Selecting Optimal Models Based on Efficiency and Robustness in Multi-valued Biological Networks

In this paper, we propose an optimization algorithm for literature-derived model and parameter identification in multi-valued biological regulatory networks. Our approach is a multi-objective optimization method where the objectives are inspired from structural Efficiency, dynamical Robustness and biological selectivity of cells in their actions. Given an incomplete model derived from literature and partially instrumented clinical observations, our method identifies the optimal model parameterization by maximizing structural Efficiency, dynamical Robustness and Selectivity. As the parameterization space is super exponential, we implemented our method in a constraint satisfaction framework by defining logical equivalences of the dynamical features. The implemented framework is then solved with a lazy clause solver known as Chuffed. We apply our method on female Hypothalamic-Pituitary-Gonadal axis (HPG) and demonstrate how it is able to identify a model that reproduces the complex menstrual cycle. The algorithm found a structure and parameterization for the 5 node 14 edge (~50% edge density) HPG model with a normalized length cost and robustness of 1.46 and 0.35 respectively in 713 seconds on an Intel core i7 machine.Our method discovered that there are at least 6 more regulatory interactions that must be added to the commonly accepted HPG basic model in order to reproduce the menstrual cycle efficiently and robustly. The discovery of additional interactions suggest that our algorithm provides new insight to the biological model identification by combining the information from literature, clinical measurements and dynamical parameters.