Unified representation of Life's basic properties by a 3-species Stochastic Cubic Autocatalytic Reaction-Diffusion system of equations

Abstract

Today we can use physics to describe in great detail many of the phenomena intervening in the process of life. But no analogous unified description exists for the phenomenon of life itself. In spite of their complexity, all living creatures are out of equilibrium chemical systems sharing four fundamental properties: they (1) handle information, (2) metabolize, (3) self-reproduce and (4) evolve. This small number of features, which in terran life are implemented with biochemistry, point to an underlying simplicity that can be taken as a guide to motivate and implement a theoretical physics style unified description of life using tools from the non-equilibrium physical-chemistry of extended systems. Representing a system with general rules is a well stablished approach to model building and unification in physics, and we do this here to provide an abstract mathematical description of life. We start by reviewing the work of previous authors showing how the properties in the above list can be individually represented with stochastic reaction-diffusion kinetics using polynomial reaction terms. These include "switches" and computation, the kinetic representation of autocatalysis, Turing instability and adaptation in the presence of both deterministic and stochastic environments. Thinking of these properties as existing on a space-time lattice each of whose nodes are subject to a common mass-action kinetics compatible with the above, leads to a very rich dynamical system which, just as natural life, unifies the above properties and can therefore be interpreted as a high level or "outside-in" theoretical physics representation of life. Taking advantage of currently available advanced computational techniques and hardware, we compute the phase plane for this dynamical system both in the deterministic and stochastic cases. We do simulations and show numerically how the system works. We review how to extract useful information that can be mapped into emergent physical phenomena and attributes of importance in life such as the presence of a "membrane" or the time evolution of an individual system's negentropy or mass. Once these are available, we illustrate how to perform some basic phenomenology based on the model's numerical predictions. Applying the above to the idealization of the general Cell Division Cycle (CDC) given almost 25 years ago by Hunt and Murray, we show from the numerical simulations how this system executes a form of the idealized CDC. We also briefly discuss various simulations that show how other properties of living systems such as migration towards more favorable regions or the emergence of effective Lotka-Volterra populations are accounted for by this general and unified view from the "top" of the physics of life. The paper ends with some discussion, conclusions, and comments on some selected directions for future research. The mathematical techniques and powerful simulation tools we use are all well established and presented in a "didactical" style. We include a very rich but concise SI where the numerical details are thoroughly discussed in a way that anyone interested in studying or extending the results would be able to do so.

Keywords: Bottom-up approach; Living systems; Non-linear reaction-diffusion equations; Properties of life; Top-down approach; Turing instability.