Phase-resetting as a tool of information transmission
Introduction
Phase-resetting [1, 2, 3, 4, 5, 6, 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.
Section snippets
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 the intrinsic period Pi instead) in proportion to elapsed time (ϕ = t/Pi) for an
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 (Pi Δϕ(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
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.
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
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
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
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
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
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
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
Conflict of interest statement
Nothing declared.
References and recommended reading
Papers of particular interest, published within the period of review, have been highlighted as:
• of special interest
•• of outstanding interest
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.
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