Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Estimation of biochemical network parameter distributions in cell populations

Populations of heterogeneous cells play an important role in many biological systems. In this paper we consider systems where each cell can be modelled by an ordinary differential equation. To account for heterogeneity, parameter values are different among individual cells, subject to a distribution function which is part of the model specification. Experimental data for heterogeneous cell populations can be obtained from flow cytometric fluorescence microscopy. We present a heuristic approach to use such data for estimation of the parameter distribution in the population. The approach is based on generating simulation data for samples in parameter space. By convex optimisation, a suitable probability density function for these samples is computed. To evaluate the proposed approach, we consider artificial data from a simple model of the tumor necrosis factor (TNF) signalling pathway. Its main characteristic is a bimodality in the TNF response: a certain percentage of cells undergoes apoptosis upon stimulation, while the remaining part stays alive. We show how our modelling approach allows to identify the reasons that underly the differential response.Comment: 14 pages, 5 figure

Tailored parameter optimization methods for ordinary differential equation models with steady-state constraints

Background: Ordinary differential equation (ODE) models are widely used to describe (bio-)chemical and biological processes. To enhance the predictive power of these models, their unknown parameters are estimated from experimental data. These experimental data are mostly collected in perturbation experiments, in which the processes are pushed out of steady state by applying a stimulus. The information that the initial condition is a steady state of the unperturbed process provides valuable information, as it restricts the dynamics of the process and thereby the parameters. However, implementing steady-state constraints in the optimization often results in convergence problems. Results: In this manuscript, we propose two new methods for solving optimization problems with steady-state constraints. The first method exploits ideas from optimization algorithms on manifolds and introduces a retraction operator, essentially reducing the dimension of the optimization problem. The second method is based on the continuous analogue of the optimization problem. This continuous analogue is an ODE whose equilibrium points are the optima of the constrained optimization problem. This equivalence enables the use of adaptive numerical methods for solving optimization problems with steady-state constraints. Both methods are tailored to the problem structure and exploit the local geometry of the steady-state manifold and its stability properties. A parameterization of the steady-state manifold is not required. The efficiency and reliability of the proposed methods is evaluated using one toy example and two applications. The first application example uses published data while the second uses a novel dataset for Raf/MEK/ERK signaling. The proposed methods demonstrated better convergence properties than state-of-the-art methods employed in systems and computational biology. Furthermore, the average computation time per converged start is significantly lower. In addition to the theoretical results, the analysis of the dataset for Raf/MEK/ERK signaling provides novel biological insights regarding the existence of feedback regulation. Conclusion: Many optimization problems considered in systems and computational biology are subject to steady-state constraints. While most optimization methods have convergence problems if these steady-state constraints are highly nonlinear, the methods presented recover the convergence properties of optimizers which can exploit an analytical expression for the parameter-dependent steady state. This renders them an excellent alternative to methods which are currently employed in systems and computational biology

Schlussbericht der Universität Bonn

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Mechanistic description of spatial processes using integrative modelling of noise-corrupted imaging data

Spatial patterns are ubiquitous on the subcellular, cellular and tissue level, and can be studied using imaging techniques such as light and fluorescence microscopy. Imaging data provide quantitative information about biological systems; however, mechanisms causing spatial patterning often remain elusive. In recent years, spatio-temporal mathematical modelling has helped to overcome this problem. Yet, outliers and structured noise limit modelling of whole imaging data, and models often consider spatial summary statistics. Here, we introduce an integrated data-driven modelling approach that can cope with measurement artefacts and whole imaging data. Our approach combines mechanistic models of the biological processes with robust statistical models of the measurement process. The parameters of the integrated model are calibrated using a maximum-likelihood approach. We used this integrated modelling approach to study in vivo gradients of the chemokine (C-C motif) ligand 21 (CCL21). CCL21 gradients guide dendritic cells and are important in the adaptive immune response. Using artificial data, we verified that the integrated modelling approach provides reliable parameter estimates in the presence of measurement noise and that bias and variance of these estimates are reduced compared to conventional approaches. The application to experimental data allowed the parametrization and subsequent refinement of the model using additional mechanisms. Among other results, model-based hypothesis testing predicted lymphatic vessel-dependent concentration of heparan sulfate, the binding partner of CCL21. The selected model provided an accurate description of the experimental data and was partially validated using published data. Our findings demonstrate that integrated statistical modelling of whole imaging data is computationally feasible and can provide novel biological insights

Federated difference-in-differences with multiple time periods in DataSHIELD

Difference-in-differences (DID) is a key tool for causal impact evaluation but faces challenges when applied to sensitive data restricted by privacy regulations. Obtaining consent can shrink sample sizes and reduce statistical power, limiting the analysis’s effectiveness. Federated learning addresses these issues by sharing aggregated statistics rather than individual data, though advanced federated DID software is limited. We developed a federated version of the Callaway and Sant’Anna difference-in-differences (CSDID), integrated into the DataSHIELD platform, adhering to stringent privacy protocols. Our approach reproduces key estimates and standard errors while preserving confidentiality. Using simulated and real-world data from a malaria intervention in Mozambique, we demonstrate that federated estimates increase sample sizes, reduce estimation uncertainty, and enable analyses when data owners cannot share treated or untreated group data. Our work contributes to facilitating the evaluation of policy interventions or treatments across centers and borders

AMICI: High-Performance Sensitivity Analysis for Large Ordinary Differential Equation Models

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. 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

Identification of models of heterogeneous cell populations from population snapshot data

Background: Most of the modeling performed in the area of systems biology aims at achieving a quantitative description of the intracellular pathways within a "typical cell". However, in many biologically important situations even clonal cell populations can show a heterogeneous response. These situations require study of cell-to-cell variability and the development of models for heterogeneous cell populations. Results: In this paper we consider cell populations in which the dynamics of every single cell is captured by a parameter dependent differential equation. Differences among cells are modeled by differences in parameters which are subject to a probability density. A novel Bayesian approach is presented to infer this probability density from population snapshot data, such as flow cytometric analysis, which do not provide single cell time series data. The presented approach can deal with sparse and noisy measurement data. Furthermore, it is appealing from an application point of view as in contrast to other methods the uncertainty of the resulting parameter distribution can directly be assessed. Conclusions: The proposed method is evaluated using artificial experimental data from a model of the tumor necrosis factor signaling network. We demonstrate that the methods are computationally efficient and yield good estimation result even for sparse data sets

Spatially Resolved Association of Structural Biomarkers on Retinal Function in Non-Exudative Age-Related Macular Degeneration Over 4 Years

PURPOSE. To longitudinally assess the impact of high-risk structural biomarkers for natural disease progression in non-exudative age-related macular degeneration (AMD) on spatially resolved mesopic and scotopic fundus-controlled perimetry testing. METHODS. Multimodal retinal imaging data and fundus-controlled perimetry stimuli points were semiautomatically registered according to landmark correspondences at each annual visit over a period of up to 4 years. The presence of sub-RPE drusen, subretinal drusenoid deposits, pigment epithelium detachments (PEDs), hyper-reflective foci (HRF), vitelliform lesions, refractile deposits, and incomplete RPE and outer retinal atrophy (iRORA) and complete RPE and outer retinal atrophy (cRORA) were graded at each stimulus position and visit. Localized retinal layer thicknesses were extracted. Mixed-effect models were used for structure–function correlation. RESULTS. Fifty-four eyes of 49 patients with non-exudative AMD (mean age, 70.7 ± 9.1 years) and 27 eyes of 27 healthy controls (mean age, 63.4 ± 8.9 years) were included. During study course, presence of PED had the highest functional impact with a mean estimated loss of −1.30 dB (P P P = 0.001) and −0.87 dB (scotopic, P = 0.005). Subretinal drusenoid deposits were associated with a stronger visual impairment (mesopic, −0.38 dB; P = 0.128; scotopic, −0.37 dB; P = 0.172) compared with sub-RPE drusen (−0.22 dB, P = 0.0004; −0.18 dB, P = 0.006). With development of c-RORA, scotopic retinal sensitivity further significantly decreased (−2.15 dB; P = 0.02). Thickening of the RPE–drusen–complex and thinning of the outer nuclear layer negatively impacted spatially resolved retinal sensitivity. CONCLUSIONS. The presence of PED and HRF had the greatest prognostic impact on progressive point-wise sensitivity losses. Higher predominant rod than cone-mediated localized retinal sensitivity losses with early signs of retinal atrophy development indicate photoreceptor preservation as a potential therapeutic target for future interventional AMD trials