Diffusion laws in dendritic spines

Recognized more than 100 hundreds years ago by Ramón y Cajal, dendritic spines are small terminal protrusions on neuronal dendrites, and are considered to be the main locus of excitatory synaptic connections. The general spine geometry consists of a relatively narrow cylindrical neck connected to a bulky head (the round part in Figure 1). Their geometrical shape correlates with their physiological function [1-6]. More than three decades ago, the spine-dendrite communication associated with the particle transfer was already anticipated [7] to be mediated not only by pure diffusion but it was hypothesized to involve other mechanisms such as twitching. This idea was reinforced by the findings [8] that inside the spine, the cytoplasmic actin is organized in filaments, involved in various forms of experimentally induced synaptic plasticity by changing the shape or volume of the pre- and postsynaptic side and by retracting and sprouting synapses. The fast dendritic spine contraction was finally confirmed in cultured hippocampal neurons [9] and consequences were studied theoretically in [10-12]. Interestingly, a serial electron microscopy and three-dimensional reconstructions of dendritic spines from Purkinje spiny branchlets of normal adult rats allowed to relate spine geometry to synaptic efficacy [1]. This image reconstruction approach leads to the conclusion that the cerebellar spine necks are unlikely to reduce transfer of synaptic charge by more than 5-20%, even if their smooth endoplasmic reticulum were to completely block passage of current through the portion of the neck that it occupies. The constricted spine neck diameter was proposed to isolate metabolic events in the vicinity of activated synapses by reducing diffusion to neighboring synapses, without significantly influencing the transfer of synaptic charge to the postsynaptic dendrite [1].Change of spine morphology can be induced by synaptic potentiation protocols [13-15] and indeed intracellular signaling s