arXiv subjects

Helen Byrne

Publications and source records attributed to Helen Byrne.

7 recordsLinked to original sources

arXiv2026

Adaptive therapy under parametric, structural, and measurement uncertainty

Adaptive therapy has emerged as a promising treatment strategy that exploits within-tumour competition to delay disease progression. Implementation, however, typically relies on indirect measurements of tumour burden and must account for potentially substantial patient heterogeneity. In this work, we capture patient-to-patient variability, parameter uncertainty, and imperfect biomarker measurements with a mathematical and statistical model that we calibrate to clinical prostate cancer data using a Bayesian inference framework. We use the resulting virtual cohort to demonstrate that, within the simple but now well-established Lotka-Volterra-based model, adaptive therapy robustly improves time-to-progression for the subset of patients that are predicted to eventually progress by the model. To account for other risk factors associated with larger tumour volumes, we introduce a new metric based on the risk of metastasis that demonstrates how adaptive therapy may be disadvantageous when sustained tumour burden is also considered. Given the ubiquity of uncertainty in oncology, we then describe several future modelling directions that also capture uncertainty in the temporal evolution of the underlying tumour or biomarker dynamics. Finally, we demonstrate how model misspecification and non-identifiability can lead to unreliable predictions, especially if uncertainty is inadequately captured.

q-bio.TO↗

arXiv2026

Quantifying the effect of phenotype on clustering behaviour in melanoma: from monoculture to co-culture

Melanoma is an aggressive form of skin cancer. Survival rates are excellent if it is detected early but fall markedly if it metastasises. A key step in early tumour progression is the formation of cell clusters, which can promote metastasis. However, the mechanisms driving cell clustering, and the role of phenotypic heterogeneity in the dynamics of these clusters, remain poorly understood. In this work, we propose a system of ordinary differential equations that models cluster formation dynamics within a coagulation-fragmentation-proliferation framework. Using Bayesian inference, we fit this model to in vitro time-lapse microscopy data from two melanoma phenotypes-proliferative and invasive-to uncover the predominant mechanisms driving cluster formation and how these differ between phenotypes. Additionally, we provide preliminary insights into how clustering behaviour in co-cultures contrasts with that observed in monocultures. The model quantifies phenotypic differences in clustering dynamics: invasive cells in monoculture exhibit nearly threefold higher coagulation rates than proliferative cells, whereas proliferative cells display slightly higher proliferation rates. These differences align with known gene expression profiles. When applied to co-culture data, the model predicts hybrid coagulation behaviour of the clusters influenced by both proliferative and invasive cells but dominated by the invasive cells, and an elevated proliferation rate, suggesting a mutually beneficial effect of phenotypic heterogeneity on cell proliferation.

q-bio.CB↗

arXiv2024

Algebraic identifiability of partial differential equation models

Differential equation models are crucial to scientific processes. The values of model parameters are important for analyzing the behaviour of solutions. A parameter is called globally identifiable if its value can be uniquely determined from the input and output functions. To determine if a parameter estimation problem is well-posed for a given model, one must check if the model parameters are globally identifiable. This problem has been intensively studied for ordinary differential equation models, with theory and several efficient algorithms and software packages developed. A comprehensive theory of algebraic identifiability for PDEs has hitherto not been developed due to the complexity of initial and boundary conditions. Here, we provide theory and algorithms, based on differential algebra, for testing identifiability of polynomial PDE models. We showcase this approach on PDE models arising in the sciences.

q-bio.QM↗

arXiv2018

Local migration quantification method for scratch assays

Motivation: The scratch assay is a standard experimental protocol used to characterize cell migration. It can be used to identify genes that regulate migration and evaluate the efficacy of potential drugs that inhibit cancer invasion. In these experiments, a scratch is made on a cell monolayer and recolonisation of the scratched region is imaged to quantify cell migration rates. A drawback of this methodology is the lack of its reproducibility resulting in irregular cell-free areas with crooked leading edges. Existing quantification methods deal poorly with such resulting irregularities present in the data. Results: We introduce a new quantification method that can analyse low quality experimental data. By considering in-silico and in-vitro data, we show that the method provides a more accurate statistical classification of the migration rates than two established quantification methods. The application of this method will enable the quantification of migration rates of scratch assay data previously unsuitable for analysis. Availability and Implementation: The source code and the implementation of the algorithm as a GUI along with an example dataset and user instructions, are available in https://bitbucket.org/anavictoria-ponce/local_migration_quantification_scratch_assays/src/master/. The datasets are available in https://ganymed.math.uni-heidelberg.de/~victoria/publications.shtml.

q-bio.QM↗

arXiv2018

Reactions, Diffusion and Volume Exclusion in a Heterogeneous System of Interacting Particles

Complex biological and physical transport processes are often described through systems of interacting particles. Excluded-volume effects on these transport processes are well studied, however the interplay between volume exclusion and reactions between heterogenous particles is less well known. In this paper we develop a novel framework for modeling reaction-diffusion processes which directly incorporates volume exclusion. From an off-lattice microscopic individual based model we use the Fokker--Planck equation and the method of matched asymptotic expansions to derive a low-dimensional macroscopic system of nonlinear partial differential equations describing the evolution of the particles. A biologically motivated, hybrid model of chemotaxis with volume exclusion is explored, where reactions occur at rates dependent upon the chemotactic environment. Further, we show that for reactions due to contact interactions the appropriate reaction term in the macroscopic model is of lower order in the asymptotic expansion than the nonlinear diffusion term. However, we find that the next reaction term in the expansion is needed to ensure good agreement with simulations of the microscopic model. Our macroscopic model allows for more direct parameterization to experimental data than the models available to date.

cond-mat.stat-mech↗

arXiv2016

Optimisation of Simulations of Stochastic Processes by Removal of Opposing Reactions

Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a large number of algorithms have been developed to speed up simulations. However, a drawback of many of these algorithms is that their implementation is more complicated than, for instance, the Gillespie algorithm, which is widely used to simulate the chemical master equation, and can be implemented with a few lines of code. Here, we present an algorithm which does not modify the way in which the master equation is solved, but instead modifies the transition rates, and can thus be implemented with a few lines of code. It works for all models in which reversible reactions occur by replacing such reversible reactions with effective net reactions. Examples of such systems include reaction-diffusion systems, in which diffusion is modelled by a random walk. The random movement of particles between neighbouring sites is then replaced with a net random flux. Furthermore, as we modify the transition rates of the model, rather than its implementation on a computer, our method can be combined with existing algorithms that were designed to speed up simulations of the stochastic master equation. By focusing on some specific models, we show how our algorithm can significantly speed up model simulations while maintaining essential features of the original model.

physics.bio-ph↗

arXiv2015

Hybrid approaches for multiple-species stochastic reaction-diffusion models

Reaction-diffusion models are used to describe systems in fields as diverse as physics, chemistry, ecology and biology. The fundamental quantities in such models are individual entities such as atoms and molecules, bacteria, cells or animals, which move and/or react in a stochastic manner. If the number of entities is large, accounting for each individual is inefficient, and often partial differential equation (PDE) models are used in which the stochastic behaviour of individuals is replaced by a description of the averaged, or mean behaviour of the system. In some situations the number of individuals is large in certain regions and small in others. In such cases, a stochastic model may be inefficient in one region, and a PDE model inaccurate in another. To overcome this problem, we develop a scheme which couples a stochastic reaction-diffusion system in one part of the domain with its mean field analogue, i.e. a discretised PDE model, in the other part of the domain. The interface in between the two domains occupies exactly one lattice site and is chosen such that the mean field description is still accurate there. This way errors due to the flux between the domains are small. Our scheme can account for multiple dynamic interfaces separating multiple stochastic and deterministic domains, and the coupling between the domains conserves the total number of particles. The method preserves stochastic features such as extinction not observable in the mean field description, and is significantly faster to simulate on a computer than the pure stochastic model.

physics.comp-ph↗