LONG-RANGE TEMPORAL CORRELATIONS IN THE SPONTANEOUS SPIKING OF NEURONS IN THE HIPPOCAMPAL–AMYGDALA COMPLEX OF HUMANS J. BHATTACHARYA, a * J. EDWARDS, b A. N. MAMELAK c,d AND E. M. SCHUMAN b a Commission for Scientific Visualization, Austrian Academy of Sci- ences, Tech-Gate, Donau City Str. 1, Vienna, A-1220 Austria b Howard Hughes Medical Institute, Division of Biology, MC 114-96, California Institute of Technology, Pasadena, CA 91125, USA c Epilepsy and Brain Mapping Program, Huntington Hospital, Pasadena, CA 91105, USA d Department of Neurosurgery, City of Hope Cancer Center, Duarte, CA 91010, USA Abstract—The spontaneous or background discharge pat- terns of in vivo single neuron is mostly considered as neu- ronal noise, which is assumed to be devoid of any correlation between successive inter-spike-intervals (ISI). Such random fluctuations are modeled only statistically by stochastic point process, lacking any temporal correlation. In this study, we have investigated the nature of spontaneous irregular fluctu- ations of single neurons from human hippocampus–amygdala complex by three different methods: (i) detrended fluctuation analysis (DFA), (ii) multiscale entropy (MSE), (iii) rate esti- mate convergence. Both the DFA and MSE analysis showed the presence of long-range power-law correlation over time in the ISI sequences. Moreover, we observed that the individual spike trains presented non-random structure on longer time- scales and showed slow convergence of rate estimates with increasing counting time. This power-law correlation and the slow convergence of statistical moments were eliminated by randomly shuffling the ISIs even though the distributions of ISIs were preserved. Thus the power-law relationship arose from long-term correlations among ISIs that were destroyed by shuffling the data. Further, we found that neurons which showed long-range correlations also showed statistically sig- nificant correlated firing as measured by correlation coeffi- cient or mutual information function. The presence of long- range correlations indicates the history-effect or memory in the firing pattern by the associative formation of a neuronal assembly. © 2005 Published by Elsevier Ltd on behalf of IBRO. Key words: spontaneous discharge, single-unit, fractal pro- cess, scaling, long-range correlation, hippocampus. The spontaneous in vivo activities of single neurons are less frequently studied than stimulus-induced activity. Classically, the spontaneous firing pattern of a neuron, which is often irregular, is considered to be neuronal noise that can be modeled as a stochastic point process (e.g. a renewal process; Fitzhugh, 1957; Tuckwell, 1988). A re- newal process is essentially memory-less: successive in- tervals in the inter-spike-interval (ISI) sequence are inde- pendent and identically distributed (Cox and Lewis, 1966). A recently emerging alternative view is that spontaneous neuronal activity may produce spatiotemporally coherent patterns, which, in turn, can influence stimulus-induced responses (Jansen and Rit, 1995; Arieli et al., 1996; Tsodyks et al., 1999; Kenet et al., 2003). In order to investigate the higher-order variability of the ISI sequences of single neurons located in either the hip- pocampus or the amygdala of human subjects implanted with intracranial hybrid depth electrodes, we used de- trended fluctuation analysis (DFA; Peng et al., 1995) and multiscale entropy (MSE; Costa et al., 2002). Activity was recorded in the absence of any explicit cognitive task while the subjects were awake. Both the DFA and MSE tech- niques indicate that the spontaneous firing patterns of most of the recorded neurons are not well described by a renewal process or by any process with short correlation (i.e. Markov process); rather they show long-range power- law correlations, representing ongoing memory effects in the ISI sequence. These neurons showed slow conver- gence of rate-estimates. Such long-range correlations were not observed when the analysis was conducted on shuffled data sets that preserve the mean firing rate (and ISI distribution function) of the original data set. Neurons that exhibited long-range correlations also exhibited corre- lations in firing patterns with other neighboring neurons, thus indicating the formation of a neuronal assembly. The presence of a long-range power-law correlation is a characteristic of a fractal dynamics (Bak et al., 1987; Stanley et al., 1994) found in diverse physiological sys- tems (Peng et al., 1992; Gilden et al., 1995; Hausdorff et al., 1995; Chen et al., 1997; Teich et al., 1997; Ashkenazy et al., 2001; Lewis et al., 2001; Linkenkaer-Hansen et al., 2001; Poupard et al., 2001; Segev et al., 2002; Worrell et al., 2002). A fractal process is also characterized by a scale-invariant power-law distribution function; the lack of any unique scale reflects the self-organizing or self- regulating feature of a complex system which shows sig- nificant correlation over longer distances in space and in time. The presence of such long-range correlation in the ISI sequences represents ‘memory’ or history in the firing patterns: two spikes that are temporally remote are not fully independent. A biophysical origin of the long-range correlations (and their transfer from one neuron to another) *Corresponding author. Tel: +43-1-51581-6706; fax: +43-1-20501- 18900. E-mail address: joydeep@oeaw.ac.at (J. Bhattacharya). Abbreviations: DFA, detrended fluctuation analysis; HP, homoge- neous Poisson process; IHP, inhomogeneous Poisson process; ISI, inter-spike-interval; MRI, magnetic resonance imaging; MSE, multiscale entropy; SampEn, sample entropy; SOC, self-organized criticality. Neuroscience 131 (2005) 547–555 0306-4522/05$30.00+0.00 © 2005 Published by Elsevier Ltd on behalf of IBRO. doi:10.1016/j.neuroscience.2004.11.013 547