# Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art

## TL;DR

This paper reviews the evolution and current state of computational algorithms for simulating and inferring stochastic biochemical reaction networks, emphasizing practical MATLAB implementations for researchers.

## Contribution

It provides a comprehensive, accessible overview of historical developments and advanced computational techniques, including detailed algorithms and MATLAB code, for stochastic biochemical modeling.

## Key findings

- Summarizes key historical developments in stochastic biochemical modeling.
- Describes state-of-the-art algorithms for simulation and inference.
- Provides MATLAB implementations for practical use.

## Abstract

Stochasticity is a key characteristic of intracellular processes such as gene regulation and chemical signalling. Therefore, characterising stochastic effects in biochemical systems is essential to understand the complex dynamics of living things. Mathematical idealisations of biochemically reacting systems must be able to capture stochastic phenomena. While robust theory exists to describe such stochastic models, the computational challenges in exploring these models can be a significant burden in practice since realistic models are analytically intractable. Determining the expected behaviour and variability of a stochastic biochemical reaction network requires many probabilistic simulations of its evolution. Using a biochemical reaction network model to assist in the interpretation of time course data from a biological experiment is an even greater challenge due to the intractability of the likelihood function for determining observation probabilities. These computational challenges have been subjects of active research for over four decades. In this review, we present an accessible discussion of the major historical developments and state-of-the-art computational techniques relevant to simulation and inference problems for stochastic biochemical reaction network models. Detailed algorithms for particularly important methods are described and complemented with MATLAB implementations. As a result, this review provides a practical and accessible introduction to computational methods for stochastic models within the life sciences community.