The chronODE framework for modelling multi-omic time series with ordinary differential equations and machine learning
Beatrice Borsari, Mor Frank, Eve S. Wattenberg, Ke Xu, Susanna X. Liu, Xuezhu Yu, Mark Gerstein
bioRxiv preprint
An ODE-based framework for modelling logistic and peak-like time-series multi-omic signals, and machine learning models that predicted gene expression over time from linked chromatin features.
The chronODE pipeline for monotonic fitting is written in Nextflow DSL2.
The list of dependencies is provided in the chronode.yml file (see above).
git clone https://github.com/gersteinlab/chronODE
cd chronODE
conda env create -f chronode.yml
conda activate chronode_env
cwd=$(pwd)
nextflow run scripts/chronode.nf --infile $cwd/example_data/input/input.matrix.tsv --out example.output --size 3 --dir $cwd/example_data/test --timesfile $cwd/example_data/input/mouse.timecourse.csv
Usage: nextflow run chronode.nf [options]
Parameters:
--infile Input matrix
--size Chunk size (affects speed but not final output). We recommend ~10% of the file length, depending on available resources.
--out Prefix for output files
--dir Output directory
--timesfile File of time-points
Nextflow offers a number of other optional parameters, including --help and -with-trace that may be useful for debugging if errors occur.
The tab-separated main input file needs one row per gene/regulatory element, one index column, and a column for each time point in the original data. Below, we provide an example for two candidate cis-regulatory elements (cCREs):
cCRE_id E10.5 E11.5 E12.5 E13.5 E14.5 E15.5 E16.5 PN
EM10D0144246 1.92265260038112 1.89139781357557 1.90998930285207 2.24724966250699 2.44195099910917 2.56235923617873 2.40102884091981 2.5533492607186
EM10D1047237 1.44726021325062 1.39525207794537 1.41927175130354 1.3478911616366 1.16733471629674 1.09028685205392 1.08475277892454 1.07986151310049
The time course must be specified using a .csv file listing all time points in numeric form on one line. Please consider that in our example we have numerically encoded the first post-natal day (e.g., PN) as day 21.
10.5,11.5,12.5,13.5,14.5,15.5,16.5,21
The parameters output will be tab-separated and have a row for each gene/regulatory element:
cCRE_id k b_starred MSE a b R_min R_max z_min z_max z_start kinetic_class switching_time saturation_time minimum_time
EM10D0144246 1.02066198626769 0.972883868461625 0.0162867863978315 1.89139110389425 2.54416517604565 1e-05 1 1.89139781357557 2.56235923617873 1.92265260038112 switcher 13.429223902119 17.9313214740467 -22.6663317113752
EM10D1047237 -1.99779861566745 1.00103040140379 0.00245095219378508 1.07985783907675 1.44763878517272 1e-05 1 1.07986151310049 1.44726021325062 1.44726021325062 switcher 13.9426932656304 11.6426016477376 32.3836718502493
This file contains the following information:
k,a, andb: the three logistic ODE parameters in the real range of the data.b_starred: the upper asymptote of the logistic curve in the normalized range of the data (simplified form of the logistic ODE).R_min,R_max,z_min, andz_max: scaling factors used in the data normalization step (see Methods section of the manuscript "Data normalization").z_start: the gene/element's signal at the first experimental time point in the real range of the data.MSE: the Mean Squared Error of the fit in the normalized range of the data.kinetic_class,switching_time,saturation_time, andminimum_time: kinetic characterization of the element (see Methods, section "Kinetic Classification", and Supplementary Note 1).
The derivatives, fitted values, and restored values output files will also be tab-separated and have a row for each gene/element and a column for each timepoint. Please see below an example of the output file for the restored.values.tsv output file:
cCRE_id E10.5 E11.5 E12.5 E13.5 E14.5 E15.5 E16.5 PN
EM10D0144246 1.92265260038112 2.01453994115168 2.22955836852258 2.43480368195092 2.51693257926945 2.53807509249146 2.54283806152758 2.54387763550249
EM10D1047237 1.44726021325062 1.44020555489426 1.34014945343893 1.11954446308323 1.08206670365814 1.07996880889247 1.07986338380165 1.07985811604938
python scripts/piecewise.fitting.py
python scripts/chronODE_biRNN_model.py
Inside models/biRNN, we have made available a separate file for each of the four trained models (Enhancer Monopattern, Enhancer Polypattern, Silencer Monopattern, Silencer Polypattern).
Copyright 2025 Yale University. Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the “Software”), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.
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