Equations of Motion that Recognize Biochemical Patterns

TL;DR

This paper introduces a set of partial differential equations designed to recognize and approximate biochemical patterns and complex dynamical behaviors in biological and non-biological continuum systems.

Contribution

It presents a novel mathematical framework of equations of motion capable of approximating any orbits in complex dynamical systems, including biological patterns.

Findings

Equations can approximate any orbits in complex systems.

The framework applies to both biological and non-biological continua.

Mathematically demonstrated universal approximation property.

Abstract

Equations of motion that recognize biochemical patterns are described. The equations are partial differential equations in a continuous multiple component system in which adequate initial and boundary conditions are given. The biochemical patterns are spatiotemporal distributions of multiple biochemical components that can be regarded as a continuum in concentration and mass flux. Recognizing biochemical patterns lead to a universal property of the equations, which is also mathematically demonstrated, that the devised equations are sufficient to approximate any orbits in an arbitrary dynamical system, even though that of expectedly seen in complex biological systems. This theory can be applied to also a non-biological system that can be regarded as a continuum comprised of any multiple components such as liquids, solids, and nonlinear viscoelastic materials.