• AUSTRALIAN MATHEMATICAL SCIENCES STUDENT CONFERENCE
  • Keynote Lecture
  • Speaker: A/Prof Matthew Simpson, Discipline of Mathematical Sciences, Queensland University of Technology
  • Title: Mathematical models of transport through crowded environments
  • Location: Room V07, Mathematics Building (Callaghan Campus) The University of Newcastle
  • Time and Date: 10:00 am, Fri, 4th Jul 2014
  • Abstract:

    Many biological environments, both intracellular and extracellular, are often crowded by large molecules or inert objects which can impede the motion of cells and molecules. It is therefore essential for us to develop appropriate mathematical tools which can reliably predict and quantify collective motion through crowded environments.

    Transport through crowded environments is often classified as anomalous, rather than classical, Fickian diffusion. Over the last 30 years many studies have sought to describe such transport processes using either a continuous time random walk or fractional order differential equation. For both these models the transport is characterized by a parameter $\alpha$, where $\alpha=1$ is associated with Fickian diffusion and $\alpha<1$ is associated with anomalous subdiffusion. In this presentation we will consider the motion of a single agent migrating through a crowded environment that is populated by impenetrable, immobile obstacles and we estimate $\alpha$ using mean squared displacement data. These results will be compared with computer simulations mimicking the transport of a population of such agents through a similar crowded environment and we match averaged agent density profiles to the solution of a related fractional order differential equation to obtain an alternative estimate of $\alpha$. I will examine the relationship between our estimate of $\alpha$ and the properties of the obstacle field for both a single agent and a population of agents; in both cases $\alpha$ decreases as the obstacle density increases, and that the rate of decrease is greater for smaller obstacles. These very simple computer simulations suggests that it may be inappropriate to model transport through a crowded environment using widely reported approaches including power laws to describe the mean squared displacement and fractional order differential equations to represent the averaged agent density profiles.

    More details can be found in Ellery, Simpson, McCue and Baker (2014) The Journal of Chemical Physics, 140, 054108.


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