Journal of Robotics, Networking and Artificial Life, Vol. 1, No. 1 (June 2014), 49-53

A model for low-frequency bursts in subthalamic nucleus neurons
Shigeru Kubota*

Graduate School of Science and Engineering, Yamagata University,
4-3-16 Jonan, Yonezawa, Yamagata, 992-8510, Japan

Jonathan E. Rubin

Department of Mathematics, University of Pittsburgh,
301 Thackeray Hall, Pittsburgh, PA 15260, USA*

Corresponding author. E-mail: kubota@yz.yamagata-u.ac.jp
Tel: +81-238-26-3766, Fax: +81-238-26-3299

Abstract
Burst firing in subthalamic nucleus (STN) has been suggested to be highly associated with the motor symptoms in
Parkinson’s disease, which result from a loss of dopamine. Although it is clinically very important to clarify themechanism underlying the bursting dynamics, complex interactions between STN and other brain areas make it
difficult to understand. In anesthetized rats, STN neurons exhibit low-frequency ( 1 Hz) bursts, which aresynchronous with cortical slow oscillations and are significantly strengthened by dopamine depletion. To reproduce
these low-frequency bursts, we examine a conductance-based model of an STN neuron that includes NMDA-typeglutamatergic inputs reflecting cortical oscillations. In addition, the neuron model contains GABAergic inhibitory
inputs, which are assumed to result from the activities of globus pallidus (GP). We show that the STN neuronmodel can reproduce low-frequency bursts synchronized with cortical activity, in the presence of GABAergicinhibition. In addition, we demonstrate that increased GABA activity leads to enhanced burstiness whereas
increased NMDA conductances mainly augment STN firing rate. The induction of burst firing additionallydecreases the coherence between STN and cortical activities. These results may give insights into how thecomplicated interactions between the STN, cortex, and GP can modulate the dynamics of bursting oscillations inthe basal ganglia.
Keywords: subthalamic nucleus, cortex, globus pallidus, Parkinson’s disease, burst oscillations

1. Introduction
The subthalamic nucleus (STN) is a key componentof the basal ganglia, a group of subcortical brain nuclei
involved in motor control.1 Bursting oscillations in theSTN are suggested to be highly associated with motor
disabilities in Parkinson’s disease.2,3 Although it isclinically important to clarify the mechanisms
underlying bursting dynamics, complex interactions
between STN and other brain regions complicate efforts
to do so.
Experiments using anesthetized rats have shown thatSTN neurons exhibit low-frequency bursts that aresynchronized with cortical slow-wave activity ( 1Published by Atlantis Press
Copyright: the authors
49

S. Kubota and J. E. Rubin

Hz).4,5 Cortical ablation abolished these burst
oscillations and produced nearly regular firing in STN.
This observation implies that the cortical inputs to STN,
which are transmitted through the hyperdirect
corticosubthalamic pathway, play a critical role inmaintaining the oscillatory component of STN activity.
Furthermore, in the case of pharmacological dopamine
depletion, a condition that mimics a parkinsonian state,
the firing rate of STN neurons was significantly
increased to more than twice its original value.5 The lossof dopamine also evoked low-frequency oscillations in
the GABAergic interneurons in globus pallidus (GP),which are reciprocally connected with STN.5 These data
may suggest that the low-frequency bursting in STN isconsiderably modulated by GABA inhibition originatingfrom GP interneurons, in addition to oscillatory inputs
from the cortex.
In this study, we simulate a model STN neuron tostudy how STN bursts depend on cortical inputs,
mediated by NMDA currents, and GABAergicinhibition. In the model, synaptic NMDA currents areactivated by slow cortical oscillations consisting ofactive phases of high-frequency activity alternating withinactive quiescent phases, as observed in experiments.6-8
We examine the changes in burst properties that arise
with changes in the magnitudes of both the NMDA andGABA conductances. We show that enhanced
GABAergic inhibition leads to stronger burstiness while
enhanced NMDA activation mainly acts to increase
STN firing rate. In addition, the occurrence of strong
bursts is correlated with a decrease in coherence
between the STN and cortical activities. These results
may provide insights on how the complex interaction
between STN and other associated brain areas
modulates dynamical properties of bursting oscillationsin the basal ganglia.

membrane potential
described asCdV  I leak  I Na  I K  I T  I Ca  I AHPdt
 I DIC  I NMDA  I GABA ,(1)

where I leak is a leak current; I Na and I K are voltagegated Na+ and K+ currents, respectively, which arerequired for action potential generation; I T is a low
threshold T-type Ca2+ current; I Ca is a high-threshold
Ca2+ current; and I AHP is a Ca2+-activated K+ current.

I DIC is a depolarization-activated inward current(DIC), which is activated by the intracellular Ca2+
entering through NMDA receptors (NMDARs).9 I NMDA
andI GABA are the NMDA and GABA currents,respectively. The active currents other than I NMDA andI GABA were taken from previous models of an STN
neuron.9,10 The NMDA current is described as

I NMDA  g N mN hN (V  VNMDA ) ,whereassociated reversal potential, and mN and hN are theactivation and inactivation variables, respectively. Thevariable

mN is governed by a pair of first-orderequations as follows.11dmNm  mN x N (1  mN )  NN ,mdt(3)dx NxN  xN (1  x N )   (t  t excj )  N . (4)xdtjexc

denotes the arrival time of the j th corticalinput (see below).  m and  x are the time constants toN

2.1 STN neuron model
We constructed a conductance-based model STN
neuron including synaptic NMDA and GABA currents.
The NMDA conductance is stochastically activated by
the arrival of cortical inputs, while the GABA
conductance has a temporally constant magnitude. The(2)g N is the peak conductance, VNMDA is theHere, t j
2. MethodsV of the model neuron isN

regulate the decay and rise time constants of NMDA
activation. The GABA current follows

I GABA  gG (V  VGABA ) ,(5)where g G is the conductance and VG is the reversal
potential. The parameters used in the model are selected
to reproduce various firing characteristic of STN

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50Subthalamic
Snuclleus neuron modeel

neurons and the voltage-ddependent properties of acttive
currents.9, 10
2.2 Slow corttical oscillatioon
Experimeental findings show that duringdsleep andadeep anesthessia, cortical neurons
nexhibiit low-frequenncy
oscillations ( 1 Hz) with each cycle composed of twot
6-8phases. In one phase, which we referr to as the acttiveo membrane potential
pinduces
phase, the deppolarization ofhigh-frequenccy spiking. Inn the subsequeent phase, whhichion
we refer to as the inacttive phase, hyperpolarizat
hpgenerration. To model
rapidly supprresses action potential
the abrupt chhange betweenn the two phaases, we dividded
time into thee intervals corrresponding too the active andainactive phasses, occurringg alternately. We define TAand TI to beb the time intervals for the active anda
inactive phasses, respectively. Then, thhe values of TAand TI are determined as follows:fTA xA(1  0.2 y A ) ,fc

(6)

TI 

(1  x A )(1  0.22 y I ) ,fc(7)

3. Results
We examinned the firinng dynamics of the STN
N
neeuron modell driven byy low-frequeency corticaal
oscillatory activvity. As show
wn in Fig. 1,1 burst firingg
occcurred in thhe presence ofo GABAerggic inhibitionn,whhich can produce
pslow
w membranee oscillationss
unnderlying burssting.1,9,10 Higgher STN firing rates wereefouund around thhe times wheen the active phases of theecoortical oscillatiions occurredd (Fig. 1). Thiss result agreessweell with the observationn that STN bursts occurr
syynchronously withw slow corttical oscillatioons.4,5The increaseed activation frequency
fof ccortical inputss
evvoked NMDA activation (FFigs. 1A and 1B).
1
While theeovverall high leevels of NMD
DA activationn presumablyy
heelped support burst firing,9 STN burst onset
ooccurredd
neear the troughh of NMDA activation, whichwbuilt upp
thrroughout the period
pof corttical and STN bursting (Figg.
1CC). That is, sinnce NMDA cuurrent evolvess slowly, STN
N
activity during bursts
bin the modelm
did not depend on theepreecise timing ofo cortical firinng.
W also invvestigated thee effects of changing theeWecoonductances ofo GABA andd NMDA currrents (Fig. 2)).
Ennhancing GAB
BA conductannce consideraably increasedd
thee coefficient ofo variation (CV)(of intersspike intervalss

where x A = 0.4 is the fraaction of eachh cortical periodve phase, and f c = 0.7 Hzz iscorrespondingg to the activ
the mean freequency of thhe slow corticcal oscillationns.5

yA

and

yI

are

raandomvariaables

obtainned

independentlyy for each cyycle from a staandard Gausssian
distribution.
excathat NMDAN
activaation times ( t jWe also assumed

in Eq. 4) are determined byb an inhomoggeneous Poissson
point processs with phase--dependent (fiiring) rates. TheTfrequency r of the NMDA
A activation iss described asp
 rA ((1  0.2 yr ,1 ), (active phase)r
(8) rI (1  0.2 yr ,2 ), (inactive phase)where yr ,1 aand yr ,2 are randomrvariabbles taken frrom

Fig. 1 An examF
mple of the resp
ponse of the ST
TN neuronmodel for= 30 and= 2 mS/cm2. The time

Gaussian distribution. rA = 30 Hz andd rI = 3 Hz arecourses of the firing rate r ofo cortical inpu
uts (A), theof thee NMDA currennt (B), andactivation variaableathe mean acctivation freqquencies for the active andinactive phases, respectively.

the membrane voltage (C). The dashed lines
lshow
the center of thet time period
d of the activee phase ofcortical oscillattions.

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51

S. Kubota and J. E. Rubin

to track corticaal activity, whichw
may bee harmful forr
cooordinating acctivities betw
ween the corttex and basaal
gaanglia.

4. Conclusionns
In this studdy, we constru
ucted a modeel of an STN
N
neeuron influencced by corticall slow-wave activity,
awhichhrepproduced burrsting oscillattions. The buursting in theemoodel was found to depeend not onlyy on NMDA
A
associated withh cortical inpu
uts but also onn GABAergicc
A is a slow current, STN
Ninhhibition. Beecause NMDA
firring times duuring bursts werew
not stronngly linked too
coortical firing times. Indeedd, we observved that STN
Nfirring during burstsbwas lessl
coherentt than duringg
reggular firing (inn the absencee of GABAerggic inputs) andd
beecame more irregular withw
increases in GABA
Acoonductance (FFig 2B). Theese results maymsuggest a
useful framewo
ork for how the complexx interactionssammong the STN
N, cortex and GP shape network activityy
paatterns, particularly in conditions ofo dopaminee
deepletion when oscillations anda bursting arre enhanced.

References
Fig. 2 Chang
ges in the firinng rate (A), thee coefficient offvariation (CVV) of interspikee intervals (ISIIs) (B), and theecoherence beetween the STN
N and cortical activities
aat 0.77
Hz (C) as function of GABA
Gconductaance. Theek conductance wasNMDA peak= 15 (dotted) or 300(solid) mS/cm
m2.

(ISIs) (Fig. 22B), suggestinng that GABA
Aergic inhibition
plays a key roole in the strenngthening of burstinessbin ouromodel. On tthe other hannd, the increease in NMD
DA
conductancess was found tot mainly auggment the firring
rate (Fig. 2AA). Interestinglly, the inductiion of burstin
nessby turning oon GABAerg
gic inhibition also tended todecrease the coherence beetween the corrtical inputs andaT
result indicates that theSTN firing (Fig. 2C). ThisS
neuron frromenhanced burrst firing may prevent the STN
abruptly traccking the chaange in the cortical activvity
phases. The depletion of dopamine, a key feature ofParkinson’s disease, is known
kto ennhance GAB
BAomediated outtward currennts in STN12. Based on ourresults, in thee case of dopaamine depletioon, higher levvelsof GABA inhhibition couldd suppress thee ability of ST
TN

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