Emergence of Function

TL;DR

This paper presents a mathematical framework for tissue dynamics, showing how genome behavior within cells and diffusion between cells lead to emergent tissue functions, with convergence guaranteed under certain conditions.

Contribution

It introduces a novel concept of monotonicity and proves that combined with hardwiring, it ensures global convergence of tissue dynamics.

Findings

Monotonicity and hardwiring guarantee convergence.

Mathematical model links genome dynamics to tissue function.

Provides conditions for stable tissue behavior.

Abstract

This work gives a mathematical study of tissue dynamics. We combine within-cell genome dynamics and diffusion between cells, where the synthesis of the two gives rise to the emergence of function. We introduce a concept of monotonicity and prove that monotonicity together with hardwiring, defined as all cells of the same tissue having the same genome dynamics, is sufficient for the global convergence of the tissue dynamics.