Modeling the shape of synaptic spines by their actin dynamics

Abstract

Dendritic spines are the morphological basis of excitatory synapses in the cortex and their size and shape correlates with functional synaptic properties. Recent experiments show that spines exhibit large shape fluctuations that are not related to activity-dependent plasticity but nonetheless might influence memory storage at their synapses. To investigate the determinants of such spontaneous fluctuations, we propose a mathematical model for the dynamics of the spine shape and analyze it in 2D -- related to experimental microscopic imagery -- and in 3D. We show that the spine shape is governed by a local imbalance between membrane tension and the expansive force from actin bundles that originates from discrete actin polymerization foci. Experiments have shown that only few such polymerization foci co-exist at any time in a spine, each having limited life time. The model shows that the momentarily existing set of such foci pushes the membrane along certain directions until foci are replaced and other directions may now be affected. We explore these relations in depth and use our model to predict shape and temporal characteristics of spines from the different biophysical parameters involved in actin polymerization. Reducing the model further to a single recursive equation we finally demonstrate that the temporal evolution of the number of active foci is sufficient to predict the size of the model-spines. Thus, our model provides the first platform to study the relation between molecular and morphological properties of the spine with a high degree of biophysical detail.\n\nAuthor summarySynaptic spines are post-synaptic contact points for pre-synaptic signals in many cortical neurons and it has been shown that synaptic transmission is correlated with spine size. However, spine size and shape can vary quite strongly on short time scales and it is currently unknown how these shape variations emerge. In this study we present a biophysical model that links spine shape fluctuations to the dynamics of the spines actin-based cytoskeleton. We show that shape fluctuations arise from the fact that fast actin polymerization in a spine is a discrete process happening at only few polymerization foci. Life and death of these foci determine from moment to moment how the membrane bulges or retracts. We provide an in-depth analysis of this effect for a large set of biophysical parameters and quantify the spatial-temporal structure of the spines. Our model, thus, provides a quantitative characterization of the link between spine morphology and the underlying molecular processes, which forms an essential step towards a better understanding of synaptic transmission during steady state but also during synaptic plasticity.