arXiv subjects

Keith L. Chambers

Publications and source records attributed to Keith L. Chambers.

3 recordsLinked to original sources

arXiv2026

A quantitative model for the emergent population dynamics of the melanoma MITF rheostat

Cancer progression is driven by the ability of cells with identical driver mutations to adopt biologically distinct adaptive phenotypes. Yet the population dynamics implied by intratumour phenotypic heterogeneity is poorly understood. Melanoma is an excellent setting to study phenotype switching, in part because phenotypic identity is conferred by melanocyte inducing transcription factor (MITF) activity. Here we develop a multiscale phenotype-structured partial differential equation model for epidermal melanoma cell populations, first considering subcellular MITF and then spatially uniform and spatially heterogeneous populations. The model admits three stable long-term behaviours: slow growth with proliferative cells and non-cycling differentiated cells; faster expansion, with an invasive core; and rapid growth with oscillatory core dynamics. More broadly, the analysis highlights that phenotype reversibility by individual cells does not imply reversibility of phenotype population distributions. Hence, single-cell properties (e.g., reversibility of invasive capacity) must be extrapolated with caution to populations with coupled cell dynamics.

q-bio.CB↗

arXiv2026

A multiscale discrete-to-continuum framework for structured population models

Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions can improve analytical tractability and scalability of numerical solutions. Common upscaling approaches based solely on Taylor expansions may, however, introduce ambiguities in truncation order, uniform validity and boundary conditions. To address this, here we introduce a discrete multiscale framework to systematically derive continuum approximations of structured population models. Using the method of multiple scales and matched asymptotic expansions applied to discrete systems, we identify regions of structure space for which a continuum representation is appropriate and derive the corresponding partial differential equations. The leading-order dynamics are given by a nonlinear advection equation in the bulk domain and advection-diffusion processes in small inner layers about the leading wavefronts and stagnation point. We further derive discrete boundary layer descriptions for regions where a continuum representation is fundamentally inappropriate. Finally, we demonstrate the method on a simple lipid-structured model for early atherosclerosis and verify consistency between the discrete and continuum descriptions. The multiscale framework we present can be applied to other heterogeneous systems with discrete structure in order to obtain appropriate upscaled dynamics with asymptotically consistent boundary conditions.

q-bio.PE↗

arXiv2025

A spatially resolved and lipid-structured model for macrophage populations in early human atherosclerotic lesions

Atherosclerosis is a chronic inflammatory disease of the artery wall. The early stages of atherosclerosis are driven by interactions between lipids and monocyte-derived-macrophages (MDMs). The mechanisms that govern the spatial distribution of lipids and MDMs in the lesion remain poorly understood. In this paper, we develop a spatially-resolved and lipid-structured model for early atherosclerosis. The model development and analysis are guided by images of human coronary lesions by Nakashima et al. 2007. Consistent with their findings, the model predicts that lipid initially accumulates deep in the intima due to a spatially non-uniform LDL retention capacity. The model also qualitatively reproduces the global internal maxima in the Nakashima images only when the MDM mobility is sufficiently sensitive to lipid content, and MDM lifespan sufficiently insensitive. Introducing lipid content-dependence to MDM mobility and mean lifespan produced minimal impact on model behaviour at early times, but strongly impacted lesion composition at steady state. Increases to the sensitivity of MDM lifespan to lipid content yield lesions with fewer MDMs, less total lesion lipid content and reduced mean MDM infiltration depth. Increases to the sensitivity of MDM mobility to lipid content also reduces the MDM infiltration depth, but increases the proportion of lipid-laden MDMs. We find that MDM lipid content increases with spatial depth, regardless of blood LDL and HDL content. These results shed light on the mechanisms that drive spatial variation in the composition of early atherosclerotic lesions, and the role of macrophage lipid content in disease progression.

q-bio.CB↗