A Bayesian framework for the analysis of systems biology models of the brain

Systems biology models are used to understand complex biological and physiological systems. Interpretation of these models is an important part of developing this understanding. These models are often fit to experimental data in order to understand how the system has produced various phenomena or behaviour that are seen in the data. In this paper, we have outlined a framework that can be used to perform Bayesian analysis of complex systems biology models. In particular, we have focussed on analysing a systems biology of the brain using both simulated and measured data. By using a combination of sensitivity analysis and approximate Bayesian computation, we have shown that it is possible to obtain a more complete understanding of the parameter space as compared to a maximum likelihood estimate based approach. This is done through analysis of simulated and experimental data. NIRS measurements were simulated using the same simulated systemic input data for the model in a ‘healthy’ and ‘impaired’ state. By analysing both of these datasets, we show that different parameter spaces can be distinguished and compared between different physiological states or conditions. Finally, we analyse experimental data using the new Bayesian framework and the previous maximum likelihood estimate approach, showing that the Bayesian approach provides a more complete understanding of the parameter space. Author summary Systems biology models are mathematical representations of biological processes that reproduce the overall behaviour of a biological system. They are comprised by a number of parameters representing biological information. We use them to understand the behaviour of biological systems, such as the brain. We do this by fitting the model’s parameter to observed or simulated data; and by looking at how these values change during the fitting process we investigate the mechanisms controlling the behaviour of our system. We are interested in understanding differences between a healthy and an injured brain. Here we outline a statistical framework that uses a Bayesian approach during the fitting process that can provide us with a distribution of parameters rather than single parameter number. We apply this method when simulating the physiological responses between a healthy and a vascular compromised brain to a drop in oxygenation. We then use experimental data that demonstrates the healthy brain response to an increase in arterial CO2 and fit our brain model predictions to the measurements. In both instances we show that our approach provides more information about the overlap between healthy and unhealthy brain states than a fitting process that provides a single value parameter estimate.