**Population-Based Parameter Identification for Dynamical Models of Biological Networks with an Application to** *Saccharomyces cerevisiae*

**Ewelina Weglarz-Tomczak 1,\*,†, Jakub M. Tomczak 2,\*,†, Agoston E. Eiben 2 and Stanley Brul 1**


**Abstract:** One of the central elements in systems biology is the interaction between mathematical modeling and measured quantities. Typically, biological phenomena are represented as dynamical systems, and they are further analyzed and comprehended by identifying model parameters using experimental data. However, all model parameters cannot be found by gradient-based optimization methods by fitting the model to the experimental data due to the non-differentiable character of the problem. Here, we present POPI4SB, a Python-based framework for population-based parameter identification of dynamic models in systems biology. The code is built on top of PySCeS that provides an engine to run dynamic simulations. The idea behind the methodology is to provide a set of derivative-free optimization methods that utilize a population of candidate solutions to find a better solution iteratively. Additionally, we propose two surrogate-assisted population-based methods, namely, a combination of a k-nearest-neighbor regressor with the Reversible Differential Evolution and the Evolution of Distribution Algorithm, that speeds up convergence. We present the optimization framework on the example of the well-studied glycolytic pathway in *Saccharomyces cerevisiae*.

**Keywords:** dynamic models; evolutionary computing; derivative-free optimization; metabolism; glycolysis; yeas<sup>t</sup>
