Shaping and Dilating the Fitness Landscape for Parameter Estimation in Stochastic Biochemical Models

The parameter estimation (PE) of biochemical reactions is one of the most challenging tasks in systems biology given the pivotal role of these kinetic constants in driving the behavior of biochemical systems. PE is a non-convex, multi-modal, and non-separable optimization problem with an unknown fitness landscape; moreover, the quantities of the biochemical species appearing in the system can be low, making biological noise a non-negligible phenomenon and mandating the use of stochastic simulation. Finally, the values of the kinetic parameters typically follow a log-uniform distribution; thus, the optimal solutions are situated in the lowest orders of magnitude of the search space. In this work, we further elaborate on a novel approach to address the PE problem based on a combination of adaptive swarm intelligence and dilation functions (DFs). DFs require prior knowledge of the characteristics of the fitness landscape; therefore, we leverage an alternative solution to evolve optimal DFs. On top of this approach, we introduce surrogate Fourier modeling to simplify the PE, by producing a smoother version of the fitness landscape that excludes the high frequency components of the fitness function. Our results show that the PE exploiting evolved DFs has a performance comparable with that of the PE run with a custom DF. Moreover, surrogate Fourier modeling allows for improving the convergence speed. Finally, we discuss some open problems related to the scalability of our methodology.