Parameter estimation in stochastic biochemical reactions

Abstract

Gene regulatory, signal transduction and metabolic networks are major areas of interest in the newly emerging field of systems biology. In living cells, stochastic dynamics play an important role; however, the kinetic parameters of biochemical reactions necessary for modelling these processes are often not accessible directly through experiments. The problem of estimating stochastic reaction constants from molecule count data measured, with error, at discrete time points is considered. For modelling the system, a hidden Markov process is used, where the hidden states are the true molecule counts, and the transitions between those states correspond to reaction events following collisions of molecules. Two different algorithms are proposed for estimating the unknown model parameters. The first is an approximate maximum likelihood method that gives good estimates of the reaction parameters in systems with few possible reactions in each sampling interval. The second algorithm, treating the data as exact measurements, approximates the number of reactions in each sampling interval by solving a simple linear equation. Maximising the likelihood based on these approximations can provide good results, even in complex reaction systems.

Parameter Estimation of Kinetic Rates in Stochastic Reaction Networks by the EM Method

“…The obtained rates can be transformed into the kinetic rates of the stochastic model. As pointed out however in [14] this is not always possible. For this reason some recent studies have attempted to give an estimate of the kinetic rates based on the stochastic view introduced by [8].…”

“…For this reason some recent studies have attempted to give an estimate of the kinetic rates based on the stochastic view introduced by [8]. Bayesian inference methods were used in [10,2], maximum likelihood methods were applied in [14,4,16].…”

Approximate Bayesian Parameter Inference for Dynamical Systems in Systems Biology

“…In the more general case, this approach does not allow for a complete and physically correct representation of the basic stochastic processes that take place in a living cell. On the other hand, the discrete and stochastic evolution takes into account the discrete number of entities in the system and the random nature of the events taking place, drawing nearer to the theories of thermodynamics and stochastic processes [2].…”

Development of the MCR Method for Estimation of Parameters in Continuous Time Markov Chain Models

“…Parameter estimation techniques for deterministic models have been developed extensively (see [3] and the many references therein); however, techniques for parameter estimation in stochastic models is still relatively in its infancy [22]. Some techniques involve the likelihood-based methods [17,19,20,21,22], likelihood-free or bayesian methods [4,6,10,11,12,16,7,14], and approximation methods using deterministic systems [3,18].…”