Parameter estimation for biochemical reaction networks using Wasserstein distances

Öcal, Kaan; Grima, Ramon; Sanguinetti, Guido

doi:10.1088/1751-8121/ab5877

Cited by 28 publications

(19 citation statements)

References 36 publications

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“…by measuring nascent RNA numbers using live-cell imaging techniques (such as the MS2 system) at several time points for many cells [35, 36]. Our ANN based inference method rests upon the matching of distributions and hence similar to non-ANN based methods developed in Refs [37, 38], it avoids the pitfalls of moment-based inference [39,40]. We note that the ability to approximate solutions of delay master equations from simulated data while simultaneously optimizing for the parameters has not been demonstrated before; deep learning frameworks have previously achieved similar feats for deterministic models [13, 16] and more recently for stochastic models described by multi-dimensional Fokker-Planck equations [41, 42].…”

Section: Discussionmentioning

confidence: 99%

Neural network aided approximation and parameter inference of stochastic models of gene expression

Jiang

Yan

et al. 2020

Preprint

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Non-Markov models of stochastic biochemical kinetics often incorporate explicit time delays to effectively model large numbers of intermediate biochemical processes. Analysis and simulation of these models, as well as the inference of their parameters from data, are fraught with difficulties because the dynamics depends on the system's history. Here we use an artificial neural network to approximate the time dependent distributions of non-Markov models by the solutions of much simpler time-inhomogeneous Markov models; the approximation does not increase the dimensionality of the model and simultaneously leads to inference of the kinetic parameters. The training of the neural network uses a relatively small set of noisy measurements generated by experimental data or stochastic simulations of the non-Markov model. We show using a variety of models, where the delays stem from transcriptional processes and feedback control, that the Markov models learnt by the neural network accurately reflect the stochastic dynamics across parameter space.

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Section: Discussionmentioning

confidence: 99%

Neural network aided approximation and parameter inference of stochastic models of gene expression

Jiang

Yan

et al. 2020

Preprint

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“…The discrepancy between empirical distributions and predicted distributions by our jump diffusion process is measured by Wasserstein distance for its smoothness (Arjovsky et al, 2017). Wasserstein distance is also used in parameter estimation of biochemical reaction networks (Öcal et al, 2019). Wasserstein-1 distance, also called Earth-Mover distance, is defined by where Π( P 1 , P 2 ) denotes the set of every joint distribution γ whose marginals are P 1 , P 2 respectively.…”

Section: Methodsmentioning

confidence: 99%

A data-driven method to learn a jump diffusion process from aggregate biological gene expression data

Gao

Wang

Zhang

et al. 2021

Preprint

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Dynamic models of gene expression are urgently required. Different from trajectory inference and RNA velocity, our method reveals gene dynamics by learning a jump diffusion process for modeling the biological process directly. The algorithm needs aggregate gene expression data as input and outputs the parameters of the jump diffusion process. The learned jump diffusion process can predict population distributions of gene expression at any developmental stage, achieve long-time trajectories for individual cells, and offer a novel approach to computing RNA velocity. Moreover, it studies biological systems from a stochastic dynamics perspective. Gene expression data at a time point, which is a snapshot of a cellular process, is treated as an empirical marginal distribution of a stochastic process. The Wasserstein distance between the empirical distribution and predicted distribution by the jump diffusion process is minimized to learn the dynamics. For the learned jump diffusion equation, its trajectories correspond to the development process of cells and stochasticity determines the heterogeneity of cells. Its instantaneous rate of state change can be taken as "RNA velocity", and the changes in scales and orientations of clusters can be noticed too. We demonstrate that our method can recover the underlying nonlinear dynamics better compared to parametric models and diffusion processes driven by Brownian motion for both synthetic and real world datasets. Our method is also robust to perturbations of data because it only involves population expectations.

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“…(2) and (4) simplify to while the covariances and between the species are zero; here, the subscript c denotes the constitutive limit. This drastic simplification reflects the fact that, in the constitutive limit, the distributions of mature RNA and local RNAP are Poissonian: as the regulatory network is effectively given by then, the result follows directly from the exact solution provided in Jahnke and Huisinga ( 2007 ).…”

Section: Detailed Stochastic Model Of Transcription: Set-up and Analymentioning

confidence: 99%

“…Thus far, we have derived expressions for the first two moments of the distributions of total RNAP and mature RNA. Naturally, it would also be useful to derive closed-form expressions for the distributions themselves; such a derivation is, however, analytically intractable in general (Jahnke and Huisinga 2007 ) due to the presence of the catalytic reaction , which models initiation of the transcription process. Still, there are two special cases where analytical distributions are known: (i) when the elongation time is considered to be fixed, which corresponds to our model with at constant (Heng et al.…”

Section: Approximate Distributions Of Total Rnap and Mature Rnamentioning

confidence: 99%

Statistics of Nascent and Mature RNA Fluctuations in a Stochastic Model of Transcriptional Initiation, Elongation, Pausing, and Termination

2020

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Recent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. We derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations on gene segments, as well as of total nascent RNA on a gene. We also obtain exact expressions for the first two moments of mature RNA fluctuations and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

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Parameter estimation for biochemical reaction networks using Wasserstein distances

Cited by 28 publications

References 36 publications

Neural network aided approximation and parameter inference of stochastic models of gene expression

Neural network aided approximation and parameter inference of stochastic models of gene expression

A data-driven method to learn a jump diffusion process from aggregate biological gene expression data

Statistics of Nascent and Mature RNA Fluctuations in a Stochastic Model of Transcriptional Initiation, Elongation, Pausing, and Termination

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