Bayesian inference of biochemical kinetic parameters using the linear noise approximation

TL;DR

This paper introduces a Bayesian method using the linear noise approximation for efficient estimation of biochemical kinetic parameters from gene reporter data, avoiding complex data augmentation.

Contribution

The paper presents a computationally efficient Bayesian algorithm for biochemical parameter inference using linear noise approximation, eliminating the need for data augmentation.

Findings

Efficient parameter estimation demonstrated on simulated data.

Method handles unobserved variables and measurement error.

Provides an alternative to diffusion approximation methods.

Abstract

Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the development of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data. We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo. The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods.