A quantitative model suggests immune memory involves the colocalization of B and Th cells

HIV-1 POPULATION DYNAMICS IN VIVO: IMPLICATIONS FOR PATHOGENESIS, EFFECT OF CYTOKINE AND THERAPY STRATEGY

In this paper, we present a dynamical model to study the spread of HIV-1 in vivo. Our goal is to better understand the interaction between HIV-1 and the human immune system. Making use of the Hill function, we describe two kinds of processions occurring in the immune response: the activation interactions or inhibitory interactions occurring between different components in the immune response, and the autocatalytic maintenance of the CD4+ T cells and CD8+ T cells populations. We also consider the impact of the cytokine interleukin-2 (IL-2) and the CD8 antiviral factor (CAF) on HIV-1 infection. Through numerical simulations we get several results. First, we find that the effects of IL-2 and CAF in the treatment for the infected are limiting. Namely, the curative effect will not always increase along with the dose of IL-2 or CAF or both. The increasing trend will stagnate at a certain dose that we used. Second, we find some possible reasons for the collapse of the lymph system in HIV-1 infection — the loss of these restraining functions, and/or the genetic variability of the virus due to immune escape that enhances the virulence, which then bring the collapse of the immune system. In some conditions the system will produce a Hopf bifurcation. We also simulate the theoretical warrant of the feasibility of the combined chemotherapy strategies for the HIV-1 infected patient.

The evolution of mathematical immunology

The types of mathematical models used in immunology and their scope have changed drastically in the past 10 years. Classical models were based on ordinary differential equations (ODEs), difference equations, and cellular automata. These models focused on the 'simple' dynamics obtained between a small number of reagent types (e.g. one type of receptor and one type of antigen or two T-cell populations). With the advent of high-throughput methods, genomic data, and unlimited computing power, immunological modeling shifted toward the informatics side. Many current applications of mathematical models in immunology are now focused around the concepts of high-throughput measurements and system immunology (immunomics), as well as the bioinformatics analysis of molecular immunology. The types of models have shifted from mainly ODEs of simple systems to the extensive use of Monte Carlo simulations. The transition to a more molecular and more computer-based attitude is similar to the one occurring over all the fields of complex systems analysis. An interesting additional aspect in theoretical immunology is the transition from an extreme focus on the adaptive immune system (that was considered more interesting from a theoretical point of view) to a more balanced focus taking into account the innate immune system also. We here review the origin and evolution of mathematical modeling in immunology and the contribution of such models to many important immunological concepts.

Contributions of memory B cells to secondary immune response

The secondary immune response is one of the most important features of immune systems. During the secondary immune response, the immune system can eliminate the antigen, which has been encountered by the individual during the primary invasion, more rapidly and efficiently. Both T and B memory cells contribute to the secondary response. In this paper, we only concentrate on the functions of memory B cells. We explore a model describing the memory contributed by the specific long-lived clone which is maintained by continued stimulation with a small amount of antigens sequestered on the surfaces of the follicular dendritic cells (FDC). The behavior of the secondary response provided by the model can be compared with experimental observations. The model shows that memory B cells indeed play an important role in the secondary response. It is found that a single memory cell in a long-lived clone may not be long-lived. In the present note, the influences of relevant parameters on the secondary response are also explored.

A basic mathematical model of the immune response

Interaction of the immune system with a target population of, e.g., bacteria, viruses, antigens, or tumor cells must be considered as a dynamic process. We describe this process by a system of two ordinary differential equations. Although the model is strongly idealized it demonstrates how the combination of a few proposed nonlinear interaction rules between the immune system and its targets are able to generate a considerable variety of different kinds of immune responses, many of which are observed both experimentally and clinically. In particular, solutions of the model equations correspond to states described by immunologists as "virgin state," "immune state" and "state of tolerance." The model successfully replicates the so-called primary and secondary response. Moreover, it predicts the existence of a threshold level for the amount of pathogen germs or of transplanted tumor cells below which the host is able to eliminate the infectious organism or to reject the tumor graft. We also find a long time coexistence of targets and immune competent cells including damped and undamped oscillations of both. Plausibly the model explains that if the number of transformed cells or pathogens exeeds definable values (poor antigenicity, high reproduction rate) the immune system fails to keep the disease under control. On the other hand, the model predicts apparently paradoxical situations including an increased chance of target survival despite enhanced immune activity or therapeutically achieved target reduction. A further obviously paradoxical behavior consists of a positive effect for the patient up to a complete cure by adding an additional target challenge where the benefit of the additional targets depends strongly on the time point and on their amount. Under periodically pulsed stimulation the model may show a chaotic time behavior of both target growth and immune response. (c) 1995 American Institute of Physics.