Abstract

This study aimed to develop mathematical models with important physiological parameters involving immune response for antibody by using Gamma and Psi functions, which could be used in many aspects, for instance to explain the controversies concerning antibody concentration with biological reasons and mathematical calculations, to optimize the antibody yield in large scale production. In this paper, we establish two new logarithmically completely monotonic functions involving the gamma function according to two preferred interaction geometries, necessary and sufficient conditions are presented for one of them to be logarithmically completely monotonic. As a consequence, a sharp inequality involving the gamma function is deduced to solve the problems of genetically engineered antibody. This approach would aid to utilize the engineered antibodies and their derivatives for various biomedical applications.

Keywords: Gamma function; Genetically engineered antibody; Logarithmically completely monotonic; Inequality; PSI function