Repetitive transcranial magnetic stimulation (rTMS) triggers dose-dependent homeostatic rewiring in recurrent neuronal networks

Repetitive transcranial magnetic stimulation (rTMS) is a non-invasive brain stimulation technique used to induce neuronal plasticity in healthy individuals and patients. Designing effective and reproducible rTMS protocols poses a major challenge in the field as the underlying biomechanisms remain elusive. Current clinical protocol designs are often based on studies reporting rTMS-induced long-term potentiation or depression of synaptic transmission. Herein, we employed computational modeling to explore the effects of rTMS on long-term structural plasticity and changes in network connectivity. We simulated a recurrent neuronal network with homeostatic structural plasticity between excitatory neurons, and demonstrated that this mechanism was sensitive to specific parameters of the stimulation protocol (i.e., frequency, intensity, and duration of stimulation). The feedback-inhibition initiated by network stimulation influenced the net stimulation outcome and hindered the rTMS-induced homeostatic structural plasticity, highlighting the role of inhibitory networks. These findings suggest a novel mechanism for the lasting effects of rTMS, i.e., rTMS-induced homeostatic structural plasticity, and highlight the importance of network inhibition in careful protocol design, standardization, and optimization of stimulation.

Repetitive transcranial magnetic stimulation (rTMS) is a non-invasive brain 2 stimulation method used in basic and clinical neuroscience (1,2,3). Based on the 3 principle of electromagnetic induction, rTMS induces electric fields that activate cortical 4 neurons and modulate cortical excitability beyond the stimulation period (4,5,6). This 5 makes rTMS a suitable tool for studying and modulating brain plasticity in healthy and 6 disease states [7,8,9,10,11]. 7 Experiments in animal models have shown that rTMS induces specific changes in 8 excitatory synapses, that are consistent with a long-term potentiation (LTP) of 9 neurotransmission (12,13,14,15). Using animal models (both in vitro and in vivo), we 10 also previously demonstrated rTMS-induced changes in inhibitory neurotransmission, 11 wherein a reduction in dendritic but not somatic inhibition was observed (16). These 12 findings provide an explanation of how rTMS may assert its effects-by mediating 13 disinhibition and priming stimulated networks for the expression of physiological 14 context-specific plasticity (17). Nevertheless, it remains unknown how exogenous 15 electric brain stimulation that is not linked with specific environmental or endogenous 16 signals asserts therapeutic effects in patients. 17 In recent years, a considerable degree of variability (or even absence) of rTMS 18 induced "LTP-like" plasticity-measured as a change in the evoked potential of the 19 target muscle upon stimulation of the motor cortex (18,19,20,21)-has been reported 20 in human participants, often leading to difficulties in reproducing results (22). Efforts to 21 explain this variability have largely focused on the assessment of possible confounding 22 factors that may affect the outcome of a given rTMS protocol as well as on prospective 23 optimization of induced electrical fields for standardization of stimulation protocols and 24 dosing across participants (23,24). This has also led to discussions on alternative 25 underlying mechanisms, such as the impact of rTMS on glial cells and rTMS-induced 26 structural remodeling of neuronal networks (25,26,27,28). There has been emerging 27 evidence of structural plasticity induced by rTMS. Studies have demonstrated that 28 rTMS facilitates reorganization of abnormal cortical circuits (10,11), which may be 29 pertinent to its therapeutic effects and cognitive benefits (29,30). Moreover, structural 30 connectivity changes induced by rTMS have been shown to underlie anti-depressant 31 effects in chronic treatment-resistant depression (31,32,33). Vlachos et al. (12) also 32 demonstrated structural remodeling imposed by 10 Hz repetitive magnetic stimulation 33 on small dendritic spines in an in vitro setting. More recently, structural synaptic 34 plasticity in response to low-intensity rTMS was demonstrated using longitudinal 35 two-photon microscopy in the motor cortex of mice (14). Towards this direction, we 36 used network simulations to evaluate the dose-dependent effects of rTMS on the 37 structural remodeling of neuronal networks in this study. We evaluated rTMS-induced 38 structural changes that may occur even in the absence of changes in synaptic weights 39 (i.e., LTP-like plasticity). Specifically, we employed an inhibition-dominated recurrent 40 neuronal network with homeostatic structural plasticity that follows a negative feedback 41 rule (34,35,36). In this network, continuous synaptic remodeling takes place in order to 42 maintain neuronal activity at a stable point. Deviation from this level of activity are restored using synaptic formation or deletion at regular intervals. Based on our previous 44 experimental findings that 10 Hz stimulation induces structural remodeling of excitatory 45 synapses and dendritic spines (12), we assessed the effects of stimulation intensity, pulse 46 number, and frequency-including clinically established intermittent theta burst 47 stimulation (iTBS)-on rTMS-induced homeostatic structural plasticity. 48 Materials and methods 49 Neuron model 50 All large-scale simulations in the present study were performed using NEST simulator 51 2.20.0 (37), using MPI based parallel computation. Single neurons were modeled as 52 linear current based leaky integrate and fire (LIF) point neurons, having subthreshold 53 dynamics expressed by the following ordinary differential equation: where τ m is the membrane time constant. The membrane potential of neuron i is 55 denoted by V i . The neurons rest at 0 mV and have a firing threshold (V th ) of 20 mV. 56 The spike trains generated by neuron i is given by arrives. As multiple synapses can exist from neuron j to neuron i, the amplitude J ij is 62 an integer multiple of J E or J I , respectively, depending on the type of the presynaptic 63 neuron. ∆V rTMS denotes the membrane potential deviation induced by magnetic 64 stimulation which will be introduced in the following section. An action potential is 65 generated when the membrane potential V i (t) of the neuron reaches V th , following which 66 the membrane potential is reset to V reset = 10 mV. All parameters are listed in Table 1 The plastic network has the same network architecture as the static network, except 84 that the E-E connections were grown from zero following the homeostatic structural 85 plasticity rule implemented in previous works (35,36,39). By setting the target firing 86 rate to 7.8 Hz, the network will grow into an equilibrium status driven by the external 87 Poissonian input (r ext = 30 kHz), where the average connection probability is around 88 10% and all neurons fire irregularly and asynchronously around the target rate (7.8 Hz). 89 While using a plastic network, any repetitive magnetic stimulation is only applied after 90 completion of the growth period. Network parameters can be found in Table 2.

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Homeostatic structural plasticity rule 92 As mentioned above, the connections among excitatory neurons (E-E) followed a 93 homeostatic structural plasticity (HSP) rule, and were subject to continuous remodeling. 94 This rule has been inspired by precursor models by Dammasch (40) (45) and neurogenesis in adult dentate gyrus (46,47).

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However, we use a more recent implementation of this model in NEST (48) which does 99 not include a distance-dependent kernel, previously used to demonstrate associative 100 properties of homeostatic structural plasticity (35,39). The authors demonstrated that 101 without the need of an enforced Hebbian plasticity rule, this homeostatic rule can cause 102 network remodeling which displays emergent properties of Hebbian plasticity. Following 103 external stimulation, the affected neurons underwent synaptic remodeling that lead to 104 formation of a cell assembly among these neurons, thus exhibiting activity driven Each neuron i in this model has a discrete number of dendritic spines (presynaptic 109 elements, z d i ) and axonal buotons (postsynaptic elements, z a i ), which are paired to form 110 functional synapses. Synapses can only be formed if free synaptic elements are available. 111 Each synapse has a uniform strength of J E = 0.1 mV. The growth rule we use is a 112 rate-based rule, as implemented in NEST (48). The rule follows the set-point 113 hypothesis, which states that there is a set-point of intracellular calcium concentration 114 that a neuron tries to achieve, in order to maintain stability. Deviations from this 115 set-point level are met by global (whole neuron) efforts to restore it via synaptic 116 turnover. This is in line with experimental results that have shown that neurite growth 117 and deletion are controlled by intracellular calcium concentration (50,51,52). 118 Therefore, in the model of homeostatic structural plasticity used here, the growth and 119 deletion of synaptic elements of a neuron i are governed by its intracellular calcium The variable ϕ i (t) has been shown to be a good indicator of a neuron's firing rate (53). 125 According to the synaptic growth rule we use, each neuron i maintains a time-varying 126 estimate of its own firing rate, using its intracellular calcium concentration as a 127 surrogate. This estimate is used by the neuron to control the number of its synaptic 128 elements. When the firing rate falls below the prescribed set-point, indicated by a 129 target firing rate, the neuron grows new synaptic elements to form additional synapses. 130 Following this, freely available pre-and postsynaptic elements are randomly paired with 131 free synaptic elements of other neurons, forming new synapses. These synapses enable 132 the neuron to receive additional excitatory inputs, thus bringing the firing rate back to 133 the set-point. Similarly, when the firing rate rises above the set-point, the neuron 134 breaks existing synapses in order to limit the net excitatory inputs received. The 135 elements from these broken synapses are added to the pool of free synaptic elements.

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Both the pre-and post-synaptic elements follow this linear growth rule (35,36), where i is the index of the neuron, ν is the growth rate and ϵ is the target level of 138 calcium. The parameters of the homeostatic structural plasticity rule are listed again in 139 Table 3. The effect of rTMS over networks of neurons has often been described using canonical 160 cortical microcircuit models (62)   In order to investigate the effects of protocol structure, we modeled repetitive 169 stimulation protocols (Fig 1D) of different frequencies and intensities. We also modeled 170 the clinically relevant US FDA approved protocol, namely intermittent theta burst 171 stimulation (iTBS) with 600 pulses, described in following sections. Parameters of TMS 172 protocols used throughout this study are summarised in Table 4.  The membrane depolarisation applied are: a = 20 mV, b = 39 mV, c = 68 mV, d = 160 mV. 3 The pulse numbers used are 300, 600, 900, 1200, 3000 and 9000.

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intermittent theta burst stimulation (iTBS) protocol has a more temporally complex  The membrane potential deviation in the leaky integrate and fire neurons caused by 198 current injection was estimated using Ohm's Law. Accordingly, a current pulse of 199 amplitude A yields a membrane potential response, U (t): 200 where R = 80 MΩ is the membrane leak resistance, τ = 20 ms is the membrane time where t = 0.5 ms is the duration of the TMS pulse. We used the above formulation to 205 calculate the membrane potential deviation caused by TMS pulses to single neurons.

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March 14, 2023 7/25 . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The spiking activity of individual neurons are read out using a spike-detector, as 208 available in NEST. The firing rate is calculated as a spike count average, across defined 209 time-steps of simulation, typically of 1000 ms duration. Mean firing rate of a population 210 are calculated as the arithmetic mean of firing rates of all the neurons from the group.
Time constant of connectivity saturation 220 In order to characterise the stimulation duration required to reach connectivity 221 saturation during stimulation, we perform a curve-fitting of the data-points using an 222 exponential function: where τ decay = 1/b represents the time constant of the decay of connectivity during Multi-scale compartmental modeling demonstrates that the electric fields induced by 230 TMS generally cause changes in the membrane potential of individual principal neurons, 231 eventually resulting in action potential induction and characteristic intracellular calcium 232 level changes (66,67,68). Therefore, we first evaluated the effects of TMS-like electric 233 stimulation on the membrane potentials at a single neuron level (Fig 1). For this 234 purpose, single neurons-those receiving balanced excitatory and inhibitory Poissonian 235 spike trains-were stimulated with 0.5 ms rectangular current pulse injections of 236 different amplitudes (Fig 1A and B). A linear interrelation between current injections 237 and membrane potential deviation was observed, consistent with Ohm's law (Fig 1C). 238 With this approach, implementation of suprathreshold repeated stimulations, i.e., ∆V = 239 68 mV at 1, 10 or 50 Hz, induced robust action potentials in the individual 240 neurons (Fig 1D). We conclude that TMS-like neuronal spiking can be readily induced 241 in our experimental setting. In realistic applications, TMS activates a network of connected neurons rather than a 244 single neuron. Therefore, we evaluated the effects of increasing stimulation intensities 245 on a subpopulation of neurons embedded in a recurrent network of 10000 excitatory and 246 2500 inhibitory neurons (Fig 2A). We modeled a focal stimulation that directly 247 affected 10% of the excitatory neurons and studied the network response in terms of the 248 firing rate changes among the following populations: stimulated excitatory neurons (S), 249 non-stimulated excitatory neurons (E), and inhibitory interneurons (I). We first 250 delivered a sample train of rTMS pulses (900 pulses at 10 Hz, c.f., 12, 69, with a pulse 251 intensity that would cause a 68 mV membrane potential deviation) to the subpopulation. 252 As shown in the raster plot, the spiking activity in the stimulated subpopulation was 253 elevated (Fig 2B). We also observed a weaker synchronization throughout the To examine the impact of distinct stimulation protocols on network activity, we 257 performed a series of simulations with varying intensities and frequencies (each at 900 258 pulses). Examples of the firing rates of the defined subpopulations of interest are shown 259 in Fig 2C. We found that the stimulated population responded at lower stimulation 260 intensities and frequencies (i.e., 1 Hz and 10 Hz), with a proportional increase in the 261 firing rates, which peaked at a stimulus-induced depolarization of 68 mV. With stronger 262 stimulation, the firing rate response of the stimulated subpopulation declined as the 263 firing rate of the inhibitory neurons increased owing to recurrent inhibition. Eventually, 264 a plateau was reached. For higher frequencies (i.e., 50 Hz), changes in the firing rate did 265 not follow the exact same trend as for the lower frequencies (e.g., 1 Hz). This may be 266 attributed to the strong high-frequency stimulation that forced the network to enter 267 into a different stable regime. Nevertheless, the impact of recurrent inhibition on the 268 stimulated neurons was still observable (Fig 2C). The effects of distinct stimulation 269 intensities on the network firing dynamics were carefully examined by plotting the firing 270 rate distributions of the respective sub-populations in response to those intensities (Fig 271  2D). Weak stimulation did not cause noticeable additional activation of the inhibitory 272 subpopulation. At the peak intensity, the inhibitory neurons were evidently activated. 273 The strong stimulation significantly activated the inhibitory interneurons. The evoked 274 recurrent inhibition had a profound effect on the stimulated subpopulation, resulting in 275 suppression of its firing rate response. The same firing rate of the stimulated neurons 276 was achieved at much lower stimulation intensities that did not recruit inhibition, 277 including strong-equivalent intensity (c.f., Fig 2C). Based on these results, we selected 278 four intensities, characteristic of different states of the network, for further exploration. 279 The resulting values were expressed in terms of the induced changes in the membrane  Fig 2E, bottom). Herein, we observed lower peak firing rates of the 288 stimulated neurons, demonstrating that recurrent inhibition was more effectively 289 recruited when larger populations of neurons were directly stimulated. Taken together, 290 these simulations suggest that an "optimal" stimulation intensity that effectively 291 increases the firing rate of stimulated neurons exists. Exceeding this intensity leads to 292 further recruitment of inhibition, which dampens the activity of the stimulated 293 excitatory neurons. Lower strong-equivalent stimulation intensities can be determined 294 at which the same effects on the firing rates of stimulated neurons are observed, without 295 major effects on network inhibition.

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Structural remodeling of network connectivity in response to 297 rTMS 298 We switched to a plastic network that remodels its connections in an 299 activity-dependent homeostatic manner (Fig 3). This network follows a plasticity rule 300 where an increase in the firing rate of excitatory neurons leads to retraction and 301 disconnection, while a reduction in the firing rate promotes outgrowth and formation of 302 new excitatory contacts between principal neurons (Fig 3A; c.f., 35,36). In this study, 303 stimulation was performed after an initial growth stage, which allowed the network to 304 reach a steady state with 10% connectivity between the excitatory neurons and a mean 305 . CC-BY 4.0 International license available under a (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted March 21, 2023. ; https://doi.org/10.1101/2023.03.20.533396 doi: bioRxiv preprint firing rate of 7.8 Hz (Fig 3B). We applied a 10 Hz stimulation protocol consisting of 900 306 pulses at peak intensity to a subset of 10% of excitatory neurons (c.f., Fig 2B). As 307 described above, the stimulation elicited an instant increase in the firing rates of the 308 stimulated neurons as well as non-stimulated excitatory and inhibitory neurons (Fig   309   3C). This sudden increase in the firing rates was accompanied with a homeostatic 310 structural response where the principal neurons reduced existing input synapses to 311 restore baseline activity. This disconnection was most prominently observed among the 312 stimulated neurons, but also occurred between the stimulated and non-stimulated 313 excitatory neurons (Fig 3C). The end of stimulation, which was also marked by a 314 sudden drop in the net input received by the non-stimulated excitatory and inhibitory 315 neurons, led to an instant drop in firing rates. This was followed by the formation of  We also assessed the outcome of the distinct stimulation intensities on homeostatic 327 structural plasticity and network connectivity (Fig 3D). The same stimulation protocol 328 (10 Hz, 900 pulses) was applied with weak, peak, strong, and strong-equivalent 329 intensities (c.f., Fig 2B and C). As shown in Fig 3D, the largest change in the 330 connectivity among the stimulated neurons was seen in response to the peak amplitude 331 (i.e., a 68 mV membrane potential increase). The weak amplitude elicited a small 332 response in neural activity, and only minor changes in lasting connectivity were 333 observed ( Fig 3D). The strong and strong-equivalent amplitudes yielded different effects 334 on connectivity. The network receiving strong-amplitude stimulation failed to rapidly 335 restore its activity to baseline by homeostatic structural plasticity during stimulation, 336 which was reflected in a weaker overall connectivity change. This may be attributed to 337 the recurrent inhibition recruited by a strong electric stimulation, which then affected 338 the stimulated neurons. This phenomenon was not observed in the strong-equivalent 339 stimulation, while a considerable remodeling of network connectivity was noted (Fig   340   3D).

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Influence of the stimulation duration on network remodeling 342 We noted that the extent of network connectivity changes after stimulation depended 343 on the degree of reorganization caused during stimulation. Indeed, a proportional 344 interrelation was observed between these two parameters (Fig 4A). This observation had 345 important implications for the stimulation duration, including the number of pulses 346 applied at a given frequency. The finding suggests that once the increase in the firing 347 rate is compensated, the application of additional pulses will not have a further effect   stimulated neurons (Fig 4B). We observed an increasing post-stimulation peak 353 connectivity with an increasing stimulation duration. However, this relationship did not 354 hold beyond a certain point. For 10 Hz stimulation, we found that stimulation beyond 355 ∼3000 pulses did not contribute to further changes in the peak connectivity. This 356 allowed us to conclude that the connectivity change has reached a saturation point, and 357 10 Hz stimulation for longer durations would not have a stronger effect on network 358 connectivity ( Fig 4B). Indeed, the outcome of a stimulation with 22500 pulses was 359 comparable to that observed with 3000 and 9000 pulses, as shown in Fig 4B.

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We followed up on this observation by extending our simulations to include a range of 361 frequencies from 10 Hz to 50 Hz, as summarized in Fig 4C. The trend of connectivity 362 saturation was maintained, with lower frequencies taking larger pulse numbers to reach 363 the saturation point. Considering that the pulse number is equal to the total  a trend of inverse proportionality in case of peak stimulation intensity. We deduce that 369 the total stimulation duration has a major impact on the net stimulation outcome, 370 irrespective of the frequency.

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Effects of the clinically approved iTBS protocol on network 372 activity and connectivity 373 Finally, we evaluated the effects of the clinically approved iTBS protocol, which we 374 found to have a more complex stimulation pattern with inter-train intervals (Fig 5A). 375 We systematically applied the four relevant stimulation intensities, namely weak, peak, 376 strong, and strong-equivalent, and assessed the changes in network connectivity (Fig   377   5B). Similar to what we observed with 10 Hz stimulation, the weak and peak stimulation 378 intensities led to small and large changes in connectivity, respectively. Comparatively, 379 the strong-equivalent intensity induced intermediate changes in connectivity, while the 380 strong stimulation intensity led to only small changes in connectivity. 381 We then evaluated distinct stimulation durations, including the pulse numbers at 382 peak stimulation intensity, and found that a plateau was reached between 600 and 1200 383 pulses, with 900 pulses showing approximately the same effect as 1200 pulses on 384 network connectivity (Fig 5C). An additional increase in connectivity was evident at In this study, we explored the effects of rTMS on network dynamics and connectivity 398 using simulations of an inhibition-dominated recurrent neural network with homeostatic 399 structural plasticity. rTMS was found to increase the activity of neurons and induce (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted March 21, 2023. ; https://doi.org/10.1101/2023.03.20.533396 doi: bioRxiv preprint activation and plasticity. We also observed that increasing the number of stimulation 407 pulses beyond a certain point may saturate the structural network reorganization. Thus, 408 optimal stimulation protocols where no additional desired effects will be observed by 409 further increasing the intensity of stimulation or number of TMS pulses may exist. 410 However, for the FDA-approved iTBS protocol, we observed an additive effect on the 411 changes in network activity at larger pulse numbers. We attribute this effect to the 412 complex pattern of the iTBS protocol, specifically the inter-train intervals. iTBS at 900 413 pulses seems to be more effective than iTBS at 600 pulses in our simulations. Notably, 414 however, the effects of iTBS on the structural remodeling of the stimulated networks

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While some experimental evidence supports the existence of homeostatic structural 444 plasticity (79, 80,81, for overview, see 82), its biological significance and the underlying 445 molecular mechanisms warrant further investigation. In our previous work, in which we 446 used live cell microscopy to study the effects of rTMS on dendritic spines of cultured 447 hippocampal CA1 neurons, we did not find any significant changes in the synapse 448 numbers, including spine density changes following 10 Hz repetitive magnetic 449 stimulation (12). This is consistent with the finding of a recent in vivo two-photon 450 imaging study demonstrating subtle structural changes in dendritic spines in response 451 to repeated sessions of low-intensity rTMS (14). Synaptic (un)-silencing could be one of 452 the biological implementations of homeostatic structural plasticity (82,83,84).

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Synapses that are typically found on small dendritic spines or filopodia containing 454 mainly NMDA receptors are referred to as "silent", as NMDA receptors are blocked by 455 magnesium ions at resting membrane potential. They can be activated after the (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint this version posted March 21, 2023. ; https://doi.org/10.1101/2023.03.20.533396 doi: bioRxiv preprint accumulation of depolarizing AMPA receptors (85,86,87,88). Indeed, our previous 457 work revealed that 10 Hz repetitive magnetic stimulation promotes the accumulation of 458 AMPA receptors at small preexisting spine synapses and triggers the growth of these 459 presumably silent dendritic spines (12). Thus, rTMS may mediate homeostatic 460 structural plasticity by conveying to neurons the ability to remove or form functional 461 synaptic connections by regulating the accumulation of AMPA-receptors at preexisting 462 synapses, without the need to recruit the complete molecular machinery to remove or 463 form new spines and/or synapses.

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In a network without structural plasticity, we observed a non-linear relationship 465 between the stimulation intensity and neuronal firing rate changes. This non-linearity in 466 the firing rate response can be attributed to recurrent inhibition. We observed 467 increasing feedback inhibition in response to higher stimulation intensities. This effect 468 had a major impact on the outcome of rTMS-induced structural plasticity. Accordingly, 469 we defined four critical stimulation intensities for closer examination: weak, peak, 470 strong and strong-equivalent. At amplitudes below the peak value, the inhibitory 471 subpopulation was not strongly activated. Meanwhile, with stimulation stronger than 472 the peak amplitude, stronger recurrent activity recruited the inhibitory subpopulation, 473 which consequently inhibited the stimulated subpopulation, causing a weaker firing rate 474 response. Indeed, stimulation stronger than the peak amplitudes yielded weaker effects 475 on structural remodeling than did stimulation at a lower intensity, despite their 476 comparable effects on the firing rates of the stimulated neurons. In general, this 477 highlights the important role of inhibitory networks in rTMS-induced plasticity. 478 Experimental evidence suggests that single pulse TMS inhibits neocortical dendrites by 479 directly activating axons within the upper cortical layers, which leads to the activation 480 of dendrite-targeting inhibitory neurons in the neocortex of mice (89). Moreover, our 481 previous work showed that 10 Hz rTMS remodels inhibitory synapses: Dendritic but not 482 somatic inhibition as well as the strength, sizes, and numbers of inhibitory synapses 483 were reduced after stimulation (16). These findings emphasize that rTMS also induces 484 structural changes in inhibitory networks. In line with these findings, rTMS has been 485 shown to trigger the remodeling of visual cortical maps (90,91). However, the direct and inhibitory synapses warrant further investigation (92,93,94). Regardless of these 490 considerations our findings suggest that strong stimulation may lead to less effective 491 structural remodeling of stimulated networks as compared with weak stimulation that 492 causes equivalent changes in the firing rates.

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Our model also makes predictions relevant for translational applications of rTMS.

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Based on our findings, we propose a model of "connectivity saturation". Stimulating 495 networks of neurons initiates homeostatic synaptic remodeling that leads to loss in 496 connectivity among the neurons. The end of stimulation period is followed by further 497 synaptic remodeling causing increase in connectivity among the affected neurons. We 498 used an exponential function to fit the trajectory of connectivity during the stimulation 499 period and extracted time constants of connectivity decay, τ decay . This value can be 500 roughly interpreted as the least time required to attain structural equilibrium during 501 stimulation. This translates to the maximum remodeling that is attainable once 502 stimulation is turned off. We found that the τ decay values were comparable for low 503 stimulation intensities across a wide range of frequencies, emphasizing the relevance of 504 the stimulation duration rather than the pulse numbers. At the peak stimulation a longer time to achieve connectivity saturation. A similar connectivity saturation was 507 not observed in the iTBS protocol. However, the effects of iTBS on structural 508 remodeling were much weaker than those of pulse matched 10 Hz stimulation or cTBS. 509 This effect may be attributed to the inter-train intervals, which enabled the network to 510 rewire during the stimulation protocol. Translational frameworks that combine