Optimizing static thermodynamic models of transcriptional regulation

Motivation: Modeling transcriptional regulation using thermodynamic modeling approaches has become increasingly relevant as a way to gain a detailed understanding of transcriptional regulation. Thermodynamic models are able to model the interactions between transcription factors (TFs) and DNA that lead to a specific transcriptional output of the target gene. Such models can be `trained' by fitting their free parameters to data on the transcription rate of a gene and the concentrations of its regulating factors. However, the parameter fitting process is computationally very expensive and this limits the number of alternative types of model that can be explored. Results: In this study, we evaluate the 'optimization landscape' of a class of static, quantitative models of regulation and explore the efficiency of a range of optimization methods. We evaluate eight optimization methods: two variants of simulated annealing (SA), four variants of gradient descent (GD), a hybrid SA/GD algorithm and a genetic algorithm. We show that the optimization landscape has numerous local optima, resulting in poor performance for the GD methods. SA with a simple geometric cooling schedule performs best among all tested methods. In particular, we see no advantage to using the more sophisticated 'LAM' cooling schedule. Overall, a good approximate solution is achievable in minutes using SA with a simple cooling schedule.