2 Lognormal distribution of firing time and rate from a single neuron ? 3 4 5

1 2 Lognormal distribution of firing time and rate from a single neuron? 3 4 5 Eszter A. Kish , Claes-Göran Granqvist , András Dér , Laszlo B. Kish 4,a 6 7 1 Center for Learning and Memory, The University of Texas at Austin, 1 University 8 Station, Stop C7000, Austin, TX 78712-0805 9 10 2 Department of Engineering Sciences, The Ångström Laboratory, Uppsala University, P. 11 O. Box 534, SE-75121 Uppsala, Sweden 12 13 3 Institute of Biophysics, Biological Research Centre of the Hungarian Academy of 14 Sciences, Temesvári krt. 62, P.O.B. 521, Szeged, H-6701, Hungary 15 16 4 Department of Electrical and Computer Engineering, Texas A&M University, College 17 Station, TX 77843-3128, USA 18 19 20 Abstract. Even a single neuron may be able to produce significant lognormal features in 21 its firing statistics due to noise in the charging ion current. A mathematical scheme 22 introduced in advanced nanotechnology is relevant for the analysis of this mechanism in 23 the simplest case, the integrate-and-fire model with white noise in the charging ion 24 current. 25 26 27 In a recent review [1] the wide occurrence of lognormal-like distributions in the structural 28 organization parameters and the firing rate of neurons were surveyed and their assumed 29 functionalities were explored. It was assumed that the lognormal distribution of firing 30 rates is the consequence of the specially organized circuit connectivity and the high 31 complexity of the nervous system. 32