Counting Cells by Age Tells Us About How, and Why, and When, We Grow, and Become Old and Ill

Abstract

Growth and aging are fundamental features of animal life. The march from fertilization to oblivion comes in enormous variety: days and hundreds of cells for nematodes, decades and trillions of cells for humans.1-4Since Verhulst (18385) proposed the Logistic Equation - exponential growth with a countervailing linear decline in rate – biologists have searched for ever better density-dependent growth equations,6-12none of which accurately capture the relationship between size and time for real animals.13-15Furthermore, while growth and aging run in parallel, whether the relationship is causal has yet to be determined. Similarly unknown has been the reason behind the exponentialForce of Mortality, described by Gompertz in 1825 for all-cause mortality16and reported by Levin et al. in 2020 for COVID-19.17Here we report that examination in units of numbers of cells,N, Cellular Phylodynamic Analysis,6reveals that growth, lifespan, and mortality, are linked to the reduction in the fraction of cells dividing, occurring by a simple expression, theUniversal Mitotic Fraction Equation. Lifespan is correlated with an age when fewer than one-in-a-thousand cells are dividing, quantifying the long-appreciated mechanism of aging, the failure of cells to be rejuvenated by dilution with new materials made and DNA repaired at mitosis.29-31These observations provide practical mathematical tools for comprehending and managing the challenges of growth and aging, for such tasks as deciphering COVID-19 lethality and its amelioration by vaccination.