Global parameter identification of stochastic reaction networks from single trajectories

We consider the problem of inferring the unknown parameters of a stochastic biochemical network model from a single measured time-course of the concentration of some of the involved species. Such measurements are available, e.g., from live-cell fluorescence microscopy in image-based systems biology. In addition, fluctuation time-courses from, e.g., fluorescence correlation spectroscopy provide additional information about the system dynamics that can be used to more robustly infer parameters than when considering only mean concentrations. Estimating model parameters from a single experimental trajectory enables single-cell measurements and quantification of cell--cell variability. We propose a novel combination of an adaptive Monte Carlo sampler, called Gaussian Adaptation, and efficient exact stochastic simulation algorithms that allows parameter identification from single stochastic trajectories. We benchmark the proposed method on a linear and a non-linear reaction network at steady state and during transient phases. In addition, we demonstrate that the present method also provides an ellipsoidal volume estimate of the viable part of parameter space and is able to estimate the physical volume of the compartment in which the observed reactions take place.Comment: Article in print as a book chapter in Springer's "Advances in Systems Biology

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

Investigating modularity in the analysis of process algebra models of biochemical systems

Compositionality is a key feature of process algebras which is often cited as one of their advantages as a modelling technique. It is certainly true that in biochemical systems, as in many other systems, model construction is made easier in a formalism which allows the problem to be tackled compositionally. In this paper we consider the extent to which the compositional structure which is inherent in process algebra models of biochemical systems can be exploited during model solution. In essence this means using the compositional structure to guide decomposed solution and analysis. Unfortunately the dynamic behaviour of biochemical systems exhibits strong interdependencies between the components of the model making decomposed solution a difficult task. Nevertheless we believe that if such decomposition based on process algebras could be established it would demonstrate substantial benefits for systems biology modelling. In this paper we present our preliminary investigations based on a case study of the pheromone pathway in yeast, modelling in the stochastic process algebra Bio-PEPA

Jump-Diffusion Approximation of Stochastic Reaction Dynamics: Error bounds and Algorithms

Biochemical reactions can happen on different time scales and also the abundance of species in these reactions can be very different from each other. Classical approaches, such as deterministic or stochastic approach, fail to account for or to exploit this multi-scale nature, respectively. In this paper, we propose a jump-diffusion approximation for multi-scale Markov jump processes that couples the two modeling approaches. An error bound of the proposed approximation is derived and used to partition the reactions into fast and slow sets, where the fast set is simulated by a stochastic differential equation and the slow set is modeled by a discrete chain. The error bound leads to a very efficient dynamic partitioning algorithm which has been implemented for several multi-scale reaction systems. The gain in computational efficiency is illustrated by a realistically sized model of a signal transduction cascade coupled to a gene expression dynamics.Comment: 32 pages, 7 figure

Inferring rate coefficents of biochemical reactions from noisy data with KInfer

Dynamical models of inter- and intra-cellular processes contain the rate constants of the biochemical reactions. These kinetic parameters are often not accessible directly through experiments, but they can be inferred from time-resolved data. Time resolved data, that is, measurements of reactant concentration at series of time points, are usually affected by different types of error, whose source can be both experimental and biological. The noise in the input data makes the estimation of the model parameters a very difficult task, as if the inference method is not sufficiently robust to the noise, the resulting estimates are not reliable. Therefore "noise-robust" methods that estimate rate constants with the maximum precision and accuracy are needed. In this report we present the probabilistic generative model of parameter inference implemented by the software prototype KInfer and we show the ability of this tool of estimating the rate coefficients of models of biochemical network with a good accuracy even from very noisy input data

A Molecular Implementation of the Least Mean Squares Estimator

In order to function reliably, synthetic molecular circuits require mechanisms that allow them to adapt to environmental disturbances. Least mean squares (LMS) schemes, such as commonly encountered in signal processing and control, provide a powerful means to accomplish that goal. In this paper we show how the traditional LMS algorithm can be implemented at the molecular level using only a few elementary biomolecular reactions. We demonstrate our approach using several simulation studies and discuss its relevance to synthetic biology.Comment: Molecular circuits, synthetic biology, least mean squares estimator, adaptive system