Dealing with Stochasticity in Biological ODE Models

TL;DR

This paper introduces a method to convert deterministic biological ODE models into Dynamic Bayesian Networks, enabling better handling of uncertainty and noisy data through particle filtering for improved inference.

Contribution

It presents a novel approach to model biological systems with uncertainty by converting ODEs into DBNs and applying particle filtering for parameter and state inference.

Findings

DBNs handle missing and noisy data effectively.

High accuracy in variable inference with incomplete data.

Automatic re-estimation of model parameters using temporal evidence.

Abstract

Mathematical modeling with Ordinary Differential Equations (ODEs) has proven to be extremely successful in a variety of fields, including biology. However, these models are completely deterministic given a certain set of initial conditions. We convert mathematical ODE models of three benchmark biological systems to Dynamic Bayesian Networks (DBNs). The DBN model can handle model uncertainty and data uncertainty in a principled manner. They can be used for temporal data mining for noisy and missing variables. We apply Particle Filtering algorithm to infer the model variables by re-estimating the models parameters of various biological ODE models. The model parameters are automatically re-estimated using temporal evidence in the form of data streams. The results show that DBNs are capable of inferring the model variables of the ODE model with high accuracy in situations where data is missing, incomplete, sparse and irregular and true values of model parameters are not known.