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.