A model for analyzing phenomena in multicellular organisms with multivariable polynomials: Polynomial life

Abstract

Most of life maintains itself through turnover, namely cell proliferation, movement and elimination. Hydra’s cells, for example, disappear continuously from the ends of tentacles, but these cells are replenished by cell proliferation within the body. Inspired by such a biological fact, and together with various operations of polynomials, I here propose polynomial-life model toward analysis of some phenomena in multicellular organisms. Polynomial life consists of multicells that are expressed as multivariable polynomials. A cell is expressed as a term of polynomial, in which point [Formula: see text] is described as a term [Formula: see text] and the condition is described as its coefficient. Starting with a single term and following reductions by set of polynomials, I simulate the development from a cell to a multicell. In order to confirm uniqueness of the eventual multicell-pattern, Gröbner base can be used, which has been conventionally used to ensure uniqueness of normal form in the mathematical context. In this framework, I present various patterns through the polynomial-life model and discuss patterns maintained through turnover. Cell elimination seems to play an important role in turnover, which may shed some light on cancer or regenerative medicine.