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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. 

Abstract Advances in mass spectrometry (MS) have enabled high-throughput analysis of proteomes in biological systems. The state-of-the-art MS data analysis relies on database search algorithms to quantify proteins by identifying peptide–spectrum matches (PSMs), which convert mass spectra to peptide sequences. Different database search algorithms use distinct search strategies and thus may identify unique PSMs. However, no existing approaches can aggregate all user-specified database search algorithms with a guaranteed increase in the number of identified peptides and a control on the false discovery rate (FDR). To fill in this gap, we proposed a statistical framework, Aggregation of Peptide Identification Results (APIR), that is universally compatible with all database search algorithms. Notably, under an FDR threshold, APIR is guaranteed to identify at least as many, if not more, peptides as individual database search algorithms do. Evaluation of APIR on a complex proteomics standard dataset showed that APIR outpowers individual database search algorithms and empirically controls the FDR. Real data studies showed that APIR can identify disease-related proteins and post-translational modifications missed by some individual database search algorithms. The APIR framework is easily extendable to aggregating discoveries made by multiple algorithms in other high-throughput biomedical data analysis, e.g., differential gene expression analysis on RNA sequencing data. The APIR R package is available at https://github.com/yiling0210/APIR. 

Abstract High-throughput biological data analysis commonly involves identifying features such as genes, genomic regions, and proteins, whose values differ between two conditions, from numerous features measured simultaneously. The most widely used criterion to ensure the analysis reliability is the false discovery rate (FDR), which is primarily controlled based onp-values. However, obtaining validp-values relies on either reasonable assumptions of data distribution or large numbers of replicates under both conditions. Clipper is a general statistical framework for FDR control without relying onp-values or specific data distributions. Clipper outperforms existing methods for a broad range of applications in high-throughput data analysis.