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Biomedical subjects

A S Perelson

Publications and source records attributed to A S Perelson.

18 recordsLinked to original sources
PubMed1992

Plasmid copy number control: a case study of the quasi-steady-state assumption.

Perelson & Brendel (1989, J. molec. Biol. 208, 245-255) have proposed kinetic models for the control of plasmid copy number, based on experiments by J. Tomizawa and his associates. The quasi-steady-state assumptions (QSSA) made in the analysis of these models are justified in the present paper, thereby providing an example of how QSSA can provide a powerful and reliable tool in the analysis of biological kinetics.

Models, Genetic↗
PubMed1992

Pattern formation in one- and two-dimensional shape-space models of the immune system.

A large-scale model of the immune network is analyzed, using the shape-space formalism. In this formalism, it is assumed that the immunoglobulin receptors on B cells can be characterized by their unique portions, or idiotypes, that have shapes that can be represented in a space of a small finite dimension. Two receptors are assumed to interact to the extent that the shapes of their idiotypes are complementary. This is modeled by assuming that shapes interact maximally whenever their coordinates in the space-space are equal and opposite, and that the strength of interaction falls off for less complementary shapes in a manner described by a Gaussian function of the Euclidean "distance" between the pair of interacting shapes. The degree of stimulation of a cell when confronted with complementary idiotypes is modeled using a log bell-shaped interaction function. This leads to three possible equilibrium states for each clone: a virgin, an immune, and a suppressed state. The stability properties of the three possible homogeneous steady states of the network are examined. For the parameters chosen, the homogeneous virgin state is stable to both uniform and sinusoidal perturbations of small amplitude. A sufficiently large perturbation will, however, destabilize the virgin state and lead to an immune reaction. Thus, the virgin system is both stable and responsive to perturbations. The homogeneous immune state is unstable to both uniform and sinusoidal perturbations, whereas the homogeneous suppressed state is stable to uniform, but unstable to sinusoidal, perturbations. The non-uniform patterns that arise from perturbations of the homogeneous states are examined numerically. These patterns represent the actual immune repertoire of an animal, according to the present model. The effect of varying the standard deviation sigma of the Gaussian is numerically analyzed in a one-dimensional model. If sigma is large compared to the size of the shape-space, the system attains a fixed non-uniform equilibrium. Conversely if sigma is small, the system attains one out of many possible non-uniform equilibria, with the final pattern depending on the initial conditions. This demonstrates the plasticity of the immune repertoire in this shape-space model. We describe how the repertoire organizes itself into large clusters of clones having similar behavior. These results are extended by analyzing pattern formation in a two-dimensional (2-D) shape-space.(ABSTRACT TRUNCATED AT 400 WORDS)

B-Lymphocytes↗
PubMed1992

Modeling immune reactivity in secondary lymphoid organs.

Models of the dynamical interactions important in generating immune reactivity have generally assumed that the immune system is a single well-stirred compartment. Here we explicitly take into account the compartmentalized nature of the immune system and show that qualitative conclusions, such as the stability of the immune steady state, depend on architectural details. We examine a simple model idiotypic network involving only two types of B cells and antibody molecules. We show, for model parameters used by De Boer et al. (1990, Chem. Eng. Sci. 45, 2375-2382), that the immune steady state is unstable in a one compartmental model but stable in a two compartment model that contains both a lymphoid organ, such as the spleen, and the circulatory system.

Antibodies↗
PubMed1992

Evidence for p55-p75 heterodimers in the absence of IL-2 from Scatchard plot analysis.

The high affinity receptor for IL-2 is composed of at least two chains, a p55 chain that binds IL-2 with low affinity and a p75 chain that binds with intermediate affinity. Two molecular mechanisms have been proposed for the formation of the high affinity receptor-ligand complex: The affinity conversion model proposes that the high affinity receptor is formed via stepwise binding in which IL-2 first binds to the p55 chain and the resulting complex then associates with the p75 chain to form a high affinity ternary complex. In the performed heterodimer model the p55 and p75 chains form a non-covalently linked high affinity heterodimer in the absence of IL-2. We show that these two models can be distinguished on the basis of equilibrium binding experiments using cell lines expressing different numbers of p55 chains. To make this distinction we develop a general model for the interaction of IL-2 with its various receptors. We than analyze the case in which heterodimers exist in the absence of IL-2 and the case in which no preformed heterodimers exist. For both cases we predict the shape of equilibrium Scatchard plots. We then show that published IL-2 binding studies are consistent with a model in which a large concentration of preformed heterodimers is present on the cell surface and inconsistent with a model in which preformed heterodimers are absent from the cell surface. The models that we develop should have general applicability to the entire class of receptor systems in which low and intermediate affinity chains interact to constitute a high affinity receptor.

Cell Membrane↗
PubMed1992

A mechanism of immune escape by slow-replicating HIV strains.

Strains of human immunodeficiency virus (HIV) differ greatly in their ability to replicate in T4 cells. Fast-replicating strains are observed during the early and late stages of HIV infection, while slow-replicating strains prevail during the intermediate, latent, stage. The prevalence of slow-replicating strains has been attributed to these strains' ability to escape the immune response. However, how these strains are able to avoid being eliminated by an immune response for several years has not been explained. Recent experiments indicate that HIV may be selectively transferred from infected macrophages to T4 cells specific for HIV antigens. Thus, HIV may preferentially infect those T4 cells necessary for generating a protective immune response. To determine the conditions under which an HIV-specific immune response can be blocked, we developed a mathematical model incorporating the process of viral transfer from infected macrophages to HIV-specific T4 cells along with the known processes of macrophage-T4 interaction, immune stimulation, and viral infection of T4 cells and macrophages. Our model shows that the mechanism of viral transfer to HIV-specific T4 cells can allow slow-replicating strains of HIV to escape immune response under conditions in which an immune response occurs against fast-replicating strains. The model also suggests that in addition to slow replication, the ability to reduce or block T-cell activation may be an important characteristic of escape mutants.

CD4-Positive T-Lymphocytes↗
PubMed1978

A singular perturbation approach to diffusion reaction equations containing a point source, with application to the hemolytic plaque assay.

Many cells secrete factors which diffuse and bind to receptors on neighboring cells. These processes can be described by a nonlinear diffusion equation with a point source and spatially distributed binding reaction. We show via perturbation analysis how approximate solutions can be obtained for such equations when the binding reaction is fast compared to diffusive transport. We base our analysis on an example which is of great practical importance in immunology, the hemolytic plaque technique.

Binding Sites↗
PubMed1978

Optimal strategies in immunology. II. B memory cell production.

After a first encounter with most antigens, the immune system responds to susequent encounters with a faster, more efficient and more strenuous antibody response. The memory of previous antigen contacts is carried by lymphocytes. Expanding on the model developed in Part 1 of this paper, we examine the optimal strategy available to the immune system for B memory cell production. We again find that the strategy should be of the bang-bang variety. The model we consider assumes that antigen triggers a subpopulation of B-lymphocytes. These triggered lymphocytes can proliferate and secrete modest amounts of antibody, or differentiate into non-dividing plasma cells which secrete large amounts of antibody, or differentiate into non-antibody secreting memory cells. Given injections of antigen at two widely spaced times we compute the strategy which minimizes a linear combination of the primary and secondary response times. We find that for all biologically reasonable parameter values the best strategies are ones in which memory cells are produced at the end of the primary response. Exerimental results which bear on the actual strategies employed are discussed.

Antibody Formation↗
PubMed1977

Mathematical models for the evolution of multigene families by unequal crossing over.

Mathematical models of homologous but unequal crossing over between sister chromatids are presented. For mispairing by one repeat, the evolution of a multigene family by unequal crossing over can be represented by a linear birth-death process. The fixation rate of one repeat in a multigene family is estimated. For mispairing by more than one repeat, some approximate results are obtained.

Alleles↗
PubMed1977

Antigen modulation of antibody forming cells: the relationship between direct plaque size, antibody secretion rate and antibody affinity.

Using the mathematical theory of direct plaque growth, we have analyzed the expected variation of plaque size with IgM affinity and secretion rate. We use the theory to comment on recent effector cell blockage experiments and show how the theory can be used to determine the change in the secretion rate of a single antibody-forming cell subjected to blockage by a multivalent antigen. We also argue, using the mathematical theory, that under the usual experimental conditions employed in the plaque assay, cells that produce low affinity IgM antibodies will give rise to smaller plaques than cells that produce high affinity IgM antibodies.

Antibody Formation↗
PubMed1976

Optimal strategies in immunology. I. B-cell differentiation and proliferation.

The optimal strategy available to the immune system for responding to a non-replicating thymus-independent antigen is examined. By applying Pontryagin's maximum principle to a set of mathematical models of lymphocyte populations and their antibody production, it is found that the optimal strategy of bang-bang control appears robust. In a variety of structurely related biological models, similar behaviour is observed. The models that we consider assume that antigen triggers a population of B-lymphocytes. These triggered lymphocytes can either proliferate and secrete modest amounts of antibody or differentiate into nondividing plasma cells which secrete large amounts of antibody. For biologically reasonable parameter values it is found that for low doses of antigen, immediate differentiation into plasma cells is optimal, while for high antigen doses a proliferative state followed by differentiation is the best strategy.

Antibody Formation↗
PubMed1976

The electrophoretic hemolytic plaque assay -- theory.

We use the mathematical theory of plaque qrowth to determine if there is merit in performing a hemolytic plaque assay in the presence of an external electric field. In particular, we study the effects of an electric field on the transport of antibodies secreted by a single lymphocyte and on the size and shape of the plaques they produce. Our results indicate that in the presence of an applied electric field: (1) The mobility of the antibodies produced by the antibody forming cell can be determined from the plaque shape. (In the electric field the plaques are no longer circular, but cigar shaped.) (2) By changing the magnitude or direction of the applied electric field more than one plaque can be generated by a single AFC. Thus changes in mobility or the rate of antibody secretion can be assayed. (3) Plaques will reach a steady state size; for good emitters (cells that secrete antibodies at a high rate or that secrete high affinity antibodies) this steady state will be achieved rapidly. Equations are given which describe both the temporal development and steady state plaque size and shape. From the equations, computer generated plots of plaques produced by typical antibody forming cells are presented. These plots are then used to show how pictures of plaques formed in an electric field can be analyzed to determine the antibody mobility.

Electrophoresis↗