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

Effect of Distillers Grains Plus Solubles and Monensin Supplementation on Grazing Steers

Yearling steers rotationally grazing smooth bromegrass were individually supplemented monensin at 0 or 200 mg with modified distillers grains plus solubles (MDGS) at .05, 0.4, 0.6, and 0.8% BW. Cannulated steers continuously grazing smooth bromegrass were assigned randomly to one of two treatments: 0.4% BW MDGS supplementation with 0 or 200 mg monensin. Monensin did not affect ADG of steers supplemented MDGS ≥ 0.4% BW. Steers supplemented with monensin had a decreasein estimated average forage intakefrom 16.16 lb to 14.75 lb/OM daily

An integrated strategy for prediction uncertainty analysis

Motivation: To further our understanding of the mechanisms underlying biochemical pathways mathematical modelling is used. Since many parameter values are unknown they need to be estimated using experimental observations. The complexity of models necessary to describe biological pathways in combination with the limited amount of quantitative data results in large parameter uncertainty which propagates into model predictions. Therefore prediction uncertainty analysis is an important topic that needs to be addressed in Systems Biology modelling

Cross-evaluation of modelled and remotely sensed surface soil moisture with in situ data in southwestern France

The SMOSMANIA soil moisture network in Southwestern France is used to evaluate modelled and remotely sensed soil moisture products. The surface soil moisture (SSM) measured in situ at 5 cm permits to evaluate SSM from the SIM operational hydrometeorological model of Météo-France and to perform a cross-evaluation of the normalised SSM estimates derived from coarse-resolution (25 km) active microwave observations from the ASCAT scatterometer instrument (C-band, onboard METOP), issued by EUMETSAT and resampled to the Discrete Global Grid (DGG, 12.5 km gridspacing) by TU-Wien (Vienna University of Technology) over a two year period (2007–2008). A downscaled ASCAT product at one kilometre scale is evaluated as well, together with operational soil moisture products of two meteorological services, namely the ALADIN numerical weather prediction model (NWP) and the Integrated Forecasting System (IFS) analysis of Météo-France and ECMWF, respectively. In addition to the operational SSM analysis of ECMWF, a second analysis using a simplified extended Kalman filter and assimilating the ASCAT SSM estimates is tested. The ECMWF SSM estimates correlate better with the in situ observations than the Météo-France products. This may be due to the higher ability of the multi-layer land surface model used at ECMWF to represent the soil moisture profile. However, the SSM derived from SIM corresponds to a thin soil surface layer and presents good correlations with ASCAT SSM estimates for the very first centimetres of soil. At ECMWF, the use of a new data assimilation technique, which is able to use the ASCAT SSM, improves the SSM and the root-zone soil moisture analyses

STAMINA: Stochastic Approximate Model-Checker for Infinite-State Analysis

Stochastic model checking is a technique for analyzing systems that possess probabilistic characteristics. However, its scalability is limited as probabilistic models of real-world applications typically have very large or infinite state space. This paper presents a new infinite state CTMC model checker, STAMINA, with improved scalability. It uses a novel state space approximation method to reduce large and possibly infinite state CTMC models to finite state representations that are amenable to existing stochastic model checkers. It is integrated with a new property-guided state expansion approach that improves the analysis accuracy. Demonstration of the tool on several benchmark examples shows promising results in terms of analysis efficiency and accuracy compared with a state-of-the-art CTMC model checker that deploys a similar approximation method