(647b) Parameter Estimation in Stochastic Kinetic Models

In deterministic settings, we can use a chemical kinetic description
in terms of continuous ODE to model a chemically reacting system.
However, there are situations where the deterministic description of
the chemically reacting systems in terms of continuous ODE model is
inaccurate and unsatisfactory.  One such situation occurs when some
reactant, intermediate, or product species is present in a small
concentration (e.g. only $10-1000$ molecules in the whole
reactor). Another situation occurs inside a cell or tissue where
several proteins/RNAs/DNAs are present in small amount (e.g. $1-100$
molecules). For these situations researchers have developed
alternative representation for the chemically reacting system known as
stochastic chemical kinetics (SCK). This alternative representation
considers reactions as micro scale interaction between
molecules. Unlike the continuous ODE model where in a small time
instant all reactions occur with their respective rates, the SCK
representation considers the probabilities of different reactions
within a small amount of time. One of the salient features of SCK
description is that in the limit of populations of all species tending
to very large values, it converges to continuous ODE model
representation.

Even though the SCK description is an accurate way to model a system
with small population of some species, estimation of parameters for
this description remains still difficult. The reason for the
difficulty of the estimation problem is primarily due to two reasons.
First, the estimation problem either requires the solution of infinite
dimensional chemical master equation governing the probabilistic
evolution of the system or it requires too many stochastic simulations
of the realization of the system. Second, it is difficult to get
accurate gradients and Hessians of the objective function for which
we only have an estimator.

In this talk, we present reasons for accommodating measurement noise in experimental data. Then we present a new expression for experimental data likelihood.Next, we show utility of this new likelihood and methods of sensitivity estimation of this likelihood. Finally, we present methods of optimizing this new likelihood expression.