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Biological systems exhibit complex dynamics that differential equations can often adeptly represent. Ordinary differential equation models are widespread; until recently their construction has required extensive prior knowledge of the system. Machine learning methods offer alternative means of model construction: differential equation models can be learnt from data via model discovery using sparse identification of nonlinear dynamics (SINDy). However, SINDy struggles with realistic levels of biological noise and is limited in its ability to incorporate prior knowledge of the system. We propose a data-driven framework for model discovery and model selection using hybrid dynamical systems: partial models containing missing terms. Neural networks are used to approximate the unknown dynamics of a system, enabling the denoising of the data while simultaneously learning the latent dynamics. Simulations from the fitted neural network are then used to infer models using sparse regression. We show, via model selection, that model discovery using hybrid dynamical systems outperforms alternative approaches. We find it possible to infer models correctly up to high levels of biological noise of different types. We demonstrate the potential to learn models from sparse, noisy data in application to a canonical cell state transition using data derived from single-cell transcriptomics. Overall, this approach provides a practical framework for model discovery in biology in cases where data are noisy and sparse, of particular utility when the underlying biological mechanisms are partially but incompletely known. 

Single-cell genomic technologies offer vast new resources with which to study cells, but their potential to inform parameter inference of cell dynamics has yet to be fully realized. Here we develop methods for Bayesian parameter inference with data that jointly measure gene expression and Ca²⁺dynamics in single cells. We propose to share information between cells via transfer learning: for a sequence of cells, the posterior distribution of one cell is used to inform the prior distribution of the next. In application to intracellular Ca²⁺signalling dynamics, we fit the parameters of a dynamical model for thousands of cells with variable single-cell responses. We show that transfer learning accelerates inference with sequences of cells regardless of how the cells are ordered. However, only by ordering cells based on their transcriptional similarity can we distinguish Ca²⁺dynamic profiles and associated marker genes from the posterior distributions. Inference results reveal complex and competing sources of cell heterogeneity: parameter covariation can diverge between the intracellular and intercellular contexts. Overall, we discuss the extent to which single-cell parameter inference informed by transcriptional similarity can quantify relationships between gene expression states and signalling dynamics in single cells. 

Abstract Oxygen evolution reaction (OER) is of great significance for hydrogen production via water electrolysis, which, however, demands development of highly active, durable, and cost‐effective electrocatalysts in order to stride into a renewable energy era. Herein, highly efficient and long‐term durable OER by coupling B and P into an amorphous porous NiFe‐based electrocatalyst is reported, which possesses an amorphous porous metallic bulk structure and high corrosion resistance, and overcomes the issues associated with currently used catalyst nanomaterials. The PB codoping in the activated NiFePB (a‐NiFePB) delocalizes both Fe and Ni at Fermi energy level and enhances p–d hybridization as simulated by density functional theory calculations. The harmonized electronic structure and unique porous framework of the a‐NiFePB consequently improve the OER activity. The activated NiFePB thus exhibits an extraordinarily low overpotential of 197 mV for harvesting 10 mA cm⁻²OER current density and 233 mV for reaching 100 mA cm⁻²under chronopotentiometry condition, with the Tafel slope harmoniously conforming to 34 mV dec⁻¹. Impressive long‐term stability of this new catalyst is evidenced by only limited activity decay after 1400 h operation at 100 mA cm⁻². This work strategically directs a way for heading up a promising energy conversion alternative.