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.

pyPESTO: a modular and scalable tool for parameter estimation for dynamic models.

SUMMARY: Mechanistic models are important tools to describe and understand biological processes. However, they typically rely on unknown parameters, the estimation of which can be challenging for large and complex systems. pyPESTO is a modular framework for systematic parameter estimation, with scalable algorithms for optimization and uncertainty quantification. While tailored to ordinary differential equation problems, pyPESTO is broadly applicable to black-box parameter estimation problems. Besides own implementations, it provides a unified interface to various popular simulation and inference methods. AVAILABILITY AND IMPLEMENTATION: pyPESTO is implemented in Python, open-source under a 3-Clause BSD license. Code and documentation are available on GitHub (https://github.com/icb-dcm/pypesto).

Efficient computation of adjoint sensitivities at steady-state in ODE models of biochemical reaction networks.

Dynamical models in the form of systems of ordinary differential equations have become a standard tool in systems biology. Many parameters of such models are usually unknown and have to be inferred from experimental data. Gradient-based optimization has proven to be effective for parameter estimation. However, computing gradients becomes increasingly costly for larger models, which are required for capturing the complex interactions of multiple biochemical pathways. Adjoint sensitivity analysis has been pivotal for working with such large models, but methods tailored for steady-state data are currently not available. We propose a new adjoint method for computing gradients, which is applicable if the experimental data include steady-state measurements. The method is based on a reformulation of the backward integration problem to a system of linear algebraic equations. The evaluation of the proposed method using real-world problems shows a speedup of total simulation time by a factor of up to 4.4. Our results demonstrate that the proposed approach can achieve a substantial improvement in computation time, in particular for large-scale models, where computational efficiency is critical.

Epidemiological and Serological Analysis of a SARS-CoV-2 Outbreak in a Nursing Home: Impact of SARS-CoV-2 Vaccination and Enhanced Neutralizing Immunity Following Breakthrough Infection.

Background: Despite a vaccination rate of 82.0% (n = 123/150), a SARS-CoV-2 (Alpha) outbreak with 64.7% (n = 97/150) confirmed infections occurred in a nursing home in Bavaria, Germany. Objective: the aim of this retrospective cohort study was to examine the effects of the Corminaty vaccine in a real-life outbreak situation and to obtain insights into the antibody response to both vaccination and breakthrough infection. Methods: the antibody status of 106 fully vaccinated individuals (54/106 breakthrough infections) and epidemiological data on all 150 residents and facility staff were evaluated. Results: SARS-CoV-2 infections (positive RT-qPCR) were detected in 56.9% (n = 70/123) of fully vaccinated, compared to 100% (n = 27/27) of incompletely or non-vaccinated individuals. The proportion of hospitalized and deceased was 4.1% (n = 5/123) among fully vaccinated and therewith lower compared to 18.5% (n = 5/27) hospitalized and 11.1% (n = 3/27) deceased among incompletely or non-vaccinated. Ct values were significantly lower in incompletely or non-vaccinated (p = 0.02). Neutralizing antibodies were detected in 99.1% (n = 105/106) of serum samples with significantly higher values (p < 0.001) being measured post-breakthrough infection. α-N-antibodies were detected in 37.7% of PCR positive but not in PCR negative individuals. Conclusion: Altogether, our data indicate that SARS-CoV-2 vaccination does provide protection against infection, severe disease progression and death with regards to the Alpha variant. Nonetheless, it also shows that infection and transmission are possible despite full vaccination. It further indicates that breakthrough infections can significantly enhance α-S- and neutralizing antibody responses, indicating a possible benefit from booster vaccinations.

Mini-batch optimization enables training of ODE models on large-scale datasets.

Quantitative dynamic models are widely used to study cellular signal processing. A critical step in modelling is the estimation of unknown model parameters from experimental data. As model sizes and datasets are steadily growing, established parameter optimization approaches for mechanistic models become computationally extremely challenging. Mini-batch optimization methods, as employed in deep learning, have better scaling properties. In this work, we adapt, apply, and benchmark mini-batch optimization for ordinary differential equation (ODE) models, thereby establishing a direct link between dynamic modelling and machine learning. On our main application example, a large-scale model of cancer signaling, we benchmark mini-batch optimization against established methods, achieving better optimization results and reducing computation by more than an order of magnitude. We expect that our work will serve as a first step towards mini-batch optimization tailored to ODE models and enable modelling of even larger and more complex systems than what is currently possible.

Efficient gradient-based parameter estimation for dynamic models using qualitative data.

MOTIVATION: Unknown parameters of dynamical models are commonly estimated from experimental data. However, while various efficient optimization and uncertainty analysis methods have been proposed for quantitative data, methods for qualitative data are rare and suffer from bad scaling and convergence. RESULTS: Here, we propose an efficient and reliable framework for estimating the parameters of ordinary differential equation models from qualitative data. In this framework, we derive a semi-analytical algorithm for gradient calculation of the optimal scaling method developed for qualitative data. This enables the use of efficient gradient-based optimization algorithms. We demonstrate that the use of gradient information improves performance of optimization and uncertainty quantification on several application examples. On average, we achieve a speedup of more than one order of magnitude compared to gradient-free optimization. In addition, in some examples, the gradient-based approach yields substantially improved objective function values and quality of the fits. Accordingly, the proposed framework substantially improves the parameterization of models from qualitative data. AVAILABILITY AND IMPLEMENTATION: The proposed approach is implemented in the open-source Python Parameter EStimation TOolbox (pyPESTO). pyPESTO is available at https://github.com/ICB-DCM/pyPESTO. All application examples and code to reproduce this study are available at https://doi.org/10.5281/zenodo.4507613. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

AMICI: high-performance sensitivity analysis for large ordinary differential equation models.

SUMMARY: Ordinary differential equation models facilitate the understanding of cellular signal transduction and other biological processes. However, for large and comprehensive models, the computational cost of simulating or calibrating can be limiting. AMICI is a modular toolbox implemented in C++/Python/MATLAB that provides efficient simulation and sensitivity analysis routines tailored for scalable, gradient-based parameter estimation and uncertainty quantification. AVAILABILITYAND IMPLEMENTATION: AMICI is published under the permissive BSD-3-Clause license with source code publicly available on https://github.com/AMICI-dev/AMICI. Citeable releases are archived on Zenodo. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

PEtab-Interoperable specification of parameter estimation problems in systems biology.

Reproducibility and reusability of the results of data-based modeling studies are essential. Yet, there has been-so far-no broadly supported format for the specification of parameter estimation problems in systems biology. Here, we introduce PEtab, a format which facilitates the specification of parameter estimation problems using Systems Biology Markup Language (SBML) models and a set of tab-separated value files describing the observation model and experimental data as well as parameters to be estimated. We already implemented PEtab support into eight well-established model simulation and parameter estimation toolboxes with hundreds of users in total. We provide a Python library for validation and modification of a PEtab problem and currently 20 example parameter estimation problems based on recent studies.

Parameterization of mechanistic models from qualitative data using an efficient optimal scaling approach.

Quantitative dynamical models facilitate the understanding of biological processes and the prediction of their dynamics. These models usually comprise unknown parameters, which have to be inferred from experimental data. For quantitative experimental data, there are several methods and software tools available. However, for qualitative data the available approaches are limited and computationally demanding. Here, we consider the optimal scaling method which has been developed in statistics for categorical data and has been applied to dynamical systems. This approach turns qualitative variables into quantitative ones, accounting for constraints on their relation. We derive a reduced formulation for the optimization problem defining the optimal scaling. The reduced formulation possesses the same optimal points as the established formulation but requires less degrees of freedom. Parameter estimation for dynamical models of cellular pathways revealed that the reduced formulation improves the robustness and convergence of optimizers. This resulted in substantially reduced computation times. We implemented the proposed approach in the open-source Python Parameter EStimation TOolbox (pyPESTO) to facilitate reuse and extension. The proposed approach enables efficient parameterization of quantitative dynamical models using qualitative data.

Efficient parameterization of large-scale dynamic models based on relative measurements.

MOTIVATION: Mechanistic models of biochemical reaction networks facilitate the quantitative understanding of biological processes and the integration of heterogeneous datasets. However, some biological processes require the consideration of comprehensive reaction networks and therefore large-scale models. Parameter estimation for such models poses great challenges, in particular when the data are on a relative scale. RESULTS: Here, we propose a novel hierarchical approach combining (i) the efficient analytic evaluation of optimal scaling, offset and error model parameters with (ii) the scalable evaluation of objective function gradients using adjoint sensitivity analysis. We evaluate the properties of the methods by parameterizing a pan-cancer ordinary differential equation model (>1000 state variables, >4000 parameters) using relative protein, phosphoprotein and viability measurements. The hierarchical formulation improves optimizer performance considerably. Furthermore, we show that this approach allows estimating error model parameters with negligible computational overhead when no experimental estimates are available, providing an unbiased way to weight heterogeneous data. Overall, our hierarchical formulation is applicable to a wide range of models, and allows for the efficient parameterization of large-scale models based on heterogeneous relative measurements. AVAILABILITY AND IMPLEMENTATION: Supplementary code and data are available online at http://doi.org/10.5281/zenodo.3254429 and http://doi.org/10.5281/zenodo.3254441. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Benchmarking optimization methods for parameter estimation in large kinetic models.

MOTIVATION: Kinetic models contain unknown parameters that are estimated by optimizing the fit to experimental data. This task can be computationally challenging due to the presence of local optima and ill-conditioning. While a variety of optimization methods have been suggested to surmount these issues, it is difficult to choose the best one for a given problem a priori. A systematic comparison of parameter estimation methods for problems with tens to hundreds of optimization variables is currently missing, and smaller studies provided contradictory findings. RESULTS: We use a collection of benchmarks to evaluate the performance of two families of optimization methods: (i) multi-starts of deterministic local searches and (ii) stochastic global optimization metaheuristics; the latter may be combined with deterministic local searches, leading to hybrid methods. A fair comparison is ensured through a collaborative evaluation and a consideration of multiple performance metrics. We discuss possible evaluation criteria to assess the trade-off between computational efficiency and robustness. Our results show that, thanks to recent advances in the calculation of parametric sensitivities, a multi-start of gradient-based local methods is often a successful strategy, but a better performance can be obtained with a hybrid metaheuristic. The best performer combines a global scatter search metaheuristic with an interior point local method, provided with gradients estimated with adjoint-based sensitivities. We provide an implementation of this method to render it available to the scientific community. AVAILABILITY AND IMPLEMENTATION: The code to reproduce the results is provided as Supplementary Material and is available at Zenodo https://doi.org/10.5281/zenodo.1304034. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Community-driven roadmap for integrated disease maps.

The Disease Maps Project builds on a network of scientific and clinical groups that exchange best practices, share information and develop systems biomedicine tools. The project aims for an integrated, highly curated and user-friendly platform for disease-related knowledge. The primary focus of disease maps is on interconnected signaling, metabolic and gene regulatory network pathways represented in standard formats. The involvement of domain experts ensures that the key disease hallmarks are covered and relevant, up-to-date knowledge is adequately represented. Expert-curated and computer readable, disease maps may serve as a compendium of knowledge, allow for data-supported hypothesis generation or serve as a scaffold for the generation of predictive mathematical models. This article summarizes the 2nd Disease Maps Community meeting, highlighting its important topics and outcomes. We outline milestones on the roadmap for the future development of disease maps, including creating and maintaining standardized disease maps; sharing parts of maps that encode common human disease mechanisms; providing technical solutions for complexity management of maps; and Web tools for in-depth exploration of such maps. A dedicated discussion was focused on mathematical modeling approaches, as one of the main goals of disease map development is the generation of mathematically interpretable representations to predict disease comorbidity or drug response and to suggest drug repositioning, altogether supporting clinical decisions.

Efficient Parameter Estimation Enables the Prediction of Drug Response Using a Mechanistic Pan-Cancer Pathway Model.

Mechanistic models are essential to deepen the understanding of complex diseases at the molecular level. Nowadays, high-throughput molecular and phenotypic characterizations are possible, but the integration of such data with prior knowledge on signaling pathways is limited by the availability of scalable computational methods. Here, we present a computational framework for the parameterization of large-scale mechanistic models and its application to the prediction of drug response of cancer cell lines from exome and transcriptome sequencing data. This framework is over 104 times faster than state-of-the-art methods, which enables modeling at previously infeasible scales. By applying the framework to a model describing major cancer-associated pathways (>1,200 species and >2,600 reactions), we could predict the effect of drug combinations from single drug data. This is the first integration of high-throughput datasets using large-scale mechanistic models. We anticipate this to be the starting point for development of more comprehensive models allowing a deeper mechanistic insight.

PESTO: Parameter EStimation TOolbox.

Summary: PESTO is a widely applicable and highly customizable toolbox for parameter estimation in MathWorks MATLAB. It offers scalable algorithms for optimization, uncertainty and identifiability analysis, which work in a very generic manner, treating the objective function as a black box. Hence, PESTO can be used for any parameter estimation problem, for which the user can provide a deterministic objective function in MATLAB. Availability and implementation: PESTO is a MATLAB toolbox, freely available under the BSD license. The source code, along with extensive documentation and example code, can be downloaded from https://github.com/ICB-DCM/PESTO/. Contact: jan.hasenauer@helmholtz-muenchen.de. Supplementary information: Supplementary data are available at Bioinformatics online.

MIA: non-targeted mass isotopolome analysis.

UNLABELLED: MIA detects and visualizes isotopic enrichment in gas chromatography electron ionization mass spectrometry (GC-EI-MS) datasets in a non-targeted manner. It provides an easy-to-use graphical user interface that allows for visual mass isotopomer distribution analysis across multiple datasets. MIA helps to reveal changes in metabolic fluxes, visualizes metabolic proximity of isotopically enriched compounds and shows the fate of the applied stable isotope labeled tracer. AVAILABILITY AND IMPLEMENTATION: Linux and Windows binaries, documentation, and sample data are freely available for download at http://massisotopolomeanalyzer.lu MIA is a stand-alone application implemented in C ++ and based on Qt5, NTFD and the MetaboliteDetector framework. CONTACT: karsten.hiller@uni.lu.

Bridging the gap between non-targeted stable isotope labeling and metabolic flux analysis.

BACKGROUND: Metabolism gained increasing interest for the understanding of diseases and to pinpoint therapeutic intervention points. However, classical metabolomics techniques only provide a very static view on metabolism. Metabolic flux analysis methods, on the other hand, are highly targeted and require detailed knowledge on metabolism beforehand. RESULTS: We present a novel workflow to analyze non-targeted metabolome-wide stable isotope labeling data to detect metabolic flux changes in a non-targeted manner. Furthermore, we show how similarity-analysis of isotopic enrichment patterns can be used for pathway contextualization of unidentified compounds. We illustrate our approach with the analysis of changes in cellular metabolism of human adenocarcinoma cells in response to decreased oxygen availability. Starting without a priori knowledge, we detect metabolic flux changes, leading to an increased glutamine contribution to acetyl-CoA production, reveal biosynthesis of N-acetylaspartate by N-acetyltransferase 8-like (NAT8L) in lung cancer cells and show that NAT8L silencing inhibits proliferation of A549, JHH-4, PH5CH8, and BEAS-2B cells. CONCLUSIONS: Differential stable isotope labeling analysis provides qualitative metabolic flux information in a non-targeted manner. Furthermore, similarity analysis of enrichment patterns provides information on metabolically closely related compounds. N-acetylaspartate and NAT8L are important players in cancer cell metabolism, a context in which they have not received much attention yet.

Non-targeted Tracer Fate Detection.

Stable isotopes have been used to trace atoms through metabolism and quantify metabolic fluxes for several decades. Only recently non-targeted stable isotope labeling approaches have emerged as a powerful tool to gain insights into metabolism. However, the manual detection of isotopic enrichment for a non-targeted analysis is tedious and time consuming. To overcome this limitation, the non-targeted tracer fate detection (NTFD) algorithm for the automated metabolome-wide detection of isotopic enrichment has been developed. NTFD detects and quantifies isotopic enrichment in the form of mass isotopomer distributions (MIDs) in an automated manner, providing the means to trace functional groups, determine MIDs for metabolic flux analysis, or detect tracer-derived molecules in general. Here, we describe the algorithmic background of NTFD, discuss practical considerations for the freely available NTFD software package, and present potential applications of non-targeted stable isotope labeling analysis.

Isotopologue ratio normalization for non-targeted metabolomics.

Robust quantification of analytes is a prerequisite for meaningful metabolomics experiments. In non-targeted metabolomics it is still hard to compare measurements across multiple batches or instruments. For targeted analyses isotope dilution mass spectrometry is used to provide a robust normalization reference. Here, we present an approach that allows for the automated semi-quantification of metabolites relative to a fully stable isotope-labeled metabolite extract. Unlike many previous approaches, we include both identified and unidentified compounds in the data analysis. The internal standards are detected in an automated manner using the non-targeted tracer fate detection algorithm. The ratios of the light and heavy form of these compounds serve as a robust measure to compare metabolite levels across different mass spectrometric platforms. As opposed to other methods which require high resolution mass spectrometers, our methodology works with low resolution mass spectrometers as commonly used in gas chromatography electron impact mass spectrometry (GC-EI-MS)-based metabolomics. We demonstrate the validity of our method by analyzing compound levels in different samples and show that it outperforms conventional normalization approaches in terms of intra- and inter-instrument reproducibility. We show that a labeled yeast metabolite extract can also serve as a reference for mammalian metabolite extracts where complete stable isotope labeling is hard to achieve.

How metabolites modulate metabolic flux.

Adaptation to metabolic needs and changing environments is a basic requirement of every living system. These adaptations can be very quick and mild or slower but more drastic. In any case, cells have to constantly monitor their metabolic state and requirements. In this article we review general concepts as well as recent advances on how metabolites can regulate metabolic fluxes. We discuss how cells sense metabolite levels and how changing metabolite levels regulate metabolic enzymes on different levels, from specific allosteric regulation to global transcriptional regulation. We thereby focus on local metabolite sensing in mammalian cells and show that several major discoveries have only very recently been made.