Fourier surrogate models of dilated fitness landscapes in Systems Biology: or how we learned to torture optimization problems until they confess

One of the most complex problems in Systems Biology is Parameter estimation (PE), which consists in inferring the kinetic parameters of biochemical systems. The identification of an accurate parameterization, able to reproduce any observed experimental behavior, is fundamental for the definition of predictive models. PE is a non-convex, multi-modal, and non-separable problem that is usually tackled by using Computational Intelligence methods. When the biochemical species appear in the system in a very low amount, the intrinsic noise due to the randomness of molecular collisions cannot be neglected. In this case, stochastic simulation algorithms should be employed to properly reproduce the system dynamics. Stochastic fluctuations make the PE problem even more complicated, as they can lead to radically different values of the fitness function for the same candidate parameterization. In addition, the kinetic parameters generally follow a log-uniform distribution, so that global optima tend to be localized in the lowest orders of magnitude of the search space. To simultaneously tackle all the aforementioned issues, in this work we investigate a novel approach based on the combination of dilation functions with Fourier surrogate modeling and filtering on the fitness landscape. The results show that our approach is able to strongly simplify the PE problem for low-dimensional optimization instances