Regulatory network modelling: Correlation for structure and parameter optimisation

Due to the limitations of available gene expression data, (i.e. noise and size of time series), modelling gene regulatory networks is still restricted, especially in terms of their quantitative analysis. To date, the only criterion used for model evaluation is the residual error between observed and simulated data. This does not assign good fitness to models that can simulate the general oscillation, but are shifted with respect to observed data. Given that oscillatory behaviour of such complex systems is mostly driven by the topology of regulatory networks, these models may contain important information on network structure, which can shed light on evolutionary parameter optimisation. In consequence, a second model evaluation criterion is introduced here, namely the Pearson correlation coefficient between simulated and observed time series, which enables good fit to be assessed for candidate solutions able to approximate the general behaviour seen in the data. This is employed in a nested optimisation algorithm, which separately analyses the structure and parameters of the models. The method is evaluated using both synthetic and real microarray gene expression data, (Yeast cell cycle), and results show that models obtained in this way display more plausible connections, also contributing to simulation of quantitative behaviour.