  Stochastic Boolean networks, or more generally, stochastic discrete networks,
are an important class of computational models for molecular interaction
networks. The stochasticity stems from the updating schedule. Standard updating
schedules include the synchronous update, where all the nodes are updated at
the same time, and the asynchronous update where a random node is updated at
each time step. The former produces a deterministic dynamics while the latter a
stochastic dynamics. A more general stochastic setting considers propensity
parameters for updating each node. Stochastic Discrete Dynamical Systems (SDDS)
is a modeling framework that considers two propensity parameters for updating
each node and uses one when the update has a positive impact on the variable,
that is, when the update causes the variable to increase its value, and uses
the other when the update has a negative impact, that is, when the update
causes it to decrease its value. This framework offers additional features for
simulations but also adds a complexity in parameter estimation of the
propensities. This paper presents a method for estimating the propensity
parameters for SDDS. The method is based on adding noise to the system using
the Google PageRank approach to make the system ergodic and thus guaranteeing
the existence of a stationary distribution. Then with the use of a genetic
algorithm, the propensity parameters are estimated. Approximation techniques
that make the search algorithms efficient are also presented and Matlab/Octave
code to test the algorithms are available at
http://www.ms.uky.edu/~dmu228/GeneticAlg/Code.html.
