ISRES+: An improved evolutionary strategy for function minimization to estimate the free parameters of Systems Biology models

Abstract

Model development is essential to gain a mathematical understanding of the underlying phenomena in systems biology. In most models, it is typically hard to estimate the values of the biophysical/phenomenological parameters that characterize the model. The parameters are estimated by minimizing a function that reduces a measure of the error between model predictions and experimental data. In this work, we build on an algorithm for function minimization proposed by Runnarson and Yao, named Improved Evolutionary Strategy by Stochastic Ranking (ISRES), that finds a best-fit individual by evolving a population in the direction of minimizing error by using information at most from a pair of individuals in any generation to create a new population. Our algorithm, named ISRES+, builds on it by combining information from all individuals across the population and across all generations to gain a better sense of direction to evolve the population. ISRES+ makes use of the additional information generated by the creation of a large population in the evolutionary methods to approximate the local neighborhood around the best-fit individual using linear least squares fit in one and two dimensions. We compared the performance of the two algorithms on three systems biology models with varying complexities and found that not only does the ISRES+ lead to fitter individuals, but it also leads to a tighter distribution of fittest individuals over successive runs.