The chronODE framework for modelling multi-omic time series with ordinary differential equations and machine learning

Abstract Many genome-wide studies capture isolated moments in cell differentiation or organismal development. Conversely, longitudinal studies provide a more direct way to study these kinetic processes. Here, we present an approach for modeling gene-expression and chromatin kinetics from such studie...

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Main Authors: Beatrice Borsari, Mor Frank, Eve S. Wattenberg, Ke Xu, Susanna X. Liu, Xuezhu Yu, Mark Gerstein
Format: Article
Language:English
Published: Nature Portfolio 2025-08-01
Series:Nature Communications
Online Access:https://doi.org/10.1038/s41467-025-61921-9
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author Beatrice Borsari
Mor Frank
Eve S. Wattenberg
Ke Xu
Susanna X. Liu
Xuezhu Yu
Mark Gerstein
author_facet Beatrice Borsari
Mor Frank
Eve S. Wattenberg
Ke Xu
Susanna X. Liu
Xuezhu Yu
Mark Gerstein
author_sort Beatrice Borsari
collection DOAJ
description Abstract Many genome-wide studies capture isolated moments in cell differentiation or organismal development. Conversely, longitudinal studies provide a more direct way to study these kinetic processes. Here, we present an approach for modeling gene-expression and chromatin kinetics from such studies: chronODE, an interpretable framework based on ordinary differential equations. chronODE incorporates two parameters that capture biophysical constraints governing the initial cooperativity and later saturation in gene expression. These parameters group genes into three major kinetic patterns: accelerators, switchers, and decelerators. Applying chronODE to bulk and single-cell time-series data from mouse brain development reveals that most genes (~87%) follow simple logistic kinetics. Among them, genes with rapid acceleration and high saturation values are rare, highlighting biochemical limitations that prevent cells from attaining both simultaneously. Early- and late-emerging cell types display distinct kinetic patterns, with essential genes ramping up faster. Extending chronODE to chromatin, we find that genes regulated by both enhancer and silencer cis-regulatory elements are enriched in brain-specific functions. Finally, we develop a bidirectional recurrent neural network to predict changes in gene expression from corresponding chromatin changes, successfully capturing the cumulative effect of multiple regulatory elements. Overall, our framework allows investigation of the kinetics of gene regulation in diverse biological systems.
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issn 2041-1723
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spelling doaj-art-ae5012d684b941d8992ab0184f352b5f2025-08-24T11:39:15ZengNature PortfolioNature Communications2041-17232025-08-0116111610.1038/s41467-025-61921-9The chronODE framework for modelling multi-omic time series with ordinary differential equations and machine learningBeatrice Borsari0Mor Frank1Eve S. Wattenberg2Ke Xu3Susanna X. Liu4Xuezhu Yu5Mark Gerstein6Program in Computational Biology and Biomedical Informatics, Yale UniversityProgram in Computational Biology and Biomedical Informatics, Yale UniversityProgram in Computational Biology and Biomedical Informatics, Yale UniversityDepartment of Computer Science, Yale UniversityProgram in Computational Biology and Biomedical Informatics, Yale UniversityProgram in Computational Biology and Biomedical Informatics, Yale UniversityProgram in Computational Biology and Biomedical Informatics, Yale UniversityAbstract Many genome-wide studies capture isolated moments in cell differentiation or organismal development. Conversely, longitudinal studies provide a more direct way to study these kinetic processes. Here, we present an approach for modeling gene-expression and chromatin kinetics from such studies: chronODE, an interpretable framework based on ordinary differential equations. chronODE incorporates two parameters that capture biophysical constraints governing the initial cooperativity and later saturation in gene expression. These parameters group genes into three major kinetic patterns: accelerators, switchers, and decelerators. Applying chronODE to bulk and single-cell time-series data from mouse brain development reveals that most genes (~87%) follow simple logistic kinetics. Among them, genes with rapid acceleration and high saturation values are rare, highlighting biochemical limitations that prevent cells from attaining both simultaneously. Early- and late-emerging cell types display distinct kinetic patterns, with essential genes ramping up faster. Extending chronODE to chromatin, we find that genes regulated by both enhancer and silencer cis-regulatory elements are enriched in brain-specific functions. Finally, we develop a bidirectional recurrent neural network to predict changes in gene expression from corresponding chromatin changes, successfully capturing the cumulative effect of multiple regulatory elements. Overall, our framework allows investigation of the kinetics of gene regulation in diverse biological systems.https://doi.org/10.1038/s41467-025-61921-9
spellingShingle Beatrice Borsari
Mor Frank
Eve S. Wattenberg
Ke Xu
Susanna X. Liu
Xuezhu Yu
Mark Gerstein
The chronODE framework for modelling multi-omic time series with ordinary differential equations and machine learning
Nature Communications
title The chronODE framework for modelling multi-omic time series with ordinary differential equations and machine learning
title_full The chronODE framework for modelling multi-omic time series with ordinary differential equations and machine learning
title_fullStr The chronODE framework for modelling multi-omic time series with ordinary differential equations and machine learning
title_full_unstemmed The chronODE framework for modelling multi-omic time series with ordinary differential equations and machine learning
title_short The chronODE framework for modelling multi-omic time series with ordinary differential equations and machine learning
title_sort chronode framework for modelling multi omic time series with ordinary differential equations and machine learning
url https://doi.org/10.1038/s41467-025-61921-9
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