School of BioSciences - Research Publications

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    A group theoretic approach to model comparison with simplicial representations
    Vittadello, ST ; Stumpf, MPH (SPRINGER HEIDELBERG, 2022-11)
    The complexity of biological systems, and the increasingly large amount of associated experimental data, necessitates that we develop mathematical models to further our understanding of these systems. Because biological systems are generally not well understood, most mathematical models of these systems are based on experimental data, resulting in a seemingly heterogeneous collection of models that ostensibly represent the same system. To understand the system we therefore need to understand how the different models are related to each other, with a view to obtaining a unified mathematical description. This goal is complicated by the fact that a number of distinct mathematical formalisms may be employed to represent the same system, making direct comparison of the models very difficult. A methodology for comparing mathematical models based on their underlying conceptual structure is therefore required. In previous work we developed an appropriate framework for model comparison where we represent models, specifically the conceptual structure of the models, as labelled simplicial complexes and compare them with the two general methodologies of comparison by distance and comparison by equivalence. In this article we continue the development of our model comparison methodology in two directions. First, we present a rigorous and automatable methodology for the core process of comparison by equivalence, namely determining the vertices in a simplicial representation, corresponding to model components, that are conceptually related and the identification of these vertices via simplicial operations. Our methodology is based on considerations of vertex symmetry in the simplicial representation, for which we develop the required mathematical theory of group actions on simplicial complexes. This methodology greatly simplifies and expedites the process of determining model equivalence. Second, we provide an alternative mathematical framework for our model-comparison methodology by representing models as groups, which allows for the direct application of group-theoretic techniques within our model-comparison methodology.
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    Cohesin couples transcriptional bursting probabilities of inducible enhancers and promoters
    Robles-Rebollo, I ; Cuartero, S ; Canellas-Socias, A ; Wells, S ; Karimi, MM ; Mereu, E ; Chivu, AG ; Heyn, H ; Whilding, C ; Dormann, D ; Marguerat, S ; Rioja, I ; Prinjha, RK ; Stumpf, MPH ; Fisher, AG ; Merkenschlager, M (NATURE PORTFOLIO, 2022-07-27)
    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.
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    HyperGraphs.jl: representing higher-order relationships in Julia
    Diaz, LPM ; Stumpf, MPH ; Martelli, PL (OXFORD UNIV PRESS, 2022-07-11)
    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.
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    Bayesian and Algebraic Strategies to Design in Synthetic Biology
    Araujo, RP ; Vittadello, ST ; Stumpf, MPH (IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2022-05)
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    Turing pattern design principles and their robustness
    Vittadello, ST ; Leyshon, T ; Schnoerr, D ; Stumpf, MPH (ROYAL SOC, 2021-12-27)
    Turing patterns have morphed from mathematical curiosities into highly desirable targets for synthetic biology. For a long time, their biological significance was sometimes disputed but there is now ample evidence for their involvement in processes ranging from skin pigmentation to digit and limb formation. While their role in developmental biology is now firmly established, their synthetic design has so far proved challenging. Here, we review recent large-scale mathematical analyses that have attempted to narrow down potential design principles. We consider different aspects of robustness of these models and outline why this perspective will be helpful in the search for synthetic Turing-patterning systems. We conclude by considering robustness in the context of developmental modelling more generally. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.
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    Gaining confidence in inferred networks
    Diaz, LPM ; Stumpf, MPH (NATURE PORTFOLIO, 2022-02-14)
    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, functional assortativity, offers a reliable and informative route for comparing different inference algorithms.
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    Pathway dynamics can delineate the sources of transcriptional noise in gene expression
    Ham, L ; Jackson, M ; Stumpf, MPH (eLIFE SCIENCES PUBL LTD, 2021-10-12)
    Single-cell expression profiling opens up new vistas on cellular processes. Extensive cell-to-cell variability at the transcriptomic and proteomic level has been one of the stand-out observations. Because most experimental analyses are destructive we only have access to snapshot data of cellular states. This loss of temporal information presents significant challenges for inferring dynamics, as well as causes of cell-to-cell variability. In particular, we typically cannot separate dynamic variability from within cells ('intrinsic noise') from variability across the population ('extrinsic noise'). Here, we make this non-identifiability mathematically precise, allowing us to identify new experimental set-ups that can assist in resolving this non-identifiability. We show that multiple generic reporters from the same biochemical pathways (e.g. mRNA and protein) can infer magnitudes of intrinsic and extrinsic transcriptional noise, identifying sources of heterogeneity. Stochastic simulations support our theory, and demonstrate that 'pathway-reporters' compare favourably to the well-known, but often difficult to implement, dual-reporter method.
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    Model comparison via simplicial complexes and persistent homology
    Vittadello, ST ; Stumpf, MPH (ROYAL SOC, 2021-10-13)
    In many scientific and technological contexts, we have only a poor understanding of the structure and details of appropriate mathematical models. We often, therefore, need to compare different models. With available data we can use formal statistical model selection to compare and contrast the ability of different mathematical models to describe such data. There is, however, a lack of rigorous methods to compare different models a priori. Here, we develop and illustrate two such approaches that allow us to compare model structures in a systematic way by representing models as simplicial complexes. Using well-developed concepts from simplicial algebraic topology, we define a distance between models based on their simplicial representations. Employing persistent homology with a flat filtration provides for alternative representations of the models as persistence intervals, which represent model structure, from which the model distances are also obtained. We then expand on this measure of model distance to study the concept of model equivalence to determine the conceptual similarity of models. We apply our methodology for model comparison to demonstrate an equivalence between a positional-information model and a Turing-pattern model from developmental biology, constituting a novel observation for two classes of models that were previously regarded as unrelated.
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    Non-equilibrium statistical physics, transitory epigenetic landscapes, and cell fate decision dynamics
    Guillemin, A ; Stumpf, MPH (AMER INST MATHEMATICAL SCIENCES-AIMS, 2020-01-01)
    Statistical physics provides a useful perspective for the analysis of many complex systems; it allows us to relate microscopic fluctuations to macroscopic observations. Developmental biology, but also cell biology more generally, are examples where apparently robust behaviour emerges from highly complex and stochastic sub-cellular processes. Here we attempt to make connections between different theoretical perspectives to gain qualitative insights into the types of cell-fate decision making processes that are at the heart of stem cell and developmental biology. We discuss both dynamical systems as well as statistical mechanics perspectives on the classical Waddington or epigenetic landscape. We find that non-equilibrium approaches are required to overcome some of the shortcomings of classical equilibrium statistical thermodynamics or statistical mechanics in order to shed light on biological processes, which, almost by definition, are typically far from equilibrium.
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    Gene Regulatory Network Inference
    Babtie, AC ; Stumpf, MPH ; Thorne, T (Elsevier, 2020-01-01)