Talks in Physics A1
10:30 Joseph Shuttleworth (University of Nottingham)
Title: A framework for modelling auxin signalling pathways in plants
Abstract: Auxins are a group of plant hormones which are involved in various processes across plant tissues and species. The auxin signalling pathway (ASP) consists of interacting transcription factors and repressors, and governs an individual cell's response to changes in auxin concentration. Alongside its role in plant growth (through both cell division and cell growth) this pathway determines cell fates, and is implicated in processes such as root-hair formation, phototropism, and other responses to environmental stimuli. Different responses to different auxin concentrations at different timescales are governed by different subnetworks, where the dominant signalling components vary. This profound diversity in response is reflected by the many copies of each signalling component found in different species. We present a general framework for ODE-based models of auxin signalling networks with the flexibility to model the promotion and repression of genes by any combination of transcriptional regulators. Using this framework, we present examples of plausible emergent behaviour and discuss the effect that network dynamics have on the response times of different genes.
10:50 Charlotte Taylor Barca (University of Manchester)
Title: A mathematical model of cell-state dynamics in melanoma
Abstract: Melanoma cells can transition between cell states, contributing to therapy resistance and immune evasion. These state changes involve dynamic and reversible shifts in gene expression, making it essential to understand the underlying regulatory mechanisms for developing effective therapies. We present a mathematical model of a minimal gene regulatory network comprising key transcription factors associated with melanoma cell states. Using deterministic temporal and spatio-temporal differential equation models, we analyse gene expression dynamics and classify stable states in a biologically meaningful way. We exploit an approximation, based on cooperative binding of transcription factors, in which the models are piecewise smooth. At the population level, we use a naïve model of intercellular communication to explore how cells within a tumour can exhibit coordinated behaviour through travelling waves of gene expression. Additionally, we propose a method for deriving a condition that determines the final state of a population of communicating cells. This model provides a framework for better understanding some of the mechanisms driving gene expression dynamics and to inform and validate experimental hypotheses.
11:10 Charli Austin (University of Edinburgh)
Title: The Impact of Cell Division on Cellular Decision Making
Abstract: Whilst the biological realism of GRN models has improved in recent years, there has been little consideration of cell division and its effects on the surrounding networks. This talk will present novel findings from investigations incorporating cell division into models of the bistable toggle switch. I will discuss the formulation of a Boolean modelling framework that addresses the highly non-linear nature of the original toggle switch model and allows us to find analytical expressions for the separatrix of toggle switch, both with and without division, ultimately highlighting the impact of cell division on the steady state attraction of the model.
Move to Physics C29
11:30 Leah Band (University of Nottingham)
Title: Combining parameter estimation and asymptotic analysis to identify parsimonious network models.
Abstract: Developing effective strategies to use models in conjunction with experimental data is essential to understand the dynamics of regulatory networks. In this talk, I will describe modelling of two plant hormone networks, demonstrating how combining parameter estimation with asymptotic analysis can reveal the key features of a network and lead to simplified models that capture the observed network dynamics.
In the first project, we created an ODE model to interpret data from the DII-VENUS sensor, a fluorescent sensor that is rapidly degraded by the plant hormone auxin. Parameterising this model led us to identify a reduced model, which enabled us to use DII-VENUS data to predict auxin dynamics.
Building on this approach, the second project analyses the biosynthesis network of the plant hormone gibberellin (GA). Our methodology involved fitting the model to experimental data and using the profile likelihood to identify small parameters or instances where model dynamics are insensitive to changing particular individual parameters. Such parameter diagnostics provided understanding of the dominant features of the model and motivated asymptotic model reductions to derive a series of simpler models.
Thus, in both projects, our approach allowed us to select parsimonious models with identifiable parameters. The reduced models provided insights into the network dynamics, as well as forming key components of larger multiscale models.
12:15 Lunch in Physics A1
13:00 Smitha Maretvadakethope (Imperial College London)
Title: Let there be multifunctionality: Uncovering the criticality zoo of the AC-DC genetic circuit
Abstract: Gene regulatory networks (GRNs) govern cell fate, patterning, and adaptation. Although multistability and oscillations are both common in GRNs, they are usually studied and engineered separately. Here we challenge this divide using the AC–DC circuit, a minimal three-gene network that combines a toggle switch with a repressilator. Using a thermodynamic formalism and Bayesian inference, we show that even a single-inducer circuit can exhibit rich multifunctional dynamics, including coexisting oscillations and multistability. We analyse robustness, classify emergent behaviours, and study critical slowing down and regime transitions. Remarkably, the AC–DC circuit supports over 30 topologically distinct bifurcation diagrams, challenging the view that network topology tightly constrains dynamics. This flexibility enables synthetic behaviours coupling hysteresis, oscillations, and reversibility, and highlights new design principles for exploiting emergent complexity in minimal genetic circuits.
13:45 Charlotte Manser (Kings College London)
Title: A mathematical framework for measuring and tuning tempo in developmental gene regulatory networks
Abstract: Embryo development is a dynamic process governed by the regulation of timing and sequences of gene expression, which control the proper growth of the organism. Although many genetic programmes coordinating these sequences are common across species, the timescales of gene expression can vary significantly among different organisms. Currently, substantial experimental efforts are focused on identifying molecular mechanisms that control these temporal aspects. In contrast, the capacity of established mathematical models to incorporate tempo control while maintaining the same dynamical landscape remains less understood. In our recent work we have addressed this gap by developing a mathematical framework that links the functionality of developmental programmes to the corresponding gene expression orbits (or landscapes). We demonstrate that this framework allows for the prediction of molecular mechanisms governing tempo in synthetic networks such as the repressilator, and a gene network governing brain development.
14:30 Tea and Coffee in Physics A1
15:00 Kamil Drynda (University of Nottingham)
Title: Title: How Plants Cope with Stress: A Mathematical Model of SUMOylation Dynamics
Abstract: As the climate warms, plants are increasingly exposed to environmental stresses that threaten growth and productivity. The SUMO (Small Ubiquitin-like Modifier) pathway plays a central role in mediating plant stress responses by regulating the post-translational modification of target proteins. As part of an interdisciplinary project, we are developing mathematical models to investigate how SUMOylation transduces environmental signals into specific physiological outcomes.We formulate a system of nonlinear ordinary differential equations describing the core processes of the SUMO cycle,. The model is used to simulate dynamic changes in SUMO-pathway components following salt and drought stress in different root tissues, integrating newly generated experimental data from the SUMOcode project (www.sumocode.org). Through this approach, we aim to identify key regulatory mechanisms that shape SUMOylation dynamics and determine how these contribute to plant resilience under stress.
15:20 Amruta Vasudevan (University of Liverpool)
Title: Systematic analysis of gene regulatory network topologies provides insights into the robustness of symmetry breaking in mouse gastruloids
Abstract: Symmetry breaking is a critical early step in mammalian embryonic axis specification. Gastruloids, which are embryo-like 3D stem cell aggregates, self-organise to create all 3 embryonic axes, and are more amenable to experimentation than mouse embryos. Our analysis of published scRNA-seq, spatial transcriptomics, and proteomics datasets on mouse gastruloids and embryos has identified 3 spatially distinct, conserved signalling modules to be active throughout early symmetry breaking (72-96hAA), viz. Wnt, Nodal, and Notch. We hypothesise that a GRN comprising key genes from some or all these signalling modules govern early symmetry breaking and anteroposterior axis specification. We model the gastruloid as a sheet of nuclei and examine the parameter space of all possible GRN topologies that successfully achieve symmetry breaking. We find that only specific GRN sub-topologies can recreate the experimentally observed spatial patterning of transcription factors T/Brachyury and Sox2 in 72hAA mouse gastruloids. Our analysis further reveals that Nodal signalling alters the bifurcation structures of certain GRN topologies and provides increased resilience to variations in a) size of gastruloids and b) strength of external signalling factors. This study provides a mathematical understanding of the importance of Nodal signalling for robustness and error tolerance in symmetry breaking events in mouse gastruloids.
15:40 Matt Owen (University of Bristol)
Title: Hybrid multiscale modelling of gene regulatory networks in Julia
Abstract: Gene regulatory networks can give rise to complex emergent phenomena across multicellular environments, but these dynamics may be hybrid, multiscale and heterogeneous in nature. We have developed a Julia package, Mermaid.jl, which can simulate these systems through a component-based architecture where modular components (sub-models) are stepped forwards in time and synchronized through variables passed along user defined inter-connections. The interface to include a model in Mermaid is minimal and easily implemented, and Mermaid already has implementations of this interface for many common modelling paradigms covering agent-based systems and differential equations. We will demonstrate this approach through a simulation of an engineered genetic oscillator in a growing population of cells that combines agent-based modelling with a stochastic gene regulatory network and an ODE of cell growth.
16:00 Juan David Marmolejo Lozano (University of Edinburgh)
Title: Model Reduction and Frequency-Dependent Information Flow in Gene Regulatory Networks
Abstract: Reduced stochastic models are widely used in the mathematical analysis of gene regulatory networks (GRNs), typically justified by timescale separation or quasi-steady-state assumptions. While such reductions often preserve mean behavior and low-order statistics, it is less clear whether they retain dynamical features relevant to signal transmission.
In this work, we analyze how model reduction affects frequency-dependent noise propagation and information flow in stochastic GRNs. Using linear noise approximations and spectral methods, we show that reduced models can systematically distort coherence spectra and information rates, even when stationary variances are accurately reproduced. In particular, eliminating fast regulatory components can alter intermediate- and high-frequency filtering properties that are essential for characterizing dynamical information processing.
Through canonical examples of transcriptional regulation and enzyme-mediated control, we identify structural conditions under which reduced descriptions faithfully capture frequency-resolved behavior. Our results highlight theoretical limitations of common reduction strategies and provide guidance for constructing simplified GRN models that preserve both statistical and dynamical aspects of stochastic regulation.