A Model of NMDA Receptor Control of F-actin Treadmilling in Synaptic Spines and Their Growth

Synaptic spines grow as a consequence of the formation of F-actin filaments at the spine head. The dynamics of F-actin in the spine head upon excitation of N-methy-D-aspartate (NMDA) receptors has recently been investigated experimentally, but there is no quantitative account of how these dynamic changes occur upon activation of these receptors; this we now supply. Dynamics of F-actin at the apex of lamellipodia have been investigated in detail, giving rise to the treadmilling theory of F-actin dynamics, involving catalysis by profilin, for which quantitative models are now available. Here, we adapt such a model to describe the dynamics of F-actin in the synaptic-spine head and show that it gives quantitative descriptions of this treadmilling phenomena which are well fitted by Monte Carlo simulations. Next, the means by which excitation of NMDA receptors enhances the activity of profilin through activity of the Rho small GTPase RhoA and the specific kinase ROCK is discussed. This is then used to model the NMDA receptor excitatory enhancement of profilin and so the treadmilling process of F-actin dynamics in spine growth. Such modelling provides a quantitative description of the synaptic-spine dynamics of the filamentous to globular actin ratio that is observed experimentally.