Neuronal gamma-band synchronization regulated by instantaneous modulations of the oscillation frequency

Neuronal gamma-band synchronization shapes information flow during sensory and cognitive processing. A common view is that a stable and shared frequency over time is required for robust and functional synchronization. To the contrary, we found that non-stationary instantaneous frequency modulations were essential for synchronization. First, we recorded gamma rhythms in monkey visual area V1, and found that they synchronized by continuously modulating their frequency difference in a phase-dependent manner. The frequency modulation properties regulated both the phase-locking and the preferred phase-relation between gamma rhythms. Second, our experimental observations were in agreement with a biophysical model of gamma rhythms and were accurately predicted by the theory of weakly coupled oscillators revealing the underlying theoretical principles that govern gamma synchronization. Thus, synchronization through instantaneous frequency modulations represents a fundamental principle of gamma-band neural coordination that is likely generalizable to other brain rhythms.

We now show how the observed synchronization behavior can be accounted for within the 2 1 6 mathematical framework of the theory of weakly coupled oscillators (Ermentrout and Kleinfeld, 2 1 7 2001; Hoppensteadt and Izhikevich, 1998;Kopell and Ermentrout, 2002;Kuramoto, 1991; 2 1 8 Pikovsky et al., 2002;Winfree, 1967). Many oscillatory phenomena in the natural world 2 1 9 represent dynamic systems with a limit-cycle attractor (Winfree, 2001). Although the underlying 2 2 0 system might be complex (e.g. a neuron or neural population), the dynamics of the system can be 2 2 1 reduced to a phase-variable if the interaction among oscillators is weak. If interaction strength is 2 2 2 weak, amplitude changes are relatively small and play a minor role in the oscillatory dynamics. In this way, V1 neural populations can be approximated as oscillators, 'weakly coupled' by 2 2 4 horizontal connections. The manner in which mutually coupled oscillators adjust their phases, by 2 2 5 phase-delay and phase-advancement, is described by the phase response curve, the PRC (Brown 2 2 6 et al ., 2004;Canavier, 2015;Izhikevich, 2007;Kopell and Ermentrout, 2002; Schwemmer and 2 2 7 Lewis, 2012). The PRC is important, because if the PRC of a system can be described, the 2 2 8 synchronization behavior can be understood at a more general level and hence predicted across 2 2 9 various conditions. According to the theory, the synchronization of two coupled oscillators can be predicted from the 2 3 1 forces they exert on each other as a function of their instantaneous phase difference. The amount 2 3 2 of force is here defined as interaction strength and the interaction function as the PRC. Each oscillator has an intrinsic (natural) frequency and additionally an own source of phase noise, 2 3 4 making the oscillators stochastic. The phase precession of two oscillators is given by (Fig.3A shape G(θ), and the modulation amplitude ε . Around the preferred phase-relation, the 2 6 0 instantaneous frequency difference is reduced ('slow' precession in Fig.3D), whereas away from 2 6 1 the preferred phase-relation, the instantaneous frequency is larger ('fast' precession in Fig.3D).

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In this regime, PLV between 0 and 1 can be obtained. Including phase noise (σ>0) has important slips) that also lead to instantaneous frequency modulations. Hence, for noisy oscillators, the 2 6 6 intermittent synchronization regime is the default regime for a large parameter range. can be observed (Fig.3I). The oscillator with a higher frequency led the oscillator with a lower 2 9 5 frequency in terms of their phases. To demonstrate the underlying principles of V1 gamma synchronization, we aimed to reconstruct 2 9 9 its Arnold tongue, a central prediction of the theory. For comparison, we did the same for the aimed to directly test its accuracy by comparing analytical predictions to experimental 3 0 2 observations in V1, and to simulation data from coupled PING networks. The theory predicts that the phase difference dependent modulations of instantaneous 3 0 4 frequency difference (∆IF(θ)) are determined by the detuning ∆ ω and the interaction term ε G(θ).

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In experimental data, we observed these systematic modulations. Thus, these modulations give information about the detuning and the properties of the interaction term. Specifically, the time- single G(θ) function (mutual PRC) and σ value for a given dataset (i.e. each monkey and the presence of the Arnold tongue in simulation data, we modulated detuning and interaction G(θ), which was approximately a sinusoidal function. This is noteworthy given that the We then tested whether the theory predicted the in vivo data with equal success. In the same 3 5 0 manner as with the PING modeling data, we estimated the underlying parameters using the  analytical predictions well (model accuracy: M1: R 2 =0.83, M2: R 2 = 0.86, both n=638). In tongue across the V1 middle-superficial layers was confirmed also for deep layer contacts 3 7 0 (Fig.S4). We then mapped the mean phase difference (preferred phase-relation) between V1 led to a reduction of the phase difference. Over all single contact pairs the mean phase difference analytical predictions precisely (model accuracy: M1: R 2 =0.92, M2: R 2 =0.88, both n=638).

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We confirmed the PLV and phase difference analysis in spike-CSD (spike-field) and  interaction strength and amplitude as factors (Fig.6). The contributions were expressed in 4 0 2 explained variance (R 2 ). We found that the TWCO (Fig.6A) reflected the same pattern of 4 0 3 contributions as we observed for PING (Fig.6B) and V1 gamma rhythms (Fig.6C). The phase (interaction effect in Fig.6). In addition to the predictions of TWCO, we observed weak effects of   The present study shows that gamma synchronization in awake monkey V1 adheres to 4 3 1 theoretical principles of weakly coupled oscillators (Ermentrout and Kleinfeld, 2001;4 3 2 Hoppensteadt and Izhikevich, 1998;Kopell and Ermentrout, 2002;Kuramoto, 1991;Pikovsky et 4 3 3 al., 2002;Winfree, 1967), thereby providing insight into the synchronization regime of gamma 4 3 4 rhythms and its principles. Given the generality of the synchronization principles, they are likely 4 3 5 to apply to other brain regions and frequency bands. We show that the shape of the frequency modulations reflects the underlying interaction basic function of the widely-used Kuramoto-model (Breakspear et al., 2010). This is in  Izhikevich, 2007;Kopell and Ermentrout, 2002;Pikovsky et al., 2002). Importantly, here we The former was modulated by input drive differences, and the latter by connectivity strength. synchronization. In this perspective, large shifts in the frequency-range could selectively turn on 4 9 8

3.5). (B) PING network simulations (n=697) including different inter-network connection
or off gamma-mediated information flow between brain regions, whereas fine frequency 4 9 9 detuning modulates the exact strength and direction of the gamma-mediated information flow. show that these cycle-by-cycle modulations are essential for regulating synchronization 5 1 0 properties between gamma rhythms. In our experiment, detuning was dependent on the local contrast difference (Ray and Maunsell, band coordination. The horizontal connectivity in V1 is not only local, but also exhibits 5 2 2 remarkable tuning to visual features, orientation being a prime example (Stettler et al., 2002).

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Hence, innate and learned connectivity patterns likely affect the interaction strength and hence temporally coordinating local neural activity as a function of sensory input and connectivity.

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However, in line with previous studies (Eckhorn et al., 2001;Palanca and DeAngelis, 2005), V1 5 2 8 gamma synchronization was found to be mainly local and hence not likely to 'bind' whole 5 2 9 perceptual objects. Furthermore, recent studies on the gamma-band response during natural power for different natural images. In line with these observations, the revealed Arnold tongue of 5 3 2 V1 gamma implies that natural image parts with high input/detuning variability (heterogeneity) 5 3 3 will induce no or weak synchronization, whereas parts with low input/detuning variability 5 3 4 (homogeneity) will induce strong synchronization. This is also in line with proposals linking interpretation shed new light onto the operation of gamma synchronization in the brain and will 5 3 8 permit new and more detailed description of the mechanisms by which synchronization is  Two adult male rhesus monkeys were used in this study. A chamber was implanted above early