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.

Nonsynaptic plasticity model of long-term memory engrams

Using steady-state electrical properties of non-ohmic dendrite based on cable theory, we derive electrotonic potentials that do not change over time and are localized in space. We hypothesize that clusters of such stationary, local and permanent pulses are the electrical signatures of enduring memories which are imprinted through nonsynaptic plasticity, encoded through epigenetic mechanisms, and decoded through electrotonic processing. We further hypothesize how retrieval of an engram is made possible by integration of these permanently imprinted standing pulses in a neural circuit through neurotransmission in the extracellular space as part of conscious recall that acts as a guiding template in the reconsolidation of long-term memories through novelty characterized by uncertainty that arises when new fragments of memories reinstate an engram by way of nonsynaptic plasticity that permits its destabilization. Collectively, these findings seem to reinforce this hypothesis that electrotonic processing in non-ohmic dendrites yield insights into permanent electrical signatures that could reflect upon enduring memories as fragments of long-term memory engrams.