Using a rank selection genetic algorithm to optimize parameter estimation allows for prediction of cellular responses in in silico biological models

The ability to infer or predict skin cellular responses offers the potential to investigate immune regulation in the face of environmental changes, and the consequence of these changes on the disease state. One possibility is the use of in silico modelling as a predictive tool, utilizing mathematical kinetic models that are based on current understanding of a biological system. The NFκB and IκB network are thought to play a role in the development and differentiation of the epidermis, and depletion of key NFκB subunits has been linked to increased cell death in keratinocytes. Therefore, investigating responses with an in silico model of the NFκB system could provide new insights into skin health. A mathematical model of the NFκB and IκB signalling module was outlined and developed by Hoffmann et al. (2002). They were able to use partial datasets from mouse fibroblasts to demonstrate that the temporal control of NFκB activation can be successfully modelled using a mechanistic network composed of a system of ordinary differential equations. However, the process of parameterizing such a model can be challenging, or even impossible, to accomplish by hand and thus a computational alternative is often necessary, particularly for large models such as the NFκB signalling module. We present the rank selection genetic algorithm (RSGA) as a tool for parameter estimation which is able to infer behaviour of a biological system from partial datasets, allowing for the parameterization of biological models such that it is possible to predict cellular responses to environmental changes. The RSGA takes an initial user-defined search range and estimates a set of parameter values. It then performs a fitness test using the average relative error between the model solution and observed data, before carrying out a rank selection procedure to determine the optimal solutions to retain for the next algorithm generation. Termination of the RSGA is dependent on the average relative error reaching a defined threshold, or the algorithm reaching 100 000 iterations. The RSGA was tested on multiple biological models in addition to the NFκB system, including the extracellular regulated kinase, heat shock and circadian rhythm models, and was reliably able to provide estimated parameter values that gave a more successful fit to partial noisy data than other available parameter estimation approaches, allowing a model parameterization that enabled the prediction of extended datasets and changes to the cellular environment