Work

Dynamic Programming-Based Approach to Model Antigen-Driven Immune Repertoire Synthesis

Year: 2024

Type: article

Abstract: This paper presents a novel approach to modeling the repertoire of the immune system and its adaptation in response to the evolutionary dynamics of pathogens associated with their genetic variability. It is based on application of a dynamic programming-based framework to model the antigen-driven immune repertoire synthesis. The processes of formation of new receptor specificity of lymphocytes (the growth of their affinity during maturation) are described by an ordinary differential equation (ODE) with a piecewise-constant right-hand side. Optimal control synthesis is based on the solution of the Hamilton–Jacobi–Bellman equation implementing the dynamic programming approach for controlling Gaussian random processes generated by a stochastic differential equation (SDE) with the noise in the form of the Wiener process. The proposed description of the clonal repertoire of the immune system allows us to introduce an integral characteristic of the immune repertoire completeness or the integrative fitness of the whole immune system. The quantitative index for characterizing the immune system fitness is analytically derived using the Feynman–Kac–Kolmogorov equation.

Source: Mathematics

DOI: 10.3390/math12203291

Authors: Alexander S. Bratus, Gennady Bocharov, Dmitry Grebennikov

Institutions: Russian Academy of Sciences, Russian University of Transport, Institute of Numerical Mathematics, Sechenov University, Moscow Center of Fundamental and Applied Mathematics

Language: English

Topic: Artificial Immune Systems Applications

Subfield: Biomedical Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

Funder: Ministry of Science and Higher Education of the Russian Federation