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Spectral neural approximations for models of transcriptional dynamics

Gorin, Gennady and Carilli, Maria and Chari, Tara and Pachter, Lior (2022) Spectral neural approximations for models of transcriptional dynamics. . (Unpublished)

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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.

Item Type:Report or Paper (Discussion Paper)
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URLURL TypeDescription Discussion Paper ItemCode
Gorin, Gennady0000-0001-6097-2029
Carilli, Maria0000-0002-8977-7224
Chari, Tara0000-0002-6953-4313
Pachter, Lior0000-0002-9164-6231
Additional Information:The copyright holder for this preprint is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made available under a CC-BY 4.0 International license. We thank Dr. Yisong Yue, Yongin Choi, Dr. John J. Vastola, and Dr. Zachary Fox for valuable discussions. G.G. and L.P. were partially funded by NIH U19MH114830. Figures 1, 2, 3, and S3 use color palettes from MetBrewer, developed by Blake R. Mills and available at Data and code availability. All training and validation datasets, trained models, scripts to generate manuscript figures, and a small Google Colaboratory demonstration are available at The authors have declared no competing interest.
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Record Number:CaltechAUTHORS:20220706-964999000
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Official Citation:Spectral neural approximations for models of transcriptional dynamics Gennady Gorin, Maria Carilli, Tara Chari, Lior Pachter bioRxiv 2022.06.16.496448; doi:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:115348
Deposited By: George Porter
Deposited On:08 Jul 2022 22:29
Last Modified:25 Jul 2022 23:13

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