Inferring extrinsic noise from single-cell gene expression data using approximate Bayesian computation.

BACKGROUND: Gene expression is known to be an intrinsically stochastic process which can involve single-digit numbers of mRNA molecules in a cell at any given time. The modelling of such processes calls for the use of exact stochastic simulation methods, most notably the Gillespie algorithm. However, this stochasticity, also termed "intrinsic noise", does not account for all the variability between genetically identical cells growing in a homogeneous environment. Despite substantial experimental efforts, determining appropriate model parameters continues to be a challenge. Methods based on approximate Bayesian computation can be used to obtain posterior parameter distributions given the observed data. However, such inference procedures require large numbers of simulations of the model and exact stochastic simulation is computationally costly. In this work we focus on the specific case of trying to infer model parameters describing reaction rates and extrinsic noise on the basis of measurements of molecule numbers in individual cells at a given time point. RESULTS: To make the problem computationally tractable we develop an exact, model-specific, stochastic simulation algorithm for the commonly used two-state model of gene expression. This algorithm relies on certain assumptions and favourable properties of the model to forgo the simulation of the whole temporal trajectory of protein numbers in the system, instead returning only the number of protein and mRNA molecules present in the system at a specified time point. The computational gain is proportional to the number of protein molecules created in the system and becomes significant for systems involving hundreds or thousands of protein molecules. CONCLUSIONS: We employ this simulation algorithm with approximate Bayesian computation to jointly infer the model's rate and noise parameters from published gene expression data. Our analysis indicates that for most genes the extrinsic contributions to noise will be small to moderate but certainly are non-negligible

Modelling capture efficiency of single-cell RNA-sequencing data improves inference of transcriptome-wide burst kinetics

Motivation: Gene expression is characterized by stochastic bursts of transcription that occur at brief and random periods of promoter activity. The kinetics of gene expression burstiness differs across the genome and is dependent on the promoter sequence, among other factors. Single-cell RNA sequencing (scRNA-seq) has made it possible to quantify the cell-to-cell variability in transcription at a global genome-wide level. However, scRNA-seq data are prone to technical variability, including low and variable capture efficiency of transcripts from individual cells. // Results: Here, we propose a novel mathematical theory for the observed variability in scRNA-seq data. Our method captures burst kinetics and variability in both the cell size and capture efficiency, which allows us to propose several likelihood-based and simulation-based methods for the inference of burst kinetics from scRNA-seq data. Using both synthetic and real data, we show that the simulation-based methods provide an accurate, robust and flexible tool for inferring burst kinetics from scRNA-seq data. In particular, in a supervised manner, a simulation-based inference method based on neural networks proves to be accurate and useful when applied to both allele and nonallele-specific scRNA-seq data. // Availability and implementation: The code for Neural Network and Approximate Bayesian Computation inference is available at https://github.com/WT215/nnRNA and https://github.com/WT215/Julia_ABC, respectively

Modelling capture efficiency of single-cell RNA-sequencing data improves inference of transcriptome-wide burst kinetics

MOTIVATION: Gene expression is characterised by stochastic bursts of transcription that occur at brief and random periods of promoter activity. The kinetics of gene expression burstiness differs across the genome and is dependent on the promoter sequence, among other factors. Single-cell RNA sequencing (scRNA-seq) has made it possible to quantify the cell-to-cell variability in transcription at a global genome-wide level. However, scRNA-seq data is prone to technical variability, including low and variable capture efficiency of transcripts from individual cells. RESULTS: Here, we propose a novel mathematical theory for the observed variability in scRNA-seq data. Our method captures burst kinetics and variability in both the cell size and capture efficiency, which allows us to propose several likelihood-based and simulation-based methods for the inference of burst kinetics from scRNA-seq data. Using both synthetic and real data, we show that the simulation-based methods provide an accurate, robust and flexible tool for inferring burst kinetics from scRNA-seq data. In particular, in a supervised manner, a simulation-based inference method based on neural networks proves to be accurate and useful when applied to both allele and non-allele-specific scRNA-seq data. AVAILABILITY: The code for Neural Network and Approximate Bayesian Computation inference is available at https://github.com/WT215/nnRNA and https://github.com/WT215/Julia_ABC respectively. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online

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

Efficient parametric inference for stochastic biological systems with measured variability

Stochastic systems in biology often exhibit substantial variability within and between cells. This variability, as well as having dramatic functional consequences, provides information about the underlying details of the system's behaviour. It is often desirable to infer properties of the parameters governing such systems given experimental observations of the mean and variance of observed quantities. In some circumstances, analytic forms for the likelihood of these observations allow very efficient inference: we present these forms and demonstrate their usage. When likelihood functions are unavailable or difficult to calculate, we show that an implementation of approximate Bayesian computation (ABC) is a powerful tool for parametric inference in these systems. However, the calculations required to apply ABC to these systems can also be computationally expensive, relying on repeated stochastic simulations. We propose an ABC approach that cheaply eliminates unimportant regions of parameter space, by addressing computationally simple mean behaviour before explicitly simulating the more computationally demanding variance behaviour. We show that this approach leads to a substantial increase in speed when applied to synthetic and experimental datasets.Comment: 11 pages, 4 fig

The role of extrinsic noise in biomolecular information processing systems: an in silico analysis

The intrinsic stochasticity of biomolecular systems is a well studied phe- nomenon. Less attention has been paied to other sources of variability, so called extrinsic noise. While the precise definition of extrinsic noise de- pends on the system in question, it affects all cells and its significance has been demonstrated experimentally. Information theory provides a rigorous mathematical framework for quan- tifying both the amount of information available to a signalling system and its ability to transmit this information. Intracellular signal transduction re- mains a relatively unexplored frontier for the application of information theory. In this thesis, we rely on a metric called mutual information to quantify in- formation flow in models of biochemical signalling systems. After briefly discussing the theoretical background and some of the practical difficulties of estimating mutual information in Chapter 2, we apply it in the context of simplified models of intracellular signalling, referred to as motifs. Using a comprehensive set of two-node motifs we explore the effects of extrin- sic noise, model parameters and various combinations of interaction, on the system’s ability to transmit information about an input signal, repre- sented by a telegraph process. Our results illustrate the importance of the system’s response time and demonstrate a trade-off in transmitting infor- mation about the current state of the input or its average intensity over a period of time. In Chapter 4, we address the problem of determining the magnitude of ex- trinsic noise in the presence of intrinsic stochasticity. Using the Approxi- mate Bayesian Computation - sequential Monte Carlo algorithm, together with published experimental data, we infer parameters describing extrinsic noise in a model of E. coli gene expression. Lastly, in Chapter 5, we construct and analyse models of bacterial two- component signalling, bringing together insights gleaned from earlier work. The results show how the abundances of different molecular species in the system may transmit information about the input signal despite its stochas-tic nature and considerable variation in the numbers of protein molecules present.Open Acces

Probabilistic modelling of noise as a driving force in biological systems

Systems biology takes a mechanistic, relational approach to the study of biological processes, commonly finding expression in mathematical models. Hypotheses about systems can be tested when formulated as models, and promising avenues for further study identified. A model sufficiently faithful to the system under study can be used to guide experiments, to probe the system in silico, and to learn about emergent features not evident from the static picture of the system. In this work, three contributions to the modelling community are proffered. First, a computational package is presented that implements an algorithm for the validation and parametrisation of a model. In validation, we are asking how likely we were to make some observation, given the model, or, equivalently, how able the model is to explain the data. The subsequent two contributions concern noise in biological systems. Biological systems display inherent variability, or noise, due to the stochastic mechanisms through which biochemical processes occur. This variability can be critical to the behaviour of a system and to the fates of individual cells. With this in mind, the second contribution is the development of a methodology to model protein-dependent population dynamics. The idea is to model cell population dynamics that result of noisy intracellular protein dynamics. The method's application is demonstrated in population-level models of a protein-dependent cell cycle and yeast antibiotic resistance. Given an appreciation of the pivotal effects of noise, the third and final contribution is a study of the mechanism of noise propagation. I present an analysis of the contributions of biochemical reaction motifs to the creation and transmission of noise that ultimately manifest in observations of biological systems. This study points to specific processes that enhance or attenuate noise, with the aim of beginning to unravel the flow of noise through a system.Open Acces