Ion-concentration gradients induced by synaptic input increase the voltage depolarization in dendritic spines.

The vast majority of excitatory synaptic connections occur on dendritic spines. Due to their extremely small volume and spatial segregation from the dendrite, even moderate synaptic currents can significantly alter ionic concentrations. This results in chemical potential gradients between the dendrite and the spine head, leading to measurable electrical currents. In modeling electric signals in spines, different formalisms were previously used. While the cable equation is fundamental for understanding the electrical potential along dendrites, it only considers electrical currents as a result of gradients in electrical potential. The Poisson-Nernst-Planck (PNP) equations offer a more accurate description for spines by incorporating both electrical and chemical potential. However, solving PNP equations is computationally complex. In this work, diffusion currents are incorporated into the cable equation, leveraging an analogy between chemical and electrical potential. For simulating electric signals based on this extension of the cable equation, a straightforward numerical solver is introduced. The study demonstrates that this set of equations can be accurately solved using an explicit finite difference scheme. Through numerical simulations, this study unveils a previously unrecognized mechanism involving diffusion currents that amplify electric signals in spines. This discovery holds crucial implications for both numerical simulations and experimental studies focused on spine neck resistance and calcium signaling in dendritic spines.

Tuft dendrites of pyramidal neurons operate as feedback-modulated functional subunits.

Dendrites of pyramidal cells exhibit complex morphologies and contain a variety of ionic conductances, which generate non-trivial integrative properties. Basal and proximal apical dendrites have been shown to function as independent computational subunits within a two-layer feedforward processing scheme. The outputs of the subunits are linearly summed and passed through a final non-linearity. It is an open question whether this mathematical abstraction can be applied to apical tuft dendrites as well. Using a detailed compartmental model of CA1 pyramidal neurons and a novel theoretical framework based on iso-response methods, we first show that somatic sub-threshold responses to brief synaptic inputs cannot be described by a two-layer feedforward model. Then, we relax the core assumption of subunit independence and introduce non-linear feedback from the output layer to the subunit inputs. We find that additive feedback alone explains the somatic responses to synaptic inputs to most of the branches in the apical tuft. Individual dendritic branches bidirectionally modulate the thresholds of their input-output curves without significantly changing the gains. In contrast to these findings for precisely timed inputs, we show that neuronal computations based on firing rates can be accurately described by purely feedforward two-layer models. Our findings support the view that dendrites of pyramidal neurons possess non-linear analog processing capabilities that critically depend on the location of synaptic inputs. The iso-response framework proposed in this computational study is highly efficient and could be directly applied to biological neurons.

A Uniform and Isotropic Cytoskeletal Tiling Fills Dendritic Spines.

Dendritic spines are submicron, subcellular compartments whose shape is defined by actin filaments and associated proteins. Accurately mapping the cytoskeleton is a challenge, given the small size of its components. It remains unclear whether the actin-associated structures analyzed in dendritic spines of neurons in vitro apply to dendritic spines of intact, mature neurons in situ. Here, we combined advanced preparative methods with multitilt serial section electron microscopy (EM) tomography and computational analysis to reveal the full three-dimensional (3D) internal architecture of spines in the intact brains of male mice at nanometer resolution. We compared hippocampal (CA1) pyramidal cells and cerebellar Purkinje cells in terms of the length distribution and connectivity of filaments, their branching-angles and absolute orientations, and the elementary loops formed by the network. Despite differences in shape and size across spines and between spine heads and necks, the internal organization was remarkably similar in both neuron types and largely homogeneous throughout the spine volume. In the tortuous mesh of highly branched and interconnected filaments, branches exhibited no preferred orientation except in the immediate vicinity of the cell membrane. We found that new filaments preferentially split off from the convex side of a bending filament, consistent with the behavior of Arp2/3-mediated branching of actin under mechanical deformation. Based on the quantitative analysis, the spine cytoskeleton is likely subject to considerable mechanical force in situ.