Motivation Mathematical models in systems biology help generate hypotheses, guide experimental design, and infer the dynamics of gene regulatory networks. These models are characterized by phenomenological or mechanistic parameters, which are typically hard to measure. Therefore, efficient parameter estimation is central to model development. Global optimization techniques, such as evolutionary algorithms (EA), are applied to estimate model parameters by inverse modeling, i.e., calibrating models by minimizing a function that evaluates a measure of the error between model predictions and experimental data. EAs estimate model parameters “fittest individuals” by generating a large population of individuals using strategies like recombination and mutation over multiple “generations”. Typically, only a few individuals from each generation are used to create new individuals in the next generation. Improved Evolutionary Strategy by Stochastic Ranking (ISRES), proposed by Runnarson and Yao, is one such EA that is widely used in systems biology to estimate parameters. ISRES uses information at most from a pair of individuals in any generation to create a new population to minimize the error. In this paper we propose an efficient evolutionary strategy, ISRES+, which builds on ISRES by combining information from all individuals across the population and across all generations to develop a better understanding of the fitness landscape. Results ISRES+ uses the additional information generated by the algorithm during evolution to approximate the local neighborhood around the best-fit individual using linear least squares fits in one and two dimensions, enabling efficient parameter estimation. ISRES+ outperforms ISRES and results in fitter individuals with a tighter distribution over multiple runs, such that a typical run of ISRES+ estimates parameters with a higher goodness-of-fit compared to ISRES. Availability Algorithm and implementation: Github - https://github.com/gtreeves/isres-plus-bandodkar-2022. Supplementary information Supplementary data are available at Bioinformatics online.

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.