Unraveling power-law scaling through exponential cell division dynamics

A primary objective of biology is the development of universal laws that define how organic form develops and how it evolves as a function of size, both ontogenetically and across evolutionary time. Scaling theory has been essential in reaching this goal by giving a complete perspective point, particularly in illuminating the fundamental biological features produced within scaling exponents defining families of equations. Nonetheless, the theoretical basis of the allometric equation within scaling theory are inadequately explained, particularly when it comes to establishing links between micro-level processes at the cellular level and macro-level phenomena. We proposed an unlimited cell bipartition, resulting in an exponential growth in cell numbers during an individual's lifespan, to bridge this conceptual gap between cellular processes and allometric scaling. The power-law scaling between body mass and organ weight was produced by the synchronous exponential increments and the allometric exponent is rate of logarithmic cell proliferation rate. Substituting organ weight for erythrocyte weight aided in the development of a power-law scaling relationship between body mass and metabolic rate. Furthermore, it is critical to understand how cell size affects the exponent in power-law scaling. We find that a bigger exponent will result from an increase in the average weight of organ cells or a decrease in the average weight of all cells. Furthermore, cell proliferation dynamics showed a complex exponential scaling between body mass and longevity, defying the previously reported power-law scaling. We discovered a quadratic link between longevity and logarithmic body mass. Notably, all of the parameters included in these relationships are explained by indices linked to cell division and embryonic development. This research adds to our understanding of the complex interaction between cellular processes and overarching scaling phenomena in biology.