Synaptic Size Dynamics as an Effectively Stochastic Process

Abstract

Long-term, repeated measurements of individual synaptic properties have revealed that synapses can undergo significant directed and spontaneous changes over time scales of minutes to weeks. These changes are presumably driven by a large number of activity-dependent and independent molecular processes, yet how these processes integrate to determine the totality of synaptic size remains unknown. Here we propose, as an alternative to detailed, mechanistic descriptions, a statistical approach to synaptic size dynamics. The basic premise of this approach is that the integrated outcome of the myriad of processes that drive synaptic size dynamics are effectively described as a combination of multiplicative and additive processes, both of which are stochastic and taken from distributions parametrically affected by physiological signals. We show that this seemingly simple model, known in probability theory as the Kesten process, can generate rich dynamics which are qualitatively similar to the dynamics of individual glutamatergic synapses recorded in long-term time-lapse experiments in ex-vivo cortical networks. Moreover, we show that this stochastic model, which is insensitive to many of its underlying details, quantitatively captures the distributions of synaptic sizes measured in these experiments, the long-term stability of such distributions and their scaling in response to pharmacological manipulations. Finally, we show that the average kinetics of new postsynaptic density formation measured in such experiments is also faithfully captured by the same model. The model thus provides a useful framework for characterizing synapse size dynamics at steady state, during initial formation of such steady states, and during their convergence to new steady states following perturbations. These findings show the strength of a simple low dimensional statistical model to quantitatively describe synapse size dynamics as the integrated result of many underlying complex processes.

Scale free topology as an effective feedback system

“…One important property of biological networks that has raised much interest is their heterogeneous topology. Analyses of metabolic, protein interaction, gene regulatory and neural networks all show heterogeneous connectivity distributions, including heavy tails and modular structure [8][9][10][11][12][13][14]. Heterogeneous networks, such as those with a broad connectivity distribution, are generally more difficult to analyze; inferring their detailed topology requires exceedingly high statistics.…”

The dynamic connectome

“…Recent experiments using time lapse imaging of dendritic spines have suggested that such distributions can arise from stochastic fluctuations that have a multiplicative component [3]. Another important finding is that the bigger and stronger synapses are more stable than the smaller and weaker ones [4,9,13]. This makes particularly strong synapses a good candidate for the anatomical substrate ofthose long-term memories which we may maintain for a lifetime.…”

Modeling the Shape of Synaptic Spines by their Actin Dynamics

“…Interestingly, foci generated with fast nucleation rate also tend to have a shorter lifetime 540 evidencing a saturating mechanism or self-regulation (compare [13]). Moreover, we used 541 our model to test the influence of the nucleation location of these foci.…”

“…Experiments imaging the shape of dendritic spines can provide snapshots at 14 distinct time points, but mathematical models are needed to bridge between these time 15 points and to understand shape fluctuations and their properties. However, so far only 16 phenomenological models have been proposed [9,[12][13][14] that describe fluctuation 17 coarsely on a timescale of days. Here, we take a different approach by modelling the fast 18 actin dynamics underlying shape fluctuations.…”

“…In the future, the model can be extended in various directions: On the one hand, the 569 shape fluctuations may, on longer timescales, influence the model parameters such as 570 PSD size, molecule concentrations and reaction rates. Hence, the mean area around 571 which the spine fluctuates as well as other fluctuation characteristics could be 572 continuously adapted giving rise to a slower feedback-loop (compare [9] and [13]). On activity-dependent plasticity (LTP/LTD) by explicitely modelling the actin recycling 576 pathway that is modulated during plasticity (compare [17]).…”