Lecture Notes in Computer Science
Applying the String Method to Extract Bursting
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Applying the String Method to Extract Bursting
Information from Microelectrode Recordings in Subthalamic Nucleus and Substantia Nigra Pei-Kuang Chao 1 , Hsiao-Lung Chan 1,4 , Tony Wu 2,4 , Ming-An Lin 1 , and Shih-Tseng Lee 3,4 1 Department of Electrical Engineering, Chang Gung University 2 Department of Neurology, Chang Gung Memorial Hospital 3 Department of Neurosurgery, Chang Gung Memorial Hospital 4 Center of Medical Augmented Virtual Reality, Chang Gung Memorial Hosipital 259 Wen-Hua First Road, Gui-Shan, 333, Taoyuan, Taiwan peikuang@ms16.hinet.net
rameters in classifying and identifying neural activities from subthalamic nu- cleus (STN) and substantia nigra (SNr). The string method was performed to quantify bursting patterns in microelectrode recordings into indexes. Inter- spike-interval (ISI) was used as one of the independent variables to examine ef- fectiveness and consistency of the method. The results show consistent findings about bursting patterns in STN and SNr data across all ISI constraints. Neurons in STN tend to release a larger number of bursts with fewer spikes in the bursts. Neurons in SNr produce a smaller number of bursts with more spikes in the bursts. According to our statistical evaluation, 50 and 80 ms are suggested as the optimal ISI constraint to classify STN and SNr’s bursting patterns by the string method. Keywords: Subthalamic nucleus, substantia nigra, inter-spike-interval, burst, microelectrode. 1 Introduction Subthalamic nucleus (STN) is frequently the target to study and to treat Parkinson’s disease [1, 2]. Placing a microelectrode to record neural activities in deep brain nuclei provides useful information for localization during deep brain stimulation (DBS) neurosurgery. DBS has been approved by FDA since 1998[3]. The surgery implants a stimulator to deep brain nuclei, usually STN, to alleviate Parkinson’s symptoms, such as tremor and rigidity. To search for STN in operation, a microelectrode probe is often used to acquire neural signals from outer areas to the specific target. With assis- tance of imagery techniques, microelectrode signals from different depth are read and recorded. Then, an important step to determine STN location is to distinguish signals of STN from its nearby areas, e.g. subtantia nigra (SNr) (which is a little ventral and medial to STN). Therefore, characterizing and quantifying firing patterns of STN and Applying the String Method to Extract Bursting Information 49 SNr are essential. Firing rate defined as the number of neural spikes within a period is the most common variable used for describing neural activities. However, STN and SNr have a broad range of firing rate and mostly overlapped [4] (although SNr has a slightly higher mean firing rate than STN). This makes it difficult to depend on firing rate to target STN. Bursting patterns may provide a better solution to separate signals from different nuclei. Bursting, defined as clusters of high-frequency spikes released by a neuron, is believed storing important neural information. To establish long-term responses, cen- tral synapses usually require groups of action potentials (bursts) [5,6]. Exploring bursting information in neural activities has recently become fundamental in Parkin- son’s studies [1,2]. Also, that spike arrays are more regular in SNr than in STN sig- nals is observed [7]. However, the regularity of firing or grouping of spikes in STN and SNr potentials has not been investigated thoroughly. This study aims to extract bursting information from STN and SNr. A quantifying method for bursting, the string method, will be applied. The string method quantifies bursting information relying on inter-spike-interval (ISI) and spike number [8]. Although some other methods for quantifying bursts exist [9,10], the string method is the one which can provide information about what spike members contributing to the detected bursts. In addition, because various ISIs have been used in research [8,9] to define bursts, this study will also evaluate the effect of ISI constraints on discriminating STN and SNr signals. 2 Method The neuronal data used in this study were acquired during DBS neurosurgery in Chang Gung Memorial Hospital. With assistance of imagery localization systems [11], trials (10s for each) of microelectrode recordings were collected at a sampling
a
Fig. 1. MRI images from one patient: a. In the sagittal plane – the elevation angle of the probe (yellow line) from the inter-commissural line (green line) was around 50 to 75 ° ; b. In the fron- tal plane – the angle of the probe (yellow lines) from the midline (green line) was about 8 to 18 ° to right or left. 50 P.-K. Chao et al. rate of 24,000 Hz. Based on several observations, e.g. magnetic resonance imaging (MRI), computed topography (CT), motion/perception-related responses and probe location according to a stereotactic system, experienced neurologists diagnosed 18 trials as neural signals from STN, and the other 23 trials as from SNr. The trials which were collected outside STN and SNr and/or confused between STN and SNr were excluded. In this paper, the data are from 3 Parkinson’s patients (2 females, 1 male, age=73.3 ± 8.3 y/o) who received DBS treatment. Due to the patients’ individual dif- ference, e.g. head size, the depth of STN from the scalp was found varied between 15 and 20 cm. During surgery, the elevation angle of the probe from the inter- commissural line was around 50 to 75 ° (Fig 1a) and the angle between the probe and the midline was about 8 to 18 ° toward either right or left (Fig 1b). 2.1 Spike Detection Each trial of microelectrode recordings includes 2 types of signals, spikes and back- ground signals. The background signals are interference from nearby neural areas or environment. Because background signals can be interpreted as a Gaussian distribu- tion, signals which are 3 standard deviations (SD) above or below mean can be treated as non-background signals or spikes. Therefore, a threshold in the level of mean plus 3 SD is applied in this study to detect spikes (Fig 2). 5.175
5.18 5.185
5.19 5.195
5.2 5.205
5.21 10 20 30 40 50 60 70 80 90 100
time (s) amplitude Fig. 2. A segment of microelectrode recording – the red horizontal line is threshold; the green stars indicate the found spikes; most signals around the baseline are background signals Applying the String Method to Extract Bursting Information 51
Every detected spike was plotted as a circle in a spike sequential number versus spike occurring time figure (Fig 3). The spike sequential number is starting at 1 for the first spike in a trial. The spikes which are closer to each other are labeled as strings [8] and defined as bursts. Two parameters were controlled and manipulated to determine bursts: (1) the minimum number of spikes to form a burst was 5; (2) the maximum ISI of the adjacent spikes in a burst was set as 20ms, 50ms, 80ms, and 110ms separately to find an optimal condition to distinguish STN and SNr bursting patterns. 5 5.5
6 6.5
7 80 100 120 140
160 180
time (s) spike sequential number
starting spikes of a burst; the black triangles mean the ending spikes of a burst 2.3 Dependent Variables Three dependent variables were computed: (1) Firing rate (FR) was calculated as total spike number divided by trial duration (10 s). (2) Number of bursts (NB) was deter- mined by the string method as the total burst number in a trial. (3) The average of spike number in each burst (SB) was also counted in every trial.
Independent sample’s t-test was applied to test firing rate difference between STN and SNr signals. MANOVA was performed to evaluate NB and SB separately among different ISI constraints ( α =.05).
52 P.-K. Chao et al. 3 Results The signals from STN and SNr showed similar firing rate but different bursting pat- terns. There is no significant difference between STN and SNr in firing rate (STN: 57.0
± 22.1; SNr: 68.8 ± 23.5) (p>.05). The results of NB and SB are listed in Table 1 and Table 2. In NB, SNr has significantly fewer bursts than STN while ISI setting is 50ms and 80 ms (p<.05). In SB, SNr has significant more spikes in bursts than STN while ISI setting is 20ms, 50ms and 80 ms (p<.05). Based on the findings, 2 points can be addressed: First, STN and SNr have different bursting patterns, although their total numbers of spikes (firing rate) are similar. Comparing to STN, SNr releases fewer bursts but each burst contains more spikes. Second, setting ISI constraints around 50~80 ms in the string method can be effective to distinguish the difference between STN and SNr signals. Table 1. NB results in SNr and STN ISI constraint SNr STN
p 20ms
32.1 ± 15.7 38.2 ± 23.1
>.05 50ms
8.9 ± 6.8 23.9 ± 7.7
<.05* 80ms
5.2 ± 5.8 10.7
± 7.5
<.05* 110ms
3.1 ± 3.4 4.9
± 4.4
>.05
Table 2. SB results in SNr and STN ISI constraint SNr STN
p 20ms
21.6 ± 27.8 8.5 ± 2.2
<.05* 50ms
202.5 ± 309.9 28.1 ± 24.1
<.05* 80ms
396.0 ± 373.9 124.2
± 141.3
<.05* 110ms
515.1 ± 367.6 337.7
± 342.8
>.05
4 Discussion and Conclusion Microelectrode recordings from STN and SNr show valuable information in bursting patterns which may be useful to assist neurosurgery in the future. From the results, STN and SNr show very different patterns in bursting. Neurons in STN tend to release more “small” bursts which contain fewer spikes. Neurons in SNr tend to produce “giant” bursts which contain a big number of spikes. These bursting characteristics are quantified into NB and SB which may assist in making decision about localizing stimulation probes during DBS operations. Also, the simplicity of the string method can offer quick information and be efficient in real-time analysis.
Applying the String Method to Extract Bursting Information 53 Different bursting characterisitcs in STN and SNr are revealed across all ISI con- straints (20, 50, 80, 110 ms) in both variables, although statistical significance only shows in 50 and 80ms. Because there is no “gold standard” to determine ISIs of adja- cent spikes in bursts, several ISI constraint settings were tested in this study. No matter in which setting, STN has a larger NB and smaller SB than what SNr has. Statistical significance only shows in both dependent variables in 50 and 80 ms set- tings. Therefore, we suggest the optimal ISI setting for identifying bursts in STN and SNr signals should be around 50 and 80 ms. For further studies, signals from other deep brain nuclei may be analyzed to enrich the application of bursting information. Also, since the bioelectrical signals from deep brain nuclei are non-stationary, non-linear methods, e.g. complexity, would be per- formed and compared with current results to provide more nucleus-identifying clues in the future. Acknowledgments. The authors would like to express sincere appreciation to the grant support from the Ministry of Economic Affairs in Taiwan, under contract 95-EC-17-A-19-S1-035.
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tion. IEEE Eng. Med. Biol. Mag. 21, 109–116 (2002) Population Coding of Song Element Sequence in the Songbird Brain Nucleus HVC Jun Nishikawa 1 , Masato Okada 1 ,2 , and Kazuo Okanoya 1 1 RIKEN Brain Science Institute, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan 2 Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8561, Japan Abstract. Birdsong is a complex vocalization composed of various song elements organized according to sequential rules. To reveal the neural representation of song element sequence, we recorded the neural re- sponses to all possible element pairs of stimuli in the Bengalese finch brain nucleus HVC. Our results show that each neuron has broad but differential response properties to element sequences. We calculated the time course of population activity vectors and mutual information be- tween auditory stimuli and neural activities. The clusters of population vectors responding to second elements had a large overlap, whereas the clusters responding to first elements were clearly divided. At the same timing, confounded information also significantly increased. These results indicate that the song element sequence is encoded in a neural ensemble in HVC via population coding. 1 Introduction Songbirds have a complex learned vocalization composed of various song ele- ments with a typical sequential rule. In Bengalese finches, these rules follow individually distinctive finite state syntax [1]. Songbirds have been intensively studied as a model for the syntactical properties of human language [2]. It is im- portant to reveal the neural representation of complex song element sequences in the songbird brain. Based on the finding of sequential selective neurons [3,4], it has been thought that the song element sequence is encoded in a chain of the rigid selective neurons [5]. Alternatively, it can be encoded in a neural ensemble of relatively broadly selective neurons in a distributed manner [6,7]. We attempted to determine which neural representation actually occurs in the songbird brain. Songbirds have a specialized brain area for generating and learning complex vocalizations, and the area is called as a song system. From the importance of auditory feedback in song learning, numerous studies have investigated auditory neural representation in the song system [3,4]. Especially, HVC is one of the ma- jor sensory-motor integration sites in the song system; these neurons selectively respond to the bird’s own song (BOS) in a time-locked manner. Margoliash and Fortune found the neurons selectively responded to only typical element pair stimuli included in their own song [3,4]. This type of neuron was named the temporal combination selective neuron (TCS neuron). Since the discovery of M. Ishikawa et al. (Eds.): ICONIP 2007, Part I, LNCS 4984, pp. 54–63, 2008. c Springer-Verlag Berlin Heidelberg 2008
Population Coding of Song Element Sequence 55 TCS neurons, it has been thought that the song element sequence is encoded in a series of different types of TCS neurons. However, TCS neurons were found only in a small portion of the recorded data. Many song-selective neurons lack TCS properties. In addition, the stimuli used in these experiments were only partial presentations of the entire sequence, such as EE, EF, FE, or FF within ABCDEFGHI. This design did not test for responses to other element pairs, such as AB, GC, or any other combination. To more fully understand the neural representation of song element sequences, we must evaluate activity in response to all possible song element pairs within ABCDEFGHI. In this study, we recorded single-unit activities of HVC neurons driven by all possible song element pair stimuli in anesthetized Bengalese finches. Then, we used sequential response distribution analysis, population dynamics analysis, and information-theoretic analysis to show that the song element sequence is encoded within a neural ensemble in HVC neurons by population coding. These findings led us postulate an alternative scheme for encoding the song element sequence in the songbird HVC, with distributed neural representation rather than the chain model of rigid selective TCS neurons. 2 Material and Methods 2.1 Animals
Twenty-three adult Bengalese finches (> 180 days post-hatch) were used in this study. All experimental procedures were performed according to established animal care protocols approved by the animal care and use committee at RIKEN. 2.2
Stimuli Undirected songs were recorded in a quiet soundproof box using a microphone and amplifier connected to a computer with a sampling rate of 44.1 kHz and 16-bit resolution. We calculated sonograms from the recorded song using sound analysis software (SASLab Pro; Avisoft, Berlin, Germany). A birdsong consists of a series of discrete song elements with silent intervals among them. Song elements were divided into distinct types by visual inspection of the spectro- temporal structure of each sonogram. The transition matrix, representing the transition probability between each song element, was then calculated. We can evaluate the syntactical structure of song in individual Bengalese finches using this transition matrix. We prepared five different types of sound stimuli: BOS, REV, OREV, element, and element pair. BOS is the forward playback of the bird’s own song, while REV is the reversed playback of the same song. OREV is a modified version of the song, in which the spectro-temporal composition of each song element is retained, but the order of the song elements has been reversed. Element stimuli are isolated playbacks of each song element. For example, if the song has nine elements, element stimuli are A, B, C, and so on. Element pair stimuli are combinations of all possible element pairs. In this case, we prepared 81 stimuli, including AA, AB, · · ·, IH, and II. 56 J. Nishikawa, M. Okada, and K. Okanoya 2.3 Recording Procedure Before electrophysiological recording sessions, birds were anesthetized with 4 to 7 doses of 10% urethane (40 μl per dose) at 20-min intervals. The birds were restrained in a custom-made chamber on a stereotaxic device (David Kopf Instruments, Tujunga, CA, USA). The birds were fixed with ear-bars and a beak-holder that positioned the beak tip at an angle of 45 degrees below the horizontal plane. The head was treated with Xylocaine gel and the feathers and skin were removed. A custom-made three-point fixation device (Narishige, Tokyo, Japan) was attached to the rostral part of the skull surface with den- tal cement. Small holes were made in the skull just above the HVC. Finally, the dura was removed, and tungsten electrodes were set on the surface. The ear-bars were removed before making physiological recordings. The birds were located in an electromagnetically shielded sound-attenuation box while in the stereotaxic device. The electrodes were lowered into the brain using a hydraulic micro- positioner (MODEL640, David Kopf Instruments), and extracellular signals from HVC were recorded. The signals from the electrodes were amplified (gain 10,000) and filtered (100 Hz-10 kHz bandpass) using an extracellular recording amplifier (ER-91, Cygnus Technology, Water Gap, PA, USA). The data were digitized at 20 kHz with 16-bit resolution using the data acquisition system (Micro1401, Cambridge Electronic Design, Cambridge, UK) and the associated software (Spike2, Cambridge Electronic Design). The data were stored in a computer disk for off-line analysis. During the neural recording session, sound stimuli were presented at a peak sound pressure of 70 dB. At first, we presented BOS, REV, OREV, and the silent stimuli. Next, each of the elements and silent stimuli were delivered. Finally, we presented element pairs and silent stimuli. Each sound stimulus was presented 20 times in a random order with an interstimulus interval of 3 to 5 s. The computer for neural recording and that for stimulus presentation were synchronized by a trigger-signal generated simultaneously with the stimuli. 2.4
Data Analysis Analyses were performed using custom-made programs written by MATLAB (Mathworks, Natick, MA, USA). The mean spontaneous firing rate was cal- culated from the baseline activity registered during the silent stimulus. The re- sponse strength RS was calculated by subtracting the spontaneous rate from the firing rate R registered during stimulus presentation. R and RS were measured in each 10 ms bin, from which we calculated the average R, RS, and variance σ 2 R , σ 2 RS across the stimulus presentation period. To determine the selectivity of each neuron, we calculated the psychophysical measure , as previously described [8]. d (x
A /x B ) = 2(x
A − x
B ) σ 2 x A + σ 2 x B . (1) In this equation, x A is the response to stimulus A, and x B is the response to stimulus B. d (x A /x B ) represents the response selectivity to stimulus A relative to stimulus B based on the mean and variation of the responses. We considered a neuron to be selective for a stimulus when the selectivity satisfies d > 1.0 [9]. Population Coding of Song Element Sequence 57 2.5 Population Dynamics Analysis To analyze neural activity at the population level, we performed a population dynamics analysis [10]. With our experimental design, we were not able to com- bine the data from different individuals because their songs and elements thereof were completely different from each other. Therefore, we presented the data for one typical bird in which we could register activity from six distinct single units throughout the presentation of all stimuli. Note that the qualitative property for the obtained results was similar in the other birds. For each stimulus, we calcu- lated a population activity vector, which is the set of instantaneous mean firing rates for each neuron in a 50 ms time window. In this case, each population activity vector had six dimensions. Since this typical bird had four song ele- ments, we calculated 16 population activity vectors for 16 element pair stimuli, within the 50 ms time window. The time window shifted by increments of 1 ms from -200 to 600 ms (stimulus onset = 0 ms). The data were smoothed using a Gaussian filter with a variance of 10 ms. These procedures enabled us to observe the temporal aspects of the neuronal population. The multidimensional scaling method (MDS) [11] is a dimension-reduction method that rearranges data from a high-dimensional space into a lower-dimensional space, while preserving as much of the information as possible. MDS was applied to the set of population activity vectors for each time window. Finally, the population response to each stimulus was represented in two-dimensional MDS space, and the clustering of these responses was analyzed. 2.6 Information-Theoretic Analysis To evaluate how much information is transmitted by each neuron, we calcu- lated the mutual information between the stimulus and the neural response [12]. Mutual information was quantified as the decrease in entropy of the stimulus occurrence: I(S; R) = H(S) − H(S|R), (2)
= − s p(s) log p(s) − − s p(s|r) log p(s|r) r . In this equation, S is the set of stimuli s, and R is the set of neural responses r, i.e., spike count. p(s|r)is the conditional probability of stimulus s given an observed spike count r , and p(s) is the a priori probability of stimulus s. The brackets indicate an average of the signal distribution p(r). To examine the time course of the information, the response was evaluated using a 50 ms sliding window. The center of the window was moved in 10 ms steps, beginning 200 ms before the stimulus onset and lasting until 600 ms after the stimulus. To test the statistical significance, we estimated the mean and standard deviation of the information during the 200 ms period before the stimulus onset. If the value exceeded the mean + 3SD, we considered the information significant (P < 0.001).
58 J. Nishikawa, M. Okada, and K. Okanoya 3 Results
3.1 Selective Auditory Response to BOS We used a spike sorting procedure to classify the signals recorded from the Bengalese finch HVC, which yielded well identified single units (n = 104, 23 birds). We analyzed these data using the psychophysical measure d . In total, 86% of HVC neurons selectively responded to BOS compared to the silent con- dition (d (RS BOS
/RS Baseline
) > 1.0, 89/104 cells). In addition, 63% of neu- rons were more responsive to BOS than to REV (d (RS BOS /RS
REV ) > 1.0,
65/104 cells), and 28% of neurons were more responsive to BOS than to OREV (d (RS
BOS /RS
OREV ) > 1.0, 29/104 cells). These results are consistent with past studies [4]. The mean of d (RS BOS
/RS REV
) was 1.25, and the mean of d (RS
BOS /RS
OREV ) was 0.63. These results indicate that BOS-selective neu- rons in HVC are largely variable, especially in terms of sequential response properties. A. Elements -0.2
0 0.5 (s)
0 100
0 20 ret sa R HT SP )z H( B C D B. Element pairs -0.2
0 0.5 (s)
0 100
0 20 ret sa R HT SP )z H( C A C B
C C C D
D A D B
D C D D
A A A
A B A C
A D B A
B B B C
B D Fig. 1. An example of the auditory response to song elements (A) and element pairs (B) in a single unit from HVC
Population Coding of Song Element Sequence 59 Fig. 2. Song transition matrices of self-generated songs (first row) and sequential re- sponse distribution matrices of each single unit (second to seventh rows) 3.2
Responses to Song Element Pair Stimuli To investigate the neural selectivity to song element sequences, we recorded neu- ral responses to all possible element pair stimuli. Because the playback of these stimuli is extremely time-consuming, we could only maintain 34% of the recorded single units stable throughout the entire presentation (35/104 cells, 12/23 birds). In total, 70% of the stable single-units were BOS-selective (d (RS BOS /RS
REV ) > 1.0, 27/35 cells, 12/12 birds). Thereafter, we focused on these data. A typical example of neural responses to each song element is shown in Fig. 1 (A). The neuron responded to a single element A or C with single pha- sic activity, but it did not respond to element B. It responded to element D with double phasic activity. These results indicate that the neuron has various response properties even during single element presentation. In addition, the neuron exhib- ited more complex response properties during the presentation of element pairs (Fig. 1(B)). The neuron responded more strongly to most of the element pairs when the second element was A or C, compared to single presentation of each ele- ment. However, the response was weaker when the first and second elements were the same. When the second element was B, no differences were observed between single and paired stimuli. When the second element was D, we measured single
60 J. Nishikawa, M. Okada, and K. Okanoya phasic responses, and a strong response to BD. These response properties were not correlated with the element-to-element transition probabilities in the song structure. The dotted boxes indicate the sequences included in BOS. However, the neuron responded only weakly to some sequences that were included in BOS (brack arrows). In contrast, the neuron responded strongly to other sequences that were not included in BOS (white arrows). Thus, the neuron had broad response properties to song element pairs beyond the structure of self-generated song. To quantitatively evaluate sequential response properties, we calculated the response strength measure d (RS S /RS Baseline ) to the element pair stimuli S. The sequential response distributions were created for each neuron in two indi- viduals with more than five well identified single units. Song transition matrices and sequential response distributions are shown in Fig. 2. The response distribu- tions were not correlated with the associated song transition matrices. However, each HVC neuron in the same individual had broad but different response distri- bution properties. This tendency was consistent among individuals. This result indicates that the song element sequence is encoded at the population level, within broadly but differentially selective HVC neurons. 3.3 Population Dynamics Analysis To analyze the information coding of song element sequences at the population level, we calculated the time course of population activity vectors, which is the set of instantaneous mean firing rates for each neuron in a 50 ms time win- dow. Snapshots of population responses to stimuli are shown in eight panels of Fig. 3A (n = 6, bird 2 of Fig. 2). Each point in the panel represents the popu- lation vector toward each stimulus on the MDS space. The ellipses in the upper four panels indicate the group of vectors whose stimuli have the same first el- ement, while the ellipses in the lower four panels indicate the group of vectors whose stimuli have the same second element. Note that the population activ- ity vectors in the upper four panels are identical to those in the bottom four panels, and only the ellipses differ. Before the stimulus presentation ([-155 ms: -105 ms], upper and lower panels), only spontaneous activities were observed around the origin. After the first element presentation ([50 ms: 100 ms], upper panel), groups with the same first elements split. After the second element pre- sentation ([131 ms: 181 ms] of the lower panel), groups with the same second elements were still largely overlapping. In the next section, we will show that confounded information, which represents the relation between first and second elements, increased significantly in this timing. After sufficient time ([480 ms: 530 ms], upper and lower panels), the neurons returned to spontaneous activity. The result indicates that the population response to the first and second element is drastically different. Subsequently, we will show that this overlap is derived from the information in the song element sequence. 3.4 Information-Theoretic Analysis To determine the origin of the overlap in the population response, we calculated the time course of mutual information between the stimulus and neural activity. Population Coding of Song Element Sequence 61 Fig. 3. Responses of HVC neurons at the population level (A) and encoded informa- tion (B) The mutual information for first elements I(S 1 ; R), the second elements I(S 2 ; R),
and that of element pairs I(S 1 , S 2 ; R) was calculated within each time window; the window was shifted to analyze the temporal dynamics of information coding (left upper 3 graphs in Fig. 3B). Narrow lines in each graph indicate the cumula- tive trace of mutual information in each neuron. The thick line is the cumulative trace of all neurons in the individual. The bottom-left graph in Fig. 3B shows the probability of stimulus presentation. After the presentation of the first elements, mutual information for the first elements increased, showing a statistically sig- nificant peak (P < 0.001). After the presentation of the second elements, mutual information for the second elements significantly increased (P < 0.001). At the 62 J. Nishikawa, M. Okada, and K. Okanoya same time, mutual information for element pairs also showed a significant peak (P < 0.001). Intuitively, information for element pairs I(S 1 , S
2 ; R) would con- sist of information for the first elements I(S 1 ; R) and second elements I(S 2 ; R).
However, the consecutive calculation of I(S 1 , S 2 ; R) − I(S 1 ; R) − I(S 2 ; R) in
each time window causes a statistical peak after the presentation of element pairs (P < 0.001; forth graph from left in Fig. 3B). The difference C represents the conditional mutual information between the first and second elements for a given neural response, otherwise known as confounded information [13]. There- fore, confounded information represents the relationship between the first and second elements encoded in the neural responses. The I(S 1 ; R) peak occurred at the same time that groups of population vectors with the same first elements were splitting ([50 ms: 100 ms]). The peaks for I(S 2 ; R), I(S 1 , S
2 ; R), and C occurred during the same time that groups with the same second elements were still largely overlapping ([131 ms: 181 ms]). This indicates that the sequential information causes an overlap in the population response. In the population dynamics analysis, we cannot combine the data from differ- ent birds because each bird has a different number and types of song elements. However, in the mutual information analysis, we can combine and average the data from different birds. The five graphs on the right in Fig. 3B show the time courses for I(S 1 ; R), I(S 2 ; R), I(S 1 , S
2 ; R), C, and the stimulus presentation probability, which were calculated from all stable single units with BOS selectiv- ity (n = 27, 12 birds). The combined mutual information for first elements was very similar to that from one bird, showing a significant peak after the presenta- tion of the first elements (P < 0.001). Mutual information for second elements, element pairs, and confounded information also had significant peaks after the presentation of the second elements (P < 0.001). These results show that the song element sequence is encoded into a neural ensemble in HVC by population coding.
4 Conclusion In this study, we recorded auditory responses to all possible element pair stimuli from the Bengalese finch HVC. By determining the sequential response distribu- tions for each neuron, we showed that each neuron in HVC has broad but differ- ential response properties to song element sequences. The population dynamics analysis revealed that population activity vectors overlap after the presentation of element pairs. Using mutual information analysis, we demonstrated that this overlap in the population response is due to confounded information, namely, the sequential information of song elements. These results indicate that the song element sequence is encoded into the HVC microcircuit at the population level. Song element sequences are encoded in a neural ensemble with broad and dif- ferentially selective neuronal populations, rather than the chain-like model of differential TCS neurons. Population Coding of Song Element Sequence 63 Acknowledgment This study was partially supported by the RIKEN Brain Science Institute, and by a Grant-in-Aid for young scientists (B) No. 18700303 from the Japanese Ministry of Education, Culture, Sports, Science, and Technology. References 1. Okanoya, K.: The Bengalese finch: a window on the behavioral neurobiology of birdsong syntax. Ann. N.Y. Acad. Sci. 1016, 724–735 (2004) 2. Doupe, A.J., Kuhl, P.K.: The Bengalese finch: a window on the behavioral neu- robiology of birdsong syntax. Birdsong and human speech: common themes and mechanisms. Annu. Rev. Neurosci. 22, 567–631 (1999) 3. Margoliash, D., Fortune, E.S.: Temporal and harmonic combination-selective neu- rons in the zebra finch’ s HVc. J. Neurosci. 12, 4309–4326 (1992) 4. Lewicki, M.S., Arthur, B.J.: Hierarchical organization of auditory temporal context sensitivity. J. Neurosci. 16, 6987–6998 (1996) 5. Drew, P.J., Abbott, L.F.: Model of song selectivity and sequence generation in area HVc of the songbird. J. Neurophysiol. 89, 2697–2706 (2003) 6. Deneve, S., Latham, P.E., Pouget, A.: Reading population codes: a neural imple- mentation of ideal observers. Nat. Neurosci. 2, 740–745 (2001) 7. Pouget, A., Dayan, P., Zemel, R.: Information processing with population codes. Nat. Rev. Neurosci. 1, 125–132 (2000) 8. Green, D., Swets, J.: Signal Detection Theory and Psychophysics. Wiley, New York (1966) 9. Theunissen, F.E., Doupe, A.J.: Temporal and spectral sensitivity of complex audi- tory neurons in the nucleus HVc of male zebra finches. J. Neurosci. 18, 3786–3802 (1998)
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