239 results found
Vittadello ST, Stumpf MPH, 2022, Open problems in mathematical biology, Mathematical Biosciences, Vol: 354, ISSN: 0025-5564
Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.
Vittadello ST, Stumpf MPH, 2022, A group theoretic approach to model comparison with simplicial representations, JOURNAL OF MATHEMATICAL BIOLOGY, Vol: 85, ISSN: 0303-6812
Ham L, Coomer MA, Stumpf MPH, 2022, The chemical Langevin equation for biochemical systems in dynamic environments, JOURNAL OF CHEMICAL PHYSICS, Vol: 157, ISSN: 0021-9606
Robles-Rebollo I, Cuartero S, Canellas-Socias A, et al., 2022, Cohesin couples transcriptional bursting probabilities of inducible enhancers and promoters, Nature Communications, Vol: 13, ISSN: 2041-1723
Innate immune responses rely on inducible gene expression programmes which, in contrast to steady-state transcription, are highly dependent on cohesin. Here we address transcriptional parameters underlying this cohesin-dependence by single-molecule RNA-FISH and single-cell RNA-sequencing. We show that inducible innate immune genes are regulated predominantly by an increase in the probability of active transcription, and that probabilities of enhancer and promoter transcription are coordinated. Cohesin has no major impact on the fraction of transcribed inducible enhancers, or the number of mature mRNAs produced per transcribing cell. Cohesin is, however, required for coupling the probabilities of enhancer and promoter transcription. Enhancer-promoter coupling may not be explained by spatial proximity alone, and at the model locus Il12b can be disrupted by selective inhibition of the cohesinopathy-associated BET bromodomain BD2. Our data identify discrete steps in enhancer-mediated inducible gene expression that differ in cohesin-dependence, and suggest that cohesin and BD2 may act on shared pathways.
Diaz LPM, Stumpf MPH, 2022, HyperGraphs.jl: representing higher-order relationships in Julia., Bioinformatics, Vol: 38, Pages: 3660-3661
SUMMARY: HyperGraphs.jl is a Julia package that implements hypergraphs. These are a generalization of graphs that allow us to represent n-ary relationships and not just binary, pairwise relationships. High-order interactions are commonplace in biological systems and are of critical importance to their dynamics; hypergraphs thus offer a natural way to accurately describe and model these systems. AVAILABILITY AND IMPLEMENTATION: HyperGraphs.jl is freely available under the MIT license. Source code and documentation can be found at https://github.com/lpmdiaz/HyperGraphs.jl. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.
Araujo RP, Vittadello ST, Stumpf MPH, 2022, Bayesian and Algebraic Strategies to Design in Synthetic Biology, Proceedings of the IEEE, Vol: 110, Pages: 675-687, ISSN: 0018-9219
Innovation in synthetic biology often still depends on large-scale experimental trial and error, domain expertise, and ingenuity. The application of rational design engineering methods promises to make this more efficient, faster, cheaper, and safer. However, this requires mathematical models of cellular systems. For these models, we then have to determine if they can meet our intended target behavior. Here, we develop two complementary approaches that allow us to determine whether a given molecular circuit, represented by a mathematical model, is capable of fulfilling our design objectives. We discuss algebraic methods that are capable of identifying general principles guaranteeing desired behavior; we provide an overview of Bayesian design approaches that allow us to choose a model that has the highest probability of fulfilling our design objectives from a set of models. We discuss their uses in the context of biochemical adaptation and, then, consider how robustness can and should affect our design approach.
Vittadello ST, Leyshon T, Schnoerr D, et al., 2021, Turing pattern design principles and their robustness, PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, Vol: 379, ISSN: 1364-503X
Vittadello ST, Stumpf MPH, 2021, Model comparison via simplicial complexes and persistent homology, ROYAL SOCIETY OPEN SCIENCE, Vol: 8, ISSN: 2054-5703
Ham L, Jackson M, Stumpf MPH, 2021, Pathway dynamics can delineate the sources of transcriptional noise in gene expression, ELIFE, Vol: 10, ISSN: 2050-084X
Stadler T, Pybus OG, Stumpf MPH, 2021, Phylodynamics for cell biologists., Science, Vol: 371
Multicellular organisms are composed of cells connected by ancestry and descent from progenitor cells. The dynamics of cell birth, death, and inheritance within an organism give rise to the fundamental processes of development, differentiation, and cancer. Technical advances in molecular biology now allow us to study cellular composition, ancestry, and evolution at the resolution of individual cells within an organism or tissue. Here, we take a phylogenetic and phylodynamic approach to single-cell biology. We explain how "tree thinking" is important to the interpretation of the growing body of cell-level data and how ecological null models can benefit statistical hypothesis testing. Experimental progress in cell biology should be accompanied by theoretical developments if we are to exploit fully the dynamical information in single-cell data.
Guillemin A, Roesch E, Stumpf MPH, 2021, Uncertainty in cell fate decision making: Lessons from potential landscapes of bifurcation systems
<jats:title>Abstract</jats:title><jats:p>Cell fate decision making is known to be a complex process and is still far from being understood. The intrinsic complexity, but also features such as molecular noise represent challenges for modelling these systems. Waddington’s epigenetic landscape has become the overriding metaphor for developmental processes: it both serves as pictorial representation, and can be related to mathematical models. In this work we investigate how the landscape is affected by noise in the underlying system. Specifically, we focus on those systems where minor changes in the parameters cause major changes in the stability properties of the system, especially bifurcations. We analyse and quantify the changes in the landscape’s shape as the effects of noise increase. We find ample evidence for intricate interplay between noise and dynamics which can lead to qualitative change in a system’s dynamics and hence the corresponding landscape. In particular, we find that the effects can be most pronounced in the vicinity of the bifurcation point of the underlying deterministic dynamical systems, which would correspond to the cell fate decision event in cellular differentiation processes.</jats:p>
Guillemin A, Stumpf MPH, 2021, Noise and the molecular processes underlying cell fate decision-making, PHYSICAL BIOLOGY, Vol: 18, ISSN: 1478-3967
Coomer MA, Ham L, Stumpf MPH, 2020, Noise Distorts the Epigenetic Landscape and Shapes Cell Fate Decisions
<jats:title>Abstract</jats:title><jats:p>The Waddington epigenetic landscape has become an iconic representation of the cellular differentiation process. Recent single-cell transcriptomic data provide new opportunities for quantifying this originally conceptual tool, offering insight into the gene regulatory networks underlying cellular development. While many methods for constructing the landscape have been proposed, by far the most commonly employed approach is based on computing the landscape as the negative logarithm of the steady-state probability distribution. Here, we use simple models to highlight the complexities and limitations that arise when reconstructing the potential landscape in the presence of stochastic fluctuations. We consider how the landscape changes in accordance with different stochastic systems, and show that it is the subtle interplay between the deterministic and stochastic components of the system that ultimately shapes the landscape. We further discuss how the presence of noise has important implications for the identifiability of the regulatory dynamics from experimental data.</jats:p>
Stumpf MPH, 2020, Multi-model and network inference based on ensemble estimates: avoiding the madness of crowds, JOURNAL OF THE ROYAL SOCIETY INTERFACE, Vol: 17, ISSN: 1742-5689
Stumpf MPH, 2020, Multi-model and network inference based on ensemble estimates: Avoiding the madness of crowds: Multi-model and network inference based on ensemble estimates: Avoiding the madness of crowds, Journal of the Royal Society Interface, Vol: 17, ISSN: 1742-5689
Recent progress in theoretical systems biology, applied mathematics and computational statistics allows us to compare the performance of different candidate models at describing a particular biological system quantitatively. Model selection has been applied with great success to problems where a small number - typically less than 10 - of models are compared, but recent 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 suggest that the careful construction of an ensemble - choosing good predictors - is of paramount importance, more than had perhaps been realized 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.
Ham L, Jackson M, Stumpf MPH, 2020, Pathway dynamics can delineate the sources of transcriptional noise in gene expression
<jats:p>Single-cell expression profiling has opened up new vistas on cellular processes. Among other important results, one stand-out observation has been the confirmation of extensive cell-to-cell variability at the transcriptomic and proteomic level. Because most experimental analyses are destructive we only have access to snapshot data of cellular states. This loss of temporal information presents significant challenges in inferring dynamics, as well as causes of cell-to-cell variability. In particular, we are typically unable to separate dynamic variability from within individual systems (“intrinsic noise”) from variability across the population (“extrinsic noise”). Here we mathematically formalise this non-identifiability; but we also use this to identify how new experimental set-ups coupled to statistical noise decomposition can resolve this non-identifiability. For single-cell transcriptomic data we find that systems subject to population variation invariably inflate the apparent degree of burstiness of the underlying process. Such identifiability problems can, in principle, be remedied by dual-reporter assays, which separates total gene expression noise into intrinsic and extrinsic contributions; unfortunately, however, this requires pairs of strictly independent and identical gene reporters to be integrated into the same cell, which is difficult to implement experimentally in most systems. Here we demonstrate mathematically that, in some cases decomposition of transcriptional noise is possible with non-identical and not-necessarily independent reporters. We use our result to show that generic reporters lying in the same biochemical pathways (e.g. mRNA and protein) can replace dual reporters, enabling the noise decomposition to be obtained from only a single gene. Stochastic simulations are used to support our theory, and show that our “pathway-reporter” method compares favourably to the dual-reporter method.</jat
Diaz LPM, Stumpf MPH, 2020, Gaining confidence in inferred networks
<jats:title>Abstract</jats:title><jats:p>Network inference is a notoriously challenging problem. Inferred networks are associated with high uncertainty and likely riddled with false positive and false negative interactions. Especially for biological networks we do not have good ways of judging the performance of inference methods against real networks, and instead we often rely solely on the performance against simulated data. Gaining confidence in networks inferred from real data nevertheless thus requires establishing reliable validation methods. Here, we argue that the expectation of mixing patterns in biological networks such as gene regulatory networks offers a reasonable starting point: interactions are more likely to occur between nodes with similar biological functions. We can quantify this behaviour using the assortativity coefficient, and here we show that the resulting heuristic,<jats:italic>functional assortativity</jats:italic>, offers a reliable and informative route for comparing different inference algorithms.</jats:p>
Croydon Veleslavov IA, Stumpf MPH, 2020, Repeated Decision Stumping Distils Simple Rules from Single Cell Data
<jats:title>Abstract</jats:title><jats:p>Here we introduce repeated decision stumping, to distill simple models from single cell data. We develop decision trees of depth one – hence ‘stumps’ – to identify in an inductive manner, gene products involved in driving cell fate transitions, and in applications to published data we are able to discover the key-players involved in these processes in an unbiased manner without prior knowledge. The approach is computationally efficient, has remarkable predictive power, and yields robust and statistically stable predictors: the same set of candidates is generated by applying the algorithm to different subsamples of the data.</jats:p>
He F, Stumpf M, Kleijn I, et al., 2020, GpABC: a Julia package for approximate Bayesian computation with Gaussian process emulation, Bioinformatics, Vol: 36, Pages: 3286-3287, ISSN: 1367-4803
MotivationApproximate Bayesian computation (ABC) is an important framework within which to infer the structure and parameters of a systems biology model. It is especially suitable for biological systems with stochastic and nonlinear dynamics, for which the likelihood functions are intractable. However, the associated computational cost often limits ABC to models that are relatively quick to simulate in practice.ResultsWe here present a Julia package, GpABC, that implements parameter inference and model selection for deterministic or stochastic models using i) standard rejection ABC or ABC-SMC, or ii) ABC with Gaussian process emulation. The latter significantly reduces the computational cost.Availability and Implementationhttps://github.com/tanhevg/GpABC.jlSupplementary informationSupplementary data are available at Bioinformatics online.
Ham L, Schnoerr D, Brackston RD, et al., 2020, Exactly solvable models of stochastic gene expression, JOURNAL OF CHEMICAL PHYSICS, Vol: 152, ISSN: 0021-9606
Ham L, Brackston R, Stumpf MPH, 2020, Extrinsic Noise and Heavy-Tailed Laws in Gene Expression, PHYSICAL REVIEW LETTERS, Vol: 124, ISSN: 0031-9007
Ham L, Schnoerr D, Brackston RD, et al., 2020, Exactly solvable models of stochastic gene expression
<jats:p>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.</jats:p>
<jats:title>Abstract</jats:title><jats:p>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.</jats:p>
Scholes NS, Schnoerr D, Isalan M, et al., 2019, A Comprehensive Network Atlas Reveals That Turing Patterns Are Common but Not Robust, CELL SYSTEMS, Vol: 9, Pages: 515-517, ISSN: 2405-4712
Roesch E, Stumpf MPH, 2019, Parameter inference in dynamical systems with co-dimension 1 bifurcations, ROYAL SOCIETY OPEN SCIENCE, Vol: 6, ISSN: 2054-5703
Scholes N, Schnoerr D, Isalan M, et al., 2019, A comprehensive network atlas reveals that Turing patterns are common but not robust, Cell Systems, Vol: 9, Pages: 243-257.e4, ISSN: 2405-4712
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, amounting to 7,625 networks and more than 3 × 10^11 analyzed scenarios. We find that network structure alone neither implies nor guarantees emergent TPs. A large fraction (>61%) 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. We deduce compositional rules for TP systems that are almost necessary and sufficient (96% of TP networks contain them, and 92% of networks implementing them produce TPs). This comprehensive network atlas provides the blueprints for identifying natural TPs and for engineering synthetic systems.
Stumpf M, 2019, LislPisl/Bifurcations: First release of Bifurcations
LislPisl/Bifurcations: First release of Bifurcations
He F, Stumpf MPH, 2019, Quantifying Dynamic Regulation in Metabolic Pathways with Nonparametric Flux Inference, BIOPHYSICAL JOURNAL, Vol: 116, Pages: 2035-2046, ISSN: 0006-3495
Chan TE, Stumpf MPH, Babtie AC, 2019, Gene Regulatory Networks from Single Cell Data for Exploring Cell Fate Decisions., Methods Mol Biol, Vol: 1975, Pages: 211-238
Single cell experimental techniques now allow us to quantify gene expression in up to thousands of individual cells. These data reveal the changes in transcriptional state that occur as cells progress through development and adopt specialized cell fates. In this chapter we describe in detail how to use our network inference algorithm (PIDC)-and the associated software package NetworkInference.jl-to infer functional interactions between genes from the observed gene expression patterns. We exploit the large sample sizes and inherent variability of single cell data to detect statistical dependencies between genes that indicate putative (co-)regulatory relationships, using multivariate information measures that can capture complex statistical relationships. We provide guidelines on how best to combine this analysis with other complementary methods designed to explore single cell data, and how to interpret the resulting gene regulatory network models to gain insight into the processes regulating cell differentiation.
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