Excitation Balanced by Proportional Inhibition during Gamma Oscillations In Vivo
(A) Whole-cell recording of EPSCs in CA3 cell (red) and simultaneously recorded LFP (black, positivity is up) during gamma oscillations in anesthetized rat. IPSCs (cyan) and inverted LFP recorded from the same cell. Note correlated fluctuations in the amplitude of LFP and synaptic currents.
(B) Coherence between LFP and IPSCs (cyan) or EPSC (red); jack-knifed 95% confidence interval (thin lines); arrows mark peak coherence frequencies. Summary of peak coherence frequency (bottom) and peak coherence (right). Average shown as a vertical or horizontal bar (n = 7 cells).
(C) Oscillation triggered average (OTA) of EPSC (red), IPSC (cyan) and LFP. LFP was recorded simultaneously with EPSCs, IPSC (black and dotted traces, respectively). EPSC is inverted for illustration purposes. Overlaid POTH (green, data from Figure 1D, aligned to the LFP also in green) illustrates spike timing during oscillation cycle. Note that maximal spiking precedes peak of inhibition. (Bottom) Summary of EPSC-IPSC lag during an oscillation cycle; vertical bar is average.
(D) OTA of EPSCs (red), IPSCs (cyan) computed for four different bins of LFP oscillation amplitude (black; dotted and solid traces were recorded simultaneously with IPSC and EPSCs, respectively, same cell as A–C).
(E) Summary of correlation between average inhibitory (gI) and excitatory (gE) conductance in vivo; individual cells are each represented by a different color linear regression. Note, although excitation and inhibition are proportional, the inhibitory conductance is approximately five times larger (dotted line is at unity).
(F) OTA of IPSC (middle) computed for four different bins of LFP oscillation interevent interval (top). Vertical arrows illustrate IPSC amplitude and horizontal arrows the correlated changes in the time to the next oscillation event (IEI). (Bottom) IPSC amplitude during an oscillation event correlated with the time to the next oscillation in the LFP (IEI); blue dots correspond to the four OTA shown above.
... Gamma Oscillation Amplitude Predicts Latency to Next Oscillation Cycle
(A) (Top) Broadband (gray) and gamma-band filtered local field potential (LFP, 5–100 Hz) recorded in the stratum radiatum of area CA3 of an anesthetized rat. Raster plot marks the peak of each oscillation cycle. (Bottom, left) Autocorrelation of LFP and power spectral density of gamma-band LFP. (Bottom, right) Histograms of oscillation amplitude and interevent interval (IEI). (Inset) LFP recording illustrating the measurement of peak-to-peak amplitude and IEI (expansion of the recording marked by a horizontal bracket in the top panel). Positivity is up.
(B) (Top) IEI correlated against amplitude of the previous cycle illustrated in histogram. Note the correlation between oscillation amplitude and IEI. (Bottom) Summary of correlations, n = 6 rats. Vertical bar is average.
(C) Broadband extracellular recording (top), gamma-band LFP (middle, 5–100 Hz band-pass), multiunit spiking (green, 0.2–2 kHz) from stratum pyramidale of area CA3. Negativity is up.
(D) Oscillation triggered average of LFP, peri-oscillation spike-time histogram (POTH), and local linear fit to POTH (green).
(E) (Left) Average LFP and POTH fit calculated separately for large (mean amplitude = 313 μV) and small (99 μV, dotted) oscillation cycles. Arrows illustrate the increased latency between spiking events after large-amplitude cycles. (Inset) Small POTH scaled to the peak of the large POTH. (Right) Summary of full-width at half-maximum (FWHM) of POTH for large (solid) and small (open) oscillation cycles (n = 6 rats). Averages are illustrated with horizontal bars. Note that spiking occurs in a narrow time window during each oscillation cycle independent of oscillation amplitude.
... Larger, Longer Hyperpolarization of Pyramidal Cells following Large-Amplitude Oscillation Cycles
(A) LFP and simultaneously recorded membrane potential (Vm; whole-cell current-clamp configuration: IC) during in vitro gamma oscillations (dotted line is mean Vm). Positivity is up.
(B) Oscillation cycles were binned according to LFP amplitude and the oscillation triggered average (OTA) of Vm computed for each bin (different colors): average time course of LFP in four bins of increasing amplitude (top) and corresponding (color coded) Vm averages (middle). Note that Vm undergoes larger and longer hyperpolarization during large-amplitude oscillation cycles. (Bottom, left) Cycle-by-cycle correlation between the peak hyperpolarization and LFP amplitude. Bins in upper panels are illustrated with solid dots of respective colors. (Bottom, right) Summary of correlation (n = 11 cells).
(C) (Top) Oscillation cycles were binned according to LFP interevent interval and the OTA of membrane potential computed for each bin (different cell than A and B). Arrows illustrate “recovery time,” i.e., time from onset of oscillation cycle till membrane potential recovers to mean Vm (horizontal dotted line). (Bottom) LFP interevent interval plotted as a function of Vm recovery time. Colored dots and black line correspond to the above cell, other cells shown in gray. Note, mean slope, m = 1.16; SD = 0.3, suggesting that changes in the time for recovery from hyperpolarization in individual cells can account for the entire range of oscillation intervals observed in the LFP.
... Excitation Instantaneously Balanced by Proportional Inhibition during Each Gamma Oscillation Cycle
(A) (Top) Broadband (gray) and gamma-band filtered (black) LFP recorded in the stratum radiatum of area CA3 in acute hippocampal slice. Raster plot marks the peak of each oscillation cycle. (Bottom, left) Autocorrelation of LFP and power spectral density of gamma-band LFP. (Bottom, right) Histograms of oscillation amplitude and interevent interval (IEI). (Inset) LFP recording illustrating the measurement of peak-to-peak amplitude and IEI (expansion of the recording marked by a horizontal bracket in the top panel). Positivity is up.
(B) (Top) IEI correlated against amplitude of the previous cycle. (Bottom) Summary of correlations, n = 6 slices. Vertical bar is the average. Note the correlation between oscillation amplitude and IEI.
(C) Dual patch-clamp recording from two neighboring CA3 pyramidal cells. Oscillations are monitored with an LFP electrode (black, positivity is up). EPSCs (red) and IPSCs (cyan) simultaneously recorded by holding two cells at the reversal potential for inhibition (−3 mV) and excitation (−87 mV), respectively. Note the correlated fluctuations in the amplitude of excitation and inhibition.
(D) (Left) Average time course of EPSC and IPSC (same cell as C) during an oscillation cycle recorded in the LFP, i.e., oscillation triggered average. EPSC is inverted for illustration purposes. LFPs recorded simultaneously with EPSCs and IPSCs are shown as black and gray traces, respectively. (Right) Summary of EPSC-IPSC lag during an oscillation cycle. Horizontal bar is the average.
(E) (Top) Cycle-by-cycle correlation between excitatory and inhibitory conductances recorded in the pair shown in (C). Summary of correlation between excitation and inhibition (bottom) and ratio of mean excitatory and inhibitory conductances (right) (n = 8 pairs). Vertical and horizontal bars illustrate respective averages.
... Correlated Amplitude and Frequency in Simple Model of CA3 Circuit
(A) Average excitatory (gE, red) and inhibitory (gI, cyan) synaptic conductance received by model pyramidal cells. LFP (black) is approximated as the sum of the two conductances.
(B) (Top) Autocorrelation and power spectrum of simulated LFP. (Bottom) Interevent interval correlated against amplitude of the previous cycle.
(C) The membrane potential (Vm) of an individual pyramidal cell in modeled circuit (spike truncated), gE (red) and gI (cyan); dotted line illustrates the average Vm.
(D) Oscillation cycles were binned according to gI amplitude and the oscillation triggered amplitude of Vm computed for each bin (different colors): average time course of gI in four bins of increasing amplitude (middle) and corresponding (color coded) Vm averages (top). The arrows illustrate that it takes longer for Vm to recover to the average potential (horizontal dotted line) after large-amplitude cycles. (Bottom) Cycle-by-cycle correlation between Vm hyperpolarization and the gI. Bins in upper panels are illustrated with solid dots of respective colors.
Contributors:Eric Maris, Marieke van Vugt, Michael Kahana
In the analysis of the activation period wPLFs, 36 reliable PAC patterns were identified: two subjects had four reliable PAC patterns, eight had two, 12 had one, and four had none. In the analysis of the baseline period wPLFs, 17 reliable PAC patterns were identified: four subjects had two reliable PAC patterns, nine had one, and 13 had none. Reliability was defined in terms of the split-half correlation between two independent estimates of the spatial and the frequency spectra produced by the tensor decomposition. All identified PAC patterns had reliabilities much larger than what can be expected under the hypothesis of a random PAC (see Materials and methods). A representative selection of reliable PAC patterns is shown in Supplemental Fig. 3.... Our conclusion about the number of sources involved in PAC depends on our definition of a source. We defined a source in terms of two patterns: (1) a spatial map that specifies how strongly source activity affects the measurements at the sensor level, and (2) its frequency spectrum. We showed that, with this source definition, the array of PAC-measures (wPLFs) can be written as a tensor product of two spatial maps (one complex- and one real-valued) and two frequency spectra (both real-valued), which is exactly the structure that is extracted by our tensor decomposition (see Supplemental Methods). However, we cannot exclude PAC-generating source configurations that cannot be characterized in this way. In fact, we have argued that PAC-patterns may also be generated by a source configuration that would be considered a single source when viewed from the perspective of the mechanism that generates the physiological signal. This confronts us with the problem that sources can be defined both in terms of their formal characteristics (i.e., in terms of a spatial map and a frequency spectrum) and in terms of the neuronal network that generates the physiological signal. The difference between the two definitions is most clear if the physiological mechanism consist of multiple components, such as networks of inhibitory neurons that are connected to one or multiple classes of principal neurons, each with its own network topology. This whole multi-component network may be considered as a single source, but also as multiple sources, each one corresponding to one component. Importantly, if these components differ with respect to their spatial maps and frequency spectra, then they can be extracted by means of tensor decomposition. This shows there may be a need for a linking of the set of extracted source configurations on the basis of the neuronal interactions that may have produced them.... Package of figures showing the spatial maps and the frequency spectra of a representative set of reliable cross-frequency patterns extracted from the activation period wPLFs. The figures belonging to one cross-frequency patterns are each in one folder, of which the name refers to the patient. The files that have freqspectra_and_compass as a part of their name contain a figure of which the left panel show the frequency spectra of a coupling oscillation and the associated phase-coupled bursts, and the right panel shows the preferred phases of the PAC in a compass plots. The files that have _IA_ (instantaneous amplitude) as a part of their name contain figures of the magnitudes of the spatial maps for the phase-coupled bursts. Different figures show different subsets of the electrodes, each from on optimal viewpoint. Electrode subsets on the medial side of the brain are shown from two viewpoints, lateral and occipital. The files that have _AWIP_ (amplitude-weighted instantaneous phase) as a part of their name contain figures of the spatial maps of the coupling oscillation. Again, different figures show different subsets of the electrodes, each from on optimal viewpoint.
... Spatial maps of the phase-coupled bursts are smaller than the spatial maps of the associated coupling oscillation. Both panels show scatter plots of the extent of the spatial maps of the phase-coupled bursts (horizontal axis) against the extent of the corresponding spatial maps of the coupling oscillation (vertical axis). Panels a and b show the scatter plots for, respectively, the baseline and the activation period. Panels a and b show the scatter plots for, respectively, the baseline and the activation period. In both periods, for most of the PAC patterns, the extent of the spatial map of the phase-coupled bursts is substantially smaller than the extent of the spatial map of the associated coupling oscillation.
... Illustration of a tensor decomposition of the four-dimensional array of weighted phase-locking factors (wPLFs). The two spatial maps and the two frequency spectra (see text) are each denoted by a different color (red, yellow, green, and blue) and a different index (i, i', f, f'). The same colors are used both for the boundaries of the panels and the symbols in the formula for the wPLF. In panels a and b, with red and index i, we show the complex-valued spatial map of the high-frequency bursts that are coupled to a common low-frequencyoscillation (the coupling oscillation). In panel a, we show the magnitude (absolute value) of this complex-valued spatial map (one colored circle per channel), which expresses the strength of the coupling. In panel b we show the phases of the coupling oscillation to which the high-frequency bursts are locked (one arrow per channel). In panel c, with yellow and index i', we show the spatial map of the coupling oscillation (one colored circle per channel). The more a coefficient bi’ deviates from zero, the more this channel is affected by the coupling oscillation. In panel d, with green and index f, we show the frequency spectrum of the phase-coupled bursts (shown on a logarithmic scale). In panel e, with blue and index f', we show the frequency spectrum of the coupling oscillation. The spectra shown in panels a, b, c, d and e are all in arbitrary units (a.u.). This is because the spectra are produced by a tensor decomposition which involves an arbitrary multiplicative scaling (see Supplemental Material). In panels f, h, and j, we show the magnitudes of the complex wPLFs for three selected channel pairs (see text). By means of arrows, we connect the channels in panels a and c for which these wPLFs were calculated, with the corresponding x-axes (showing the frequency of the coupling oscillation), respectively, y-axes (showing the frequency of the phase-coupled bursts), in panels f, h, and j. In panels g and i, we show the phases of the complex wPLFs that correspond to panels f and h, respectively.
... Simulated field potentials with bursts of gamma oscillations (60Hz) that are phase-coupled to the rising phase of a theta oscillation (5Hz).
... Spectral signature of the PAC patterns. Panels a and b show the results for, respectively, the baseline and the activation period. Both panels show a scatter plot of the central frequencies of the phase-coupled bursts (horizontal axis) against the central frequencies of the coupling oscillations (vertical axis). The central frequency of the phase-coupled bursts is always smaller than the one for the associated coupling oscillation. For all PAC patterns above the thick black line, the central frequency for the phase-coupled bursts is larger than the central frequency for the associated coupling oscillation. There is not a dominant frequency, neither for the phase-coupled bursts, nor for the associated coupling frequencies.
Contributors:George M. Ibrahim, Simeon M. Wong, Ryan A. Anderson, Gabrielle Singh-Cadieux, Tomoyuki Akiyama, Ayako Ochi, Hiroshi Otsubo, Tohru Okanishi, Taufik A. Valiante, Elizabeth Donner, James T. Rutka, O. Carter Snead III, Sam M. Doesburg
Quantification of amplitude-to-phase cycle relationship. (A) Mean amplitudes of high frequencyoscillations, sorted by concurrent low-frequency phase into 60 bins of 0.105rad, for an example time window during a seizure; (B) an ideal cosine; and (C) a sine is modeled. (D) Phasor demonstrating the amplitude–phase cycle relationship. (E) The argument (angle) of the example phasor is a single contribution to be incremented onto a cumulative polar histogram spanning multiple subjects for one of ten given time periods in the seizure.
... Cross-frequency coupling... Modulation of high frequency amplitude by low-frequency phase. In the seizure-onset zone, significant modulation of high-frequency amplitude (40–300Hz) is observed, mainly by the phase of theta and alpha oscillations during the ictal period. In the interictal period, no specific CFC with slower oscillations is observed. There is also less cross-frequency coupling in the early propagation zone during seizures and no significant coupling is noted in the non-epileptogenic cortex. The z-axis demonstrates the modulation of amplitudes of different narrow-band frequencies (x-axis) by the phases of other narrow-band frequencies (y-axis). Lower and upper planes represent uncorrected and corrected statistical thresholds at p<0.05, respectively.
... High frequencyoscillations... Simulated data demonstrating expected polar histogram distribution. The high frequency amplitude is represented by the blue solid line, whereas the low-frequency phase is represented by the black dashed line. When the high frequency amplitude is maximal at the peak and trough of the low frequency phase, the polar histograms will indicate pi and 0, respectively.
... Individual seizure short-time Fourier transform spectrograms. The seizure onset zone contained predominantly low-frequency power, which was fairly heterogenous across the population. High frequency activity was also evident in all seizures as bursts of high power oscillatory activity.
... Topographic mapping of cross-frequency interactions in a representative subject. (A) Intraoperative image of grid demonstrating seizure onset and early propagation zones. (B) Fast-ripple amplitudes sorted by alpha phase for all grid electrodes. Cosine wave represents alpha phase from −π to π. Increased pHFO-to-low-frequency coupling occurs in the resected cortex (black borders). Values normalized by 95% confidence interval such values above 0 are significant at pfrequency modulation index for all electrodes, where the X-axis represents low frequency phase (1 to 40Hz; left to right), and the Y-axis denotes envelope amplitude (1 to 300Hz; top to bottom). Values exceeding Bonferroni correction threshold shown. Significant modulation of pHFO amplitudes by low-frequency phase is observed in the epileptogenic cortex.
... To characterize the ictal dynamics of relations between pHFO amplitude and low frequency phase, we measured the preferred slow oscillatory phase at which high amplitude pHFOs occurred at various times throughout the seizure. When the preferred phases from all bins from all subjects were plotted cumulatively on polar histograms, it was observed that pathological fast-ripple amplitudes preferentially occurred during the trough of alpha oscillations, whereas pathological ripple amplitudes preferentially occurred between 0rad and π/2rad of alpha and theta oscillatory cycles (Fig. 5; poscillations (p=0.14 and p=0.68, respectively). At seizure termination (i.e. the last bin), pHFO amplitudes occurred at the trough of the alpha oscillatory cycle (pathological ripple amplitude: p<0.01; pathological fast-ripple amplitude: p=0.03). Ripple amplitude maxima were also found at the peak of delta phase irrespective of the seizure progression (Supplementary Fig. S9). To ensure that differences in bin length did explain the measures of CFC, a reanalysis of the data with fixed length segments comprised of the first and last 2000ms of seizures, revealed the same pattern.
Contributors:Landig, Andreas J., Koski, Jonne V., Scarlino, Pasquale, Müller, Clemens, Abadillo Uriel, Jose C., Kratochwil, Benedikt, Reichl, Christian, Wegscheider, Werner, Coppersmith, Susan N., Friesen, Mark, Wallraff, Andreas, Ihn, Thomas, Ensslin, Klaus
Spin qubits and superconducting qubits are among the promising candidates for realizing a solid state quantum computer. For the implementation of a hybrid architecture which can profit from the advantages of either approach, a coherent link is necessary that integrates and controllably couples both qubit types on the same chip over a distance that is several orders of magnitude longer than the physical size of the spin qubit. We realize such a link with a frequency-tunable high impedance SQUID array resonator. The spin qubit is a resonant exchange qubit hosted in a GaAs triple quantum dot. It can be operated at zero magnetic field, allowing it to coexist with superconducting qubits on the same chip. We spectroscopically observe coherent interaction between the resonant exchange qubit and a transmon qubit in both resonant and dispersive regimes, where the interaction is mediated either by real or virtual resonator photons.,Nature Communications, 10 (1),ISSN:2041-1723,
Contributors:Li Wang, Qingmei Kong, Ke Li, Yunai Su, Yawei Zeng, Qinge Zhang, Wenji Dai, Mingrui Xia, Gang Wang, Zhen Jin, Xin Yu, Tianmei Si
Brain regions showing significant group and frequency (slow-4 and slow-5) interaction effects on ALFF.
... The group and frequency (slow-4 and slow-5) interaction effects on ALFF. The regions showing significant group and frequency interaction effects on ALFF (hot colors): the left ventromedial prefrontal cortex (a), the left inferior frontal gyrus/precentral gyrus (b), and the bilateral posterior cingulate cortex/precuneus (c). The bar maps show the mean ALFF values for these regions.
... Low-frequencyoscillation... Frequency dependence... Main effects of group and frequency on ALFF. (a) The group main effects on ALFF. Hot colors represent increased ALFF in the MDD group compared with HC, while the blue colors represent the opposite. (b) Frequency main effects on ALFF. Hot colors represent increased ALFF in the slow-5 as compared to slow-4 band, while the blue colors represent the opposite. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Contributors:Tigges, Marcel, Dénervaud, Nicolas, Greber, David, Stelling, Jörg, Fussenegger, Martin
Circadian clocks have long been known to be essential for the maintenance of physiological and behavioral processes in a variety of organisms ranging from plants to humans. Dysfunctions that subvert gene expression of oscillatory circadian-clock components may result in severe pathologies, including tumors and metabolic disorders. While the underlying molecular mechanisms and dynamics of complex gene behavior are not fully understood, synthetic approaches have provided substantial insight into the operation of complex control circuits, including that of oscillatory networks. Using iterative cycles of mathematical model-guided design and experimental analyses, we have developed a novel low-frequency mammalian oscillator. It incorporates intronically encoded siRNA-based silencing of the tetracycline-dependent transactivator to enable the autonomous and robust expression of a fluorescent transgene with periods of 26 h, a circadian clock-like oscillatory behavior. Using fluorescence-based time-lapse microscopy of engineered CHO-K1 cells, we profiled expression dynamics of a destabilized yellow fluorescent protein variant in single cells and real time. The novel oscillator design may enable further insights into the system dynamics of natural periodic processes as well as into siRNA-mediated transcription silencing. It may foster advances in design, analysis and application of complex synthetic systems in future gene therapy initiatives.,Nucleic acids research, 38 (8),