Europhys. Lett., 58 (2), pp. 306–311 (2002) EUROPHYSICS LETTERS 15 April 2002 Multifractal properties of brain neuron signals A. Bershadskii 1 , E. Dremencov 2 , D. Fukayma 3 and G. Yadid 2 1 ICAR - P.O. Box 31155, Jerusalem 91000, Israel and Mason Laboratory, Yale University - New Haven, USA 2 Faculty of Life Sciences, Bar-Ilan University - Ramat-Gan 52900, Israel 3 Department of Physics, Chuo University - Tokyo 112-8551, Japan and Information and Mathematical Science Laboratory Inc. 2-43-1, Ikebukuro, Toshima-ku, Tokyo, 171-0014, Japan (received 2 May 2001; accepted in final form 25 January 2002) PACS. 87.19.La – Neuroscience. PACS. 87.18.Sn – Neural networks. PACS. 87.17.-d – Cellular structure and processes. Abstract. – Data (irregular spiking time-series) obtained in vivo from singular neurons be- longing to brain’s Red Nucleus are analyzed using multifractal tools and long-range correlations possessing scaling properties are found. A broad probability distribution (log-normal–like) is identified for generalized interspike intervals using the multifractal tools. A possibility of ex- cessive utilization of stochastic resonance mechanism by genetically defined depressive brains has been briefly discussed in the light of the experimental results. Introduction. – Multifractal methods have been widely used in different areas of natural sciences in the last twenty years [1, 2]. Recently these methods were also used in physiol- ogy [3–6] and for mathematical models related to neuroscience [7, 8]. Time-series generated by neurons have a specific form. All types of information which are received by sensory sys- tem, are encoded by nerve cells into sequences of pulses of similar shape (spikes) before they are transmitted to the brain. Brain neurons use such sequences as the main instrument for in- tercell connection. The information is reflected in the time intervals between successive firings (interspike intervals of the action potential train or ISIs). There need be no loss of information in principle when converting from dynamical amplitude information to spike trains [9] and the irregular spike sequences are the foundation of neural information processing. Methods com- monly used in the field, such as “firing rate analysis” or “bursting activity analysis”, turned out to be practically ineffective in the neural coding problem context (see, for instance, [10] and references therein). The commonly used methods are concentrated mainly on short-range correlations while just long-range correlations in the neural time-series can provide a universal coding information and presumably exhibit scaling properties. Though understanding of the origin of interspike intervals irregularity has important im- plications for elucidating the temporal components of the neuronal code and for the treat- ment of such mental disorders as depression and schizophrenia, the problem is still very far c  EDP Sciences