Optimal discovery of a stochastic genetic network

In this paper, we present a parameter identification algorithm for the discovery of a genetic regulatory network. The genetic network is modeled, via a mechanistic approach, as a nonlinear stochastic regulatory network, in which transcription, translation and degradation processes are described as discrete stochastic events which depend nonlinearly on the number of molecules inside the cell. The system depends on several unknowns, namely the rates of transcription, the rates of translation and the degradation rates. Furthermore, the system is observable through the measure, at regular time intervals, of the factorial cumulants of the molecule counts. The unknown parameters are uncovered by studying the system output response to an arbitrary command input. The parameter search is posed as an optimization program, in which the cost function is the deviation between the observed factorial cumulants and the model output, and in which the constraint is the parameterized ordinary differential equation (ODE) governing the time evolution of the factorial cumulants. The optimization problem is solved via an adjoint-based quasi- Newton algorithm. The command input is found to have an important impact on the parameter search: Oscillatory input signals yield better parameter discovery than flat input signals. Finally, numerical results are presented for two systems: a Hill feedback and a Michaelis Menten process.