Analysis of long-term depression in the Purkinje cell circuit (a model study)
In the cerebellum, long-term depression (LTD) plays a key function in sculpting neuronal circuits to store information, since motor learning and memory are thought to be associated with such long-term changes in synaptic efficacy. To better understand the principles of transmission of information...
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nasplib_isofts_kiev_ua-123456789-1482492025-02-09T13:32:30Z Analysis of long-term depression in the Purkinje cell circuit (a model study) Аналіз довготривалої депресії в нейронній мережі клітини пуркін̕ є (модельне дослідження) Zhang, X.C. Liu, Sh.Q. Ren, H. Zeng, Y.I. Zhan, G.X. In the cerebellum, long-term depression (LTD) plays a key function in sculpting neuronal circuits to store information, since motor learning and memory are thought to be associated with such long-term changes in synaptic efficacy. To better understand the principles of transmission of information in the cerebellum, we, in our model, distinguished different types of neurons (type 1- and type 2-like) to examine the neuronal excitability and analyze the interspike interval (ISI) bifurcation phenomenon in these units, and then built a Purkinje cell circuit to study the impact of external stimulation on LTD in this circuit. According to the results of computational analysis, both climbing fiber-Purkinje cell and granule cell-Purkinje cell circuits were found to manifest LTD; the external stimuli would influence LTD by changing both depression time and depression intensity. All of the simulated results showed that LTD is a very significant factor in the Purkinje circuit networks. Finally, to deliver the learning regularities, we simulated spike timing-dependent plasticity (STDP) by increasing the CaP conductance. У мозочку довготривала депресія (ДД) відіграє ключову роль у пристосуванні нейронних мереж до накопичення інформації, оскільки моторне навчання та пам’ять, як вважають, асоційовані з подібними тривалими змінами синаптичної ефективності. Намагаючись краще зрозуміти принципи передачі інформації в мозочку, в перебігу дослідження збудливості нервових клітин та аналізу феномена біфуркації міжімпульсних інтервалів у цих нейронах ми диференціювали в нашій моделі різні види нейронів (першого і другого типів). Потім була сформована модель нервової мережі клітини Пуркін̕ є для дослідження впливів зовнішньої стимуляції на ДД у такій мережі. Відповідно до результатів комп’ютерного аналізу, ДД проявляється і в мережі «ліаноподібне волокно–клітина Пуркін̕ є», і в мережі «гранулярна клітина–клітина Пуркін̕ є». Зовнішня стимуляція може впливати на ДД, змінюючи як час, так і інтенсивність депресії. Згідно з результатами моделювання, ДД є дуже істотним фактором при функціонуванні мереж, котрі містять у собі клітини Пуркін̕ є. Нарешті, ми, щоб виявити закономірності процесу навчання, за допомогою збільшення CaP-провідності моделювали пластичність, залежну від часу генерації піка (STDP). The authors would like to acknowledge the generous support by the National Undergraduates Innovating Experimentation Project of China, No. 111056144. 2014 Article Analysis of long-term depression in the Purkinje cell circuit (a model study) / X.C. Zhang, Sh.Q. Liu, H. Ren, Y.I. Zeng, G.X. Zhan // Нейрофизиология. — 2014. — Т. 46, № 1. — С. 28-36. — Бібліогр.: 27 назв. — англ. 0028-2561 https://nasplib.isofts.kiev.ua/handle/123456789/148249 519.876.5+612.827 en Нейрофизиология application/pdf Інститут фізіології ім. О.О. Богомольця НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
In the cerebellum, long-term depression (LTD) plays a key function in sculpting neuronal
circuits to store information, since motor learning and memory are thought to be associated
with such long-term changes in synaptic efficacy. To better understand the principles of
transmission of information in the cerebellum, we, in our model, distinguished different types
of neurons (type 1- and type 2-like) to examine the neuronal excitability and analyze the
interspike interval (ISI) bifurcation phenomenon in these units, and then built a Purkinje cell
circuit to study the impact of external stimulation on LTD in this circuit. According to the
results of computational analysis, both climbing fiber-Purkinje cell and granule cell-Purkinje
cell circuits were found to manifest LTD; the external stimuli would influence LTD by
changing both depression time and depression intensity. All of the simulated results showed
that LTD is a very significant factor in the Purkinje circuit networks. Finally, to deliver the
learning regularities, we simulated spike timing-dependent plasticity (STDP) by increasing
the CaP conductance. |
| format |
Article |
| author |
Zhang, X.C. Liu, Sh.Q. Ren, H. Zeng, Y.I. Zhan, G.X. |
| spellingShingle |
Zhang, X.C. Liu, Sh.Q. Ren, H. Zeng, Y.I. Zhan, G.X. Analysis of long-term depression in the Purkinje cell circuit (a model study) Нейрофизиология |
| author_facet |
Zhang, X.C. Liu, Sh.Q. Ren, H. Zeng, Y.I. Zhan, G.X. |
| author_sort |
Zhang, X.C. |
| title |
Analysis of long-term depression in the Purkinje cell circuit (a model study) |
| title_short |
Analysis of long-term depression in the Purkinje cell circuit (a model study) |
| title_full |
Analysis of long-term depression in the Purkinje cell circuit (a model study) |
| title_fullStr |
Analysis of long-term depression in the Purkinje cell circuit (a model study) |
| title_full_unstemmed |
Analysis of long-term depression in the Purkinje cell circuit (a model study) |
| title_sort |
analysis of long-term depression in the purkinje cell circuit (a model study) |
| publisher |
Інститут фізіології ім. О.О. Богомольця НАН України |
| publishDate |
2014 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/148249 |
| citation_txt |
Analysis of long-term depression in the Purkinje cell circuit (a model study) / X.C. Zhang, Sh.Q. Liu, H. Ren, Y.I. Zeng, G.X. Zhan // Нейрофизиология. — 2014. — Т. 46, № 1. — С. 28-36. — Бібліогр.: 27 назв. — англ. |
| series |
Нейрофизиология |
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NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2014.—T. 46, № 128
UDC 519.876.5+612.827
X. C. ZHANG1, SH. Q. LIU1, H. REN1, Y. I. ZENG2, and G. X. ZHAN1
ANALYSIS OF LONG-TERM DEPRESSION IN THE PURKINJE CELL CIRCUIT
(A MODEL STUDY)
Received March 8, 2013
In the cerebellum, long-term depression (LTD) plays a key function in sculpting neuronal
circuits to store information, since motor learning and memory are thought to be associated
with such long-term changes in synaptic efficacy. To better understand the principles of
transmission of information in the cerebellum, we, in our model, distinguished different types
of neurons (type 1- and type 2-like) to examine the neuronal excitability and analyze the
interspike interval (ISI) bifurcation phenomenon in these units, and then built a Purkinje cell
circuit to study the impact of external stimulation on LTD in this circuit. According to the
results of computational analysis, both climbing fiber-Purkinje cell and granule cell-Purkinje
cell circuits were found to manifest LTD; the external stimuli would influence LTD by
changing both depression time and depression intensity. All of the simulated results showed
that LTD is a very significant factor in the Purkinje circuit networks. Finally, to deliver the
learning regularities, we simulated spike timing-dependent plasticity (STDP) by increasing
the CaP conductance.
Keywords: long-term depression (LTD), interspike interval (ISI), ion currents, depression
time, depression intensity, spike timing-dependent plasticity (STDP).
1 Department of Mathematics, South China University of Technology,
Guangzhou, China
2 Biomedical Engineering Center, Beijing University of Technology, Beijing,
China
Correspondence should be addressed to: X. C. Zhang
(e-mail: xuch0206@gmail.com).
INTRODUCTION
Long-term depression (LTD) is a well-known
neurophysiological phenomenon; it is manifested
as activity-dependent reduction in the efficacy of
neuronal synapses developing after long patterned
stimulations and lasting hours or longer. LTD is
observed in many areas of the CNS; its mechanisms are
dissimilar in different brain regions and depend upon
the developmental stage [1]. In the cerebellum, LTD
occurs in synapses on cerebellar Purkinje neurons;
the latter receive two forms of excitatory inputs, one
from a single climbing fiber and one from hundreds of
parallel fibers [2].
Ito and colleagues were the first to documente LTD
in the cerebellar cortex [3, 4]. They observed that LTD
results from coincident activation of parallel fiber and
climbing fiber inputs onto Purkinje cells. Subsequent
experiments were designed to test a hypothesis
that LTD of excitatory synaptic transmission in the
cerebellar cortex is caused by a rise in the postsynaptic
Ca2+ concentration [5]. Considering the importance of
the cerebellum for motor learning, it has been widely
proposed that LTD may serve as a cellular substrate
of motor learning and memory in cerebellar cortical
circuits [4, 6, 7].
There are numerous studies on LTD induction in the
climbing fiber-Purkinje cell and parallel fiber-Purkinje
cell circuits. The LTD induced from climbing fibers
was not associated with changes in the input or series
resistance or with alterations in the strength of action
of parallel fiber synapses [8]. Chen and Thompson
applied a field potential recording technique from
cerebellar slices to examine temporal conditions for
the LTD development. The results suggested that
these conditions for LTD induction demonstrate some
similarity to those of associative learning for discrete
motor responses [9]. Ekerot and Kano found that
climbing fibers heterosynaptically depress parallel
fiber-related responses in Purkinje cells [10].
According to the known pattern of the connecting
system between different cells in the cerebellar
cortex, we constructed a model of the Purkinje circuit
network; this allowed us to separately study some
dynamic properties of different types of cerebellar
neuronal activity and LTD in the Purkinje circuit.
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2014.—T. 46, № 1 29
ANALYSIS OF LONG-TERM DEPRESSION IN THE PURKINJE CELL CIRCUIT
Also, we analyzed some ion currents (Ca2+, K+, and
Na+) in these interconnected neurons. Finally, we
simulated the spike timing-dependent plasticity
(STDP) phenomenon and its relation to LTD in this
model network.
METHODS
Based on the results of anatomy studies [11, 12] and
data on the connection system between neurons [13],
the following mode was accepted. The constructed
Purkinje circuit network contains a Purkinje cell, a
climbing fiber, granule cells, and Golgi cells. In order
to effectively simplify the model, we used a certain
proportion to reduce the complexity of the real Purkinje
circuit system. One hundred seventy five parallel
fibers from 175 granule cells are connected with
175 remote dendrites of the Purkinje cell; the axon of
the climbing fiber intertwines with the main dendrite
of the Purkinje cell and formes 13 synaptic connections
[14]. Ten dendrites of the Golgi cells are connected
with 10 parallel fibers, and 10 axons are connected
with 10 dendrites of granule cells (Fig. 1). It should
be noted that we used data related to climbing fibers
of the rat considering that information on these fibers
in mice could not be obtained.
According to the existing data, the hierarchy of the
Purkinje circuit network is rather clear and easy to
understand; some necessary physiological parameters
in this model about all simulated neurons can be
obtained from the respective papers [15-17]. Despite
the introduced simplifications, the Purkinje circuit
network constructed in our study is sufficiently similar
to the real system.
According to the data of theoretical analysis,
single neurons in our model are described as being
based on the conduction model, and the morphology
of each neuron is characterized by a compartmental
model. Considering the morphological characteristics,
different parts of the neurons can be depicted by
various compartment numbers. The basic theory
of electrical signal transmission is described by
the Rall’s cable model, and its discrete format is a
neuronal compartment model [15-18]. Naturally,
different compartments of the cells possess different
compositions of ion channels and some specific initial
ion variables. Some necessary parameters and neuronal
equations employed in our network can be acquired in
the paper by Eccles et al. [19].
The Purkinje circuit network in our study was
modeled using NEURON software, and we used
MATLAB software to process the data; the simulation
results have been repeatedly proved.
RESULTS
As was described in former publications [20, 21],
the Purkinje cell receives two significantly differing
afferent excitatory fiber inputs. Parallel fibers
establish synaptic contacts with cortical granule cells,
while climbing fibers form synapses on the dendrites
of the Purkinje cells. Before we further analyzed
LTD in the Purkinje circuit, we dynamically analyzed
the processes in the above-mentioned three kinds of
F i g. 1. Scheme of the modeled cerebellar cortex circuit.
One Purkinje cell, 175 granule cells, one climbing fiber,
10 Golgi cells, and 175 parallel fibers are included.
Only Golgi cells exert inhibitory influences on granule
cells; other neuronal types produce excitatory effects.
Р и с. 1. Схема модельованої мережі мозочкової
кори.
Parallel fiber
Granule cell
(175)
Golgi cell
(10)
Purkinje cell
(1)
Climbing fiber
(1)
Stimulation
Stimulation
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2014.—T. 46, № 130
X. C. ZHANG, SH. Q. LIU, H. REN, et al.
neurons separately.
Dynamic analysis to the Purkinje circuit network.
The respective neurons and dynamical models of
spike generation displayed two different types of
threshold behavior under conditions of steady-current
stimulation. Type 1-like neurons demonstrated firing
frequency vs. current (f-I) curves with continuous
transition from a zero frequency to arbitrarily low
frequencies of firing. Type 2-like neurons were
characterized by f-I curves showing an abrupt onset
of repetitive firing at a nonzero firing frequency [22].
Since different types of neurons determine various
dynamic properties, we classified different neurons in
this circuit firstly to compare the neuronal excitability.
In Fig. 2, it is easy to distinguish three different
types of neurons. With increase in the strength of
external stimuli (direct current), the spiking frequency
of granule cells and Purkinje cell both increased
continuously; thus, they belong to type 1-like neurons.
In contrast, the frequency of climbing fiber spiking
suddenly jumped from 0 to 0.042; thus this unit belongs
to type 2-like neurons. It seems that the climbing fiber
is relatively insensitive to the stimulus intensity. We
can gain an insight into the ample dynamic properties
between the two above types. This includes phase-
response curves, synchrony, and adaptation. Then, we
primarily studied the ISI bifurcation among the above
three different neuronal types.
In Fig. 3, we can see that when we stimulate three
different neurons with rectangular current pulses and
change the parameters of the latter, the respective
ISI bifurcation diagrams demonstrate significant
specificities. The ISI diagram of the granule cell shows
distinct period-adding bifurcation and period-doubling
bifurcation phenomena. The climbing fiber exhibits
an inverse period-adding bifurcation phenomenon.
However, the respective changes in the Purkinje
cell are relatively mild. The diversiform dynamic
F i g. 2. Frequency vs. current (f–I) curves (A–C) for three different neurons included in the model. A) Granule cell, B) climbing fiber,
C) Purkinje cell. Abscissa) Intensity of direct-current stimulation, nA; ordinate) discharge frequency, mean ISI–1, msec–1.
Р и с. 2. Графіки залежності частоти розряду від струму (f–I) для трьох видів різних нейронів (A–C), включених у модель.
F i g. 3. ISI bifurcation diagrams (A–C) for three different neuronal types. A) Granule cell; B) climbing fiber; C) Purkinje cell. The
stimulus intensities were 0.9, 0.05, and 0.29 (t/100<m), where t is the threshold, and m changes from 1 to 100.
Р и с. 3. Діаграми біфуркацій міжімпульсних інтервалів для трьох видів нейронів (A–C).
A|S|–1 |S|–1 |S|–1
0.06 0.060.14
0.05 0.050.12
0.04 0.04
0.10
0.03 0.03
0.08
0.02 0.02
0.06
0.01 0.010.02
0.04
0.00 0.000.00
0 0 00.2 0.75 0.35nA nA nA
B C
A
120
100
80
60
40
20
0
0 0 010 10 1020 20 2030 30 3040 40 4050 50 5060 60 6070 70 7080 80 8090 90 90100 100 100
B C
msec msec msec
msec
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120 9
100 8
80 7
60 6
40 5
20 4
0 3
msec msec
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2014.—T. 46, № 1 31
ANALYSIS OF LONG-TERM DEPRESSION IN THE PURKINJE CELL CIRCUIT
F i g. 4. Firing patterns of the Purkinje cell and Ca, K, and Na currents in the absence of stimulation of the granule cell (A1–3, respec-
tively) and the corresponding records at a 0.9 nA stimulation of the granule cell (B1–3).
Р и с. 4. Патерни розряду клітини Пуркін ̕ є та кальцієвих, калієвих та натрієвих струмів за відсутності стимуляції гранулярної
клітини (A1–3 відповідно) та аналогічні записи при стимуляції гранулярної клітини струмом 0.9 нА (B1–3).
A B20
–5
2.0 3.0
2.0
1.0
0.0
–1.0
–2.0
–3.0
–4.0
1.5
1.0
0.5
0.0
–0.5
–1.0
–1.5
–2.0
–2.5
–3.0
0
–10
–20
–30
–40
–50
–60
20
10
–10
10
0
–15
0
–10
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–25
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0
500
500 500
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01000
750
750 750
750
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msec
msec
msec msec
msec
msec
mV
pA
pA pA
pA
mV
1 1
2 2
3 3
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2014.—T. 46, № 132
X. C. ZHANG, SH. Q. LIU, H. REN, et al.
F i g. 5. Characteristics
of spiking and LTD in
the modeled circuits.
A) Climbing fiber-Purkinje
cell circuit. A1–3) Firing of
the Purkinje cell at stimulus
intensity applied to the
climbing fiber of 0.7, 0.9,
and 1.1 nA, respectively.
A4 and A5) Depression
time and depression
intensity in the climbing
fiber, respectively. B1–5)
Analogous illustrations for
the granule cell-Purkinje
cell circuit.
Р и с. 5. Характери-
стики імпульсації та
довготривалої депресії в
модельованих мережах.
638.8
–46.714
–46.712
–46.716
–46.718
–46.720
–46.722
–46.724
638.7
638.6
638.5
638.4
638.3
638.2
0.7
0.7
1.1
1.1
0.9
0.9
nA
nA
msec
msec
A
10
0
0
–10
–20
–30
–40
–50
–60
–10
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–30
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–60
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500
500 1200
1200
1200
msec
msec
msec
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–10
–20
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–40
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–60
mV
mV
mV
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100
–47.4
–47.5
–47.6
–47.7
–47.8
–47.9
–48.0
–48.1
–48.2
–48.3
160
0.7 1.1
1.1
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nA
nA
msec
msec
0.7 0.9
B
0
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msec
msec
msec
mV
mV
mV
1 1
2 2
3 3
4 4
5 5
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2014.—T. 46, № 1 33
ANALYSIS OF LONG-TERM DEPRESSION IN THE PURKINJE CELL CIRCUIT
F i g. 6. Normalized changes in the EPSP potential with change in the spike time (A), those in the mean ISI with change in the CaP
conductance (B), and change in the mean potential with change in the CaP conductance (C) in the granule cell-Purkinje cell circuit (1) and
climbing fiber-Purkinje cell circuit (2).
Р и с. 6. Нормовані зміни величини ЗПСП при варіюванні тривалості імпульсу (А), середнього міжімпульсного інтервалу при
варіюванні CaP-провідності (В) та середнього значення потенціалу при варіюванні цієї провідності (С) у мережах гранулярний
нейрон – клітина Пуркін ̕ є (1) та ліаноподібне волокно – клітина Пуркін ̕ є (2).
properties motivated us to roundly analyze the LTD
development in the above neurons.
Synaptic depression in the stimulated Purkinje
circuit network. The elementary concept of the
Marr–Albus theory is that the climbing fiber serves
as a source of the “teaching signal,” which induces
long-lasting changes in the strength of synchronous
activation of the parallel fiber inputs. Observations of
LTD in the latter inputs have provided some support
for theories of this type, but their validity remains
controversial. So, we assay the LTD phenomenon in
the granule cell-Purkinje cell circuit principally, since
LTD can transfer information necessary for memory
and motor learning processes [23-25]. In order to
better research LTD in the Purkinje cell, we first
examined the depression function in the respective
synapses.
We stimulated the granule cell within a 500 to
501 msec window whith 1-msec-long stimuli. Figure 4
illustrates the detailed firing pattern of the Purkinje
cell and different ion currents in this cell without any
stimulation applied to the granule cells (A1–3) and the
respective records in the case of stimulation whith a
0.9 nA intensity applied to the parallel fiber (B1–3).
It is easy to observe a clear depression after 500 msec
and the patterns of ICa, IK, and INa related to every spike
generated by the Purkinje cell. The depression period
in the Purkinje cell and those of ICa, IK, and INa are
synchronous. The analogous results could be observed
upon climbing fiber-Purkinje cell stimulation.
To make the aforementioned analyses more
conclusive, we changed the intensity of external stimuli
to study the impact of this parameter on depression.
In Fig. 5, it can be seen that during climbing fiber-
Purkinje cell stimulation, the depression duration and
depression intensity changed to a limited extent when
the stimulus intensity increased, although the A4 and
A5 panels both show a slow upward trend. However,
the depression time changes were clear during granule
cell-Purkinje cell circuit stimulation. The depression
time shortened with increases in the stimulus intensity
(B4). In addition, the depression strength decreased in
A
1
2
B C
0.15 0.05
0.05
0.10 0.04
0.04
0.05 0.03
0.03
0.00 0.02
0.02
–0.05 0.01
0.01
–0.10
0
0
–0.15
–1.0
–1.8
–0.8 0 0
00–1.6
–0.6
–1.4
–0.4
–1.2
–0.2 5 5
55–1.0
–0.0
–0.8
–0.2
–0.6
–0.4
–0.4
–0.6
–0.2
–0.8
0.0
–1.0 15 15
1515
10 10
1010
msec uA/cm2 uA/cm2
uA/cm2uA/cm2msec
0.20 0.06 1.6
1.6
1.4
1.4
1.2
1.2
1.0
1.0
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0.0
0.0
–0.2
–0.2
0.06
0.00
–0.05
–0.01
–0.15
–0.20
% % %
%%%
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2014.—T. 46, № 134
X. C. ZHANG, SH. Q. LIU, H. REN, et al.
a parallel manner (B5). Thus, the simulation results
demonstrate that the characteristics of external stimuli
have a strong influence on the depression parameters.
Spike timing-dependent synaptic plasticity
(STDP) in the Purkinje circuit network. Synaptic
plasticity is the ability of a synaptic connection
between two neurons to change the strength of
its action in response to either use or disuse of
transmission over this synaptic pathway [26].
According to the Hebbian theory, synaptic plasticity
is one of the most important neurophysiological/
neurochemical mechanisms responsible for learning
and memory processes in the CNS. In hippocampal
neurons, Bi and Poo [27] have already simulated
some critical windows for the induction of synaptic
potentiation and depression. Based on the results of
their research, we mainly analyzed synaptic depression
or potentiation in the cerebellum.
As was mentioned above in the Introduction, Ca2+
plays a crucially significant role in the induction of
LTD and LTP (long-term potentiation), especially in
the cerebellum. As can be seen in Fig. 6 A1, when
we gradually increased the CaP conductance, the
simulated critical window for the induction of synaptic
depression or potentiation in the granule cell – Purkinje
cell cirquit looks like a recumbent “S.” This is rather
similar to the assumed rule of synaptic modification,
and the graph from Bi and Poo [27] looks like a part of
A1, where the spike time is the difference between the
postsynaptic spike time and presynaptic spike time.
Meanwhile, the mean ISI and potential both increase
with increase in the CaP conductance (B1, C1). From
A2, it is obvious that the normalized change in the
EPSP potential in the climbing fiber – Purkinje cell
decreases first and then increases gradually, and both
changes in the mean ISI and potential increase with
increase in the CaP conductance (B2, C2).
In previous experiments, only LTD appeared in the
Purkinje cell. The opposite phenomena, i.e., LTP could
not be produced. However, the simulation results
described above showed that both LTD and LTP may
be observed in the granule cell-Purkinje cell circuit.
This finding may help us to more deeply understand
regularities of the learning process in the Purkinje
circuit.
DISCUSSION
Considering the results of previous studies, the
constructed model Purkinje network is rather similar
to the real system. In this paper, we mainly analyzed
some dynamic properties of spiking, ion currents,
LTD, and STDP in the Purkinje circuit. There are
some aspects of the respective findings, which should
be discussed.
(i) The examined three different neuronal types
possess abundant dynamic properties. According to
the classification of the types of neuronal excitability,
granule cells and Purkinje cells belong to type 1-like
neurons, while climbing fibers belong to type 2-like
neurons that are not dramatically sensitive to stimulus
intensity. The ISI bifurcation diagrams plotted for
different neuronal types display abundant period-
adding bifurcation and period-doubling bifurcation
phenomena.
(ii) Long-term depression appears in both the
granule cell-Purkinje cell circuit and the climbing
fiber-Purkinje cell circuit. In the former cell circuit,
external stimuli can influence firing of the Purkinje
cell, intensely affecting the depression time and
depression intensity. During the depression period,
all examined ion currents (including Ca2+, K+, and
Na+ currents) are synchronized in the Purkinje cell.
Comparable results were obtained for the climbing
fiber-Purkinje cell circuit.
(iii) The results of simulation related to spike
timing-dependent synaptic plasticity (STDP) are more
convincing. In the granule cell-Purkinje cell circuit,
we found that both LTD and LTP develop when the
CaP conductance increases. Furthermore, changes
in the mean ISI and potential increase gradually.
However, only LTD is produced in the climbing fiber-
Purkinje cell circuit. The mean ISI and potential also
increase here with increase in the CaP conductance.
Based on the findings in the previous analyses,
the constructed Purkinje circuit has a clear network
configuration and encompasses many functions.
Thus, this type of circuit modeling should attract
considerable attention. In this paper, we analyzed,
as was mentioned above, some dynamic properties
of three different neuronal types, LTD in the
Purkinje network, and STDP, i.e., the phenomenon
influencing learning regularities. This prepares us
to thoroughly understand the mechanisms of motor
learning and memory; these mecanisms will be our
goal in future research. In fact, some results described
in this paper are surprisingly similar to results of
neurophysiological experiments in vivo. We believe
that certain basic properties related to motor learning
in the cerebellum may be further clarified using our
simulations of the cerebellar Purkinje circuit network.
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2014.—T. 46, № 1 35
ANALYSIS OF LONG-TERM DEPRESSION IN THE PURKINJE CELL CIRCUIT
The authors, X. C. Zhang, Sh. Q. Liu, H. Ren, Y. I. Zeng,
and G. X. Zhan, confirm that they have no conflict of interest.
The authors would like to acknowledge the generous support
by the National Undergraduates Innovating Experimentation
Project of China, No. 111056144.
Appendix. Supporting information. Supplementary data
associated with this article can be found in the online version at
http://neuromorpho.org/
Кс. Ц. Жанг1, Ш. К. Лю1, Х. Рен1, Ю. І. Зенг2, Г. Кс. Жан1
АНАЛІЗ ДОВГОТРИВАЛОЇ ДЕПРЕСІЇ В НЕЙРОННІЙ
МЕРЕЖІ КЛІТИНИ ПУРКІН ̕ Є (МОДЕЛЬНЕ
ДОСЛІДЖЕННЯ)
1 Відділ математики, Південно-Китайський університет
технології, Гуанчжоу (Китай)
2 Центр біомедицинських технологій Пекинського
університету технології (Китай)
Р е з ю м е
У мозочку довготривала депресія (ДД) відіграє ключо-
ву роль у пристосуванні нейронних мереж до накопичен-
ня інформації, оскільки моторне навчання та пам’ять, як
вважають, асоційовані з подібними тривалими змінами си-
наптичної ефективності. Намагаючись краще зрозуміти
принципи передачі інформації в мозочку, в перебігу дослі-
дження збудливості нервових клітин та аналізу феномена
біфуркації міжімпульсних інтервалів у цих нейронах ми ди-
ференціювали в нашій моделі різні види нейронів (першо-
го і другого типів). Потім була сформована модель нервової
мережі клітини Пуркін ̕ є для дослідження впливів зовніш-
ньої стимуляції на ДД у такій мережі. Відповідно до ре-
зультатів комп’ютерного аналізу, ДД проявляється і в ме-
режі «ліаноподібне волокно–клітина Пуркін ̕ є», і в мережі
«гранулярна клітина–клітина Пуркін ̕ є». Зовнішня стиму-
ляція може впливати на ДД, змінюючи як час, так і інтен-
сивність депресії. Згідно з результатами моделювання, ДД
є дуже істотним фактором при функціонуванні мереж, котрі
містять у собі клітини Пуркін ̕ є. Нарешті, ми, щоб виявити
закономірності процесу навчання, за допомогою збільшення
CaP-провідності моделювали пластичність, залежну від
часу генерації піка (STDP).
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