Biophysical modeling of membrane-actin interactions governing the morphology of dendritic spines

Dendritic spines are primary excitatory postsynaptic sites and are associated with characteristic shapes. While it is well known that dendritic spines are rich in actin and have a complex cytoskeletal organization that aids in their function, how actin forces and membrane mechanics contribute to dendritic spine morphology from a mechanical standpoint remains poorly understood. In this study, we developed a minimal biophysical model to investigate the role of membrane-actin interactions in governing dendritic spine geometries. We identified the relationship between heterogeneous actin-mediated forces and tension necessary to reproduce the characteristic range of dendritic spine protrusions. We were also able to compare our analytical solutions to our numerical simulations with high degrees of agreement and provide scaling laws between different biophysical characteristics. A key result from this work is that we showed the cooperation between different mechanisms provides various mechanical pathways to sustain different spine shapes and found that some mechanisms may be energetically more favorable than others. We believe our findings provide a framework for the experimental and computational investigation of dendritic spine size and shape due to heterogeneous force distributions.