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272666 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.

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