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.

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. Availability 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.

Ordinary differential equation models are nowadays widely used for the mechanistic description of biological processes and their temporal evolution. These models typically have many unknown and nonmeasurable parameters, which have to be determined by fitting the model to experimental data. In order to perform this task, known as parameter estimation or model calibration, the modeller faces challenges such as poor parameter identifiability, lack of sufficiently informative experimental data and the existence of local minima in the objective function landscape. These issues tend to worsen with larger model sizes, increasing the computational complexity and the number of unknown parameters. An incorrectly calibrated model is problematic because it may result in inaccurate predictions and misleading conclusions. For nonexpert users, there are a large number of potential pitfalls. Here, we provide a protocol that guides the user through all the steps involved in the calibration of dynamic models. We illustrate the methodology with two models and provide all the code required to reproduce the results and perform the same analysis on new models. Our protocol provides practitioners and researchers in biological modelling with a one-stop guide that is at the same time compact and sufficiently comprehensive to cover all aspects of the problem.

SerpinB2 (plasminogen activator inhibitor type 2) has been called the “undecided serpin” with no clear consensus on its physiological role, although it is well described as an inhibitor of urokinase plasminogen activator (uPA). In macrophages, pro-inflammatory stimuli usually induce SerpinB2; however, expression is constitutive in Gata6+ large peritoneal macrophages (LPM). Interrogation of expression data from human macrophages treated with a range of stimuli using a new bioinformatics tool, CEMiTool, suggested that SerpinB2 is most tightly co- and counter-regulated with genes associated with cell movement. Using LPM from SerpinB2 −/− and SerpinB2 R380A (active site mutant) mice, we show that migration on Matrigel was faster than for their wild-type controls. Confocal microscopy illustrated that SerpinB2 and F-actin staining overlapped in focal adhesions and lamellipodia. Genes associated with migration and extracellular matrix interactions were also identified by RNA-Seq analysis of migrating RPM from wild-type and SerpinB2 R380A mice. Subsequent gene set enrichment analyses (GSEA) suggested SerpinB2 counter-regulates many Gata6-regulated genes associated with migration. These data argue that the role of SerpinB2 in macrophages is inhibition of uPA-mediated plasmin generation during cell migration. GSEA also suggested that SerpinB2 expression (likely via ensuing modulation of uPA-receptor/integrin signaling) promotes the adoption of a resolution phase signature.

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.