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Published in final edited form as: Curr Opin Neurobiol. 2014 Dec 17;31:206–213. doi: 10.1016/j.conb.2014.12.003

Phase-resetting as a tool of information transmission

Carmen C Canavier 1
PMCID: PMC4375052  NIHMSID: NIHMS647487  PMID: 25529003

Abstract

Models of information transmission in the brain largely rely on firing rate codes. The abundance of oscillatory activity in the brain suggests that information may be also encoded using the phases of ongoing oscillations. Sensory perception, working memory and spatial navigation have been hypothesized to use phase codes, and cross-frequency coordination and phase synchronization between brain areas have been proposed to gate the flow of information. Phase codes generally require the phase of the oscillations to be reset at specific reference points for consistent coding, and coordination between oscillators requires favorable phase resetting characteristics. Recent evidence supports a role for neural oscillations in providing temporal reference windows that allow for correct parsing of phase-coded information.

Introduction

Phase-resetting [1-7] is defined in terms of ongoing self-sustained oscillatory (rhythmic) activity, which is abundant in the brain [8]. Brain rhythms reflect synchronized fluctuations in excitability across a population of neurons and are grouped by frequency: delta (0.5-4 Hz), theta (4-10 Hz), alpha (8-12 Hz), beta (10-30 Hz) and gamma (30-100 Hz) [9]. Neural oscillations may provide timing windows that chunk information, and the phase within a cycle may serve as a frame of reference for both internal and external events. Phase-resetting performs three main functions: 1) align the phase of an oscillation to a specific reference point for a given event or stimulus so that the phasic information can be decoded consistently, 2) allow a periodic stimulus to control the frequency and phase of a neural oscillator to provide the appropriate time frame for encoding and decoding and 3) allow mutually coupled oscillators to coordinate their frequencies and phases. Here, we summarize recent progress on identifying putative information coding and transmission schemes in the mammalian brain that employ phase-resetting of ongoing neural oscillations. The scope of this review is how the theory of phase-resetting of nonlinear oscillators constrains the implementation of these schemes. Alternate approaches to describe the dynamics of rhythm generators, such as those based on many-body physics [10], are beyond the scope of this review.

Phase-Resetting

Phase-resetting characteristics can be measured for a single oscillating neuron [11,12] or for network oscillators [13,14]. Figure 1 defines the phase of an oscillator and shows how it can be reset, using a simple network oscillator model [15] that consists of the average firing rates of two neural populations, one excitatory (E) and one inhibitory (I). The phase φ evolves from 0 to 1 (some choose modulo 2π or Pi instead) in proportion to elapsed time (φ=t/Pi) for an undisturbed oscillator, but can be permanently reset by an external stimulus. The advance or delay is tabulated as the phase resetting Δφ in a phase response curve (PRC), or alternatively as the phase transition curve (PTC) with the new phase as a function of the old phase φnew = φold + Δφ. In Figure 1C, the new phase is established within a single cycle, but in practice more cycles may be required. A continuous PRC is shown for a relatively weak stimulus (Figure 1D1), and a discontinuous one is shown for a stronger stimulus (Figure 1D2). The discontinuity results from the abrupt transition between delays due to prolonging an existing peak (Figure 1C1) and advances due to initiating a new peak (Figure 1C2). The distinction between the two types of PRCs is much clearer in the PTC. Both PTCs depict partial resetting, although that in E2 is more complete than in E1. Many coding schemes require complete resetting, meaning that the PTC is flat and the new phase is independent of the old phase. Complete resetting is not guaranteed for arbitrary stimuli to a given oscillator.

Figure 1. Phase-resetting explained using the Wilson-Cowan model.

Figure 1

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A. Excitatory (E) and inhibitory (I) activity and the simulated local field potential (LFP). Phase 0 is the peak of the E activity. B. Phase is marked on the cycle in the plane of the firing rates of the two populations. Magenta and green arrows indicate the direction of an external excitation (applied to the excitatory population). C. An external perturbation (vertical colored arrows) phase shifts the perturbed (colored) traces for the excitatory poplation compared to unperturbed (black) traces by the amount shown by horizontal arrows. (C1) An input at phase 0.05 causes a delay. (C2). An input at phase 0.4 causes an advance. The old phase just prior to the stimulus is repeated on the unperturbed (black) waveform at multiples of the cycle period (vertical dashed line) after the input, but the new phase on the colored traces at that point differs from the old phase by the phase shift. D. The PRC plots the phase shift as a function of the phase of the input perturbation. Slopes outside the stabilizing range (−2 to 0) are indicated in red. (D1) Weak input. (D2) Strong input. The arrows correspond to the perturbations in B and C. E. The phase transition curve plots the new phase (modulo one) versus the old phase. E1. For a weak input, the range of new phases is equal to that of old phases. E2. For a strong input, the range of new phases can be much smaller than the range of old phases.

The LFP and EEG measure synchronization of collective neural activity. A robust debate is ongoing regarding the role of phase resetting in event-related potentials detected in the EEG in response to a single sensory stimulus [16,17], and in the stimulus-synchronized response to a periodic train of such inputs [18,19]. A recent study [20] listed several mechanisms for generating a stimulus-synchronized response: 1) additional stimulus-locked activity that is recruited by the stimulus, 2) resetting of a single oscillator with no change in power, or 3) a complete reset by a common input that synchronizes a population of uncoupled oscillators with the same frequency but random initial phases, producing an increase in measured power. A phase-resetting mechanism as in (2) does not require the power to be unchanged. For example, the amplitude of the forced oscillation in the center trace of Figure 2B is larger than that of the unforced oscillation, which would result in a change in power as well as phase. Changes in the amplitude of an oscillation caused by a phase resetting stimulus are ignored, but not precluded, by phase resetting theory. The statistical test commonly used to detect phase coherence is more sensitive than that used to detect response power [20], so simple power and phase analyses may be insufficient to distinguish between mechanisms 1 and 2, for example.

Figure 2. Phase-locking explained using the Wilson-Cowan model.

Figure 2

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A. Phase response curve for strong input as in Figure 1D2. B. Forcing with a periodic train of stimuli (open triangles) at different PF/Pi ratios produces phase-locking only in the middle three traces, in which the corresponding point on the PRC exists and a slope within the stable range (see inset). Red indicates an unstable slope. Note that the position of the triangles within the forced cycle shifts as the forcing frequency changes.

For electrophysiological signals with variable cycle shape and amplitude, signal processing methods such as the Hilbert transform or convolution with a Morlet wavelet can be used instead of picking reference points to determine the phase, but caution should be exercised to determine that there is indeed an underlying nonlinear oscillation with a well-defined phase. Moreover, the frequency may also fluctuate due to external input [21,22] or intrinsic noise [23], and the PRC may be frequency dependent [24]. Nevertheless, this conceptual framework for phase resetting is quite generally applicable to nonlinear oscillators.

Phase-locking

A single input can reset the phase of an oscillator, and a train of inputs may phase-lock an oscillator such that the phase of the oscillator has a consistent relationship to each input. For an oscillator with intrinsic period Pi to be phase-locked by a stimulus with period PF, the change in period (PiΔφ(φ) ) due to the forcing must equal the difference between the intrinsic and forced periods (Pi-PF). The phasic relationships therefore change as the forcing period changes (Figure 2). The PRC limits the range of frequencies that allow a stable one-to-one locking because a point on the PRC must exist that has both the required amount of resetting and the correct slope for stability. Unfortunately, the theory of phase-locking is incomplete, and the theory presented here strictly applies only if the phase resetting can be assumed to be either pulsatile or weak or both. For pulsatile coupling [2,3,25,26], the effect of an arbitrary input is assumed to be complete before the next one arrives (but see [27,28]). For weak coupling [3,13,29], the response to an arbitrary input can be predicted using the infinitesimal PRC (iPRC), defined as the phase resetting curve obtained in the limit as the perturbation becomes very small. In order for a unidirectional forcing to be stable, the slope of the PRC at the locking point must be between −2 and 0 [2,25].

For mutual coupled oscillators, the phase-resetting can be measured for the input from the partner oscillator, and must allow a common frequency to be reached. An approximate stability criterion [26] is that the sum of the slopes at the locking point φi for each oscillator Δφ’(φ1)+Δφ’(φ2) must be negative but again, not too steep. Perhaps surprisingly, delays may facilitate synchrony between two oscillators with mutual coupling [26,30] by allowing the inputs to fall in PRC regions with stabilizing slope. Reciprocally coupled oscillators embedded in larger circuits also facilitate zero-lag synchronization in these larger circuits [30]. The stabilizing effects of negative PRC slopes generalize to all-to-all networks [31] and cross-frequency synchronization [32], resulting in wide implications of this theory. Recent modeling studies generalize these results to include the interaction of synaptic plasticity with phase-resetting properties [33,34].

Theta-Gamma Hypothesis

The theta-gamma hypothesis [35] of phase coding suggests that sequences in working memory are replayed with each item represented by cell assemblies active during sequential gamma cycles at different phases within a theta cycle, so theta phase codes for sequence order. Cross-frequency coupling of theta and gamma and phase synchronization between brains areas are thought to be critical mechanisms [36] in the formation of the cell assemblies that are activated on a particular gamma cycle. Partitioning neural responses recorded in monkey visual and auditory cortex using theta cycles permits the extraction of significantly more information that can be obtained otherwise [37], and robust increases in theta (and delta) band synchronization between brain areas are observed when patients correctly retrieve information from memory [38], support the role of the theta cycle as a temporal windowing mechanism. Phase-resetting theory can provide insight into cross-frequency phase-locking of gamma within a theta cycle [32,39,40] by establishing constraints on the existence and stability of N:1 locking modes, and by establishing constraints on the type of phase resetting required in different coding schemes described below, for example complete versus partial resetting.

Rhythmic Motor Activity for Active Sensing

Whisking and sniffing in rats at theta frequency [41] are rhythmic motor processes that are hypothesized to underlie active sensing. A proposed encoding scheme for active sensing postulates that internally generated oscillations, together with feedback from an element that detects the phase between external inputs and the internal rhythm, comprise a phase-locked loop [42]. This loop adjusts its frequency to stably phase-lock to the rhythmic inputs, in a manner constrained by phase-resetting theory. The phase detector, hypothesized to be implemented in thalamocortical neurons, smoothly encodes the phase of a novel input within the cycle of the rhythmic input. The angle of contact within the whisking cycle [42] is hypothesized to encode the boundaries of a perceived shape using the phase within the active sensing rhythm. Saccades may also mediate active sensing, as they can entrain delta and theta oscillations in primary visual cortex [43]. The effects of active sensing extend beyond the primary sensory cortices; hippocampal theta phase in monkeys is also reset by saccades [44], which may be important for the coding schemes described in the section on Hippocampal Phase Codes.

Rhythmic Sensory Coding and Decoding

Rhythmic auditory stimuli can phase-lock delta oscillations in primary auditory cortex [18], suggesting that the brain has specific mechanisms for processing rhythmic inputs [19]. Rhythmic stimulation produces no increase in delta power [18], and the alignment of the delta oscillation with expected stimulus times persists for a few cycles after the stimuli stopped, providing evidence for a phase-resetting mechanism. Moreover, attention controls delta phase-resetting so that for an attended stream of rhythmic stimuli, the time of the next expected stimulus occurs at the maximum excitability phase in regions tuned to the frequency of the stimulus, but at the minimum in those regions tuned to a different frequency. Periodic auditory stimuli can also entrain alpha oscillations that control excitability levels in visual cortex [45], suggesting that this cross-modal resetting by non-preferred stimuli contributes temporal information to multisensory integration [46].

The ability of auditory cortex to entrain to periodic inputs has motivated a theory of speech perception in which delta entrains to the rhythms of speech phrases and theta to syllables. A recent model [47,48] uses a phase-locked loop to allow the frequency of the intrinsic theta oscillator to vary within the theta range and remain locked to the slowly-varying input syllabic rhythm. Beta and gamma model oscillators are phase-locked at multiples of the theta frequency in a cascade, and the phase of the nested oscillators must be reset to a constant value at the beginning of each theta cycle for consistent coding. Information in the model is encoded by cell firing binned within each gamma cycle. The cascaded oscillator theory is supported by the ability of delta band entrainment to predict speech recognition scores [49], as well as a recent study showing that envelope tracking information improves the intelligibility of speech [50].

Communication Through Coherence

The communication through coherence (CTC) hypothesis [21] posits that groups of neurons in lower cortical areas (for example V1) compete to drive the gamma oscillation in higher areas (like V2). Attended stimuli compete more successfully, and phase-lock the higher area so that their inputs alone arrive consistently during the maximal excitability phase of the gamma oscillation in the higher area. Gamma oscillations in vivo are thought to result from the interaction between excitatory pyramidal cells and inhibitory interneurons, likely via multiple mechanisms [51]. However, the phase-resetting characteristics of network gamma oscillators have only recently begun to be examined, and there is no guarantee that their phase resetting characteristics are favorable for unidirectional or bidirectional phase locking. The PRC has recently been measured for gamma oscillations induced in hippocampal area CA3 in slices by carbachol or optogenetic stimulation [14]. The resultant biphasic PRCS were simulated using the same two-population firing rate model [15] used in Figures 1 and 2.

Two-population models comprised of several hundred conductance-based excitatory and inhibitory spiking neurons, in which individual neurons fire sparsely and randomly, have also been used to gain insight into the PRC for network oscillators. In this model [52], the PRC for simulated pulses of optogenetic stimulation was monophasic, with phase advances during the latter part of the rising phase of the simulated LFP, and little effect at other phases. Furthermore, two similar model gamma generators coupled via mutual excitation phase-locked, but only approximately, and in a bistable manner because either generator could lead the other. A recent review suggests that the faster (more strongly excited) gamma generator of this type would most effectively drive its mutually coupled partner in the manner required by CTC [51]. Another study [21] used a similar model comprised of populations of spiking neurons to respond to a recent challenge to the CTC hypothesis, namely that gamma frequency in areas V1 and V2 varies from moment to moment as a result of changing stimulus contrast. The experimental part of the study found that variation in gamma frequency between the two areas is correlated [21]. The computational part of the study showed that a model V2 network driven by excitatory input from a similar model V1 network oscillator [21] was able to follow fluctuations in frequency that were induced in V1, so that the oscillations remained coherent. More work is required to determine if and how population oscillators can coordinate their activity with the correct phasic relationship for coherence [51].

Hippocampal Phase Codes

The oscillatory interference model [53] posits that spatial locations are encoded using the relative phases between a reference theta oscillator and additional oscillators whose frequencies are increased by velocity in their respective preferred directions. The phases of the velocity controlled oscillators (VCOs) will slip with respect to the reference oscillator. Phase resetting theory imposes the constraint that distinct oscillators must be functionally uncoupled to prevent locking [54] or sticking [23]. As they slip, the peak of each VCO will coincide with the reference oscillator each time a characteristic distance has been traversed in its preferred direction. The exact spatial location of the place fields depends on how the phase of the oscillators is initialized: the phase difference between the velocity modulated oscillators and the reference oscillator is the integral of the velocity modulation plus the initial phase difference. Therefore, in this model, phase resetting of the oscillators plays a critical role in establishing place fields and changing the firing fields based on context [55], as well as correcting for noise in path integration. Reward locations, turning points, and other environmental boundaries have been suggested to provide resetting signals, usually complete resetting signals that reset the phases of all oscillators to zero. This theory is not universally accepted: a competing theory of hippocampal encoding of spatial information uses firing rate coding rather than phases, and is implemented in continuous attractor models [56] with moving bumps of activity that code for an animal’s location by exploiting the spatial tuning (place fields) of the component neurons. However, an oscillatory interference model can also be implemented as a continuous attractor model [57].

A different proposed phase code suggests that the biphasic ability of excitatory synaptic inputs to jitter the spike timing of CA1 and CA3 hippocampal pyramidal neurons phase-locked by a sinusoidal theta oscillation is useful for encoding memories [58]. The biphasic response is due to the unconventional protocol; when CA1 neurons are biased in a pacemaker regime they exhibit a monophasic PRC [11].

Cerebellar Timing Mechanisms

As evidenced above, neural oscillations are often hypothesized to serve as clocks, providing a reference phase to use for information coding; moreover, complete phase-resetting of the clock is often required for encoding. Mechanisms for complete resetting are varied. One example is provided by pacemaking cerebellar Golgi cells, which pause for one cycle period before resuming pacing after a burst evoked by depolarization, so the burst completely resets their phase. A recent review suggested that such resetting may allow specific Golgi neurons to escape entrainment with the local theta rhythm in order to emit a signal coded with respect to theta phase [59]. Subtheshold theta frequency oscillations in inferior olivary neurons may serve as a master clock for cerebellar generation of temporal patterns. In order to achieve precision greater than a theta period, it was recently suggested that the coupling between olivary neurons allows them to break into phase-locked clusters able to keep time at a higher resolution [60]. Phase-resetting theory constrains the tendency of networks to break up into clusters [31].

Spike timing in oscillatory neurons is determined by the iPRC

The spike-triggered average (STA) and covariance (STC) of the input preceding a spike can provide insight into the feature space encoded by a neuron. Both the STA [61] and the STC have been derived from the iPRC [62]. The relationship of the STA and STC to phase codes, if any, has not been determined. The serial cross-correlation coefficients for a series of interspike intervals in a noisy pacemaker have also been recently derived from the iPRC [63]. Moreover, the iPRC has also been used to predict spike timing in the presence of strong noise [29]. STN neurons are regular pacemakers in vitro, but fire irregularly in healthy intact animals. The biophysical basis of their phase resetting curve has been explained [12,64]. The deterministic interaction of the measured iPRC [29] with the known noise stimulus pattern was sufficient to predict spike times under weak coupling assumptions [24]. This is remarkable because the neurons appeared to be firing in a fluctuation-driven rather than pacemaking regime. Heterogeneity in the PRCs across the population may serve to actively decorrelate STN neurons [65]. Surprisingly, another study [66] showed that for low input correlations, heterogeneous oscillators exhibited more noise-induced stochastic synchronization than homogeneous oscillators.

Conclusions

Phase-locking and phase-resetting are two related and important concepts that contribute to and constrain schemes for encoding of information by phasic relationships. Rhythmic sensing (including speech decoding) and active sensing seem to be the most promising areas in which to firmly establish the use of phase codes. Although phase and frequency are hypothesized to act as direct carriers of information in some cases, this review also highlights how controlling the relative phase and frequency of neural oscillations is critical in order for various coding strategies to work. The role of neural oscillations to bin, or chunk, information, and the cross-frequency synchronization implicit in the gamma-theta hypothesis are emerging as universal organizational principles. Areas requiring more investigation include complete resetting mechanisms required to initialize phase codes, the phase-resetting properties of network oscillators, and the mechanisms by which network oscillators coordinate their activity, as well as the effects of noise on this coordination, and better statistical tools to determine the degree to which phase resetting mechanisms contribute to observed EEG and LFP activity.

*Highlights (for review).

  • The phase of population oscillators underlying brain rhythms can be reset.

  • Phase-resetting theory can help explain how brain rhythms phase-lock.

  • Phase-locking between brain rhythms may facilitate information transfer.

  • Oscillator phases, or relative phases, may encode information.

  • Coding schemes based on relative phases generally rely on complete phase-resetting.

Acknowledgements

This work was supported in part by the National Institutes of Health grant R01NS054281 to CCC as well as the computational core of P30GM103340, and the Mathematical Biosciences Institute and the National Science Foundation under grant DMS 0931642.

Footnotes

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Conflict of interest statement

Nothing declared.

References and recommended reading

Papers of particular interest, published within the period of review, have been highlighted as:

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