Computing with oscillations by phase encoding and decoding

Transcription

1 Computing with oscillations by phase encoding and decoding (Invited Paper) Ole Jensen F.C. Donders Centre for Cognitive Neuroimaging University of Nijmegen P.O. Box 9101 NL-6500 HB Nijmeegen Abstract Even though brain oscillations are found in many brain regions, the role of oscillations in neural computation remains an open question. Experimental work in the hippocampus has provided examples where the phase of firing of neurons with respect to ongoing network oscillations codes for information. This scheme has been termed phase coding. A network receiving the phase encoded firing patterns must receive the oscillatory signal as well in order to utilize the phase code. Thus, the oscillatory coupling between brain networks often observed experimentally might reflect exchange of phase coded information. In this work I will demonstrate that phase encoding and decoding allow for a set of simple computations. These computations include simple list manipulations such as forward and backward sequence read-out as well as controlling the information flow between several networks. The mechanisms can be implemented in simple network models of integrate-and-fire neurons. The principle of phase coding provides an alternative to theories and models on neuronal computations based on rate coding. I. INTRODUCTION Brain oscillations are observed in various frequency bands and different brain regions of all species. These oscillations are produced by large ensembles of neurons oscillating at the same frequency. What is the role of these oscillations in neuronal computation? In the behaving rat it is possibly experimentally to record single neurons in the hippocampus together with ongoing oscillations. This work has identified cells that only fire when the rat is in a given region of a spatial environment (1). The firing of these place cells is strongly modulated by ongoing theta oscillations (510 Hz). When a rat enters a place field, the corresponding place cell fires late in the theta cycle. As the rat advanced through the place field, the firing advances to earlier and earlier phases of the theta cycles (2; 3). This phenomenon is termed the theta phase precession. By a Bayesian approach, it is possible to reconstruct a rat s position in an environment using only the firing rates of a set of place cells. If the phase of firing with respect to the theta oscillations is taken into account as well, one can significantly improve the reconstruction of the rat s position (4). These findings support the notion of phase coding and provide a direct role for brain oscillations in neuronal processing. A. Models for phase encoding Several computational models have been constructed which can account for the theta phase precession. Many of these models accounts for theta phase precession by repeated readout of sequences within subsequent theta cycles as illustrated in Figure 1a (5; 6; 7; 8). A to E represent spatial locations encoded by different groups of neurons. As the rat advances, each new location probes the recall of a time-compressed sequence of upcoming locations. This principle has been implemented in network models of integrate-and-fire neurons (Figure 1b) (6; 8). The sequence read-out is produced in the feedback of asymmetric synaptic connections. These models remain true to various physiological parameters such as the time constants of synaptic communication. Simulations have demonstrated that these models can produce phase coded firing patterns quite similar to those observed experimentally (5; 6; 7; 8). The principle of phase encoding has also been applied to models of working memory. As in the models for hippocampal phase encoding, the individual representations are segmented in time. These individual representations are activated sequentially at a rate determined by the faster gamma rhythm (30 80 Hz). This scheme is repeated in each theta cycle (Figure 1c). Bi-stable membrane properties serve to bring the neurons back to firing threshold in each theta cycle. Thus individual memory representations are encoded at different phases of the theta cycle. This model can account for important behavioral data on working memory (9). In addition, the scheme has received experimental support by behavioral experiments as well as intracranial and MEG recordings in humans (10; 11; 12; 13; 14; 15; 16). B. Models for phase decoding A network receiving the phase coded information also needs to receive the oscillatory signals in order to utilize the phase coded firing patterns (Figure 1b). Interestingly, oscillatory coupling is often observed between different brain networks. For instance the entorhinal and cingulate cortices exhibit oscillations at theta frequency. These oscillations are occasionally phase- locked to the hippocampal theta rhythm (17; 18). All these regions receive an oscillatory signals from a common pace maker, the medial septum (19). Thus, the medial septum might play an essential role in orchestrating the oscillatory coupling between the various limbic areas. Interestingly, also neurons in the prefrontal cortex of the rat have been found

2 to be phase-locked to the hippocampal theta rhythm (20). A simple model that can perform phase decoding has been proposed (8). Each neuron in this model will fire when it changing the phase and frequency between the encoder and the decoder. The general principles will be outlined, however, they will not at this stage be supported by simulations. Nevertheless, implementation and simulations would be straight forward according to the principles outlined in previous work (6; 8) a) A A A A A b) C C C C C c) Fig. 1. a) Accounting for the theta phase precession. In each theta cycle short sequences of 5 representations are recalled. Representations at early phases represent elements early in the list; late phase representations represent elements late in the list. When observing a cell participating in the representation of E, a gradual phase advance occurs over time. This scheme provides a plausible explanation for the theta phase advance observed in the rat hippocampus (2; 3). b) A network model which can generate phase coded information (Encoder) and decode it (Decoder). The theta drive is imposed on the network by a pacemaker. The recurrent connections can either serve to produce a sequence read-out (6; 8) or support repeated activation of the same set of memory representations (21). The inhibitory feedback serves to keep the representations apart in time. The phase decoder receives the phase coded information together with the theta input. Neurons in the decoder fire when they receive input from the encoder together with a depolarizing drive from the theta rhythm. c) Maintenance of 5 representations by repeated activation of the representations at each theta cycle. This scheme has been proposed as a mechanism for maintenance of working memory representations (22; 21; 9). is sufficiently depolarization by the oscillatory input timed with the hippocampal phase coded firing patterns. Simulations demonstrated that phase coded information could be reliably decoded : the phase decoder could extract information from the different phases of the theta cycle. The only parameter that was changed in order to different information was the phase difference between the encoder and the decoder. In this paper I will further explore the principles of phase coding and decoding by investigating the consequences of Fig. 2. Phase decoding of a list of 5 representations. The upper panels symbolize representations in the encoder and the lower panels representations in the decoder. a) When the phase difference between the phase encoder and decoder is about 120 degrees, the first item in the list (A) is transferred to the decoder. b) When the phase difference is about 0 degrees the representation in the middle of the list (C) is transferred. c) When the encoder and decoder are in anti-phase information transfer is blocked. II. MAIN RESULTS In the rest of this paper I will assume that a phase encoder produces the repeated activation of 5 firing patterns: A, B, C, D and E as illustrated in Figure 1c. A. Simple phase decoding and blocking; f enc = f dec, φ enc φ dec. By adjusting the phase difference between the decoder (φ dec ) and the encoder (φ enc ) different results can be achieved. Figure 2a shows an example where the phase difference between the networks is about 120 degrees. As a result the first element, A, is repeatedly being transferred to the decoder. When the phase difference is 0 degrees representations from the center of the list is transferred to the decoder, i.e. C (Figure 2b). Thus it is possible to transfer different information from the phase encoder only by changing the phase relationship to the decoder. An example would be that the encoder maintains

3 five working memory representations. Recalling the first item in the list is achieved by dynamically adjusting the phase difference to 120 degrees. Likewise, other items in the list can be recalled by changing the phase difference accordingly. If the encoder and decoder oscillate in anti-phase, the information flow is blocked as shown in Figure 2c. Thus, by adjusting the phase relationship it is possible to block the information flow. This could be advantageous when several networks are anatomically connected, however, different networks would need to communicate at different times. Indeed, multiple EEG and MEG studies point to task dependent phaselocking between different networks(23). B. Forward sequence read-out, f enc > f dec Assume that the encoding network is maintaining a set of items in working memory. Often it is required to read-out the representations at a slower rate than they are repeated in the working memory store. In humans the slower recall is for A E Fig. 3. Forward read-out of a list represented in the encoder. As the frequency is slower in the decoder than the encoder, a new representation is transferred to the decoder at each theta cycle. As a consequence the representations in the encoder are sequentially scanned. instance necessary when the representations in the working memory story have to be articulated. This can be achieved if the decoder oscillates at a slower frequency than the encoder. As shown in Figure 3, memory representations from the encoder are transferred sequentially to the decoder. This is accomplished since the oscillatory cycles of the decoder peaks at later and later phases with respect to the encoder at each cycle. As a consequence, the representations in the encoder are sequentially scanned at the rate of one presentation per theta cycle. C. Backward sequence read-out, f enc < f dec Simple by adjusting the frequency of the encoder to be lower than the frequency of the decoder it is possible to achieve backward sequence read-out. As seen in Figure 4 the representation late in the list (E) is first transferred to the decoder. In the following theta cycle D is transferred etc. As a consequence the list is being inverted. D. Combining phase coded representations from several networks The scheme of information transfer between oscillatory networks can be extended to multiple networks. By changing the phases and/or frequencies of these networks it is possible to achieve various results. In the following example I will illustrate some of the possibilities. Figure 5a shows two networks E D C B A Fig. 4. Backward read-out of a list represented in the decoder. As the frequency of the decoder is faster than the frequency of the encoder, the list in the encoder is read-out backwards. connected to a common decoder. The encoders function as in Figure 1b and c. The decoder is similar to the one described in Figure 1b with the exception that a neuron only fires when it receives input from the neurons in both Encoder 1 and 2 coinciding with the peak of the oscillatory drive. In other words, it functions as a comparator that identifies common representations in the encoders. A common pacemaker serves to independently control the phases and frequencies of the 3 networks. In the example in Figure 5b, the two encoders initially oscillate in anti-phase. This means that the firing patterns never combine leaving the decoder unaffected. However, after 3 cycles the phase of Encoder 1 is changed (arrow) and the decoder will receive input from both encoders simultaneously. Since the decoder oscillates at a slower frequency than the encoders it will compare the representations sequentially. The encoders have representation B and D in common which then result in the firing of neurons in the decoder at cycle 5 and 7. This example illustrates two points: the phase relationship between the two encoders determines if information is transferred to the decoder. The phase relationship between the encoders determines which elements are compared. Thus different computations are achieved simply by dynamically changing the phase relationships between the networks. III. CONCLUSIONS In this paper I have outlined how simple computations can be performed by the principle of phase encoding and decoding. This is achieved by networks of spiking neurons which are driven by a pacemaker. If the frequencies were the same between the encoder and decoder but the phases different, it was possible to either open or block the transfer of information. Additionally, by adjusting the phase difference it was possible to allow representations from specific phases of the encoder to be transferred. When the frequencies between the encoder and decoder were different other scenarios were possible. As the decoder oscillated slower than the encoder, the list in the encoder was read-out at a pace of one representation per cycle. However, if the decoder oscillated faster than the encoder the list was read-out backwards. Finally, I have outlined how several networks could work together. Two encoders were connected to the same decoder. The phase relationship between the encoders determined whether the decoder would process the information. Moreover, the phase difference between the encoders and the decoder determined which representations in

4 a) Encoder 1 Encoder 2 Decoder/ comperator b) D E Encoder 1 Encoder 2 B D Decoder/ comperator Fig. 5. a) Combining presentations from two networks (Encoder 1 and 2) in a common network, the decoder. The three networks receive oscillatory drives from a central pacemaker that controls the frequency and phases individually. b) Encoder 1 and 2 repeatedly activate two different lists of representations. Initially the two networks oscillate in anti-phase, i.e. not information is transferred to the decoder. After 3 cycles (arrow) the phase of Encoder 1 is changed such that it is in phase with Encoder 2. This allows for transfer to the decoder. The decoder oscillates slower than the encoders (as in Figure 3). Thus it compares pairs of representations of the encoders one by one. Only Representation B and D are the same and they are transferred to the decoder. the encoders were compared. This allowed for the decoder to sequentially compare the representations in the encoders. All these functions were made possible by changing the phase relationship and frequencies between the encoder(s) and the decoder. In other words, they were achieved by changing the dynamic rather than adjusting parameters. Even though the principles in this paper only are outlined, the implementation is straight forward in networks of physiologically plausible integrate-and-fire neurons. For instance, several network models have been proposed that implement phase encoding by sequence read out (5; 21; 7; 8) or repeated list activation (22; 21). Also other models which can produce phase coded firing patterns have been proposed (24; 25; 26). Likewise, a simple network model based on integrate-and-fire neurons that can perform phase decoding has been implemented (8). These models are readily combined and simulated in order to produce the computations described in this paper. The principle of phase encoding and decoding deserves to be further explored experimentally. This requires intracranial recordings in which single cell firing is registered together with ongoing oscillatory activity. As described in the introduction, this has been done in the hippocampus of behaving rats (2; 3) and in monkeys as well (27). This methodology can be extended such that spiking and oscillatory activity is registered simultaneously from multiple regions known to be involved in a given task. The recording of single cells activity in the hippocampus of epileptic patients opens the possibility of exploring the principle of phase coding in humans (28). The human motor system allows for investigating the principle of phase coding as well. Motor unit spikes can be detected in the electromyogram of contracted muscles. These spikes have been shown to be strongly coupled to oscillations produced in the motor cortex (29; 30). Thus the human motor system might provide an experimental model system for further exploring phase coding in the central nervous system. If exchange of information is based on phase encoding and decoding then it follows that regions exchanging phase coded information are phase-locked or frequency locked (e.g. at ratios such as 5:6). Indeed, several examples of long- range phase-locking have been observed in humans and animals (23). Interestingly, phase-locking particular in the theta band has been observed in various memory task (31; 11; 12). These studies demonstrated a change in the theta power or coherence depending on working memory engagement. Other studies have identified changes in theta band phase-locking between frontal and posterior regions also in working memory tasks (32; 33). Moreover, future studies not only investigation longrange phase synchronization but also synchronization as different frequency ratios (e.g. 5:6) would be highly informative. In conclusion, I have outlined how a set of simple computations can be performed by the principles of phase encoding and decoding. These mechanisms can be implemented in simple physiologically plausible networks. Further theoretical research is likely to reveal new computational principles which can be performed by exchange of phase coded representations between oscillatory networks. Experimental work investigating the relationship between single neuron spiking and ongoing

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