Equations of Motion that Recognize Biochemical Patterns

Yokohama, Kanagawa 230-0045, Japan * Author to whom correspondence should be addressed. Tel.: +81-45-503-9490. Fax: +81-45-503-9489. E-mail: [email protected]. 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.