Multiplicative Dynamics Underlie the Emergence of the Log-Normal Distribution of Spine Sizes in the Neocortex In Vivo

Abstract

What fundamental properties of synaptic connectivity in the neocortex stem from the ongoing dynamics of synaptic changes? In this study, we seek to find the rules shaping the stationary distribution of synaptic efficacies in the cortex. To address this question, we combined chronic imaging of hundreds of spines in the auditory cortex of mice in vivo over weeks with modeling techniques to quantitatively study the dynamics of spines, the morphological correlates of excitatory synapses in the neocortex. We found that the stationary distribution of spine sizes of individual neurons can be exceptionally well described by a log-normal function. We furthermore show that spines exhibit substantial volatility in their sizes at timescales that range from days to months. Interestingly, the magnitude of changes in spine sizes is proportional to the size of the spine. Such multiplicative dynamics are in contrast with conventional models of synaptic plasticity, learning, and memory, which typically assume additive dynamics. Moreover, we show that the ongoing dynamics of spine sizes can be captured by a simple phenomenological model that operates at two timescales of days and months. This model converges to a log-normal distribution, bridging the gap between synaptic dynamics and the stationary distribution of synaptic efficacies.

Increased axonal bouton dynamics in the aging mouse cortex

“…Interestingly, the size of boutons showed a statistically significant variation over time (P < 0.05; ANOVA) for 42% of the axons in the Ag brain (Fig. 5D), in contrast to the results for dendritic spine volumes on L5 cells (22). To estimate fluctuations in the volumes of boutons that were present through consecutive sessions, we tracked bouton intensity over time using EPBscore.…”

“…A sizeable proportion of axons in both the Ag (42%) (Fig. 5D) and the YA (58%) brain show correlated changes in the size of their EPBs, in contrast to findings of independent changes in the size of spines on L5 cells (22). Correlated bouton size changes might arise because boutons form contacts with postsynaptic cells displaying similar tuning properties (e.g., in the same cortical column), whereas spines along a dendrite likely make synapses with axons exhibiting different firing patterns.…”

“…Indeed changes in the volume of spine heads have been measured successfully in vivo both in normal (22) and altered (14,23,40) sensoryexperience paradigms and can correlate with functional changes. We find that even over extensive periods of time EPBs undergo substantial volume fluctuations (Ag 4-d intensity ratio: 42%; range, 0-618%; YA 4-d intensity ratio, 36%; range, 0-383%) comparable to those in dendritic spines in vivo (14,22) and in vitro (42). Spatial and temporal coordination of the fluctuation in EPB volume may drive significant alterations in network function.…”

“…15) and behavioral training (13,16). Because the size of a synapse is directly related to its strength (17)(18)(19)(20), changes in the size of persistent synapses could play a significant role in mediating optimal cognitive function and experience-dependent plasticity alongside synapse formation, elimination, and stabilization (13,14,16,(21)(22)(23). However, little is known about structural changes of persistent synapses in the living brain.…”

Integrating Hebbian and homeostatic plasticity: the current state of the field and future research directions

“…Furthermore, spine size is not only controlled by LTP, LTD and during synaptic scaling, but also by intrinsic fluctuations that happen even in the absence of neural activity [42]. Fluctuations of spine size increase approximately linearly with the initial size and this relationship explains the steady-state distribution of spine sizes with a long tail [42,43]. A simulation study of recurrently connected networks suggests that such fluctuations can stabilize network activity by constitutively restoring the spine size distribution close to the physiological steady-state distribution, while ongoing Hebbian plasticity forms and maintains cell assemblies [44,45].…”