Erdos, B. | Search bioRxiv

bioRxiv2025

Extracting host-specific developmental signatures from longitudinal microbiome data

Longitudinal microbiome studies provide critical insights into microbial community dynamics and their relation to host health. Tensor decompositions offer a powerful framework for the unsupervised analysis of such data, yielding interpretable low-dimensional temporal patterns. However, existing approaches based on the CANDECOMP/PARAFAC (CP) model assume common temporal dynamics for all subjects and therefore cannot capture subject-specific trajectories. To address this limitation, we introduce a novel analytical framework based on PARAFAC2 to explicitly model subject-specific variations, such as shifts and delays in temporal patterns. Through systematic comparisons on simulated and real-world datasets--including studies of infant gut maturation and dietary interventions--we demonstrate that PARAFAC2 outperforms CP in capturing subject-specific temporal trajectories, and enables the discovery of biologically relevant patterns that are overlooked by CP. Furthermore, we introduce replicability as a robust criterion for selecting the number of components and demonstrate that the extracted patterns are replicable. Author summaryLongitudinal microbiome datasets are complex, consisting of repeated high-dimensional compositions that track changes in microbial abundance across individuals over time. While tensor decompositions are powerful tools for unraveling structure in these data, standard models like CANDECOMP/PARAFAC (CP) impose a critical limitation: they assume that temporal dynamics are identical across all individuals. This assumption often fails to capture the heterogeneity of biological processes, such as the varying pace of gut microbiome maturation or distinct individual responses to dietary changes. In this work, we introduce a novel analytical framework leveraging the PARAFAC2 model to overcome these constraints. By explicitly modeling subject-specific temporal variations, our PARAFAC2-based approach allows for the detection of individual time shifts and delays. We validated this framework using both simulation and real-world cohorts, demonstrating its ability to recover personalized trajectories that CP obscures. Additionally, we implemented a robust criterion to guide model selection, ensuring that the discovered patterns are replicable.

bioinformatics↗

bioRxiv2024

Physiology-informed regularization enables training of universal differential equation systems for biological applications

Systems biology tackles the challenge of understanding the high complexity in the internal regulation of homeostasis in the human body through mathematical modelling. These models can aid in the discovery of disease mechanisms and potential drug targets. However, on one hand the development and validation of knowledge-based mechanistic models is time-consuming and does not scale well with increasing features in medical data. On the other hand, more data-driven approaches such as machine learning models require large volumes of data to produce generalizable models. The integration of neural networks and mechanistic models, forming universal differential equation (UDE) models, enables the automated learning of unknown model terms with less data than the neural network alone. Nevertheless, estimating parameters for these hybrid models remains difficult with sparse data and limited sampling durations that are common in biological applications. In this work, we propose the use of physiology-informed regularization, penalizing biologically implausible model behavior to guide the UDE towards more physiologically plausible regions of the solution space. In a simulation study we show that physiology-informed regularization not only results in a more accurate forecasting of model behaviour, but also supports training with less data. We also applied this technique to learn a representation of the rate of glucose appearance in the glucose minimal model using meal response data measured in healthy people. In that case, the inclusion of regularization reduces variability between UDE-embedded neural networks that were trained from different initial parameter guesses. Author summarySystems biology concerns the modelling and analysis of biological processes, by viewing these as interconnected systems. Modelling is typically done either using mechanistic differential equations that are derived from experiments and known biology, or using machine learning on large biological datasets. While mathematical modelling from biological experiments can provide useful insights with limited data, building and validating these models takes a long time and often requires highly invasive measurements in humans. Efforts to combine this classical technique with machine learning have resulted in a framework termed universal differential equations, where the model equations contain a neural network to describe unknown biological interactions. While these methods have shown success in numerous fields, applications in biology are more challenging due to limited data-availability, high data sparsity. In this work, we have introduced physiology-informed regularization to overcome these instabilities and to constrain the model to biologically plausible behavior. Our results show that by using physiology-informed regularization, we can accurately predict future unseen observations in a simulated example, with much more limited data than a similar model without regularization. Additionally, we show an application of this technique on human data, applying a neural network to learn the appearance of glucose in the blood plasma after a meal.

systems biology↗