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In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the…
The antibody repertoire of each individual is continuously updated by the evolutionary process of B cell receptor mutation and selection. It has recently become possible to gain detailed information concerning this process through…
When our immune system encounters foreign antigens (i.e., from pathogens), the B cells that produce our antibodies undergo a cyclic process of proliferation, mutation, and selection, improving their ability to bind to the specific antigen.…
Affinity maturation of antibodies during immune responses is achieved by multiple rounds of somatic hypermutation and subsequent preferential selection of those B cells that express B cell receptors with improved binding characteristics for…
Many events in the vertebrate immune system are influenced by some element of chance. The objective of the present work is to describe affinity maturation of B lymphocytes (in which random events are perhaps the most characteristic), and to…
We use a one-dimensional random walk on $D$-dimensional hyper-spheres to determine the critical behavior of statistical systems in hyper-spherical geometries. First, we demonstrate the properties of such walk by studying the phase diagram…
Somatic hypermutations of immunoglobulin (Ig) genes occuring during affinity maturation drive B-cell receptors' ability to evolve strong binding to their antigenic targets. The landscape of these mutations is highly heterogeneous, with…
Lymphocyte selection is a fundamental operation of adaptive immunity. In order to produce B-lymphocytes with a desired antigenic profile, a process of mutation-selection occurs in the germinal center, which is part of the lymph nodes. We…
How does immune system evolve functional proteins - potent antibodies - in such a short time? We address this question using a microscopic, protein-level, sequence-based model of humoral immune response with explicitly defined interactions…
In order to target threatening pathogens, the adaptive immune system performs a continuous reorganization of its lymphocyte repertoire. Following an immune challenge, the B cell repertoire can evolve cells of increased specificity for the…
We study random walk with adaptive move strategies on a class of directed graphs with variable wiring diagram. The graphs are grown from the evolution rules compatible with the dynamics of the world-wide Web [Tadi\'c, Physica A {\bf 293},…
A central feature of vertebrate immune response is affinity maturation, wherein antibody-producing B cells undergo evolutionary selection in microanatomical structures called germinal centers, which form in secondary lymphoid organs upon…
Random walks are studied on disordered cellular networks in 2-and 3-dimensional spaces with arbitrary curvature. The coefficients of the evolution equation are calculated in term of the structural properties of the cellular system. The…
We analyze the interactions between division, mutation and selection in a simplified evolutionary model, assuming that the population observed can be classified into fitness levels. The construction of our mathematical framework is…
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…
Random walk is one of the basic mechanisms found in many network applications. We study the epidemic spreading dynamics driven by biased random walks on complex networks. In our epidemic model, each time infected nodes constantly spread…
The evolution of the adaptive immune system is characterized by changes in the relative abundances of the B- and T-cell clones that make up its repertoires. To fully capture this evolution, we need to describe the complex dynamics of the…
We study biological evolution in a high-dimensional genotype space in the regime of rare mutations and strong selection. The population performs an uphill walk which terminates at local fitness maxima. Assigning fitness randomly to…
In this paper we consider a model based on branching process theory for the proliferation and the dissemination network of T cells in the adaptive immune response. A multi-type Galton Watson branching process is assumed as the basic…
In this work we adopt a statistical mechanics approach to investigate basic, systemic features exhibited by adaptive immune systems. The lymphocyte network made by B-cells and T-cells is modeled by a bipartite spin-glass, where, following…