Modeling immune reactivity in secondary lymphoid organs

Perelson, Alan S.; Weisbuch, Gérand

doi:10.1016/s0092-8240(05)80080-1

Cited by 13 publications

(1 citation statement)

References 21 publications

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“…In the past years, differential equation models have been used for immune system modelling [9][10][11][12][13][14][15][16] . In these models, populations of antigens and immune cell types are continuous variables in systems of ordinary differential equations (ODEs).…”

Section: Visual Tri-tier Immune Modelmentioning

confidence: 99%

Modeling and Simulation of Visual Tri-Tier Immune System

Gong

2011

AMM

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A visual modelling approach and its computational technique were proposed to represent and simulate a kind of immune system, which is comprised of immune cells and immune molecules etc. To study natural immune system and artificial immune system according to information theories and computational methodologies, the hierarchical model of the immune system was proposed, more faithful and suitable for visual simulation than traditional models. The hierarchical immune system basically consisted of innate immune tier, adaptive immune tier and immune cell tier. Thus, the tri-tier model of the immune system was seamless and coherent with the architecture of the artificial immune system, so that the research on the natural immune system and the research on the artificial one could improve and synchronize each other. Though the structure and features of the natural immune system were difficult to measure and test, the tri-tier architecture and qualitative features of the artificial immune system were built, changed and verified. To validate the new approach to visualize and explore the natural immune system, many experiments were tested on the tri-tier artificial immune system. At last, the visual results of the simulations show that the visual modelling approach can provide an effective and better way of understanding the natural immune system.

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Section: Visual Tri-tier Immune Modelmentioning

confidence: 99%

Modeling and Simulation of Visual Tri-Tier Immune System

Gong

2011

AMM

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Immune networks modeled by replicator equations

1994

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In order to evaluate the role of idiotypic networks in the operation of the immune system a number of mathematical models have been formulated. Here we examine a class of B-cell models in which cell proliferation is governed by a non-negative, unimodal, symmetric response function f (h), where the field h summarizes the effect of the network on a single clone. We show that by transforming into relative concentrations, the B-cell network equations can be brought into a form that closely resembles the replicator equation. We then show that when the total number of clones in a network is conserved, the dynamics of the network can be represented by the dynamics of a replicator equation. The number of equilibria and their stability are then characterized using methods developed for the study of second-order replicator equations. Analogies with standard Lotka-Volterra equations are also indicated. A particularly interesting result of our analysis is the fact that even though the immune network equations are not second-order, the number and stability of their equilibria can be obtained by a superposition of second-order replicator systems. As a consequence, the problem of finding all of the equilibrium points of the nonlinear network equations can be reduced to solving linear equations.

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Immune network behavior—I. From stationary states to limit cycle oscilations

Boer

Perelson

Kevrekidis

1993

Bltn Mathcal Biology

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We develop a model for the idiotypic interaction between two B cell clones. This model takes into account B cell proliferation, B cell maturation, antibody production, the formation and subsequent elimination of antibody-antibody complexes and recirculation of antibodies between the spleen and the blood. Here we investigate, by means of stability and bifurcation analysis, how each of the processes influences the model's behavior. After appropriate nondimensionalization, the model consists of eight ordinary differential equations and a number of parameters. We estimate the parameters from experimental sources. Using a coordinate system that exploits the pairwise symmetry of the interactions between two clones, we analyse two simplified forms of the model and obtain bifurcation diagrams showing how their five equilibrium states are related. We show that the so-called immune states lose stability if B cell and antibody concentrations change on different time scales. Additionally, we derive the structure of stable and unstable manifolds of saddle-type equilibria, pinpoint their (global) bifurcations and show that these bifurcations play a crucial role in determining the parameter regimes in which the model exhibits oscillatory behavior.

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Modeling immune reactivity in secondary lymphoid organs

Cited by 13 publications

References 21 publications

Modeling and Simulation of Visual Tri-Tier Immune System

Modeling and Simulation of Visual Tri-Tier Immune System

Immune networks modeled by replicator equations

Immune network behavior—I. From stationary states to limit cycle oscilations

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