Dendritic spines mediate essentially all excitatory connections and are thus critical elements in the brain but their function is still poorly understood. In particular, a key question is whether or not they are electrical compartments. To explore this, researchers have used cable theory and Goldman-Hodgkin-Huxley-Katz models, which form a theoretical foundation responsible for many cornerstone advances in neuroscience. However, these theories break down when applied to small neuronal compartments, such as dendritic spines, because they assume spatial and ionic homogeneity. Taking advantage of advances in computational power, we will explore the application of a broader theory that incorporates the Poisson-Nernst-Planck (PNP) approximation and electrodiffusion to more accurately model the constraints that the nanostructure of the spines place on electrical current flow. Specifically, we will combine multiscale modeling, asymptotic and simulations of partial differential equations to extract features from data and experimental approaches to study how the geometry and composition of a dendritic spine affect the electrical and ionic fluxes and the coupling between the synapse and the dendrite. We will test the predictions of electrodiffusion combining cutting-edge voltage imaging methods with 2-photon glutamate uncaging in vitro and in vivo and nanopipette recordings of spines from mouse pyramidal neurons. Our broader theoretical analysis of could be instrumental to understand their physiological role in neuronal circuits. This work will explore an alternative theoretical formulation to the established cable theory, in order to understand quantitatively the biophysical properties of dendritic spines. We aim to generate the most rigorous mathematical model of spines to date and tackle key questions in neurobiology: how synaptic voltages in neuron are shaped at spines, how they propagate to dendrites and how this is regulated by ionic channels and dendritic and spine geometry. Finally, this proposal will help to link the form and the function of neurons, with a detail which has never been carried out before, something that could help interpret functionally many peculiar morphological characteristics of neuronal microstructures, in both normal and pathological processes.

The proposed research will help us understand how synaptic voltages are shaped by dendritic spines, a phenomenon that could be affected in many mental and neurological diseases. Indeed, abnormalities in spine structure and function have been described in a host of diseases, like epilepsy, mental retardation, dementia and schizophrenia, and it is still not understood how these abnormalities relate to the pathophysiology or symptomatology of these diseases.