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

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

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

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

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

Retest variability and patient reliability indices of quantitative fundus autofluorescence in age-related macular degeneration: a MACUSTAR study report

This study aimed to determine the retest variability of quantitative fundus autofluorescence (QAF) in patients with and without age-related macular degeneration (AMD) and evaluate the predictive value of patient reliability indices on retest reliability. A total of 132 eyes from 68 patients were examined, including healthy individuals and those with various stages of AMD. Duplicate QAF imaging was conducted at baseline and 2 weeks later across six study sites. Intraclass correlation (ICC) analysis was used to evaluate the consistency of imaging, and mean opinion scores (MOS) of image quality were generated by two researchers. The contribution of MOS and other factors to retest variation was assessed using mixed-effect linear models. Additionally, a Random Forest Regressor was trained to evaluate the extent to which manual image grading of image quality could be replaced by automated assessment (inferred MOS). The results showed that ICC values were high for all QAF images, with slightly lower values in AMD-affected eyes. The average inter-day ICC was found to be 0.77 for QAF segments within the QAF8 ring and 0.74 for peripheral segments. Image quality was predicted with a mean absolute error of 0.27 on a 5-point scale, and of all evaluated reliability indices, MOS/inferred MOS proved most important. The findings suggest that QAF allows for reliable testing of autofluorescence levels at the posterior pole in patients with AMD in a multicenter, multioperator setting. Patient reliability indices could serve as eligibility criteria for clinical trials, helping identify patients with adequate retest reliability

Threshold-Free Population Analysis Identifies Larger DRG Neurons to Respond Stronger to NGF Stimulation

Sensory neurons in dorsal root ganglia (DRG) are highly heterogeneous in terms of cell size, protein expression, and signaling activity. To analyze their heterogeneity, threshold-based methods are commonly used, which often yield highly variable results due to the subjectivity of the individual investigator. In this work, we introduce a threshold-free analysis approach for sparse and highly heterogeneous datasets obtained from cultures of sensory neurons. This approach is based on population estimates and completely free of investigator-set parameters. With a quantitative automated microscope we measured the signaling state of single DRG neurons by immunofluorescently labeling phosphorylated, i.e., activated Erk1/2. The population density of sensory neurons with and without pain-sensitizing nerve growth factor (NGF) treatment was estimated using a kernel density estimator (KDE). By subtraction of both densities and integration of the positive part, a robust estimate for the size of the responsive subpopulations was obtained. To assure sufficiently large datasets, we determined the number of cells required for reliable estimates using a bootstrapping approach. The proposed methods were employed to analyze response kinetics and response amplitude of DRG neurons after NGF stimulation. We thereby determined the portion of NGF responsive cells on a true population basis. The analysis of the dose dependent NGF response unraveled a biphasic behavior, while the study of its time dependence showed a rapid response, which approached a steady state after less than five minutes. Analyzing two parameter correlations, we found that not only the number of responsive small-sized neurons exceeds the number of responsive large-sized neurons—which is commonly reported and could be explained by the excess of small-sized cells—but also the probability that small-sized cells respond to NGF is higher. In contrast, medium-sized and large-sized neurons showed a larger response amplitude in their mean Erk1/2 activity

Clinical Impact of Monoclonal Antibodies in the Treatment of High-Risk Patients with SARS-CoV-2 Breakthrough Infections:The ORCHESTRA Prospective Cohort Study

The clinical impact of anti-spike monoclonal antibodies (mAb) in Coronavirus Disease 2019 (COVID-19) breakthrough infections is unclear. We present the results of an observational prospective cohort study assessing and comparing COVID-19 progression in high-risk outpatients receiving mAb according to primary or breakthrough infection. Clinical, serological and virological predictors associated with 28-day COVID-19-related hospitalization were identified using multivariate logistic regression and summarized with odds ratio (aOR) and 95% confidence interval (CI). A total of 847 COVID-19 outpatients were included: 414 with primary and 433 with breakthrough infection. Hospitalization was observed in 42/414 (10.1%) patients with primary and 8/433 (1.8%) patients with breakthrough infection (p &lt; 0.001). aOR for hospitalization was significantly lower for breakthrough infection (aOR 0.12, 95%CI: 0.05–0.27, p &lt; 0.001) and higher for immunocompromised status (aOR:2.35, 95%CI:1.08–5.08, p = 0.003), advanced age (aOR:1.06, 95%CI: 1.03–1.08, p &lt; 0.001), and male gender (aOR:1.97, 95%CI: 1.04–3.73, p = 0.037). Among the breakthrough infection group, the median SARS-CoV-2 anti-spike IgGs was lower (p &lt; 0.001) in immunocompromised and elderly patients &gt;75 years compared with that in the immunocompetent patients. Our findings suggest that, among mAb patients, those with breakthrough infection have significantly lower hospitalization risk compared with patients with primary infection. Prognostic algorithms combining clinical and immune-virological characteristics are needed to ensure appropriate and up-to-date clinical protocols targeting high-risk categories.</p