Exact solutions to a spatially extended model of kinase–receptor interaction

Abstract

B and Mast cells are activated by the aggregation of the immune receptors. Motivated by this phenomena we consider a simple spatially extended model of mutual interaction of kinases and membrane receptors. It is assumed that kinase activates membrane receptors and in turn the kinase molecules bound to the active receptors are activated by transphosphorylation. Such a type of interaction implies positive feedback and may lead to bistability. In this study we apply the Steklov eigenproblem theory to analyze the linearized model and find exact solutions in the case of non-uniformly distributed membrane receptors. This approach allows us to determine the critical value of receptor dephosphorylation rate at which cell activation (by arbitrary small perturbation of the inactive state) is possible. We found that cell sensitivity grows with decreasing kinase diffusion and increasing anisotropy of the receptor distribution. Moreover, these two effects are cooperating. We showed that the cell activity can be abruptly triggered by the formation of the receptor aggregate. Since the considered activation mechanism is not based on receptor crosslinking by polyvalent antigens, the proposed model can also explain B cell activation due to receptor aggregation following binding of monovalent antigens presented on the antigen presenting cell.

A Computational Model for Early Events in B Cell Antigen Receptor Signaling: Analysis of the Roles of Lyn and Fyn

“…In short, setting c = 0 makes receptor-bound kinases inactive, and setting c > 0 makes these kinases active in proportion to the value c . This approach is partly inspired by recent, related modeling studies (47, 48). It should be noted that there may be a nonlinear relationship between c and antigen dose and the immediate effects of antigen interaction with BCR that impact signaling, which may include antigen-induced receptor conformational changes and (re)ordering of receptor spatial positions and configurations within receptor clusters (46).…”

Regularity of solutions to a reaction–diffusion equation on the sphere: the Legendre series approach

“…As the celebrated example of such a process, one can consider the waves of calcium concentration observed on the surface of the Medaka egg after fertilization, travelling from the sperm entry point (animal point) to the antipodal point (vegetal point) . Another example can be found in the papers or , where we proposed a simple model of immune cells activation.…”