Geometric principles of second messenger dynamics in dendritic spines

Andrea Cugno,Padmini Rangamani,Ravi Iyengar,Thomas M Bartol,Terrence J Sejnowski

doi:10.1038/s41598-019-48028-0

Abstract

Dendritic spines are small, bulbous protrusions along dendrites in neurons and play a critical role in synaptic transmission. Dendritic spines come in a variety of shapes that depend on their developmental state. Additionally, roughly 14–19% of mature spines have a specialized endoplasmic reticulum called the spine apparatus. How does the shape of a postsynaptic spine and its internal organization affect the spatio-temporal dynamics of short timescale signaling? Answers to this question are central to our understanding the initiation of synaptic transmission, learning, and memory formation. In this work, we investigated the effect of spine and spine apparatus size and shape on the spatio-temporal dynamics of second messengers using mathematical modeling using reaction-diffusion equations in idealized geometries (ellipsoids, spheres, and mushroom-shaped). Our analyses and simulations showed that in the short timescale, spine size and shape coupled with the spine apparatus geometries govern the spatiotemporal dynamics of second messengers. We show that the curvature of the geometries gives rise to pseudo-harmonic functions, which predict the locations of maximum and minimum concentrations along the spine head. Furthermore, we showed that the lifetime of the concentration gradient can be fine-tuned by localization of fluxes on the spine head and varying the relative curvatures and distances between the spine apparatus and the spine head. Thus, we have identified several key geometric determinants of how the spine head and spine apparatus may regulate the short timescale chemical dynamics of small molecules that control synaptic plasticity.

Highlights

Cell size, shape, and organelle location tightly regulate the dynamics of biochemical signal transduction; even small molecule second messengers such as calcium (Ca2+), cyclic adenosine monophosphate, and inositol trisphosphate (IP3) are reported to have distinct spatial microdomains within cells[1,2]
We used a general framework to study the effect of spine geometry including the internal organization in an idealized mathematical model with the goal of identifying some governing principles that regulate the spatio-temporal dynamics of second messengers
We developed and analyzed a general mathematical model, in which, a reaction-diffusion partial differential equation (PDE) with time-dependent mixed boundary conditions (BCs) we re analytically and numerically solved

Summary

Introduction

Shape, and organelle location tightly regulate the dynamics of biochemical signal transduction; even small molecule second messengers such as calcium (Ca2+), cyclic adenosine monophosphate (cAMP), and inositol trisphosphate (IP3) are reported to have distinct spatial microdomains within cells[1,2]. The presynaptic terminals release neurotransmitters that are taken up by the post-synaptic spines to initiate a series of electrical, chemical, and mechanical events Many of these events are tightly coupled to the dynamics of Ca2+, cAMP, and IP314–16. It is generally accepted that changes in dendritic spine calcium levels, as well as localized protein synthesis, play a central role in structural plasticity, and these two processes may be influenced by the presence and shape of a spine apparatus. It has been hypothesized that computational modeling of the processes underlying structural plasticity could help to identify the regulatory feedback that governs the switch between LTD and LTP in ER-containing spines[49]

Methods

Results

Conclusion