The Distribution of Mutational Effects on Fitness in a Simple Circadian Clock

The distribution of mutational effects on fitness (DME F ) is of fundamental importance for many questions in biology. Previously, wet-lab experiments and population genetic methods have been used to infer the sizes of effects of mutations. Both approaches have important limitations. Here we propose a new framework for estimating the DME F by constructing fitness correlates in molecular systems biology models. This new framework can complement the other approaches in estimating small effects on fitness. We present a notation for the various DMEs that can be present in a molecular systems biology model. Then we apply this new framework to a simple circadian clock model and estimate various DMEs in that system. Circadian clocks are responsible for the daily rhythms of activity in a wide range of organisms. Mutations in the corresponding genes can have large effects on fitness by changing survival or fecundity. We define potential fitness correlates, describe methods for automatically measuring them from simulations and implement a simple clock using the Gillespie stochastic simulation algorithm within StochKit. We determine what fraction of examined mutations with small effects on the rates of the reactions involved in this system are advantageous or deleterious for emerging features of the system like a fitness correlate, cycle length and cycle amplitude. We find that the DME can depend on the wild type reference used in its construction. Analyzing many models with our new approach will open up a third source of information about the distribution of mutational effects, one of the fundamental quantities that shape life.