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

Alexander S. Bratus (), Gennady Bocharov () and Dmitry Grebennikov ()
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Alexander S. Bratus: Institute of Management and Digital Technologies, Russian University of Transport, 127055 Moscow, Russia
Gennady Bocharov: Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia
Dmitry Grebennikov: Marchuk Institute of Numerical Mathematics, Russian Academy of Sciences, 119333 Moscow, Russia

Mathematics, 2024, vol. 12, issue 20, 1-19

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.

Keywords: antigen evolution; immune system repertoire; complementary receptor synthesis; dynamic programming; Hamilton–Jacobi–Bellman equation; Feynman–Kac–Kolmogorov equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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