Introduction Materials and methods

BioSystems 58 2000 249 – 257 Dynamics of a hybrid system of a brain neural network and an artificial nonlinear oscillator Norihiro Katayama , Mitsuyuki Nakao, Hiroaki Saitoh, Mitsuaki Yamamoto Laboratory of Neurophysiology and Bioinformatics, Graduate School of Information Sciences, Tohoku Uni6ersity, Aobayama 05 , Sendai 980 - 8579 , Japan Abstract In the brain, many functional modules interact with each other to execute complex information processing. Understanding the nature of these interactions is necessary for understanding how the brain functions. In this study, to mimic interacting modules in the brain, we constructed a hybrid system mutually coupling a hippocampal CA3 network as an actual brain module and a radial isochron clock RIC simulated by a personal computer as an artificial module. Return map analysis of the CA3-RIC system’s dynamics showed the mutual entrainment and complex dynamics dependent on the coupling modes. The phase response curve of CA3 was modeled regarding the CA3 as a nonlinear oscillator. Using the phase response curves of CA3 and RIC, we reconstructed return maps of the hybrid system’s dynamics. Although the reconstructed return maps almost agreed with the experimental data, there were deviations dependent on the coupling mode. In particular, we noted that the deviation was smaller under the bidirectional coupling conditions than during the one-way coupling from RIC to CA3. These results suggest that brain modules may flexibly change their dynamical properties through interaction with other modules. © 2000 Elsevier Science Ireland Ltd. All rights reserved. Keywords : Hippocampal neurons; Field potential; Coupled oscillators; Phase resetting; Mutual entrainment; Synchronization www.elsevier.comlocatebiosystems

1. Introduction

The brain is a complex system that consists of many functional modules. Higher-order brain functions are thought to be realized though inter- actions among these modules. For example, func- tional modules in the visual cortex have been revealed to work in parallel and hierarchically to process complex information Felleman and Van Essen, 1991, and synchronous neuronal activities in the different modules have been anticipated to play an important role in solving the ‘binding problems’ in the brain Milner, 1974; von der Malsburg and Schneider, 1986. This suggests practical aspects of the inter-module interactions. Therefore, in order to understand the mechanisms underlying the brain’s information processing, it Corresponding author. Tel.: + 81-22-2177179; fax: + 81- 22-2639438. E-mail address : katayamaecei.tohoku.ac.jp N. Katayama. 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 2 9 - 5 is essential to know the dynamical characteristics of each module, as well as the nature of interac- tions among the modules. In this study, as a framework for investigating the dynamics of a multi-module system, we con- structed a hybrid system consisting of a neural network in the hippocampal CA3 region as an actual brain module and a nonlinear oscillator as an artificial module working together as a mini- mal unit representing interacting modules in the brain. In this framework, we analyzed the dynam- ics of the hybrid system under varied coupling conditions. Considering the close relationship be- tween the dynamical properties and the function of the modules, variation of the dynamics of the hybrid system implies diversity in the modules’ functions. For considering these variations, we investigated how interactions determine the func- tion of each module in a multi-module system.

2. Materials and methods

2 . 1 . Brain module : hippocampal CA 3 region We adopted the neural network in the CA3 region of a hippocampal slice preparation abbre- viated CA3 as the brain module. Transverse slices 0.4 mm thickness of hippocampi were obtained from the brains of guinea pigs 300 9 20 g by the conventional method Ito et al., 1989 and kept in normal artificial cerebrospinal fluid ACSF containing in mM NaCl 124, KCl 3.5, NaH 2 PO 4 1.25, MgSO 4 2.0, CaCl 2 2.0, NaHCO 3 22.0, and glucose 10.0 pH 7.4, which was equili- brated with a gas mixture of 5 CO 2 in O 2 . All the experiments were conducted in a perfusing fluid chamber kept at 34 9 1°C. In order to detect neural activities, we measured the extracellular field potential at the CA3 pyramidal cell layer with a single glass pipette filled with the ACSF. The potential was amplified through the band- pass filter 0.3 – 25 Hz and sampled with 200 Hz by a personal computer IBM-PC compatible, CPU AMD K6-233; abbreviated PC with an AD and DA converter card National Instru- ments, AT-MIO-16E-2, 12-bit precision. The PC simultaneously simulated the artificial module see below, which provided electric stimuli to the mossy fiber MF bundle with a bipolar tungsten electrode. Before starting experiments, pulse-cur- rent stimuli with an amplitude of 0.5 – 1 mA and duration of 200 ms were applied every 30 s to MF. Only the slices showing stable responses to those stimuli for 30 min were used for the following experiments. The CA3 neurons are known to have recurrent excitatory synaptic connections, which tend to cause a rhythmic neural activity. We adopted a CA3 neural network as a model of a rhythmic- acting brain module. Actually, when the ACSF was replaced with an experimental ACSF contain- ing 8.5 mM KCl and 2 mM penicillin chloride, the CA3 neurons exhibited spontaneous bursts Hayashi and Ishizuka, 1995. The CA3 always responded with a burst to a stimulus stronger than a threshold level 0.03 – 0.07 mA. When threshold-level stimuli were applied, the neural responses were strongly dependent on the tempo- ral pattern of the stimuli. In order to study the organizing process of the response, we used threshold-level stimuli. 2 . 2 . Artificial module : radial isochron clock As the artificial module, we used a radial isochron clock RIC model to mimic a rhythmic- acting brain module, because it is the simplest model of a biological oscillator Winfree, 1980; Glass and Mackey, 1988; Nomura et al., 1994. Fig. 1b shows the dynamics of the RIC, which is described by the following equations: r ; =Kr1−r 1a u : = 1 T RIC 1b where r = x 2 + y 2 , u is the normalized ‘phase’ of the RIC’s state point ranging between 0 and 1, T RIC is the period of the limit cycle, and K is a constant. In this study, we set T RIC = 5 s and K “ . When the RIC is stimulated with an impulse, the RIC’s state point indicated by P in Fig. 1b is moved toward the direction of the x-axis responsible for the stimulus intensity A P. Then, the state point instantaneously ap- proaches the point on the limit cycle P along with the isochron because of K “ . The relation- ship between the old phase u at P and the new phase u at P is described below: u = 1 2p arctan sin 2pu A + cos 2pu u + D RIC u 2 where D RIC is called the phase response curve PRC of the RIC. In practice, RIC was simulated by the PC, which executed real-time processing of Eq. 1b Eq. 2. When the RIC’s phase passed across zero, the RIC was considered to have fired. At this moment, the PC generated a pulse by the DA converter to stimulate the CA3. On the other hand, when a CA3 bursting was detected, the RIC was stimulated by an impulse with an amplitude of A. The occurrence of a CA3 bursting was detected when the band-pass-filtered field poten- tial crossed a threshold level about 0.1 mV. Time series of the CA3 burstings and RIC firings were recorded under varied coupling modes, each for 10 min, where intensity of the stimulus to the RIC was changed from A = 0.95, − 0.95 and then A = 0. If one views the RIC as a single pacemaker neuron, a positive A corresponds to an excitatory coupling, whereas a negative A corresponds to an inhibitory one Nomura et al., 1994. In the case of A = 0, corresponding to one-way coupling from RIC to CA3, periodic stimulation with an interval of T RIC is realized.

3. Results