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When exact values of model parameters in systems biology are not available from experiments, they need to be inferred so that the resulting simulation reproduces the experimentally known phenomena. For the purpose, Bayesian statistics with Markov chain Monte Carlo (MCMC) is a useful method. Biological experiments are often performed with cell population, and the results are represented by histograms. On another front, experiments sometimes indicate the existence of a specific bifurcation pattern. In this study, to deal with both type of such experimental results and information for parameter inference, we introduced functions to evaluate fitness to both type of experimental results, named quantitative and qualitative fitness measures respectively. We formulated Bayesian formula for those hybrid fitness measures (HFM), and implemented it to MCMC (MCMC-HFM). We tested MCMC-HFM first for a kinetic toy model with a positive feedback. Inferring kinetic parameters mainly related to the positive feedback, we found that MCMC-HFM reliably infer them with both qualitative and quantitative fitness measures. Then, we applied the MCMC-HFM to an apoptosis signal transduction network previously proposed. For kinetic parameters related to implicit positive feedbacks, which are important for bistability and irreversibility of the output, the MCMC-HFM reliably inferred these kinetic parameters. In particular, some kinetic parameters that have the experimental estimates were inferred without these data and the results were consistent with the experiments. Moreover, for some parameters, the mixed use of quantitative and qualitative fitness measures narrowed down the acceptable range of parameters. Taken together, our approach could reliably infer the kinetic parameters of the target systems.

Bayesian Parameter Inference by Markov Chain Monte Carlo with Hybrid Fitness Measures: Theory and Test in Apoptosis Signal Transduction Network