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

Stochastic reaction networks with input processes: Analysis and application to gene expression inference

International audienceStochastic reaction network modelling is widely utilized to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. The statistical analysis of the response of these systems to perturbation inputs is typically dependent on specific perturbation models. Motivated by reporter gene systems, widely utilized in biology to monitor gene activity in individual cells, we address the analysis of reaction networks with state-affine rates in presence of an input process. We develop a generalization of the so-called moment equations that precisely accounts for the first- and second-order moments of arbitrary inputs without the need for a model of the input process, as well as spectral relationships between the network input and state. We then apply these results to develop a method for the reconstruction of the autocovariance function of gene activity from reporter gene population-snapshot data, a crucial step toward the investigation of gene regulation, and demonstrate its performance on a simulated case study

Comprehensive estimation of input signals and dynamics in biochemical reaction networks

Motivation: Cellular information processing can be described mathematically using differential equations. Often, external stimulation of cells by compounds such as drugs or hormones leading to activation has to be considered. Mathematically, the stimulus is represented by a time-dependent input function. less thanbrgreater than less thanbrgreater thanParameters such as rate constants of the molecular interactions are often unknown and need to be estimated from experimental data, e.g. by maximum likelihood estimation. For this purpose, the input function has to be defined for all times of the integration interval. This is usually achieved by approximating the input by interpolation or smoothing of the measured data. This procedure is suboptimal since the input uncertainties are not considered in the estimation process which often leads to overoptimistic confidence intervals of the inferred parameters and the model dynamics. less thanbrgreater than less thanbrgreater thanResults: This article presents a new approach which includes the input estimation into the estimation process of the dynamical model parameters by minimizing an objective function containing all parameters simultaneously. We applied this comprehensive approach to an illustrative model with simulated data and compared it to alternative methods. Statistical analyses revealed that our method improves the prediction of the model dynamics and the confidence intervals leading to a proper coverage of the confidence intervals of the dynamic parameters. The method was applied to the JAK-STAT signaling pathway