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The inherent behavioral variability exhibited by stochastic biochemicalsystems makes it a challenging task for human experts to manually analyze them.Computational modeling of such systems helps in investigating and predictingthe behaviors of the underlying biochemical processes but at the same timeintroduces the presence of several unknown parameters. A key challenge faced inthis scenario is to determine the values of these unknown parameters againstknown behavioral specifications. The solutions that have been presented so farestimate the parameters of a given model against a single specification whereasa correct model is expected to satisfy all the behavioral specifications wheninstantiated with a single set of parameter values. We present a new method,BioMETA, to address this problem such that a single set of parameter valuescauses a parameterized stochastic biochemical model to satisfy all the givenprobabilistic temporal logic behavioral specifications simultaneously. Ourmethod is based on combining a multiple hypothesis testing based statisticalmodel checking technique with simulated annealing search to look for a singleset of parameter values so that the given parameterized model satisfiesmultiple probabilistic behavioral specifications. We study two stochasticrule-based models of biochemical receptors, namely, Fc$\epsilon$RI and T-cellas our benchmarks to evaluate the usefulness of the presented method. Ourexperimental results successfully estimate $26$ parameters of Fc$\epsilon$RIand $29$ parameters of T-cell receptor model against three probabilistictemporal logic behavioral specifications each.

BioMETA: A multiple specification parameter estimation system for stochastic biochemical models