematical models to study the kinetics of drug action and decay within vertebrate hosts has a long history with a major objective being to derive drug dosage regimens that optimize efficacy and minimize toxicity to the patient. Mathematical models of the relationship between dosage, route of delivery, drug concentration in defined sites and effect on a particular pathogen are widely used in the pharmacological literature. A more recent literature is that concerned with the population dynamics of pathogen replication within the host subjected to pressures exerted by the human immune system. In this paper we develop a theoretical framework to meld both approaches with the aim of identifying threshold criteria that dictate the optimum pattern of drug administration for pathogen clearance from the host. In particular we show how the percentage reduction in microparasite abundance is related to the pharmacokinetic parameter, AUC, recording the area under the drug concentration-time curve within the treated patient, in terms of the parameters that define the population dynamics of the pathogen and the properties of the drug. Two particular pathogens are examined to illustrate the principles underpinning the dynamics of the pharmacokinetic-population dynamic models, namely HIV and Plasmodium falciparum. Criteria for pathogen persistence or elimination are derived for these specific models based on the definition of a basic reproductive number, R0, which measures the average number of secondary infected target cells in a host generated by a single infected cell (CD4 lymphocyte for HIV, and erythrocyte for P. falciparum) within a population of susceptible cells. For the pathogen to invade the host and persist over time, R0

Solid tumours do not develop as a homogeneous mass of mutant cells, rather, they grow in tandem with normal tissue cells initially present, and may also recruit other cell types including lymphatic and endothelial cells. Many solid tumours contain a high proportion of macrophages, a type of white blood cell which can have a variety of effects upon the tumour, leading to a delicate balance between growth promotion and inhibition. In this paper we present a brief review of the main properties and interactions of such tumour-associated macrophages, leading to a description of a mathematical model of the spatial interactions of macrophages, tumour cells and normal tissue cells, focusing on the ability of macrophages to kill mutant cells. Analysis of the homogeneous steady states shows that, for this model, normal tissue is unstable to the introduction of mutant cells despite such an immune response, but that the composition of the resulting tumour can be significantly altered. Including random cell movement and chemical diffusion, we demonstrate the existence of travelling wave solutions connecting the normal tissue and tumour steady states, corresponding to a growing tumour, and of the development of a spatial instability behind the wave front. Numerical solutions are illustrated on one and two dimensions. We go on to estimate macrophage motility parameters using data from Boyden chamber experiments. We then extend our model to include macrophage chemotaxis, that is, their directed movement in response to gradients of chemicals secreted by tumours. Solutions in one dimension indicate the possibility of spatiotemporal irregularities with the growing tumour, which are deduced to be the result of a series of bifurcations as the effective domain length increases, leading to a permanently transient solution. These results suggest that tumour heterogeneity may arise, in part, as a natural consequence of the macrophage infiltration. Recent experiments suggest that macrophages may indeed by involved in spatiotemporal variations within some human tumours.

Though the importance of the non-specific immune response is well known, it has often been neglected in theoretical studies. Whereas adaptive or antigen-specific immune responses arise from the proliferation of clones of antigenic-specific cells to form populations sufficiently large to control the parasite, the non-specific response involves the activation of cells such as macrophages from a reservoir consisting of a fixed number of cells. In this paper, we use simple mathematical models to investigate the dynamics of the non-specific immune response to parasites. In particular we describe the conditions under which the non-specific immune response can clear a parasite, control a parasite, or merely reduce the growth rate of a parasite. We also show that non-specific response to concurrent infections of hosts with two parasites can lead to competitive exclusion of one of the parasites. The model incorporating non-specific immunity is then expanded to include specific immune responses. This more complex model, is used to investigate the relative roles of non-specific and specific immunity in dealing with parasites and shows that the non-specific immune system may control the density of parasites prior to the generation of specific immune responses which are capable of clearing them. Finally we show that the predictions of the models conform with results from published experiments on listeria infections.

This paper establishes the conditions under which a class of differential equations which appear in the study of immune systems (Varela et al., 1988a, In: Theoretical Immunology Part II. New Jersey: Addison Wesley), are globally stable. This is proved by adapting a Liapunov functional originally proposed by Cohen & Grossberg (1983, IEEE Transac SMC 13, 815–826) for competitive systems. The global stability thus obtained is valid on the fast time scale where only idiotypic interactions are relevant, thus excluding both lymphocyte proliferation processes and repertoire change via recruitment from immature bone marrow B cells.

The probability distributions for the number of bound antigens and antibodies during immune response are obtained in this paper. Biological significance of this work and directions for further application are discussed along with some illustrative numerical results.

Experimental studies of the effect on antibody affinity of antigen dose and time after immunization show that average affinity increases progressively with time after immunization, and that this increase is greater at lower doses of antigen. In this paper we describe a polyclonal computer model of the immune system that yields all the essential phenomena of affinity maturation, including dose-dependency. Our main findings are (1) the dose-dependency relationship is not produced when typical assumptions regarding B-cell populations and binding reactions are employed, and (2) it is possible to reproduce this dependency by assuming two classes of lymphocytes: generalists and specialists. Generalists have a low threshold for response and produce antibody of low effectiveness, whereas specialists have a high threshold for response, and produce highly effective antibody. We make an analogy between the generalists and a pioneer species in ecological succession, and suggest how the generalists may contribute to a more effective defense against real infections.

We present a kinetic model of the onset of a tumor which involves the coupling of three principal phenomena:(1) the transformation of normal into neoplastic cells,(2) the replication of transformed cells,(3) the immunological interaction of the host organism with transformed cells and/or oncogenic viruses.We assume that the immunological component has two opposite (destructing and facilitating) functions, each of which is regulated by activators and inhibitors. In this paper our analysis is devoted to the cell-mediated neoplastic cell destruction and its negative regulation by blocking factors or by other immunosuppressive agents. We assume that the immunological system may reach different stationary states (nonactivated, activated, suppressed, etc.). In each of these immunological stationary states, Michaelian-like kinetics for the cell-mediated cytotoxic reaction allow to describe the homogeneous stationary states of the neoplastic cell population in term of three adimensional parameters: (1) α, which represents the relative rate of cellular transformation; (2) β, which characterizes the relative rate of neoplastic cell destruction, and (3) θ, α parameter whose value determines the presence of a metastable region for the neoplastic transition of the tissue.The application of our model to the kinetic analysis of the immunological rejection of MSV-M induced tumors confirms our kinetic hypotheses and predicts the minimum ratio of aggressor to target cells that must be reached within the tumor mass to obtain a rejection. Since during rejection this level is not attained with the immune T-cells, we suggest additional co-operative mechanisms involving antibodies and other effector cell types.In the framework of our model we propose the following conclusions:(1) Under physiological conditions tissues contain at least, one neoplastic cell to 1014–1018 normal cells, suggesting that they are exempted from neoplastic cells.(2) The cell to cell cytotoxic activity of the different types of effectors seems to increase in the order: activated macrophages < immune T lymphocytes and natural activity of T lymphocytes.(3) Whereas the cytotoxic activity of T lymphocytes is sufficiently high to cope with allogenic tumor rejection, in syngeneic tumor systems a complex interaction between differejnt effector cells and humoral factors must certainly take place in order to obtain a successful surveillance against cancer.(4) The transition of normal to neoplastic tissues may bear some analogy with metastability phenomena., info:eu-repo/semantics/published

A theory of immunity presented previously showed that many immune phenomena could be explained in terms of a simple model involving interactions between (i) the receptors on immunologically competent cells, (ii) antigenic determinants, (iii) natural antibody and (iv) complement. Several features of the theory subsequently gained experimental support. The present paper extends the analysis and predicts that two mechanisms operate in the induction of immunological tolerance to self antigenic determinants. High specificity anti-self cells are destroyed by a mechanism involving complement. In contrast, low specificity anti-self cells are stimulated by self determinants and increase in numbers. This increases the concentration of the natural antibody secreted by these cells which acts as a “blocking” antibody preventing their continued stimulation by self determinants. The expanded clones of low specificity anti-self cells, which may be of high specificity for “near-self” determinants, (i) are responsible for the greater immunological responsiveness between non-identical members of the same species than between members of different species (“alloaggression”), and (ii) provide a barrier opposing the progressive evolution of the surface determinants of a pathogen into forms identical with the surface determinants of its host. Following exposure to a given self or not-self antigenic determinant, the distribution curve for cells of varying specificities for the determinant shows a sharp cut-off point between high and low specificity cells. The position of this cut-off point is critical in determining the subsequent response of the organism to the determinant. Variables affecting the cut-off point include, antibody present prior to the exposure of cells to the determinant, complement, complement inhibitors, the cell membrane and certain drugs. Autoimmune diseases are improved by drugs (e.g. chloroquine) which move the position of the cut-off point towards cells of low specificities for self determinants.