Mathematical Analysis of Antibody Rhythms

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The aim of this study is to develop biomathematical models with important physiological parameters involving immune response for antibody rhythms by using the circadian, infradian and ultradian rhythms of IgY antibody, which could be used in many aspects, for instance to explain the controversies concerning antibody concentration with biological reasons and biomathematical calculations, to optimize the antibody yield in large scale production. In general, this approach could be extended to construct computational models for other antibodies using their biological rhythms to describe their physiological and pathophysiological mechanisms. This approach would aid to utilize the engineered antibodies and their derivatives for various biomedical applications.

The immune system of all living things shows regularly recurring rhythmic variations in numerous frequencies, and the responses of the immune system to an antigen entry could vary in accordance to the chronobiological phenomena. These cyclic oscillations in living things occur for many essential biological processes in order to deal with environmental changes and challenges. Chronobiological phenomena are ubiquitous in living organisms; these periodic (cyclic) episodes are called as biological rhythms (a rhythm is a change that is repeated with a similar pattern). Most of the early reports on biological rhythms focused on circadian rhythms (roughly 24-hours cycle), which could be observed in chicken serum IgY, it has been depicted in mathematics by Forger and Kronauer in 2002 through “van der Pol oscillator”, written in the Lienard phase plane form:

This treats the state variables as some kind of “stuff”, the second of which is converted to the first, but whose creation is blocked or accelerated by light. In light of, this is not necessarily unrealistic; however it is only a first attempt at modeling changes in circadian rhythms [1]. The further investigations have imposed that, biological cycles having periods shorter or longer than circadian rhythm. For instance, cycles that have periods less than 20-hours are called ultradian rhythms, while cycles that have periods longer than 28-hours are called infradian rhythms. Collectively, these three rhythmic domains comprise a network or web of rhythmic oscillations that in many ways can be linked to the various chemical pathways that perform different functions and occur simultaneously within the same organelle or cell [2]. These cyclic oscillations in living things occur for many essential biological processes in order to deal with environmental changes and challenges.