arXiv subjects

Karen M. Page

Publications and source records attributed to Karen M. Page.

9 recordsLinked to original sources

arXiv2026

Mathematical modelling of immune persistence and relapse pathways in CAR T-cell therapy for B-ALL

Chimeric antigen receptor (CAR) T-cell therapy has transformed the treatment of B-cell acute lymphoblastic leukaemia (B-ALL). Despite high initial response rates, a substantial fraction of patients relapse, often due to loss of CAR T-cell persistence, antigen escape, or immune-privileged sites that shield tumour cells. Prolonged CAR T-cell persistence is clinically associated with durable remission, but why it is required remains poorly understood. To address this, we develop and analyse the BEAM (Blast, Effector, Activated, Memory) model of CAR T-cell dynamics in B-ALL. BEAM extends predator--prey models with three CAR T-cell states (memory, activated, effector) coupled to a logistic growth equation for the blasts, calibrated against the FELIX trial of obecabtagene autoleucel in adult B-ALL. We find that both memory and effector persistence prevent relapse, but for distinct reasons: memory persistence sustains surveillance against low-burden or slowly proliferating residual disease, while effector persistence clears isolated blasts emerging from immune-privileged sites. The model further predicts a trade-off between immediate cytotoxicity and durable surveillance, and identifies initial tumour burden as a key modifiable factor for reducing antigen-negative relapse. Together, these results offer a framework for designing more durable, individually tailored CAR T-cell therapies.

q-bio.PE↗

arXiv2026

Construction and simulation of a path-valued model of dendrite development

Neurons receive information through their dendrites. During development, when synaptic connections are forming, dendrites grow, retract, and branch. The resulting dendritic tree shapes the structure of the broader neural network. Crucially, retraction and branching make it necessary to track whole dendritic paths rather than only their endpoints. While this is handled implicitly in some existing simulations, here we construct an explicitly path-valued stochastic process for dendrite growth. Combining this with a branching process, using ideas from measure-valued branching particle systems, we show that the model produces the typical tree structures of real dendrites. To complement this analytical work, we also outline several methods for numerical simulation, including time discretisations at different temporal scales and an approximation using a dynamic graph. This provides both a more rigorous mathematical framework and more structured simulation methods for modelling dendrite development.

math.PR↗

arXiv2024

Modelling the Impact of Organic Molecules and Phosphate Ions on Biosilica Pattern Formation in Diatoms

The rapid and complex patterning of biosilica in diatom frustules is of great interest in nanotechnology, although it remains incompletely understood. Specific organic molecules, including long-chain polyamines, silaffins, and silacidins are essential in this process. The molecular structure of the synthesized polyamines significantly affects the quantity, size, and shape of silica precipitates. Experimental findings show that silica precipitation occurs at specific phosphate ion concentrations. We focus on the hypothesis that pattern formation in diatom valve structures is driven by phase separation of species-specific organic molecules. The resulting organic structures serve as templates for silica precipitation. We investigate the role of phosphate ions in self-assembly of organic molecules and analyze how the reaction between them affects the morphology of the organic template. Using mathematical and computational techniques, we gain an understanding of the range of patterns that can arise in a phase-separating system. By varying the degree of dissociation and the initial concentrations of reacting components we demonstrate that the resulting geometric features are highly dependent on these factors. This approach provides insights into the parameters controlling patterning. Additionally, we consider the effects of prepatterns, mimicking silica ribs that preexist the pores, on the final patterns.

physics.bio-ph↗

arXiv2024

An agent-based modelling framework to study growth mechanisms in EGFR-L858R mutant alveolar type II cells

Mutations in the epidermal growth factor receptor (EGFR) are common in non-small cell lung cancer (NSCLC), particularly in never-smoker patients. However, these mutations are not always carcinogenic, and have recently been reported in histologically normal lung tissue from patients with and without lung cancer. To investigate the outcome of EGFR mutation in healthy lung stem cells, we grew murine alveolar type-II organoids monoclonally in a 3D Matrigel. Our experiments showed that the \textit{EGFR-L858R} mutation induced a change in organoid structure: mutated organoids displayed more `budding', in comparison to non-mutant controls, which were nearly spherical. We perform on-lattice computational simulations, which suggest that this can be explained by the concentration of division amongst a small number of cells on the surface of the organoid, which may arise from several possible biological mechanisms. These results suggest that the L858R mutation produces structures which expand quickly from surface protrusions. We are currently unable to distinguish the cell-based mechanisms that lead to this spatial heterogeneity in growth, but suggest a number of future experiments which could be used to do so. We suggest that the likelihood of L858R-fuelled tumorigenesis is affected not just by random fluctuations in cell fitness, but by whether the mutation arises in a spatial environment that allows mutant cells to reproduce without being forced to encounter each other. These data may have implications for cancer prevention strategies and for understanding NSCLC progression.

q-bio.CB↗

arXiv2021

Cooperative success in epithelial public goods games

Cancer cells obtain mutations which rely on the production of diffusible growth factors to confer a fitness benefit. These mutations can be considered cooperative, and studied as public goods games within the framework of evolutionary game theory. The population structure, benefit function and update rule all influence the evolutionary success of cooperators. We model the evolution of cooperation in epithelial cells using the Voronoi tessellation model. Unlike traditional evolutionary graph theory, this allows us to implement global updating, for which birth and death events are spatially decoupled. We compare, for a sigmoid benefit function, the conditions for cooperation to be favoured and/or beneficial for well mixed and structured populations. We find that when population structure is combined with global updating, cooperation is more successful than if there were local updating or the population were well-mixed. Interestingly, the qualitative behaviour for the well-mixed population and the Voronoi tessellation model is remarkably similar, but the latter case requires significantly lower incentives to ensure cooperation.

q-bio.PE↗

arXiv2018

Evolution of cooperation on an epithelium

Cooperation is prevalent in nature, not only in the context of social interactions within the animal kingdom, but also on the cellular level. In cancer for example, tumour cells can cooperate by producing growth factors. The evolution of cooperation has traditionally been studied for well-mixed populations under the framework of evolutionary game theory, and more recently for structured populations using evolutionary graph theory. The population structures arising due to cellular arrangement in tissues however are dynamic and thus cannot be accurately represented by either of these frameworks. In this work we compare the conditions for cooperative success in an epithelium modelled using evolutionary graph theory, to those in a mechanical model of an epithelium =- the Voronoi tessellation model. Crucially, in this latter model cells are able to move, and birth and death are not spatially coupled. We calculate fixation probabilities in the Voronoi tessellation model through simulation and an approximate analytic technique and show that this leads to stronger promotion of cooperation in comparison with the evolutionary graph theory model.

q-bio.PE↗

arXiv2018

Degradation rate uniformity determines success of oscillations in repressive feedback regulatory networks

Ring oscillators are biochemical circuits consisting of a ring of interactions capable of sustained oscillations. The non-linear interactions between genes hinder the analytical insight into their function, usually requiring computational exploration. Here we show that, despite the apparent complexity, the stability of the unique steady state in an incoherent feedback ring depends only on the degradation rates and a single parameter summarizing the feedback of the circuit. Concretely, we show that the range of regulatory parameters that yield oscillatory behaviour, is maximized when the degradation rates are equal. Strikingly, this results holds independently of the regulatory functions used or number of genes. We also derive properties of the oscillations as a function of the degradation rates and number of nodes forming the ring. Finally, we explore the role of mRNA dynamics by applying the generic results to the specific case with two naturally different degradation time scales

q-bio.MN↗

arXiv2017

The power of the AC-DC circuit: Operating principles of a simple multi-functional transcriptional network motif

Genetically encoded regulatory circuits control biological function. A major focus of systems biology is to understand these circuits by establishing the relationship between specific structures and functions. Of special interest are multifunctional circuits that are capable of performing distinct behaviors without changing their topology. A particularly simple example of such a system is the AC-DC circuit. Found in multiple regulatory processes, this circuit consists of three genes connected in a combination of a toggle switch and a repressilator. Using dynamical system theory we analyze the available dynamical regimes to show that the AC-DC can exhibit both oscillations and bistability. We found that both dynamical regimes can coexist robustly in the same region of parameter space, generating novel emergent behaviors not available to the individual subnetwork components. We demonstrate that the AC-DC circuit provides a mechanism to rapidly switch between oscillations and steady expression and, in the presence of noise, the multi-functionality of the circuit offers the possibility to control the coherence of oscillations. Additionally, we provide evidence that the availability of a bistable oscillatory regime allows the AC-DC circuit to behave as an excitable system capable of stochastic pulses and spatial signal propagation. Taken together these results reveal how a system as simple as the AC-DC circuit can produce multiple complex dynamical behaviors in the same parameter region and is well suited for the construction of multifunctional synthetic genetic circuits. Likewise, the analysis reveals the potential of this circuit to facilitate the evolution of distinct patterning mechanisms.

q-bio.MN↗

arXiv2017

Minimum Action Path theory reveals the details of stochastic biochemical transitions out of oscillatory cellular states

Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Tran- sitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible multidimensional paths, with probabilities depending non-locally on the noise. Here we characterize the escape from an oscillatory biochemical state by minimizing the Freidlin-Wentzell action, deriving from it the stochastic spiral exit path from the limit cycle. We also use the minimized action to infer the escape time probability density function.

physics.bio-ph↗