Biology subjects

Stapor, P.

Publications and source records attributed to Stapor, P..

9 recordsLinked to original sources

bioRxiv2026

Nonlinear mixed-effect models and tailored parametrization schemes enables integration of single cell and bulk data

Experimental methods for characterizing single cells and cell populations have improved tremendously over the past decades. This progress has enabled the development of quantitative, mechanistic models for cellular processes based on either single cell or bulk data. However, coherent statistical frameworks for the model-based integration of different data types at the single-cell and population levels are still missing. In this work, we present a mathematical modeling approach for integrating single-cell time-lapse, single-cell snapshot, single-cell time-to-event and population-average data. Utilizing a formulation based on nonlinear mixed-effect modeling, we enable the description of multiple data types, with and without single-cell resolution, and we propose a tailored parameter estimation method. Furthermore, we propose a tailored parameter estimation scheme that facilitates the assessment of underlying process parameters. Our study demonstrates that the proposed approach can reliably integrate diverse data types, thereby improving parameter identifiability and prediction accuracy. Applying this framework of extrinsic apoptosis reveals that simultaneously considering multiple data types can be essential, particularly when experimental constraints limit data availability. The proposed approach is broadly applicable and may significantly advance our understanding of complex biological processes.

systems biology↗

bioRxiv2023

A more expressive spline representation for SBML models improves code generation performance in AMICI

AbstractsSpline interpolants are commonly used for discretizing and estimating functions in mathematical models. While splines can be encoded in the Systems Biology Markup Language (SBML) using piecewise functions, the resulting formulas are very complex and difficult to derive by hand. Tools to create such formulas exist but only deal with numeric data and thus cannot be used for function estimation. Similarly, simulation tools suffer from several limitations when handling splines. For example, in the AMICI library splines with large numbers of nodes lead to long model import times. We have developed a set of SBML annotations to mark assignment rules as spline formulas. These compact representations are human-readable and easy to edit, in contrast to the piecewise representation. Different boundary conditions and extrapolation methods can also be specified. By extending AMICI to create and recognize these annotations, model import can be sped up significantly. This allows practitioners to increase the expressivity of their models. While the performance improvement is limited to AMICI, our tools for creating spline formulas can be used for other tools as well and our syntax for compact spline representation may be a starting point for an SBML-native way to represent spline interpolants.

bioinformatics↗

bioRxiv2022

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. Author summaryLarge-scale dynamical models are nowadays widely used for the analysis of complex processes and the integration of large-scale data sets. However, computational cost is often a bottleneck. Here, we propose a new gradient computation method that facilitates the parameterization of large-scale models based on steady-state measurements. The method can be combined with existing gradient computation methods for time-course measurements. Accordingly, it is an essential contribution to the environment of computationally efficient approaches for the study of large-scale screening and omics data, but not tailored to biological applications, and, therefore, also useful beyond the field of computational biology.

systems biology↗

bioRxiv2020

Benchmarking of numerical integration methods for ODE models of biological systems

Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when unknown parameters need to be inferred. This renders efficient and reliable numerical integration methods essential. However, these methods depend on various hyperparameters, which strongly impact the ODE solution. Despite this, and although hundreds of published ODE models are freely available in public databases, a thorough study that quantifies the impact of hyperparameters on the ODE solver in terms of accuracy and computation time is still missing. In this manuscript, we investigate which choices of algorithms and hyperparameters are generally favorable when dealing with ODE models arising from biological processes. To ensure a representative evaluation, we considered 167 published models. Our study provides evidence that most ODEs in computational biology are stiff, and we give guidelines for the choice of algorithms and hyperparameters. We anticipate that our results will help researchers in systems biology to choose appropriate numerical methods when dealing with ODE models.

systems biology↗

bioRxiv2019

Cell-to-cell variability in JAK2/STAT5 pathway components and cytoplasmic volumes define survival threshold in erythroid progenitor cells

Survival or apoptosis is a binary decision in individual cells. Yet, at the cell population level, a graded increase in survival of CFU-E cells is observed upon stimulation with Erythropoietin (Epo). To identify components of JAK2/STAT5 signal transduction that contribute to the graded population response, a cell population-level model calibrated with experimental data was extended to study the behavior in single cells. The single-cell model showed that the high cell-to-cell variability in nuclear phosphorylated STAT5 is caused by variability in the amount of EpoR:JAK2 complexes and of SHP1 as well as the extent of nuclear import due to the large variance in the cytoplasmic volume of CFU-E cells. 24 to 118 pSTAT5 molecules in the nucleus for 120 min are sufficient to ensure cell survival. Thus, variability in membrane-associated processes are responsible to convert a switch-like behavior at the single-cell level to a graded population level response. HighlightsO_LIMathematical modeling enables integration of heterogeneous data C_LIO_LISingle-cell modeling captures binary decision process C_LIO_LIMultiple sources of cell-to-cell variability in erythroid progenitor cells C_LIO_LIMinimal amount of active STAT5 sufficient for survival of erythroid progenitor cells C_LI

systems biology↗

bioRxiv2019

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

Quantitative dynamical models are widely used to study cellular signal processing. A critical step in modeling 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. However, 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 modeling 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 modeling of even larger and more complex systems than what is currently possible.

systems biology↗

bioRxiv2019

Dirac mixture distributions for the approximation of mixed effects models

Mixed effect modeling is widely used to study cell-to-cell and patient-to-patient variability. The population statistics of mixed effect models is usually approximated using Dirac mixture distributions obtained using Monte-Carlo, quasi Monte-Carlo, and sigma point methods. Here, we propose the use of a method based on the Cramer-von Mises Distance, which has been introduced in the context of filtering. We assess the accuracy of the different methods using several problems and provide the first scalability study for the Cramer-von Mises Distance method. Our results indicate that for a given number of points, the method based on the modified Cramer-von Mises Distance method tends to achieve a better approximation accuracy than Monte-Carlo and quasi Monte-Carlo methods. In contrast to sigma-point methods, the method based on the modified Cramer-von Mises Distance allows for a flexible number of points and a more accurate approximation for nonlinear problems.

systems biology↗

bioRxiv2019

Challenges in the calibration of large-scale ordinary differential equation models

Mathematical models based on ordinary differential equations have been employed with great success to study complex biological systems. With soaring data availability, more and more models of increasing size are being developed. When working with these large-scale models, several challenges arise, such as high computation times or poor identifiability of model parameters. In this work, we review and illustrate the most common challenges using a published model of cellular metabolism. We summarize currently available methods to deal with some of these challenges while focusing on reproducibility and reusability of models, efficient and robust model simulation and parameter estimation.

systems biology↗

bioRxiv2018

Optimization and uncertainty analysis of ODE models using second order adjoint sensitivity analysis

MotivationParameter estimation methods for ordinary differential equation (ODE) models of biological processes can exploit gradients and Hessians of objective functions to achieve convergence and computational efficiency. However, the computational complexity of established methods to evaluate the Hessian scales linearly with the number of state variables and quadratically with the number of parameters. This limits their application to low-dimensional problems.\n\nResultsWe introduce second order adjoint sensitivity analysis for the computation of Hessians and a hybrid optimization-integration based approach for profile likelihood computation. Second order adjoint sensitivity analysis scales linearly with the number of parameters and state variables. The Hessians are effectively exploited by the proposed profile likelihood computation approach. We evaluate our approaches on published biological models with real measurement data. Our study reveals an improved computational efficiency and robustness of optimization compared to established approaches, when using Hessians computed with adjoint sensitivity analysis. The hybrid computation method was more than two-fold faster than the best competitor. Thus, the proposed methods and implemented algorithms allow for the improvement of parameter estimation for medium and large scale ODE models.\n\nAvailabilityThe algorithms for second order adjoint sensitivity analysis are implemented in the Advance MATLAB Interface CVODES and IDAS (AMICI, https://github.com/ICB-DCM/AMICI/). The algorithm for hybrid profile likelihood computation is implemented in the parameter estimation toolbox (PESTO, https://github.com/ICB-DCM/PESTO/). Both toolboxes are freely available under the BSD license.\n\nContactjan.hasenauer@helmholtz-muenchen.de\n\nSupplementary informationSupplementary data are available at Bioinformatics online.

systems biology↗