An Analytical Theory of Cellular Growth

Abstract

The biological fitness of unicellular organisms is largely determined by their balanced growth rate, i.e., by the rate with which they replicate their biomass composition. Natural selection on this growth rate occurred under a set of physicochemical constraints, including mass conservation, reaction kinetics, and limits on dry mass per volume; mathematical models that maximize the balanced growth rate while accounting explicitly for these constraints are inevitably nonlinear and have been restricted to small, non-realistic systems. Here, we lay down a general theory of balanced growth states, providing explicit expressions for protein concentrations, fluxes, and the growth rate. These variables are functions of the concentrations of cellular components, for which we calculate marginal fitness costs and benefits that can be related to metabolic control coefficients. At maximal growth rate, the net benefits of all concentrations are equal. Based solely on physicochemical constraints, the growth balance analysis (GBA) framework introduced here unveils fundamental quantitative principles of cellular growth and leads to experimentally testable predictions.