Electro-diffusion modulation of synaptic input in dendritic spines using deconvolved voltage sensor time series

Abstract

The inward current flowing inside the post-synaptic terminal of a neuron modulates transiently the membrane voltage potential. Most of the excitatory connections are made on dendritic spines characterized by a large variability in their geometry.How the voltage in a spine is modulated by geometry remains elusive due in part to the absence of direct measurements. To understand the spine voltage-current relation, we develop here a model for the voltage and we use it to extract electrical properties from live cell imaging data. We first deconvolve the genetically encoded voltage sensor expressed in hippocampal neurons and then use electro-diffusion theory, to compute the electric field and the ionic flows induced in a dendritic spine.The ionic flow is driven by the electric field coupled to the charge densities that interact through the non-cylindrical spine geometry. We determine the I-V relation and conclude that the spine effective resistance is mostly determined by the neck geometry. This modulation of synaptic inputs by the spine neck is significantly larger than what was expected from traditional cable models. Thus modulating the postsynaptic current can be achieved by changing the number of receptors or by altering the spine geometry which independently affects the transformation of current into voltage.\n\nSignificance statementDendritic spines are geometrical structures receiving most of the excitatory transmission, yet how they modulate voltage from the synaptic current is not clear due to their submicron small size and specific non-cylindrical geometry. We study here the conversion of the synaptic current into voltage modulated by the spine geometry. Our approach is based on the electro-diffusion theory and we show that the spine neck is the main resistance filter, while the voltage is maintained constant in the head. Finally, we extract the effective resistance using a deconvolution of the genetically encoded voltage indicators expressed in hippocampal neurons. The present approach allows studying the electrical properties of many other structures such as glial small protrusions, cilia, and many others.