Long-Term Relationships between Synaptic Tenacity, Synaptic Remodeling, and Network Activity

Long term time-lapse imaging reveals that individual synapses undergo significant structural remodeling not only when driven by activity, but also when network activity is absent, raising questions about how reliably individual synapses maintain connections

Differential Sensitization of Muscle versus Fascia in Individuals with Low Back Pain

Muscles and the deep fascia surrounding them have been suggested to play an important role in various musculoskeletal pain conditions including low back pain. Both have been shown to host rich nociceptive innervation and to undergo changes in individuals with chronic pain. However, evidence for the respective contribution of muscle and fascia sensitization in humans with myofascial pain syndrome is lacking. Here, we studied the sensitization of muscle and fascia in individuals with myofascial low back pain. Twenty individuals with acute (5) and chronic (15) myofascial low back pain of the quadratus lumborum muscle and a matched control group of twenty healthy individuals were recruited and clinically evaluated. All participants underwent ultrasound-guided needling of their subcutaneous tissue, deep fascia and quadratus lumborum muscle. Reported pain intensity and episodes of muscle twitching were recorded and analyzed. Among pain patients, both muscles and deep fascia demonstrated pain hypersensitivity, but muscles were significantly more sensitized than the deep fascia. No difference between acute- or chronic-pain patients was observed. Results of this study suggest that while both deep fascia and muscle show pain sensitization in both early and chronic stages of low back pain, muscles are more sensitized than fascia

Synaptic Size Dynamics as an Effectively Stochastic Process

<div><p>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 <i>ex-vivo</i> 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.</p></div

Estimating Kesten parameters in experimental data.

<p>An estimate of the parameter can be obtained from k-times iterated mappings of the data as explained in text. These mappings are shown for 1, 8, 24 and 48 time-steps, corresponding to 0.5, 4, 12 and 24 hours respectively (<b>A–D</b>); from each such mapping the slope of the linear regression (solid black line) is extracted. (<b>E</b>) The logarithmic values of these slopes (circles) plotted as a function of iteration number and fit by linear regression (solid black line) to obtain an estimate of . (<b>F</b>) The measured slopes (circles) with the predicted slope values (red line) over an extended time scale.</p

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Properties of the Kesten process in estimated parameter regime.

<p><b>(A)</b> Simulated synaptic trajectories of 14 out of 1075 synapses, evolved for 160 hours at 30 min intervals. Synapses were sorted according to initial size and then every 76^th trajectory was selected for display (compare with <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003846#pcbi-1003846-g001" target="_blank">Fig. 1D</a>). The Kesten process parameters used here were based on the estimate shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003846#pcbi-1003846-g004" target="_blank">Fig. 4</a> ( = 0.9923±0.05; 〈<i>η</i>〉 = 0.0077±0.03) and values were obtained from Gaussian distributions with these parameters. The initial data set (1087 synapses) was identical to that shown in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003846#pcbi-1003846-g002" target="_blank">Figs. 2A</a> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003846#pcbi-1003846-g004" target="_blank">4</a>; 12 synapses were ‘lost’ during the simulation (i.e. their values reduced to 0) and were excluded from subsequent analysis. (<b>B</b>) Synaptic distributions along time, starting from a measured distribution (thick black line) and applying the time evolution of the Kesten process to this initial population. Four subsequent time points are plotted as indicated. Inset shows the same distributions on a semi-logarithmic scale. (<b>C,D</b>) Examples of k-times iterated mappings corresponding to 24 and 48 time-steps (compare with <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003846#pcbi-1003846-g004" target="_blank">Fig. 4C,D</a>). (<b>E</b>) Slope of k-times iterated mappings as a function of k in simulated trajectories (circles) and in a theoretical prediction based on <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003846#pcbi.1003846.e003" target="_blank">Eq. (3)</a> (red solid line, red equation). (<b>F</b>) Scatter plot of changes in synapse size as a function of initial size for simulated trajectories for the period covering first 24 hours of the simulation. Note the strong resemblance with the experimental measurements of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003846#pcbi-1003846-g002" target="_blank">Fig. 2A</a>.</p

Invariance of Kesten limiting distribution shape to different ε- and η- distributions.

<p>(<b>A</b>) Simulated limiting distributions of Kesten processes with the three different ε-distributions shown in inset, all belonging to the same μ-class 6, that is, 〈<i>ε</i>⁶〉 = 1. The distribution of η was held fixed. The same three distributions after scaling are shown on the right. (<b>B</b>) Simulated limiting distributions of Kesten processes with the three different η-distributions shown in the inset. The distribution of <i>ε</i> was held fixed. The same three distributions after scaling are shown on the right.</p