Computational Theory of Biological Function I

This series presents an approach to mathematical biology which makes precise the function of biological molecules. Because biological systems compute, the theory is a general purpose computer language. I build a language for efficiently representing the function of protein-like molecules in a cell. The first paper only presents the kinematic part of the formalism, but this is already useful for representing large-scale protein networks. The full formalism allows us to investigate the properties of protein interaction models, ultimately yielding an estimate of the random-access memory of the proteins, a measure of their capacity for computation. 1 On Biological Function We can understand the struggle for existence which characterizes the biological world as a competition for computational resources. The computer is the organism, and the program is its behavior. The computing on the cellular level is done by molecules and molecular complexes, which control the transformation of the information encoded in their configurations. Although the computation is internal, the resources to continue it come from outside. If we view life in this way, the goal of an organism is to reorganize as large a part of the physical world as possible to perform its computation. Replication is one way of arranging this, but so is growth and uptake of nutrients— any process which lets the program of the organism expand. Because the total available memory and processing is limited, organisms must compete with one another. A mathematical theory of biological function is a precise description of the internal program of an organism. The goal of is to describe it abstractly, in a formal language which describes the data and algorithm, not the physical motions of the parts. Since the smallest computing objects in a cell are molecules, the first practical objective is to find a description of molecular interactions. 2 A Physical Description Is Too Large We want to describe the function of biological molecules, so we start with the a physical description of their state. Biology is classical, so this is ultimately just the position and velocity of all the atoms. This data is not only enough to predict the biological behavior, it is clearly much too large.