bioRxiv preprint doi: https://doi.org/10.1101/428490; this version posted January 11, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.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 available under aCC-BY-NC-ND 4.0 International license. 1 High-order theta harmonics account for the detection of slow gamma 2 3 4 Abbreviated Title: Harmonics Account for Slow Gamma 5 6 7 Y. Zhou1, A. Sheremet1,2, Y. Qin1, J.P. Kennedy2, N.M. DiCola2, A. P. Maurer1,2,3 8 9 1Engineering School of Sustainable Infrastructure and Environment, University of 10 Florida, Gainesville, FL. 32611. 11 2McKnight Brain Institute, Department of Neuroscience, University of Florida, 12 Gainesville, FL. 32610. 13 3Department of Biomedical Engineering, University of Florida, Gainesville, FL. 32611. 14 15 16 17 Correspondence: Drew Maurer 18 McKnight Brain Institute, 19 1149 Newell Dr., RM L1-100E 20 University of Florida 21 Gainesville, Florida 32610 22 Tel: (352) 273-5092 23 Email: [email protected] 24 25 26 Number of pages: 50 27 Number of figures: 13 28 Number of tables: 0 29 Abstract words: 149 30 Introduction words: 989 31 Discussion words: 1936 32 33 The authors declare no conflict of interest. 34 35 36 Key words: Velocity, low gamma, nonlinearity, EEMD 37 38 Acknowledgements: This work was supported by the McKnight Brain Research 39 Foundation, and NIH grants- Grant Sponsor: National Institute on Aging; Grant number: 40 AG055544 and Grant Sponsor: National Institute of Mental Health; Grant Number: 41 MH109548 and a Diversity Supplement to NIH grant R01MH109548 (JPK). Special 42 thanks to S.D. Lovett for technical support. bioRxiv preprint doi: https://doi.org/10.1101/428490; this version posted January 11, 2019. The copyright holder for this preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity.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 available under aCC-BY-NC-ND 4.0 International license. 43 ABSTRACT. 44 Local field potential (LFP) oscillations are the superposition of excitatory/inhibitory postsynaptic 45 potentials. In the hippocampus, the 20-55 Hz range (‘slow gamma’) is proposed to support 46 cognition independent of other frequencies. However, this band overlaps with theta harmonics. 47 We aimed to dissociate the generators of slow gamma versus theta harmonics with current 48 source density and different LFP decompositions. Hippocampal theta harmonic and slow 49 gamma generators were not dissociable. Moreover, comparison of wavelet, ensemble empirical- 50 mode (EEMD), and Fourier decompositions produced distinct outcomes with wavelet and EEMD 51 failing to resolve high-order theta harmonics well defined by Fourier analysis. The varying sizes 52 of the time-frequency atoms used by wavelet distributed the higher-order harmonics over a 53 broader range giving the impression of a low frequency burst (“slow gamma”). The absence of 54 detectable slow gamma refutes a multiplexed model of cognition in favor of the energy cascade 55 hypothesis in which dependency across oscillatory frequencies exists. bioRxiv preprint doi: https://doi.org/10.1101/428490; this version posted January 11, 2019. The copyright holder for this preprint (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 available under aCC-BY-NC-ND 4.0 International license. 56 Introduction 57 In vivo neurophysiology has been a major tool in attempting to understand how the brain 58 organizes behavior, with local-field potential (LFP) oscillations taking center stage. The large 59 rhythmic oscillation in the hippocampus, theta (4-12Hz), was among the first to be characterized 60 in the freely behaving animal (Jung and Kornmüller, 1938; Green and Arduini, 1954; Green and 61 Machne, 1955; Vanderwolf and Heron, 1964; Vanderwolf, 1969; for review, see Buzsáki, 2005). 62 The smaller amplitude, faster gamma oscillation (Stumpf, 1965; Leung, 1992; Bragin et al., 63 1995; Chrobak and Buzsáki, 1998; Penttonen et al., 1998), initially defined as a single, broad 64 frequency range (e.g., 40-100 Hz, Bragin et al., 1995), has recently been subdivided into two, 65 sometimes three independent ranges referred to as slow-, medium- and fast gamma (Colgin et 66 al., 2009; Belluscio et al., 2012; Carr et al., 2012; Colgin, 2012; Schomburg et al., 2014; Colgin, 67 2015; Fernández-Ruiz et al., 2017; Lopes-Dos-Santos et al., 2018; Michaels et al., 2018). While 68 the exact definition of these sub-bands varies across publications, they have been generally 69 identified as 20-55Hz (slow), 55-90Hz (medium), and fast (90-120Hz). The identification of more 70 than one gamma band has led to the multiple-gammas hypothesis of cognition, which proposes 71 that different gamma frequencies reflect different synaptic inputs to the hippocampus and 72 possibly distinct cognitive processing states (for review, see Colgin, 2015). Notably, the data 73 have been equivocal on what those states might be, with both slow and fast gamma being 74 linked to memory retrieval processes (Shirvalkar et al., 2010; Kemere et al., 2013; Newman et 75 al., 2013; Bieri et al., 2014; Igarashi et al., 2014; Schomburg et al., 2014; Takahashi et al., 2014; 76 Trimper et al., 2014; Yamamoto et al., 2014). Moreover, the theta and gamma oscillations are 77 not strictly memory-dependent. Rather, a substantial literature base demonstrates that these 78 oscillations are velocity modulated (Chen et al., 2011; Ahmed and Mehta, 2012; Kemere et al., 79 2013; Zheng et al., 2015; Sheremet et al., 2018b). bioRxiv preprint doi: https://doi.org/10.1101/428490; this version posted January 11, 2019. The copyright holder for this preprint (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 available under aCC-BY-NC-ND 4.0 International license. 80 Therefore, the exact relationship between the different gamma ranges and behavior is 81 not straight forward. The problem is further complicated by the existence of theta harmonics 82 (Harper, 1971; Coenen, 1975; Leung et al., 1982; Buzsaki et al., 1983; Leung and Buzsáki, 83 1983; Buzsáki et al., 1985; Ning and Bronzino, 1993; Czurkó et al., 1999; Terrazas et al., 2005), 84 which are frequency integer, phase coupled oscillations that precipitate in spectral 85 decomposition as a consequence of the fundamental 8Hz rhythm becoming both skewed and 86 asymmetric. As the harmonics of theta have been observed to go as high as 48 Hz (Sheremet 87 et al., 2016; Sheremet et al., 2018b), caution has been emphasized when examining the slow 88 gamma band to avoid harmonic contamination (Schomburg et al., 2014; Scheffer-Teixeira and 89 Tort, 2016). Specifically, theta harmonics (8, 16, 24, 32, 40, and 48 Hz) spill into the slow 90 gamma range (25-50 Hz as defined by Colgin et al., 2009), potentially obfuscating spectral 91 analyses. 92 In order to address the overlap between slow gamma and high-order theta harmonics in 93 the power spectra, we sought to disambiguate the theta harmonics from slow gamma using 94 current source density analysis across hippocampal lamina as well as spectral decomposition. 95 Contemporary theories of slow gamma suggest that the oscillation is generated via CA3 to CA1 96 projections whereas the fast gamma is generated by entorhinal to CA1 projections (Colgin et al., 97 2009; Belluscio et al., 2012; Schomburg et al., 2014; Colgin, 2015; Hsiao et al., 2016; Zheng et 98 al., 2016; Fernández-Ruiz et al., 2017). As these projections terminate in different layers of the 99 hippocampus, str. radiatum and str. lacunosum-moleculare respectively, we hypothesized that a 100 dissociation in the current source density pattern between these two oscillatory frequencies 101 could be identified. Remarkably, in neither our own data nor data provided from another 102 laboratory (Pastalkova et al., 2015; gift from the Buzsaki laboratory), were we able to find this 103 dissociation. This concern was increased in our failure to detect slow gamma-theta phase 104 coupling via bicoherence analysis which does not require any data preprocessing (Sheremet et bioRxiv preprint doi: https://doi.org/10.1101/428490; this version posted January 11, 2019. The copyright holder for this preprint (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 available under aCC-BY-NC-ND 4.0 International license. 105 al., 2016; Sheremet et al., 2018b). Furthermore, using the methods of Masimore and colleagues 106 of determining the correlation coefficients between Fourier decompositions in order to identify 107 fundamental frequencies and cross-frequency interactions (2004; 2005), coupling was only 108 evident between theta harmonics and a single 50-120 Hz gamma band; there was a notable 109 absence of slow gamma (Sheremet et al., 2018b). Finally, the absence of slow gamma was 110 further supported by recapitulating the phase-amplitude analyses of Colgin et al. (2009) as a 111 function of velocity (Sheremet et al., 2018b), which only revealed theta, theta harmonics and a 112 broad 50-120Hz band coupling. 113 In light of these incongruencies, we revisited many of the major tenets that have led to 114 the subdivision of the gamma band. Primary support for identifying the presence of an 115 oscillation is an increase in power relative to background activity (i.e., the noise spectrum). 116 Although initial approaches using Fourier based decompositions did not observe a deviation that 117 is supportive of slow gamma (e.g., Buzsáki et al., 2003), wavelet decomposition (Colgin et al., 118 2009) and more recently, ensemble empirical mode decomposition (Lopes-Dos-Santos et al., 119 2018), indicate a power deviation in the slow gamma range.