Reconstruction of transcriptional dynamics from gene reporter data using differential equations

Abstract

Motivation: Promoter-driven reporter genes, notably luciferase and green fluorescent protein, provide a tool for the generation of a vast array of time-course data sets from living cells and organisms. The aim of this study is to introduce a modeling framework based on stochastic differential equations (SDEs) and ordinary differential equations (ODEs) that addresses the problem of reconstructing transcription time-course profiles and associated degradation rates. The dynamical model is embedded into a Bayesian framework and inference is performed using Markov chain Monte Carlo algorithms.Results: We present three case studies where the methodology is used to reconstruct unobserved transcription profiles and to estimate associated degradation rates. We discuss advantages and limits of fitting either SDEs ODEs and address the problem of parameter identifiability when model variables are unobserved. We also suggest functional forms, such as on/off switches and stimulus response functions to model transcriptional dynamics and present results of fitting these to experimental data.Contact: b.f.finkenstadt@warwick.ac.ukSupplementary Information: Supplementary data are available at Bioinformatics online.

Novel approaches to in vitro transgenesis

“…Increasing our understanding of dynamic and stochastic gene expression requires the facility to monitor rapid changes in the transcriptional rate of the gene-of-interest (Raser & O'Shea 2004). Accurate quantitative data for reporter gene synthesis and degradation is essential in order to incorporate mathematical modelling and systems biology approaches into studies (Finkenstädt et al 2008). Thus, reporter gene development is an ongoing process and is important to ensure that reporter molecules can be selected and tailored to meet the requirements of specific gene expression studies.…”

Determining transcription factor profiles from fluorescent reporter systems involving regularization of inverse problems

“…However, Manuscript the relationship between the concentration of the transcription factors and the observed fluorescence is not straightforward as it involves dynamic processes dealing with transcription, translation, and post-translational modification of GFP [4]. A number of mathematical models describing these processes have been developed [5][6][7][8][9] and these models have been used for estimating the mRNA or transcription dynamics from gene expression data. In most of these works, a certain nature of the dynamic profile of the compound was assumed and then the parameters were estimated to characterize the profile [6][7]10].…”

“…A number of mathematical models describing these processes have been developed [5][6][7][8][9] and these models have been used for estimating the mRNA or transcription dynamics from gene expression data. In most of these works, a certain nature of the dynamic profile of the compound was assumed and then the parameters were estimated to characterize the profile [6][7]10]. One drawback of this approach is that it restricts the functional form of the estimated profiles.…”

Inferring Nonstationary Gene Networks from Longitudinal Gene Expression Microarrays

“…Various approaches have been proposed to reverseengineer gene interactions over time, ranging from highly detailed models, such as differential equations [10], to highly abstract models, such as Boolean networks [11]. The former describes the molecular kinetic reactions taking place in a cell, and the latter quantizes expression levels as binary variables that are linked to each other through logical relationships.…”