Efficient identification of parameter space structure with Modified Metropolis-Hastings algorithm

Mathematical models of natural processes rely on parameter values to produce scientifically meaningful simulation behaviour such as bistability or oscillations. Frequently, the parameter values cannot be estimated from experimental data and have to be randomly selected and then evaluated whether they satisfy system constraints. Evaluating these constraints for a randomly chosen vector of parameter values can be computationally very costly, preventing efficient learning of the model parameter space. We propose a novel application of a Markov chain methodology to generate a large number of parameter vectors for high-dimensional models with potentially complicated parameter space structures. The method is based on a modification of the Metropolis-Hastings algorithm which learns the parameter space as the chain progresses, reducing unnecessary evaluations of model constraints and resulting in many working parameter vectors that generate a desired model behaviour. We show that the method outperforms commonly used parameter generating schemes in terms of speed and accuracy of parameter space learning. Further, we demonstrate how the learned parameter space can be used to identify bistability mechanisms in a model of protein phosphorylation. The method can be applied to any mathematical or computational models for efficient parameter generation and discovery of underlying parameter space structure.