Mathematics-informed machine learning for mapping cell development
DOI:
https://doi.org/10.14295/bjs.v5i4.842Keywords:
neural ordinary differential equations, single-cell trajectory inference, biologically constrained modeling, causal gene regulatory networks, predictive cancer therapeuticsAbstract
Single-cell RNA sequencing provides high-resolution snapshots of cellular states, yet descriptive trajectory inference methods are limited to interpolation, struggle with extrapolation, perturbation prediction, and causal mechanism discovery, constraining their utility in predictive developmental biology, cancer therapeutics, and reprogramming. This study introduces and evaluates a Mathematics-Informed Machine Learning (MIML) framework that embeds biological priors mass conservation, attractor dynamics, geometry-aware manifolds, and causal GRN inference into Neural Ordinary Differential Equations to enable continuous, predictive, and mechanistically interpretable modeling of single-cell dynamics. MIML was benchmarked against descriptive baselines (PAGA-like) and standard Neural ODEs across extrapolation, perturbation simulation (knockout/overexpression), out-of-distribution generalization, causal discovery, stage-specific prediction, drug response forecasting, cancer progression reconstruction, and cellular reprogramming efficiency using quantitative metrics (R², MSE, precision/recall/F1, synergy scores, fate probabilities). MIML achieves 1.1-1.3× better prediction/extrapolation, 8-21× gains in perturbation and OOD tasks, ~10-11× improvement in causal GRN accuracy, 82-86% reprogramming success, and 66% HDAC inhibitor response prediction with synergistic combination insights. Overall clinical impact score: 0.82. This is the first framework to jointly enforce biophysical constraints (mass homeostasis, stable attractors), manifold geometry, and directed causal inference within a unified Neural ODE paradigm, yielding unprecedented predictive power and mechanistic insight beyond existing continuous or discrete single-cell models. MIML substantially outperforms existing methods in predictive fidelity, biological plausibility, and translational relevance, establishing a foundation for mechanism-guided single-cell analysis. Prospective interventional validation, spatial/multi-omics integration, stochastic extensions, and interpretability enhancements will further position MIML as a cornerstone for precision biomedicine.
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