Copyright © 2020 the authors

Research Articles: Development/Plasticity/Repair

Activity dependent and independentdeterminants of synaptic size diversity

https://doi.org/10.1523/JNEUROSCI.2181-19.2020

Cite as: J. Neurosci 2020; 10.1523/JNEUROSCI.2181-19.2020

Received: 10 September 2019Revised: 4 February 2020Accepted: 13 February 2020

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JN-RM-2181-19R2 Activity dependent and independent determinants of synaptic size diversity Liran Hazan1 and Noam E. Ziv1,2 1Technion Faculty of Medicine, Rappaport Institute and Network Biology Research Laboratories, Fishbach Building, Technion City, Haifa, 32000, Israel. 2 Corresponding author: Noam E. Ziv Technion Faculty of Medicine and Network Biology Research Laboratories, Fishbach Building Technion city Haifa 32000, Israel noamz@netvision.net.il Abbreviated title: Determinants of synaptic size diversity Number of Pages: 48 Number of Figures: 12 Number of words:

Abstract: 249 Introduction: 648 Discussion: 1498

The authors declare no competing financial interests Acknowledgements We are grateful to Tamar Galateanu, Leonid Odesski, Ayub Bolous, Tamar Ziv and the Smoler Proteomics Center, as well as members of the Ciechanover lab for their invaluable assistance. We are also grateful to Naama Brenner, Omri Barak and Aseel Shomar for many helpful discussions. We are particularly grateful to an anonymous reviewer for suggesting the formulation of the Kesten process as a non-linear Langevin process. This work was supported by funding from the Israel Science Foundation (1175/14; 1470/18), The Rappaport Institute, the Allen and Jewel Prince Center for Neurodegenerative Disorders of the Brain and the state of Lower-Saxony and the Volkswagen Foundation, Hannover, Germany. 1 2

2

Abstract 3

The extraordinary diversity of excitatory synapse sizes is commonly attributed to activity- 4

dependent processes that drive synaptic growth and diminution. Recent studies also point to 5

activity-independent size fluctuations, possibly driven by innate synaptic molecule dynamics, 6

as important generators of size diversity. To examine the contributions of activity-dependent 7

and independent processes to excitatory synapse size diversity, we studied glutamatergic 8

synapse size dynamics and diversification in cultured rat cortical neurons (both sexes), 9

silenced from plating. We found that in networks with no history of activity whatsoever, 10

synaptic size diversity was no less extensive than that observed in spontaneously active 11

networks. Synapses in silenced networks were larger, size distributions were broader, yet 12

these were rightward-skewed and similar in shape when scaled by mean synaptic size. 13

Silencing reduced the magnitude of size fluctuations and weakened constraints on size 14

distributions, yet these were sufficient to explain synaptic size diversity in silenced networks. 15

Model-based exploration followed by experimental testing indicated that silencing- 16

associated changes in innate molecular dynamics and fluctuation characteristics might 17

negatively impact synaptic persistence, resulting in reduced synaptic numbers. This, in turn, 18

would increase synaptic molecule availability, promote synaptic enlargement, and ultimately 19

alter fluctuation characteristics. These findings suggest that activity-independent size 20

fluctuations are sufficient to fully diversify glutamatergic synaptic sizes, with activity- 21

dependent processes primarily setting the scale rather than the shape of size distributions. 22

Moreover, they point to reciprocal relationships between synaptic size fluctuations, size 23

distributions and synaptic numbers mediated by the innate dynamics of synaptic molecules 24

as they move in, out and between synapses. 25

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Significance Statement 35

Sizes of glutamatergic synapses vary tremendously, even when formed on the same neuron. 36

This diversity is commonly thought to reflect the outcome of activity-dependent forms of 37

synaptic plasticity, yet activity-independent processes might also play some part. Here we 38

show that in neurons with no history of activity whatsoever, synaptic sizes are no less 39

diverse. We show that this diversity is the product of activity-independent size fluctuations, 40

which are sufficient to generate a full repertoire of synaptic sizes at correct proportions. By 41

combining modeling and experimentation we expose reciprocal relationships between size 42

fluctuations, synaptic sizes and synaptic counts, and show how these phenomena might be 43

connected through the dynamics of synaptic molecules as they move in, out and between 44

synapses. 45

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Introduction 47

Properties of mammalian glutamatergic synapses can be extremely diverse. This diversity 48

is manifested in the broad distributions of many functional and morphological properties, 49

such as postsynaptic current amplitude, dendritic spine volume and postsynaptic density 50

(PSD) area. Such distributions are not only broad but also rightward skewed and heavy- 51

tailed, and are often described as log-normal (e.g. Murthy et al., 1997; Harms and Craig, 52

2005; Harms et al., 2005; Song et al., 2005; Arellano et al., 2007; Minerbi et al., 2009; Lefort 53

et al., 2009; Loewenstein et al., 2011; Ikegaya et al., 2013; Keck et al., 2013; Statman et al. 54

2014; Zhang et al., 2015; Cossell et al., 2015; Santuy et at., 2018; Ishii et al., 2018; Sammons 55

et al., 2018; Sakamoto et al., 2018; Masch et al., 2018; Wegner et al., 2018; Hobbiss et al., 56

2018; reviewed in Barbour et al., 2007; Buzsáki and Mizuseki, 2014; Scheler, 2017). Such 57

distributions, reflecting of a majority of weak/small synapses and a diminishing tail of 58

increasingly stronger/larger synapses, were suggested to optimize storage capacity, 59

neuronal firing rates and long-distance information transfer and thus impart important 60

properties to neuronal networks (Song et al., 2005; Barbour et al., 2007; Lefort et al., 2009; 61

Ikegaya et al., 2013; Buzsáki and Mizuseki, 2014; Scheler, 2017; Humble et al., 2019). 62

The diversity of synaptic sizes reflected in these distributions is commonly assumed to 63

result from activity-dependent synaptic plasticity that drives the growth of some synapses 64

and the downsizing of others. Moreover, the skewed shape of these distributions is assumed 65

to reflect the cumulative outcome of such processes (van Rossum et al., 2000; Song et al., 66

2005; Lefort et al., 2009; Gilson and Fukai, 2011; Zheng et al., 2013; Buzsáki and Mizuseki, 67

2014; Effenberger et al., 2015; Scheler, 2017; Uzan et al., 2018). Somewhat unexpectedly, 68

however, synaptic size diversity does not seem to be markedly reduced in animals that 69

develop in the complete absence of synaptic transmission (Sando et al., 2017; see also Sigler 70

et al., 2017; Lu et al., 2013), echoing findings of earlier cell-culture studies (e.g. Harms and 71

Craig, 2005; Harms et al., 2005; Yasumatsu et al., 2008). 72

Longitudinal in-vitro and in-vivo imaging reveals that sizes of individual glutamatergic 73

synapses fluctuate considerably over time scales of hours and days (e.g. Yasumatsu et al., 74

2008; Minerbi et al., 2009; Loewenstein et al., 2011; Kaufman et al., 2012; Fisher-Lavie and 75

Ziv 2013; Cane et al., 2014; Ishii et al., 2018; reviewed in Ziv and Brenner, 2018). Importantly, 76

such fluctuations persist following abrupt suppressions of network activity or synaptic 77

transmission (Yasumatsu et al., 2008; Minerbi et al., 2009; Dvorkin and Ziv, 2016). These 78

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intrinsic fluctuations, probably driven by the innate dynamics of synaptic molecules – 79

binding, unbinding and turnover (Kasai, 2010; Fisher-Lavie and Ziv, 2014; Shomar et al., 80

2017; Triesch et al., 2018) – were suggested to drive synaptic size diversification and 81

determine the shape and scale of size distributions (Yasumatsu et al., 2008; Minerbi et al., 82

2009; Kasai, 2010, Loewenstein et al., 2011; Kaufman et al., 2012; Statman et al., 2014; 83

Shomar et al., 2017; Ishii et al., 2018; Ziv and Brenner 2018; Humble et al., 2019). It remains 84

unclear, however, if intrinsic size fluctuations are indeed sufficient to give rise to a full 85

repertoire of synaptic sizes and at the right proportions. 86

Given the significance attributed to synaptic ‘weights’, understanding the fundamental 87

forces that drive synaptic size diversification and define proportions of differently sized 88

synapses would seem to be important. We therefore set out to examine the contributions of 89

activity-dependent and -independent processes to synaptic size diversification. We first 90

asked whether intrinsic, activity-independent size fluctuations are sufficient to give rise to a 91

full repertoire of synaptic sizes. We then examined how innate processes that drive intrinsic 92

fluctuations might set the shape and scale of synaptic size distributions and define the sizes 93

of synaptic populations. Finally, we studied interrelationships between these processes and 94

how these are affected by network activity. 95

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Materials and Methods 97

Experimental design and statistical analyses 98

Due to the long duration of each experiment (~1 week), data could not be collected as 99

age-matched pairs from the same cell culture preparations. Thus, individual experiments 100

typically came from separate cell culture preparations, resulting in extensive sampling of 101

preparations, reducing sensitivity to this source of variability. Comparisons between 102

treatments were typically based on tens (neurons) or thousands (synapses) of data points 103

except for biochemical and proteomic studies (Fig. 8) which were based on 2(7) and 2(4) 104

separate experiments (replicates), respectively. 105

Statistical tests used were based on minimal assumptions. Specific tests used and 106

significance values are provided in the main text and figure legends. Error bars are either 107

Standard Deviation or Standard Error of the Mean (SEM) as indicated in legends. 108

All software used for simulations of Fig. 5 and 6 (Visual Basic for Applications) and Figs. 109

7,9,10 (C code), data used to create all plots and the full proteomic dataset is available upon 110

request. 111

112

Cell culture 113

Primary cultures of rat cortical neurons were prepared as described previously (Minerbi 114

et al., 2009) using a protocol approved by the Technion committee for the supervision of 115

animal experiments (IL-116-08-71). Briefly, cortices of newborn (1 day-old) Wistar rats 116

(either sex; Charles River, UK) were dissected, dissociated by trypsin treatment followed by 117

trituration using a siliconized Pasteur pipette. A total of 1–1.5x106 cells were then plated on 118

thin-glass multielectrode array (MEA) dishes (MultiChannelSystems—MCS, Germany), pre- 119

coated with polyethylenimine (Sigma) to facilitate cell adherence. The preparations were 120

then transferred to a humidified tissue culture incubator and maintained at 37°C in a gas 121

mixture of 5% CO2, 95% air, and grown in medium containing minimal essential medium 122

(MEM, Sigma), 25 mg/l insulin (Sigma), 20 mM glucose (Sigma), 2 mM L-glutamine (Sigma), 5 123

mg/ml gentamycin sulfate (Sigma) and 10% NuSerum (Becton Dickinson Labware). 7 days 124

after plating, half of the culture medium was replaced with feeding medium similar to the 125

medium described above, but devoid of NuSerum, containing a lower L-glutamine 126

concentration (0.5 mM) and 2% B-27 supplement (Invitrogen). About half of the medium 127

was then replaced three to four times a week. 128

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129

DNA constructs, lentivirus production and transduction 130

A third generation lentiviral expression system was used to introduce exogenous DNA 131

into rat cortical neurons. The vector used here {FU(PSD-95:EGFP)W} was described in detail 132

in Minerbi et al., (2009). Lentiviral particles were produced using a mixture of the expression 133

vector and the packaging vector mix of the ViraPower plasmid lentiviral expression system 134

(Invitrogen). HEK293T cells were co-transfected with a mixture of FU(PSD-95:EGFP)W and 135

the three packaging plasmids: pLP1, pLP2, and pLP\VSVG. Transfection was performed in T75 136

flasks when the cells had reached 80% confluence, using 3 μg of the vector, 9 μg of the 137

packaging mixture, and 36 μl of Lipofectamine 2000 (Invitrogen). Supernatant was collected 138

after 48 and 72h, filtered through 0.45-μm filters, aliquoted, and stored at −80°C. 139

Transduction of cortical cultures was performed on day 4-5 in vitro by adding 20μl of the 140

filtered supernatant to each MEA dish. 141

Pharmacological manipulations 142

To chronically silence network activity, a mixture of three pharmacological agents was 143

used: TTX (Alomone Labs), APV (Sigma-Aldrich) and CNQX (Sigma-Aldrich). The agents were 144

first applied on day one in vitro, and additionally applied to feeding media every three 145

consecutive days to maintain the same concentration in media. Final concentrations in the 146

MEA dish were 1 μM (TTX), 10 μM (CNQX) and 50 μM (APV). These agents were also added 147

to the perfusion media during long term imaging sessions. 148

Electrophysiological recordings 149

Network activity was recorded continuously from MEA electrodes (59 electrodes, 30μm 150

diameter, arranged in an 8x8 array, spaced 200μm apart). A submerged platinum wire loop 151

connected to a custom designed cap covering the MEA dish was used as a common 152

reference (ground). Recordings from MEA dishes were performed using a commercial 60- 153

channel headstage (inverted MEA-1060-BC, MCS) with a gain of 53x and frequency limits of 154

0.02 to 8,500 Hz. This signal was further filtered with frequency limits of 150 to 3,000 Hz and 155

amplified (20x) using a filter/amplifier (FA60S-BC, MCS). The 60 channels of amplified and 156

filtered data were connected to 60 of the 64 analog to digital input channels of a data 157

acquisition board (PD2-MF-64-3M/12; United Electronic Industries, Walpole, MA, USA) using 158

a home built connection box. Data acquisition was performed using custom software (Closed 159

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Loop Experiment Manager – CLEM; Hazan and Ziv, 2017). Data were collected at 16 160

kSamples/sec. Action potentials were identified as negative threshold-crossing events, with 161

the threshold calculated as 5x root-mean-square of traces recorded at the beginning of each 162

experiment. Data were imported, converted and analyzed using custom scripts in Matlab 163

(MathWorks, USA). 164

Long-term imaging 165

All fluorescence and bright-field images were obtained from neurons growing on thin 166

glass MEA dishes, as described above. These particular dishes are fabricated of very thin 167

glass (180 μm), which allows for the use of high numerical aperture, oil immersion objectives 168

and are thus ideally suited for high-resolution imaging. Images were acquired using a 169

custom-built confocal laser scanning (inverted) microscope based on a Zeiss Axio Observer 170

Z1 using a 40×, 1.3 N.A. Plan-Fluar objective. The system was controlled by custom software 171

and includes provisions for automated, multisite time-lapse microscopy. MEA dishes were 172

mounted on the headstage/amplifier which was attached to the microscope’s motorized 173

stage. The dish was covered with a custom-designed cap containing inlet and outlet ports for 174

perfusion and air as well as a reference ground electrode as mentioned above. Continuous 175

perfusion with fresh feeding medium (described above) was carried out at a rate of 4ml per 176

day using an ultra-low-flow peristaltic pump (Instech Laboratories), and a pair of silicon 177

tubes. The tubes were connected to the dish through the appropriate ports in the custom- 178

designed cap. A mixture of 95% air and 5% CO2 was continuously streamed into the dish at 179

very low rates through a third port, with flow rates regulated by a high-precision flow meter 180

(Gilmont Instruments). The base of the headstage/amplifier and the objective were heated 181

to 37°C and 36°C, respectively, using resistive elements, separate temperature sensors, and 182

controllers, resulting in temperatures of approximately 37°C in the culture medium. Images 183

of PSD-95:EGFP were obtained by excitation at 488nm using a solid state continuous wave 184

laser (Coherent) and emissions were read simultaneously through a 500–550-nm bandpass 185

filter (Semrock, USA) and >570nm (Chroma) after splitting the emission between two 186

detectors using a 555nm longpass filter (Chroma). Time-lapse recordings were usually 187

performed by averaging five frames at 10 focal planes spaced 0.8 μm apart. All data were 188

collected at a resolution of 640×480 pixels, at 12 bits/pixel. Data were collected sequentially 189

from multiple sites using a motorized stage to cycle automatically through these sites at 60- 190

9

min intervals. Focal drift was corrected automatically by using the confocal microscope 191

autofocus system. 192

Fluorescence recovery after photobleaching 193

Photobleaching was performed by defining 16x16 pixel (~3.2 x 3.2μm) regions of interest 194

and scanning them repeatedly at 488nm at high illumination intensity using the imaging 195

systems’ acousto-optical tunable filter (AOTF) to limit illumination to the defined regions. 196

Photobleaching was controlled through the confocal microscope’s ActiveX interface from 197

scripts written in Visual Basic for Applications executed in Microsoft Excel. Fluorescence of 198

each photobleached synapse was normalized (Ft, norm) according to 199

, = −− Where Ft is the fluorescence at time t, Fmin is fluorescence at the end of the photobleaching 200

procedure and F0 is the fluorescence just before the photobleaching procedure. 201

202

Image analysis 203

All image analysis was performed using custom written software ("OpenView") which 204

allows for automated or manual tracking of individual fluorescent puncta and measuring 205

their fluorescence intensities over time (see Kaufman et al., 2012 for further details). 9 × 9 206

pixel (~1.8 x 1.8μm) areas were centered on fluorescent puncta and mean pixel intensities 207

within these areas were obtained from maximal intensity projections of Z section stacks. For 208

measuring distributions of puncta intensities, areas were placed programmatically on 209

fluorescent puncta at each time step using identical parameters. For tracking identified 210

puncta, areas were placed initially over all puncta and then a smaller subset (typically 200 211

per site) was tracked thereafter. As the reliability of automatic tracking was not absolute, all 212

tracking was verified and, whenever necessary, corrected manually. Puncta for which 213

tracking was ambiguous were excluded. 214

To correct for some neuron to neuron variability in PSD-95:EGFP expression levels, raw 215

puncta fluorescence measurements were normalized to mean PSD-95:EGFP puncta 216

fluorescence of each neuron at the first time point (determined by placing areas 217

programmatically on fluorescent puncta in the field of view), allowing us to pool data from 218

different neurons and experiments. 219

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Images for figures were processed by uniform contrast enhancement and low pass 220

filtering using Adobe Photoshop and prepared for presentation using Microsoft PowerPoint. 221

222

Western blots 223

Cortical cell preparations were grown in 12-well plates whose surface had been 224

pretreated with polyethylenimine (Sigma) to facilitate cell adherence. Cells were washed 225

using Tyrode’s solution (119mM NaCl, 2.5mM KCl, 2mM CaCl2, 25mM HEPES, 30mM glucose, 226

buffered to pH 7.4) and lysed in RIPA buffer, 8M urea, 100 mM Tris–HCl. Protein 227

concentrations were measured by the Bradford assay, using BSA as the standard. Equal 228

protein amounts (25μm) were separated by SDS gel electrophoresis and transferred to 229

nitrocellulose membranes. Membranes were blocked by non-fat milk, and then staining was 230

performed using anti PSD-95 (Clone 108E10; Synaptic Systems; 1:1000) and anti-Actin 231

(Merck; 1:10,000) as primary antibodies. As a secondary antibody, peroxidase-conjugated, 232

anti-mouse (ImmunoResearch Laboratories, 1:10,000) was used. Prior to exposure, ECL 233

(Enhanced Chemiluminescence; Pierce) was used for immunodetection. 234

Multiplexed SILAC and Mass Spectrometry 235

For multiplexed SILAC experiments, cells were prepared, raised in, and fed with lysine and 236

arginine-free MEM (Biological Industries) to which 'heavy' (H) variants (Lys8, [13C6, 15N2]; 237

Arg10, [13C6, 15N4]) or ‘medium’ (M) variants (Lys6 ,[13C6]; Arg6,[13C6]), were added to match 238

nominal lysine and arginine concentrations in standard cell culture media (0.4mM and 239

0.6mM respectively). Cells were harvested after 21-22 days in culture by scraping in lysis 240

buffer containing 10% SDS, mixed together (as pairs of silenced and control sets) and run on 241

preparative gels as follows: 20% of protein mixtures with additional concentrated Laemmli 242

buffer were sonicated, boiled and separated on 4-15% SDS-PAGE (Polyacrylamide Gel 243

Electrophoresis). Each lane was sliced into 5 sections (one being the stacking gel section) 244

which were analyzed separately. Proteins in each slice were reduced with 3 mM DTT (60°C 245

for 30 min), modified with 10 mM iodoacetamide in 100 mM ammonium bicarbonate (in the 246

dark, room temperature for 30 min) and digested in 10% acetonitrile and 10 mM ammonium 247

bicarbonate with modified trypsin (Promega) at a 1:10 enzyme-to-substrate ratio, overnight 248

at 37°C. An additional second trypsinization was done for 4 hours. The resulting tryptic 249

peptides were desalted using C18 tips (Harvard) dried and re-suspended in 0.1% Formic acid. 250

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Peptides were analyzed by LC-MS/MS using a Q Exactive HF mass spectrometer (Thermo) 251

fitted with a capillary HPLC (Easy nLC 1000, Thermo). The peptides were loaded onto a 252

homemade capillary column (25 cm, 75 micron ID) packed with Reprosil C18-Aqua (Dr 253

Maisch GmbH, Germany) in solvent A (0.1% formic acid in water). Peptide mixtures were 254

resolved with a 5 to 28% linear gradient of solvent B (95% acetonitrile with 0.1% formic 255

acid) for 105 minutes followed by gradient of 15 minutes gradient of 28 to 95% and 15 256

minutes at 95% acetonitrile with 0.1% formic acid in water at flow rates of 0.15 μl/min. MS 257

was performed in positive mode (m/z 300–1800, resolution 120,000) using repetitive full MS 258

scans followed by collision induced dissociation (HCD, at 27 normalized collision energy) of 259

the 20 most dominant ions (>1 charges) selected from the first MS scan. A dynamic exclusion 260

list was enabled with exclusion duration of 20s. 261

MS data was analyzed using MaxQuant 1.5.2.8. (www.maxquant.org) searching against 262

the rat Uniprot database with mass tolerance of 20 ppm for the precursor masses and 20 263

ppm for the fragment ions and 4.5ppm after calibration. Oxidation on methionine, 264

phosphorylation on STY, gly-gly on K and protein N-terminus acetylation were accepted as 265

variable modifications and carbamidomethyl on cysteine was accepted as static 266

modifications. Minimal peptide length was set to six amino acids and a maximum of two 267

miscleavages was allowed. Peptide- and protein-level false discovery rates (FDRs) were 268

filtered to 1% using the target-decoy strategy. Protein tables were filtered to eliminate 269

identifications from the reverse database, common contaminants and single peptide 270

identifications. SILAC analysis was performed using the same software. H/M ratios for all 271

peptides belonging to a particular protein species were pooled by the software, providing an 272

average ratio for each protein. Data used in subsequent analyses were filtered according to 273

the following criteria: 1) H/M ratios were quantified for at least 2 peptides in 3 out of 4 274

experiments, and 2) no less than 8 peptides were quantified in total. For the set of 226 275

synaptic proteins, total peptide numbers per protein were ~38±25 and ~32 (average ± 276

standard deviation and median, respectively). All ratios were normalized to median H/M 277

ratios in each sample (2,630 stringent proteins only). A median H/M ratio of 1.06 was 278

obtained for 85 ribosomal proteins after this normalization, indicating that normalization 279

was acceptable. 280

Simulation of synaptic dynamics as Kesten processes 281

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Simulation of synapse size dynamics as stochastic Kesten processes was done as 282

described in Statman et al., 2014. At the beginning of each simulation, simulated synapses 283

were set to initial values (see below). Their sizes were then evolved as follows: At each step 284

and for each synapse, random values for ϵ and η were obtained from Gaussian distributions 285

with means of and and standard deviations as indicated in Fig. 5 A,D,K,L. The 286

random ϵ and η values were then used to calculate the new synapse size xt+1 from the prior 287

size xt such that 288 = + . Synapses whose ‘sizes’ fell below zero were eliminated (set to zero) and 289 not evolved further. Distributions of synaptic sizes were calculated only for synapses with 290

non-zero sizes. 291

for each condition (silenced, control) was obtained from experimental data using 292

multilinear regression fits to scatter plots such as those shown in Figs. 4D-I (see Statman et 293

al., 2014 for a detailed explanation of this fitting process). For stationary size distributions 294

and for normalized fluorescence data, the value of is (1 - ) (Statman et al., 2014) and 295

thus was set to (1 - ). For the plots in Fig. 5A-J, initial synapse sizes were taken from 296

the t=24h time point of the ~2,000 synapses tracked in each condition, and these were 297

evolved for 320 time steps. For the plots in Fig. 5K-M, 4,000 synapses were initialized to an 298

identical value of 0.1 and thereafter evolved for 480 time steps. 299

Simulations were carried out using Visual Basic for Applications within Microsoft Excel. 300

Simulation of synaptic dynamics as a Langevin process 301

During the review of this manuscript, it was pointed out by one of the reviewers that the 302

aforementioned Kesten process can be also formulated as a non-linear Langevin process, if 303

the noise terms of ϵ and η are assumed to be normally distributed random variables. 304

Specifically, given that the Kesten process is expressed as 305 = + then 306 Δx = ( − 1) + (note that in this discrete mapping, the actual values of ϵ and η depend on the time interval 307

Δt. For simplicity, we assume Δt = 1 and that ϵ and η values are for this specific time 308

interval). 309

Assuming that ( − 1) and are normally distributed random variables then 310

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Δx = ( , ) + ( , ) 311 where N1 and N2 are the random variables with means and variances of a,b (for N1) and c,d 312

(for N2) respectively such that = 〈 − 1〉 (the mean of − 1), = (the variance of 313 − 1), = 〈 〉 (the mean of ) and = (the variance of ). 314 As ϵ and η are assumed to be independent (but see below) 315 Δx = [( + ) , ( + )] 316 Thus, the Kesten process can be expressed as a non-linear Langevin process: 317 Δx = ( + ) + + (0,1) 318 5) After substituting a,b,c,d with the equivalent Kesten process terms we arrive at 319 Δx = (〈 − 1〉 + 〈 〉) + + (0,1) which is a form of a non-linear Langevin process. 320

Although fluctuations in momentary values of ϵ and η are assumed to occur 321

independently (as this is the simplest assumption), the validity of this assumption is 322

unknown. The formulation of the process as a non-linear Langevin process sidesteps this 323

matter by employing a single noise term which is assumed to be a normally distributed 324

random variable. Note, however, that in the most general case, the Kesten process makes no 325

assumptions on the independence of ϵ and η or the shape of their distributions. 326

Using this formulation, values for 〈 − 1〉, 〈 〉, , for Δt = 8h were obtained from 327 linear regression fits to binned synaptic size changes as shown in Fig. 6A,B (Control: -0.0913, 328

0.1024, 0.2294, 0.0828; Silenced -0.0481, 0.0675, 0.1220, 0.1138, respectively). Then, 329

starting with the experimentally observed distributions in control and silenced networks, we 330

evolved the size of each synapse iteratively for 40, 8-hour steps using the Langevin process 331

described, specifically 332 = + (〈 − 1〉 + 〈 〉) + + (0,1) 333 Here too, synapses whose sizes fell below zero were eliminated and not evolved further. 334

Distributions of synaptic sizes were calculated only for synapses with non-zero sizes. 335

Simulations were carried out using Visual Basic for Applications within Microsoft Excel. 336

337

Mesoscopic model of size dynamics 338

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The mesoscopic model used to explore relationships between binding and unbinding 339

kinetics of synaptic molecules, size fluctuations and distributions was based on the model 340

described in Shomar et al., 2017. Here, each synapse was modeled as a 50x50 square matrix 341

of sites/slots to which scaffold molecules can bind. Scaffold molecules could bind 342

nonspecifically directly to the matrix with a low but non-zero probability α and to scaffold 343

molecules in adjacent slots (see Fig. 7A) such that the probability of binding to a particular 344

slot increased linearly with the number of occupied neighboring slots. At each time step and 345

for each unoccupied slot, the fraction of occupied neighboring slots χ, was determined. 346

Then, the probability Pon for a free scaffold molecule to bind to that slot was determined 347

according to a) λon, the maximal binding probability (a constant); b) χ, the fraction of 348

neighboring occupied slots, and c) Nfree, the amount of free (unbound) scaffold molecules, as 349

well as α, such that 350

Pon = Nfree · λon · χ + α. 351

A random number was then sampled from a uniform distribution between 0 and 1. Binding 352

‘occurred’ if this number was smaller than Pon, in which case, Nfree was decremented. 353

Similarly, for each step and each occupied site, the chances of unbinding were calculated 354

according to χ, the fraction of occupied neighboring sites and λoff, the maximal unbinding 355

probability (a constant) such that 356

Poff = λoff · (1-χ). 357

Here too, a random number between 0 and 1 was sampled from a uniform distribution and 358

unbinding occurred if this number was smaller than Poff, in which case, Nfree was 359

incremented. 360

At the beginning of each simulation, all scaffold molecules were placed in the free pool, 361

and matrices were set to be empty. Synaptic size at any time step was defined as the 362

momentary number of molecules bound to its matrix. The procedure described above was 363

run for 800 steps for 4,000 synapses (matrices), all of which shared (and competed over) a 364

common pool of scaffold molecules. All presented data was taken from the last 72 365

simulation steps (steps 727 to 799). 366

FRAP was simulated by marking the bound molecules of 200 synapses as ‘bleached’ at 367

simulation step 600, and then following their exchange with ‘unbleached’ molecules from 368

the pool of free molecules over the subsequent 200 steps. As typical FRAP data in 369

experiments were obtained from medium to large–sized synapses, FRAP curves in 370

15

simulations were prepared only from synapses whose average size in the 24 time steps 371

preceding the simulated bleach procedure was equal to or exceeded average synaptic size 372

during this period. 373

Unless stated otherwise, the following parameters were used: λon=1.25·10-6; λoff=0.5; α= 374

1·10-9; Total scaffold molecules=640,000. 375

To attain good performance, simulations were written in C, using the fast cryptographic 376

random number generator ISAAC (Indirection, Shift, Accumulate, Add, and Count; 377

http://burtleburtle.net/bob/rand/isaacafa.html) to generate streams of pseudorandom 378

numbers. Size trajectories and FRAP data were saved as text files and thereafter imported 379

into Excel for further analysis and presentation. 380

Code accessibility 381

Code for simulations of synaptic size fluctuations, distributions, and loss modeled as 382

Kesten and non-linear Langevin processes (Figs. 5, 6; Visual Basic for Applications within 383

Microsoft Excel) can be found on Model DB (http://modeldb.yale.edu/262059). 384

Code for mesoscopic simulations of synaptic size fluctuations and distributions (Figs. 385

7,9,10; C code) can be found on Model DB (http://modeldb.yale.edu/262060). 386

387

388

16

Results 389

Distributions of synaptic sizes in chronically silenced networks are broad and rightward 390

skewed 391

As described in the Introduction, much of synaptic size diversity is attributed to myriad 392

synaptic plasticity processes, which depend, in turn, on network activity. It thus might be 393

expected that in neurons with no history of network activity or synaptic transmission, size 394

diversity would be less extensive, and this difference would be manifested in distributions of 395

synaptic sizes. To examine this expectation, we raised networks of cultured rat cortical 396

neurons from day one in culture in Tetrodotoxin (TTX, 1 μM), 6-cyano-7-nitroquinoxaline- 397

2,3-dione (CNQX 10μM), and (2R)-amino-5 phosphono pentanoate (APV, 50μM), potent 398

inhibitors of voltage gated sodium channels, AMPA-type and NMDA-type glutamate 399

receptors, respectively. No overt effects on cell viability were observed, in agreement with 400

many early studies (e.g. van Huizen et al., 1985, Ramakers et al., 1993; Verderio et al., 1994; 401

Craig et al., 1994; Benson and Cohen, 1996; Murthy et al., 2001) as well as more recent ones 402

(Wrosch et al., 2017; Hobbiss et al., 2018). 403

To verify the elimination of all spiking activity, the networks were grown on thin-glass 404

multi-electrode array (MEA) dishes, which allow for chronic, non-invasive recordings of 405

network activity from 59 electrodes (Fig. 1A). As shown in Fig. 1B-D, these pharmacological 406

agents fully suppressed the vigorous spontaneous activity typical of such networks. 407

The effects of chronic silencing on excitatory synapse sizes were determined by 408

expressing an EGFP-tagged variant of the PSD protein PSD-95 (PSD-95:EGFP) in a small 409

number of neurons (Fig. 1E). PSD-95 is a major postsynaptic scaffold protein that regulates 410

the number of AMPA and NMDA receptors at the postsynaptic membrane (Won et al., 411

2017). PSD-95:EGFP fluorescence is correlated with PSD area (Cane et al., 2014) and thus 412

represents a good proxy of synaptic size. Expression was carried out using lentiviral vectors, 413

resulting in very low PSD-95:EGFP overexpression (Minerbi et al., 2009). 414

Experiments were carried out on networks raised in culture for about three weeks. At this 415

stage, the developmental phases of rapid dendritic growth, axonal arborization and synapse 416

formation are over for the most part, and neuronal structure becomes relatively stable, 417

allowing individual synapses to be followed reliably for 24-48 hours and beyond. Silenced (or 418

control) networks growing on MEA dishes were mounted at day 19-21 in culture on a 419

combined MEA recording / imaging system used in prior studies from our lab (Minerbi, et al., 420

17

2009; Kaufman et al., 2012, Rubinski et al., 2015; Dvorkin et al., 2016). The MEA dishes were 421

maintained at 37°C in an atmospheric environment of 5% CO2 / 95% air and perfused at very 422

slow rates (2 volumes / day) with fresh cell culture media containing (or free of) the 423

aforementioned pharmacological agents. After 24 hour adjustment periods, automated 424

multisite confocal microscopy was initiated, during which images of four to ten fields of view 425

(portions of dendritic arbors of different neurons expressing PSD-95:EGFP) were obtained at 426

60-min intervals at ten focal planes, using the microscopes ‘autofocus’ system to correct for 427

focal drift. 428

Following the experiments, PSD-95:EGFP puncta were identified anew at each time point 429

(programmatically, using a puncta detection algorithm as described in Materials and 430

Methods) and intensities and numbers of all puncta were determined (Silenced networks: 23 431

neurons, from 5 separate experiments, ~6,800 synapses; Control networks: 20 neurons from 432

6 separate experiments, ~9,000 synapses). As shown in Fig. 2A, distributions of synaptic PSD- 433

95:EGFP fluorescence in chronically silenced networks were broad and rightward skewed 434

(skewness ≈ +1.4 and +2.2, silenced and control networks, respectively; note that 435

skewness=0 for normal distributions). In fact, distributions in the silenced networks were 436

much broader than those observed in active networks, with mean PSD-95:EGFP fluorescence 437

being ~1.5 times greater than mean fluorescence measured in active networks (Fig. 2B; 438

p=4.6 ּ10-6 by neuron; p=0.019 by experiment; t-test, assuming unequal variances; see also 439

Kim et al., 2007; Noritake et al., 2009; Sun and Turrigiano, 2011; Shin et al., 2012) suggesting 440

that chronic silencing was associated with significant synaptic growth (Murthy et al., 2001; 441

Sando et al., 2017; but see Harms et al., 2005; Yasumatsu et al., 2008). Distributions at early 442

and late time points (1 and 24h, respectively) were very similar (Fig. 2A). Mean synaptic PSD- 443

95:EGFP fluorescence was also stable (Fig. 2B). Plotting distributions of PSD-95:EGFP 444

fluorescence in control networks in scaled units (that is, multiplying the fluorescence of each 445

synapse by ~1.5), suggested that shapes of synaptic size distributions in chronically silenced 446

and active networks were similar (Fig. 2C), in excellent agreement with prior findings in 447

acutely silenced networks in vitro (e.g. Turrigiano et al., 1998; Hobbiss et al., 2018) and in 448

vivo (Keck et al., 2013). Finally, distributions of synaptic sizes in both silenced and active 449

networks were well approximated by log-normal distributions (Fig. 2D). 450

These findings thus confirm prior reports that extensive synaptic size diversification can 451

occur in the absence of activity-dependent synaptic plasticity processes (e.g. Van Huizen et 452

18

al., 1985; Harms and Craig, 2005; Harms et al., 2005; Yasumatsu et al., 2008; Sigler et al., 453

2017; Sando et al., 2017). Moreover, they reveal that the emergence of broad, rightward 454

skewed and stable size distributions, remarkably similar to those observed in active 455

networks, can arise de novo, rather than through the scaling of distributions initially 456

established in active networks. Thus, activity-independent processes can play decisive roles 457

in synaptic size diversification and in establishing appropriate proportions of differently sized 458

synapses. 459

460

Intrinsic size fluctuations are sufficient to produce differently sized synapses at appropriate 461

proportions 462

As mentioned in the introduction, prior studies suggest that synaptic sizes are affected by 463

intrinsic size fluctuations, as are the shape and scale of synaptic size distributions 464

(Yasumatsu et al., 2008; Lowenstein et al., 2011; Kaufman et al., 2012; Statman et al, 2014; 465

Rubinski et al., 2015; Ziv and Brenner, 2018; Ishii et al., 2018; Humble et al., 2019). Yet, as 466

characteristics of intrinsic size fluctuations in neurons with no prior history of network 467

activity were not measured to date, it remained unknown if such intrinsic fluctuations are 468

sufficient to produce the extensive diversity and broad, skewed distributions of synaptic 469

sizes observed in chronically silenced networks. 470

To examine this possibility, we followed individual synapses in chronically silenced (and 471

active) networks for 24-48 hours, measuring PSD-95:EGFP fluorescence of each synapse at 472

each time point as illustrated in Fig. 3A (see also Minerbi et al., 2009; Fisher-Lavie and Ziv 473

2013; Rubinski et al., 2015; Dvorkin et al., 2016). Fluorescence measurements were made 474

from maximal intensity projections of all Z-sections to minimize the effects of focal 475

positioning errors. Only synapses that could be tracked reliably were included in these 476

analyses, excluding PSD-95:EGFP puncta that disappeared, split, or merged during the 477

experiments. To correct for some variability in PSD-95:EGFP expression levels and to allow 478

for data pooling, the fluorescence of each synapse was normalized to the mean puncta 479

fluorescence of its respective neuron, measured at the first time point. Additionally, to 480

minimize the influence of measurement noise, all data were smoothed using a 3 time-point 481

low pass filter (see Statman et al., 2014). As illustrated for 16 synapses in Fig. 3A, synaptic 482

sizes changed considerably over time scales of many hours, even in chronically silenced 483

networks (Fig. 3B). Comparing the initial synaptic ‘configuration’ (the set of inputs to this 484

19

dendrite in terms of synaptic sizes) to synaptic configurations at later time points suggests 485

that size fluctuations are associated with a gradual ‘erosion’ of synaptic configurations (Fig. 486

3C,D). 487

Magnitudes of temporal fluctuations in synaptic sizes were quantified for 2,032 and 1,922 488

synapses (23 and 20 neurons, 5 and 6 separate experiments, silenced and control networks, 489

respectively) by calculating the standard deviation, coefficient of variation, and the 490

range/mean (Fisher Lavie et al., 2011; Zeidan and Ziv, 2012; Ziv, 2013) of the normalized 491

fluorescence of each synapse over 24 hour periods. As shown in Fig. 4A-C, all three measures 492

suggested that magnitudes of size fluctuations were reduced in silenced networks relative to 493

control (active) networks, but only by 20% to 34%. 494

To determine if these somewhat subdued fluctuations could give rise to the broad and 495

skewed size distributions observed in chronically silenced networks, we analyzed these 496

within the context of a statistical framework we previously developed (Statman et al., 2014). 497

The basic premise of this framework is that synaptic size dynamics are driven by continuous, 498

noisy multiplicative downscaling, which is continuously offset by noisy additive growth, 499

resulting in size fluctuations that have noisy multiplicative and additive components. This 500

statistical process, known as a Kesten process, faithfully reproduces many experimental 501

observations concerning synaptic size fluctuations, size distributions, their stability and their 502

scaling (Statman et al., 2014; Rubinski et al., 2015; Ziv and Brenner, 2018). Importantly, this 503

framework provides means for parametrically comparing synaptic size fluctuations under 504

different experimental conditions and determining their effects on synaptic size 505

distributions. 506

In more formal terms, this framework stipulates that for a synapse of size x at time t (xt), 507

its size (xt+1) after some discrete time period will be 508 = + (1) 509 where εt and ηt are the aforementioned multiplicative downscaling and additive growth 510

parameters. Importantly, εt and ηt are not fixed values but random variables drawn 511

independently at each time step from some distribution. Iterations of process (1) (i.e. 512 = + ; = + ; etc.) result in fluctuating size 513 ‘trajectories’ similar to those observed experimentally. Note that expressing the change in 514

synaptic size(Δxt+1) at t=t+1 using equation 1 515 ∆ = − = + −

20

∆ = ( − 1) + (2) 516 suggests that the Kesten process can be thought of as a combination of myriad, noisy first 517

and zero order reactions (for example protein loss/degradation and protein 518

supply/synthesis, respectively) with 〈 − 1〉 and 〈 〉 (the mean values of these parameters) 519 representing aggregate, effective ‘rate constants’ of such reactions, respectively (Statman et 520

al., 2014). 521

The mean downscaling factor () is an important parameter in this framework, and can 522

be derived in stationary distributions by multiple linear regression analyses of synaptic sizes 523

as a function of time as illustrated in Fig 4D-J (see Statman et al., 2014 for further details). 524

Derivation of in this manner revealed that continuous downscaling was substantially 525

weakened in silenced networks in comparison to active networks, that is was closer to 526

1.0 (0.995 and 0.985, silenced and control networks, respectively; Fig. 4J). In addition, this 527

analysis revealed that synaptic configuration ‘erosion’ rates were roughly halved (Fig. 4K); 528

notably, however, erosion rates were still considerable. Plotting the change in synaptic size 529

(that is, subtracting, for each synapse, its fluorescence at t=24 from its fluorescence at t=1) 530

as a function of its size at t=1 illustrates how lessened downscaling weakens the constraints 531

on synaptic size distributions (Fig. 4L). This weakening might explain the broader 532

distributions of synaptic sizes in silenced networks (Fig. 2A). On the other hand, it remained 533

unclear if fluctuations with such weak downscaling would be sufficient to generate and 534

maintain the broad, skewed and stable synaptic size distributions observed in silenced 535

networks. 536

To address this question, we simulated populations of ‘synapses’ whose size fluctuations 537

were modeled as Kesten processes using the experimentally derived values of and 538

for silenced and control networks. In the first set of simulations, synaptic sizes were 539

initialized using the experimentally measured, normalized PSD-95:EGFP fluorescence values 540

of 2,032 and 1,922 synapses (data of Fig. 4; silenced and control networks respectively). As 541

shown in Fig. 5, excellent fits to the experimental data were obtained for both silenced and 542

control conditions not only in distribution shape and stability (Fig. 5C,F) but also in terms of 543

synaptic configuration erosion rates (compare Fig. 5A,B,D,E with Fig. 4F,I,L) and measures of 544

size fluctuations (Fig. 5G-I and 4A-C). 545

In these simulations, synapses whose ‘sizes’ were reduced momentarily to zero were 546

treated as ‘eliminated’ and not considered further. Interestingly, rates of synapse 547

21

‘elimination’ were greater in simulations based on parameters obtained in silenced networks 548

(Fig. 5J; ~0.63±0.05% per 24 simulation cycles, silenced networks; 0.06±0.02%, control 549

networks; mean ± standard deviation, 5 runs per condition) indicating that the weaker 550

constraints on intrinsic fluctuations observed in silenced networks might reduce the chances 551

of (small) synapses to escape elimination (see also Holtmaat et al., 2006; Yasumatsu et al., 552

2008; Minerbi et al., 2009). 553

In a second set of simulations, we simulated 4,000 synapses for each condition, setting 554

the initial ‘size’ of all synapses to 0.1 (the dimmest synapses identified in our experimental 555

data sets, in normalized units), and followed the evolution of synaptic size distributions using 556

the experimentally derived values of and . As shown in Fig. 5K,L, in both conditions, 557

size distributions gradually converged to the experimentally measured skewed and stable 558

distributions. Interestingly, however, convergence was much slower in silenced networks, 559

and even after 480 simulated ‘hours’ (20 ‘days’) convergence was incomplete. Here too, the 560

negative effects of silencing on (small) synapse survival were very evident (Fig. 5M). 561

Collectively, these findings suggest that fluctuations in synaptic sizes measured in chronically 562

silenced networks are sufficient to drive the emergence of the broad, rightward skewed and 563

stable synaptic size distributions observed in these networks. 564

The Kesten process described above is based on the assumption that , and their 565

noise terms do not depend on momentary synaptic size (as might be expected for simple 566

first and zero order reactions). In a prior study (Yasumatsu et al., 2008), size fluctuations 567

were modeled using a generic framework that does not necessitate this assumption. Here 568

fluctuations were modeled as a non-linear Langevin process in which fluctuations were 569

grouped into deterministic ( ( )) and stochastic terms ( ( )), both formulated as functions 570 of momentary synaptic size (xt). 571

Assuming that the two noise terms in the Kesten process (2) are distributed normally with 572

standard deviations of and , it can be shown that the Kesten process (2) can also be 573

formulated as a non-linear Langevin process (see Materials and Methods). Here, the change 574

in momentary synaptic size Δ after some time interval (Δt) is expressed as 575 Δ = ( )Δ + ( ) (0,1)Δ (3) 576 with 577 ( ) = (〈 − 1〉 + 〈 〉) (4) 578

22

( ) = −12 2 + 2 or ( ) = −12 2 + 2 (5) 579 where (0,1) is a random variable taken from a normal distribution with a mean of 0 and a 580 variance of 1. 581

This formulation allowed us to test the aforementioned assumptions: if , are 582

indeed independent of momentary synaptic size, then plotting the fluctuation magnitude 583 ( ) as a function of synaptic size at that time ( ) should result in a straight line with a 584 slope of 〈 − 1〉 and an intercept of 〈 〉, (both scaled by ∆t; see equation 4). Similarly, if the 585 variances of ϵ and η do not depend on momentary synaptic size, plotting the fluctuation 586

variance ( ( ) ) as a function of should result in a straight line with a slope of and 587 an intercept of (equation 5). To test these predictions, size changes measured over 8 hour 588

intervals were divided into 20 equally-sized bins according to synaptic size at the beginning 589

of each interval. The average and variance of size changes in each bin were then plotted 590

against average initial synaptic size for that bin. As shown in Fig. 6A,B, excellent linear fits 591

were observed for both the control and silenced conditions, justifying the aforementioned 592

assumptions. The only noticeable deviation was for ( ) and for the smallest synapses in 593 the silenced data set, which might hint that in silenced networks, ϵ and/or η might slightly 594

differ for the smallest synapses. 595

Linear regression fits of the data in Fig. 6A,B allowed us to obtain estimates of 596 〈 〉, 〈 〉, , (for 8 hour intervals) for control and silenced networks. These estimates were 597 then used to examine if synaptic size fluctuations modeled as the Langevin process 598

described above give rise to the size distributions measured experimentally. To that end, 599

experimentally measured synaptic sizes (as in Fig. 5C,F) were evolved for 320 simulated 600

hours (40, 8-hour intervals) using equations 3 to 5 (see Materials and Methods for further 601

details). As shown in Fig. 6C,D, distributions remained faithful to the experimentally 602

measured distributions for both control and silenced networks. As expected, identical results 603

were obtained when synaptic sizes were evolved as a Kesten process using the same 604

parameters (data not shown). 605

Collectively these findings suggest that synaptic size distributions, in both active and 606

chronically silenced networks, can arise from size fluctuations that effectively behave as 607

combinations of noisy first and zero order processes. Interestingly, the Langevin 608

transformation of the Kesten process (equations 3 to 5) is very similar to the non-linear 609

23

Langevin process previously formulated by Yasumatsu and colleagues as an effective 610

description of size fluctuations in cultured slices of hippocampal neurons (Yasumatsu et al., 611

2008). Thus analytical approaches coming from different directions and theoretical 612

backgrounds, applied to data obtained in different experimental systems, converged to a 613

very similar quantitative description of synaptic size dynamics. 614

615

Although synaptic dynamics in both active and silenced networks were well-described by 616

stochastic Kesten and Langevin processes (Figs. 4-6), we noted one qualitative deviation in 617

active but not in silenced (or simulated) networks, that is, a minor but conspicuous 618

population of small synapses that exhibited rapid growth over the imaging period (Fig. 4F, 619

shaded area; compare with Fig. 4I). We return to this population later. 620

621

Relationships between activity levels, innate molecular dynamics, intrinsic fluctuations, and 622

size distributions 623

The data described so far suggests that activity-independent, intrinsic size fluctuations are 624

sufficient to generate a full range of synaptic sizes at correct proportions as reflected in the 625

breadth and shape of the resulting size distributions. The source of these fluctuations, 626

however, is not clear. As mentioned in the Introduction, these have been suggested to stem 627

from the innate dynamics of synaptic molecules at synaptic sites. Moreover, network activity 628

levels have been shown to affect these dynamics (reviewed in Fisher-Lavie and Ziv, 2014). It 629

is thus plausible that the altered size fluctuations (and consequential changes in synaptic size 630

distributions) observed in silenced networks reflect, at least in part, changes in the 631

underlying dynamics of synaptic molecules associated with low network activity levels. 632

To obtain a better understanding of the relationships between activity levels, innate 633

molecular dynamics, intrinsic fluctuations, and size distributions, we used a mesoscopic 634

model developed previously to study such relationships (Shomar et al., 2017). Specifically, 635

we used this model to generate hypotheses on the manners by which activity might affect 636

relationships between innate molecular dynamics, intrinsic fluctuations and size 637

distributions, and then tested these hypotheses experimentally. It should be emphasized 638

that the model was used to explore potential explanations, not to generate precise fits to 639

experimental data. 640

24

The aforementioned model (illustrated in Fig. 7A) consists of a neuron with a fixed 641

number of ‘synapses’ (S) each of which is composed of two components: a postsynaptic 642

‘membrane’, modeled as a 50x50 matrix of potential binding sites (‘slots’) for synaptic 643

scaffold molecules; and synaptic scaffold molecules which can bind to, or unbind from these 644

slots. The ‘size’ of a given synapse at any time is defined as the momentary number of 645

occupied slots, that is, the number of scaffold molecules bound to its matrix. In the variant 646

of the model used here, scaffold molecules come from a common (global) pool (Ntotal) shared 647

and competed over by all synapses. The global amount of free molecules (Nfree) at any 648

moment is equal to the total amount of molecules in the cell (Ntotal) after subtracting all 649

molecules presently bound to synaptic membranes (matrices). Binding and unbinding are 650

modeled as stochastic events characterized by probabilities per unit time. Consequently, the 651

number of molecules binding to a matrix per unit time depends on the binding probability, 652

the number of free molecules (Nfree, serving as a proxy of free molecule concentration) and 653

on the number of vacant slots in that matrix. Similarly, the number of molecules dissociating 654

from each matrix per unit time depends on the unbinding probability per unit time and on 655

the number of bound molecules (=occupied slots). In this stochastic description, the binding 656

and unbinding of scaffold molecules result in temporal fluctuations in synaptic sizes, i.e. in 657

the momentary numbers of molecules bound to the matrices, while occupancies at all S 658

matrices give rise to momentary synaptic size distributions. The model as described so far is 659

insufficient to explain the rightward skewed, experimentally observed distributions of 660

synaptic sizes. However, when the probabilities of binding to (and unbinding from) each slot 661

depend positively (and negatively) on the number of its immediately neighboring occupied 662

slots (gray area in Fig. 7A, right hand side), synaptic size dynamics and distributions become 663

remarkably similar to those observed experimentally (Shomar et al., 2017). This dependence, 664

justified by the multiplicity of binding sites typical of most synaptic molecules (e.g. Won et 665

al., 2017), is essentially a form of cooperativity, and thus both binding and unbinding in this 666

model are cooperative (see Materials and Methods for a more detailed description of the 667

model). 668

Prior studies suggest that chronic suppression of network activity can slow the binding 669

and unbinding (exchange) kinetics of synaptic molecules (reviewed in Fisher-Lavie and Ziv, 670

2014). We thus used this model to examine the possibility that reduced synaptic size 671

fluctuations and broader size distributions in silenced networks might stem from slower 672

25

exchange kinetics. Specifically, we explored the expected consequences of reducing the 673

unbinding probability of molecules bound to ‘synaptic’ matrices. As shown in Fig. 7, lower 674

unbinding probabilities would be expected to drive the broadening of synaptic size 675

distributions (Fig. 7B) increase mean synaptic size (Fig. 7C), reduce the rate at which the 676

slope declines in plots such as Fig. 7D (that is, drive to values closer to 1.0; Fig. 7D-E,G), 677

slow changes in synaptic size configurations (Fig. 7F), and reduce size fluctuation magnitudes 678

(Fig. 7H-J), all in good agreement with observations made in real neurons (Figs. 2, 4). 679

Lower unbinding probabilities also predict slower exchange rates of scaffold molecules at 680

synapses (Fig. 7K). If this hypothesis is correct, experimentally measured exchange rates of 681

PSD-95 might be expected to be slower in chronically silenced networks {due to, for example 682

Ser-295 phosphorylation (Kim et al., 2007) or palmitoylation (Sturgill et al., 2009; Noritake et 683

al., 2009; Fukata et al., 2013)}. To test this prediction, we measured PSD-95:EGFP exchange 684

rates using fluorescence recovery after photobleaching (FRAP) in chronically silenced and 685

control networks. To that end, a small number of well separated PSD-95:EGFP puncta were 686

photobleached by intense laser illumination and subsequently followed by time lapse 687

imaging, initially at 10 min intervals (for the first hour) and then at one hour intervals, 688

chosen to match to the slow exchange rates of PSD-95 (Sturgill et al., 2009; Zeidan and Ziv, 689

2012; Fukata et al., 2013). One example is shown in Fig. 8A-C. Here, three photobleached 690

PSD-95:EGFP puncta in a chronically silenced network were followed for 90 hours after the 691

bleaching procedure. The fluorescence traces obtained here (Fig. 8C) illustrate that over 692

these long time scales, fluorescence recovery measurements are confounded by ongoing 693

changes in synaptic sizes, complicating accurate estimations of recovery kinetics. 694

Nevertheless, pooling measurements over shorter time scales (24h or less) allowed us to 695

compare mean fluorescence recovery profiles for synapses in chronically silenced (77 696

synapses from 6 experiments) and control networks (72 synapses from 7 experiments). 697

Surprisingly, mean fluorescence recovery curves for silenced and control networks did not 698

differ significantly (Fig. 8D). These experiments thus did not support the possibility that 699

altered size fluctuations, synaptic sizes and distributions in chronically silenced networks 700

reflect slower unbinding kinetics of PSD-95. 701

We thus explored an alternative explanation that relates to PSD-95 abundance. As shown 702

in (Fig. 2A,B) mean synaptic PSD-95:EGFP fluorescence was, on average ~50% greater in 703

chronically silenced networks, possibly indicating that chronic silencing is associated with 704

26

increased cellular PSD-95 levels due to, for example, effects on synaptic protein synthesis 705

(e.g. Schanzenbächer et al., 2016) or degradation (e.g. Jakawich et al., 2010). Using the 706

aforementioned model to examine the expected effects of increased scaffold molecule 707

abundance we found that merely increasing Ntotal by 25% was sufficient to qualitatively 708

recapitulate all of the experimental findings described so far (Fig. 9A-H), including the similar 709

recovery kinetics in FRAP experiments. 710

To experimentally test this potential explanation, we measured and compared global 711

PSD-95 abundance in chronically silenced and control networks by means of Western blots. 712

Here too, however, the prediction was not supported by the experimental data, as no 713

consistent increases in global PSD-95 abundance were observed in silenced networks (Fig. 714

9I,J; 7 replicates from 2 separate experiments; see also Kim et al., 2007; Shin et al., 2012; 715

Lazarevic et al., 2011). 716

To examine if this observation applies to synaptic proteins in general, we used 717

multiplexed SILAC (Stable Isotope Labeling with Amino acids in Cell culture) combined with 718

MS (Mass Spectrometry; reviewed in Hoedt et al., 2019) to compare synaptic protein 719

quantities in silenced and control preparations. To that end, neurons were prepared and 720

grown in lysine and arginine-free media supplemented with lysine and arginine containing 721

stable, heavy isotopes of carbon and nitrogen. Silenced preparations were labeled with 722

‘Heavy’ amino acids (Lys8 - 13C6, 15N2 and Arg10 - 13C6, 15N4) whereas control preparations 723

were labeled with ‘Medium’ variants (Lys6 - 13C6 and Arg6 - 13C6), which are isotopically 724

separable from both Heavy and unlabeled lysine and arginine. After 21-22 days in culture, 725

during which most of the proteome becomes labeled (Hakim et al., 2016), the preparations 726

were lysed, the extracts mixed together and run on preparative gels which were 727

subsequently sliced and subjected to MS analysis (See Materials and Methods and Hakim et 728

al., 2016 for further details). This method, based on mixing and analyzing samples 729

simultaneously, eliminates much of the variability associated with proteomic approaches; 730

moreover, it provides a Heavy/Medium (H/M) ratio reading for each peptide and protein, 731

which reflects the ratio of labeled proteins from silenced and control preparations, 732

respectively. Average H/M ratios were obtained from 4 replicates (2 separate experiments) 733

using stringent criteria (see Materials and Methods). Stringent H/M ratios obtained for 226 734

synaptic proteins (categorized as such as in Hakim et al., 2016; 2,630 proteins in total) 735

resulted in average and median H/M ratios of 0.89 and 0.86, respectively. Data for 15 and 21 736

27

well-studied post- and presynaptic proteins are shown in Fig. 9K. Evidently, these data do 737

not support the possibility that chronic silencing increases synaptic protein abundance (if 738

anything, we noted a slight reduction), although confounds related to differences in labeling 739

rates (due to differential metabolism) or cell counts cannot be entirely ruled out. 740

How could synaptic contents of PSD-95 increase by ~50% without detectable changes in 741

PSD-95 abundance? One possible explanation is that increased synaptic size in silenced 742

networks was associated with a commensurate decrease in synaptic number (e.g. van 743

Huizen et al., 1985; Kossel et al., 1997; see also Annis et al., 1994; Barnes et al., 2017) 744

resulting is no net change in total PSD-95 levels. Indeed, such decreases were predicted by 745

the simulations shown in Figs. 5J,M. 746

We thus used the aforementioned mesoscopic model to examine how a reduction in 747

synaptic numbers might affect intrinsic fluctuations and synaptic size distributions. To that 748

end, the number of synapses (matrices) was reduced by 40% (from 4,000 to 2,400) without 749

changing Ntotal. As shown in Fig. 10A-G the model with these parameters recapitulated the 750

main experimental findings obtained in silenced networks – increased synaptic size, 751

broadening of synaptic size distributions, values closer to 1.0, reduced magnitudes of 752

synaptic size fluctuations, slower changes in synaptic configurations and similar FRAP curves. 753

To examine if the experimental findings were congruent with this prediction, we revisited 754

the data set of Fig. 2, finding (Fig. 10H) that PSD-95:EGFP puncta counts were indeed 755

reduced in chronically silenced networks (by ~37%; ~296 vs. ~470 puncta per field of view, 756

23 fields of view in 5 experiments and 20 fields of view in 6 experiments, silenced and 757

control networks, respectively). Moreover, the summed (rather than average) fluorescence 758

of PSD-95:EGFP puncta in each field of view was practically identical in silenced and active 759

networks (Fig. 10I) - in agreement with the explanation proposed above as well as the data 760

of Fig. 9I-K. Differences in synaptic numbers were not associated with changes in synaptic 761

density (4.91±1.18 and 5.02±0.87 synapses per 10μm dendrite length; 11 and 10 fields of 762

view from 6 and 5 experiments; silenced and control networks respectively) and thus seem 763

to reflect lessened dendritic arborization in silenced networks (in agreement with van Huizen 764

et al., 1985; Benson and Cohen, 1996). Indeed, the summed length of dendritic segments 765

within each field of view was reduced by ~33% (Fig. 10J; 20 fields of view for each condition, 766

P= 1.3·10-7; two-sample t-test assuming unequal variances). Moreover, Scholl analysis of 767

reconstructed neurons confirmed that dendritic arborization was substantially reduced (Fig. 768

28

11; see also Benson and Cohen, 1996). Interestingly, whereas PSD-95:EGFP puncta counts in 769

silenced networks were ~stable over 24 hour periods (Fig. 10H), counts in active networks 770

tended to increase slowly over the same time frame (see also Okabe et al., 1999), as did the 771

summed fluorescence of PSD-95:EGFP puncta in active networks (Fig. 10I). 772

These findings are thus most congruent with an interpretation suggesting that synaptic 773

enlargement in chronically silenced networks, as well as broader size distributions, subdued 774

size fluctuations and values closer to 1.0, might be attributed to the redistribution of 775

PSD-95 (and probably other synaptic molecules) among the fewer synaptic connections 776

formed in the absence of network activity (Fig 12A). 777

778

Relationships between activity levels and synaptic numbers 779

Why are less synapses formed in chronically silenced networks? Our data provides 780

potentially interesting clues, although, as we show below, interpretation is not as 781

straightforward as it might seem at first sight. 782

We note that in active (Fig. 4D), but not in silenced networks (Fig. 4I), a minor population 783

of synapses (~1-2% per day) exhibited rapid growth in manners not predicted by any of the 784

models explored here. In a prior study (Minerbi et al., 2009) we found that this phenomenon 785

reflects the rapid formation and enlargement of (post)synaptic sites during periods of 786

particularly strong, synchronous network activity, which presumably drives strong 787

presynaptic activation and possibly long-term potentiation associated spine formation and 788

growth (e.g. Smith and Jahr, 1992; Engert and Bonhoeffer, 1999; Maletic-Savatic et al., 1999; 789

Matsuzaki et al., 2004; Kwon and Sabatini, 2011; Meyer et al., 2014; Bosch et al., 2014; Sigler 790

et al., 2017; Hobbiss et al., 2018 reviewed in Andreae and Burrone, 2014). Conversely, acute 791

suppression of network activity was found to abruptly arrest and even reverse trends of 792

synaptic proliferation (Minerbi et al., 2009). It thus seems that network silencing might 793

suppress activity-dependent forms of synapse formation (in line with prior predictions, e.g. 794

Yasumatsu et al., 2008), ultimately resulting in lower synaptic numbers. This, in turn, would 795

negatively affect dendritic arborization (reviewed in Cline and Haas, 2008) potentially 796

explaining the major findings described above. 797

Our data also indicates, however, that causal relationships between synaptic numbers 798

and network activity might be more complex. The increase in PSD-95 availability and 799

synaptic size associated with reduced synaptic numbers (Fig. 12A) is also associated with 800

29

changes in size fluctuation characteristics, specifically in and (Fig. 4J). When 801

expected size change is plotted against present synaptic size using experimentally measured, 802

absolute values of and (Fig. 12B) it becomes apparent that for particularly small 803

synapses (Fig. 12B gray shading), the bias toward growth is weaker in silenced networks (see 804

also Fig. 6A). Consequently, the chances of small synapses to persist in silenced networks is 805

lowered, and thus more synapse elimination (or less stabilization of nascent synapses) is 806

expected, as predicted by the simulations of Figs. 5J,M. This bias is not affected by 807

recalculating and for active networks after removing the population of rapidly 808

growing synapses from the data set, although this does not preclude the possibility that 809

some of this bias is created by activity-dependent potentiation of nascent synapses. 810

To test this prediction, we returned to the time-lapse images obtained in control and 811

silenced networks, focusing this time on small (dim) PSD-95:EGFP puncta. As shown in Fig. 812

12C, tracking such synapses revealed greater rates of puncta loss in silenced networks (5.7% 813

vs. 12.6% in 24 hours; 17/299 and 41/324, 4 control and 4 silenced networks, respectively). 814

In further agreement with this prediction, lost puncta were particularly dim (333±147 and 815

373±125; arbitrary fluorescence units at first time point, average ± standard deviation, 816

control and silenced networks, respectively) as compared to the entire synaptic population 817

(600±357 and 911±558). 818

These predictions (Fig. 5J,M, Fig. 12B) and findings (Fig. 10H-J, Fig. 12C) suggest that 819

synaptic loss might be both the cause and the product of altered synaptic size dynamics. 820

Stated differently, innate molecular dynamics, intrinsic size fluctuations and synaptic sizes 821

might be related reciprocally, possibly in self-reinforcing fashion as illustrated in Fig. 12D, 822

potentially obscuring simple cause and effect relationships between these phenomena. 823

824

Discussion 825

Here we set out to determine the contributions of activity dependent and independent 826

processes to excitatory synapse size diversity. To that end, we pharmacologically silenced 827

networks of cortical neurons from the time of plating and then examined synaptic size 828

distributions and remodeling dynamics using PSD-95:EGFP fluorescence as a proxy of 829

synaptic size. We found that even in networks with no history of activity, size diversity was 830

extensive and size distributions were broad, stable, and rightward skewed. Comparisons 831

with spontaneously active networks revealed that silencing was associated with a 832

30

broadening of synaptic size distributions and a significant (~50%) increase in mean synaptic 833

size, yet distribution shapes were similar when scaled by mean synaptic size. Silencing was 834

associated with reductions in size fluctuation magnitudes, as well as considerable weakening 835

of constraints on size distributions. Nevertheless, these fluctuations and constraints were 836

still sufficient to generate broad, skewed and stable size distributions. To better understand 837

relationships between activity levels, size fluctuations, size distributions and innate dynamics 838

of synaptic molecules, we used a previously published mesoscopic model to derive potential 839

explanations which were then tested experimentally. Explanations attributing the effects of 840

chronic silencing to changes in PSD-95 binding/unbinding kinetics or expression levels were 841

not supported by FRAP experiments, Western blots or quantitative proteomics. Conversely, 842

the experimental findings fully supported the possibility that changes in synaptic size 843

dynamics and distributions primarily reflect PSD-95 redistribution among fewer synapses. 844

These findings thus suggest that intrinsic, activity-independent size fluctuations are sufficient 845

to give rise to full repertoires of synaptic sizes at appropriate proportions. Moreover, they 846

are suggestive of reciprocal and possibly self-reinforcing relationships between synaptic size 847

fluctuations, size distributions and synaptic counts mediated by the innate dynamics of 848

synaptic molecules as they continuously move in, out and between synapses 849

850

The source of broad and rightward skewed synaptic size distributions 851

As mentioned above, broad, rightward skewed distributions of synaptic sizes are 852

ubiquitously observed. Explanations have typically fallen into two classes: 853

The first attributes their emergence to various activity-dependent, synaptic plasticity 854

processes (van Rossum et al., 2000; Song et al., 2005; Lefort et al., 2009; Gilson and Fukai, 855

2011; Zheng et al., 2013; Buzsáki and Mizuseki, 2014; Effenberger et al., 2015; Scheler, 2017; 856

Uzan et al., 2018). Given that synaptic diversity was not reduced or distribution shapes 857

grossly affected in chronically silenced networks (Fig. 2; see also Harms and Craig, 2005; 858

Harms et al., 2005), this class of explanations would seem to be somewhat unsatisfactory. 859

Indeed, recent studies reported that in chronically silenced mouse forebrains (Sando et al., 860

2017) and in hippocampal organotypic cultures prepared from Munc13-1 and Munc13-2 861

knockout mice (which are essentially devoid of presynaptic release; Sigler et al., 2017), spine 862

types (mushroom, thin, stubby) are present at normal proportions. 863

31

A second explanation class attributes these distributions to intrinsic size fluctuations that 864

contain multiplicative (and additive) components (Yasumatsu et al., 2008; Lowenstein et al., 865

2011; Kaufman et al., 2012; Statman et al, 2014; Rubinski et al., 2015; Ziv and Brenner, 2018; 866

Ishii et al., 2018, Humble et al., 2019). Most of such explanations are based on descriptive 867

models in which size fluctuations are treated statistically without addressing their sources. 868

One exception is the mesoscopic model of Shomar et al., 2017 used here (Figs. 7,9,10) which 869

showed how cooperative, stochastic binding and unbinding of synaptic molecules can drive 870

intrinsic size fluctuations that shape synaptic size distributions (see also Ranft et al., 2017; 871

Triesch et al., 2018). Here we extended these findings, showing that changes in synaptic 872

molecule abundance or synapse numbers can affect the magnitude of intrinsic fluctuations 873

and ultimately synaptic diversity (Figs. 9,10), in good agreement with the recent modeling 874

study of Triesch and colleagues (2018). These findings thus suggest that activity- 875

independent, intrinsic size fluctuations, whose source can be traced to the innate dynamics 876

of synaptic molecules, contribute enormously to excitatory synapse size diversity (see also 877

Yasumatsu et al., 2008). In fact, they indicate that synaptic size distributions might be 878

primarily shaped by activity-independent processes, with activity levels mainly setting the 879

scale, rather than the shape of these distributions. 880

881

Synaptic size distribution scaling in silenced networks 882

The finding that chronic suppression of network activity increases average synaptic size 883

and scales up synaptic size distributions resembles the homeostatic scaling-up of synaptic 884

strengths and sizes often observed following acute suppressions of network activity 885

(reviewed in Turrigiano, 2008; Pozo and Goda, 2010; Chowdhury and Hell, 2018). In most 886

such studies – both in culture and in vivo – manipulations of activity levels were carried out 887

in networks in which numerous synapses had already formed (e.g. Turrigiano et al., 1998; 888

Murthy et al., 2001; Minerbi et al., 2009; Sun and Turrigiano, 2011; Keck et al., 2013; Barness 889

et al., 2017; Hobbiss et al., 2018) and thus the observed scaling presumably reflected 890

changes in preexisting synaptic populations. This was clearly not the case in our 891

experiments, as activity was suppressed long before synapses had formed and thus the 892

semblance is somewhat superficial. Nevertheless, the larger synapses and broader size 893

distributions in chronically silenced networks are in line with prior suggestions that synaptic 894

sizes are continually constrained by activity-dependent processes, and that silencing- 895

32

associated relaxation of these constraints results in synaptic enlargement (Minerbi et al., 896

2009; Kaufman et al., 2012; Statmann et al., 2014; Ziv and Brenner, 2018). Indeed, a recent 897

study (Sando et al., 2017) reported a 30-40% enlargement of spines (and presynaptic 898

boutons) in chronically silenced mouse forebrains analyzed by light and electron-microscopy. 899

Interestingly, synapse enlargement was associated with comparable reductions in synaptic 900

counts and arbor complexity in some (although not all) forebrain regions. Similarly, spine 901

enlargement in sensory deprived animals was recently shown to be preceded by, and 902

correlate with spine loss in the same dendritic branches (Barnes et al., 2017) further 903

supporting our observations on reciprocal relationships between synaptic sizes and 904

numbers. Understanding how relaxed constraints might reduce synaptic numbers is less 905

intuitive, but can be understood by appreciating how the weaker bias toward growth 906

increases the likelihood of small synapses to become even smaller and ultimately lost (Fig. 907

12). The putative intermediate – a shared pool of synaptic building blocks (Fig. 12) - is in line 908

with many reports on synaptic competition over limited resources (e.g. Harms et al, 2005; 909

Mondin et al., 2011; Ramiro-Cortés et al., 2013; Levy et al., 2015; Ryglewski et al., 2017; 910

Triesch et al., 2018). Obviously, the process proposed in Fig. 12D is not the only determinant 911

of synaptic numbers and dendrite arborization, since large numbers of synapses ultimately 912

form on relatively stable dendritic trees even in silenced networks. This might be expected 913

given that synaptogenesis is governed by many processes not touched on here. Moreover, 914

while dendritic extension and arborization are influenced by synaptogenesis (Cline and Haas, 915

2008), these typically precede synaptogenesis and do not strictly depend on it. 916

In this study we found no evidence that silencing slows PSD-95 exchange kinetics. Other 917

molecules, however, might be affected differently. For example, prolonged silencing was 918

shown to slow the exchange kinetics of Shank3/ProSAP2 and Munc13-1 (Tsuriel et al., 2006; 919

Kalla et al., 2006); Thus, relationships between molecular dynamics and size distributions 920

might differ among synaptic molecules. Finally, many additional mechanisms have been 921

implicated in synaptic size/strength distribution scaling (Turrigiano, 2008; Pozo and Goda, 922

2010; Chowdhury and Hell, 2018) including mechanisms directly involving PSD-95 (e.g. Sun 923

and Turrigiano, 2011; Chowdhury et al., 2018) further highlighting the explanatory 924

challenges these phenomena pose. 925

926

Activity dependent and independent determinants of synaptic sizes 927

33

In vivo studies consistently report substantial fluctuations in spine volume or PSD size 928

over hours to day time scales (Grutzendler et al., 2002; Zuo et al., 2005; Holtmaat et al, 929

2006; Loewenstein et al., 2011; Cane et al., 2014; Ishii et al., 2018). Moreover, a recent study 930

(using PSD-95:EGFP) suggests that nanoscale PSD organization in the mouse visual cortex 931

undergoes remarkable ‘morphing’ over these time scales (Wegner et al., 2018). As these 932

studies were carried out in live animals, it was not possible to separate intrinsic fluctuations 933

from activity-dependent synaptic remodeling. In fact, it was recently proposed that synaptic 934

size fluctuations are the product of ongoing potentiation and depression caused by external 935

stimuli and internal neuronal activity which ride on top of synaptic scaling related to changes 936

in activity levels (Keck et al., 2017). Our findings suggest, however, that PSD morphing, size 937

fluctuations, size distributions and their scaling are tightly interconnected phenomena, 938

whose root causes relate, at least in part, to the innate dynamics of synaptic molecules. 939

Interestingly, the size dynamics these produce – noisy additive growth offset by noisy 940

multiplicative downscaling – inherently ‘solve’ one of the thorny issues of Hebbian forms of 941

synaptic plasticity, that is the requisite for continuous synaptic size normalization (e.g. Zenke 942

et al., 2017). Of course, these dynamics introduce thorny issues of their own, such the poor 943

preservation of size relationships during this normalization process (Minerbi et al., 2009; 944

Kaufman et al., 2012; Statman et al., 2014). For now, reconciliation of these thorny issues 945

with common notions on synaptic plasticity still awaits resolution (Mongillo et al., 2017; 946

Chambers and Rumpel, 2017; Ziv and Brenner 2018). 947

948

949

950

34

References 951

Andreae LC, Burrone J (2014) The role of neuronal activity and transmitter release on 952 synapse formation. Curr Opin Neurobiol 27:47-52. 953

Annis CA, Dowd DKO, Robertson RT (1994) Activity-dependent regulation of dendritic spine 954 density on cortical