Introduction Directory UMM :Data Elmu:jurnal:B:Biosystems:Vol58.Issue1-3.2000:

BioSystems 58 2000 117 – 124 Measures of complexity in neural spike-trains of the slowly adapting stretch receptor organs M.A. Jime´nez-Montan˜o a , H. Penagos a , A. Herna´ndez Torres a , O. Diez-Martı´nez b, a Departamento de Fı´sica y Matema´ticas, Uni6ersidad de las Ame´ricas-Puebla, Cholula, Puebla 72820 , Mexico b Departamento de Psicologı´a, Uni6ersidad de las Ame´ricas-Puebla, Cholula, Puebla 72820 , Mexico Abstract Discrete sequence analysis methods were applied to study spike-trains generated by the isolated neuron of the slowly adapting stretch receptor organ. Calculation of the algorithmic complexity and block entropies of digitized individual spike-train forms allowed us to distinguish different classes of neural behavior. While some spike-trains exhibited significant structure, others displayed diverse degrees of randomness. The sequences recorded during the stimulated portions of the intermittent and walk-through forms, differed considerably from their randomly shuffled surrogates. Informational and grammar complexity measures in two, four and eight-letter alphabets, tell us things about the structure of spike-trains that are not obtained with conventional spike analysis. Comparison of the conditional entropies for the digitized signals showed that the method distinguishes between different stimulated conditions. Additionally, comparison of the different stimulated conditions with their corresponding surrogates showed that, both, conditional entropies and complexities were significantly different for the two groups. Although the original and the randomly shuffled sequences had the same distribution and average firing rate, their complexity values were different. The results obtained with both measures of sequence structure were quite consistent © 2000 Elsevier Science Ireland Ltd. All rights reserved. Keywords : Stretch receptor organ; Spike-trains; Grammar-complexity; Block-entropies; Randomly shuffled surrogates www.elsevier.comlocatebiosystems

1. Introduction

This communication describes the new informa- tion that may be obtained by applying informa- tional and algorithmic measures of complexity to the analysis of neural spike-trains. We address an essential question concerning the value of this type of analysis: do these measures provide in- sights into the description of certain categories of neural behaviors that could not be obtained by other methods? Our results suggest that the an- swer is positive. Calculation of the algorithmic complexity and block entropies allowed us to distinguish different classes of neural behavior. While some spike-trains exhibited significant structure, others displayed diverse degrees of ran- domness. We applied discrete sequence analysis Corresponding author. Fax: + 52-22-292634. E-mail address : odiezmmail.udlap.mx O. Diez-Martı´nez. 0303-264700 - see front matter © 2000 Elsevier Science Ireland Ltd. All rights reserved. PII: S 0 3 0 3 - 2 6 4 7 0 0 0 0 1 1 4 - 3 methods to study spike-trains generated by the isolated neuron of the slowly adapting stretch receptor organ SAO. Our objective was to cor- relate the informational and algorithmic measures of complexity with different known neural behav- iors i.e. individual spike-train forms. Segundo et al., 1987 observed the influence of regularly and irregularly arriving stimuli. These were pulse-like lengthenings applied to the muscle element of the SAO. The SAO neuron is a pacemaker cell that responds to isolated stimuli much like other cells respond to the arrival of EPSPs Bryant et al., 1973; Diez-Martı´nez and Segundo, 1983. The effects of stimuli include shortening of the inter- vals in which they occur, i.e. they excite. Diez- Martı´nez et al. 1988 studied the consequences of periodically applied stimuli in pacemaker SAO neurons. Two individual spike-train forms are pervasive and straightforward: i locking is char- acterized by almost fixed phases; ii intermittency is distinguished by discharges that shift irregu- larly between prolonged epochs where spike phases barely change, and brief bursts with marked variations. As stimulus frequencies change, locking alternates with intermittency. Locked domains have simple, rational spike to tug ratios e.g. 1:1, 2:1, etc.. This approach, based upon Dynamical System Theory, could not be applied as conveniently to study the effect of irregular perturbations. Since situations where pacemaker neurons are influenced by irregular inputs must be common in nature, other methods of analysis are needed. Furthermore, particularly with small amplitudes, other spike-train forms appear which are less clear. These include Se- gundo et al., 1998: i phase walk-through, i.e. phases vary cyclically, increasing or decreasing respectively depending on whether stimulus fre- quency is larger or smaller than the natural one; ii ‘messy’, i.e. difficult to describe succinctly. Furthermore, with prolonged stimulation periods, irregular transitions between behaviors could oc- cur. Thus, many important facets of periodic driving remain puzzling; indeed, whereas behav- iors at some frequencies are summarized and un- derstood clearly, others are unclear. Therefore, to improve the comprehension of these ill-defined issues, we complement standard statistical meth- ods and non-linear analytical techniques, em- ployed in former publications, with informational and algorithmic complexity mea- sures.

2. Materials and methods