(703h) Mathematical Modeling of Intracellular Transport in the Squid Giant Axon

Intracellular transport of cargo,
including macromolecules, vesicles and organelles, through the attachment to
microtubules via molecular motors, such as kinesin
and dynein, is a complex process that plays a significant role in neuronal
function. Disruption of this transport has been linked to neurodegenerative
diseases, such as Alzheimer's and Parkinson's
diseases. Thus, studying the interactions among different types of cargo and
molecular motors can lead to a better understanding of the complicated processes
involved during intracellular transport.

Here, we present a mathematical model
based on traffic-like partial differential equations to describe coupled cargo
transport within the squid giant. The model is informed using direct
microscopic measurements of nano-bead transport within
the squid giant axon which allows for meaningful
validation of the model framework. 
An analytical solution of the model equations is obtained under
conditions characterized by an excess of molecular motors within the cytoplasm.  The solution exhibits wave-like
hyperbolic behavior at short times and a convective/diffusive behavior at
longer times.  A new model is
presented for conditions characterized by a deficiency of molecular
motors.  Under these conditions,
transport of different cargo species is nonlinearly coupled. As a first step
towards understanding this phenomenon, we analyze experiments in which a protein
(APP-C) is co-injected with protein-coated nano-beads
in the squid giant axon leading to competition for motors.