arXiv subjects

Rachel N. Bearon

Publications and source records attributed to Rachel N. Bearon.

5 recordsLinked to original sources

arXiv2024

An innovative in silico model of the oral mucosa reveals the impact of extracellular spaces on chemical permeation through epithelium

In pharmaceutical therapeutic design or toxicology, accurately predicting the permeation of chemicals through human epithelial tissues is crucial, where permeation is significantly influenced by the tissue's cellular architecture. Current mathematical models for multi-layered epithelium such as the oral mucosa only use simplistic 'bricks and mortar' geometries and therefore do not account for the complex cellular architecture of these tissues at the microscale level, such as the extensive plasma membrane convolutions that define the extracellular spaces between cells. Chemicals often permeate tissues via this paracellular route, meaning that permeation is underestimated. To address this, measurements of human buccal mucosal tissue were conducted to ascertain the width and tortuosity of extracellular spaces across the epithelium. Using mechanistic mathematical modelling, we show that the convoluted geometry of extracellular spaces significantly impacts chemical permeation and that this can be approximated, provided that extracellular tortuosity is accounted for. We next developed an advanced physically-relevant in silico model of oral mucosal chemical permeation using partial differential equations, fitted to chemical permeation in vitro assays on tissue-engineered human oral mucosa. Tissue geometries were measured and captured in silico, and permeation examined and predicted for chemicals with different physicochemical properties. The effect of altering the extracellular space to mimic permeation enhancers was also assessed by perturbing the in silico model. This novel in vitro-in silico approach has the potential to expedite pharmaceutical innovation for testing oromucosal chemical permeation, providing a more accurate, physiologically-relevant model which can reduce animal testing with early screening based on chemical properties.

q-bio.TO↗

arXiv2023

The interplay between bulk flow and boundary conditions on the distribution of micro-swimmers in channel flow

While previous experimental and numerical studies of dilute micro-swimmer suspensions have focused on the behaviours of swimmers in the bulk flow and near boundaries, models typically do not account for the interplay between bulk flow and the choice of boundary conditions imposed in continuum models. In our work, we highlight the effect of boundary conditions on the bulk flow distributions, such as through the development of boundary layers or secondary peaks of cell accumulation in bulk-flow swimmer dynamics. For the case of a dilute swimmer suspension in Poiseuille flow, we compare the distribution (in physical and orientation space) obtained from individual based stochastic models with those from continuum models, and identify mathematically sensible continuum boundary conditions for different physical scenarios (i.e. specular reflection, uniform random reflection and absorbing boundaries). We identify that the spread of preferred cell orientations is dependent on the interplay between rotation driven by the shear flow (Jeffery orbits) and rotational diffusion. We find that in the absence of hydrodynamic wall-interactions, swimmers preferentially approach the walls perpendicular to the surface in the presence of high rotational diffusion, and that the preferential approach of swimmers to the walls is shape-dependent at low rotational diffusion (when suspensions tend towards a fully deterministic case). In the latter case, the preferred orientations are nearly parallel to the surface for elongated swimmers and nearly perpendicular to the surface for near-spherical swimmers. Furthermore, we highlight the effects of swimmer geometries and shear throughout the bulk-flow on swimmer trajectories and show how the full history of bulk-flow dynamics affects the orientation distributions of micro-swimmer wall incidence.

physics.flu-dyn↗

arXiv2022

A local approximation model for macroscale transport of biased active Brownian particles in a flowing suspension

A dilute suspension of motile microorganisms subjected to a strong ambient flow, such as algae in the ocean, can be modelled as a population of non-interacting, orientable active Brownian particles (ABPs). Using the Smoluchowski equation (i.e. Fokker-Planck equation in space and orientation), one can describe the non-trivial transport phenomena of ABPs such as taxis and shear-induced migration. This work transforms the Smoluchowski equation into a transport equation, in which the drifts and dispersions can be further approximated as a function of the local flow field. The new model can be applied to any global flow field due to its local nature, unlike previous methods such as those utilising the generalised Taylor dispersion theory. The transformation shows that the overall drift includes both the biased motility of individual particles in the presence of taxis and the shear-induced migration in the absence of taxis. In addition, it uncovers other new drifts and dispersions caused by the interactions between the orientational dynamics and the passive advection-diffusion of ABPs. Finally, the performance of this model is assessed using examples of gyrotactic suspensions, where the proposed model is demonstrated to be most accurate when the biased motility of particles (i.e. taxis) is weak.

physics.flu-dyn↗

arXiv2020

Bifurcation and stability of downflowing gyrotactic micro-organism suspensions in a vertical pipe

In the experiment that first demonstrated gyrotactic behaviour of bottom-heavy swimming microalgae (e.g. Chlamydomonas), Kessler (Nature, vol. 313, 1985, pp. 218-220) showed that a beam-like structure, often referred to as a gyrotactic plume, would spontaneously appear from a suspension of gyrotactic swimmers in a downflowing pipe. Such a plume is prone to an instability to form blips. This work models the gyrotactic plume as a steady parallel basic state and its subsequent breakdown into blips as an instability, employing both the Generalised Taylor Dispersion (GTD) theory and the Fokker-Planck model for comparison. Upon solving for the basic state, it is discovered that the steady plume solution undergoes sophisticated bifurcations. When there is no net flow, there exists a non-trivial solution of the plume structure other than the stationary uniform suspension, stemming from a transcritical bifurcation with the average cell concentration. When a net downflow is prescribed, there exists a cusp bifurcation. Furthermore, there is a critical concentration, at which the cell concentration at the centre would blow up for the GTD model. The subsequent stability analysis using the steady plume solution shows that the Fokker-Planck model is inconsistent with what was experimentally observed, as it predicts stabilisation of axisymmetric blips at high concentration of the plume and destabilisation of the first non-axisymmetric mode at low flow rates.

physics.flu-dyn↗

arXiv2014

Modeling the dynamics of hypoxia inducible factor-1α (HIF-1α) within single cells and 3D cell culture systems

HIF (Hypoxia Inducible Factor) is an oxygen-regulated transcription factor that mediates the intracellular response to hypoxia in human cells. There is increasing evidence that cell signaling pathways encode temporal information, and thus cell fate may be determined by the dynamics of protein levels. We have developed a mathematical model to describe the transient dynamics of the HIF-1α protein measured in single cells subjected to hypoxic shock. The essential characteristics of these data are modeled with a system of differential equations describing the feedback inhibition between HIF-1α and Prolyl Hydroxylases (PHD) oxygen sensors. Heterogeneity in the single-cell data is accounted for through parameter variation in the model. We previously identified the PHD2 isoform as the main PHD responsible for controlling the HIF-1α transient response, and make here testable predictions regarding HIF-1α dynamics subject to repetitive hypoxic pulses. The model is further developed to describe the dynamics of HIF-1α in cells cultured as 3D spheroids, with oxygen dynamics parameterized using experimental measurements of oxygen within spheroids. We show that the dynamics of HIF-1α and transcriptional targets of HIF-1α display a non-monotone response to the oxygen dynamics. Specifically we demonstrate that the dynamic transient behavior of HIF-1α results in differential dynamics in transcriptional targets.

q-bio.CB↗