Biology subjects

Burrage, K.

Publications and source records attributed to Burrage, K..

13 recordsLinked to original sources

bioRxiv2026

PSoup: an R package for simulating biological networks from a qualitative perspective

Mathematical modelling is essential for understanding how complex biological systems respond to genetic, physiological, and environmental changes. Existing approaches, however, often require trade-offs between mechanistic detail, model size, parameter uncertainty, and interpretability. Ordinary differential equation (ODE) models capture biochemical processes with quantitative precision but can demand extensive parameterisation. In contrast, large statistical and machine-learning models rely on substantial datasets and frequently lack mechanistic transparency. Qualitative approaches such as Boolean networks improve scalability but may oversimplify biological behaviour. To address some of these limitations, we present PSoup, an R package that automatically converts knowledge graphs into transparent, parameter-free, qualitative models. PSoup uses algebraic update rules designed around a fixed, biologically interpretable baseline, enabling predictions of relative change across diverse perturbations without requiring kinetic parameters. This design allows PSoup to integrate information across biological scales and from heterogeneous experimental sources. We evaluated PSoup using the well-studied shoot branching network of Bertheloot et al. (2019), which incorporates hormonal (auxin, strigolactone, cytokinin) and metabolic (sucrose) regulation. Across 78 experimental conditions, PSoup correctly predicted 88.5%of perturbation outcomes, including 89.5%accuracy for unique, biologically consistent comparisons. We further demonstrate how PSoup can distinguish among alternative plausible network topologies, revealing how structural differences influence emergent system behaviour. PSoup offers an intuitive, accessible, and mathematically transparent framework for exploring biological networks. Its capacity to integrate diverse knowledge and test alternative hypotheses positions it as a powerful tool for biological discovery and a valuable complement to existing modelling approaches.

plant biology↗

bioRxiv2026

Directional heritability and the geometry of multivariate constraint

Evolutionary responses to selection depend on how additive genetic variance is distributed across trait combinations. We focus on directional heritability--the fraction of phenotypic variance that is additive genetic along a given selection gradient--and treat its distribution across directions as a central object for describing multivariate constraint. Using a geometric transformation that rescales trait space so that phenotypic variance is isotropic, we show that directional heritability becomes a quadratic form in a whitened genetic matrix G* = P-1/2GP-1/2. Under uniformly distributed selection directions, the squared coefficient of variation of directional heritability satisfies CV2(h2) = (2/(p + 2)) Vrel(G*), where Vrel(G*) is the relative eigenvalue variance of the whitened matrix and p is the number of traits. Simulations show that alignment between the eigenvector systems of G and P has a larger effect on the spread of directional heritability than correlation strength. Analyses of 55 empirical G-P matrix pairs from 11 studies reveal wide variation across biological systems in how often selection encounters low-heritability directions: over two thirds of the populations examined had more than 25% of phenotypic directions with h2 < 0.25. The eigenvalue spectrum of G* provides a sufficient summary for characterising how matrix geometry shapes evolutionary constraint on the phenotypic scale.

evolutionary biology↗

bioRxiv2025

The emerging role of receptor trafficking insignalosome formation and sustained long-termWnt/β-catenin signaling

Despite its central role in development, cell homeostasis, and cancer, the mechanisms that govern canonical Wnt signaling, particularly how receptor internalization and membrane organization shape signalosome formation and downstream pathway activation, remain a topic of ongoing debate. To resolve this longstanding controversy, we developed a mechanistic model that integrates seemingly contradictory experimental observations into a coherent explanatory framework. Using an optimized multi-level rule-based modeling approach the model explicitly captures lateral membrane organization, receptor complex dynamics, endocytic routing and downstream signaling. Simulations reveal a previously unrecognized compensatory mechanism in which rapid recycling of partially immobilized receptor assemblies amplifies and stabilizes signalosome formation. The results further indicate that internalization and recycling are essential for stable long-term {beta}-catenin activation, offering an explanation why these processes are required for excessive signaling in cancer cells. The model further predicts that ordered membrane domains enhance signaling not merely by colocalizing receptors and DVL but by increasing effective residence time through rebinding-driven cluster stabilization. Integrating diverse experimental measurements into a unified simulation framework quantitatively reconciles conflicting experimental reports on the necessity of receptor internalization for pathway activation. By resolving these debates and providing falsifiable predictions for how trafficking and membrane organization jointly tune pathway output, the study offers a mechanistic foundation for targeted modulation of Wnt signaling in developmental and disease contexts.

systems biology↗

bioRxiv2024

Optimal control of Multiple Myeloma assuming drug evasion and off-target effects

Multiple Myeloma (MM) is a plasma cell cancer that occurs in the bone marrow. A leading treatment for MM is the monoclonal antibody Daratumumab, targeting the CD38 receptor, which is highly overexpressed in myeloma cells. In this work we model drug evasion via loss of CD38 expression, which is a proposed mechanism of resistance to Daratumumab treatment. We develop an ODE model that includes drug evasion via two mechanisms: a direct effect in which CD38 expression is lost without cell death in response to Daratumumab, and an indirect effect in which CD38 expression switches on and off in the cancer cells; myeloma cells that do not express CD38 have lower fitness but are shielded from the drug action. The model also incorporates competition with healthy cells, death of healthy cells due to off-target drug effects, and a Michaelis-Menten type immune response. Using optimal control theory, we study the effect of the drug evasion mechanisms and the off-target drug effect on the optimal treatment regime. We identify a general increase in treatment duration and costs, with varying patterns of response for the different controlling parameters. Several distinct optimal treatment regimes are identified within the parameter space. Author summaryIn this work we investigate a model of Multiple Myeloma, a cancer of the bone marrow, and its treatment with the drug Daratumumab. The model incorporates proposed mechanisms by which the cancer evades Daratumumab by reduced expression of the receptor CD38, which is the drug target and normally abundent in the cancer cells. The model includes an off-target effect, meaning that the drug treatment destroys some healthy cells alongside the targeted cancer cells. Both mechanisms can reasonably be expected to reduce the efficacy of the drug. We investigate the model using optimal control methods, which are used to find the drug dose over time which best balances the financial and health costs of treatment against cancer persistence, according to a specified cost function. We show that this drug resistence and off-target effect prolongs the optimal treatment and increase the burden of both the disease and drug. We analyse the distinct effects of the controlling parameters on each of these costs factors as well as the time course, and identify conditions under which extended treatment is required, with either intermittant treatment or a steady reduced dose. Extended treatment may be indefinite or for a fixed period.

systems biology↗

bioRxiv2021

Quantitative analysis of tumour spheroid structure

Tumour spheroids are common in vitro experimental models of avascular tumour growth. Compared with traditional two-dimensional culture, tumour spheroids more closely mimic the avascular tumour microenvironment where spatial differences in nutrient availability strongly influence growth. We show that spheroids initiated using significantly different numbers of cells grow to similar limiting sizes, suggesting that avascular tumours have a limiting structure; in agreement with untested predictions of classical mathematical models of tumour spheroids. We develop a novel mathematical and statistical framework to study the structure of tumour spheroids seeded from cells transduced with fluorescent cell cycle indicators, enabling us to discriminate between arrested and cycling cells and identify an arrested region. Our analysis shows that transient spheroid structure is independent of initial spheroid size, and the limiting structure can be independent of seeding density. Standard experimental protocols compare spheroid size as a function of time; however, our analysis suggests that comparing spheroid structure as a function of overall size produces results that are relatively insensitive to variability in spheroid size. Our experimental observations are made using two melanoma cell lines, but our modelling framework applies across a wide range of spheroid culture conditions and cell lines.

cancer biology↗

bioRxiv2021

Implementation and acceleration of optimal control for systems biology

Optimal control theory provides insight into complex resource allocation decisions. The forward-backward sweep method (FBSM) is an iterative technique commonly implemented to solve two-point boundary value problems (TPBVPs) arising from the application of Pontryagins Maximum Principle (PMP) in optimal control. In this review we discuss the PMP approach to optimal control and the implementation of the FBSM. By conceptualising the FBSM as a fixed point iteration process, we leverage and adapt existing acceleration techniques to improve its rate of convergence. We show that convergence improvement is attainable without prohibitively costly tuning of the acceleration techniques. Further, we demonstrate that these methods can induce convergence where the underlying FBSM fails to converge. All code used in this work to implement the FBSM and acceleration techniques is available on GitHub at https://github.com/Jesse-Sharp/Sharp2021.

systems biology↗

bioRxiv2020

Listen to the noise: identifiability analysis for stochastic differential equation models in systems biology

Mathematical models are routinely calibrated to experimental data, with goals ranging from building predictive models to quantifying parameters that cannot be measured. Whether or not reliable parameter estimates are obtainable from the available data can easily be overlooked. Such issues of parameter identifiability have important ramifications for both the predictive power of a model, and the mechanistic insight that can be obtained. Identifiability analysis is well-established for deterministic, ordinary differential equation (ODE) models, but there are no commonly-adopted methods for analysing identifiability in stochastic models. We provide an accessible introduction to identifiability analysis and demonstrate how existing ideas for analysis of ODE models can be applied to stochastic differential equation (SDE) models through four practical case studies. To assess structural identifiability, we study ODEs that describe the statistical moments of the stochastic process using open-source software tools. Using practically-motivated synthetic data and Markov-chain Monte Carlo (MCMC) methods, we assess parameter identifiability in the context of available data. Our analysis shows that SDE models can often extract more information about parameters than deterministic descriptions. All code used to perform the analysis is available on Github.

systems biology↗

bioRxiv2019

Persistence is an optimal hedging strategy for bacteria in volatile environments

Bacteria invest in a slow-growing subpopulation, called persisters, to ensure survival in the face of uncertainty. This hedging strategy is remarkably similar to financial hedging, where diversifying an investment portfolio protects against economic uncertainty. We provide a new theoretical foundation for understanding cellular hedging by unifying the study of biological population dynamics and the mathematics of financial risk management through optimal control theory. Motivated by the widely accepted role of volatility in the emergence of persistence, we consider several novel models of environmental volatility described by continuous-time stochastic processes. This allows us to study an emergent cellular hedging strategy that maximizes the expected per-capita growth rate of the population. Analytical and simulation results probe the optimal persister strategy, revealing results that are consistent with experimental observations and suggest at new opportunities for experimental investigation and design. Overall, we provide a new way of conceptualising and modelling cellular decision-making in volatile environments by explicitly unifying theory from mathematical biology and finance.

systems biology↗

bioRxiv2019

Designing combination therapies using multiple optimal controls

Strategic management of populations of interacting biological species routinely requires interventions combining multiple treatments or therapies. This is important in key research areas such as ecology, epidemiology, wound healing and oncology. Despite the well developed theory and techniques for determining single optimal controls, there is limited practical guidance supporting implementation of combination therapies. In this work we use optimal control theory to calculate optimal strategies for applying combination therapies to a model of acute myeloid leukaemia. We consider various combinations of continuous and bang-bang (discrete) controls, and we investigate how the control dynamics interact and respond to changes in the weighting and form of the pay-off characterising optimality. We demonstrate that the optimal controls respond non-linearly to treatment strength and control parameters, due to the interactions between species. We discuss challenges in appropriately characterising optimality in a multiple control setting and provide practical guidance for applying multiple optimal controls. Code used in this work to implement multiple optimal controls is available on GitHub.

systems biology↗

bioRxiv2019

Administration of defective virus via bang-bang optimal control inhibits dengue transmission

The host-vector shuttle and the bottleneck in dengue transmission is a significant aspect with regard to the study of dengue outbreaks. As mosquitoes require 100-1000 times more virus to become infected than human, the transmission of dengue virus from human to mosquito is a vulnerability that can be targeted to improve disease control. In order to capture the heterogeneity in the infectiousness of an infected patient population towards the mosquito pool, we calibrate a population of host-to-vector virus transmission models based on an experimentally quantified infected fraction of a mosquito population. Once the population of models is well-calibrated, we deploy a population of controls that helps to inhibit the human-to-mosquito transmission of the dengue virus indirectly by reducing the viral load in the patient body fluid. We use an optimal bang-bang control on the administration of the defective virus (transmissible interfering particles, known as TIPs) to symptomatic patients in the course of their febrile period and observe the dynamics in successful reduction of dengue spread into mosquitoes.

systems biology↗

bioRxiv2019

Perlin Noise Generation of Physiologically Realistic Patterns of Fibrosis

Fibrosis, the pathological excess of fibroblast activity, is a significant health issue that hinders the function of many organs in the body, in some cases fatally. However, the severity of fibrosis-derived conditions depends on both the positioning of fibrotic affliction, and the microscopic patterning of fibroblast-deposited matrix proteins within afflicted regions. Variability in an individuals manifestation of a type of fibrosis is an important factor in explaining differences in symptoms, optimum treatment and prognosis, but a need for ex vivo procedures and a lack of experimental control over conflating factors has meant this variability remains poorly understood. In this work, we present a computational methodology for the generation of patterns of fibrosis microstructure, demonstrating the technique using histological images of four types of cardiac fibrosis. Our generator and automated tuning method prove flexible enough to capture each of these very distinct patterns, allowing for rapid generation of new realisations for high-throughput computational studies. We also demonstrate via simulation, using the generated fibrotic patterns, the importance of micro-scale variability by showing significant differences in electrophysiological impact even within a single class of fibrosis.

physiology↗

bioRxiv2018

A population of bang-bang switches of defective interfering particles makes within-host dynamics of dengue virus controllable

The titre of virus in a dengue patient and the duration of this viraemia has a profound effect on whether or not a mosquito will become infected when it feeds on the patient and this, in turn is a key driver of the magnitude of a dengue outbreak. As mosquitoes require 100-1000 times more virus to become infected than a patient, the transmission of dengue virus from a patient to a mosquito is a vulnerability that may be able to be targeted to improve disease control. The intrinsic variability in the within-host dynamics of viraemias is explored for a population of patients using the method of population of models (POMs). A dataset from 207 patients is used to calibrate 20,000 models for the infection kinetics for each of the four dengue virus serotypes. The effect of adding defective dengue virus interfering particles to patients as a therapeutic is evaluated using the calibrated POMs in a bang-bang optimal control setting.\n\nAuthor summaryDengue virions with deletions or defects in their genomes can be recovered from dengue patients. These defective viruses can only replicate with the assistance of fully functional viruses and they reduce the yield of the fully functional viruses. They are known as defective interfering (DI) particles. By administering additional, defined, DI particles to patients it may be possible to reduce the titre and duration of their viraemia. This, in turn may reduce the severity of the disease and the likelihood that dengue virus will be passed from the patient to a mosquito vector. This study estimates the number of DI particles that would need to be administered, and over what period, to have a significant effect on patient viraemia and subsequent dengue fever severity.

systems biology↗

bioRxiv2018

Optimal control of acute myeloid leukaemia

Acute myeloid leukaemia (AML) is a blood cancer affecting the haematopoietic stem cells of the myeloid cell line. AML is routinely treated with chemotherapy, and so it is of great interest to develop optimal chemotherapy treatment strategies. In this work, we incorporate an immune response into a stem cell model of AML, since we find that previous models lacking an immune response are inappropriate for deriving optimal control strategies. Using optimal control theory, we produce continuous controls and bang-bang controls, corresponding to a range of objectives and parameter choices. Through example calculations, we provide a practical approach to applying optimal control using Pontryagins maximum principle. In particular, we describe and explore factors that have a profound influence on numerical convergence. We find that the convergence behaviour is sensitive to the method of control updating, the nature of the control, and to the relative weighting of terms in the objective function. All codes we use to implement optimal control are made available.

synthetic biology↗