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Dendritic Spiking Accounts for Rate and Phase Coding in a Biophysicalmodelof a Hippocampal Place Cell

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Dendritic Spiking Accounts for Rate and Phase Coding in a Biophysicalmodelof a Hippocampal Place Cell ARTICLE IN PRESS Neurocomputing 65–66 (2005) 331–341 www.elsevier.com/locate/neucom Dendritic spiking accounts for rate and phase coding in a biophysicalmodelof a hippocampal place cell Zso´ fia Huhna,Ã,Ma´ te´ Lengyela,b, Gergo+ Orba´ na,Pe´ ter E´ rdia,c aDepartment of Biophysics, KFKI Research Institute for Particle and Nuclear Physics, Hungarian Academy of Sciences, 29-33 Konkoly Thege M. u´t, Budapest H-1121, Hungary bGatsby Computational Neuroscience Unit, University College London, 17 Queen Square, London WC1N 3AR, UK cCenter for Complex Systems Studies, Kalamazoo College, 1200 Academy street, Kalamazoo, MI 49006-3295, USA Available online 15 December 2004 Abstract Hippocampal place cells provide prototypical examples of neurons jointly firing phase and rate-coded spike trains. We propose a biophysicalmechanism accounting for the generation of place cell firing at the single neuron level. An interplay between external theta-modulated excitation impinging the dendrite and intrinsic dendritic spiking as well as between frequency- modulated dendritic spiking and somatic membrane potential oscillations was a key element of the model. Through these interactions robust phase and rate-coded firing emerged in the model place cell, reproducing salient experimentally observed properties of place cell firing. r 2004 Elsevier B.V. All rights reserved. Keywords: Phase precession; Tuning curve; Active dendrite ÃCorresponding author. Fax: +36 1 3922222. E-mail address: zsofi@rmki.kfki.hu (Z. Huhn). 0925-2312/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2004.10.026 ARTICLE IN PRESS 332 Z. Huhn et al. / Neurocomputing 65–66 (2005) 331–341 1. Introduction Hippocampal place cells code the spatial position of the animal both by their firing rate and the precise timing of their firings. A place cell fires only when the rat traverses a particular portion of the environment preferred by the cell, the ‘place field’ of the cell [20]. Rate coding implies that during a single traversal, firing frequency of the cell increases in the early and decreases in the late portion of the place field [10,21]. Phase coding was demonstrated as a monotonic decrease in the phase of firings relative to the ongoing theta oscillation during a single traversal [9,10,21,24]. In most of the models that have been suggested to account for these two phenomena, hippocampal area CA3, where pyramidal cells are known to be densely interconnected by recurrent collaterals, played a key role [11,25,26]. However, experimental studies reported that place cell activity could be maintained in CA1 even when input from CA3 was severely impaired [4,19]. Recently, Lengyel et al. [15] have shown both by analytical calculations and numerical simulations of a simplified single neuron model that the doubly coded firing pattern of place cells can be generated in a cell receiving periodic perisomatic inhibitory input and dendritic excitatory input from the perforant path without the need for recurrent excitatory connections. Here we present a biologically more realistic version of this model which was extended in two ways. First, a biophysicalconductance-based modelwas adopted, and thus the dynamics of intrinsic dendritic membrane potential oscillations (DMPOs) were studied in detail. Second, theta modulation of perforant path transmission [5,6] was taken into account. The interaction of these two oscillations in the dendrite generated dendritic spiking that in turn interacted with the periodic hyperpolarization of the soma. Through these interactions robust phase and rate coded firing emerged in the model place cell. 2. Methods Following our earlier work [15], the present modelconsisted of a somatic and dendritic compartment, and received two inputs. (1) The membrane potential of the soma was modulated by a somatic oscillating current (SOC) with a constant theta frequency, in phase with the ongoing theta field potential oscillation [8,12,16]. (2) Dendritic postsynaptic current represented perforant path input from the entorhinalcortex and was a sum of two terms: (i) a sinusoidal term oscillating with the same frequency but in anti-phase with SOC [12], and (ii) a speed-dependent term that was proportionalto the speed of the rat and was switched on when the animal was inside the place field of the cell. Although, experimental evidence of the presence of velocity-dependent postsynaptic depolar- ization is lacking, a theoretical study has recently shown that realistically timed theta-modulated perforant path-specific inhibition [13] transforms position-depen- dent activity of entorhinal cells [23] into speed-dependent postsynaptic excitation in hippocampal place cells [14]. ARTICLE IN PRESS Z. Huhn et al. / Neurocomputing 65–66 (2005) 331–341 333 The dendrite sustained DMPOs within the place field that were frequency modulated by the speed-dependent term, and were in anti-phase with SOC [7,12] at the beginning of the traversal of the place field due to the oscillatory term of the input. The net excitation received by the soma of the hippocampal place cell was the sum of SOC and the current flowing from the dendrite due to DMPO. The modelcellwasa modified Pinsky–Rinzelneuron [22]. Passive parameters of 2 2 the modelwere: Cm ¼ 1 mF=cm membrane capacitance, gL ¼ 0:3mS=cm leak 2 conductance, V L ¼À60 mV leak reversal potential, gc ¼ 0:01 mS=cm axialcon- ductance between the soma and the dendrite and p ¼ 0:2 soma/cell surface area ratio. Equilibrium potentials (in mV) and maximal channel conductances (in mS/ 2 cm ) of active conductances were V Na ¼ 60; V K ¼À75; V Ca ¼ 80; and gNa ¼ 30; gKÀDR ¼ 15; gCa ¼ 10; gKÀC ¼ 15; gKÀAHP ¼ 0: In order to shorten somatic action potentials, the exponents of the m and n gating variables were increased from 2 to 3, and from 1 to 4, respectively. SOC represented various sources of synaptic inputs modulated at theta frequency 2 [5]: I sðÞ¼t As=2cosð2pf ytÞþI 0Às; where f y ¼ 8Hz; As ¼ 4 mA=cm and I 0Às ¼ À0:5 mA=cm2: The only input to the dendrite arrived from entorhinal cortex, and it had two components: I dðÞ¼t I yðÞþt I v½vtðÞ: I y was a sinusoid depolarizing current 2 in antiphase with SOC: I yðÞ¼t Ad cosðp þ 2pf ytÞþI 0Àd; where Ad ¼ 0:5 mA=cm 2 and I 0Àd ¼ 1:9 mA=cm : Velocity-dependent current arose only when the rat was within the afferent place field of the cell (i.e., the area covered by all the place fields of its presynaptic entorhinal partners), and there it was a linear function of the rat’s running speed: I v½vtðÞ ¼ kvðÞ t H½xtðÞÀxin H½xout À xtðÞ; where k ¼ 2 0:01ðm A=cm Þ=ðcm=sÞ; xtðÞis the position of the rat, and xin and xout ¼ xin þ l are the entry and exit points of the afferent place field, l is the length of the afferent place field, and H is the Heaviside function. Phase response curves (PRCs) of the separated dendrite were calculated in response to pulse and periodic perturbations. Regular dendritic spiking was elicited 2 by I 0Àd ¼ 1:82 mA=cm current injection. Perturbations were timed at different phases (t) of the spiking cycle, and consisted of current pulses of 0:5 ms duration and variable amplitude starting at t ms after a spike (Fig. 5A), or one cycle of sinusoid 2 current injection of Ad ¼ 0:5 mA=cm amplitude and f y frequency starting with its peak t ms before the expected time of the next spike (Fig. 5B). Phase response was measured as a phase advancement of the dendritic spiking oscillation in response to the perturbation compared to the unperturbed case: positive or negative values showed shortening or lengthening of the spiking cycle, respectively. As a control, PRCs for periodic perturbation were also calculated from pulse PRCs by integrating the product of the pulse PRC with the sinusoid perturbation. Moving direction of the animal was always from left to right (Figs. 3,4). 3. Results First we analyzed the behavior of the separated dendrite (gc ¼ 0) in response to constant current injection (data not shown). Depending on the level of depolariza- ARTICLE IN PRESS 334 Z. Huhn et al. / Neurocomputing 65–66 (2005) 331–341 tion, the dendrite either settled to a resting membrane potential (stable fixed point) or sustained an intrinsic membrane potential oscillation. Amplitude of oscillation decreased while frequency increased with increasing external current amplitude. In the relevant frequency regime, that is close to the 8 Hz theta frequency, these oscillations were high amplitude dendritic calcium spikes (see Fig. 2B). The interaction between a theta frequency (8 Hz) sinusoid externalcurrent oscillating around a given mean value (‘offset’) and intrinsic membrane potential dynamics was also studied in the separated dendrite, so that the offset of the external oscillation was varied while its amplitude (minimum to maximum depth) was kept constant (Fig. 1A). At lowest current intensities (o1:4 mA=cm2) no spikes or subthreshold oscillations were generated. After a short transition of dendritic oscillations at half theta frequency, dendritic spikes appeared and were driven by the externaloscillationat 8 Hz in a wide range of medium current intensities (between 1.5 and 1:9 mA=cm2). At higher levels of injected current the offset component of external depolarization dominated, eliciting intrinsic membrane potential oscillations in the dendrite at frequencies corresponding to the offset level (frequency modulation). Due to interaction with the sinusoid component of the external current these oscillations were not perfectly regular: interspike intervals (ISIs) varied, but this variation was small enough not to mask the frequency modulation effect. In the complete model with soma and dendrite coupled through an axial conductance, the amount of current received by the dendrite during a traversalof the environment was in the medium to high ranges.
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