Different Solutions for Phase Coding
One of the critical features of phase coding is that it allocates different frequency bands for different types of information by utilizing the spatially and temporally coherent SMOs shared between coupled networks. One such frequency band is the range of phases within each oscillation period. The other frequency band is the frequency of SMO itself. It has been demonstrated that information can effectively be encoded and decoded by multiplexing the code in these two frequency bands (Nadasdy, 2009). The assignment of frequencies to features may vary across brain structures. Likewise, at the stage of sensory encoding and gamma alignment different scenarios are possible. The scenario we described earlier was that the spatial/anatomical location is encoded by phase and luminance is encoded by period cycles. However, these two features are interchangeable and phase can represent luminance and period cycles can represent the spatial/anatomical location. Within the visual system the magno, parvo, and konio cellular pathways represent the heterogeneity of these coding solutions. For instance, it is conceivable that since the magno cellular pathway is specialized to effectively transfer motion and orientation while the parvo cellular pathway transfers luminance and color with high spatial acuity, the former one encodes motion in phase, while the latter one encodes the spatial position or spatial frequency in phase. Thus, qualitative and spatial stimulus features are given different priorities in the different pathways of the visual system.
Another remarkable feature of phase coding is that with only a few parameter adjustments we can obtain different solutions to represent space and time. For example, if the cortical cytoarchitecture is homogeneous, such as in the EC, and if it allows an unconstrained propagation of SMO waves over multiple spatial SMO wavelengths, then multiple representations of the same input develop because of the spatial aliasing inherent to the interference principle (Nadasdy, 2009; also see a different solution by Burgess, 2008). Conversely, the same EC neuron exhibits spatial tuning to multiple, equidistant spatial locations, consistent with the definition of grid cells. The missing link between the spatial maps and network architecture could be the spatially and temporally periodic SMO field. Based on our simulations, the phase-coding model predicts that the phase-gradient map in the EC is coalescent with the topography of the grid cell map, i.e., with the matrix of grid cells that share space fields (Nadasdy, 2009).
The third important feature of phase coding becomes evident when we track the activity of a neuron relative to the SMO cycles under a dynamic input condition while also varying the propagation direction of the SMO field. This emulates the condition of recording place in a freely moving animal's hippocampus and computing the phase of spikes relative to ongoing theta LFP oscillations. In similar experiments, the AP phase systematically advances relative to the theta cycles, defined as phase precession (O'Keefe and Recce, 1993; Skaggs et al., 1996; Harris et al., 2002). However, recording theta not only from a single electrode but also from a larger volume around the place cell should reproduce what we found by modeling. Namely, APs should always phase-lock to the intracellular SMO (Harvey et al., 2009), but the direction of phase precession (advancement vs. lagging) will depend on the propagation direction of global SMO/LFP field around the neuron (Nadasdy, 2009). The assumption of SMO field propagation is consistent with the observation of traveling waves in the hippocampus on freely moving rats (Lubenov and Siapas, 2009). The phase-lock between the APs and the intracellular SMO has been confirmed during behavior (Harvey et al., 2009). Combining SMO, LFP, and AP measurements from multiple neurons separated by different distances would elucidate the underlying network dynamics and test the interference principle.
Among the predictions that can be derived from the phase-coding model is the phase modulation of spikes in the cortex in relationship to stimulus or behavioral manipulations. We earlier argued that reconstruction takes place in the supragranular layer of the neocortex. According to our model, layers 2–3 and 4b pyramidal cells vigorously respond to the granule cell input only if the time of input APs coincides with the cell's intracellular SMO peaks. In our simulations the optimal coincidence time window was ∼1 ms (Nadasdy, 2009). Empirically, however, this time window is a probability function, rather than a binary function, allowing neurons to fire less frequently when the input is away from the peak but still reaches threshold. When the stimulus is optimal for the neuron, the AP will be generated reliably near the intracellular SMO peak (LFP trough). The same neuron may also respond, although less likely, to a suboptimal stimulus. If the suboptimal stimulus is optimal for another neuron, it will drive that neuron at the exact intracellular SMO peak. However, due to the slight phase difference between the two intracellular SMO processes, the same depolarization that drives the other neuron at exact SMO peak will drive the first neuron at a slightly different SMO phase than would its own optimal stimulus. As a result we shall observe a modest phase difference between spikes of the same neuron when we vary the stimulus parameters within the receptive field. Studies are in progress to test this prediction. Prefrontal cortical neurons in a working memory task exhibit memory item dependent phase offset relative to the slow oscillations (Siegel et al., 2009). Other studies investigating the auditory and visual cortex found feature-dependent phase differences relative to theta in auditory (Kayser et al., 2009) and relative to alpha in primary visual cortex (Montemurro et al., 2008) and to gamma (Nadasdy and Andersen, 2009) also in primary visual cortex. It is also conceivable that the phases of local SMOs shift relative to the LFP, which integrates oscillations over a larger cell population (Harvey et al., 2009). We anticipate an increasing amount of data to arise in support of these so-far isolated examples in cortical recordings.