Probability metrics to calibrate stochastic chemical kinetics

Calibration or model parameter estimation from measured data is an ubiquitous problem in engineering. In systems biology this problem turns out to be particularly challenging due to very short data-records, low signal-to-noise ratio of data acquisition, large intrinsic process noise and limited measurement access to only a few, of sometimes several hundreds, state variables. We review state-of-the-art model calibration techniques and also discuss their relation to the general reverse-engineering problem in systems biology. For biomolecular circuits involving low-copy-number molecules we adopt a Markov process setup and discuss a calibration approach based on suitable metrics between probability measures and propose the metrics computation for the multivariate case. In particular, we use Kantorovich's distance and devise an algorithm, for the case when FACS (fluorescence-activated cell sorting) measurements are given. We discuss a case study involving FACS data for the high-osmolarity glycerol (HOG) pathway in budding yeast.