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Register a new userExact solution of stochastic gene expression models with bursting, cell cycle and replication dynamics
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The bulk of stochastic gene expression models in the literature do not have an explicit description of the age of a cell within a generation and hence they cannot capture events such as cell division and DNA replication. Instead, many models incorporate cell cycle implicitly by assuming that dilution due to cell division can be described by an effective decay reaction with first-order kinetics. If it is further assumed that protein production occurs in bursts then the stationary protein distribution is a negative binomial. Here we seek to understand how accurate these implicit models are when compared with more detailed models of stochastic gene expression. We derive the exact stationary solution of the chemical master equation describing bursty protein dynamics, binomial partitioning at mitosis, age-dependent transcription dynamics including replication, and random interdivision times sampled from Erlang or more general distributions; the solution is different for single lineage and population snapshot settings. We show that protein distributions are well approximated by the solution of implicit models (a negative binomial) when the mean number of mRNAs produced per cycle is low and the cell cycle length variability is large. When these conditions are not met, the distributions are either almost bimodal or else display very flat regions near the mode and cannot be described by implicit models. We also show that for genes with low transcription rates, the size of protein noise has a strong dependence on the replication time, it is almost independent of cell cycle variability for lineage measurements and increases with cell cycle variability for population snapshot measurements. In contrast for large transcription rates, the size of protein noise is independent of replication time and increases with cell cycle variability for both lineage and population measurements.
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A stochastic model of autoregulated bursty gene expression by Kumar et al. [Phys. Rev. Lett. 113, 268105 (2014)] has been exactly solved in steady-state conditions under the implicit assumption that protein numbers are sufficiently large such that fluctuations in protein numbers due to reversible protein-promoter binding can be ignored. Here we derive an alternative model that takes into account these fluctuations and hence can be used to study low protein number effects. The exact steady-state protein number distributions is derived as a sum of Gaussian hypergeometric functions. We use the theory to study how promoter switching rates and the type of feedback influence the size of protein noise and noise-induced bistability. Furthermore we show that our model predictions for the protein number distribution are significantly different from those of Kumar et al. when the protein mean is small, gene switching is fast, and protein binding is faster than unbinding.
In the last years, tens of thousands gene expression profiles for cells of several organisms have been monitored. Gene expression is a complex transcriptional process where mRNA molecules are translated into proteins, which control most of the cell functions. In this process, the correlation among genes is crucial to determine the specific functions of genes. Here, we propose a novel multi-dimensional stochastic approach to deal with the gene correlation phenomena. Interestingly, our stochastic framework suggests that the study of the gene correlation requires only one theoretical assumption -Markov property- and the experimental transition probability, which characterizes the gene correlation system. Finally, a gene expression experiment is proposed for future applications of the model.
The arabinose utilization system of E. coli displays a stochastic all or nothing response at intermediate levels of arabinose, where the population divides into a fraction catabolizing the sugar at a high rate (ON state) and a fraction not utilizing arabinose (OFF state). Here we study this decision process in individual cells, focusing on the dynamics of the transition from the OFF to the ON state. Using quantitative time-lapse microscopy, we determine the time delay between inducer addition and fluorescence onset of a GFP reporter. Through independent characterization of the GFP maturation process, we can separate the lag time caused by the reporter from the intrinsic activation time of the arabinose system. The resulting distribution of intrinsic time delays scales inversely with the external arabinose concentration, and is compatible with a simple stochastic model for arabinose uptake. Our findings support the idea that the heterogeneous timing of gene induction is causally related to a broad distribution of uptake proteins at the time of sugar addition.
With the wealth of high-throughput sequencing data generated by recent large-scale consortia, predictive gene expression modelling has become an important tool for integrative analysis of transcriptomic and epigenetic data. However, sequencing data-sets are characteristically large, and previously modelling frameworks are typically inefficient and unable to leverage multi-core or distributed processing architectures. In this study, we detail an efficient and parallelised MapReduce implementation of gene expression modelling. We leverage the computational efficiency of this framework to provide an integrative analysis of over fifty histone modification data-sets across a variety of cancerous and non-cancerous cell-lines. Our results demonstrate that the genome-wide relationships between histone modifications and mRNA transcription are lineage, tissue and karyotype-invariant, and that models trained on matched epigenetic/transcriptomic data from non-cancerous cell-lines are able to predict cancerous expression with equivalent genome-wide fidelity.
Inferring functional relationships within complex networks from static snapshots of a subset of variables is a ubiquitous problem in science. For example, a key challenge of systems biology is to translate cellular heterogeneity data obtained from single-cell sequencing or flow-cytometry experiments into regulatory dynamics. We show how static population snapshots of co-variability can be exploited to rigorously infer properties of gene expression dynamics when gene expression reporters probe their upstream dynamics on separate time-scales. This can be experimentally exploited in dual-reporter experiments with fluorescent proteins of unequal maturation times, thus turning an experimental bug into an analysis feature. We derive correlation conditions that detect the presence of closed-loop feedback regulation in gene regulatory networks. Furthermore, we show how genes with cell-cycle dependent transcription rates can be identified from the variability of co-regulated fluorescent proteins. Similar correlation constraints might prove useful in other areas of science in which static correlation snapshots are used to infer causal connections between dynamically interacting components.
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