Analysis of immune network dynamical system model with small number of degrees of freedom

A model of bit-strings, that uses the technique of multi-spin coding, was previously used to study the time evolution of B-cell clone repertoire, in a paper by Lagreca, Almeida and Santos. In this work we extend that simplified model to include independently the role of the populations of antibodies, in the control of the immune response, producing mechanisms of differentiation and regulation in a more complete way. Although the antibodies have the same molecular shape of the...

We study the maturation of the antibody population following primary antigen presentation as a global optimization problem. Emphasis is placed on the trade-off between the safety of mutations that lead to local improvements to the antibody's affinity and the necessity of eventual mutations that result in global reconfigurations in the antibody's shape. The model described herein gives evidence of the underlying optimization process from which the rapidity and consistency of t...

In epidemiological modelling, dynamics on networks, and in particular adaptive and heterogeneous networks have recently received much interest. Here we present a detailed analysis of a previously proposed model that combines heterogeneity in the individuals with adaptive rewiring of the network structure in response to a disease. We show that in this model qualitative changes in the dynamics occur in two phase transitions. In a macroscopic description one of these corresponds...

In spite of their many facets, the phenomena of autoimmunity and immunodeficiency seem to be related to each other through the subtle links connecting retroviral mutation and action to immune response and adaptation. In a previous work, we introduced a network model of how a set of interrelated genotypes (called a quasispecies, in the stationary state) and a set of interrelated idiotypes (an idiotypic network) interact. That model, which does not cover the case of a retrovira...

Some common systems modelling and simulation approaches for immune problems are Monte Carlo simulations, system dynamics, discrete-event simulation and agent-based simulation. These methods, however, are still not widely adopted in immunology research. In addition, to our knowledge, there is few research on the processes for the development of simulation models for the immune system. Hence, for this work, we have two contributions to knowledge. The first one is to show the im...

The host immune response can often efficiently suppress a virus infection, which may lead to selection for immune-resistant viral variants within the host. For example, during HIV infection, an array of CTL immune response populations recognize specific epitopes (viral proteins) presented on the surface of infected cells to effectively mediate their killing. However HIV can rapidly evolve resistance to CTL attack at different epitopes, inducing a dynamic network of interactin...

In the study of the basic properties observed in the immune system and, in a broader view, in biological systems, several concepts have already been mathematically formulated or treated in an analytical perspective, such as degeneracy, robustness, noise, and bow tie architecture. These properties, among others, seem to rule many aspects of the system functioning, and share among themselvesseveral characteristics, intersecting each other, and often becoming one the indivisible...

We study the Langevin dynamics of the adaptive immune system, modelled by a lymphocyte network in which the B cells are interacting with the T cells and antigen. We assume that B clones and T clones are evolving in different thermal noise environments and on different timescales. We derive stationary distributions and use statistical mechanics to study clonal expansion of B clones in this model when the B and T clone sizes are assumed to be the slow and fast variables respect...

Modeling the immune system so that its essential functionalities stand out without the need for every molecular or cellular interaction to be taken into account has been challenging for many decades. Two competing approaches have been the clonal selection theory and the idiotypic-network theory, each stemming from a relatively separate set of principles. One recent perspective holding the promise of unification is that of immunity as computation, that is, of immunity as the p...

We observed existence of periodic orbit in immune network under transitive solvable lie algebra. In this paper, we focus to develop condition of maximal Lie algebra for immune network model and use that condition to construct vector field of symmetry to study non linear pathogen model. We used two methods to obtain analytical structure of solution, namely normal generator and differential invariant function. Numerical simulation of analytical structure exhibits correlated per...