Impaired coupling of local and global functional feedbacks underlies abnormal synchronization and negative symptoms of schizophrenia
© Noh et al.; licensee BioMed Central Ltd. 2013
Received: 18 November 2012
Accepted: 14 March 2013
Published: 10 April 2013
Abnormal synchronization of brain oscillations is found to be associated with various core symptoms of schizophrenia. However, the underlying mechanism of this association remains yet to be elucidated.
In this study, we found that coupled local and global feedback (CLGF) circuits in the cortical functional network are related to the abnormal synchronization and also correlated to the negative symptom of schizophrenia. Analysis of the magnetoencephalography data obtained from patients with chronic schizophrenia during rest revealed an increase in beta band synchronization and a reduction in gamma band power compared to healthy controls. Using a feedback identification method based on non-causal impulse responses, we constructed functional feedback networks and found that CLGF circuits were significantly reduced in schizophrenia. From computational analysis on the basis of the Wilson-Cowan model, we unraveled that the CLGF circuits are critically involved in the abnormal synchronization and the dynamical switching between beta and gamma bands power in schizophrenia. Moreover, we found that the abundance of CLGF circuits was negatively correlated with the development of negative symptoms of schizophrenia, suggesting that the negative symptom is closely related to the impairment of this circuit.
Our study implicates that patients with schizophrenia might have the impaired coupling of inter- and intra-regional functional feedbacks and that the CLGF circuit might serve as a critical bridge between abnormal synchronization and the negative symptoms of schizophrenia.
KeywordsAbnormal synchrony Network topology Coupled feedback Schizophrenia Negative symptom
Schizophrenia is one of psychotic mental disorders and is characterized by various symptoms including hallucination, thought disorder, absence of behavior, and lack of motivation. These psychopathologies usually emerge as abnormalities in oscillatory activities of neurons and their synchronizations [1, 2]. A number of studies using magnetoencephalography (MEG) and electroencephalography (EEG) have demonstrated that symptoms of schizophrenia might be related to aberrantly enhanced or reduced synchrony of oscillations in high (beta and gamma) frequency bands during cognitive tasks or at rest [3–8]. These findings suggest that impaired synchronization of beta- and gamma-band oscillations could underlie the dysfunctions in cortical communications in schizophrenia. However, it is still unclear what the underlying mechanism is for the association between abnormal synchronized oscillations and the core symptoms of schizophrenia.
Anatomical investigations have shown that interregional connectivity is highly reciprocal [9, 10] and such recurrent connections have an important role in modulating visual and auditory sensory stimuli [11, 12]. Dysfunction in such a feedback structure can produce abnormal synchronization under pathological conditions. Several computational studies have shown that cortical feedback connections are critical to promote the synchronization among distributed neuronal networks [13–15]. A feedback connection is crucial to generate biological oscillations, and feedback loops coupling local oscillators contribute to inducing and modulating their synchronization. Biological experiments showed that feedback circuits are ubiquitously found in a variety of biological subjects [16–18] and theoretical studies proved the relationship between feedback loop and synchronized oscillation [19, 20]. On the basis of these findings, we hypothesize that the impairment of functional feedbacks among distributed brain areas may underlie the abnormal synchronization in schizophrenia and provide a bridge between abnormal synchrony and the symptoms of schizophrenia.
We investigate this hypothesis by constructing and analyzing the functional feedback networks of patients with schizophrenia and normal controls during rest on the basis of MEG measurements and feedback identification. Resting state, a condition in the absence of stimulus or cognitive task, is important to understand the spontaneous oscillation of brain activity and is considered as a baseline condition in many neuroimaging studies [21–24]. The analysis of power spectrum and phase synchronization showed an abnormally reduced gamma band power and an increased beta band phase synchrony in patients group. From the inferred functional feedback network, we found that coupled local and global feedback (CLGF) circuit is differently enriched in both groups. Through computational analysis based on the Wilson-Cowan model, we found that this circuit is critically involved in the abnormal neural oscillations and synchronization in schizophrenia and that this circuit mediates the dynamical switching between beta and gamma bands power. In addition, we found that the abundance of this circuit is strongly correlated with the negative symptoms of schizophrenia, suggesting that the negative symptom is closely related to the impairment of this circuit. Taken together, we suggest that the CLGF circuit might be a critical determinant of abnormal neural oscillations and synchrony in schizophrenia and that the impairment of this circuit accelerates the negative symptoms of schizophrenia. This study is to our knowledge the first attempt to identify the underlying mechanism, at a system-level, that bridges the abnormal synchronized oscillations and core symptoms of schizophrenia in consideration of the functional feedback networks of the whole cortical brain area.
Participants and clinical assessments
Healthy control subjects and schizophrenia patients overlapped with those subjects in our previous study  but not identical. This study protocol was approved by the Institutional Review Board of Seoul National University Hospital (SNUH) and the study was conducted at the MEG center in SNUH. All participants gave an informed consent form to their participation.
Demographic and clinical assessment
Mean ± SD
Mean ± SD
T or χ2
22.06 ± 2.11
23.80 ± 4.60
14.06 ± 1.20
13.27 ± 2.25
11.35 ± 1.69
10.53 ± 2.59
108.35 ± 17.26
103.33 ± 9.90
56.47 ± 13.14
Duration of illness (yrs)
6.89 ± 3.14
MEG Data acquisition and preprocessing
A 306 MEG system (Elekta Neuromag Oy, Helsinki, Finland) was used to record MEG activities. The MEG signals were band-pass filtered (0.1 to 200 Hz) and digitized at a 1000 Hz sampling rate. All subjects were instructed to focus on crossed figure at the screen to prevent random eye movements. During recording, no external stimulus was given. After recording, noise reduction and compensation of head movement were carried out using tSSS algorithm . Resting condition was recorded with open eyes during 120 seconds. Data were visually inspected to reject epochs with unnecessary noise, such as eye movement and muscle artifacts. A notch filter was used to remove artifacts of 60 Hz and its harmonics (120 and 180 Hz). MEG data were imported into MATLAB 7.8.0 (R2009a) in Windows for data processing. Using 102 magnetometers, 80 seconds time points with a 1000 Hz sampling rate were considered for all analysis in this study.
Time-frequency and power analysis
We considered 13~80 Hz frequency components of the MEG data corresponding to beta and gamma bands and carried out time-frequency analysis of MEG signals using complex Morlet wavelet transform . The width of the wavelet was defined as 7 that encompasses at least one full sinusoidal cycle for any particular frequency . The absolute values of the resulting transforms from 102 magnetometers were averaged. Mean power spectrum was calculated on the basis of the average time-frequency analysis result.
Beta-gamma power switching
MEG signals were filtered into beta (13 ~ 30 Hz) and gamma (30 ~ 80 Hz) bands by using ‘eegfilt’ in EEGLAB toolbox . We analyzed the phase synchrony of beta- and gamma-band signals using a sliding-window approach with the window size of 1000 ms and the sliding size of 200 ms. Hilbert transform was applied to get phase information in both beta and gamma bands. We found phase differences between all pairs of magnetometer sensors and considered phase locking value (PLV) as a synchronization index, , which ranges from 0 for no synchronization to 1 for perfect synchronization  where φn,m represents the phase difference between signal n and m. This index is useful in that it measures how the relative phase is distributed over a unit circle. We calculated the PLV values for all possible combinations of magnetometer sensors and averaged them for each subject.
Feedback identification based on impulse responses
Network simulations based on the Wilson-Cowan model
The details on the structure and variables of this CLGF circuit are described in Additional file 1: Figure S2C. The global connection strength between oscillators a and b (ω ab and ω ba ), and the local connection strength between oscillators a and c (ω ac and ω ca ) were set as ω ab = ω ba and ω ac = ca , respectively, and both were explored over a range from 0 to 4. These delayed differential equations were solved numerically using dde23 in MATLAB 7.8.0 (R2009a).
The simulation procedures were as follows: Initially, the constant external excitatory input ranging from 0 to 5 was applied to the excitatory population in oscillator a (Additional file 1: Figure S2A Left). This oscillator exhibited an oscillation frequency ranging from 80 to 150 Hz for input values from 1.2 to 3, and no oscillation or hyper-excitation otherwise (Additional file 1: Figure S2A Right). We selected the input value so that the oscillator a exhibits around 100 Hz frequency oscillations and then we connected the oscillator b to the oscillator a through positive feedback connection (Additional file 1: Figure S2B Left). As the connection strength was varied from 0 to 4, this structure exhibited additional frequency components generated by the positive feedback between oscillators a and b for the connection strength of 3 (Additional file 1: Figure S2B Right). We ignored any hyper-excitatory oscillation which is the typical characteristic of a highly activated positive feedback loop. In the next, we added the third oscillator c to the oscillator a through positive feedback. The resulting frequency spectrum of this structure is displayed in Figure 1A. The total beta and gamma band powers of the CLGF circuit were calculated by summing each frequency band power. Moreover, beta band phase synchronization between oscillators a and b was investigated on the basis of the phase locking value.
A two-tailed t-test was carried out to examine the group differences of power, phase synchronization, the number of positive feedbacks, the number of CLGF circuits, and the switching of beta-gamma power. The t-test was also used to compare the demographic and the clinical assessments between groups. Pearson correlation coefficients were calculated using MATLAB 7.8.0 (R2009a) to examine the correlations between the number of CLGF circuits and the clinical symptoms (PANSS) within the schizophrenia group. The α-level was set to 0.05 for all statistical tests.
Schizophrenia patients showed an abnormally reduced gamma power and increased beta phase synchronization
Patients with schizophrenia have sparse CLGF circuits
The frequency of synchronized oscillations is correlated with the distance over which synchronization occurs. It has been proposed that the gamma band activity is associated with short-distance synchronization whereas the beta band activity supports long-distance synchronization , implying that deficits in neural oscillations and synchronization might be accompanied with functional disconnection between brain areas as well as anatomical connectivity. To compare the topological difference between normal controls and patients with schizophrenia in their functional connectivities, we inferred both positive and negative feedback connections among 102 MEG magnetometer sensors by using the impulse response feedback identification method . Results showed that the total number of positive feedbacks was significantly reduced in schizophrenia patients group (p = 0.042) (Figure 2A) while there was no significant difference in negative feedback (Additional file 1: Figure S3A). Moreover, both groups exhibited relatively a less number of negative connections (Additional file 1: Figure S3B), indicating that negative feedback does not much contribute to the abnormalities of oscillation and synchronization. To investigate the spatial organization of functional feedback connectivities, we classified magnetometer sensors into 10 cortical subregions including pre-frontal, middle-frontal, temporal, parietal, and occipital regions in left and right hemispheres (Figure 2B). From the fact that the inter-regional conduction delay is longer than intra-regional delay [35, 36], we divided the positive feedback connections into two types: (i) global positive feedback between subregions having a long time delay, and (ii) local positive feedback within a subregion having a short time delay. While the number of global positive feedbacks was not significantly different between the two groups (p = 0.11) (Figure 2B, Top row), the number of local positive feedbacks was reduced in patients group (p = 0.0036) (Figure 2B, Bottom row).
From our results, we found that schizophrenia patients have sparse positive feedbacks in their cortical network although they show enhanced phase synchronization of a beta band activity. These results seem to be incompatible with the commonly observed synchronization property that a larger coupling strength between two oscillators tends to induce a higher degree of synchronization . Therefore, we presumed that the abnormal synchronization in schizophrenia is attributed not only to the abundance of feedback connections but also to the detailed coupling patterns of feedback connections. For instance, if oscillators are coupled with each other through positive feedback connections having different conduction delays, oscillators are not synchronized properly  even though they are coupled through a large number of feedback connections. On the basis of this, we further investigated a coupled structure of short and long time delay connections that constitute a coupled local and global feedback (CLGF) circuit in the referred functional feedback networks (Figure 2C, Left). In patients with schizophrenia, the number of CLGF circuits was significantly reduced relative to that of healthy controls (p = 0.031) (Figure 2C, Right). In addition, we constructed functional networks based on partial correlation and mutual information to explore the changes in functional connectivity of schizophrenia. The results showed that the functional network of schizophrenia patients have lower coupled local and global connectivity than that of controls, which is consistent with the results of the functional feedback networks inferred by applying the impulse response method (see Additional file 1: Figure S4 and S5, and supporting methods in Additional file 2). These results suggest that deficits in the CLGF circuits might be responsible for the decreased gamma band power and the increased beta band phase synchronization in schizophrenia. Hence, detailed computational analysis has been carried out to elucidate the influence of such structural impairments on the oscillatory activities and synchronization.
Deficits in the CLGF circuits induce the impairment of beta-gamma power switching
We carried out neural network simulations of the CLGF circuits using the Wilson-Cowan model  which is widely used to describe a neuronal ensemble as an oscillator model composed of excitatory and inhibitory neurons (see Methods for details). To investigate the changes in the frequency spectrum of the CLGF circuits with respect to varying connection strengths, coupled oscillators were considered as shown in Figure 1A where an oscillator a is coupled with oscillators b and c through feedback loops with long (21 ms) and short (6 ms) time delays, respectively. While the oscillator a coupled with the oscillator b through a global feedback loop exhibited mostly beta band oscillations (local connection strength = 0), the oscillator a coupled with both oscillators b and c through global and local feedback loops showed an increased gamma oscillation with a reduced beta oscillation (local connection strength = 3) as shown in Figure 1A (Bottom). In the case of weak local connection strength, the beta band power was dominant over the gamma band power although we did not remove the artifacts of beta harmonics in the gamma band (Figure 1B, Top). As the coupling of local and global feedbacks gets strengthened beyond the threshold of local connection strength, the gamma band power was abruptly increased and became dominant over the beta band. This result confirms that deficits of the CLGF circuits in a cortical network are responsible for the decreased gamma band power in patients with schizophrenia. Moreover, beta band phase synchronization was suddenly decreased in the case of strong local connection (Figure 1B, Bottom), suggesting that the increased beta band synchronization might also result from the deficit of the CLGF circuits in patients with schizophrenia. These properties were well conserved even when global and local time delays were varied over the ranges of 15–25 ms and 6–10 ms, respectively (Additional file 1: Figure S6). Note here that we adopted the inter-regional conduction delay in the range of 15~25 ms for global feedbacks and the intra-regional delay in the range of 6~10 ms for local feedbacks based on previous experiments [35, 36, 38–40].
To explore how often and how long such beta to gamma power shift occurs in MEG data, time-frequency analysis based on the wavelet transform was carried out for both groups. Figure 1C shows an example of the beta-gamma power shift in a healthy subject. We found that there exists a period where the gamma power increased, but, simultaneously, the beta power decreased. According to our simulation results, the CLGF circuits might be activated during this period. To compare the proportion of this switching period in both groups, we measured the duration in which the power switching between beta and gamma occurred. In each 1 ms time step, we assigned 1 when temporal profiles of beta and gamma powers satisfy three conditions, (d β / dt < 0, d γ /dt > 0, and γ -β > 0), and kept this value until the beta power becomes larger than the gamma power (Figure 1D) (see Methods for details). We found that schizophrenia patients showed a significant reduction of the duration involved in the beta-gamma switching (p = 0.00015), which indicates that the CLGF circuits are deactivated in schizophrenia (Figure 1E). We further found that the frequency of switching events was also significantly reduced in the patients group (p = 0.000065) (Figure 1E) and this suggests that the impairment of dynamical switching between beta and gamma bands is also an important characteristic of schizophrenia in addition to the abnormal gamma power and beta synchronization. Taken together, deficits in the CLGF circuits in schizophrenia might be critically involved in the abnormalities in neural oscillations, synchronization, and temporal switching of frequency bands.
The CLGF circuit is inversely correlated with the negative symptoms of schizophrenia
Negative symptoms of schizophrenia are the most prominent factor that contributes to the functional impairment of patients. So, rather than positive symptoms such as hallucination and delusion, negative symptoms have been suggested as the core of the illness . In this study, we found that the CLGF circuit in cortical functional networks is closely related to the negative symptoms of schizophrenia (Figure 4B). Patients with schizophrenia were characterized by the decreased gamma band power and increased beta band synchronization relative to healthy controls, and network model simulations revealed that such abnormalities resulted from deficits in the CLGF circuit. Moreover, the dynamical switching between beta and gamma bands power in patients was reduced, which might also be induced by the impairment of local feedback connections in the CLGF circuit. Therefore, we infer that patients with schizophrenia might have impaired coupling of inter- and intra-regional functional feedbacks and that the CLGF circuit is a crucial bridge between abnormal synchronization and the negative symptoms of schizophrenia.
It is known that synchronized oscillation is mostly caused by the feedback interaction between oscillators [19, 42]. So, the goal of our network inference was to identify such feedback connections among all 102 magnetometer sensors of MEG rather than to infer functional connections that are commonly obtained by correlation or mutual information methods [43–45]. For this purpose, we employed the impulse response method as it is particularly advantageous in dealing with a large network owing to its efficient computational time compared to other methods such as Granger causality or Bayesian network inference methods [42, 46–48].
Patients with schizophrenia in our study showed three different phenomenological characteristics compared to healthy controls: (i) a reduced gamma band power, (ii) increased beta band phase synchronization, and (iii) reduced beta-gamma power switching. Consistent with our result, the gamma power reduction in schizophrenia patients under resting condition have been demonstrated in several previous studies [49, 50] and the patients were considered to experience the resting condition in a very different way compared to healthy controls. Enhanced beta band oscillation and synchronization were known to be associated with the suppression of a response during the cued choice reaction task , which suggests that the increased beta band synchronization in our results might be related to the inability of patients in the preparation for future events. Interestingly, there was a hypothetical study which suggested that abnormally increased beta band synchronization might be induced during a resting state by the rest-rest self interaction in the brain of schizophrenia patients . In addition to the abnormalities in gamma power and beta phase synchronization, the temporal switching between beta and gamma bands power in our results can also be understood in the same context. It is well known that brain frequency bands such as beta or gamma are relevant to the corresponding brain functions. However, little is known about the dynamical interaction between such frequency bands. In this study, our simulation results demonstrated that the CLGF circuit is responsible for the dynamical switching mechanism, suggesting that deficits in this circuit might induce the impairment of beta-gamma switching in schizophrenia. Abnormal temporal dynamics of cortical networks may result in impairments in synaptic plasticity, and such aberrant neurodevelopment has been observed in schizophrenia . Impaired plasticity may lead to difficulties in flexible coordination of distributed brain processes and rapid responses when a task is given. Therefore, schizophrenia patients with reduced beta-gamma band switching are likely to have cognitive deficits due to impaired dynamic interactions between multiple brain regions. Taken together, we suggest that the temporal switching across different frequency bands as well as the abnormal power and synchrony might be important factors characterizing schizophrenia although further studies including both resting and cognitive task conditions are required to clarify the role of temporal switching among frequency bands.
A brain is inherently a dynamical system that continuously reorganizes functional connections within and between brain regions [54–57]. In the present study, we identified a fundamental network structure motif, the CLGF circuit, responsible for the abnormalities in neural oscillations, synchronization, and temporal switching of frequency bands in schizophrenia. Functional disconnections of this circuit may disturb flexible communications between brain regions, hence eventually contributing to the pathogenesis of schizophrenia as shown in our result that the abundance of CLGF circuit is negatively correlated with the negative symptoms of schizophrenia. Therefore, we conclude that altered functional feedbacks, such as the CLGF circuit, serves as a critical bridge between phenomenological properties and the psychotic symptoms of schizophrenia. Over the past decade, a number of studies using functional brain imaging techniques have attempted to reveal the fundamental mechanism that underlies the association of impaired neural oscillations and synchronization with core symptoms of schizophrenia. Most of the studies, however, have dealt with functional connectivity of a whole brain using simple correlation methods or effective connectivity of a local brain network with only few regions. Here, we introduced a feedback identification method based on non-causal impulse response to construct a functional feedback network covering the whole cortical brain regions, and this enabled us to project a cortical network to a more precise cortico-cortical interaction map. In the future, a combined study with anatomical connectivity will provide further insights into the underlying mechanism on the close relationship between the abnormal neural oscillations and synchrony and the core symptoms of schizophrenia.
Coupled local and global feedback
Phase locking value
The authors thank Prof. Doheon Lee and Prof. Dongsup Kim in the Department of Bio and Brain Engineering, KAIST for their critical reading of this manuscript. This study was supported by a grant of the Korea Healthcare technology R&D project, Ministry for Health, Welfare & Family Affairs, Republic of Korea (A090096-0911-0000100). It was also supported by the National Research Foundation of Korea (NRF) grants funded by the Korea Government, the Ministry of Education, Science & Technology (MEST) (2009–0086964 and 2010–0017662) and by WCU (World Class University) program through the NRF of Korea funded by the MEST (R32-2008-000-10218-0). It was also supported by GIST Systems Biology Infrastructure Establishment Grant and KAIST Future Systems Healthcare Project.
- Uhlhaas PJ, Singer W: Abnormal neural oscillations and synchrony in schizophrenia. Nat Rev Neurosci 2010, 11: 100-113. 10.1038/nrn2774PubMedView ArticleGoogle Scholar
- Uhlhaas PJ, Haenschel C, Nikolic D, Singer W: The role of oscillations and synchrony in cortical networks and their putative relevance for the pathophysiology of schizophrenia. Schizophrenia Bull 2008, 34: 927-943. 10.1093/schbul/sbn062View ArticleGoogle Scholar
- Bob P, Palus M, Susta M, Glaslova K: EEG phase synchronization in patients with paranoid schizophrenia. Neurosci Lett 2008, 447: 73-77. 10.1016/j.neulet.2008.09.055PubMedView ArticleGoogle Scholar
- Lee KH, Williams LM, Haig A, Gordon E: "Gamma (40 Hz) phase synchronicity" and symptom dimensions in schizophrenia. Cogn Neuropsychiatry 2003, 8: 57-71. 10.1080/713752240PubMedView ArticleGoogle Scholar
- Sponheim SR, Clementz BA, Iacono WG, Beiser M: Clinical and biological concomitants of resting state EEG power abnormalities in schizophrenia. Biol Psychiat 2000, 48: 1088-1097. 10.1016/S0006-3223(00)00907-0PubMedView ArticleGoogle Scholar
- Lee SH, Wynn JK, Green MF, Kim H, Lee KJ, Nam M, Park JK, Chung YC: Quantitative EEG and low resolution electromagnetic tomography (LORETA) imaging of patients with persistent auditory hallucinations. Schizophr Res 2006, 83: 111-119. 10.1016/j.schres.2005.11.025PubMedView ArticleGoogle Scholar
- Spencer KM, Nestor PG, Perlmutter R, Niznikiewicz MA, Klump MC, Frumin M, Shenton ME, McCarley RW: Neural synchrony indexes disordered perception and cognition in schizophrenia. P Natl Acad Sci USA 2004, 101: 17288-17293. 10.1073/pnas.0406074101View ArticleGoogle Scholar
- Uhlhaas PJ, Linden DEJ, Singer W, Haenschel C, Lindner M, Maurer K, Rodriguez E: Dysfunctional long-range coordination of neural activity during Gestalt perception in schizophrenia. J Neurosci 2006, 26: 8168-8175. 10.1523/JNEUROSCI.2002-06.2006PubMedView ArticleGoogle Scholar
- Douglas RJ, Martin KAC: Neuronal circuits of the neocortex. Annu Rev Neurosci 2004, 27: 419-451. 10.1146/annurev.neuro.27.070203.144152PubMedView ArticleGoogle Scholar
- Douglas RJ, Martin KAC: Recurrent neuronal circuits in the neocortex. Curr Biol 2007, 17: R496-R500. 10.1016/j.cub.2007.04.024PubMedView ArticleGoogle Scholar
- Garrido MI, Kilner JM, Kiebel SJ, Friston KJ: Evoked brain responses are generated by feedback loops. P Natl Acad Sci USA 2007, 104: 20961-20966. 10.1073/pnas.0706274105View ArticleGoogle Scholar
- Pollen DA: Feature article on the neural correlates of visual perception. Cereb Cortex 1999, 9: 4-19. 10.1093/cercor/9.1.4PubMedView ArticleGoogle Scholar
- Vicente R, Gollo LL, Mirasso CR, Fischer I, Pipa G: Dynamical relaying can yield zero time lag neuronal synchrony despite long conduction delays. P Natl Acad Sci USA 2008, 105: 17157-17162. 10.1073/pnas.0809353105View ArticleGoogle Scholar
- Gollo LL, Mirasso CR, Atienza M, Crespo-Garcia M, Cantero JL: Theta Band Zero-Lag Long-Range Cortical Synchronization via Hippocampal Dynamical Relaying. PLoS One 2011, 6.Google Scholar
- Kopell N, Ermentrout GB, Whittington MA, Traub RD: Gamma rhythms and beta rhythms have different synchronization properties. P Natl Acad Sci USA 2000, 97: 1867-1872. 10.1073/pnas.97.4.1867View ArticleGoogle Scholar
- Shin SY, Rath O, Zebisch A, Choo SM, Kolch W, Cho KH: Functional Roles of Multiple Feedback Loops in Extracellular Signal-Regulated Kinase and Wnt Signaling Pathways That Regulate Epithelial-Mesenchymal Transition. Cancer Res 2010, 70: 6715-6724. 10.1158/0008-5472.CAN-10-1377PubMedPubMed CentralView ArticleGoogle Scholar
- Shin SY, Yang HW, Kim JR, Do Heo W, Cho KH: A hidden incoherent switch regulates RCAN1 in the calcineurin-NFAT signaling network. J Cell Sci 2011, 124: 82-90. 10.1242/jcs.076034PubMedView ArticleGoogle Scholar
- Shin SY, Rath O, Choo SM, Fee F, McFerran B, Kolch W, Cho KH: Positive- and negative-feedback regulations coordinate the dynamic behavior of the Ras-Raf-MEK-ERK signal transduction pathway. Journal of Cell Science 2009, 122: 425-435. 10.1242/jcs.036319PubMedView ArticleGoogle Scholar
- Kim JR, Shin D, Jung SH, Heslop-Harrison P, Cho KH: A design principle underlying the synchronization of oscillations in cellular systems. Journal of Cell Science 2010, 123: 537-543. 10.1242/jcs.060061PubMedView ArticleGoogle Scholar
- Kim JR, Yoon Y, Cho KH: Coupled feedback loops form dynamic motifs of cellular networks. Biophys J 2008, 94: 359-365. 10.1529/biophysj.107.105106PubMedPubMed CentralView ArticleGoogle Scholar
- Biswal B, Yetkin FZ, Haughton VM, Hyde JS: Functional Connectivity in the Motor Cortex of Resting Human Brain Using Echo-Planar Mri. Magnet Reson Med 1995, 34: 537-541. 10.1002/mrm.1910340409View ArticleGoogle Scholar
- Lowe MJ, Mock BJ, Sorenson JA: Functional connectivity in single and multislice echoplanar imaging using resting-state fluctuations. NeuroImage 1998, 7: 119-132. 10.1006/nimg.1997.0315PubMedView ArticleGoogle Scholar
- Greicius MD, Krasnow B, Reiss AL, Menon V: Functional connectivity in the resting brain: A network analysis of the default mode hypothesis. P Natl Acad Sci USA 2003, 100: 253-258. 10.1073/pnas.0135058100View ArticleGoogle Scholar
- Rogers BP, Morgan VL, Newton AT, Gore JC: Assessing functional connectivity in the human brain by fMRI. Magn Reson Imaging 2007, 25: 1347-1357. 10.1016/j.mri.2007.03.007PubMedPubMed CentralView ArticleGoogle Scholar
- Shin KS, Kim JS, Kim SN, Koh Y, Jang JH, An SK, O'Donnell BF, Chung CK, Kwon JS: Aberrant Auditory Processing in Schizophrenia and in Subjects at Ultra-High-Risk for Psychosis. Schizophr Bull 2011.Google Scholar
- Kay SR, Fiszbein A, Opler LA: The Positive and Negative Syndrome Scale (Panss) for Schizophrenia. Schizophrenia Bull 1987, 13: 261-276. 10.1093/schbul/13.2.261View ArticleGoogle Scholar
- Taulu S, Simola J: Spatiotemporal signal space separation method for rejecting nearby interference in MEG measurements. Phys Med Biol 2006, 51: 1759-1768. 10.1088/0031-9155/51/7/008PubMedView ArticleGoogle Scholar
- Sinkkonen J, Tiitinen H, Naatanen R: Gabor Filters - an Informative Way for Analyzing Event-Related Brain Activity. J Neurosci Meth 1995, 56: 99-104. 10.1016/0165-0270(94)00111-SView ArticleGoogle Scholar
- Combes JM, Grossmann A, Tchamitchian P: Wavelets: time-frequency methods and phase space: proceedings of the international conference, Marseille, France, December 14–18, 1987. Berlin. New York: Springer; 1989.Google Scholar
- Delorme A, Makeig S: EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis. J Neurosci Methods 2004, 134: 9-21. 10.1016/j.jneumeth.2003.10.009PubMedView ArticleGoogle Scholar
- Pereda E, Quiroga RQ, Bhattacharya J: Nonlinear multivariate analysis of neurophysiological signals. Prog Neurobiol 2005, 77: 1-37. 10.1016/j.pneurobio.2005.10.003PubMedView ArticleGoogle Scholar
- Dong CY, Lim J, Nam Y, Cho KH: Systematic analysis of synchronized oscillatory neuronal networks reveals an enrichment for coupled direct and indirect feedback motifs. Bioinformatics 2009, 25: 1680-1685. 10.1093/bioinformatics/btp271PubMedView ArticleGoogle Scholar
- Dong CY, Yoon TW, Bates DG, Cho KH: Identification of feedback loops embedded in cellular circuits by investigating non-causal impulse response components. J Math Biol 2010, 60: 285-312. 10.1007/s00285-009-0263-xPubMedView ArticleGoogle Scholar
- Wilson HR, Cowan JD: Excitatory and Inhibitory Interactions in Localized Populations of Model Neurons. Biophys J 1972, 12: 1.PubMedPubMed CentralView ArticleGoogle Scholar
- Miller R: Distribution and Properties of Commissural and Other Neurons in Cat Sensorimotor Cortex. J Comp Neurol 1975, 164: 361-373. 10.1002/cne.901640307PubMedView ArticleGoogle Scholar
- Swadlow HA: Efferent Neurons and Suspected Interneurons in S-1 Forelimb Representation of the Awake Rabbit - Receptive-Fields and Axonal Properties. J Neurophysiol 1990, 63: 1477-1498.PubMedGoogle Scholar
- Hauptmann C, Popovych O, Tass PA: Delayed feedback control of synchronization in locally coupled neuronal networks. Neurocomputing 2005, 65: 759-767.View ArticleGoogle Scholar
- Ferraina S, Pare M, Wurtz RH: Comparison of cortico-cortical and cortico-collicular signals for the generation of saccadic eye movements. J Neurophysiol 2002, 87: 845-858.PubMedGoogle Scholar
- Gariano RF, Groves PM: Burst Firing Induced in Midbrain Dopamine Neurons by Stimulation of the Medial Prefrontal and Anterior Cingulate Cortices. Brain Res 1988, 462: 194-198. 10.1016/0006-8993(88)90606-3PubMedView ArticleGoogle Scholar
- Simmons PA, Pearlman AL: Receptive-Field Properties of Transcallosal Visual Cortical-Neurons in the Normal and Reeler Mouse. J Neurophysiol 1983, 50: 838-848.PubMedGoogle Scholar
- Foussias G, Remington G: Negative symptoms in schizophrenia: avolition and Occam's razor. Schizophr Bull 2010, 36: 359-369. 10.1093/schbul/sbn094PubMedPubMed CentralView ArticleGoogle Scholar
- Dong CY, Cho KH: An optimally evolved connective ratio of neural networks that maximizes the occurrence of synchronized bursting behavior. BMC Syst Biol 2012, 6.Google Scholar
- Hillebrand A, Barnes GR: A quantitative assessment of the sensitivity of whole-head MEG to activity in the adult human cortex. NeuroImage 2002, 16: 638-650. 10.1006/nimg.2002.1102PubMedView ArticleGoogle Scholar
- Alonso JF, Poza J, Mananas MA, Romero S, Fernandez A, Hornero R: MEG Connectivity Analysis in Patients with Alzheimer's Disease Using Cross Mutual Information and Spectral Coherence. Ann Biomed Eng 2011, 39: 524-536. 10.1007/s10439-010-0155-7PubMedView ArticleGoogle Scholar
- Gaetz M, Weinberg H, Rzempoluck E, Jantzen KJ: Neural network classifications and correlation analysis of EEG and MEG activity accompanying spontaneous reversals of the Necker cube. Cognitive Brain Res 1998, 6: 335-346. 10.1016/S0926-6410(97)00038-4View ArticleGoogle Scholar
- Schmithorst VJ, Holland SK: Sex differences in the development of neuroanatomical functional connectivity underlying intelligence found using Bayesian connectivity analysis. NeuroImage 2007, 35: 406-419. 10.1016/j.neuroimage.2006.11.046PubMedPubMed CentralView ArticleGoogle Scholar
- Owen JP, Wipf DP, Attias HT, Sekihara K, Nagarajan SS: Accurate reconstruction of brain activity and functional connectivity from noisy MEG data. Conf Proc IEEE Eng Med Biol Soc 2009, 2009: 65-68.PubMedPubMed CentralGoogle Scholar
- Dhamala M, Rangarajan G, Ding M: Analyzing information flow in brain networks with nonparametric Granger causality. NeuroImage 2008, 41: 354-362. 10.1016/j.neuroimage.2008.02.020PubMedPubMed CentralView ArticleGoogle Scholar
- Kissler J, Muller MM, Fehr T, Rockstroh B, Elbert T: MEG gamma band activity in schizophrenia patients smd healthy subjects in a mental arithmetic task and at rest. Clin Neurophysiol 2000, 111: 2079-2087. 10.1016/S1388-2457(00)00425-9PubMedView ArticleGoogle Scholar
- Rutter L, Carver FW, Holroyd T, Nadar SR, Mitchell-Francis J, Apud J, Weinberger DR, Coppola R: Magnetoencephalographic Gamma Power Reduction in Patients with Schizophrenia During Resting Condition. Hum Brain Mapp 2009, 30: 3254-3264. 10.1002/hbm.20746PubMedPubMed CentralView ArticleGoogle Scholar
- van Wijk BCM, Daffertshofer A, Roach N, Praamstra P: A Role of Beta Oscillatory Synchrony in Biasing Response Competition? Cereb Cortex 2009, 19: 1294-1302. 10.1093/cercor/bhn174PubMedView ArticleGoogle Scholar
- Northoff G, Qin PM: How can the brain's resting state activity generate hallucinations? A 'resting state hypothesis' of auditory verbal hallucinations. Schizophr Res 2011, 127: 202-214. 10.1016/j.schres.2010.11.009PubMedView ArticleGoogle Scholar
- Stephan KE, Friston KJ, Frith CD: Dysconnection in Schizophrenia: From Abnormal Synaptic Plasticity to Failures of Self-monitoring. Schizophrenia Bull 2009, 35: 509-527. 10.1093/schbul/sbn176View ArticleGoogle Scholar
- Bullmore E, Barnes A, Bassett DS, Fornito A, Kitzbichler M, Meunier D, Suckling J: Generic aspects of complexity in brain imaging data and other biological systems. NeuroImage 2009, 47: 1125-1134. 10.1016/j.neuroimage.2009.05.032PubMedView ArticleGoogle Scholar
- Bassett DS, Gazzaniga MS: Understanding complexity in the human brain. Trends Cogn Sci 2011, 15: 200-209. 10.1016/j.tics.2011.03.006PubMedPubMed CentralView ArticleGoogle Scholar
- Albert R, Barabasi AL: Statistical mechanics of complex networks. Rev Mod Phys 2002, 74: 47-97. 10.1103/RevModPhys.74.47View ArticleGoogle Scholar
- Jhung K, Cho S-H, Jang J-H, Park JY, Shin D, Kim KR, Lee E, Cho K-H, An SK: Small-world networks in individuals at ultra-high risk for psychosis and first-episode schizophrenia during a working memory task. Neurosci Lett 2013, 535: 35-39.PubMedView ArticleGoogle Scholar