The principle of sufficiency and the evolution of control: using control analysis to understand the design principles of biological systems

Control analysis can be used to try to understand why (quantitatively) systems are the way that they are, from rate constants within proteins to the relative amount of different tissues in organisms. Many biological parameters appear to be optimized to maximize rates under the constraint of minimizing space utilization. For any biological process with multiple steps that compete for control in series, evolution by natural selection will tend to even out the control exerted by each step. This is for two reasons: (i) shared control maximizes the flux for minimum protein concentration, and (ii) the selection pressure on any step is proportional to its control, and selection will, by increasing the rate of a step (relative to other steps), decrease its control over a pathway. The control coefficient of a parameter P over fitness can be defined as (∂N/N)/(∂P/P), where N is the number of individuals in the population, and ∂N is the change in that number as a result of the change in P. This control coefficient is equal to the selection pressure on P. I argue that biological systems optimized by natural selection will conform to a principle of sufficiency, such that the control coefficient of all parameters over fitness is 0. Thus in an optimized system small changes in parameters will have a negligible effect on fitness. This principle naturally leads to (and is supported by) the dominance of wild-type alleles over null mutants.