Neuroscience Research 36 (2000) 81 – 91 When pyramidal neurons lock, when they respond chaotically, and when they like to synchronize R. Stoop a, *, K. Schindler a , L.A. Bunimovich b a Institut fu ¨r Neuroinformatik, ETHZ/UNIZH, Winterthurerstrasse 190, CH-8057 Zu ¨rich, Switzerland b Southeast Applied Analysis Center, Georgia Institute of Technology, Atlanta, GA 30332, USA Received 20 May 1999; accepted 26 October 1999 Abstract We give an overview on the locking properties of perturbed regularly firing pyramidal neurons, as a function of perturbation strength, self-spiking frequency and perturbation frequency. For inhibitory perturbations, instead of locking chaotic response emerges for a whole range of parameters. This suggests that global synchronization on the set of inhibitory connections may easily be achieved. © 2000 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Pyramidal neurons; Regular and chaotic interaction; Global synchronization; Network dynamics www.elsevier.com/locate/neures 1. Introduction Suggestions have been made in the past few years that cortical networks may typically be chaotic (Schiff, 1994). However, at what level of description such a property can rigorously be established, where it origi- nates from and what implications for the working brain this entails are questions that have not been rigorously answered. As a starting point, we recently were able to demonstrate numerically that when recurrent excita- tory – inhibitory connections are activated experimen- tally, individual neurons exhibit both regular and chaotic firing patterns (Schindler et al., 1997). In these in vitro experiments, regularly firing cortical neurons exhibit chaotic firing patterns when inhibitory pulses occur with a particular frequency relationship to the regularly firing neuron. The inhibitory input itself need not be chaotic at all, indeed it can be as regular as clockwork and nevertheless produce a chaotic firing pattern. Rather opposite to the question of chaos, we have also considered how coherent action/reaction of the brain could be established, which is believed to be a prerequisite for higher tasks of the brain. Explaining the mechanisms of synchronization over large cortical areas is also of importance for the understanding of epileptic seizures. Our investigations may contribute to both groups of questions. We are able to isolate one possible mesoscopic origin of chaotic behavior in the brain and we determine the abundance of this behavior in the natural parameter space of biological pyramidal neurons. Our findings are that (1) only inhibitory con- nections can lead to chaotic response; (2) chaotic re- sponse emerges for a whole range of the parameter space. As a consequence of the latter property, there is a tendency towards complete phase-locking among in- hibitory connections, where formerly independently chaotically spiking neurons can be brought into stable spiking patterns bv the application of small couplings. For a mathematical approach to the underlying general mechanisms, see Losson and Mackey (1994). 2. Results In our experiments with pyramidal neurons, slices of rat neocortex were prepared for in vitro recording. Following standard techniques, individual pyramidal neurons in layer 5 of barrel cortex were intracellularly recorded with sharp electrodes. To induce regular firing, a constant current was injected into the neurons (Reyes and Fetz, 1993a,b). The regular firing neuron * Corresponding author. Tel.: +41-16353063. E-mail address: ruedi@ini.phys.ethz.ch (R. Stoop) 0168-0102/00/$ - see front matter © 2000 Elsevier Science Ireland Ltd. All rights reserved. PII:S0168-0102(99)00108-X