Abstract
Reaction networks are important tools for modeling a variety of biological phenomena across a wide range of scales, for example as models of gene regulation within a cell or infectious disease outbreaks in a population. Hence, calibrating these models to observed data is useful for predicting future system behavior. However, the statistical estimation of the parameters of reaction networks is often challenging due to intractable likelihoods. Here we explore estimating equations to estimate the reaction rate parameters of density dependent Markov jump processes (DDMJP). The variance–covariance weights we propose to use in the estimating equations are obtained from an approximating process, derived from the Fokker–Planck approximation of the chemical master equation for stochastic reaction networks. We investigate the performance of the proposed methodology in a simulation study of the Lotka–Volterra predator–prey model and by fitting a susceptible, infectious, removed (SIR) model to real data from the historical plague outbreak in Eyam, England.
Highlights
Reaction networks (RNs) are a set of mathematical tools often used to describe and analyze a wide variety of biological systems at many different scales, with examples ranging from infectious disease spread throughout a population to cellular regulation of gene expression
An RN is a model of how the individual components of a system, sometimes called species, interact with each other to update the state of the system, which evolves over time
Ribosomes, which diffuse throughout the cell, interact with this new RNA molecule to translate it into the functional gene product, a protein
Summary
Reaction networks (RNs) are a set of mathematical tools often used to describe and analyze a wide variety of biological systems at many different scales, with examples ranging from infectious disease spread throughout a population to cellular regulation of gene expression. Ribosomes, which diffuse throughout the cell, interact with this new RNA molecule to translate it into the functional gene product, a protein Some of these proteins, the so-called transcription factors, go on to bind to the promoter regions of other genes and thereby modulate their expression by tuning the binding affinity of RNA polymerase to this region. For overall gene expression through the creation of many thousands of proteins, the regulatory machinery of the cell remarkably coordinates the activity of a large number of the different types of species that perform the critical tasks required to sustain life Changes in this regulatory machinery lead to the huge observed variability in biology, i.e., different cell types like skin and liver cells, healthy tissues vs cancerous ones and different organisms. Reliable and accurate models of such systems can provide insight into a wide range of different biological phenomena of interest, from uncovering the mechanisms that lead to biological diversity to developing better treatment strategies in diseases like cancer
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