Solving the chemical master equation for monomolecular reaction systems and beyond: a Doi-Peliti path integral view

Vastola, John J.

doi:10.1007/s00285-021-01670-7

Cited by 10 publications

(15 citation statements)

References 81 publications

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“…Unfortunately, we cannot simply apply existing methods from fluorescence transcriptomics; the scale and chemistry of singlecell technologies create additional desiderata. General CME solutions are computationally prohibitive and challenging to scale to thousands of genes 89 , requiring careful study of narrow model classes with tractable solutions 17,20 . In addition, connecting biological models to observations requires explicitly representing the experimental process.…”

Section: Discussionmentioning

confidence: 99%

“…Here, we explain why many naïve approaches to understanding the stochastic systems biology of single cells fall short, and describe a theoretical framework that can serve as an alternative. Our framework extends recent work on the mechanistic modeling of single-cell RNA count distributions [16][17][18][19][20][21] , and addresses both how models can be efficiently fit to single-cell data, and what features of the underlying biology we can hope to learn.…”

Section: Introductionmentioning

confidence: 94%

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Studying stochastic systems biology of the cell with single-cell genomics data

Gorin

Vastola

Pachter

2023

Preprint

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Recent experimental developments in genome-wide RNA quantification hold considerable promise for systems biology. However, rigorously probing the biology of living cells requires a unified mathematical framework that accounts for single-molecule biological stochasticity in the context of technical variation associated with genomics assays. We model a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and show how they can be integrated by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the framework.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 94%

Studying stochastic systems biology of the cell with single-cell genomics data

Gorin

Vastola

Pachter

2023

Preprint

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“…Although the presented approach is versatile and can in principle be applied to any stochastic gene regulatory network, its practical use depends on the ability to compute a reasonable approximation to the solution of the chemical master equation (CME) as well as its partial derivatives with respect to model parameters. Fortunately, there are now many relevant stochastic gene expression models for which exact or approximate analytical expressions for the CME solution are available ([55, 71, 79, 31, 10, 84]). Furthermore, the FSP and similar approaches have been used successfully to solve the CME for many non-linear and time-inhomogeneous regulatory models for which closed-form solutions do not exist ([74, 14, 45, 53, 73, 69]).…”

Section: Discussionmentioning

confidence: 99%

Analysis and design of single-cell experiments to harvest fluctuation information while rejecting measurement noise

Forero²,

Aguilera³

et al. 2021

Preprint

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Measurement error is a complicating factor that could reduce or distort the information contained in an experiment. This problem becomes even more serious in the context of experiments to measure single-cell gene expression heterogeneity, in which important quantities such as RNA and protein copy numbers are themselves subjected to the inherent randomness of biochemical reactions. Yet, it is not clear how measurement noise should be managed, in addition to other experiment design variables such as sampling size and frequency, in order to ensure that the collected data provides useful insights on the gene expression mechanism of interest. To address these experiment design challenges, we propose a model-centric framework that makes explicit use of measurement error modeling and Fisher Information Matrix-based criteria to decide between experimental methods. This unified approach not only allows us to see how different noise characteristics affect uncertainty in parameter estimation, but also enables a systematic approach to designing hybrid experiments that combine different measurement methods.

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“…Vastola [35] has recently used the Doi-Peliti path integral approach to re-derive the results of Jahnke and Huisinga [24], including also arbitrary unary reactions in his analysis. We will also use the Doi-Peliti path integral technique in this work, but will then deploy the tools of statistical field theory and show that under certain approximation, we can obtain very accurate and general results that allows us to treat generic reaction networks made up of binary reactions in addition to arbitrary unary reactions.…”

Section: Introductionmentioning

confidence: 99%

Accurate dynamics from self-consistent memory in stochastic chemical reactions with small copy numbers

Harsh,

Sollich

2023

J. Phys. A: Math. Theor.

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We present a method that captures the ﬂuctuations beyond mean ﬁeld in chemical reactions in the regime of small copy numbers and hence large ﬂuctuations, using self-consistently determined memory: by integrating information from the past we can systematically improve our approximation for the dynamics of chemical reactions. This memory emerges from a perturbative treatment of the eﬀective action of the Doi-Peliti ﬁeld theory for chemical reactions. By dressing only the response functions and by the self-consistent replacement of bare responses by the dressed ones, we show how a very small class of diagrams contributes to this expansion, with clear physical interpretations. From these diagrams, a large sub-class can be further resummed to inﬁnite order, resulting in a method that is stable even for large values of the expansion parameter or equivalently large reaction rates. We demonstrate this method and its accuracy on single and multi-species binary reactions across a range of reaction constant values.

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Solving the chemical master equation for monomolecular reaction systems and beyond: a Doi-Peliti path integral view

Cited by 10 publications

References 81 publications

Studying stochastic systems biology of the cell with single-cell genomics data

Studying stochastic systems biology of the cell with single-cell genomics data

Analysis and design of single-cell experiments to harvest fluctuation information while rejecting measurement noise

Accurate dynamics from self-consistent memory in stochastic chemical reactions with small copy numbers

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