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Canonical correlation between LFP network and spike network during working memory task in rat
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Behavioural Brain Research journal homepage: www.elsevier.com/locate/bbr
Research report
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Canonical correlation between LFP network and spike network during working memory task in rat
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Hu Yi, Xiaofan Zhang, Wenwen Bai, Tiaotiao Liu, Xin Tian ∗ School of Biomedical Engineering, Tianjin Medical University, Tianjin, 300070, China
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h i g h l i g h t s
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Multi-channel recording in freely moving rats during a working memory task. Functional connectivity in LFP network and spike network estimated by DTF and MLE. Coordination between the two networks assessed via canonical correlation analysis. Coordination between the two networks enhanced in correct trials. Network integration may provide a potential mechanism for working memory.
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Article history: Received 23 December 2014 Received in revised form 18 April 2015 Accepted 23 April 2015 Available online xxx
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Keywords: Working memory LFP network Spike network Canonical correlation analysis Rat
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1. Introduction
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Working memory refers to a system to temporary holding and manipulation of information. Previous studies suggested that local field potentials (LFPs) and spikes as well as their coordination provide potential mechanism of working memory. Popular methods for LFP-spike coordination only focus on the two modality signals, isolating each channel from multi-channel data, ignoring the entirety of the networked brain. Therefore, we investigated the coordination between the LFP network and spike network to achieve a better understanding of working memory. Multi-channel LFPs and spikes were simultaneously recorded in rat prefrontal cortex via microelectrode array during a Y-maze working memory task. Functional connectivity in the LFP network and spike network was respectively estimated by the directed transfer function (DTF) and maximum likelihood estimation (MLE). Then the coordination between the two networks was quantified via canonical correlation analysis (CCA). The results show that the canonical correlation (CC) varied during the working memory task. The CC-curve peaked before the choice point, describing the coordination between LFP network and spike network enhanced greatly. The CC value in working memory showed a significant higher level than inter-trial interval. Our results indicate that the enhanced canonical correlation between the LFP network and spike network may provide a potential network integration mechanism for working memory. © 2015 Published by Elsevier B.V.
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Working memory refers to a system to temporary holding and manipulation of information while performing complex tasks such as reasoning, comprehension and learning [1]. Accumulating evidence has shown prefrontal cortex (PFC) plays an important role in working memory [2–4]. Neural signals recorded with extracellular microelectrodes— commonly decomposed into local field potentials (LFPs) and spikes—are measurements for studying the spatiotemporal organization of information processing circuits underlying various
∗ Corresponding author.Tel./fax: +86 02283336952. E-mail addresses: [email protected], tian [email protected] (X. Tian).
cognitive functions. Previous studies tended to focus on how LFPs and spikes separately encode information in cognitive processes [5–8] and became interested in the combination of them [9,10]. Popular methods for studying the interaction between LFPs and spikes include correlation [11], coherence [12], phase-locking [13], and classification approach [14]. For instance, previous study has demonstrated that coherence between hippocampal LFPs and mPFC spikes is most marked in theta rhythms during a rat Y-maze working memory task [15]. Recent research has suggested that the coupling between spikes and theta-band LFPs in rat hippocampus and medial prefrontal cortex (mPFC) enhance during a spatial working memory task [16]. Our previous studies have also revealed the enhanced spike-LFP coordination during working memory task in healthy rats [17] as well as the incoordination in A-mediated memory deficits rats [18].
http://dx.doi.org/10.1016/j.bbr.2015.04.042 0166-4328/© 2015 Published by Elsevier B.V.
Please cite this article in press as: Yi H, et al. Canonical correlation between LFP network and spike network during working memory task in rat. Behav Brain Res (2015), http://dx.doi.org/10.1016/j.bbr.2015.04.042
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Fig. 1. Behavior setup and histology. (A) Schematic representation of Y-maze, the purple dots represent the infrared beam sensor, which mark the behavioral events. Rats can get rewards by passing the removable guillotine door (dash lines near the start box). (B) Left part: Diagram of coronal section showing the level and position of the rat mPFC, taken from the Stereotaxic Coordinates [48]. Right part: Tracks of recording electrodes in mPFC, as indicated by the black arrow.
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Typically, LFPs and spikes are analyzed separately or combined between each channel’s time series data. However the separate analyses do not enable the examination of joint information between the modalities; just combining time series data do not enable the examination the underlying mechanisms of the data [19]. These methods isolate each channel from the whole data, not considering the brain’s network architecture. Therefore, multimodal integration has become a highly desirable multimodal approach to capitalize on the strength of each modality in a joint analysis, rather than a separate analysis of each. Recently, functional connectivity has become a useful tool to explore the information about directed functional interactions and the mechanism for integration in the brain [20]. It has been investigated to explore the mechanism of working memory [21]. Previous studies have showed the connection strength of LFP network [22] and spike network [23] in PFC increased during working memory respectively. It is however not known how multimodal networks coordinate during working memory. In the present study, we simultaneously recorded LFPs and spikes from multielectrode arrays implanted in rat PFC during a Y-maze working memory task. Functional connectivity in the LFP network and spike network was respectively estimated by the directed transfer function (DTF) and maximum likelihood estimation (MLE). Then the coordination between the two networks was quantified via canonical correlation analysis (CCA), to study how the LFP network and spike network coordinate during the working memory task. This may obtain insights into how multimodal network integration could contribute to working memory.
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2. Materials and methods
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2.1. Experiment and data acquisition
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Behavioral task and electrophysiology recording procedures were in accordance with the National Institute of Health Guide for Care and Use of Laboratory Animals and the Tianjin medical University guidelines for the use and care of laboratory animals in research. Male Sprague-Dawley rats weighing 300–350 g were housed two per cage in a temperature and humidity controlled colony on a 12 h light dark cycle at the Experimental Animal Center of Tianjin Medical University. All animals were maintained at approximately 85% of their free-feeding weight and had ad libitum access to water. Animals were habituated to a Y-maze (Fig. 1A) until they were readily eating pieces of peanuts in the food wells in both arms. After habituation, rats were trained on a working memory task (delayed alternation task in Y-maze). The rats were given two training
sessions per day (10 trials per session). Each trial consisted of a sample run and a choice run. On the sample run, the rats can obtain food reward for accessing either arm. After consuming the food, the rats voluntarily ran back to the start box. After a 5-s delay, the rats would have a choice run. The rats were only rewarded for choosing the previously unvisited arm and recorded correct. Training continued until the correct rate went over 80% on two consecutive days. After reaching the criterion, the animals were anesthetized with pentobarbital sodium (1%, 40 mg/kg), and all efforts were made to minimize suffering. The rats were placed in a stereotaxic frame and implanted with 16-channel nickel-chromium microelectrode array (impedance less than 1 M) targeting the mPFC (2.5–4.5 mm anterior to bregma, 0.2–1.0 mm lateral to the midline and 2.5–3.0 mm below the brain surface). After recovery, neural data were recorded from rat mPFC using a Cerebus data Acquisition System (Cyberkinetics, USA) during the task. The time of behavioral events were marked by the infrared beam sensor (Fig. 1A) in the maze and synchronized with the recording system. Time 0 indicates the tripping time of the infrared beam sensor in the Y-maze, which means the moment when rat was at the choice point in the maze. To extract local field potentials, neural signals were filtered between 0.3 and 500 Hz and digitized at 2 kHz. To extract spikes, the same signals were filtered between 0.5 and 7.5 kHz, and waveforms that exceeding a voltage threshold were sampled at 30 kHz and stored with time stamps. The data analysis workflow is shown in Fig. 2. After neural recording, animals were perfused with saline followed by 10% formaldehyde solution, and the brains were sectioned into coronal slices at 150-m (Fig. 1B) with a vibratome (Leica, Germany) to verify the recording location. 2.2. Data analysis
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2.2.1. Functional connectivity among LFPs via directed transfer function The time-frequency (TF) representation of LFPs during the task was calculated using Complex Morlet’s wavelet. The TF representation provided a time-varying energy of the signal in each frequency band [24]. In the present study, the signal was convoluted by complex Morlet’s wavelet w(t, f0 ) w(t, f0 ) = A exp(−t 2 /2t2 ) exp(2if0 t)
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(1)
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√ −1/2 with f = 1/2t , A = (t ) . The trade-off ratio f 0 /f was chosen as 7 to create a wavelet family [25]. The time-varying energy
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Fig. 2. Flow chart for data preprocessing. LFPs and spikes were obtained from raw data via digital filters. Feature band was extracted according to the results of time-frequency analysis. Functional connectivity networks among multi-channel LFPs and spikes were respectively estimated by the DTF and MLE. Then the coordination between the two networks was quantified via canonical CCA.
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E(t, f0 ) of the signal at a frequency band is the squared norm of the convolution of a complex wavelet with the signal:
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2 E(t, f0 ) = w(t, f0 ) ∗ s(t)
where s(t) refers to LFPs data. The characteristic frequency band was extracted from the LFPs via band pass filtering. Then the functional connectivity of LFPs was analyzed by DTF method. The functional connectivity analysis utilizing DTF [26,27], which can be applied to analyze connectivity among multi-channel signals [28–30]. Multivariate autoregressive (MVAR) modeling can be applied to estimate the model parameters of signals as X(t) =
p
(i)X(t − i) + E(t)
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where X (t) is the signal data at time t, (i) are the matrices of multivariate model coefficients, p is the model order, and E(t) is a vector of multivariate white noise. After transforming MVAR model parameters into frequency domain,
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(f )X(f ) = E(f )
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matrix of the system. The DTF value ij2 (f ) from signal j to signal i can be obtained by normalizing the system transfer function matrix
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Signals which have significant directional DTF value to other signals were considered to have directional causality to other signals.
Nonparametric surrogate testing was conducted to test the significance. The shuffling procedure destroying the phase information of the original signals was repeated 5000 times and the DTF values with the significance level p < 0.05 were considered as directional significant [31]. The recording electrodes were defined as the nodes of causal network, and the edge of the causal network are elements of the matrix. The DTF matrix is a direct measurement of functional connectivity among LFPs. The mean value of elements in the DTF matrix DTFmean is defined as: DTFmean
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DTFij
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i= / j∈N
where DTFij means the functional connectivity from channel j to channel i. N is the number of nodes. 2.2.2. Functional connectivity among spikes via maximum likelihood estimation DTF has proven to be an effective method for the investigation of directional relationships between continuous valued signals [28–30,32], but cannot be applied to spike train since their discrete nature. The functional connectivity among spike trains was calculated via maximum likelihood estimation (MLE), modeled by the generalized linear model (GLM) as described previously [33,34]. MLE can be directly applied to discrete point process data and has been proved to be effective to identify the functional connectivity among the spike trains [35]. In this method, let Ni (t) denote the sample path counts the number of spikes of channel I in the time interval (0,t]. A point process model of the spike train for channel i can be completely characterized by its conditional intensity function (CIF), defined as i (t|Hi (t)) = lim
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Pr[Ni (t + ) − Ni (t) = 1|Hi (t)]
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Please cite this article in press as: Yi H, et al. Canonical correlation between LFP network and spike network during working memory task in rat. Behav Brain Res (2015), http://dx.doi.org/10.1016/j.bbr.2015.04.042
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where H i (t) denotes the spiking history of all channels up to time t for channel i. The CIF can be modeled by the GLM framework to model the effect of its own and ensemble’s spiking histories on the current spiking activity. Then a point process likelihood function was used to fit the parametric CIF and analyze the Granger causality between channels. The likelihood function of the spike train of channel i given as
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Li (i ) =
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2.2.4. Statistical analyses To determine if functional connectivity and the coordination between the two networks observed are due to chance, we shuffled the data 200 times to establish criteria for statistical significance [39]. Statistical differences were evaluated by using Two-way ANOVA and t-test. Specifically, DTFmean , GCmean and CC between the original and shuffled data, as well as between the correct and incorrect trials were analyzed using Two-way ANOVA. CC in working memory and inter-trial interval (ITI) was compared by using t-test. Error bars represent the mean ± SEM. P-values are marked statistically significant as follow: **P < 0.01.
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k=1 i
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where Ni [k] takes on the value 1 if there is one spike or 0 if there is j no spike. Similarly, Li (i ) can be calculated by excluding the spiking history of channel j. Then, a potential causal relationship from channel j to channel i defined as j
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ij = log
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To evaluate the statistical significance of the estimated casual interactions, a hypothesis test was performed based on the likelihood ratio test statistic within the 95% confidence interval, since -2 times the value of causal interactions asymptotically followed a chi-squared distribution [35]. The FDR (false discovery rate) controls the expected proportion of false positive finding among all the rejected null hypotheses [36]. If the ij has passed the significance test, it will keep as GCij otherwise it will set to zero. In this paper, all the nonzero values in GC matrix have passed the significance test with a threshold of q = 0.05, FDR corrected. GC matrix is a direct measurement of functional connectivity among spikes. Similar as the DTFmean , the mean value of functional connectivity matrix GC is defined as:
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GCmean =
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GCij
(11)
i= / j∈N
Where GCij indicates the functional connectivity from channel j to channel i.
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2.2.3. Coordination between LFP network and spike network based on Canonical correlation analysis Canonical correlation analysis (CCA) is a statistical method to extract linear components that capture correlations between two multi-variate random variables [37]. CCA finds a modal that explains both of observations in two data sets by identifying a pair of directions where the projections (namely, u and ) of the random variables, x and y yield maximum correlation:
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u,v =
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cov(u, v) u v
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where cov(u, v) denotes the covariance function and gives the standard deviation [38]. Two matrices which were being canonical correlation in this study were the DTF matrix for LFP and the GC matrix for spike. DTF matrix and GC matrix are the quantitative descriptions for functional connectivity among multi-channel LFPs and spikes respectively. CCA was chosen because CCA can express the relationship among multi-channels LFPs and the multi-channels spikes in our case, and the plain correlation only provides the relationship between LFP and spike in a single channel. The projections in this study means the linear combination of two matrices respectively. CCA finds a pair of directions in which the u,v are maximized.
3. Results We simultaneously recorded LFPs and spikes from 6 rats using 16-channel implanted electrode array while they performed the Ymaze delayed alternation task. In total, we describe 89 trials (80 correct trials and 9 incorrect trials) in the present paper. 3.1. Energy changes of LFPs in rat mPFC during the working memory task Spectral analysis was used to assess the dominant frequencies in the LFPs. To illustrate the temporal modulation of energy in different frequency bands, the LFP spectrum was calculated using Complex Morlet’s wavelet with 1 Hz resolution. Fig. 3A shows timefrequency representation of a single electrode during a single trial. Fig. 3B and C shows the averaged TF representation across all the trials and all the electrodes respectively. These data were transferred to z-score to analyze the variability of the TF representation across trials and electrodes. Fig. 3E and F represents the z-score transformation of data in Fig. 3B and C respectively. Notably, theta (4–12 Hz) energy increased before the choice point, and was much larger than those in other frequency bands. 3.2. Functional connectivity matrices in LFP network and spike network Functional connectivity matrices among multi-channel LFPs and spikes were estimated via DTF and MLE, respectively. Fig. 4A and B respectively represents the LFP network (theta-band) and spike network in working memory (0.5s pre and 0.5s post the CC peak). Each element of the matrix shows how much each node interacts one another. The scaled color represented the connectivity strengths from trigger node to target node. As can be seen from Fig. 4, the functional connectivity matrices from the LFP network and spike network were consistent with each other. We then employed the canonical correlation analysis to quantify the coordination between the two networks. 3.3. Coordination between LFP network and spike network The coordination between LFP network and spike network was assessed by CCA. Fig. 5 shows the dynamic changes of canonical correlation (CC) in the LFP network and spike network during the correct trials (window length: 1s, moving steps: 0.25 s). The time axis represents each rat’s average latency before crossing the infrared detector from the start location. In all the subjects, across the whole task time, CC were observed to increase up until the choice point, and then to decrease. To confirm whether the CC were significantly increased in WM, we further estimated the CC between the LFP network and spike network in inter-trial interval (ITI) and compared the CC values between WM and ITI. The CC value in WM was significantly higher
Please cite this article in press as: Yi H, et al. Canonical correlation between LFP network and spike network during working memory task in rat. Behav Brain Res (2015), http://dx.doi.org/10.1016/j.bbr.2015.04.042
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Fig. 3. Time-frequency representation of the energy for LFP. (A) Time-frequency representation of a single electrode during a single trial. (B) Averaged TF representation across all the trials. (C) Averaged TF representation across all the electrodes. (D) The z-score transformation of data in Fig. 3B. (E)The z-score transformation of data in Fig. 3C.
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than in ITI (Fig. 6, WM: 0.8436 ± 0.0102, ITI: 0.3291 ± 0.0121, t-test, P < 0.01).
were significantly higher than those in the shuffled data (Two-way ANOVA, P < 0.01, P < 0.01, P < 0.05, respectively).
3.4. Changes of DTFmean , GCmean and CC in the original data and shuffled data
3.5. Changes of DTFmean , GCmean and CC in correct and incorrect trials
To determine whether the functional connectivity and the coordination observed are due to chance, we shuffled all the rats’ data 1600 times to establish criteria for statistical significance [38]. Fig. 7 shows the DTFmean , GCmean and CC value in the original data and shuffled data. The DTFmean , GCmean and CC in the original data
We observed the enhanced coordination between the two networks, a pattern of canonical correlation increase, peak, and decline in correct trials during the task. To obtain more information conveyed in this, we further analyzed the functional connectivity and compared coordination between correct and incorrect trials.
Fig. 4. Functional connectivity matrices among LFPs and spikes. (A) LFP network (theta band) in working memory (0.5 s pre and 0.5 s post the CC peak). (B) Spikes functional network in working memory. The networks show how much each node interacts one another. The scaled color represented the connectivity strengths from trigger node to target node. The functional connectivity matrices shows the two networks consistent with each other.
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Fig. 5. Dynamic changes of canonical correlation (CC) between LFP network and spike network during the task (window length: 1s, moving steps: 0.25 s). The purple dot lines indicate the tripping time of the infrared beam sensor in the Y-maze. The time axis represents average latency before rats crossing the infrared detector from the start location. Error bars represent the mean ± SEM.
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Fig. 8 shows DTFmean , GCmean and CC in the correct trials (n = 80) and incorrect trials (n = 9) during the task. The DTFmean , GCmean and CC increased obviously and peaked before the choice point, followed by a steady decline. In contrast with increase tendencies in the correct trials, all three indices presented no obvious changing tendency in the incorrect trials. The DTFmean , GCmean and CC in the correct trials were significantly higher than those in the incorrect trials. (Two-way ANOVA, P < 0.01, P < 0.01, P < 0.05, respectively) Since increasing tendencies of the coordination between the LFP network and spike network were found in the correct trials while there was no significant change in incorrect trials, we proposed that the strengthened coordination between the two networks could be necessary in working memory.
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4. Discussion
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We examined the coordination between the LFP network and spike network in rat mPFC during the working memory task via CCA. Unlike other approaches in which the interaction between single channels’ signals is tested, the functional connectivity approach in this study can exploit the relationship among multi-channels
Fig. 6. Canonical correlation in working memory (0.5 s pre and 0.5 s post the CC peak) and ITI. The CC in WM was significantly higher than ITI. (t-test, **p < 0.01).
LFPs and the multi-channels spikes. We found that the canonical correlation (CC) varied during the working memory task. The CCcurve peaked before the choice point, describing the coordination between LFP network and spike network enhanced greatly. The CC value in working memory was significant higher than that in ITI. Our results indicate that the enhanced coordination between the LFP network and spike network during working memory. Recording multiple types of brain data from the same subject using various non-invasive (usually to human) imaging techniques (MRI, EEG, MEG, etc.) and invasive extracellular (usually to animals) recording techniques (LFPs and spikes) has become common practice. Each recording techniques has markedly different spatial and temporal resolutions and provides a different view of brain function or structure. Typically these data are analyzed separately, however due to the remarkable complementarity between these techniques [40]. Multimodal integration has become a highly desirable multimodal approach. The goal of multimodal fusion is to capitalize on the strength of each modality in a joint analysis, rather than a separate analysis of each. CCA allows a different mixing matrix for each modality and is used to find a transformed coordinate system that maximizes intersubject covariation across the two data sets [41]. CCA was applied to an auditory sensorimotor task, patients with schizophrenia showing significantly in three loadings compared to healthy controls [42]. Multimodal CCA is invariant to differences in the range of the data types and can be used to jointly analyze very diverse data types. It can also be extended to multi-set CCA to incorporate more than two modalities [43]. Our study sought to address how the LFP network and spike network coordinate in PFC during the working memory task. Accumulating evidence has suggested the PFC-VTA-hippocampus axis is critical for working memory. The task-related neuronal activity in rats in PFC, hippocampus and VTA is coordinated by a 4-Hz oscillation [44]. In the case of prefrontal-hippocampus circuit, theta band play a particularly important role [45,46]. Inactivating the hippocampus led to a reduction in hippocampal-PFC coherence and impaired working memory function [47]. We predicted that the coordination between LFP network and spike network should be across the prefrontal-hippocampus circuit. In summary, our results demonstrate that the canonical correlation between the LFP network and spike network increased
Please cite this article in press as: Yi H, et al. Canonical correlation between LFP network and spike network during working memory task in rat. Behav Brain Res (2015), http://dx.doi.org/10.1016/j.bbr.2015.04.042
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Fig. 7. DTFmean , GCmean and canonical correlation (CC) in the original and shuffled data. (A) Change of DTFmean of LFPs in the original (solid lines) and shuffled data (dash lines) (window length: 1 s, moving steps: 0.25 s). (B) Change of GCmean of spikes in the original and shuffled data. (C) CC in the original and shuffled data. The DTFmean , GCmean and CC in the original data were significantly higher than those in the shuffled data. (Two-way ANOVA, P < 0.01, P < 0.01, P < 0.05, respectively).
Fig. 8. DTFmean , GCmean and canonical correlation (CC) in correct (n = 80) and incorrect (n = 9) trials during the task. (A) Change of DTFmean of LFPs in the correct (solid lines) and incorrect (dash lines) trials (window length: 1s, moving steps: 0.25 s). (B) Change of GCmean of spikes in the correct and incorrect trials. (C) CC in the correct and incorrect trials. The DTFmean , GCmean and CC in the correct trials were significantly higher than those in the incorrect trials. (Two-way ANOVA, P < 0.01, P < 0.05, P < 0.01, respectively).
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during the working memory task, which reflected the rising coordination level between the two networks. These findings could lead to improved understanding of the working memory mechanism from the view of network integration.
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Acknowledgments
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Research report
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Canonical correlation between LFP network and spike network during working memory task in rat
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Hu Yi, Xiaofan Zhang, Wenwen Bai, Tiaotiao Liu, Xin Tian ∗ School of Biomedical Engineering, Tianjin Medical University, Tianjin, 300070, China
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h i g h l i g h t s
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Multi-channel recording in freely moving rats during a working memory task. Functional connectivity in LFP network and spike network estimated by DTF and MLE. Coordination between the two networks assessed via canonical correlation analysis. Coordination between the two networks enhanced in correct trials. Network integration may provide a potential mechanism for working memory.
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Article history: Received 23 December 2014 Received in revised form 18 April 2015 Accepted 23 April 2015 Available online xxx
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Keywords: Working memory LFP network Spike network Canonical correlation analysis Rat
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1. Introduction
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Working memory refers to a system to temporary holding and manipulation of information. Previous studies suggested that local field potentials (LFPs) and spikes as well as their coordination provide potential mechanism of working memory. Popular methods for LFP-spike coordination only focus on the two modality signals, isolating each channel from multi-channel data, ignoring the entirety of the networked brain. Therefore, we investigated the coordination between the LFP network and spike network to achieve a better understanding of working memory. Multi-channel LFPs and spikes were simultaneously recorded in rat prefrontal cortex via microelectrode array during a Y-maze working memory task. Functional connectivity in the LFP network and spike network was respectively estimated by the directed transfer function (DTF) and maximum likelihood estimation (MLE). Then the coordination between the two networks was quantified via canonical correlation analysis (CCA). The results show that the canonical correlation (CC) varied during the working memory task. The CC-curve peaked before the choice point, describing the coordination between LFP network and spike network enhanced greatly. The CC value in working memory showed a significant higher level than inter-trial interval. Our results indicate that the enhanced canonical correlation between the LFP network and spike network may provide a potential network integration mechanism for working memory. © 2015 Published by Elsevier B.V.
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Working memory refers to a system to temporary holding and manipulation of information while performing complex tasks such as reasoning, comprehension and learning [1]. Accumulating evidence has shown prefrontal cortex (PFC) plays an important role in working memory [2–4]. Neural signals recorded with extracellular microelectrodes— commonly decomposed into local field potentials (LFPs) and spikes—are measurements for studying the spatiotemporal organization of information processing circuits underlying various
∗ Corresponding author.Tel./fax: +86 02283336952. E-mail addresses: [email protected], tian [email protected] (X. Tian).
cognitive functions. Previous studies tended to focus on how LFPs and spikes separately encode information in cognitive processes [5–8] and became interested in the combination of them [9,10]. Popular methods for studying the interaction between LFPs and spikes include correlation [11], coherence [12], phase-locking [13], and classification approach [14]. For instance, previous study has demonstrated that coherence between hippocampal LFPs and mPFC spikes is most marked in theta rhythms during a rat Y-maze working memory task [15]. Recent research has suggested that the coupling between spikes and theta-band LFPs in rat hippocampus and medial prefrontal cortex (mPFC) enhance during a spatial working memory task [16]. Our previous studies have also revealed the enhanced spike-LFP coordination during working memory task in healthy rats [17] as well as the incoordination in A-mediated memory deficits rats [18].
http://dx.doi.org/10.1016/j.bbr.2015.04.042 0166-4328/© 2015 Published by Elsevier B.V.
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Fig. 1. Behavior setup and histology. (A) Schematic representation of Y-maze, the purple dots represent the infrared beam sensor, which mark the behavioral events. Rats can get rewards by passing the removable guillotine door (dash lines near the start box). (B) Left part: Diagram of coronal section showing the level and position of the rat mPFC, taken from the Stereotaxic Coordinates [48]. Right part: Tracks of recording electrodes in mPFC, as indicated by the black arrow.
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Typically, LFPs and spikes are analyzed separately or combined between each channel’s time series data. However the separate analyses do not enable the examination of joint information between the modalities; just combining time series data do not enable the examination the underlying mechanisms of the data [19]. These methods isolate each channel from the whole data, not considering the brain’s network architecture. Therefore, multimodal integration has become a highly desirable multimodal approach to capitalize on the strength of each modality in a joint analysis, rather than a separate analysis of each. Recently, functional connectivity has become a useful tool to explore the information about directed functional interactions and the mechanism for integration in the brain [20]. It has been investigated to explore the mechanism of working memory [21]. Previous studies have showed the connection strength of LFP network [22] and spike network [23] in PFC increased during working memory respectively. It is however not known how multimodal networks coordinate during working memory. In the present study, we simultaneously recorded LFPs and spikes from multielectrode arrays implanted in rat PFC during a Y-maze working memory task. Functional connectivity in the LFP network and spike network was respectively estimated by the directed transfer function (DTF) and maximum likelihood estimation (MLE). Then the coordination between the two networks was quantified via canonical correlation analysis (CCA), to study how the LFP network and spike network coordinate during the working memory task. This may obtain insights into how multimodal network integration could contribute to working memory.
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2. Materials and methods
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2.1. Experiment and data acquisition
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Behavioral task and electrophysiology recording procedures were in accordance with the National Institute of Health Guide for Care and Use of Laboratory Animals and the Tianjin medical University guidelines for the use and care of laboratory animals in research. Male Sprague-Dawley rats weighing 300–350 g were housed two per cage in a temperature and humidity controlled colony on a 12 h light dark cycle at the Experimental Animal Center of Tianjin Medical University. All animals were maintained at approximately 85% of their free-feeding weight and had ad libitum access to water. Animals were habituated to a Y-maze (Fig. 1A) until they were readily eating pieces of peanuts in the food wells in both arms. After habituation, rats were trained on a working memory task (delayed alternation task in Y-maze). The rats were given two training
sessions per day (10 trials per session). Each trial consisted of a sample run and a choice run. On the sample run, the rats can obtain food reward for accessing either arm. After consuming the food, the rats voluntarily ran back to the start box. After a 5-s delay, the rats would have a choice run. The rats were only rewarded for choosing the previously unvisited arm and recorded correct. Training continued until the correct rate went over 80% on two consecutive days. After reaching the criterion, the animals were anesthetized with pentobarbital sodium (1%, 40 mg/kg), and all efforts were made to minimize suffering. The rats were placed in a stereotaxic frame and implanted with 16-channel nickel-chromium microelectrode array (impedance less than 1 M) targeting the mPFC (2.5–4.5 mm anterior to bregma, 0.2–1.0 mm lateral to the midline and 2.5–3.0 mm below the brain surface). After recovery, neural data were recorded from rat mPFC using a Cerebus data Acquisition System (Cyberkinetics, USA) during the task. The time of behavioral events were marked by the infrared beam sensor (Fig. 1A) in the maze and synchronized with the recording system. Time 0 indicates the tripping time of the infrared beam sensor in the Y-maze, which means the moment when rat was at the choice point in the maze. To extract local field potentials, neural signals were filtered between 0.3 and 500 Hz and digitized at 2 kHz. To extract spikes, the same signals were filtered between 0.5 and 7.5 kHz, and waveforms that exceeding a voltage threshold were sampled at 30 kHz and stored with time stamps. The data analysis workflow is shown in Fig. 2. After neural recording, animals were perfused with saline followed by 10% formaldehyde solution, and the brains were sectioned into coronal slices at 150-m (Fig. 1B) with a vibratome (Leica, Germany) to verify the recording location. 2.2. Data analysis
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2.2.1. Functional connectivity among LFPs via directed transfer function The time-frequency (TF) representation of LFPs during the task was calculated using Complex Morlet’s wavelet. The TF representation provided a time-varying energy of the signal in each frequency band [24]. In the present study, the signal was convoluted by complex Morlet’s wavelet w(t, f0 ) w(t, f0 ) = A exp(−t 2 /2t2 ) exp(2if0 t)
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(1)
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√ −1/2 with f = 1/2t , A = (t ) . The trade-off ratio f 0 /f was chosen as 7 to create a wavelet family [25]. The time-varying energy
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Fig. 2. Flow chart for data preprocessing. LFPs and spikes were obtained from raw data via digital filters. Feature band was extracted according to the results of time-frequency analysis. Functional connectivity networks among multi-channel LFPs and spikes were respectively estimated by the DTF and MLE. Then the coordination between the two networks was quantified via canonical CCA.
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E(t, f0 ) of the signal at a frequency band is the squared norm of the convolution of a complex wavelet with the signal:
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2 E(t, f0 ) = w(t, f0 ) ∗ s(t)
where s(t) refers to LFPs data. The characteristic frequency band was extracted from the LFPs via band pass filtering. Then the functional connectivity of LFPs was analyzed by DTF method. The functional connectivity analysis utilizing DTF [26,27], which can be applied to analyze connectivity among multi-channel signals [28–30]. Multivariate autoregressive (MVAR) modeling can be applied to estimate the model parameters of signals as X(t) =
p
(i)X(t − i) + E(t)
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where X (t) is the signal data at time t, (i) are the matrices of multivariate model coefficients, p is the model order, and E(t) is a vector of multivariate white noise. After transforming MVAR model parameters into frequency domain,
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(f )X(f ) = E(f )
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X(f ) =
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(f )E(f ) = H(f )E(f )
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p
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matrix of the system. The DTF value ij2 (f ) from signal j to signal i can be obtained by normalizing the system transfer function matrix
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Signals which have significant directional DTF value to other signals were considered to have directional causality to other signals.
Nonparametric surrogate testing was conducted to test the significance. The shuffling procedure destroying the phase information of the original signals was repeated 5000 times and the DTF values with the significance level p < 0.05 were considered as directional significant [31]. The recording electrodes were defined as the nodes of causal network, and the edge of the causal network are elements of the matrix. The DTF matrix is a direct measurement of functional connectivity among LFPs. The mean value of elements in the DTF matrix DTFmean is defined as: DTFmean
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DTFij
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i= / j∈N
where DTFij means the functional connectivity from channel j to channel i. N is the number of nodes. 2.2.2. Functional connectivity among spikes via maximum likelihood estimation DTF has proven to be an effective method for the investigation of directional relationships between continuous valued signals [28–30,32], but cannot be applied to spike train since their discrete nature. The functional connectivity among spike trains was calculated via maximum likelihood estimation (MLE), modeled by the generalized linear model (GLM) as described previously [33,34]. MLE can be directly applied to discrete point process data and has been proved to be effective to identify the functional connectivity among the spike trains [35]. In this method, let Ni (t) denote the sample path counts the number of spikes of channel I in the time interval (0,t]. A point process model of the spike train for channel i can be completely characterized by its conditional intensity function (CIF), defined as i (t|Hi (t)) = lim
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Pr[Ni (t + ) − Ni (t) = 1|Hi (t)]
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where H i (t) denotes the spiking history of all channels up to time t for channel i. The CIF can be modeled by the GLM framework to model the effect of its own and ensemble’s spiking histories on the current spiking activity. Then a point process likelihood function was used to fit the parametric CIF and analyze the Granger causality between channels. The likelihood function of the spike train of channel i given as
K
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Li (i ) =
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Ni [k]
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2.2.4. Statistical analyses To determine if functional connectivity and the coordination between the two networks observed are due to chance, we shuffled the data 200 times to establish criteria for statistical significance [39]. Statistical differences were evaluated by using Two-way ANOVA and t-test. Specifically, DTFmean , GCmean and CC between the original and shuffled data, as well as between the correct and incorrect trials were analyzed using Two-way ANOVA. CC in working memory and inter-trial interval (ITI) was compared by using t-test. Error bars represent the mean ± SEM. P-values are marked statistically significant as follow: **P < 0.01.
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k=1 i
+ o(J )
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where Ni [k] takes on the value 1 if there is one spike or 0 if there is j no spike. Similarly, Li (i ) can be calculated by excluding the spiking history of channel j. Then, a potential causal relationship from channel j to channel i defined as j
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ij = log
Li (i )
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Li (i )
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To evaluate the statistical significance of the estimated casual interactions, a hypothesis test was performed based on the likelihood ratio test statistic within the 95% confidence interval, since -2 times the value of causal interactions asymptotically followed a chi-squared distribution [35]. The FDR (false discovery rate) controls the expected proportion of false positive finding among all the rejected null hypotheses [36]. If the ij has passed the significance test, it will keep as GCij otherwise it will set to zero. In this paper, all the nonzero values in GC matrix have passed the significance test with a threshold of q = 0.05, FDR corrected. GC matrix is a direct measurement of functional connectivity among spikes. Similar as the DTFmean , the mean value of functional connectivity matrix GC is defined as:
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GCmean =
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1 N∗N
GCij
(11)
i= / j∈N
Where GCij indicates the functional connectivity from channel j to channel i.
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2.2.3. Coordination between LFP network and spike network based on Canonical correlation analysis Canonical correlation analysis (CCA) is a statistical method to extract linear components that capture correlations between two multi-variate random variables [37]. CCA finds a modal that explains both of observations in two data sets by identifying a pair of directions where the projections (namely, u and ) of the random variables, x and y yield maximum correlation:
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u,v =
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cov(u, v) u v
(12)
where cov(u, v) denotes the covariance function and gives the standard deviation [38]. Two matrices which were being canonical correlation in this study were the DTF matrix for LFP and the GC matrix for spike. DTF matrix and GC matrix are the quantitative descriptions for functional connectivity among multi-channel LFPs and spikes respectively. CCA was chosen because CCA can express the relationship among multi-channels LFPs and the multi-channels spikes in our case, and the plain correlation only provides the relationship between LFP and spike in a single channel. The projections in this study means the linear combination of two matrices respectively. CCA finds a pair of directions in which the u,v are maximized.
3. Results We simultaneously recorded LFPs and spikes from 6 rats using 16-channel implanted electrode array while they performed the Ymaze delayed alternation task. In total, we describe 89 trials (80 correct trials and 9 incorrect trials) in the present paper. 3.1. Energy changes of LFPs in rat mPFC during the working memory task Spectral analysis was used to assess the dominant frequencies in the LFPs. To illustrate the temporal modulation of energy in different frequency bands, the LFP spectrum was calculated using Complex Morlet’s wavelet with 1 Hz resolution. Fig. 3A shows timefrequency representation of a single electrode during a single trial. Fig. 3B and C shows the averaged TF representation across all the trials and all the electrodes respectively. These data were transferred to z-score to analyze the variability of the TF representation across trials and electrodes. Fig. 3E and F represents the z-score transformation of data in Fig. 3B and C respectively. Notably, theta (4–12 Hz) energy increased before the choice point, and was much larger than those in other frequency bands. 3.2. Functional connectivity matrices in LFP network and spike network Functional connectivity matrices among multi-channel LFPs and spikes were estimated via DTF and MLE, respectively. Fig. 4A and B respectively represents the LFP network (theta-band) and spike network in working memory (0.5s pre and 0.5s post the CC peak). Each element of the matrix shows how much each node interacts one another. The scaled color represented the connectivity strengths from trigger node to target node. As can be seen from Fig. 4, the functional connectivity matrices from the LFP network and spike network were consistent with each other. We then employed the canonical correlation analysis to quantify the coordination between the two networks. 3.3. Coordination between LFP network and spike network The coordination between LFP network and spike network was assessed by CCA. Fig. 5 shows the dynamic changes of canonical correlation (CC) in the LFP network and spike network during the correct trials (window length: 1s, moving steps: 0.25 s). The time axis represents each rat’s average latency before crossing the infrared detector from the start location. In all the subjects, across the whole task time, CC were observed to increase up until the choice point, and then to decrease. To confirm whether the CC were significantly increased in WM, we further estimated the CC between the LFP network and spike network in inter-trial interval (ITI) and compared the CC values between WM and ITI. The CC value in WM was significantly higher
Please cite this article in press as: Yi H, et al. Canonical correlation between LFP network and spike network during working memory task in rat. Behav Brain Res (2015), http://dx.doi.org/10.1016/j.bbr.2015.04.042
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Fig. 3. Time-frequency representation of the energy for LFP. (A) Time-frequency representation of a single electrode during a single trial. (B) Averaged TF representation across all the trials. (C) Averaged TF representation across all the electrodes. (D) The z-score transformation of data in Fig. 3B. (E)The z-score transformation of data in Fig. 3C.
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than in ITI (Fig. 6, WM: 0.8436 ± 0.0102, ITI: 0.3291 ± 0.0121, t-test, P < 0.01).
were significantly higher than those in the shuffled data (Two-way ANOVA, P < 0.01, P < 0.01, P < 0.05, respectively).
3.4. Changes of DTFmean , GCmean and CC in the original data and shuffled data
3.5. Changes of DTFmean , GCmean and CC in correct and incorrect trials
To determine whether the functional connectivity and the coordination observed are due to chance, we shuffled all the rats’ data 1600 times to establish criteria for statistical significance [38]. Fig. 7 shows the DTFmean , GCmean and CC value in the original data and shuffled data. The DTFmean , GCmean and CC in the original data
We observed the enhanced coordination between the two networks, a pattern of canonical correlation increase, peak, and decline in correct trials during the task. To obtain more information conveyed in this, we further analyzed the functional connectivity and compared coordination between correct and incorrect trials.
Fig. 4. Functional connectivity matrices among LFPs and spikes. (A) LFP network (theta band) in working memory (0.5 s pre and 0.5 s post the CC peak). (B) Spikes functional network in working memory. The networks show how much each node interacts one another. The scaled color represented the connectivity strengths from trigger node to target node. The functional connectivity matrices shows the two networks consistent with each other.
Please cite this article in press as: Yi H, et al. Canonical correlation between LFP network and spike network during working memory task in rat. Behav Brain Res (2015), http://dx.doi.org/10.1016/j.bbr.2015.04.042
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Fig. 5. Dynamic changes of canonical correlation (CC) between LFP network and spike network during the task (window length: 1s, moving steps: 0.25 s). The purple dot lines indicate the tripping time of the infrared beam sensor in the Y-maze. The time axis represents average latency before rats crossing the infrared detector from the start location. Error bars represent the mean ± SEM.
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Fig. 8 shows DTFmean , GCmean and CC in the correct trials (n = 80) and incorrect trials (n = 9) during the task. The DTFmean , GCmean and CC increased obviously and peaked before the choice point, followed by a steady decline. In contrast with increase tendencies in the correct trials, all three indices presented no obvious changing tendency in the incorrect trials. The DTFmean , GCmean and CC in the correct trials were significantly higher than those in the incorrect trials. (Two-way ANOVA, P < 0.01, P < 0.01, P < 0.05, respectively) Since increasing tendencies of the coordination between the LFP network and spike network were found in the correct trials while there was no significant change in incorrect trials, we proposed that the strengthened coordination between the two networks could be necessary in working memory.
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We examined the coordination between the LFP network and spike network in rat mPFC during the working memory task via CCA. Unlike other approaches in which the interaction between single channels’ signals is tested, the functional connectivity approach in this study can exploit the relationship among multi-channels
Fig. 6. Canonical correlation in working memory (0.5 s pre and 0.5 s post the CC peak) and ITI. The CC in WM was significantly higher than ITI. (t-test, **p < 0.01).
LFPs and the multi-channels spikes. We found that the canonical correlation (CC) varied during the working memory task. The CCcurve peaked before the choice point, describing the coordination between LFP network and spike network enhanced greatly. The CC value in working memory was significant higher than that in ITI. Our results indicate that the enhanced coordination between the LFP network and spike network during working memory. Recording multiple types of brain data from the same subject using various non-invasive (usually to human) imaging techniques (MRI, EEG, MEG, etc.) and invasive extracellular (usually to animals) recording techniques (LFPs and spikes) has become common practice. Each recording techniques has markedly different spatial and temporal resolutions and provides a different view of brain function or structure. Typically these data are analyzed separately, however due to the remarkable complementarity between these techniques [40]. Multimodal integration has become a highly desirable multimodal approach. The goal of multimodal fusion is to capitalize on the strength of each modality in a joint analysis, rather than a separate analysis of each. CCA allows a different mixing matrix for each modality and is used to find a transformed coordinate system that maximizes intersubject covariation across the two data sets [41]. CCA was applied to an auditory sensorimotor task, patients with schizophrenia showing significantly in three loadings compared to healthy controls [42]. Multimodal CCA is invariant to differences in the range of the data types and can be used to jointly analyze very diverse data types. It can also be extended to multi-set CCA to incorporate more than two modalities [43]. Our study sought to address how the LFP network and spike network coordinate in PFC during the working memory task. Accumulating evidence has suggested the PFC-VTA-hippocampus axis is critical for working memory. The task-related neuronal activity in rats in PFC, hippocampus and VTA is coordinated by a 4-Hz oscillation [44]. In the case of prefrontal-hippocampus circuit, theta band play a particularly important role [45,46]. Inactivating the hippocampus led to a reduction in hippocampal-PFC coherence and impaired working memory function [47]. We predicted that the coordination between LFP network and spike network should be across the prefrontal-hippocampus circuit. In summary, our results demonstrate that the canonical correlation between the LFP network and spike network increased
Please cite this article in press as: Yi H, et al. Canonical correlation between LFP network and spike network during working memory task in rat. Behav Brain Res (2015), http://dx.doi.org/10.1016/j.bbr.2015.04.042
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Fig. 7. DTFmean , GCmean and canonical correlation (CC) in the original and shuffled data. (A) Change of DTFmean of LFPs in the original (solid lines) and shuffled data (dash lines) (window length: 1 s, moving steps: 0.25 s). (B) Change of GCmean of spikes in the original and shuffled data. (C) CC in the original and shuffled data. The DTFmean , GCmean and CC in the original data were significantly higher than those in the shuffled data. (Two-way ANOVA, P < 0.01, P < 0.01, P < 0.05, respectively).
Fig. 8. DTFmean , GCmean and canonical correlation (CC) in correct (n = 80) and incorrect (n = 9) trials during the task. (A) Change of DTFmean of LFPs in the correct (solid lines) and incorrect (dash lines) trials (window length: 1s, moving steps: 0.25 s). (B) Change of GCmean of spikes in the correct and incorrect trials. (C) CC in the correct and incorrect trials. The DTFmean , GCmean and CC in the correct trials were significantly higher than those in the incorrect trials. (Two-way ANOVA, P < 0.01, P < 0.05, P < 0.01, respectively).
Please cite this article in press as: Yi H, et al. Canonical correlation between LFP network and spike network during working memory task in rat. Behav Brain Res (2015), http://dx.doi.org/10.1016/j.bbr.2015.04.042
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during the working memory task, which reflected the rising coordination level between the two networks. These findings could lead to improved understanding of the working memory mechanism from the view of network integration.
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