publications

2024

1. 

   New and notable: Revisiting the ‘‘two cultures’’ through extrinsic noise

   Gennady Gorin, and Lior Pachter

   Biophysical Journal, Jan 2024

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   A recent article by Grima and Esmenjaud draws attention to the unexpectedly complex effects of extrinsic noise on inference of transcriptional kinetics. We contrast the authors’ mechanistic approach with the descriptive, data-scientific methods used in single-cell RNA sequencing, and discuss broader philosophical connections to Leo Breiman’s "two cultures" of statistics.

2023

1. 

   The telegraph process is not a subordinator

   Gennady Gorin, and Lior Pachter

   bioRxiv, Jan 2023

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   Investigations of transcriptional models by Amrhein et al. outline a strategy for connecting steady-state distributions to process dynamics. We clarify its limitations: the strategy holds for a very narrow class of processes, which excludes an example given by the authors.

2. 

   Length biases in single-cell RNA sequencing of pre-mRNA

   Gennady Gorin, and Lior Pachter

   Biophysical Reports, Mar 2023

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   Single-cell RNA sequencing data can be modeled using Markov chains to yield genome-wide insights into transcriptional physics. However, quantitative inference with such data requires careful assessment of noise sources. We find that long pre-mRNA transcripts are over-represented in sequencing data. To explain this trend, we propose a length-based model of capture bias, which may produce false-positive observations. We solve this model and use it to find concordant parameter trends as well as systematic, mechanistically interpretable technical and biological differences in paired data sets.

3. 

   Distinguishing biophysical stochasticity from technical noise in single-cell RNA sequencing using Monod

   Gennady Gorin, and Lior Pachter

   bioRxiv, Apr 2023

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   We present the Python package Monod for the analysis of single-cell RNA sequencing count data through biophysical modeling. Monod naturally “integrates” unspliced and spliced count matrices, and provides a route to identifying and studying differential expression patterns that do not cause changes in average gene expression. The Monod framework is open-source and modular, and may be extended to more sophisticated models of variation and further experimental observables. The Monod package can be installed from the command line using pip install monod. The source code is available and maintained at https://github.com/pachterlab/monod. A separate repository, which contains sample data and Python notebooks for analysis with Monod, is accessible at https://github.com/pachterlab/monod_examples/. Structured documentation and tutorials are hosted at https://monod-examples.readthedocs.io/.

4. 

   Biophysical modeling with variational autoencoders for bimodal, single-cell RNA sequencing data

   Maria Carilli*, Gennady Gorin*, Yongin Choi, Tara Chari, and Lior Pachter

   bioRxiv, May 2023

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   We motivate and present biVI, which combines the variational autoencoder framework of scVI with biophysically motivated, bivariate models for nascent and mature RNA distributions. While previous approaches to integrate bimodal data via the variational autoencoder framework ignore the causal relationship between measurements, biVI models the biophysical processes that give rise to observations. We demonstrate through simulated benchmarking that biVI captures cell type structure in a low-dimensional space and accurately recapitulates parameter values and copy number distributions. On biological data, biVI provides a scalable route for identifying the biophysical mechanisms underlying gene expression. This analytical approach outlines a generalizable strategy for treating multimodal datasets generated by high-throughput, single-cell genomic assays.

5. 

   Biophysically Interpretable Inference of Cell Types from Multimodal Sequencing Data

   Tara Chari, Gennady Gorin, and Lior Pachter

   bioRxiv, Sep 2023

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   Multimodal, single-cell genomics technologies enable simultaneous capture of multiple facets of DNA and RNA processing in the cell. This creates opportunities for transcriptome-wide, mechanistic studies of cellular processing in heterogeneous cell types, with applications ranging from inferring kinetic differences between cells, to the role of stochasticity in driving heterogeneity. However, current methods for determining cell types or ‘clusters’ present in multimodal data often rely on ad hoc or independent treatment of modalities, and assumptions ignoring inherent properties of the count data. To enable interpretable and consistent cell cluster determination from multimodal data, we present meK-Means (mechanistic K-Means) which integrates modalities and learns underlying, shared biophysical states through a unifying model of transcription. In particular, we demonstrate how meK-Means can be used to cluster cells from unspliced and spliced mRNA count modalities. By utilizing the causal, physical relationships underlying these modalities, we identify shared transcriptional kinetics across cells, which induce the observed gene expression profiles, and provide an alternative definition for ’clusters’ through the governing parameters of cellular processes.

6. 

   Assessing Markovian and Delay Models for Single-Nucleus RNA Sequencing

   Gennady Gorin, Shawn Yoshida, and Lior Pachter

   Bulletin of Mathematical Biology, Oct 2023

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   The serial nature of reactions involved in the RNA life-cycle motivates the incorporation of delays in models of transcriptional dynamics. The models couple a transcriptional process to a fairly general set of delayed monomolecular reactions with no feedback. We provide numerical strategies for calculating the RNA copy number distributions induced by these models, and solve several systems with splicing, degradation, and catalysis. An analysis of single-cell and single-nucleus RNA sequencing data using these models reveals that the kinetics of nuclear export do not appear to require invocation of a non-Markovian waiting time.

7. 

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

   Gennady Gorin, John J. Vastola, and Lior Pachter

   Cell Systems, Oct 2023

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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 review models for a variety of RNA transcription processes, as well as the encapsulation and library construction steps of microfluidics-based single-cell RNA sequencing, and present a framework to integrate these phenomena by the manipulation of generating functions. Finally, we use simulated scenarios and biological data to illustrate the implications and applications of the approach.

2022

1. 

   Modeling bursty transcription and splicing with the chemical master equation

   Gennady Gorin, and Lior Pachter

   Biophysical Journal, Feb 2022

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   Splicing cascades that alter gene products post-transcriptionally also affect expression dynamics. We study a class of processes and associated distributions that emerge from models of bursty promoters coupled to directed acyclic graphs of splicing. These solutions provide full time-dependent joint distributions for an arbitrary number of species with general noise behaviors and transient phenomena, offering qualitative and quantitative insights about how splicing can regulate expression dynamics. Finally, we derive a set of quantitative constraints on the minimum complexity necessary to reproduce gene coexpression patterns using synchronized burst models. We validate these findings by analyzing long-read sequencing data, where we find evidence of expression patterns largely consistent with these constraints.

2. 

   Spectral neural approximations for models of transcriptional dynamics

   Gennady Gorin*, Maria Carilli*, Tara Chari, and Lior Pachter

   bioRxiv, Jun 2022

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   Transcriptional systems involving discrete, stochastic events are naturally modeled using Chemical Master Equations (CMEs). These can be solved for microstate probabilities over time and state space for a better understanding of biological rates and system dynamics. However, closed form solutions to CMEs are available in only the simplest cases. Probing systems of higher complexity is challenging due to the computational cost of finding solutions and often compromises accuracy by treating infinite systems as finite. We use statistical understanding of system behavior and the generalizability of neural networks to approximate steady-state joint distribution solutions for a two-species model of the life cycle of RNA. We define a set of kernel functions using moments of the system and learn optimal weights for kernel functions with a neural network trained to minimize statistical distance between approximated and numerically calculated distributions. We show that this method of kernel weight regression (KWR) approximation is as accurate as lower-order generating-function solutions to the system, but faster; KWR approximation reduces the time for likelihood evaluation by several orders of magnitude. KWR also generalizes to produce probability predictions for system rates outside of training sets, thereby enabling efficient transcriptional parameter exploration and system analysis.

3. 

   RNA velocity unraveled

   Gennady Gorin, Meichen Fang, Tara Chari, and Lior Pachter

   PLOS Computational Biology, Sep 2022

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   We perform a thorough analysis of RNA velocity methods, with a view towards understanding the suitability of the various assumptions underlying popular implementations. In addition to providing a self-contained exposition of the underlying mathematics, we undertake simulations and perform controlled experiments on biological datasets to assess workflow sensitivity to parameter choices and underlying biology. Finally, we argue for a more rigorous approach to RNA velocity, and present a framework for Markovian analysis that points to directions for improvement and mitigation of current problems.

4. 

   Interpretable and tractable models of transcriptional noise for the rational design of single-molecule quantification experiments

   Gennady Gorin*, John J. Vastola*, Meichen Fang, and Lior Pachter

   Nature Communications, Dec 2022

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   Abstract The question of how cell-to-cell differences in transcription rate affect RNA count distributions is fundamental for understanding biological processes underlying transcription. Answering this question requires quantitative models that are both interpretable (describing concrete biophysical phenomena) and tractable (amenable to mathematical analysis). This enables the identification of experiments which best discriminate between competing hypotheses. As a proof of principle, we introduce a simple but flexible class of models involving a continuous stochastic transcription rate driving a discrete RNA transcription and splicing process, and compare and contrast two biologically plausible hypotheses about transcription rate variation. One assumes variation is due to DNA experiencing mechanical strain, while the other assumes it is due to regulator number fluctuations. We introduce a framework for numerically and analytically studying such models, and apply Bayesian model selection to identify candidate genes that show signatures of each model in single-cell transcriptomic data from mouse glutamatergic neurons.

2021

1. 

   Analytic solution of chemical master equations involving gene switching. I: Representation theory and diagrammatic approach to exact solution

   John J. Vastola, Gennady Gorin, Lior Pachter, and William R. Holmes

   arXiv, Mar 2021

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   The chemical master equation (CME), which describes the discrete and stochastic molecule number dynamics associated with biological processes like transcription, is difficult to solve analytically. It is particularly hard to solve for models involving bursting/gene switching, a biological feature that tends to produce heavy-tailed single cell RNA counts distributions. In this paper, we present a novel method for computing exact and analytic solutions to the CME in such cases, and use these results to explore approximate solutions valid in different parameter regimes, and to compute observables of interest. Our method leverages tools inspired by quantum mechanics, including ladder operators and Feynman-like diagrams, and establishes close formal parallels between the dynamics of bursty transcription, and the dynamics of bosons interacting with a single fermion. We focus on two problems: (i) the chemical birth-death process coupled to a switching gene/the telegraph model, and (ii) a model of transcription and multistep splicing involving a switching gene and an arbitrary number of downstream splicing steps. We work out many special cases, and exhaustively explore the special functionology associated with these problems. This is Part I in a two-part series of papers; in Part II, we explore an alternative solution approach that is more useful for numerically solving these problems, and apply it to parameter inference on simulated RNA counts data.

2020

1. 

   Protein velocity and acceleration from single-cell multiomics experiments

   Gennady Gorin, Valentine Svensson, and Lior Pachter

   Genome Biology, Feb 2020

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   The simultaneous quantification of protein and RNA makes possible the inference of past, present, and future cell states from single experimental snapshots. To enable such temporal analysis from multimodal single-cell experiments, we introduce an extension of the RNA velocity method that leverages estimates of unprocessed transcript and protein abundances to extrapolate cell states. We apply the model to six datasets and demonstrate consistency among cell landscapes and phase portraits. The analysis software is available as the protaccel Python package.

2. 

   Stochastic simulation and statistical inference platform for visualization and estimation of transcriptional kinetics

   Gennady Gorin, Mengyu Wang, Ido Golding, and Heng Xu

   PLOS ONE, Mar 2020

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   Recent advances in single-molecule fluorescent imaging have enabled quantitative measurements of transcription at a single gene copy, yet an accurate understanding of transcriptional kinetics is still lacking due to the difficulty of solving detailed biophysical models. Here we introduce a stochastic simulation and statistical inference platform for modeling detailed transcriptional kinetics in prokaryotic systems, which has not been solved analytically. The model includes stochastic two-state gene activation, mRNA synthesis initiation and stepwise elongation, release to the cytoplasm, and stepwise co-transcriptional degradation. Using the Gillespie algorithm, the platform simulates nascent and mature mRNA kinetics of a single gene copy and predicts fluorescent signals measurable by time-lapse single-cell mRNA imaging, for different experimental conditions. To approach the inverse problem of estimating the kinetic parameters of the model from experimental data, we develop a heuristic optimization method based on the genetic algorithm and the empirical distribution of mRNA generated by simulation. As a demonstration, we show that the optimization algorithm can successfully recover the transcriptional kinetics of simulated and experimental gene expression data. The platform is available as a MATLAB software package at https://data.caltech.edu/records/1287.

3. 

   Special function methods for bursty models of transcription

   Gennady Gorin, and Lior Pachter

   Physical Review E, Aug 2020

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   We explore a Markov model used in the analysis of gene expression, involving the bursty production of pre-mRNA, its conversion to mature mRNA, and its consequent degradation. We demonstrate that the integration used to compute the solution of the stochastic system can be approximated by the evaluation of special functions. Furthermore, the form of the special function solution generalizes to a broader class of burst distributions. In light of the broader goal of biophysical parameter inference from transcriptomics data, we apply the method to simulated data, demonstrating effective control of precision and runtime. Finally, we propose and validate a non-Bayesian approach for parameter estimation based on the characteristic function of the target joint distribution of pre-mRNA and mRNA.

4. 

   Intrinsic and extrinsic noise are distinguishable in a synthesis – export – degradation model of mRNA production

   Gennady Gorin, and Lior Pachter

   bioRxiv, Sep 2020

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   Intrinsic and extrinsic noise sources in gene expression, originating respectively from transcriptional stochasticity and from differences between cells, complicate the determination of transcriptional models. In particularly degenerate cases, the two noise sources are altogether impossible to distinguish. However, the incorporation of downstream processing, such as the mRNA splicing and export implicated in gene expression buffering, recovers the ability to identify the relevant source of noise. We report analytical copy-number distributions, discuss the noise sources’ qualitative effects on lower moments, and provide simulation routines for both models.