A stochastic transcriptional switch model for single cell imaging data

Abstract

Gene expression is made up of inherently stochastic processes within single cells and can be modeled through stochastic reaction networks (SRNs). In particular, SRNs capture the features of intrinsic variability arising from intracellular biochemical processes. We extend current models for gene expression to allow the transcriptional process within an SRN to follow a random step or switch function which may be estimated using reversible jump Markov chain Monte Carlo (MCMC). This stochastic switch model provides a generic framework to capture many different dynamic features observed in single cell gene expression. Inference for such SRNs is challenging due to the intractability of the transition densities. We derive a model-specific birth–death approximation and study its use for inference in comparison with the linear noise approximation where both approximations are considered within the unifying framework of state-space models. The methodology is applied to synthetic as well as experimental single cell imaging data measuring expression of the human prolactin gene in pituitary cells.

Multimodal transcriptional control of pattern formation in embryonic development

“…In order to model the process of transcription and extract the kinetic parameters of promoter switching, we augmented classic HMMs to account for memory (details about implementation of the method are given in Appendix 3). Similar approaches were recently introduced to study transcriptional dynamics in cell culture and tissue samples (Suter et al, 2011; Molina et al, 2013; Zechner et al, 2014; Zoller et al, 2015; Hey et al, 2015; Bronstein et al, 2015; Corrigan et al, 2016; Featherstone et al, 2016). We used simulated data to establish that mHMM reliably extracts the kinetic parameters of transcriptional bursting from live-imaging data (Appendix 4), providing an ideal tool for dissecting the contributions from individual bursting parameters to observed patterns of transcriptional activity across space and time.…”

Bayesian estimation for stochastic gene expression using multifidelity models

“…The adaptive MH has been used in previous works on gene expression models in combination with fluorescent time-course data and flow cytometry data. 47,48…”

Estimating numbers of fluorescent molecules in single cells by analysing fluctuations in photobleaching

“…To infer numbers of molecules, we require a model for the measurement noise generated by fluorescence microscopes. A common description of this error is additive Gaussian noise [1,2,4,18,36]. Writing N (y; µ, σ 2 ) for a Gaussian distribution in y with mean µ and standard deviation σ, y j (t) for the measured fluorescence of cell j at time point t, and ν for the fluorescence per molecule -the parameter that we wish to infer, we have…”

“…Due to their complexity, these models are no longer amenable to previous approaches [18,21], and we instead use Bayesian methods for the analyses of time-series. Briefly (see Methods for details), we employ the linear noise approximation [16,39] to describe fluctuations in the dynamics of bleaching and combine this approximation with a Kalman filter [36,40] to estimate the likelihood of the parameters. These parameters include homogenous parameters shared between all cells (ν and σ e ) and heterogeneous parameters that vary from cell to cell (λ 1,j , λ 2,j , and f j ).…”