Biology subjects

Stumpf, M. P. H.

Publications and source records attributed to Stumpf, M. P. H..

26 records · Page 2Linked to original sources

bioRxiv2020

Exactly solvable models of stochastic gene expression

Stochastic models are key to understanding the intricate dynamics of gene expression. But the simplest models which only account for e.g. active and inactive states of a gene fail to capture common observations in both prokaryotic and eukaryotic organisms. Here we consider multistate models of gene expression which generalise the canonical Telegraph process, and are capable of capturing the joint effects of e.g. transcription factors, heterochromatin state and DNA accessibility (or, in prokaryotes, Sigma-factor activity) on transcript abundance. We propose two approaches for solving classes of these generalised systems. The first approach offers a fresh perspective on a general class of multistate models, and allows us to "decompose" more complicated systems into simpler processes, each of which can be solved analytically. This enables us to obtain a solution of any model from this class. We further show that these models cannot have a heavy-tailed distribution in the absence of extrinsic noise. Next, we develop an approximation method based on a power series expansion of the stationary distribution for an even broader class of multistate models of gene transcription. The combination of analytical and computational solutions for these realistic gene expression models also holds the potential to design synthetic systems, and control the behaviour of naturally evolved gene expression systems, e.g. in guiding cell-fate decisions.

systems biology↗

bioRxiv2019

Multi-Model and Network Inference Based on Ensemble Estimates: Avoiding the Madness of Crowds

Recent progress in theoretical systems biology, applied mathematics and computational statistics allows us to compare quantitatively the performance of different candidate models at describing a particular biological system. Model selection has been applied with great success to problems where a small number -- typically less than 10 -- of models are compared, but recently studies have started to consider thousands and even millions of candidate models. Often, however, we are left with sets of models that are compatible with the data, and then we can use ensembles of models to make predictions. These ensembles can have very desirable characteristics, but as I show here are not guaranteed to improve on individual estimators or predictors. I will show in the cases of model selection and network inference when we can trust ensembles, and when we should be cautious. The analyses suggests that the careful construction of an ensemble - choosing good predictors - is of paramount importance, more than had perhaps been realised before: merely adding different methods does not suffice. The success of ensemble network inference methods is also shown to rest on their ability to suppress false-positive results. A Jupyter notebook which allows carrying out an assessment of ensemble estimators is provided.

bioinformatics↗

bioRxiv2019

Extrinsic noise and heavy-tailed laws in gene expression

Noise in gene expression is one of the hallmarks of life at the molecular scale. Here we derive analytical solutions to a set of models describing the molecular mechanisms underlying transcription of DNA into RNA. Our Ansatz allows us to incorporate the effects of extrinsic noise - encompassing factors external to the transcription of the individual gene - and discuss the ramifications for heterogeneity in gene product abundance that has been widely observed in single cell data. Crucially, we are able to show that heavy-tailed distributions of RNA copy numbers cannot result from the intrinsic stochasticity in gene expression alone, but must instead reflect extrinsic sources of variability.

systems biology↗

bioRxiv2019

Parameter inference in dynamical systems with co-dimension 1 bifurcations

Dynamical systems with intricate behaviour are all-pervasive in biology. Many of the most interesting biological processes indicate the presence of bifurcations, i.e. phenomena where a small change in a system parameter causes qualitatively different behaviour. Bifurcation theory has become a rich field of research in its own right and evaluating the bifurcation behaviour of a given dynamical system can be challenging. An even greater challenge, however, is to learn the bifurcation structure of dynamical systems from data, where the precise model structure is not known. Here we study one aspects of this problem: the practical implications that the presence of bifurcations has on our ability to infer model parameters and initial conditions from empirical data; we focus on the canonical co-dimension 1 bifurcations and provide a comprehensive analysis of how dynamics, and our ability to infer kinetic parameters are linked. The picture thus emerging is surprisingly nuanced and suggests that identification of the qualitative dynamics -- the bifurcation diagram -- should precede any attempt at inferring kinetic parameters.

systems biology↗

bioRxiv2018

Turing patterns are common but not robust

Turing patterns (TPs) underlie many fundamental developmental processes, but they operate over narrow parameter ranges, raising the conundrum of how evolution can ever discover them. Here we explore TP design space to address this question and to distill design rules. We exhaustively analyze 2- and 3-node biological candidate Turing systems: crucially, network structure alone neither determines nor guarantees emergent TPs. A surprisingly large fraction (>60%) of network design space can produce TPs, but these are sensitive to even subtle changes in parameters, network structure and regulatory mechanisms. This implies that TP networks are more common than previously thought, and evolution might regularly encounter prototypic solutions. Importantly, we deduce compositional rules for TP systems that are almost necessary and sufficient (96% of TP networks contain them, and 95% of networks implementing them produce TPs). This comprehensive network atlas provides the blueprints for identifying natural TPs, and for engineering synthetic systems.

developmental biology↗

bioRxiv2018

Empirical Bayes Meets Information Theoretical Network Reconstruction from Single Cell Data

Gene expression is controlled by networks of transcription factors and regulators, but the structure of these networks is as yet poorly understood and is thus inferred from data. Recent work has shown the efficacy of information theoretical approaches for network reconstruction from single cell transcriptomic data. Such methods use information to estimate dependence between every pair of genes in the dataset, then edges are inferred between top-scoring pairs. Dependence, however, does not indicate significance, and the definition of \"top-scoring\" is often arbitrary and a priori related to expected network size. This makes comparing networks across datasets difficult, because networks of a similar size are not necessarily similarly accurate. We present a method for performing formal hypothesis tests on putative network edges derived from information theory, bringing together empirical Bayes and work on theoretical null distributions for information measures. Thresholding based on empirical Bayes allows us to control network accuracy according to how we intend to use the network. Using single cell data from mouse pluripotent stem cells, we recover known interactions and suggest several new interactions for experimental validation (using a stringent threshold) and discover high-level interactions between sub-networks (using a more relaxed threshold). Furthermore, our method allows for the inclusion of prior information. We use in-silico data to show that even relatively poor quality prior information can increase the accuracy of a network, and demonstrate that the accuracy of networks inferred from single cell data can sometimes be improved by priors from population-level ChIP-Seq and qPCR data.

systems biology↗

bioRxiv2018

Transition State Characteristics During Cell Differentiation

Models describing the process of stem-cell differentiation are plentiful, and may offer insights into the underlying mechanisms and experimentally observed behaviour. Waddingtons epigenetic landscape has been providing a conceptual framework for differentiation processes since its inception. It also allows, however, for detailed mathematical and quantitative analyses, as the landscape can, at least in principle, be related to mathematical models of dynamical systems. Here we focus on a set of dynamical systems features that are intimately linked to cell differentiation, by considering exemplar dynamical models that capture important aspects of stem cell differentiation dynamics. These models allow us to map the paths that cells take through gene expression space as they move from one fate to another, e.g. from a stem-cell to a more specialized cell type. Our analysis highlights the role of the transition state (TS) that separates distinct cell fates, and how the nature of the TS changes as the underlying landscape changes-- change that can be induced by e.g. cellular signalling. We demonstrate that models for stem cell differentiation may be interpreted in terms of either a static or transitory landscape. For the static case the TS represents a particular transcriptional profile that all cells approach during differentiation. Alternatively, the TS may refer to the commonly observed period of heterogeneity as cells undergo stochastic transitions.

systems biology↗

bioRxiv2017

Stem cell differentiation is a stochastic process with memory

Pluripotent stem cells are able to self-renew indefinitely in culture and differentiate into all somatic cell types in vivo. While much is known about the molecular basis of pluripotency, the molecular mechanisms of lineage commitment are complex and only partially understood. Here, using a combination of single cell profiling and mathematical modeling, we examine the differentiation dynamics of individual mouse embryonic stem cells (ESCs) as they progress from the ground state of pluripotency along the neuronal lineage. In accordance with previous reports we find that cells do not transit directly from the pluripotent state to the neuronal state, but rather first stochastically permeate an intermediate primed pluripotent state, similar to that found in the maturing epiblast in development. However, analysis of rate at which individual cells enter and exit this intermediate metastable state using a hidden Markov model reveals that the observed ESC and epiblast-like macrostates conceal a chain of unobserved cellular microstates, which individual cells transit through stochastically in sequence. These hidden microstates ensure that individual cells spend well-defined periods of time in each functional macrostate and encode a simple form of epigenetic memory that allows individual cells to record their position on the differentiation trajectory. To examine the generality of this model we also consider the differentiation of mouse hematopoietic stem cells along the myeloid lineage and observe remarkably similar dynamics, suggesting a general underlying process. Based upon these results we suggest a statistical mechanics view of cellular identities that distinguishes between functionally-distinct macrostates and the many functionally-similar molecular microstates associated with each macrostate. Taken together these results indicate that differentiation is a discrete stochastic process amenable to analysis using the tools of statistical mechanics.

systems biology↗