Biology subjects

Stumpf, M. P. H.

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

At least 19 recordsLinked to original sources

bioRxiv2026

A spin glass representation of hierarchical gene regulation and the partial resolution of frustration

Gene regulatory networks are directed and often contain loops. A loop can place competing demands on its genes, so that no expression state satisfies every regulatory interaction. In statistical physics such a conflict is called frustration. Existing spin-glass models of tissues assume symmetric regulation, and studies of frustration consider single cells. We develop a nonreciprocal multicellular Ising model that couples a directed regulatory network in each cell to random, symmetric signalling between neighbouring cells. We define intracellular and intercellular frustration densities, which count the unsatisfied interactions within a cell and with its neighbours. We study six exemplar nine-gene networks that share a downstream cascade and differ in an upstream three-gene motif. In isolated cells the motif sets the frustration. Negative feedback loops pass frustration around the loop, and their genes keep switching. The incoherent feedforward loop holds frustration at a single gene and freezes. When cells communicate, they form spatial clusters with shared expression profiles, and conflict between neighbours concentrates at cluster boundaries. Stronger coupling lowers intercellular frustration and raises intracellular frustration. Frustration is therefore resolved only in part: cells satisfy more of the couplings to their neighbours by satisfying fewer of their own regulatory interactions. Varying the coupling strength reveals a transition near the value at which the combined input of a cell's eight neighbours matches a single regulatory interaction. Below it, cells follow their own networks and the tissue fragments. Our framework links the structure of gene regulatory networks to the stability of gene expression in cells and tissues.

systems biology↗

bioRxiv2025

Intercellular signaling drives robust cell fate and patterning in multicellularsystems

Cells do not act in isolation; they communicate with each other through a complex network of signals. In multicellular organisms, cell signaling buffers against fluctuations in gene expression. Its effect, however, on multistability--the ability of genetically identical cells to take on and maintain diverse stable states or phenotypes--is unclear. We develop spatially explicit stochastic models that couple fine-grained gene regulatory dynamics with intercellular signaling to study cell fate control in multicellular tissues. We show that intercellular signaling acts as a switch-like controller of cell fate, driving transitions from transient to stable states across tissues. Even weak signaling stabilizes short-lived expression states, and we derive mathematical expressions for the threshold signaling strength required to trigger tissue-wide stabilization. We also derive a universal spatial limit: stable region size grows only sublinearly with signaling strength, implying that large stable regions are prohibitively costly to maintain. The resulting trade-off between robustness and signaling in cell fate control highlights the delicate balance required during developmental processes to maintain spatial precision and provides insight into how organisms regulate tissue structure. OverviewCell fate decisions in developing tissues are governed by gene regulatory networks, but how communication between neighboring cells influences these decisions is poorly understood. We develop a mathematical framework showing that intercellular signaling acts as a controller of cell fate, suppressing spontaneous switching, and inducing stable, coordinated behaviors across tissues. Even weak signaling induces a sharp transition from unstable to stable population-wide dynamics. We also derive fundamental scaling laws showing that the size of stable regions increases sublinearly with signaling strength, revealing a trade-off between developmental robustness and resource cost. These results offer insight into how organisms achieve reliable spatial organization during development, despite molecular noise, and provide design principles for engineering synthetic tissues that balance stability, scalability, and resource efficiency.

systems biology↗

bioRxiv2025

Molecular noise modulates transitions in the cell-fate differentiation landscape

Waddingtons epigenetic landscape has become one of biologys cornerstone metaphors, widely used both conceptually and computationally. Cell types are often associated with the stable stationary points or valleys of this landscape. In previous work, we showed that the molecular noise dominating sub-cellular dynamics can distort and profoundly reshape this landscape. In non-equilibrium systems, an equally profound question arises: to what extent does noise alter the transition paths between valleys in such dynamic landscapes. We tackle this question using a set of illustrative exemplars, and show that noise gives rise to paths that differ substantially from the canonical least-action paths calculated under deterministic dynamics. We dissect the dynamics of these exemplars and determine the reactive density and transition currents, which show us, respectively, where and how transitions occur for different realisations of stochastic dynamics. Our analysis unambiguously demonstrates that reaction paths for stochastic dynamics diverge non-trivially from their deterministic least-action paths or simple barrier crossing models.

developmental biology↗

bioRxiv2023

A three-node Turing gene circuit forms periodic spatial patterns in bacteria

Turing patterns1 are well-known self-organising systems that can form spots, stripes, or labyrinths. They represent a major theory of patterning in tissue organisation, due to their remarkable similarity to some natural patterns, such as skin pigmentation in zebrafish2, digit spacing3,4, and many others. The involvement of Turing patterns in biology has been debated because of their stringent fine-tuning requirements, where patterns only occur within a small subset of parameters5,6. This has complicated the engineering of a synthetic gene circuit for Turing patterns from first principles, even though natural genetic Turing networks have been successfully identified4,7. Here, we engineered a synthetic genetic reaction-diffusion system where three nodes interact according to a non-classical Turing network with improved parametric robustness6. The system was optimised in E. coli and reproducibly generated stationary, periodic, concentric stripe patterns in growing colonies. The patterns were successfully reproduced with a partial differential equation model, in a parameter regime obtained by fitting to experimental data. Our synthetic Turing system can contribute to novel nanotechnologies, such as patterned biomaterial deposition8,9, and provide insights into developmental patterning programs10.

synthetic biology↗

bioRxiv2023

The Topological Properties of the Protein Universe

Deep learning methods have revolutionized our ability to predict protein structures, allowing us a glimpse into the entire protein universe. As a result, our understanding of how protein structure drives function is now lagging behind our ability to determine and predict protein structure. Here, we describe how topology, the branch of mathematics concerned with qualitative properties of spatial structures, provides a lens through which we can identify fundamental organizing features across the known protein universe. We identify topological determinants that capture global features of the protein universe, such as domain architecture and binding sites. Additionally, our analysis also identified highly specific properties, so-called topological generators, that can be used to provide deeper insights into protein structure-function and evolutionary relationships. We used our approach to determine structural, functional and disease consequences of mutations, explain differences in properties of proteins in mesophiles and thermophiles, and the likely structural and functional consequences of polymorphisms in a protein. Overall, we present a practical methodology for mapping the topology of the known protein universe at scale.

bioinformatics↗

bioRxiv2023

Approximate Bayesian Computation for Inferring Waddington Landscapes from Single Cell Data

Single cell technologies allow us to gain insights into cellular processes at unprecedented resolution. In stem cell and developmental biology snapshot data allows us to characterise how the transcriptional state of cells changes between successive cell types. Here we show how approximate Bayesian computation (ABC) can be employed to calibrate mathematical models against single cell data. In our simulation study we demonstrate the pivotal role of the adequate choice of distance measures appropriate for single cell data. We show that for good distance measures, notably optimal transport distances, we can infer parameters for mathematical models from simulated single cell data. We show that the ABC posteriors can be used to characterise parameter sensitivity and identify dependencies between different parameters, and to infer representations of the Waddington or epigenetic landscape, which forms a popular and interpretable representation of the developmental dynamics. In summary, these results pave the way for fitting mechanistic models of stem cell differentiation to single cell data.

systems biology↗

bioRxiv2023

The timing of cellular events: a stochastic vs deterministic perspective

Changes in cell state are driven by key molecular events whose timing can often be measured experimentally. Of particular interest is the time taken for the levels of RNA or protein molecules to reach a critical threshold defining the triggering of a cellular event. While this mean trigger time can be estimated by numerical integration of deterministic models, these ignore intrinsic noise and hence their predictions may be inaccurate. Here we study the differences between deterministic and stochastic model predictions for the mean trigger times using simple models of gene expression, post-transcriptional feedback control, and enzyme-mediated catalysis. By comparison of the two predictions, we show that when promoter switching is present there exists a transition from a parameter regime where deterministic models predict a longer trigger time than stochastic models to a regime where the opposite occurs. Furthermore, the ratio of the trigger times of the two models can be large, particularly for auto-regulatory genetic feedback loops. Our theory provides intuitive insight into the origin of these effects and shows that deterministic predictions for cellular event timing can be highly inaccurate when molecule numbers are within the range known for many cells.

systems biology↗

bioRxiv2023

BondGraphs.jl: Composable energy-based modelling in systems biology

SummaryBondGraphs.jl is a Julia implementation of bond graphs. Bond graphs provide a modelling framework that describes energy flow through a physical system and by construction enforce thermodynamic constraints. The framework is widely used in engineering and has recently been shown to be a powerful approach for modelling biology. Models are mutable, hierarchical, multi-scale, multi-physics, and BondGraphs.jl is compatible with the Julia modelling ecosystem. Availability and ImplementationBondGraphs.jl is freely available under the MIT license. Source code and documentation can be found at https://github.com/jedforrest/BondGraphs.jl. Contactpan.m@unimelb.edu.au, mstumpf@unimelb.edu.au Supplementary informationSupplementary data are available at Bioinformatics online.

systems biology↗

bioRxiv2023

Energy dependence of signalling dynamics and robustness in bacterial two component systems

One of the best known ways bacteria cells understand and respond to the environment are through Two-Component Systems (TCS). These signalling systems are highly diverse in function and can detect a range of physical stimuli including molecular concentrations and temperature, with a range of responses including chemotaxis and anaerobic energy production. TCS exhibit a range of different molecular structures and energy costs, and multiple types co-exist in the same cell. TCSs that incur relatively high energy cost are abundant in biology, despite strong evolutionary pressure to efficiently spend energy. We are motivated to discern what benefits, if any, the more energetically expensive variants had for a cell. We seek to answer this question by modelling energy flow through two variants of TCS. This was accomplished using bond graphs, a physics-based modelling framework that accurately models energy transfer through different physical domains. Our analysis demonstrates that energy availability can affect a cells signal sensitivity, noise filtering effectiveness, and the stimulus level where cell response is maximal. We also found that these properties are determined not by the molecular parameters themselves, but the reaction rate parameters that govern the reaction systems as a whole. This suggests possible connections between the molecular structure and evolutionary purpose of any two-component system. This opens the door to new synthetic circuit design in systems biology, and we propose new hypotheses about this link between structure and purpose that could be experimentally verified. Author summaryTwo-component systems are the main way many bacteria sense and respond to their environment. They exist in such well-studied bacteria as E. coli where they have been shown to detect a range of stimuli including nutrients, temperature, acidity, and pressure. Two-component systems are ubiquitous in bacteria yet have a deceptively simple structure. Knowing how they operate and the purpose of variations in signalling structure is helpful to our understanding of cellular biology and the design of synthetic biological circuits. Critical unanswered questions remain about the energy usage and functional benefits of these systems. We sought to improve our understanding of two-component systems by applying a physics-based modelling framework. We found that tracking energy flow through the cell reveals new energy-dependent behaviour in signalling sensitivity, noise filtering, and maximal cell response. We also found that these properties are not strictly dependent on the molecular properties themselves, but from the configuration of the reaction system as a whole.

biophysics↗

bioRxiv2023

Dynamical information enables inference of gene regulation at single-cell scale

Cell dynamics and biological function are governed by intricate networks of molecular interactions. Inferring these interactions from data is a notoriously difficult inverse problem. The majority of existing network inference methods work at the population level to construct population-averaged representations of gene interaction networks, and thus do not naturally allow us to infer differences in gene regulation activity across heterogeneous cell populations. We introduce locaTE, an information theoretic approach that leverages single cell dynamical information together with geometry of the cell state manifold to infer cell-specific, causal gene interaction networks in a manner that is agnostic to the topology of the underlying biological trajectory. We find that factor analysis can give detailed insights into the inferred cell-specific GRNs. Through extensive simulation studies and applications to three experimental datasets spanning mouse primitive endoderm formation, pancreatic development, and haematopoiesis, we demonstrate superior performance and the generation of additional insights compared to standard static GRN inference methods. We find that locaTE provides a powerful, efficient and scalable network inference method that allows us to distill cell-specific networks from single cell data. Graphical abstractCell-specific network inference from estimated dynamics and geometry LocaTE takes as input a transition matrix P that encodes inferred cellular dynamics as a Markov chain on the cell state manifold. By considering the coupling (X{tau}, X-{tau}), locaTE produces an estimate of transfer entropy for each cell i and each pair of genes (j, k). Downstream factor analyses can extract coherent patterns of interactions in an unsupervised fashion. O_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=188 SRC="FIGDIR/small/523176v4_ufig1.gif" ALT="Figure 1"> View larger version (34K): org.highwire.dtl.DTLVardef@12dc737org.highwire.dtl.DTLVardef@722a08org.highwire.dtl.DTLVardef@1258a03org.highwire.dtl.DTLVardef@1880a1e_HPS_FORMAT_FIGEXP M_FIG C_FIG

systems biology↗

bioRxiv2021

The chemical Langevin equation for biochemical systems in dynamic environments

Modelling and simulation of complex biochemical reaction networks form cornerstones of modern biophysics. Many of the approaches developed so far capture temporal fluctuations due to the inherent stochasticity of the biophysical processes, referred to as intrinsic noise. Stochastic fluctuations, however, predominantly stem from the interplay of the network with many other -- and mostly unknown -- fluctuating processes, as well as with various random signals arising from the extracellular world; these sources contribute extrinsic noise. Here we provide a computational simulation method to probe the stochastic dynamics of biochemical systems subject to both intrinsic and extrinsic noise. We develop an extrinsic chemical Langevin equation--a physically motivated extension of the chemical Langevin equation-- to model intrinsically noisy reaction networks embedded in a stochastically fluctuating environment. The extrinsic CLE is a continuous approximation to the Chemical Master Equation (CME) with time-varying propensities. In our approach, noise is incorporated at the level of the CME, and can account for the full dynamics of the exogenous noise process, irrespective of timescales and their mismatches. We show that our method accurately captures the first two moments of the stationary probability density when compared with exact stochastic simulation methods, while reducing the computational runtime by several orders of magnitude. Our approach provides a method that is practical, computationally efficient and physically accurate to study systems that are simultaneously subject to a variety of noise sources.

systems biology↗

bioRxiv2021

Uncertainty in cell fate decision making: Lessons from potential landscapes of bifurcation systems

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. Waddingtons 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 landscapes 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 systems 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.

systems biology↗

bioRxiv2020

Shaping the Epigenetic Landscape: Complexities and Consequences

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.

developmental biology↗

bioRxiv2020

Decision tree models and cell fate choice

Single cell transcriptomics has laid bare the heterogeneity of apparently identical cells at the level of gene expression. For many cell-types we now know that there is variability in the abundance of many transcripts, and that average transcript abun-dance or average gene expression can be a unhelpful concept. A range of clustering and other classification methods have been proposed which use the signal in single cell data to classify, that is assign cell types, to cells based on their transcriptomic states. In many cases, however, we would like to have not just a classifier, but also a set of interpretable rules by which this classification occurs. Here we develop and demonstrate the interpretive power of one such approach, which sets out to establish a biologically interpretable classification scheme. In particular we are interested in capturing the chain of regulatory events that drive cell-fate decision making across a lineage tree or lineage sequence. We find that suitably defined decision trees can help to resolve gene regulatory programs involved in shaping lineage trees. Our approach combines predictive power with interpretabilty and can extract logical rules from single cell data.

bioinformatics↗

bioRxiv2020

The Design Principles of Discrete Turing Patterning Systems

The formation of spatial structures lies at the heart of developmental processes. However, many of the underlying gene regulatory and biochemical processes remain poorly understood. Turing patterns constitute a main candidate to explain such processes, but they appear sensitive to fluctuations and variations in kinetic parameters, raising the question of how they may be adopted and realised in naturally evolved systems. The vast majority of mathematical studies of Turing patterns have used continuous models specified in terms of partial differential equations. Here, we complement this work by studying Turing patterns using discrete cellular automata models. We perform a large-scale study on all possible two-species networks and find the same Turing pattern producing networks as in the continuous framework. In contrast to continuous models, however, we find these Turing pattern topologies to be substantially more robust to changes in the parameters of the model. We also find that diffusion-driven instabilities are substantially weaker predictors for Turing patterns in the discrete modelling framework in comparison to the continuous case, and show that a more refined criterion constitutes a stronger predictor. The similarity of the results for the two modelling frameworks suggests a deeper underlying principle of Turing mechanisms in nature. Together with the larger robustness in the discrete case this suggests that Turing patterns may be more robust than previously thought.

systems biology↗

bioRxiv2020

Pathway dynamics can delineate the sources of transcriptional noise in gene expression

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.

biophysics↗

bioRxiv2020

Gaining confidence in inferred networks

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.

systems biology↗

bioRxiv2020

Repeated Decision Stumping Distils Simple Rules from Single Cell Data

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.

bioinformatics↗