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.