Stochastic reaction networks with input processes: Analysis and applications to reporter gene systems

Stochastic reaction network models are widely utilized in biology and chemistry to describe the probabilistic dynamics of biochemical systems in general, and gene interaction networks in particular. Most often, statistical analysis and inference of these systems is addressed by parametric approaches, where the laws governing exogenous input processes, if present, are themselves fixed in advance. Motivated by reporter gene systems, widely utilized in biology to monitor gene activation at the individual cell level, we address the analysis of reaction networks with state-affine reaction rates and arbitrary input processes. We derive a generalization of the so-called moment equations where the dynamics of the network statistics are expressed as a function of the input process statistics. In stationary conditions, we provide a spectral analysis of the system and elaborate on connections with linear filtering. We then apply the theoretical results to develop a method for the reconstruction of input process statistics, namely the gene activation autocovariance function, from reporter gene population snapshot data, and demonstrate its performance on a simulated case study

On observability and reconstruction of promoter activity statistics from reporter protein mean and variance profiles

International audienceReporter protein systems are widely used in biology for the indirect quantitative monitoring of gene expression activity over time. Atthe level of population averages, the relationship between the observed reporter concentration profile and gene promoter activity is established,and effective methods have been introduced to reconstruct this information from the data. At single-cell level, the relationship between population distribution time profiles and the statistics of promoter activation is still not fully investigated, and adequate reconstruction methods are lacking.This paper develops new results for the reconstruction of promoter activity statistics from mean and variance profiles of a reporter protein. Based on stochastic modelling of gene expression dynamics, it discusses the observability of mean and autocovariance function of an arbitrary random binary promoter activity process. Mathematical relationships developed are explicit and nonparametric, i.e. free of a priori assumptions on the laws governing the promoter process, thus allowing for the decoupled analysis of the switching dynamics in a subsequent step. The results of this work constitute the essential tools for the development of promoter statistics and regulatory mechanism inference algorithms

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

Inference of the statistics of a modulated promoter process from population snapshot gene expression data

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On convex problems in chance-constrained stochastic model predictive control

We investigate constrained optimal control problems for linear stochastic dynamical systems evolving in discrete time. We consider minimization of an expected value cost over a finite horizon. Hard constraints are introduced first, and then reformulated in terms of probabilistic constraints. It is shown that, for a suitable parametrization of the control policy, a wide class of the resulting optimization problems are convex, or admit reasonable convex approximations

Identification of genetic network dynamics with unate structure

Motivation: Modern experimental techniques for time course measurement of gene expression enable the identification of dynamical models of genetic regulatory networks. In general, identification involves fitting appropriate network structures and parameters to the data. For a given set of genes, exploring all possible network structures is clearly prohibitive. Modelling and identification methods for the a priori selection of network structures compatible with biological knowledge and experimental data are necessary to make the identification problem tractable. Results: We propose a differential equation modelling framework where the regulatory interactions among genes are expressed in terms of unate functions, a class of gene activation rules commonly encountered in Boolean network modelling. We establish analytical properties of the models in the class and exploit them to devise a two-step procedure for gene network reconstruction from product concentration and synthesis rate time series. The first step isolates a family of model structures compatible with the data from a set of most relevant biological hypotheses. The second step explores this family and returns a pool of best fitting models along with estimates of their parameters. The method is tested on a simulated network and compared with state-of-the-art network inference methods on the benchmark synthetic network IRMA. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Stochastic dynamics of genetic networks: modelling and parameter identification

Motivation: Identification of regulatory networks is typically based on deterministic models of gene expression. Increasing experimental evidence suggests that the gene regulation process is intrinsically random. To ensure accurate and thorough processing of the experimental data, stochasticity must be explicitly accounted for both at the modelling stage and in the design of the identification algorithms. Results: We propose a model of gene expression in prokaryotes where transcription is described as a probabilistic event, whereas protein synthesis and degradation are captured by first-order deterministic kinetics. Based on this model and assuming that the network of interactions is known, a method for estimating unknown parameters, such as synthesis and binding rates, from the outcomes of multiple time-course experiments is introduced. The method accounts naturally for sparse, irregularly sampled and noisy data and is applicable to gene networks of arbitrary size. The performance of the method is evaluated on a model of nutrient stress response in Escherichia coli. Contact: [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Méthodes de validation de modèles de population pour les dynamiques d’expression génique

The advent of experimental techniques for the time-course monitoring of gene expression at the single-cell level has paved the way to the model-based study of gene expression variability within- an across-cells. A number of approaches to the inference of models accounting for variability of gene expression over isogenic cell populations have been developed and applied to real-world scenarios. The development of a systematic approach for the validation of population models is however lagging behind, and accuracy of the models obtained is often assessed on a semi-empirical basis. In this report we study the problem of validating models of gene network dynamics for cell populations, providing statistical tools for qualitative and quantitative model validation and comparison, and guidelines for their application and interpretation based on a real biological case study.La diffusion des techniques expérimentales pour la mesure de l’expression génique au cours du temps à niveau des cellules individuelles a ouvert la voie à l’étude par modèles de la variabilité intra- et extracellulaire de l’expression génique. Plusieurs approches à l’inférence de modèles de variabilité en populations cellulaires isogéniques ont étés développés et appliques à des contextes réels. Toutefois, moins d’efforts ont étés dédies au développement d’approches systématique a la validation de ces modèles de population, et la qualité des modèles obtenus est souvent évaluée par des critères semi-empiriques. Dans ce rapport on étudie le problème de la validation de modèles des dynamiques des réseaux géniques pour populations cellulaires. On propose des outils statistiques pour la validation et la comparaison qualitative et quantitative de modèles, et on discute leur application et interprétation sur la base d’un problème biologique réel

Inference of protein kinetics by stochastic modeling and simulation of fluorescence recovery after photobleaching experiments

Motivation: Fluorescence recovery after photobleaching (FRAP) is a functional live cell imaging technique that permits the exploration of protein dynamics in living cells. To extract kinetic parameters from FRAP data, a number of analytical models have been developed. Simplifications are inherent in these models, which may lead to inexhaustive or inaccurate exploitation of the experimental data. An appealing alternative is offered by the simulation of biological processes in realistic environments at a particle level. However, inference of kinetic parameters using simulation-based models is still limited. Results: We introduce and demonstrate a new method for the inference of kinetic parameter values from FRAP data. A small number of in silico FRAP experiments is used to construct a mapping from FRAP recovery curves to the parameters of the underlying protein kinetics. Parameter estimates from experimental data can then be computed by applying the mapping to the observed recovery curves. A bootstrap process is used to investigate identifiability of the physical parameters and determine confidence regions for their estimates. Our method circumvents the computational burden of seeking the best-fitting parameters via iterative simulation. After validation on synthetic data, the method is applied to the analysis of the nuclear proteins Cdt1, PCNA and GFPnls. Parameter estimation results from several experimental samples are in accordance with previous findings, but also allow us to discuss identifiability issues as well as cell-to-cell variability of the protein kinetics. Implementation: All methods were implemented in MATLAB R2011b. Monte Carlo simulations were run on the HPC cluster Brutus of ETH Zurich. Contact: [email protected] or [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin