Biomedical subjects

A S Perelson

Publications and source records attributed to A S Perelson.

At least 19 recordsLinked to original sources

PubMed1996

Equilibrium binding of multivalent ligands to cells: effects of cell and receptor density.

We study the equilibrium binding properties of multivalent ligands to cell surface receptors. We examine the effects of cell density and number of receptors per cell, that is, receptor concentration, on ligand binding. These parameters can significantly affect the formation of receptor aggregates and cross-links. We then use our general results to show that ligand-induced cell proliferation may be self-limiting, since ligand depletion reduces the signal received by individual cells once the cell population has expanded. We discuss the concept of avidity and show its limitations. As a specific example, we examine the binding of haptenated polymers to B cells and reinterpret experiments related to the immunon theory of B-cell activation.

Animals↗

PubMed1996

HIV-1 dynamics in vivo: virion clearance rate, infected cell life-span, and viral generation time.

A new mathematical model was used to analyze a detailed set of human immunodeficiency virus-type 1 (HIV-1) viral load data collected from five infected individuals after the administration of a potent inhibitor of HIV-1 protease. Productively infected cells were estimated to have, on average, a life-span of 2.2 days (half-life t 1/2 = 1.6 days), and plasma virions were estimated to have a mean life-span of 0.3 days (t 1/2 = 0.24 days). The estimated average total HIV-1 production was 10.3 x 10(9) virions per day, which is substantially greater than previous minimum estimates. The results also suggest that the minimum duration of the HIV-1 life cycle in vivo is 1.2 days on average, and that the average HIV-1 generation time--defined as the time from release of a virion until it infects another cell and causes the release of a new generation of viral particles--is 2.6 days. These findings on viral dynamics provide not only a kinetic picture of HIV-1 pathogenesis, but also theoretical principles to guide the development of treatment strategies.

Antiviral Agents↗

PubMed1996

A new bell-shaped function for idiotypic interactions based on cross-linking.

Most recent models of the immune network are based upon a phenomenological log bell-shaped interaction function. This function depends on a single parameter, the "field," which is the sum of all ligand concentrations weighted by their respective affinities. The typical behavior of these models is dominated by percolation, a phenomenon in which a local stimulus spreads globally throughout the network. The usual reason for employing a log bell-shaped interaction function is that B cells are activated by cross-linking of their surface immunoglobulin receptors. Here we formally derive a new phenomenological log bell-shaped function from the chemistry of receptor cross-linking by bivalent ligand. Specifying how this new function depends on the ligand concentrations requires two fields: a binding field and a cross-linking field. When we compare the activation functions for ligand-receptor pairs with different affinities, the one-field and the two-field functions differ markedly. In the case of the one-field activation function, its graph is shifted to increasingly higher concentration as the affinity decreases but keeps its width and height. In the case of the two-field activation function, the graph of a low-affinity interaction is nested within the graphs of all higher-affinity interactions. We show that this difference in the relations among activation functions for different affinities radically changes the network behavior. In models that described B cell proliferation using the one-field activation function, network behavior was dominated by low-affinity interactions. Conversely, in our new model, the high-affinity interactions are the most significant. As a consequence, percolation is no longer the only typical network behavior.

Animals↗

PubMed1996

Cross-linking reconsidered: binding and cross-linking fields and the cellular response.

We analyze a model for the reversible cross-linking of cell surface receptors by a collection of bivalent ligands with different affinities for the receptor as would be found in a polyclonal anti-receptor serum. We assume that the amount of cross-linking determines, via a monotonic function, the rate at which cells become activated and divide. In addition to the density of receptors on the cell surface, two quantities, the binding field and the cross-linking field, are needed to characterize the cross-linking curve, i.e., the equilibrium concentration of cross-linked receptors plotted as a function of the total ligand site concentration. The binding field is the sum of all ligand site concentrations weighted by their respective binding affinities, and the cross-linking field is the sum of all ligand site concentrations weighted by the product of their respective binding and cross-linking affinity and the total receptor density. Assuming that the cross-linking affinity decreases if the binding affinity decreases, we find that the height of the cross-linking curve decreases, its width narrows, and its center shifts to higher ligand site concentrations as the affinities decrease. Moreover, when we consider cross-linking-induced proliferation, we find that there is a minimum cross-linking affinity that must be surpassed before a clone can expand. We also show that under many circumstances a polyclonal antiserum would be more likely than a monoclonal antibody to lead to cross-linking-induced proliferation.

Animals↗

PubMed1996

Human immunodeficiency virus fitness in vivo: calculations based on a single zidovudine resistance mutation at codon 215 of reverse transcriptase.

We monitored a subject newly infected with a zidovudine-resistant human immunodeficiency virus type 1 strain and found that in the absence of drug, the viral population with the resistance-conferring tyrosine (TAC) codon 215 of reverse transcriptase was gradually replaced. By using standard formulas to model the effects of selection at a single locus in an asexual haploid population, the relative fitness gain of the viral population with a single mutation at codon 215 creating a serine (TCC) was calculated. We concluded that a viral population with a serine at reverse transcriptase codon 215 conferring zidovudine sensitivity was between 0.4 and 2.3% more fit.

HIV Infections↗

PubMed1995

Protein evolution on partially correlated landscapes.

We extend an earlier model of protein evolution on a rugged landscape to the case in which the landscape exhibits a variable degree of correlation (i.e., smoothness). Correlation is introduced by assuming that a protein is composed of a set of independent blocks or domains and that mutation in one block affects the contribution of that block alone to the overall fitness of the protein. We study the statistical structure of such landscapes and apply our theory to the evolution by somatic hypermutation of antibody molecules composed of framework and complementarity-determining regions. We predict the expected number of replacement mutations in each region.

Adaptation, Biological↗

PubMed1995

Modeling and optimization of populations subject to time-dependent mutation.

It has become clear that many organisms possess the ability to regulate their mutation rate in response to environmental conditions. So the question of finding an optimal mutation rate must be replaced by that of finding an optimal mutation schedule. We show that this task cannot be accomplished with standard population-dynamic models. We then develop a "hybrid" model for populations experiencing time-dependent mutation that treats population growth as deterministic but the time of first appearance of new variants as stochastic. We show that the hybrid model agrees well with a Monte Carlo simulation. From this model, we derive a deterministic approximation, a "threshold" model, that is similar to standard population dynamic models but differs in the initial rate of generation of new mutants. We use these techniques to model antibody affinity maturation by somatic hypermutation. We had previously shown that the optimal mutation schedule for the deterministic threshold model is phasic, with periods of mutation between intervals of mutation-free growth. To establish the validity of this schedule, we now show that the phasic schedule that optimizes the deterministic threshold model significantly improves upon the best constant-rate schedule for the hybrid and Monte Carlo models.

B-Lymphocytes↗

PubMed1995

Towards a general function describing T cell proliferation.

A new function is proposed for describing the rate of T cell proliferation in response to peptides on antigen-presenting cells. The model improves an earlier model of ours by allowing for a true maximum proliferation rate of the T cells. This is achieved by a simple change of variables that markedly relaxes the conditions for a conventional quasi-steady-state assumption. The new model has the same "ecological" properties as the previous one. Thus the natural competition in the model allows for regulation of T cell population size in the presence of continuous stimulation by antigen. An important feature is the competitive exclusion of T cell clones recognizing the same peptide with different affinities allowing for "affinity selection". Models for the population dynamics of experienced, naïve and activated T cells are also developed. These T cell subpopulations compete with one another for antigen. In models with lymphokine production a "proliferation threshold" is obtained that allows for tolerance.

Animals↗

PubMed1995

Modeling positive and negative selection and differentiation processes in the thymus.

T cells begin their development as precursor cells in the bone marrow. These cells migrate to the thymus, where they further divide, differentiate, and mature into functional T cells. Most thymocytes (95-99%) die in the course of this process, and only relatively few exit the thymus as mature cells. Here we develop a differential equation model of cell proliferation, differentiation and death in the thymus that can account for both the total number of thymus cells and the fractions of various types of immature and mature thymocytes. Our model suggests that positive and negative selection may have more complex effects than simply deleting some cells and allowing others to survive.

Animals↗

PubMed1995

Lymphocyte memory and affinity selection.

The persistence of antigen-specific immune memory appears to require the presence of antigen--suggesting that memory may be due to restimulation of "memory" lymphocytes by persisting antigen. Persistence of antigen, in a form capable of stimulating B cell proliferation, on long-lived, follicular dendritic cells of lymphoid tissue is well documented. Existence of an analogous mechanism for T cell memory maintenance is controversial but can not be ruled out. Here we examine the consequences of immune memory maintenance by antigen-specific lymphocyte restimulation, and estimate the duration of memory as a function of model parameters. We show that the competition for restimulation among memory cell populations results in the selection of the clone having the highest overall affinity for the retained antigen. Thus affinity selection, an important attribute of immunity, is a constitutive property of memory maintenance by antigen-specific restimulation. In the case of B cells, affinity selection is predicted to continue to increase antibody affinity even after somatic mutation stops, and thus may be an important component of affinity maturation. Finally, we discuss several other hypotheses proposed to explain immune memory, including T cell stimulation by cross-reactive antigens.

Animals↗

PubMed1995

Localized or systemic in vivo heat inactivation of human immunodeficiency virus (HIV): a mathematical analysis.

Temperatures > or = 42 degrees C, maintained for > or = 25 min, inactivate approximately 25% of human immunodeficiency virus (HIV). HIV-infected T cells are more sensitive to heat than healthy lymphocytes, and susceptibility increases when the cells are presensitized by exposure to tumor necrosis factor. Thus, induction of a whole-body hyperthermia or hyperthermia specifically limited to tissues having a high viral load is a potential antiviral therapy for acquired immunodeficiency syndrome (AIDS). Accordingly, we incorporated therapeutic hyperthermia into an existing mathematical model that evaluates the interaction between HIV and CD4+ T cells. Given the assumptions and limitations of this model, the results indicate that a daily therapy lowering the population of actively infected cells by 40% or infectious virus by 40% would effectively reverse the depletion of T cells. In contrast, a daily decline of 20% of either actively infected cells or infectious virus would have a marginal effect. However, daily reduction by 20% of both actively infected cells and infectious virus could restore T-cell numbers, assuming that permanent damage had not been inflicted on the thymus. Since daily treatments would probably be excessively stressful, whole-body hyperthermia seems unlikely to be clinically useful. In contrast, heating directed specifically to areas of viral concentration may be effective and have a suitable risk/benefit ratio.

CD4 Lymphocyte Count↗

PubMed1995

Rapid turnover of plasma virions and CD4 lymphocytes in HIV-1 infection.

Treatment of infected patients with ABT-538, an inhibitor of the protease of human immunodeficiency virus type 1 (HIV-1), causes plasma HIV-1 levels to decrease exponentially (mean half-life, 2.1 +/- 0.4 days) and CD4 lymphocyte counts to rise substantially. Minimum estimates of HIV-1 production and clearance and of CD4 lymphocyte turnover indicate that replication of HIV-1 in vivo is continuous and highly productive, driving the rapid turnover of CD4 lymphocytes.

Antiviral Agents↗

PubMed1995

Modeling defective interfering virus therapy for AIDS: conditions for DIV survival.

The administration of a genetically engineered defective interfering virus (DIV) that interferes with HIV-1 replication has been proposed as a therapy for HIV-1 infection and AIDS. The proposed interfering virus, which is designed to superinfect HIV-1 infected cells, carries ribozymes that cleave conserved regions in HIV-1 RNA that code for the viral envelope protein. Thus DIV infection of HIV-1 infected cells should reduce or eliminate viral production by these cells. The success of this therapeutic strategy will depend both on the intercellular interaction of DIV and HIV-1, and on the overall dynamics of virus and T cells in the body. To study these dynamical issues, we have constructed a mathematical model of the interaction of HIV-1, DIV, and CD4+ cells in vivo. The results of both mathematical analysis and numerical simulation indicate that survival of the engineered DIV purely on a peripheral blood HIV-1 infection is unlikely. However, analytical results indicate that DIV might well survive on HIV-1 infected CD4+ cells in lymphoid organs such as lymph nodes and spleen, or on other HIV-1 infected cells in these organs.

Acquired Immunodeficiency Syndrome↗

PubMed1994

Modeling HIV infection of CD4+ T-cell subpopulations.

We develop and analyze a set of models for the interaction of HIV with CD4+ T cells. We consider three major subpopulations of T cells: virgin, activated and memory. In our first model we assume that HIV can infect activated cells but not resting cells. We then generalize the model to take into account recent reports that HIV can enter resting cells but that such entry does not lead to the production of completely reverse transcribed copies of the viral genome or integration of the DNA copy into the host cell's genome unless cell activation occurs. Our models show that T-cell memory is greatly reduced by HIV infection and that T-cell depletion may be due to the direct killing of peripheral T cells and T-cell precursors in the thymus.

CD4-Positive T-Lymphocytes↗

PubMed1994

Th1/Th2 cross regulation.

We present and analyze a model for the cross-regulation of the Th1 and Th2 helper cell subsets during an immune response by the regulatory cytokines interferon-gamma (IFN)-gamma) and interleukin-10 (IL-10). IFN-gamma, secreted by Th1 cells, can inhibit the proliferation of Th2 cells. Interleukin-10, secreted by Th2 cells, inhibits cytokine production by Th1 cells. Based on these properties, the model shows that responses are expected to be dominated by either Th1 cells or Th2 cells but not both. Which type dominates is shown to depend principally on the relative efficiencies of activation of the responding Th1 and Th2 cells. However, our model, as well as numerous experiments, show that perturbations of the system allow one to switch from a Th2 to a Th1 response, or vice versa. Our model can account for observed outcomes of parasitic infection and may also contribute to our understanding of immune responses to HIV infection as well as to tolerance to self components. It also predicts that in certain parameter ranges vaccination with low doses of live parasites can provide protection against subsequent encounters with high doses that normally induce disease. Experiments by Bretscher et al. (1992, Science 257, 539) on Leishmania major infection are consistent with this prediction. A similar strategy may also be relevant for the design of an AIDS vaccine. Lastly, our results indicate that Th1/Th2 cross-regulation is capable of generating a "sneaking through" phenomenon, and hence it may play a role in tumor immunity.

Animals↗

PubMed1994

T cell repertoires and competitive exclusion.

Self-renewal is generally thought to play a major role in the maintenance of the T-cell repertoire. Here we develop a set of mathematical models for T-cell activation by peptides on antigen presenting cells (APCs). We show that competition between T cells is inherent to the processes involved in T cells binding APCs. We prove that for each dominant peptide only one T-cell clone can ultimately survive the competition. This is analogous to a classical result from theoretical ecology known as the principle of "competitive exclusion". These findings allow for three main results. First, competitive exclusion during an immune response to antigen implies that the clone(s) with the highest affinity for the dominant peptide(s) will outcompete all others. This allows for a form of "affinity selection". Second, the competition for binding antigen gives rise to regulation of T-cell numbers within a single clone. This allows for a regulated form of T-cell memory when T cells are continuously activated by a persisting antigen. Third, competitive exclusion implies that for each peptide only one T-cell specificity can be maintained in the repertoire. If the T-cell repertoire is largely maintained owing to cross-reactivities with various antigens, competitive exclusion means that the diversity of the T-cell repertoire is limited by the number of antigens stimulating the system. If the cross-reactivities were to involve activation by self antigens this would confirm an earlier result suggesting that the T-cell repertoire is diverse owing to the diversity of the self environment.

Animals↗

PubMed1994

Immune networks modeled by replicator equations.

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.

Animals↗

PubMed1994

Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis.

We present a mathematical model of the cytotoxic T lymphocyte response to the growth of an immunogenic tumor. The model exhibits a number of phenomena that are seen in vivo, including immunostimulation of tumor growth, "sneaking through" of the tumor, and formation of a tumor "dormant state". The model is used to describe the kinetics of growth and regression of the B-lymphoma BCL1 in the spleen of mice. By comparing the model with experimental data, numerical estimates of parameters describing processes that cannot be measured in vivo are derived. Local and global bifurcations are calculated for realistic values of the parameters. For a large set of parameters we predict that the course of tumor growth and its clinical manifestation have a recurrent profile with a 3- to 4-month cycle, similar to patterns seen in certain leukemias.

Animals↗