bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Homeostatic plasticity scales dendritic spine volumes and changes the threshold and specificity of Hebbian plasticity
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Authors:
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Anna F. Hobbiss1, Yazmin Ramiro Cortés1,2, Inbal Israely1,3
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1. Champalimaud Centre for the Unknown, 1400-038 Lisbon, Portugal.
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2. Instituto de Fisiología Celular, Universidad Nacional Autónoma de México, Ciudad Universitaria,
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Circuito exterior s/n, Ciudad de México 04510, México. 3. Department of Pathology and Cell Biology in the Taub Institute for Research on Alzheimer's
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Disease and the Aging Brain, Department of Neuroscience, College of Physicians & Surgeons,
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Columbia University, New York, New York, 10032, USA.
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Corresponding author:
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Inbal Israely. Electronic address:
[email protected]
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1
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Abstract
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Information is encoded within neural networks through synaptic weight changes. Synaptic
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learning rules involve a combination of rapid Hebbian plasticity with slower homeostatic
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synaptic plasticity (HSP) that regulates neuronal activity through global synaptic scaling. While
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Hebbian plasticity has been extensively investigated, much less is known about HSP. Here we
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investigate the structural and functional consequences of HSP at dendritic spines of mouse
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hippocampal neurons. We find that prolonged activity blockade induces spine growth,
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paralleling synaptic strength increases. Following activity blockade, glutamate uncaging-
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mediated long-term potentiation at single spines leads to size-dependent structural plasticity:
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smaller spines undergo robust growth, while larger spines remain unchanged. Moreover, we
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find that neighboring spines in the vicinity of the stimulated spine exhibit volume changes
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following HSP, indicating that plasticity has spread across a group of synapses. Overall, these
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findings demonstrate that Hebbian and homeostatic plasticity shape neural connectivity
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through coordinated structural plasticity of clustered inputs.
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Introduction
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Hebbian synaptic plasticity, widely regarded as the leading biological mechanism for
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information storage, involves activity-dependent changes in synaptic connectivity (Malenka
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and Bear, 2004). Notably, these changes have a physical component and excitatory
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postsynaptic current is highly correlated with dendritic spine volume (Matsuzaki et al., 2001).
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However, left unchecked activity would lead to a positive feedback loop in which changes in
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synaptic weight are further reinforced by future events. This has been proposed to result in
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loss of functionality of the system, by either driving synapses towards saturation, or through
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silencing the population (Miller and MacKay, 1994). How neurons maintain stability in the
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face of destabilizing cellular and circuit events has been a longstanding question (LeMasson
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et al., 1993). One method neurons employ to resolve this is Homeostatic Synaptic Plasticity
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(HSP) (Turrigiano et al., 1998), a feedback mechanism through which a population of synapses
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can be maintained to function within optimal bounds. During HSP, a decrease in global activity
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drives a counteracting scalar increase in synaptic strengths to bring the network into an
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optimal functioning range, and conversely, network activity increases will promote synaptic
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weakening (Turrigiano, 2011). This scaling is instantiated in part by AMPA receptor trafficking
2
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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to and from the post-synaptic density, as well as through presynaptic changes which modify
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neurotransmitter release, leading to concomitant changes in synaptic strength (Murthy et al.,
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2001; O’Brien et al., 1998). HSP has been observed both in vitro and in vivo (Desai et al., 2002),
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supporting a fundamental role for this mechanism in the proper functioning of a neural
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system.
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It is well established that HSP modulates synaptic function; however, it is currently unknown
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how this process also correlates with spine structural changes. Moreover, how HSP affects
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the induction and longevity of subsequent forms of Hebbian plasticity at individual inputs
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remains to be determined. In this study, we examine how the induction of HSP affects the
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structure and function of hippocampal pyramidal neuron synapses, and what are the
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consequences of these changes for future Hebbian plasticity. We find that the induction of
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HSP through activity blockade leads to an overall increase in the size of spines, corresponding
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to a structural scaling that matches the functional scaling of synapses. Through precise 2-
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photon mediated glutamate uncaging, we further investigate how these homeostatic
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functional and structural plasticity changes impact the ability of individual inputs to undergo
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subsequent plasticity. We demonstrate that after HSP, spines express increased longevity of
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LTP, an increased growth rate after stimulation, and a reduced plasticity threshold. We find
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that HSP enhances the magnitude of synaptic potentiation through the preferential
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modulation of small spines and by promoting structural plasticity at clustered inputs following
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Hebbian activity at single synapses. Together, these changes provide a mechanism by which
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homeostatic plasticity can modulate synaptic efficacy and enhance future learning without
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compromising previously stored information.
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Results
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Structural correlates of homeostatic plasticity
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Hebbian plasticity at an individual input is linearly correlated with volume changes in the
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corresponding spine (Govindarajan et al., 2011; Harvey and Svoboda, 2007; Matsuzaki et al.,
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2004). Since HSP is known to change the functional properties of the spine, we reasoned that
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homeostatic modifications of efficacy would be accompanied by structural plasticity of inputs.
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We induced HSP using prolonged activity blockade through Tetrodotoxin (TTX) inhibition of
3
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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sodium channels, for either 0 h, 24 h, 48 h or 72 h (Figure 1a), as this has been shown to
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induce scaling of synaptic strengths in a variety of systems (Karmarkar and Buonomano, 2006;
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Turrigiano et al., 1998). We chose to conduct our experiments in mouse hippocampal
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organotypic slice cultures, which maintain a physiologically relevant tissue architecture and
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are amenable to genetic manipulation. To verify that functional synaptic scaling occurred, we
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recorded spontaneous miniature excitatory post-synaptic currents (mEPSCs) from both TTX
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treated and Control CA1 hippocampal pyramidal neurons at 48 h after the beginning of the
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HSP induction period (Figure 1b-d). All recordings were performed in the presence of acute
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TTX to block action potentials. As expected, we found a significant increase in mEPSC
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amplitude following 48 h of activity blockade (Figure 1b,c; Control = 18.6 ± 0.25 pA, TTX =
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20.72 ± 0.28 pA, p = 1.55e-8 Mann Whitney). The distribution of the TTX mEPSCs scaled
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linearly to overlay with the control distribution (Figure 1d), in accordance with the synaptic
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scaling theory. We next investigated whether homeostatic plasticity leads to structural
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modification of synapses by live, 2-photon imaging of GFP-labelled CA1 dendrites (Figure 1e).
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The volumes of all visible spines within the image were measured using SpineS, a custom in-
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house developed Matlab toolbox (Erdil et al., 2012). We found that spines from chronically
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TTX treated cells were significantly bigger than those from control cells beginning at 48 h
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(Figure 1e,f; Control = 0.136 ± 0.0062 µm³, TTX = 0.211 ± 0.0123 µm³). Surprisingly, as opposed
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to the linear functional scaling of mEPSCs seen in response to HSP, we found that structural
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scaling of spine volumes at 48 h are best fit to controls with a second order equation (Figure
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1g). This superlinear scaling resulted from a preponderance of large spines after TTX
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treatment, for which correspondingly large mEPSCs were not observed.
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After 72 h of activity blockade, synapses maintained the enhancement of mEPSC size (Figure
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1h; Mean ± SEM: control 72 h = 20.35 ± 0.27 pA, TTX 72 h= 22.18 ± 0.239 pA, p = 1.88e-15,
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Mann-Whitney) and spine volume increases (Figure 1i; Mean ± SEM: control 72 h= 0.16 ±
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0.0073 µm³, TTX = 0.19 ± 0.0093 µm³, p = 0.0008 Mann-Whitney). However, at this time,
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scaling was instantiated in a linear fashion at both the level of mEPSC amplitude and spine
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volumes (Figure 1j,k). This suggests that the expression of functional and structural scaling
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evolves dynamically over time in response to prolonged activity blockade.
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4
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Reversibility of homeostatic plasticity mediated structural changes
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Synaptic strength modifications that occur in response to activity blockade are reversible
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upon re-exposure of a circuit to activity (Desai et al., 2002; Wallace and Bear, 2004). We
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tested whether the structural changes that resulted following activity blockade were also
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reversible when activity is restored. After 48 h of homeostatic plasticity induction, by which
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time significant structural and functional scaling have occurred (Figure 1), we removed TTX
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allowing slices to resume activity and measured spontaneous firing using whole-cell patch
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clamp recordings (Figure 2a,b). Activity blockade for 48 h led to higher firing rates compared
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to untreated cells (Figure 2c; Control (median) = 1.33, IQ range = 0.11:18.83 spikes/min; TTX
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(median) = 13.33, IQ range = 11.5:21.06 spikes/min. p=0.03, Kruskal-Wallis post-hoc Dunn).
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To exclude the possibility that the higher firing rates we observed were due to a rebound after
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the acute withdrawal of TTX from the system, a set of control neurons were briefly incubated
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in TTX (2-4h, named “Acute TTX condition”). This manipulation did not significantly alter firing
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rates, which were similar to untreated controls (Figure 2c; Acute-TTX: med = 4.44, IQ range =
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2.0:29.33 spikes/min vs Control no-TTX: Median = 1.33, IQ range = 0.11:18.83 spikes/min,
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p>0.9 Kruskal-Wallis post-hoc Dunn). Thus, the firing rate changes we observed were the
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result of HSP and did not arise from the acute withdrawal of TTX. We then investigated
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whether the circuit would return to its original level of activity once neurons were released
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from blockade. Indeed, after having removed TTX for 48 h, firing rates were indistinguishable
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from controls (Figure 2c; Control (median) = 1.33, IQ range = 0.11:15.56. TTX reversal
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(median) = 1.67, IQ range = 0.194:11.76. p>0.05, Kruskal-Wallace post-hoc Dunn). We then
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examined whether structural modifications accompanied these firing rate changes, and
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observed a similar reversal in spine volumes (Figure 2d,e). TTX treated spines significantly
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reduced in size 48 h after TTX removal (Figure 2e; mean volume ± SEM: TTX 48 h = 0.21 ±
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0.0063 µm³; TTX 48 h reversal = 0.16 ± 0.0064 µm³; p=4.1852e-07). These findings support
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the idea that functional plasticity is matched by structural plasticity, and that spines sizes
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reversibly and accurately reflect the activity landscape.
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Enhanced Hebbian potentiation of small spines after HSP
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Functional plasticity can be enhanced upon homeostatic modulation in hippocampal slices
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(Arendt et al., 2013; Félix-Oliveira et al., 2014), but occlusion of LTP may also occur (Soares et
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al., 2017). Given our finding that robust growth of spines occurs during homeostatic plasticity,
5
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we wanted to determine whether individual inputs were able to undergo further activity-
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dependent structural plasticity. We therefore induced HSP in hippocampal slices for 48 h and
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followed this with synaptic potentiation at visually identified dendritic spines through 2-
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photon mediated glutamate uncaging (Figure 3a,b). This paradigm elicits potentiation and
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growth of only the stimulated input (Govindarajan et al., 2011; Harvey and Svoboda, 2007).
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We followed the growth of spines relative to their average baseline volumes, in both the TTX
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and control conditions (Figure 3c,d). During the initial 45 minutes post-stimulation, both TTX-
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treated and control spines grew to a similar extent, indicating that homeostatic structural
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scaling does not occlude activity-dependent structural plasticity (mean ± SEM; Control
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stimulated 45’= 1.45 ± 0.10; Control neighbors 45’= 1.08 ± 0.04; TTX stimulated 45’= 1.59 ±
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0.14; TTX neighbors 45’= 1.14 ± 0.04; p > 0.99) (Figure 3d). However, after 120 minutes, only
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the stimulated inputs in the TTX-treated neurons remain significantly larger than their
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neighbors (Figure 3d; mean ± SEM: TTX stimulated 120’= 1.53 ± 0.13; TTX neighbors 120’=
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1.16 ± 0.04), as control spines begin to return to their initial volume (Figure 3d; Control
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stimulated 120’= 1.30 ± 0.01; Control neighbors 120’= 1.14 ± 0.04). Although the TTX and
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control spines are not significantly different at 120’ (p = 0.1345, Mann Whitney), they begin
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to diverge, as seen relative to their respective neighbors. Thus, at scaled synapses, activity
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that would otherwise lead to short lived structural plasticity now elicits long lasting structural
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plasticity.
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Structural plasticity at individual inputs varies with activity and spine size. While weak
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stimulations preferentially affect small spines (Matsuzaki et al., 2004), strong stimuli can elicit
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structural plasticity across a variety of spine sizes (Govindarajan et al., 2011; Oh et al., 2013;
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Ramiro-Cortés and Israely, 2013). Our stimulated spines spanned a range of sizes, allowing us
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to test whether size interacted with prior expression of HSP when expressing synaptic
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potentiation and further spine growth (Figure 3e). We examined the amount of structural
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plasticity expressed by spines of different initial sizes after activity blockade. We found a
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negative correlation between a spine’s initial average value and its normalized final volume
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when the spine population had first undergone homeostatic plasticity, but not in the control
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population, indicating that spine volume is an important modulator of the potential for
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plasticity after HSP (Figure 3ef; r2 = 0.48 for TTX, p < 0.01, r2 = 0.06 for control, p > 0.3). To
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further examine how HSP modulates the size dependence of structural plasticity, we classified
6
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spines as ‘large’ if their initial volume was more than 150% of the median initial volume of all
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spines, and the remainder were placed in the ‘small’ category. Among the small spines, we
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observed a significant increase in the magnitude of LTP in the TTX condition compared to the
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controls (Figure 3g; p=0.046, 2-way repeated measures ANOVA). On the other hand, large
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spines expressed a short-lasting growth that quickly decayed to baseline and was not
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dependent on whether they had been subjected to activity blockade (Figure 3h; p=0.70 2-way
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repeated measures ANOVA). Therefore, small spines preferentially underwent long lasting
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structural plasticity after HSP. We further observed that small spines, which had undergone
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HSP, tended to show a greater degree of initial growth in response to the induction of
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plasticity (Figure 3g, time point 0). To quantify the dynamic growth of these spines, we
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analyzed high-speed images of the spine head taken throughout the stimulation period
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(approximately 20 Hz) and did not observe a significant difference in the growth curves
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between the control and TTX treated spines (Figure 4a,b). When we examined the rate of
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growth that each spine expressed in the first minute after the stimulation however, we found
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that TTX treated small spines grew more than control small spines (Figure 4c; p = 0.018, 1-
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way ANOVA with post-hoc Tukey’s), while large spines showed no difference between the
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two conditions. Therefore, glutamate stimulation leads to a sustained growth of
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homeostatically modified small spines, which may reflect prolonged signaling at these
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synapses. Together, these data indicate that HSP facilitates Hebbian plasticity, and that this
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is accomplished at the individual spine level through preferential structural plasticity of small
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inputs.
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Homeostatic plasticity facilitates the induction of Hebbian structural plasticity
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Having observed that small spines showed enhanced responses to stimulation after
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homeostatic plasticity, as reflected by a higher rate of growth and longer lasting structural
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plasticity (Figure 3g and 4c), we reasoned that these inputs may respond more robustly to a
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weaker stimulation. This is also supported by previous findings that loss of activity at
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individual inputs lowers their threshold for subsequent plasticity (Lee et al., 2010). To test this
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possibility, we applied a sub-threshold stimulation that utilizes a shorter laser pulse of 1 ms
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(instead of 4 ms) during the glutamate uncaging protocol, since this does not induce structural
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plasticity at spines (Govindarajan et al., 2011; Harvey and Svoboda, 2007). Indeed, control
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spines that underwent this sub-threshold stimulation showed only a transient post-stimulus
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growth that lasted 5 min, resulting in no long term plasticity (Figure 4d; Control spines, 1 ms
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stimulated vs neighbors: p > 0.05, 2-way repeated measures ANOVA, post hoc Bonferroni).
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These results were significantly different from what we had observed in response to the 4ms
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stimulation (Figure 4d; 1 ms stimulated vs 4 ms stimulated; p = 0.04, 2-way repeated
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measures ANOVA; compared to data from Figure 3c). In contrast to this, HSP modified spines
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grew significantly in response to the subthreshold stimulation and remained larger than their
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neighbors (Figure 4e; TTX spines, 1 ms stimulated vs neighbors p = 0.01 2-way repeated
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measures ANOVA, post hoc Bonferroni). Following TTX treatment, both weak and strong
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stimulations elicited similar levels of long lasting growth of spines (Figure 4e; 1ms stimulated
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vs 4 ms stimulated: p = 0.27, 2-way repeated measures ANOVA). Thus, homeostatic plasticity
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facilitates structural plasticity by lowering the threshold for stimulation, without affecting the
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magnitude of plasticity. In this way, HSP acts locally, in conjunction with activity, to increase
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the likelihood that an individual synapse will participate in the encoding of information.
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HSP influences structural plasticity of neighboring spines
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In addition to modifying synaptic inputs through scaling, homeostatic plasticity can also
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influence cellular firing rates by modulating the intrinsic excitability of neuronal membranes
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(Desai et al., 1999). We reasoned that such alterations could facilitate the expression of
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structural plasticity not only at stimulated spines but also at nearby inputs within the dendritic
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branch. To test this idea, we examined whether homeostatic plasticity altered neighboring
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spine volume dynamics following the potentiation of single inputs. We ranked neighboring
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spines according to their distance from the stimulated spine (with 1 representing the closest
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neighbor to a stimulated spine) and plotted their growth dynamics for two hours following
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the stimulation (Figure 5a). We found that spines located in close proximity to the stimulated
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spine increased in volume only in neurons that had first undergone homeostatic plasticity
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(compare the first 20 spines, from 0 to 60 minutes after stimulation, Figure 5a). We classified
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the unstimulated neighbors as “near” or “far” - located either within or beyond 5 µm of the
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stimulated spine respectively - and quantified spine volume changes over time (Figure 5b-d).
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As expected, none of the neighbors of stimulated spines changed significantly from their
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original size in untreated neurons (Figure 5b,c). However, after HSP, neighbors that were
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within 5 µm of the target spine exhibited significant growth in the 5 minutes following the
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stimulation (Figure 5b) and remained significantly larger than more distant spines (Figure
8
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5b,d; p = 0.001, 2-way repeated measures ANOVA). Interestingly, farther neighbors (located
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up to 20 µm away from the site of stimulation) tended to decrease in size for several minutes
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following activity, although this was not significantly different from baseline (Figure 5d). We
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next investigated whether there was a correlation between the structural dynamics of each
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stimulated spine and its neighbors. We calculated correlation coefficients between the
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volume change of the stimulated spine and those of its neighbors across the time-course of
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the experiment. While fluctuations in the volumes of neighboring spines in control conditions
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were independent of the stimulated input (Figure 5e; r2 = 0.00263, p = 0.61), spine volumes
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in TTX treated neurons changed in accordance with the stimulated spine (Figure 5f; r2 = 0.156,
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p < 0.001). Specifically, near TTX neighbors had a positive correlation with the stimulated
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input, reflecting growth, which eventually became a negative correlation at further distances
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from the stimulated spine. These findings indicate that HSP reduces the input specificity of
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activity in a distance dependent manner that is at once both cooperative with near, and
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competitive with far, inputs. This allows for homeostatic modulation to effect structural
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plasticity within a dendritic region through activity at a single spine, which favors clustered
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plasticity of synaptic inputs.
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Discussion
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Synaptic networks must balance the need to enhance efficacy during learning without
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saturating their capacity for further changes. Homeostatic plasticity can achieve this
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regulatory role by effecting a gain modulation on neurons in order to maintain synaptic
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activity within an optimal target range. It is unclear what are the consequences of
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implementing HSP for the network, and specifically, how its interaction with Hebbian
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plasticity impacts the subsequent encoding of information at the level of single inputs. Due
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to the linear relationship between synaptic structure and function, we used live 2-photon
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imaging and glutamate uncaging to probe the physical consequences of inducing homeostatic
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plasticity on a neuron, and to determine how this impacts the ability of single synapses to
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undergo further changes in efficacy. We show that homeostatic synaptic plasticity, induced
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by 48 hours of activity blockade, leads to the reversible growth of dendritic spines. We
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demonstrate that this form of modulation facilitates subsequent structural plasticity at single
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synapses and that this effect preferentially occurs at smaller inputs. After HSP, activity elicits
9
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a faster growth rate at these spines, and converts an otherwise subthreshold stimulation into
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one that is now capable of eliciting structural plasticity. Interestingly, we find that the
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induction of Hebbian plasticity on a background of homeostatic plasticity leads to
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compromised input specificity, as neighboring spines grow when they are located in close
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proximity to a stimulated synapse. Taken together, our results show that homeostatic
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plasticity can modulate a neuron’s response to activity by facilitating the sensitivity of smaller
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inputs and inducing structural plasticity at neighboring synapses.
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The structural scaling that we observe after 48 hours of activity blockade results in a
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non-linear upscaling of spines and an increased number of large spines (Figure 1g). By 72
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hours, this structural scaling becomes linear (Figure 1k), suggesting that the initial changes
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may represent a physical overshooting of the target size. This has also been observed on short
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timescales following glutamate stimulation of single spines, where an initial large volume
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change is followed by stabilization of the spine at a more modest size (Matsuzaki et al., 2004).
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Upon the reinstatement of activity, we find that spines return to their original size as firing
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patterns normalize by 48 hours (Figure 2c-e), indicating that homeostatic structural changes
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are plastic and reversible, similarly to homeostatic responses to fluctuating activity levels.
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We demonstrate that activity blockade increases spine sizes across the population,
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raising the question of whether further enhancement of potentiation and spine growth could
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be achieved across inputs of different sizes. Both enhancement and occlusion of plasticity
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have been reported following HSP at the population level (Arendt et al., 2013; Félix-Oliveira
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et al., 2014; Soares et al., 2017), but it is unclear how individual inputs are modulated. Further,
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while larger synapses have been shown to undergo functional homeostatic modulation
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(Thiagarajan et al., 2005), inputs show a size dependent variation in their ability to undergo
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Hebbian structural plasticity, large spines being more stable and requiring stronger
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stimulation in order to be potentiated (Govindarajan et al., 2011; Matsuzaki et al., 2004). We
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probed plasticity with glutamate uncaging and found that HSP leads to structural plasticity
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lasting over two hours preferentially at small spines, while control spines decay to baseline
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after one hour (Figure 3g,h). This suggests that a long lasting, protein synthesis dependent
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form of Hebbian plasticity was induced at these inputs (Govindarajan et al., 2011), supported
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by recent findings that TTX-mediated activity blockade leads to the specific production of
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plasticity related proteins (Schanzenbacher et al., 2018). Closer examination of the structural
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plasticity we induced revealed that the population of small spines express the majority of the
10
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growth, while large spines remain stable (Figure 3g,h). This result implies that plasticity at
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large spines is saturated after homeostatic modifications, and that their threshold for
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structural plasticity is not altered by HSP.
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Upon stimulation, we did not observe a significant difference in the magnitude of the
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potentiation that spines expressed, nor in their immediate response to the stimulation itself,
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but rather we found that spines post-HSP express a significantly faster growth rate compared
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to their counterparts in the first minute after stimulation (Figure 4a-c). This enhanced
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response may be due to amplified signaling cascades shared between these forms of plasticity
321
(Fernandes and Carvalho, 2016), which could facilitate the induction of long lasting structural
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plasticity. It was therefore not surprising to find that a subthreshold stimulation elicits long
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lasting growth only at inputs that have undergone homeostatic plasticity (Figure 4 d,e),
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without affecting the initial magnitude of the response between the HSP modified synapses
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and the control populations. Changes to NMDA receptor composition that occur following
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activity blockade could provide a means by which to enhance the calcium permeability of
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synapses and thus would allow for prolonged signaling responses (Barria and Malinow, 2005;
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Lee et al., 2010; Paoletti et al., 2013). Taken together, these data show that the effects of
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homeostatic plasticity preferentially impact small spines during Hebbian regulation of
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synaptic strength by predisposing them to undergo long lasting structural changes. Such
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modulation may result in the conversion of weaker stimuli into more salient forms, and
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proposes a more global role for HSP in information encoding beyond the optimization of
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neuronal activity.
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A hallmark of activity dependent changes during Hebbian plasticity is input specificity
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(Barrionuevo and Brown, 1983). In contrast, homeostatic plasticity is generally expressed over
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a wider synaptic range, and how this modulation impacts Hebbian learning rules at individual
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inputs is unknown (Vitureira and Goda, 2013). Computational studies have postulated that
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homeostatic plasticity can influence previous Hebbian events at a synapse (Rabinowitch and
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Segev, 2008). Additionally, several lines of evidence indicate that activity can lead to local
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homeostatic changes within dendrites (Branco et al., 2008; Ju et al., 2004; Liu, 2004; Sutton
341
et al., 2006). We therefore considered the possibility that HSP may function to influence
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subsequent Hebbian plasticity. Indeed, we find that HSP induces the spillover of Hebbian
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structural plasticity within the dendrite, as seen by the growth of neighboring unstimulated
344
spines following the activation of one input (Figure 5). Thus, homeostatic plasticity drives the
11
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
345
local expression of Hebbian plasticity and reduces input specificity. While cooperative
346
interactions have been shown to occur between inputs when multiple synapses are
347
stimulated (Govindarajan et al., 2011; Harvey and Svoboda, 2007), in the absence of such co-
348
activation, structural changes at neighbors have thus far served to counterbalance the
349
direction of plasticity (Oh et al., 2015). Our observations that HSP promotes activity-driven
350
growth of a group of synapses within a five micron area is in alignment with the observed
351
distance over which plasticity related proteins can spread between co-active synapses
352
(Harvey et al., 2008). Thus, the interaction between homeostatic and Hebbian plasticity may
353
coordinately delimit a region of clustered plasticity, which has been proposed to increase the
354
memory capacity of a neural circuit (Chklovskii et al., 2004; Govindarajan et al., 2011, 2006;
355
Ramiro-Cortés et al., 2014). Although clustered activity and its structural correlates have
356
begun to emerge (Fu et al., 2012; Kleindienst et al., 2011; Makino and Malinow, 2011; Yadav
357
et al., 2012), the mechanisms which drive the physical organization of inputs are unknown.
358
HSP may provide a basis for such organization by reducing the threshold for cooperativity
359
between inputs, allowing primed synapses located within several microns of an active spine
360
to be more easily potentiated. This may serve as a first step in the physical arrangement of
361
synapses into clusters. The broader consequence of this could be the binding together of
362
information of varying saliencies, within a delimited region, into the same engram.
363
Our finding that synaptic threshold modulation after HSP is implemented at small,
364
rather than at large spines, and in a reversible manner, suggests that synaptic scaling
365
mechanisms are separable from plasticity mechanisms. However, by promoting long-lasting
366
plasticity at select spines, and potentiating unstimulated neighboring spines within a
367
delimited dendritic region, homeostatic plasticity may interact with and reduce the input
368
specific nature of Hebbian plasticity, enhance the clustering of synaptic inputs, and shape the
369
long-term organization of neural circuits. In this way, despite the global nature of homeostatic
370
plasticity, inputs may be locally modulated in an activity-dependent manner.
12
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
371
Materials and Methods
372
1. Slice culture preparation and biolistic transfection
373
Mouse hippocampal organotypic slice cultures were prepared using p7-10 C57BL/6J mice as
374
previously described (Govindarajan et al., 2011). Briefly, hippocampi were dissected and 350
375
µm slices were cut with a tissue chopper in ice-cold artificial cerebral spinal fluid (aCSF)
376
containing 2.5 mM KCl, 26 mM NaHCO3, 1.15 mM NaH2PO4, 11 mM D-glucose, 24 mM
377
sucrose, 1 mM CaCl2 and 5 mM MgCl2. The slices were cultured on membranes (Millipore),
378
and maintained at an interface with the following media: 1x MEM (Invitrogen), 20% horse
379
serum (Invitrogen), 1 mM GlutaMAX (Invitrogen), 27 mM D-glucose, 30 mM HEPES, 6 mM
380
NaHCO3, 2mM CaCl2, 2mM MgSO4, 1.2% ascorbic acid, 1 µg/ml insulin. The pH was adjusted
381
to 7.3, and the osmolarity adjusted to 300–310 mOsm. All chemicals were from Sigma unless
382
otherwise indicated. Media was changed every 2-3 days.
383
Biolistic transfection of slice cultures was accomplished using a Helios gene gun (Bio-Rad)
384
after 4–7 days in vitro (DIV). Gold beads (10 mg, 1.6 µm diameter, Bio-Rad) were coated with
385
100 mg AFP-plasmid DNA (a GFP-expressing plasmid driven by the β-actin promoter (Inouye
386
et al., 1997) according to the manufacturer’s protocol and delivered biolistically to the slices,
387
using a pressure of 160-180 psi.
388
2. Homeostatic plasticity induction by activity block
389
TTX (1 µM) was added to the culture media at 7-9 DIV. The day of application was then
390
designated day 0 for experiments. Control experiments were maintained in normal culture
391
media, and were age- and animal-matched to treated slices for experiments.
392
3. Patch Clamp Electrophysiology
393
Hippocampal slice cultures were perfused continuously with aCSF (as above, with the addition
394
of 0.5 µM TTX for all mEPSC recordings) for a pre-incubation period of 15 to 30 min. Whole
395
cell voltage-clamp recordings were performed in CA1 pyramidal neurons, using 7–8 MΩ
396
electrodes. For mEPSC recordings, the internal solution contained 135 mM Cs-
397
methanesulfonate, 10 mM CsCl, 10 mM HEPES, 5 mM EGTA, 2 mM MgCl2, 4 mM Na-ATP and
398
0.1 mM Na-GTP, with the pH adjusted to 7.2 with KOH, at 290-295 mOsm. Cells were voltage
399
clamped at -65 mV. Cellular recordings in which series resistance was higher than 25 mV were
13
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
400
discarded. Stability was assessed throughout the experiment, with cells whose series
401
resistance changed more than 30% being discarded. mEPSCs recordings were started 3
402
minutes after break-in and continued for 10 minutes. Signals were acquired using a
403
Multiclamp 700B amplifier (Molecular Devices), and data was digitized with a Digidata 1440
404
at 3 kHz. mEPSC events were detected off-line using Mini-Analysis Program (Synaptosoft).
405
Events smaller than 15 pA fell within the range of noise in the system and were not included
406
in the analysis. For spontaneous activity recordings, slices were perfused continuously with
407
aCSF without the addition of TTX for a pre-incubation period of 5 to 10 min. The internal
408
solution for the electrodes contained 136.5 mM K-Gluconate, 9 mM NaCl, 17.5 mM KCl, 10
409
mM HEPES, 0.2 mM EGTA, and 0.025 mM Alexa 594, with the pH adjusted to 7.2 with KOH,
410
at 280-290 mOsm. In current clamp with no external current applied, an IV curve was first
411
recorded to check for spike frequency accommodation in order to validate the identity of
412
pyramidal neurons. Spiking events were then recorded for a period of 6-9 minutes. The
413
addition of Alexa-594 allowed cells to be imaged post-recording.
414
4. Two-photon Imaging
415
Two-photon imaging was performed on a BX61WI Olympus microscope, using a
416
galvanometer-based scanning system (Prairie Technologies /Bruker) with a Ti:sapphire laser
417
(910 nm for imaging AFP; Coherent), controlled by PrairieView software (Prairie
418
Technologies). Slices were perfused with oxygenated aCSF containing 127 mM NaCl, 2.5 mM
419
KCl, 25 mM NaHCO3, 1.25 mM NaH2PO4, 25 mM D-glucose, 2 mM CaCl2, 1 mM MgCl2 and 0.5
420
µM TTX (equilibrated with O2 95%/CO2 5%) at room temperature, at a rate of 1.5 ml/min.
421
Secondary or tertiary apical dendrites of CA1 neurons (where the apical trunk is counted as
422
the primary branch) were imaged using a water immersion objective (60x, 1.0 NA, Olympus
423
LUMPlan FLN) with a digital zoom of 8x. For each neuron, 2-3 dendrites were imaged. Z-stacks
424
(0.5 µm per section) were collected at a resolution of 1024 x 1024 pixels, resulting in a field
425
of view of 25.35 x 25.35 µm. 3 images were taken per dendrite at 5-minute intervals, with the
426
reported spine volume being the average of the 3 images. Images were taken at the highest
427
possible fluorescence intensity without image saturation in order to accurately quantify spine
428
volumes (see below).
14
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
429
5. Glutamate uncaging
430
Uncaging experiments (Pettit et al., 1997) and caged glutamate calibration were carried out
431
as previously described (Govindarajan et al., 2011), and briefly as follows. MNI-caged-L-
432
glutamate (MNI-Glu) (Tocris) was reconstituted in the dark in aCSF lacking MgCl2 or CaCl2 to
433
make a 10 mM stock solution. Individual aliquots were diluted to the working concentration
434
of 2.5 mM MNI-Glu in uncaging aCSF (see below), in 3 ml volumes. We tested each batch of
435
reconstituted MNI-Glu as previously described (Govindarajan et al., 2011). Briefly, five
436
uncaging test pulses of 1 ms were delivered to single spines and evoked EPSCs were measured
437
by whole cell patch clamp recordings. We compared these to spontaneous mEPSCs, and
438
determined the power needed (60mW at the back aperture) to produce an uncaging EPSC of
439
comparable size to that of an average spontaneous mEPSC. During plasticity experiments,
440
slices were incubated for 30-45 minutes in normal aCSF as described above. Uncaging was
441
performed using a Ti:sapphire laser (720 nm; Coherent), controlled by PrairieView software
442
(Prairie Technologies, Bruker). All stimuli were carried out in uncaging-aCSF containing: 2.5
443
mM MNI-Glu, 0 mM MgCl2, and 4 mM CaCl2. The uncaging train consisted of 30 pulses at 0.5
444
Hz, with a pulse width of either 4 ms (standard protocol) or 1 ms (sub-threshold protocol),
445
using 30mW power as measured at the back aperture (half the power as determined in the
446
calibration step, as previously described for an uncaging LTP protocol (Govindarajan et al.,
447
2011)). The uncaging point was positioned 0.6 µm from the end of the spine head, away from
448
the parent dendrite. Each experiment began with a sham stimulation in uncaging-aCSF lacking
449
MNI-Glu on a control dendrite of the experimental neuron, to rule out the possibility of non-
450
specific structural changes due to phototoxicity or poor neuronal health. Subsequently,
451
experimental spines on new dendrites were identified, uncaging-aCSF containing 2.5mM
452
MNI-glutamate was recirculated for 5 minutes, and the uncaging protocol was delivered. Fast
453
imaging (approximately 20 Hz) of a region of interest (ROI) of the stimulated spine head and
454
neck was performed throughout the 60 second stimulation, to record the growth dynamics
455
for this time period. After the stimulation, the perfusion was returned to normal aCSF for the
456
remainder of the experiment (1-2 hours). The first image was taken immediately after
457
returning to normal aCSF and is designated as time = 0 post stimulation.
15
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458
6. Spine Volume Determination
459
To quantify spine volume, we used the custom built Matlab plug-in SpineS, which uses semi-
460
automatic detection, automatic alignment and segmentation of spine heads (Erdil et al., 2012;
461
Ghani et al., 2017). Spine volume was calculated using the summed fluorescence intensity of
462
the spine, normalized to the median fluorescence intensity of the parent dendrite, in order
463
to correct for changes in overall fluorescence levels within a cell. Fluorescence intensity was
464
converted to real volumes by taking Full Width Half Max (FWHM) measurements of spines
465
and calculating a conversion factor between the two measures (Matsuzaki et al., 2004). For
466
the homeostatic plasticity analysis (Figures 1 & 2), all spines with a discernible head within
467
the field of view were included in the analysis, unless obstructed by other structures. For the
468
uncaging analysis (Figures 3, 4 & 5), between 2 and 8 neighboring spines were analyzed from
469
the same dendrite, within the whole field of view. Normalization of spine volumes throughout
470
the
experiment
was
performed
using
the
mean
of
three
baseline
images.
471 472
7. Statistical analyses
473
All statistical analyses were carried out in Graphpad Prism. Stars (*) represent degrees of
474
significance as follows: (*) = p < 0.05; (**) = p < 0.01; (***) = p < 0.001).
475
476
Acknowledgements
477
We thank Ali Ozgur Argunsah for his advice and help with data analysis. We thank Steven
478
Kushner, Rui Costa, and members of the Israely lab for their support and critical reading of
479
the manuscript. This work was supported by grants from the Bial Foundation (to II), Fundação
480
para a Ciência e a Technologia (to II and AH), and CONACYT 254878 (to YRC).
481 482
Author Contributions:
483
AFH, YRC and II designed the experiments. AFH performed the experiments and analyzed
484
the data. AFH, YRC and II wrote the manuscript.
16
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485
486
Competing interests
487
The authors declare no competing interests
17
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Figure 1
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bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Figure 1. Spines undergo structural scaling following activity blockade
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a) Experimental protocol to induce HSP in hippocampal organotypic slices. b) Example mEPSC
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recording traces from control and TTX-treated conditions at the 48 h time point. Bottom:
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representative individual mEPSCs. c) Quantification of mEPSC amplitudes after 48 h of activity
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blockade, represented as mean amplitudes ± SEM. ***p = 1.553e-08, Mann-Whitney. For all
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data presented, total number of spines or mEPSCs are represented by the first number (n)
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and followed by the number of independent neurons (N = in parentheses) from which they
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were collected. Number of mEPSCs (n) from independent neurons (N): Control = 552 (8), TTX
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= 742(8). d) Ranked control mEPSC amplitudes plotted against TTX condition at 48 h. Best fit
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line to the data: TTX = Control x 1.45 – 6.06. e) Representative images of dendrites at either
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0 or 48 h after TTX treatment or in control media. Asterisks indicate all the spines that were
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analyzed. Scale bar = 5µm. f) Quantification of spine volumes for the indicated conditions.
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***p = 0.91e-10, Two-way ANOVA, post-hoc Bonferroni. Number of spines (n) from
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independent neurons (N) for the 0 h, 24 h and 48 h timepoints: Control = 103(7), 245(8), 285
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(7). TTX = 172 (7), 232 (5), 208 (6). g) Ranked control spine volumes plotted against TTX
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condition at 48 h. Best fit line to the data: TTX = Control2 x 5.44 + Control x 0.25 + 0.55. h)
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Quantification of mEPSC amplitudes after 72 h in TTX. ***p = 1.883e-15, Mann-Whitney.
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Number of mEPSCs (n) from independent neurons (N): Control = 1164 (10), TTX = 1302 (12).
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i) Quantification of spine volume after 72 h in TTX. ***p = 0.0008, Mann-Whitney. Number of
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spines (n) from independent neurons (N): Control = 258 (6), TTX = 214 (6). j) Ranked control
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72 h mEPSC amplitudes plotted against TTX mEPSC amplitudes. Best fit line to the data: TTX
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= Control x 1.10 – 0.01. k) Ranked control 72 h spine volumes plotted against TTX 72 h spine
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volumes. Best fit line to the data: TTX = Control x 1.26 – 0.004).
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bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
644
Figure 2
645
25
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
646
Figure 2 Structural and functional changes after HSP are reversible
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a) Experimental timeline for reversal experiments. b) Example traces showing cell firing
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following 48 h of activity block. Spikes are demarcated with black circles. c) Quantification of
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spikes per minute throughout experiment. *p48 control – 48 TTX = 0.03, Kruskal-Wallis post hoc
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Dunn. **p48 TTX – 48 post TTX = 0.010, Kruskal-Wallis post hoc Dunn. Number of neurons: 48h TTX
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condition: 48 h Control = 17, 48 h Acute TTX = 20, 48 h TTX = 26; 48h ‘post-TTX’ Control = 15,
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48 h post-TTX Reversal = 18. d) Representative images from dendrites after 48 h of HSP
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induction and at 48 h post TTX. Scale bar = 5µm. e) Quantification of spine sizes throughout
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the experiment. Graph is plotted as mean ± SEM. All p values calculated using Kruskal-Wallis
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test, post-hoc Dunn’s. ***p48 TTX – 48 post TTX = 4.1852e-07. Number of spines (n = first number)
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of Neurons (N = in parentheses): 48 h Control = 285 (7), 48 h TTX = 208 (6), 48 h ‘post-TTX’
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Control = 514 (14), 48 h post-TTX = 430 (15).
658
26
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
659 660 661
Figure 3
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bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
662
Figure 3. Potentiation of single inputs is enhanced at smaller spines following HSP
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a) Timeline for uncaging experiments. b) Representative images of structural plasticity
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following single spine glutamate uncaging. Arrowheads and dots indicate stimulated and
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neighboring non-stimulated spines respectively. Scale bar = 5µm (main image), 1 µm (inset).
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c) Normalized volume of stimulated and neighboring spines for control and TTX-treated
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conditions over 2 hours of LTP induction. Volumes were calculated from Z-stacks taken in 5
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minute bins from time point 0 (thus the stack represented as 0 was collected between 0-5
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minutes, for example). For all data, the total number of spines are represented by the first
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number (n), and followed by the number of independent neurons (N = in parentheses) from
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which they were collected. Control Stimulated = 17 (17), TTX Stimulated = 18 (18), Control
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neighbors = 85 (17), TTX neighbors = 102 (18). d) All analyzed stimulated and neighboring
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spine volumes at time points 45 minutes and 120 minutes post stimulation. Significance was
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calculated using one-way ANOVA post-hoc Bonferroni. Control condition: **pstimulated45
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neighbors45 = 8.4246e-04. pstimulated120 – neighbors120 = 0.6881. TTX condition: ***pstimulated45 – neighbors45
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= 2.9383e-04. **pstimulated120 – neighbors120 = 0.0046. (n same as in panel c). e) Initial absolute spine
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size vs. normalized spine volume at 120 minutes. TTX spines linear regression: r2 = 0.48, **p
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= 0.002. Control linear regression: r2 = 0.06, p = 0.346. f) Distribution of all initial volumes of
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stimulated spines, with example spine images. The cut-off for defining ‘large’ spines was the
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median volume off all spines multiplied by 1.5. Scale bar = 1 µm. g) Time-course of the
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structural LTP experiment plotting only the small spines. *p = 0.0458, 2-way repeated
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measures ANOVA). Number of spines (n) from neurons (N = in parentheses): Control = 13 (13),
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TTX = 11 (11). h) Time-course of structural LTP plotting only large spines. p = 0.699, 2-way
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repeated measures ANOVA. Number of spines (n) from neurons (N = in parentheses): Control
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= 4 (4), TTX = 17 (17).
–
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28
bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Figure 4
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bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
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Figure 4. HSP increases the efficacy and reduces the threshold for induction of LTP at
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individual spines
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a) Representative image of a single spine during the course of uncaging. Scale bar = 5µm (main
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image), 1µm (inset). b) Individual traces of spine growth during glutamate uncaging
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stimulation. Control spine growth vs TTX spine growth: p = 0.198, 2-way repeated measures
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ANOVA. Number of spines (n): Control = 16, TTX = 18. c) Growth rates of stimulated spines
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for 1 minute after the end of stimulation. *psmall control–small TTX = 0.018, 1-way ANOVA with post-
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hoc Tukey’s. plarge control–large TTX < 0.99, 1-way ANOVA with post-hoc Tukey’s. Number of spines
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(n): Control small = 13, TTX small = 11, Control large = 4, TTX large = 7. d) Quantification of
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normalized spine volume with different stimulation pulse durations in the control condition.
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p1ms
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Number of spines (n) from Neurons from which they were collected (N = in parentheses):
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stimulated 1ms = 11 (11), neighbors 1ms = 52 (11), stimulated 4ms = 17 (17). *p1ms stimulated–
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4ms stimulated
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Quantification of normalized spine volume with different stimulation pulse durations in the
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TTX condition. **p1ms stimulated–1ms neighbors = 0.007, 2-way rm ANOVA. p1ms stimulated– 4ms stimulated =
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0.27, 2-way rm ANOVA). Number of spines (n) from Neurons (N): stimulated 1ms = 11 (11),
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neighbors 1ms = 52 (11), stimulated 4ms = 18 (18). Note 4ms data is the same as in Figure 3.
stimulated–1ms neighbors
= 0.292, 2-way repeated measures ANOVA post-hoc Bonferroni.
= 0.039 2-way rm ANOVA. Note 4ms data is the same as shown in Figure 3. e)
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bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
706
Figure 5
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bioRxiv preprint first posted online Apr. 26, 2018; doi: http://dx.doi.org/10.1101/308965. The copyright holder for this preprint (which was not peer-reviewed) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. All rights reserved. No reuse allowed without permission.
707
Figure 5. Stimulation of single inputs leads to plasticity of clustered neighbors after HSP
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a) Heat maps of growth dynamics of neighboring spines over time. Neighbors from all
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experiments were pooled and ranked in order distance from the stimulated spine. Index 1 is
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the spine nearest to its stimulated spine, and 80 is the furthest away. Heat map = normalized
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spine volume. Number of spines (n) from Neurons from which they were collected (N = in
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parentheses): Control = 80 (17), TTX = 80 (18). b) Mean volumes for the first 10 minutes
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following stimulation for the different neighboring conditions. ***pTTX near – TTX far = 1.0674e-
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05, Kruskal-Wallis. Number of spines (n) from Neurons from which they were collected (N =
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in parentheses): Control near = 22 (17), control far = 63 (17), TTX near = 32 (18), TTX far = 70
716
(18). c) Normalized volumes of near and far neighboring spines in the control condition. p =
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0.987, 2-way rm ANOVA. Number of spines – same as above. d) Normalized volumes of
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neighboring spines in the TTX condition. *p = 0.0124, 2-way repeated measures ANOVA.
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Number of spines – same as above. e) & f) Correlation coefficients of volume change of
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stimulated spines vs volume change of neighboring spine, plotted against the distance
721
between the neighboring spine and the stimulated spine. e) Linear regression control: r2 =
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0.003, p = 0.641. f) Linear regression TTX: r2 = 0.156, ***p = 3.91e-05).
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