A parallel algorithm for п¬Ѓtting the parameters of a stochastic model in systems biology
In recent years, stochastic models have been used intensively in systems bi- ology to describe the biochemical network dynamics. Nevertheless, the problem of п¬Ѓtting the unknown parameters in a stochastic model to experimental data remains challenging. The discrepancy between the data and the model can be captured in the likelihood function, which acts as the вЂ?distanceвЂ™ to be mini- mized by the parameter set. Many models, however, can have the identiп¬Ѓability problem or confounded parameters, and the likelihood function can be multi- modal . An optimization scheme, therefore, has to start from many diп¬Ђerent initial guesses and the п¬Ѓnal guess for the parameters demands a large number of likelihood calculations. For complicated models, this can be time-consuming, especially if implemented as a serial algorithm in which only one optimization iteration can run at a time.
In this work, we parallelize the parameter п¬Ѓtting process. Independent op- timization iterations can run from diп¬Ђerent initial guesses at the same time, therefore reducing the time cost. An inhibitory model in Escherichia coli  is used in the numerical experiment, where п¬Ѓve unknown parameters need to be п¬Ѓtted to the observed protein counts at various time points. We investigate the performance of the parallel code with respect to the number of cores, and the eп¬ѓciency of the resulting parameter set in recreating the frequencies observed in the experimental data. This work can serve as a more general framework for parameter п¬Ѓtting in demanding problems in systems biology.
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