Quantifying the Influence of the Actin Cytoskeleton on Ion Transport in Dendritic Spines by Homogenization of the Poisson-Nernst-Planck Equations

Dendritic spines are filled with a very dense actin cytoskeleton. However, due to their small size, the impact of this mesh on biophysical parameters has not been studied so far, and it remains unclear to what extent it might affect ion flow in dendritic spines. Only recently has the three-dimensional internal structure of dendritic spines been quantified in great detail in electron microscopic tomography data. Based on these results, we estimate the effect of the spine actin cytoskeleton on diffusion and permittivity. We apply a method called homogenization to estimate effective diffusion tensors and permittivity tensors in Poisson-Nernst-Planck (PNP) equations. We find that the volume taken up by the intracellular structure alone cannot explain the changes in these biophysical parameters. The characteristic architecture of the intracellular space in dendritic spines will reduce the diffusion of ions by 33% to 46% and the permittivity by 30% to 42%, compared to values found for the cytosol free of intracellular structures. These results can be used to improve computational studies using PNP equations and help to better interpret experimental results of electrical and chemical compartmentalization. ### Competing Interest Statement The authors have declared no competing interest.