Parameter estimation in models of biological oscillators: an automated regularised estimation approach

Building Digital Twins for Cardiovascular Health: From Principles to Clinical Impact

The past several decades have seen rapid advances in diagnosis and treatment of cardiovascular diseases and stroke, enabled by technological breakthroughs in imaging, genomics, and physiological monitoring, coupled with therapeutic interventions. We now face the challenge of how to (1) rapidly process large, complex multimodal and multiscale medical measurements; (2) map all available data streams to the trajectories of disease states over the patient's lifetime; and (3) apply this information for optimal clinical interventions and outcomes. Here we review new advances that may address these challenges using digital twin technology to fulfill the promise of personalized cardiovascular medical practice. Rooted in engineering mechanics and manufacturing, the digital twin is a virtual representation engineered to model and simulate its physical counterpart. Recent breakthroughs in scientific computation, artificial intelligence, and sensor technology have enabled rapid bidirectional interactions between the virtual-physical counterparts with measurements of the physical twin that inform and improve its virtual twin, which in turn provide updated virtual projections of disease trajectories and anticipated clinical outcomes. Verification, validation, and uncertainty quantification builds confidence and trust by clinicians and patients in the digital twin and establishes boundaries for the use of simulations in cardiovascular medicine. Mechanistic physiological models form the fundamental building blocks of the personalized digital twin that continuously forecast optimal management of cardiovascular health using individualized data streams. We present exemplars from the existing body of literature pertaining to mechanistic model development for cardiovascular dynamics and summarize existing technical challenges and opportunities pertaining to the foundation of a digital twin.

Missing data in amortized simulation-based neural posterior estimation

Amortized simulation-based neural posterior estimation provides a novel machine learning based approach for solving parameter estimation problems. It has been shown to be computationally efficient and able to handle complex models and data sets. Yet, the available approach cannot handle the in experimental studies ubiquitous case of missing data, and might provide incorrect posterior estimates. In this work, we discuss various ways of encoding missing data and integrate them into the training and inference process. We implement the approaches in the BayesFlow methodology, an amortized estimation framework based on invertible neural networks, and evaluate their performance on multiple test problems. We find that an approach in which the data vector is augmented with binary indicators of presence or absence of values performs the most robustly. Indeed, it improved the performance also for the simpler problem of data sets with variable length. Accordingly, we demonstrate that amortized simulation-based inference approaches are applicable even with missing data, and we provide a guideline for their handling, which is relevant for a broad spectrum of applications.

From biological data to oscillator models using SINDy

Periodic changes in the concentration or activity of different molecules regulate vital cellular processes such as cell division and circadian rhythms. Developing mathematical models is essential to better understand the mechanisms underlying these oscillations. Recent data-driven methods like SINDy have fundamentally changed model identification, yet their application to experimental biological data remains limited. This study investigates SINDy's constraints by directly applying it to biological oscillatory data. We identify insufficient resolution, noise, dimensionality, and limited prior knowledge as primary limitations. Using various generic oscillator models of different complexity and/or dimensionality, we systematically analyze these factors. We then propose a comprehensive guide for inferring models from biological data, addressing these challenges step by step. Our approach is validated using glycolytic oscillation data from yeast.

Reusable rule-based cell cycle model explains compartment-resolved dynamics of 16 observables in RPE-1 cells

The mammalian cell cycle is regulated by a well-studied but complex biochemical reaction system. Computational models provide a particularly systematic and systemic description of the mechanisms governing mammalian cell cycle control. By combining both state-of-the-art multiplexed experimental methods and powerful computational tools, this work aims at improving on these models along four dimensions: model structure, validation data, validation methodology and model reusability. We developed a comprehensive model structure of the full cell cycle that qualitatively explains the behaviour of human retinal pigment epithelial-1 cells. To estimate the model parameters, time courses of eight cell cycle regulators in two compartments were reconstructed from single cell snapshot measurements. After optimisation with a parallel global optimisation metaheuristic we obtained excellent agreements between simulations and measurements. The PEtab specification of the optimisation problem facilitates reuse of model, data and/or optimisation results. Future perturbation experiments will improve parameter identifiability and allow for testing model predictive power. Such a predictive model may aid in drug discovery for cell cycle-related disorders.

A general model-based causal inference method overcomes the curse of synchrony and indirect effect

To identify causation, model-free inference methods, such as Granger Causality, have been widely used due to their flexibility. However, they have difficulty distinguishing synchrony and indirect effects from direct causation, leading to false predictions. To overcome this, model-based inference methods that test the reproducibility of data with a specific mechanistic model to infer causality were developed. However, they can only be applied to systems described by a specific model, greatly limiting their applicability. Here, we address this limitation by deriving an easily testable condition for a general monotonic ODE model to reproduce time-series data. We built a user-friendly computational package, General ODE-Based Inference (GOBI), which is applicable to nearly any monotonic system with positive and negative regulations described by ODE. GOBI successfully inferred positive and negative regulations in various networks at both the molecular and population levels, unlike existing model-free methods. Thus, this accurate and broadly applicable inference method is a powerful tool for understanding complex dynamical systems.

Neuraxial analgesia interfered with the circadian rhythm of labor: a propensity score matched cohort study

Objectives

To investigate whether neuraxial analgesia and other medical interventions have effects on the circadian rhythm of labor.

Methods

It was a retrospective propensity score matched cohort study. Parturients were recruited, who delivered term singletons in cephalic position, from seven hospitals in Harvard University Partners Healthcare Systems, 2016–2018. The parturients were divided into two groups, neuraxial analgesia delivery and spontaneous vaginal delivery, the stratification was performed according to labor induction, oxytocin, operative delivery. The parturients in each group were divided into 12 periods in every 2 h based on the birth time of babies. Cosine function fitting was used to verify whether the birth time had the characteristic of circadian rhythm.

Results

In spontaneous vaginal deliveries, the peak of birth time was at 2:00–4:00, and the nadir was at 14:00–16:00, this showed a circadian rhythm presented by a cosine curve fitting with the formula (y = 0.0847 + 0.01711 × cos(− 0.2138 × x + 0.4471). The labor rhythm of NAD (Neuraxial Analgesia Delivery) group changed completely, inconsistent with the cosine curve fitting of the circadian rhythm. The intervention of induction and oxytocin blurred the circadian rhythm of SVD (Spontaneous Vaginal Delivery) group and increased the amplitude of the fluctuation in NAD (Neuraxial Analgesia Delivery) group. The intervention of operative delivery had changed the distribution curve completely both in the SVD (Spontaneous Vaginal Delivery) group and the NAD (Neuraxial Analgesia Delivery) group.

Conclusions

Neuraxial analgesia did affect on circadian rhythm of labor, changed the cosine rhythm of labor with spontaneous vaginal delivery, and this trend was aggravated by the use of induction, oxytocin and operative delivery.

Inferring causality in biological oscillators

MOTIVATION

Fundamental to biological study is identifying regulatory interactions. The recent surge in time-series data collection in biology provides a unique opportunity to infer regulations computationally. However, when components oscillate, model-free inference methods, while easily implemented, struggle to distinguish periodic synchrony and causality. Alternatively, model-based methods test the reproducibility of time series given a specific model but require inefficient simulations and have limited applicability.

RESULTS

We develop an inference method based on a general model of molecular, neuronal and ecological oscillatory systems that merges the advantages of both model-based and model-free methods, namely accuracy, broad applicability and usability. Our method successfully infers the positive and negative regulations within various oscillatory networks, e.g. the repressilator and a network of cofactors at the pS2 promoter, outperforming popular inference methods.

AVAILABILITY AND IMPLEMENTATION

We provide a computational package, ION (Inferring Oscillatory Networks), that users can easily apply to noisy, oscillatory time series to uncover the mechanisms by which diverse systems generate oscillations. Accompanying MATLAB code under a BSD-style license and examples are available at https://github.com/Mathbiomed/ION. Additionally, the code is available under a CC-BY 4.0 License at https://doi.org/10.6084/m9.figshare.16431408.v1.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Modeling the Nonlinear Dynamics of Intracellular Signaling Networks

This protocol illustrates a pipeline for modeling the nonlinear behavior of intracellular signaling pathways. At fixed spatial points, nonlinear signaling dynamics are described by ordinary differential equations (ODEs). At constant parameters, these ODEs may have multiple attractors, such as multiple steady states or limit cycles. Standard optimization procedures fine-tune the parameters for the system trajectories localized within the basin of attraction of only one attractor, usually a stable steady state. The suggested protocol samples the parameter space and captures the overall dynamic behavior by analyzing the number and stability of steady states and the shapes of the assembly of nullclines, which are determined as projections of quasi-steady-state trajectories into different 2D spaces of system variables. Our pipeline allows identifying main qualitative features of the model behavior, perform bifurcation analysis, and determine the borders separating the different dynamical regimes within the assembly of 2D parametric planes. Partial differential equation (PDE) systems describing the nonlinear spatiotemporal behavior are derived by coupling fixed point dynamics with species diffusion.

An optogenetic method for interrogating YAP1 and TAZ nuclear-cytoplasmic shuttling

The shuttling of transcription factors and transcriptional regulators into and out of the nucleus is central to the regulation of many biological processes. Here we describe a new method for studying the rates of nuclear entry and exit of transcriptional regulators. A photo-responsive LOV (light-oxygen-voltage) domain from Avena sativa is used to sequester fluorescently labelled transcriptional regulators YAP1 and TAZ (also known as WWTR1) on the surface of mitochondria and to reversibly release them upon blue light illumination. After dissociation, fluorescent signals from the mitochondria, cytoplasm and nucleus are extracted by a bespoke app and used to generate rates of nuclear entry and exit. Using this method, we demonstrate that phosphorylation of YAP1 on canonical sites enhances its rate of nuclear export. Moreover, we provide evidence that, despite high intercellular variability, YAP1 import and export rates correlate within the same cell. By simultaneously releasing YAP1 and TAZ from sequestration, we show that their rates of entry and exit are correlated. Furthermore, combining the optogenetic release of YAP1 with lattice light-sheet microscopy reveals high heterogeneity of YAP1 dynamics within different cytoplasmic regions, demonstrating the utility and versatility of our tool to study protein dynamics. This article has an associated First Person interview with Anna M. Dowbaj, joint first author of the paper.

A dual-parameter identification approach for data-based predictive modeling of hybrid gene regulatory network-growth kinetics in Pseudomonas putida mt-2

Data integration to model-based description of biological systems incorporating gene dynamics improves the performance of microbial systems. Bioprocess performance, typically predicted using empirical Monod-type models, is essential for a sustainable bioeconomy. To replace empirical models, we updated a hybrid gene regulatory network-growth kinetic model, predicting aromatic pollutants degradation and biomass growth in Pseudomonas putida mt-2. We modeled a complex biological system including extensive information to understand the role of the regulatory elements in toluene biodegradation and biomass growth. The updated model exhibited extra complications such as the existence of oscillations and discontinuities. As parameter estimation of complex biological models remains a key challenge, we used the updated model to present a dual-parameter identification approach (the 'dual approach') combining two independent methodologies. Approach I handled the complexity by incorporation of demonstrated biological knowledge in the model-development process and combination of global sensitivity analysis and optimisation. Approach II complemented Approach I handling multimodality, ill-conditioning and overfitting through regularisation estimation, global optimisation, and identifiability analysis. To systematically quantify the biological system, we used a vast amount of high-quality time-course data. The dual approach resulted in an accurately calibrated kinetic model (NRMSE: 0.17055) efficiently handling the additional model complexity. We tested model validation using three independent experimental data sets, achieving greater predictive power (NRMSE: 0.18776) than the individual approaches (NRMSE I: 0.25322, II: 0.25227) and increasing model robustness. These results demonstrated data-driven predictive modeling potentially leading to bioprocess' model-based control and optimisation.

A primer on model selection using the Akaike Information Criterion

A powerful investigative tool in biology is to consider not a single mathematical model but a collection of models designed to explore different working hypotheses and select the best model in that collection. In these lecture notes, the usual workflow of the use of mathematical models to investigate a biological problem is described and the use of a collection of model is motivated. Models depend on parameters that must be estimated using observations; and when a collection of models is considered, the best model has then to be identified based on available observations. Hence, model calibration and selection, which are intrinsically linked, are essential steps of the workflow. Here, some procedures for model calibration and a criterion, the Akaike Information Criterion, of model selection based on experimental data are described. Rough derivation, practical technique of computation and use of this criterion are detailed.