Bayesian inference of transcription dynamics from population snapshots of single-molecule RNA FISH in single cells

Gómez-Schiavon, Mariana; Chen, Liangfu; West, Anne E.; Buchler, Nicolas E.

doi:10.1101/109603

Cited by 4 publications

(9 citation statements)

References 34 publications

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“…This lower bound is chosen manually such that the prior bounds lie outside the support of the posterior. An example experimental estimate of a gene transcription rate is two transcripts per minute 76 . A genome-wide quantification of transcription rate estimates in mouse fibroblast cells revealed a distribution of transcription rates between 10 !!…”

Section: Prior Information On Parametersmentioning

confidence: 99%

Quantitative single-cell live imaging links HES5 dynamics with cell-state and fate in murine neurogenesis

Manning

Biga

Boyd

et al. 2018

Preprint

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During embryogenesis cells make fate decisions within complex tissue environments. The levels and dynamics of transcription factor expression regulate these decisions.Here we use single cell live imaging of an endogenous HES5 reporter and absolute protein quantification to gain a dynamic view of neurogenesis in the embryonic mammalian spinal cord. We report that dividing neural progenitors show both aperiodic and periodic HES5 protein fluctuations. Mathematical modelling suggests that in progenitor cells the HES5 oscillator operates close to its bifurcation boundary where stochastic conversions between dynamics are possible. HES5 expression becomes more frequently periodic as cells transition to differentiation which, coupled with an overall decline in HES5 expression, creates a transient period of oscillations with higher fold expression change. This increases the decoding capacity of HES5 oscillations and correlates with interneuron versus motor neuron cell fate. Thus, HES5 undergoes complex changes in gene expression dynamics as cells differentiate.

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Section: Prior Information On Parametersmentioning

confidence: 99%

Quantitative single-cell live imaging links HES5 dynamics with cell-state and fate in murine neurogenesis

Manning

Biga

Boyd

et al. 2018

Preprint

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“…Data from smFISH experiments [6][7][8]10 consist of several snapshots of many independent cells taken at discrete times t 1 , . .…”

Section: Bayesian Inference From Single-cell Datamentioning

confidence: 99%

“…44 For gene expression models, the MH has been combined with the FSP for parameter inference and model selection in several studies. 10,15 The appropriate choice of Σ is crucial for the performance of the Metropolis algorithm.…”

Section: The Metropolis-hastings and The Adaptive Metropolis Algorithmsmentioning

confidence: 99%

“…[6][7][8][9][10] A sucessful framework for building predictive models for gene expression dynamics from such data is to fit the solution of the chemical master equation (CME) 11 to the empirical histogram obtained from population snapshots at several experimental conditions or time-points. 8,10,12,13 The finite state projection (FSP), 14 which approximates the dynamics of the CME with a finite system of linear ODEs, provides a framework to analyze full distributions of stochastic gene expression models with computable error bounds. It has been observed that full distribution-based analyses using the FSP perform well, even when applied to realistically small experimental datasets on which summary statistics-based fits may fail.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian estimation for stochastic gene expression using multifidelity models

Fox

Baetica

et al. 2018

Preprint

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The finite state projection (FSP) approach to solving the chemical master equation has enabled successful inference of discrete stochastic models to predict single-cell gene regulation dynamics. Unfortunately, the FSP approach is highly computationally intensive for all but the simplest models, an issue that is highly problematic when parameter inference and uncertainty quantification takes enormous numbers of parameter evaluations. To address this issue, we propose two new computational methods for the Bayesian inference of stochastic gene expression parameters given single-cell experiments. We formulate and verify an Adaptive Delayed Acceptance Metropolis-Hastings (ADAMH) algorithm to utilize with reduced Krylov-basis projections of the FSP. We then introduce an extension of the ADAMH into a Hybrid scheme that consists of an initial phase to construct a reduced model and a faster second phase to sample from the approximate posterior distribution determined by the constructed model. We test and compare both algorithms to an adaptive Metropolis algorithm with full FSP-based likelihood evaluations on three example models and simulated data to show that the new ADAMH variants achieve substantial speedup in comparison to the full FSP approach. By reducing the computational costs of parameter estimation, we expect the ADAMH approach to enable efficient data-driven estimation for more complex gene regulation models.

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“…6−10 A successful framework for building predictive models for gene expression dynamics from such data is to fit the solution of the chemical master equation (CME) 11 to the empirical histogram obtained from population snapshots at several experimental conditions or time-points. 8,10,12,13 The finite state projection (FSP), 14 which approximates the dynamics of the CME with a finite system of linear ODEs, provides a framework to analyze full distributions of stochastic gene expression models with computable error bounds. It has been observed that full distribution-based analyses using the FSP perform well, even when applied to realistically small experimental data sets on which summary statistics-based fits may fail.…”

Section: ■ Introductionmentioning

confidence: 99%

Bayesian Estimation for Stochastic Gene Expression Using Multifidelity Models

Fox

Baetica

et al. 2019

J. Phys. Chem. B

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We will derive ergodicity results in the following sections based on Theorem 1 in the paper of Roberts and Rosenthal, 1 and we will use some proof techniques of Theorem 1 from Cui et al. 2 for part of our analysis. All random variables we will discuss below will be of the form X : Ω → X where X is a metric space with the associated Borel σ-algebra B(X ).Let X be the parameter space, assumed to have a metric space topology, and π : B(X ) → [0, 1] the target distribution to be sampled from by an adaptive MCMC algorithm. We will assume that π has a density f : X → [0, ∞). Let K γ denote a transition kernel that depends on an adaptation index γ ∈ Y, and assume that each K γ has π as an invariant distribution.We assume that for each fixed γ, an MCMC algorithm with K γ as the Markov transition kernel will eventually converge to π, that is lim n→∞ K n (x, .) − π T V = 0 where µ − ν T V = sup B∈B(X ) |µ(B) − ν(B)| is the total variation distance between two probability measures on X . Let X n be the random variable representing the state of the adaptive MCMC at iteration n, and let Γ n be the random variable representing the choice of kernel for updating from X n to X n+1 . The state of the algorithm is then modeled by the discrete-time stochastic process {(X n , Γ n )}, whose transition between steps is determined by the underlying rules of the algorithm. Finally, let G n = σ ({X 0 , . . . , X n , Γ 0 , . . . , Γ n }) denote the filtration generated by {(X n , Γ n )}. Thus, each Γ n+1 is a G n+1 -measurable random variable.Roberts and Rosenthal proved the following important result, which gives sufficient conditions for ergodicity of an adaptive MCMC.Theorem 1 (Theorem 1 in Roberts and Rosenthal 1 ). Consider an adaptive MCMC algo-

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Bayesian inference of transcription dynamics from population snapshots of single-molecule RNA FISH in single cells

Cited by 4 publications

References 34 publications

Quantitative single-cell live imaging links HES5 dynamics with cell-state and fate in murine neurogenesis

Quantitative single-cell live imaging links HES5 dynamics with cell-state and fate in murine neurogenesis

Bayesian estimation for stochastic gene expression using multifidelity models

Bayesian Estimation for Stochastic Gene Expression Using Multifidelity Models

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