Thomas Fai, Ph.D.
Assistant Professor
Department of Mathematics
Brandeis University
October 1, 2018
Active Vesicle Transport into Dendritic Spine
Neurons send messages through connections between the axon of one neuron and the dendrites of another. Synapses (the connection spot) form at the dendritic spine, which is shaped, as Dr. Fai describes it, as “a thin neck and bulbous head”. The shape must deform when vesicles are moved into the neck of the spine in order to reach the head. Dr. Fai discussed his work using computational methods to mathematically explain the geometry and dynamics of the dendritic spine.
The maintenance and reorganization of neuronal connections in the brain are fundamental questions that are beginning to be understood through the development of new experimental and computational techniques.
Axonal processes terminate along dendrites by forming synapses onto micron-sized structures known as dendritic spines. These spines are characterized by their thin necks and bulbous heads, a geometry thought to allow nearby spines to function as separate biochemical compartments. Given this geometry, one spine may be associated with a strong synaptic connection, whereas a neighboring spine may be associated with a weaker synapse, and these differences in synaptic strength may persist over long times.
The geometry of dendritic spines has other effects on synaptic regulation, as well. Membrane receptors responsible for sensing the neurotransmitters released into the synaptic cleft are critical constituents of the post-synaptic densities on spines. These membrane receptors are actively trafficked into spines by vesicles that can be larger than the spine necks and must deform significantly to squeeze into the bulbous heads of the spines. However, mechanistic understanding of this trafficking process and quantitative estimates of the force and energy required are still lacking.
Fai has used a computational technique known as the immersed boundary method to perform three-dimensional simulations of the fluid dynamics of vesicle transport into spines. In these simulations, a spine is represented by a triangulated surface obtained by stitching together a cylinder with a sphere. The applied force and neck geometry are varied to identify regions in phase space in which the vesicle can squeeze into the spine. These results have been compared to pass-stuck diagrams computed previously in the case of vesicles squeezing through narrow open channels, and the resulting estimates for the force have been found to be consistent with the physiological density of motor proteins. Resolving the thin lubricating layers between the vesicles and spine poses significant numerical challenges, and together with his colleagues Fai has used lubrication theory as an alternative to fully resolving these boundary layers.