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Brain stimulation competes with ongoing oscillations for control of spike timing in the primate brain

['Matthew R. Krause', 'Department Of Neurology', 'Neurosurgery', 'Montreal Neurological Institute', 'Mcgill University', 'Montreal', 'Quebec', 'Pedro G. Vieira', 'Jean-Philippe Thivierge', 'School Of Psychology']

Date: 2022-06

Transcranial alternating current stimulation (tACS) is a popular method for modulating brain activity noninvasively. In particular, tACS is often used as a targeted intervention that enhances a neural oscillation at a specific frequency to affect a particular behavior. However, these interventions often yield highly variable results. Here, we provide a potential explanation for this variability: tACS competes with the brain’s ongoing oscillations. Using neural recordings from alert nonhuman primates, we find that when neural firing is independent of ongoing brain oscillations, tACS readily entrains spiking activity, but when neurons are strongly entrained to ongoing oscillations, tACS often causes a decrease in entrainment instead. Consequently, tACS can yield categorically different results on neural activity, even when the stimulation protocol is fixed. Mathematical analysis suggests that this competition is likely to occur under many experimental conditions. Attempting to impose an external rhythm on the brain may therefore often yield precisely the opposite effect.

Funding: This work was supported by a Canadian Institutes of Health Research Grant to CCP (MOP-115178; https://cihr-irsc.gc.ca ), a Parkinson Canada Pilot Project Grant to MRK (PPG-2020-0000000033; https://www.parkinson.ca ), and a Natural Sciences and Engineering Council of Canada Discovery Grant to JPT (#210977; https://www.nserc-crsng.gc.ca ). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Copyright: © 2022 Krause et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

These results have important ramifications for neuromodulation applications. On the one hand, the reduction of spike entrainment that we observe is precisely the opposite of the effect intended in most studies of human participants. On the other hand, we suggest that the same mechanism could be useful in attaining specific behavioral or clinical goals that require targeted desynchronization of neural activity. More generally, these findings also offer a possible mechanistic explanation for the extensive variability reported in the human tACS literature.

Here, we characterize the interaction between ongoing oscillations and tACS by recording single-neuron activity in the nonhuman primate brain. Our results confirm that tACS can entrain neural activity, but we find that this occurs only when spike entrainment to ongoing activity is weak. Surprisingly, when neurons are strongly locked to ongoing activity, applying tACS usually leads to a decrease in entrainment, which can only be reversed at higher stimulation amplitudes. Since the effects of tACS vary categorically with the strength of ongoing neural entrainment, our data indicate that it competes with brain oscillations for control over spiking activity. Moreover, we show that this competition is a straightforward mathematical consequence of interactions between oscillators.

Most behavioral studies are currently based on the assumption that tACS enhances ongoing oscillatory activity [ 22 ], by causing neurons to fire in sync with the stimulation. Indeed, tACS is capable of creating subthreshold membrane potential fluctuations at the stimulation frequency [ 23 , 24 ], which might explain some reports that tACS and ongoing brain activity interact synergistically [ 15 ]. At the same time, it has been argued that the relatively weak influence of tACS is likely to be overwhelmed by ongoing neural activity [ 25 – 27 ]. If this were the case, tACS may be unable to alter the activity of neurons that are already entrained to an ongoing oscillation. These hypotheses can best be distinguished by measuring the influence of tACS on individual neurons with varying levels of entrainment to ongoing activity. However, prior neurophysiological experiments, including our own [ 7 – 9 ], have focused on conditions in which ongoing neuronal entrainment was weak. As a result, these experiments did not completely capture the conditions occurring during typical human tACS experiments.

Nevertheless, harnessing this mechanism to produce reliable changes in human behavior has proven to be surprisingly difficult. Studies often find that tACS produces inconsistent effects, between and within participants (e.g., [ 10 – 12 ]), even with stimulation frequencies that are known to be linked to the specific behaviors under study. Although individual differences in neuroanatomy may explain some of these inconsistencies [ 11 ], variability in the participants’ ongoing brain activity also appears to shape the effects of tACS [ 13 – 17 ]. For example, asking participants to close their eyes—which increases the amplitude of endogenous alpha oscillations—reduces the subsequent effects of tACS [ 16 , 17 ]. In contrast, increasing beta power, by imagining specific movements, seems to increase the effectiveness of tACS [ 15 ]. The nature of the interactions between tACS and ongoing brain activity thus remains unclear. Since ongoing brain activity varies between [ 18 , 19 ] and within [ 20 , 21 ] individuals, understanding these interactions is critical for determining when, how, and for whom tACS will be effective.

Transcranial electrical stimulation (tES) is a family of techniques that seek to modulate brain activity by applying electrical current noninvasively, through the scalp. This current flows through the head, producing electric fields that interact with the brain’s own electrical activity. Researchers often attempt to target brain functions that rely on oscillatory brain activity at a specific frequency by using transcranial alternating current stimulation (tACS), a form of tES that uses sinusoidal alternating current, oscillating at the same frequency (e.g., [ 1 , 2 ]). Although there have been some concerns about its effectiveness, there is now strong evidence that tACS can influence oscillatory neural activity in vitro [ 3 , 4 ], in small animal models [ 5 , 6 ], and even in the large, well-insulated primate brain [ 7 – 9 ].

Results

We examined the interplay of ongoing oscillations and tACS using recordings from nonhuman primates (Macaca mulatta), a model system that captures many aspects of human anatomy, physiology, and tACS use. Animals were trained to perform a simple visual fixation task that minimized sensory and cognitive factors that influence oscillations. As animals performed this task, we recorded single-unit activity using standard neurophysiological techniques and assessed neuronal entrainment to ongoing local field potential (LFP) and tACS oscillations.

Our experiments targeted cortical area V4, where neurons often exhibit reliable entrainment to the LFP, especially in the 3 to 7 Hz “theta” frequency band [28]. We verified that this occurred in our experiments by computing phase-locking values (PLVs) that describe the consistency of spike timing (see Materials and methods). These values range from 0 (spiking occurs randomly across an oscillation’s cycle) to 1 (spiking occurs at only a single phase of the oscillation). We first assessed V4 neurons’ entrainment to ongoing oscillations by computing PLVs summarizing neurons’ entrainment to LFP components between 1 and 100 Hz (in ±1 Hz bins). Under baseline conditions without any tACS, many V4 neurons were locked to the approximately 5 Hz component of the V4 LFP; entrainment to higher frequency components was much weaker and often approached zero (S1 Fig). Even at 5 Hz, the strength of entrainment ranged from 0 to 0.42, providing an ideal way to test how tACS influences neural entrainment across different levels of entrainment conditions.

tACS causes bidirectional changes in spike timing Next, we recorded from the same V4 neurons during the application of tACS at 5 Hz. Our stimulation methods closely mimicked those commonly used in human studies and produced an electric field of similar strength (approximately 1 V/m). The effects of tACS were assessed by comparing PLVs obtained during blocks of tACS against those computed from intervals of baseline or “sham” stimulation that were randomly interleaved as a control. Data from 4 example neurons are shown in Fig 1A, which summarizes the phases at which spikes occurred during the baseline (blue) and tACS (orange) conditions. For these cells, the entrainment to the ongoing oscillation was weak, and the application of tACS led to a significant increase in phase locking (p < 0.05, per-cell randomization tests; see Materials and methods). These effects resemble those reported previously in other brain regions [7–9], but only occurred in 11% (17/157) of the neurons from which we collected data. PPT PowerPoint slide

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TIFF original image Download: Fig 1. Applying tACS during physiological oscillations results in bidirectional changes in spike timing. (A, B) Spike density histograms for 6 example V4 neurons showing the relative amounts of spiking across an oscillatory cycle. The cells in (A) showed increased entrainment during tACS (orange), compared to baseline (blue). This was sometimes (right column), but not always (left) accompanied by a shift in preferred spiking phase. However, many more neurons, like those shown in (B), had decreased entrainment during 5 Hz tACS compared to baseline. PLV values for each condition are shown below; asterisks indicate p < 0.01. (C–E) Each point in the scatter plots represents a neuron’s PLV during baseline (horizontal position) and tACS (vertical). Data were collected (C) in the presence of a 5 Hz ongoing oscillation within V4 (N = 157), (D) also in V4, but at 20 Hz, where the oscillation is weaker (N = 123), and (E) again at 5 Hz but in the hippocampus (HC; N = 21), which also lacks strong 5 Hz oscillations under our conditions. Neurons showing individually significant changes in phase locking are denoted in red (p < 0.05; per-cell randomization tests). Inset histograms show the changes in PLV across the population. Moreover, 28/123 cells in panel D were also reported in (9); panel E adapted from (8). See also S1 Fig for comparison of entrainment during baseline conditions and S1 Data for numeric values. BL, baseline; PLV, phase-locking value; tACS, transcranial alternating current stimulation. https://doi.org/10.1371/journal.pbio.3001650.g001 Instead, the application of tACS led to a decrease in the phase locking of many more V4 neurons, as shown in the 2 example cells of Fig 1B, whose spike times became more uniform during stimulation. Statistically significant decreases in entrainment (p < 0.05; per-cell randomization tests) were found in 30% (47/157) of the neurons in our sample. Indeed, decreased entrainment was the predominant influence of 5 Hz tACS at the population level: The median PLV decreased from 0.066 (95% CI: [0.044 to 0.085]) to 0.031 [0.007 to 0.058], a statistically significant reduction in rhythmicity (p < 0.01; Z = 3.86; Wilcoxon sign-rank test). These changes were not accompanied by changes in firing rate: The median firing rate under baseline conditions was 4.6 Hz (95% CI: [3.7 to 5.8]) and 3.9 Hz (95% CI: [3.4 to 5.4]) during tACS, which was not significantly different (p > 0.1; Z = 1.63; Wilcoxon sign-rank test). This suggests that these changes in entrainment were not due to signal loss or other artifacts [8]. In fact, when multiple neurons were recorded simultaneously, we often observed that tACS increased the PLV of one neuron, while decreasing the PLV of neurons recorded on an adjacent channel (150 μm apart). Neurons that had higher levels of baseline entrainment tended to become less entrained during tACS, as can be seen in the example cells of Fig 1A and 1B. This pattern was evident in our complete data set (Fig 1C), where baseline entrainment was significantly and negatively correlated with the subsequent changes during tACS (ρ = −0.38; p < 0.01). This correlation persisted even after the application of Oldham’s method [29] to guard against regression to the mean; a permutation-based analysis [30] yielded similar results.

Decreased entrainment is not specific to stimulation frequency or brain region The decreased entrainment we have observed may seem at odds with results from previous studies, which have consistently reported increased entrainment with tACS for spikes recorded from different brain regions and with different tACS frequencies [5–9]. We therefore asked whether the lack of entrainment was due to our choice of brain region or stimulation frequency. As a within-area control, we applied 20 Hz tACS instead (Fig 1D). Neurons in V4 were weakly entrained to the 20 Hz LFP component under baseline conditions (median: 0.01; 95% CI: [0 to 0.018]), with only 1/123 neurons having a PLV above 0.1. Applying 20 Hz tACS to V4 caused 22% (27/123) of neurons to fire significantly more rhythmically (p < 0.05; per-cell randomization test; Fig 1D). The population PLV was significantly increased (p < 0.01, Z = −3.945; Wilcoxon sign-rank test), tripling from 0.01 to 0.029 [0 to 0.050]. These data demonstrate that V4 neurons can be entrained by tACS at a different frequency, suggesting that the 5 Hz results are not attributable to brain area. As a within-frequency control, we also examined neural entrainment in the hippocampus, where baseline entrainment at 5 Hz was weak (Fig 1E). Here, the median baseline PLV was 0.01, and none of the 21 neurons in our sample had a 5 Hz PLV above 0.1. Applying 5 Hz tACS increased entrainment in 9 of 21 hippocampal neurons (42%), with the median PLV rising from 0.0083 [0 to 0.02] under baseline conditions to 0.04 [0.01 to 0.05] during stimulation (p < 0.01; Z = -3.06; Wilcoxon sign-rank test; Fig 1E). Together, these results show that decreased entrainment is neither a feature of V4 neurons nor of 5Hz tACS, both of which can be associated with increased entrainment under the right circumstances, as shown in Fig 1D and 1E.

tACS alters the strength and phase of entrainment Some cells, such as the examples shown in the right column of Fig 1A, also showed a shift in the oscillatory phase at which spiking most often occurred. The specific timing of spikes within an oscillation (i.e., phase) may encode additional information [31], so shifts in preferred phases represent another dimension along which tACS can alter neural activity. In principle, these changes could occur even when the overall levels of entrainment are not affected by tACS. We therefore examined the subset of neurons whose PLVs were not significantly affected by tACS to see if their preferred phase of spiking shifted during stimulation. Since phase shifts require neurons to have a preexisting phase preference, we first analyzed the 22/93 neurons that had individually significant phase preferences (p < 0.05; Rayleigh tests) under baseline conditions. Fig 2 plots the PLVs and preferred phases jointly for each neuron in each condition. The radial distance from the origin corresponds to a neuron’s PLV, while the angular position denotes the phase preference. Vectors connecting the baseline values (blue dots) with those measured during tACS (orange dots) therefore completely describe the effects of stimulation on spike timing. For these neurons, applying tACS consistently shifted the neurons’ spiking phase, so that they developed a statistically significant (p < 0.01; Hodges–Ajne omnibus test) preference for firing during the rising phase of the tACS waveform (35.6°, red arrow in Fig 2A). PPT PowerPoint slide

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TIFF original image Download: Fig 2. Ongoing oscillations determine the strength and phase of tACS entrainment. These polar plots summarize the combined effects of tACS on entrainment strength (PLV, eccentric direction) and entrainment phase (polar angle). Each vector begins during baseline (blue dot) and extends to 1 mA tACS condition (gray dot). (A) Individual vectors for the 22 neurons that had no significant change in PLV but a significant phase preference during baseline. The red arrow indicates their average direction of change. Spike phase histograms are shown for the 4 example cells circled in red. The violet histogram shows similar changes in direction across the entire population of 93 neurons whose PLVs were not significantly affected by tACS. It also peaks at 38°, near the red arrow tip. (B, C) Neurons showing individually significant increases (B) and decreases (C) in PLV, plotted in the same style. No red arrows are included in these panels because the population has no net phase preference (p > 0.05; Hodges–Ajne omnibus test), in part because neurons had weak phase preferences in either the baseline condition (B) or tACS condition (C), as indicated by the clustering near the origin. See S1 Data for numeric values. PLV, phase-locking value; tACS, transcranial alternating current stimulation. https://doi.org/10.1371/journal.pbio.3001650.g002 Repeating this analysis using all 93 neurons where 5Hz tACS had no effect on PLV revealed a similar result: a statistically significant phase-shift toward 38° (p < 0.01; Hodges–Ajne omnibus test). The direction of these shifts is shown in the violet histogram of Fig 2A. These phase changes cannot be attributed to differences in referencing in the baseline and tACS conditions or to spike waveform distortions caused by tACS (see Materials and methods). In fact, shifts toward this early rising phase of the tACS cycle have been predicted from biophysical properties of neuronal membranes [32]. Similar visualizations for neurons that showed significant changes in PLV are provided in Fig 2B and 2C. Neurons that became entrained by tACS tend to start near the origin under baseline conditions and proceed outward during stimulation (Fig 2B). Likewise, when tACS reduced a neuron’s entrainment to the ongoing oscillation, its spiking activity started in the periphery under baseline conditions and proceeded inwards (Fig 2C). We therefore suggest that the phase shifts observed in the cells where PLV values were not significantly changed reflect a balanced combination of these effects: tACS has decoupled neurons from their entrainment to the ongoing oscillation and imposed a similar amount of synchronization to the stimulus waveform at a new phase.

Current intensity shifts the dominant effect of tACS To test this possibility, we collected additional data from 47 V4 neurons using ±1 mA and ±2 mA stimulation. We reasoned that if weak stimulation were partially reducing entrainment to a physiological oscillation, stronger electric fields could completely overcome it and lead to increased entrainment to the tACS waveform [33]. Fig 3 shows the results of this experiment. As in Fig 2, the location of each blue dot represents a neuron’s baseline entrainment, in terms of overall PLV (radial distance from the origin) and preferred phase (angle). Spike timing during ±1 mA is depicted by orange dots and ±2 mA by red dots, forming a trajectory that shows the effects of increasing current on spike timing. Our hypothesis predicts that these trajectories should have a specific form: Starting from the neurons’ baseline levels of entrainment, they first move toward the origin as the tACS and LFP vie for control of spike timing. Once tACS overwhelms the baseline entrainment, it imposes its own rhythm and the vectors extend outward from origin toward the rising phase of the tACS. PPT PowerPoint slide

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TIFF original image Download: Fig 3. tACS reduces entrainment, then reinstates it at a different phase, as the stimulation amplitude increases. (A–C) Polar vectors indicating the phase and strength of V4 neurons’ entrainment (as in Fig 3). The dots indicate baseline conditions (blue), followed by ±1 mA tACS (orange) and ±2 mA tACS (red). Shading indicates the median and 95% CI of the phase preference during baseline (blue) and ±2 mA tACS (red). Panels A and B show an example trajectory for one neuron exhibiting reinstated entrainment (A) and another undergoing progressive decreases in entrainment (B). Panel C shows population data from 27 neurons with significant changes in PLV at either amplitude. (D) Data from N = 9 hippocampal neurons during baseline (blue dot) and ±2 mA tACS (olive), plotted as in panel A. Note that ±2 mA tACS produces an electrical field within the hippocampus that is 3 times weaker than the ±1 mA condition for V4. See S1 Data for numeric values. PLV, phase-locking value; tACS, transcranial alternating current stimulation. https://doi.org/10.1371/journal.pbio.3001650.g003 Many neurons exhibited this pattern: Applying ±1 mA tACS decreased or eliminated entrainment relative to baseline, but the stronger ±2 mA stimulation reinstated some entrainment, often at a different phase. The example neuron shown in Fig 3A had a PLV of 0.159 under baseline conditions, no detectable entrainment during ±1 mA tACS (PLV ≈ 0), and a PLV that again reached 0.158 during ± 2 mA stimulation. During this transition from 0 to ±2 mA stimulation, its preferred phase rotated from 191° to 83°. While a naive analysis that considered only changes in PLV might conclude that this neuron was insensitive to tACS, these data demonstrate that the structure of its spike timing is, in fact, altered by the stimulation. Other neurons progressively lost entrainment as the stimulation amplitude increased. This pattern appears in the example cell shown in Fig 3B, whose PLVs decreased from 0.21 to 0.092, to nearly 0 as the tACS amplitude increased, with the phase consistently remaining near 225° (223°, 235°, and 221°, respectively). Both patterns are common in our data, as shown in Fig 3C, which depicts the trajectories through 0, ±1, and ±2 mA for the 28/47 neurons (60%) in our data set that showed significant changes from their baseline PLV at either tACS intensity. One possible interpretation of these data is that neurons vary in their susceptibility to the electric field (e.g., due to their morphology or orientation relative to the field) and that stimulation above ±2 mA would be necessary to completely desynchronize and reentrain the cells in the latter group. We present a similar diagram for our hippocampal data in Fig 3D. Although the electric field reaching this deep structure was far weaker (0.2 to 0.3 V/m; 8), nearly half of these neurons (9/21; Fig 1E) showed increased entrainment, reminiscent of the ±2 mA condition in V4. Critically, these neurons’ baseline levels of entrainment were near zero, so it was not necessary to overcome any substantial baseline entrainment before entraining their spike timing. Interestingly, the preferred phase for these neurons was similar to that observed in V4 (Fig 3C). This similarity has been suggested to indicate that both populations were directly affected by tACS via the same biophysical mechanism and that the deep structure was not merely entrained by modifying its more superficial inputs [6]. Overall, these results, across stimulation frequencies, stimulation amplitudes, and brain regions, consistently show that tACS influences spiking activity in a manner that depends strongly on the levels of preexisting entrainment.

Similar patterns of effects emerge from a simple oscillator model Our experimental results show a specific pattern where weaker stimulation reduces entrainment relative to baseline, while stronger stimulation successfully entrains neurons. Although there are many ways in which tACS could interact with ongoing oscillations (reviewed in 34), most previous experimental work has not reported decreased entrainment. We therefore sought to determine whether decreased entrainment has a theoretical basis in the properties of coupled oscillators. Specifically, we explored the properties of a simple oscillator model [35] consisting of 2 equations: Here, x and y represent the dynamics of 2 coupled populations of neurons, whose interactions generate an oscillation. For simplicity, we assumed that higher amplitude oscillations were associated with stronger phase locking, as found in previous experimental work [6,24]. We simulated the effects of tACS by changing the properties of the external drive s(t), setting it either to zero (for baseline conditions) or a sine wave of given frequency and phase offset for the tACS condition. The parameter k determines how strongly this external drive affects the neuronal population and is given here as a percentage of the ongoing oscillation’s amplitude. We first asked whether phase mismatches between an ongoing oscillation and tACS at the same frequency could account for our results. They cannot. Most phase offsets do not reduce the oscillation’s amplitude, even transiently, but instead lead to a shift in phase with the amplitude preserved or increased. Phase offsets near 180 degrees can produce brief reductions in amplitude, but the oscillation rapidly recovers and eventually exceeds the baseline amplitude. Fig 4A shows the most extreme example of this effect. Applying completely out-of-phase stimulation (180° mismatch) initially depresses the oscillation’s amplitude, but these effects only last 3 to 6 cycles; the amplitude subsequently increases by 5%, 26%, and 49%, depending on the stimulation intensity. Since our data was collected in blocks where hundreds or thousands of tACS cycles were applied, any transient decrease in the oscillation would be overwhelmed by the subsequent long-lasting amplitude increase. Moreover, our data were collected during an open-loop stimulation paradigm, where the onset of stimulation was unrelated to the ongoing oscillation’s phase, so conditions where even these transient decreases occur were unlikely. PPT PowerPoint slide

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TIFF original image Download: Fig 4. A simple oscillator model replicates these results. (A) Stimulating the Stuart–Landau model at the same frequency tends to increase entrainment and shift phase. The model’s output, x(t), is shown during a no-stimulation condition (blue) and during the application of tACS (yellow) at low (top), medium (middle), and high (bottom) stimulation intensities. Dotted lines indicate oscillation’s amplitude in the absence of stimulation. The other component of the model, y(t), is simply a phase-shifted version of x(t) and shows the same pattern of effects, as shown in S2 Fig. (B) Stimulation applied at a slightly different frequency tends to reduce entrainment instead. The model output is plotted as in panel A. (C) Changes in entrainment, as a function of frequency mismatch and stimulation intensity. (D) Changes in total entrainment, calculated by integrating the curves in panel C. Colors correspond to those used in panel C. See also S1 Appendix and the figures therein. See S2 Data for numeric values. tACS, transcranial alternating current stimulation. https://doi.org/10.1371/journal.pbio.3001650.g004 We next asked whether slight differences between the frequencies of tACS and the ongoing oscillation could account for our results. This did seem to be the case. Fig 4B shows that applying stimulation at a frequency that was only 6% below that of the ongoing oscillation led to a 29% decrease in amplitude at moderate stimulation intensities (k = 30%; middle row of Fig 4B), but a 35% increase at higher intensities (k = 75%; bottom row of Fig 4B). Similar effects were observed when stimulation frequency was slightly higher instead: The weaker stimulation decreased the oscillation’s amplitude by 25%, while the stronger stimulation increased it by 44% instead. These effects are summarized in Fig 4C for a wide range of stimulation strengths and relative frequencies. To mimic the open-loop nature of our experiments, these data were averaged across evenly spaced phase offsets, so these effects are independent of the relative phases of the tACS and ongoing oscillation. In summary, stimulation that precisely matched the oscillation’s frequency, regardless of phase, eventually led to increased oscillation strength but detuning the frequency by even a fraction of a cycle reduced the amplitude noticeably when the stimulation amplitude was relatively weak. In real experiments, such a mismatch is likely unavoidable, given variability in spike timing [36] and peak frequencies within an oscillation [37], as well as the nonsinusoidal nature of neural oscillations [38,39]. We obtained similar results, shown in S1 Appendix, from simulations using Ornstein–Uhlenbeck processes, which mimic the irregular nature of real neural oscillations [40]. Since entrainment is typically measured across a range of frequencies, as in the 2 Hz bins used in our analysis above, tACS at a single frequency cause mixed effects on entrainment. We therefore examined the net effect of stimulation on narrow-band oscillations, by integrating the curves of Fig 4C across frequencies for each stimulation intensity (Fig 4D). Initially, the total entrainment within these narrow frequency bands decreased, but when the stimulation amplitude exceeded about 66% of the ongoing oscillation’s amplitude, entrainment increased, just as we have observed in our data (Fig 3).

Baseline frequency preference determines the effects of tACS A straightforward prediction of this model is that entrainment should be most strongly reduced for neurons already entrained to frequencies that differ slightly from the stimulation frequency (i.e., in the flank of the entrainment versus frequency mismatch curve in Fig 4C). We tested this prediction in our experimental data by identifying each V4 neuron’s baseline frequency preference. To do so, we filtered the baseline LFP into narrow frequency bands between 2 and 8 Hz (±0.25 Hz around the center frequency) and calculated the PLV between spiking activity and each LFP component. The center frequency of the component with the highest PLV was assigned as the neuron’s preferred frequency, as summarized in Fig 5A. PPT PowerPoint slide

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TIFF original image Download: Fig 5. Preexisting frequency preference determines the effects of tACS. (A) Histogram of narrowband preferred frequency for the 47 V4 neurons with significantly decreased entrainment during 5 Hz tACS. (B) Changes in these neurons’ PLV as a function of the difference between their narrowband preferred frequency and the 5 Hz tACS frequency. Note the qualitative similarity to the flank of Fig 4C. See S1 Data for numeric values. PLV, phase-locking value; tACS, transcranial alternating current stimulation. https://doi.org/10.1371/journal.pbio.3001650.g005 Fig 5B shows that, of the 47 neurons showing significantly decreased entrainment during 5 Hz tACS, neurons with baseline frequency preferences 1 to 2 Hz away from the stimulation frequency had the largest decrease in PLV. This is reminiscent of the flank of Fig 4C. Only one neuron with decreased entrainment had a baseline frequency preference between 4.75 and 5.25 Hz. Owing to their low baseline entrainment, no preexisting frequency preference could be identified for the 17 neurons that exhibited increased entrainment during tACS. The model also predicts that stimulation far from the baseline frequency preference should have little effect on entrainment at that frequency. Consistent with this hypothesis, we found little change in entrainment to the 5 Hz component of the LFP during 20 Hz tACS: Only 13/123 or 10.5% of cells had significantly altered PLVs, a percentage that is expected given our p = 0.05 threshold for individual cells (χ2(1) = 2.2; p = 0.14). Taken together, these results demonstrate a strong but qualitative agreement with models of competing oscillators.

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