Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study
The circuit of the tail-withdrawal reflex in Aplysia opens up possibilities to construct model systems allowing researchers to effectively investigate simple forms of learning and memory. Using the Python interface of the NEURON software, we simulated this reflex circuit and studied various chara...
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Інститут фізіології ім. О.О. Богомольця НАН України
2013
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irk-123456789-1482402019-02-18T01:25:41Z Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study Ye, W. Liu, S.Q. Zeng, Y.J. The circuit of the tail-withdrawal reflex in Aplysia opens up possibilities to construct model systems allowing researchers to effectively investigate simple forms of learning and memory. Using the Python interface of the NEURON software, we simulated this reflex circuit and studied various characteristics of the latter. The phenomenon of spike frequency adaptation (SFA) and the period-adding bifurcation of the minimum were found in sensory neurons, when the latter were stimulated by square-wave stimuli. In all neurons of the circuit, variation of the stimulus strength first increased and then decreased the number of spikes in a burst. In addition, with decreases in the number of stimulated sensory neurons, a subliminal firing other than that in an intact burst appeared at the outputs of interneurons and motor neuron. Moreover, the potentials produced in the motor neuron induced corresponding oscillations of the muscle fiber force, which was indicative of a procedure of excitement-contraction coupling in the tail part of Aplysia. Finally, upon alteration of the conductance of synapses between interneurons and motoneuron, the duration of long-lasting responses increased regularly, implying synaptic plasticity Організація нервової мережі відсмикування „хвоста” в аплізії дозволяє побудувати модельну систему, за допомогою якої можна ефективно досліджувати прості форми навчання та пам’яті. Використовуючи інтерфейс Python та програмний засіб NEURON, ми змоделювали даний рефлекс та дослідили декілька властивостей модельної мережі. Феномени адаптації частоти розряду (SFA) та біфуркації з доданням періоду при мінімумі частоти спостерігалися в сенсорних нейронах в умовах стимуляції прямокутними стимулами. В усіх нейронах мережі зміни сили стимуляції призводили спочатку до збільшення числа піків у пачках, а потім до його зменшення. Окрім того, при зменшенні кількості стимульованих сенсорних нейронів на виходах інтернейронів та моторного нейрона з’являлася підпорогова кайма, що відрізнялася від такої в інтактних пачок. Більш того, потенціали, продуковані моторним нейроном, індукували відповідні осциляції сили, розвинутої м’язовим волокном, що свідчило про сполучення процесів збудження/скорочення у хвостовій частині аплізії. Нарешті, при змінах провідності синапсів між інтернейронами та мотонейронами тривалість „довгих” імпульсних відповідей закономірно збільшувалася, що вказувало на прояви синаптичної пластичності. 2013 Article Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study / W. Ye, S.Q. Liu, Y.J. Zeng // Нейрофизиология. — 2013. — Т. 45, № 6. — С. 505-514. — Бібліогр.: 18 назв. — англ. 0028-2561 http://dspace.nbuv.gov.ua/handle/123456789/148240 612.014.42+612.019 en Нейрофизиология 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 |
The circuit of the tail-withdrawal reflex in Aplysia opens up possibilities to construct model
systems allowing researchers to effectively investigate simple forms of learning and memory.
Using the Python interface of the NEURON software, we simulated this reflex circuit and
studied various characteristics of the latter. The phenomenon of spike frequency adaptation
(SFA) and the period-adding bifurcation of the minimum were found in sensory neurons,
when the latter were stimulated by square-wave stimuli. In all neurons of the circuit, variation
of the stimulus strength first increased and then decreased the number of spikes in a burst.
In addition, with decreases in the number of stimulated sensory neurons, a subliminal firing
other than that in an intact burst appeared at the outputs of interneurons and motor neuron.
Moreover, the potentials produced in the motor neuron induced corresponding oscillations
of the muscle fiber force, which was indicative of a procedure of excitement-contraction
coupling in the tail part of Aplysia. Finally, upon alteration of the conductance of synapses
between interneurons and motoneuron, the duration of long-lasting responses increased
regularly, implying synaptic plasticity |
| format |
Article |
| author |
Ye, W. Liu, S.Q. Zeng, Y.J. |
| spellingShingle |
Ye, W. Liu, S.Q. Zeng, Y.J. Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study Нейрофизиология |
| author_facet |
Ye, W. Liu, S.Q. Zeng, Y.J. |
| author_sort |
Ye, W. |
| title |
Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study |
| title_short |
Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study |
| title_full |
Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study |
| title_fullStr |
Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study |
| title_full_unstemmed |
Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study |
| title_sort |
peculiarities of the tail-withdrawal reflex circuit in aplysia: a model study |
| publisher |
Інститут фізіології ім. О.О. Богомольця НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148240 |
| citation_txt |
Peculiarities of the Tail-Withdrawal Reflex Circuit in Aplysia: a Model Study / W. Ye, S.Q. Liu, Y.J. Zeng // Нейрофизиология. — 2013. — Т. 45, № 6. — С. 505-514. — Бібліогр.: 18 назв. — англ. |
| series |
Нейрофизиология |
| work_keys_str_mv |
AT yew peculiaritiesofthetailwithdrawalreflexcircuitinaplysiaamodelstudy AT liusq peculiaritiesofthetailwithdrawalreflexcircuitinaplysiaamodelstudy AT zengyj peculiaritiesofthetailwithdrawalreflexcircuitinaplysiaamodelstudy |
| first_indexed |
2025-07-12T18:41:48Z |
| last_indexed |
2025-07-12T18:41:48Z |
| _version_ |
1837467672892145664 |
| fulltext |
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2013.—T. 45, № 6 505
UDC 612.014.42+612.019
W. YE,1 S.Q. LIU,1 and Y.J. ZENG2
PECULIARITIES OF THE TAIL-WITHDRAWAL REFLEX CIRCUIT IN APLYSIA:
A MODEL STUDY
Received January 12, 2013.
The circuit of the tail-withdrawal reflex in Aplysia opens up possibilities to construct model
systems allowing researchers to effectively investigate simple forms of learning and memory.
Using the Python interface of the NEURON software, we simulated this reflex circuit and
studied various characteristics of the latter. The phenomenon of spike frequency adaptation
(SFA) and the period-adding bifurcation of the minimum were found in sensory neurons,
when the latter were stimulated by square-wave stimuli. In all neurons of the circuit, variation
of the stimulus strength first increased and then decreased the number of spikes in a burst.
In addition, with decreases in the number of stimulated sensory neurons, a subliminal firing
other than that in an intact burst appeared at the outputs of interneurons and motor neuron.
Moreover, the potentials produced in the motor neuron induced corresponding oscillations
of the muscle fiber force, which was indicative of a procedure of excitement-contraction
coupling in the tail part of Aplysia. Finally, upon alteration of the conductance of synapses
between interneurons and motoneuron, the duration of long-lasting responses increased
regularly, implying synaptic plasticity.
Keywords: Aplysia, tail-withdrawal reflex, spike frequency adaptation, synaptic
plasticity, muscle fiber force.
INTRODUCTION
The nervous system of a marine mollusk, Aplysia
(Gastropoda), is an extensively used object in the
studies of reflexes, due to the relatively simple structure
of this system [1]. In Aplysia, there are two important
motor reflex reactions, the tail-withdrawal reflex and
the gill-withdrawal reflex (note that the term “tail” is
conventionally attributed to the posterior part of the
mollusk’s body despite the fact that the tail per se, in
the strict sense of the term, exists only in Chordata).
Both the above-mentioned motor phenomena are
examined because data obtained help researchers to
understand the general principles of functioning of the
reflex neuronal networks [2]. Owing to the relatively
simpler pattern of the neuronal circuit, considerable
attention was focused on the tail-withdrawal reflex.
In reality, the arc of this reflex includes three kinds
of neurons: sensory units, interneurons, and motor
1 South China University of Technology, Guangzhou, China
2 Biomedical Engineering Center, Beijing University of Technology, Beijing,
China
Correspondence should be addressed to: Y.J.Zeng or S.Q.Liu
(e-mail: (yjzeng@bjut.edu.cn)
neurons. Many studies were focused mainly on the
monosynaptic connections between sensory neurons
and motor neurons, which were thought to be a
site of plasticity [3]. For example, Phares et al. [4]
studied the contribution of synaptic depression to the
monosynaptic circuit. Although these authors could
simulate the properties of basic firing, the long-
duration (long-lasting) responses observed in the
physiological experiments could not be reproduced,
and the role of interneurons interposed between the
sensory and motor neurons was not analyzed. White et
al. [1] improved the former models by constructing a
polysynaptic circuitry that included interneurons. This
circuitry, consisting of monosynaptic and polysynaptic
pathways, reproduced long-lasting responses and drew
attention to the phenomenon of the synaptic plasticity
modifying the synaptic connection. Baxter et al. [5]
developed this polysynaptic model by adding synaptic
depression and potentiation to modulate synaptic
connection. Most of the above-mentioned researches,
however, focused only on the correspondence of
the spiking patterns between actual neurons and the
model network. The properties of the muscle, i. e., the
effector of the reflex, were not discussed in the above
papers.
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2013.—T. 45, № 6506
W. YE, S.Q. LIU, and Y.J. ZENG
Motor neurons are central elements that provide
connections between the CNS and muscle fibers
[6, 7]. Due to the fundamental difficulties of
experimental research, there are still lots of problems
on how motor neurons or a neural network control
muscle fibers to achieve certain characteristics of the
activities. Consequently, much attention was focused
on the computational approach to simulate the neural
network and muscle fibers. Bashor [8] constructed a
neural network simulating that in the cat; this network
associated two antagonistic muscles to study the
influences coming to the muscles from the network.
Cisi and Kohn discretized the critically damped second-
order system that was further developed by Fuglevand
et al. [6, 9]. This discrete model made simulation
much simpler, and its simulation/reality accuracy
provided a relatively high level of successfulness in the
reproduction of experimental data.
METHODS
Our tail-withdrawal reflex-simulating circuit consists
of a muscle fiber model and a neural model. The
neural model constructed by White et al. [5] includes
four sensory neurons, two interneurons, and one motor
neuron. There are two kinds of synapses between
the interneurons and motoneuron: the increased-
conductance and decreased-conductance synapses.
The muscle fiber model constructed by Cisi and Kohn
[6] receives action potentials (APs) from the motor
neuron directly. These neurons, synapses, and muscle
fiber form a four-layer network model (Fig. 1).
The muscle force is described by a motor unit-
twitch model. It is the discrete-time impulse response
of a second-order critically damped system, as follows
[6, 9, 10]:
(1)
In equations (1), ni represents the times of
motor unit activation, Apeak is the twitch amplitude
whose value is between 5 and 12.5 gram force
(~ 0.05 to 0.125 N), tpeak represents the twitch
contraction time (between 80 and 250 msec), T is the
time step (msec), e(n) represents the discrete-time
spike train generated by the motor neuron, and f(n)
represents the muscle force.
In the circuit, every neuron is described by Hodgkin-
Huxley-type equations,
, (2)
where Vi is the membrane potential of the neuron
i, ILeak(i) is the leakage current, I ion(ik) represents the
current in the neuron i due to the ion k, Isyn(ij) is the
synaptic current in the cell i due to the influence
of the presynaptic cell j, and Cm(i) is the membrane
capacitance (Cm(i) is 0.001 μF in sensory neurons and
interneurons and 0.01 μF in motor neuron). Each
current can be modeled by I=g(V - E) where g is
the conductance and E is the reversal potential. The
conductance gion(ik) of an ion channel k in every neuron
was obtained from the following equations:
,
(3)
where X represents A and B. When there is IKS in
the sensory neuron or IKV in motor neuron, nexp = 2;
for other channels, it is 1. The conductance of the
increased-conductance synapse is described by gsyn(ij =
gmax(ij) αIC Asyn(ij) , and the conductance of the decreased-
conductance synapse is obtained from the following
equation: gsyn(ij) = gmax(ij)/ (1+αDC Asyn(ij)) where αDC equals
7. The other synapse conductance can be described by
ICa
ICa
Muscle fiber
IKS
IKA IKV
IKV
IKV
INa
SN
LPI17
LPI17
SN
SN
SN
MN
INa
INa
F i g. 1. Scheme of the tail-withdrawal reflex-simulating network.
Р и с. 1. Схема модельованої мережі рефлексу відсмикування
„хвоста”.
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2013.—T. 45, № 6 507
PECULIARITIES OF THE TAIL-WITHDRAWAL REFLEX CIRCUIT
gsyn(ij) = gmax(ij) Asyn(ij), where Asyn(ij) is a synaptic
activation function that can be obtained from the
equation 2 2 2
( )
( )
( )( ) ( )( )) // ( 2syn ij sy
syn ij
syn ijn ij syn ijX t
dA
d A dt A
dt
τ τ+= − −
. All parameters in the equations are listed in
Tables 1 and 2.
The network was simulated in the Python interface
of NEURON [11]. All charts were plotted using the
Python library Matplotlib.
RESULTS
Square-Wave Stimulus Makes Sensory Neurons
Reveal Two Characteristics. In the tail-withdrawal
reflex, a sensory neuron is the site that receives
external stimuli, whose nature plays an important
role in modifying the circuit output. To reveal the
properties of the sensory neuron, simulations were
performed by applying square-wave stimuli. As a
result, the sensory neuron produced burst discharges
that displayed some interesting characteristics. First,
the frequency of action potentials (APs) declined, a
phenomenon known as spike frequency adaptation,
SFA (Fig. 2E). Second, an increment in the stimulus
strength caused the minimum of the AP number to
change regularly (Fig. 2F).
From Fig. 2 A and B, we can see that series of
bursts were induced by square-wave stimuli, and
the distance between two APs gradually increased.
Figure 2E shows the frequency of spikes fired
by the modeled sensory neuron depending on the
Table 1. Parameters describing the membrane currents
Таблиця 1. Параметри трансмембранних струмів
Iion
E
mV
gmax
µS
hA
mV
sA
mV
p
τA(max)
msec
τA(min)
msec
hτA
mV
sτA
mV
hB
mV
sB
mV
Bmin
τB(max)
msec
τB(min)
msec
hτB
mV
sτB
mV
SN
INa 70 10.0 -18.2 -8.8 3 2.0 0.56 -9.0 7.0 -40 3.2 0.0 10.0 2.8 -9.0 7.0
IKA -70 0.25 -20.7 -26.0 2 15.0 5.0 -33.8 2.9 -49.3 23.3 0.0 140.0 46.2 -30.0 5.8
IKV -70 2.2 -3.7 -9.5 3 28. 2.8 22.0 17.5 -22.9 12.4 0.0 360.0 36.0 5.7 1.9
ICa 60 0.01 -20.0 -10.8 3 50.0 6.0 -20.0 21.8 -20.0 7.9 0.75 300.0 225.0 -40.1 33.3
IKS -70 0.62 21.2 -19.7 1 250.0 60.0 -15.0 10.0
-46.0 -6.5
ILeak -18 0.033
MN
INa 67 5.5 -30.1 -5.8 3 1.4 0.39 -8.7 1.9 -27.5 9.2 0.0 23.8 5.7 -15.2 3.5
IKV -75 10.0 3.9 -6.6 1 145.0 0.0 -0.4 12.6 -8.0 12.8 0.0 1066 202.6 -8.0 7.4
-23.0 -13.3
ICa 87 0.2 -1.3 -10.8 1 8.7 1.0 -42.8 21.8 -16.3 7.9 0.24 372.6 67.1 -40.1 33.3
ILeak -19.0 0.035
LPl17
INa 70 8.0 -18.1 -8.8 3 2.0 0.56 -9.0 7.0 -37.0 3.2 0.0 10.0 2.8 -9.0 7.0
IKV -70 4.2 -3.7 -9.5 3 28.0 2.8 22.0 17.5 -22.9 12.4 0.0 460.0 46.0 5.7 1.9
ILeak -51.0 0.02
Table 2. Parameters of synaptic connections
Таблиця 2. Параметри синаптичних зв ̕ язків
Connection gmax , µS Esyn , mV τsyn , msec
SN → MN 0.16 30 2.7
SN → LPl17 0.007 30 4.0
LPl17 → MN 0.05 30 2.0
LPl17 → MN 0.035 -70 6000
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2013.—T. 45, № 6508
W. YE, S.Q. LIU, and Y.J. ZENG
ordinal on the interval between two APs. As the
ordinal increases, the frequency of firing shows a
corresponding reduction (i.e., SFA). The formation of
SFA was mainly determined by the properties of the
potassium channels. With time increase, an inactive
state of the potassium channels is prolonged gradually
(Fig. 2 C, D). As a result, the frequency decreases
correspondingly.
Figure 2 F shows that the minimum of the AP
number varies with increase in the stimulus strength.
Initially, the minimum exhibits the period-adding
bifurcation. When the stimulus strength exceeds
1.08 nA, an inverse motion could be observed.
Effect of the Stimulus Strength on the Circuit
Firing Pattern. To study how the stimulus strength
influences the circuit, we applied different stimuli
to the sensory neuron. With increase in stimulus,
the network output changes regularly, and the three
kinds of neurons manifest synchronized firing
(Fig. 3 A-H). When the stimulus strength was 0.1 nA,
the sensory neuron, interneuron, and motor neuron
all fired a single AP (Fig. 3 A). After cessation of
the stimulus, the motor neuron became resting for
1500 msec and then generated a long-lasting response
for 4500 msec. As the stimulus strength increased, the
three kinds of neurons all fired series of bursts, and
the number of spikes in the bursts increased until the
stimulus strength reached 1.1 nA (Fig. 3 I). When the
stimulus strength exceeded this value, its increment
began to cause decreases in the number of spikes in
the bursts (Fig. 3 I). However, independently of the
stimuli strength, a long-duration response was still
generated after cessation of stimulation.
In this procedure, the sensory neuron, interneuron,
and motor neuron fired synchronously and generated
the same number of APs when the stimulation strength
was below 1.25 nA.
The Number of Stimulated Sensory Neurons
Affects the Circuit Output. In our simulated network,
the first layer of the circuit consists of four sensory
neurons. The same stimulus was applied to different
numbers of sensory neurons in order to detect the role
of this parameter. The responses of such simulations
are shown in Fig. 4.
When only one sensory neuron was stimulated, the
potential produced by this sensory neuron did not
lead to intense bursts in both interneurons and motor
neuron but made them generate single spikes and
subliminal firing alternately (Fig. 4A). As the number
of stimulated sensory neurons increased, subliminal
firing in a burst of interneurons decreased gradually,
and suprathreshold firing increased correspondingly.
0
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gka
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F i g. 2. Responses of the sensory neuron to stimulation. A) Series of burst discharges evoked by square-wave stimuli; B) enlargement of one
burst shown in A. C) Variation of the conductance in each ion channel; D) enlargement of C. E) Instantaneous frequency of spikes (sec–1)
related to their ordinal number. F) Minimum of the potential (mV) varying depending on the stimulus strength (nA).
Р и с. 2. Відповіді сенсорного нейрона на стимуляцію.
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2013.—T. 45, № 6 509
PECULIARITIES OF THE TAIL-WITHDRAWAL REFLEX CIRCUIT
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F i g. 3. Contribution of the stimulus strength to behavior of the circuit.
A–H) When strength of a square wave stimulus is 0.1, 0.3, 0.5, 0.7, 1.0,
1.3, 1.6, and 3.0 nA, respectively, the network fires in different modes.
In each panel, the upper trace is the firing pattern of the sensory neuron,
the middle trace is spiking of the interneuron, and the lower trace is
output of the motoneuron. I) Diagram of the relationship between the
stimulus strength and number of spikes.
Р и с. 3. Вплив сили стимуляції на відповіді мережі.
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2013.—T. 45, № 6510
W. YE, S.Q. LIU, and Y.J. ZENG
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F i g. 5. Muscle fiber force responses (gram force) to changes in the membrane potential of the motor neuron. A-D) Outputs of the motor
neuron and muscle fiber when the stimulus strength was 0.1, 0.4, 0.7, and 1.0 nA, respectively. The upper traces are firing patterns of the
motor neuron, while lower ones are responses of the muscle fiber.
Р и с. 5. Силові відповіді м’язового волокна (грам сили) на зміни мембранного потенціалу в моторному нейроні.
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F i g. 4. Responses of the network model to stimulation of different numbers of sensory neurons. A–D) Numbers of stimulated sensory
neurons were 1, 2, 3, and 4, respectively. In each panel, the upper traces are the number of stimulated sensory neurons, the middle traces
illustrate the firing patterns of interneurons, and the lower traces are responses of the motor neuron.
Р и с. 4. Відповіді мережі на стимуляцію різної кількості сенсорних нейронів.
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PECULIARITIES OF THE TAIL-WITHDRAWAL REFLEX CIRCUIT
Although there was no subliminal firing in the
motor neuron, the amplitudes of some APs were
still relatively low (Fig. 4B-C). While all sensory
neurons were stimulated, subliminal firing was not
observed, and series of intact bursts were produced
in the interneurons and motor neuron. If the number
of stimulated sensory neurons was less than three, the
bursts produced in the interneuron and motor neuron
were incomplete. This seems to be a factor related
significantly to signal encoding in the tail-withdrawal
reflex.
The Tail-Withdrawal Network Controls the
Muscle Fiber Force. In order to find out how motor
neurons control the muscle force, we linked our muscle
fiber model to the tail-withdrawal reflex neural model.
In this model, the electrical signal produced by the
neural network controls the physical force developed
by the muscle. Because sensory neurons, interneurons,
and motor neuron fire synchronously, Fig.5 depicts the
responses of the motor neuron and muscle fiber only.
As might be expected, each AP produced in the
motor neuron led to oscillation of the muscle fiber
force. The depolarizing potential in the motor neuron
induced the muscle fiber force to increase rapidly.
Moreover, the burst that contains several subsequent
APs produced a greater muscle force. As we can see
in Fig. 5, a single AP led to the maximal muscle fiber
force of 0.72 gram force, while bursts containing
3, 6, and 11 subsequent spikes made the maximum
of the muscle force reach 1.39, 2.39, and 3.68 gram
force, respectively. However, when the motor neuron
entered into the phase of hyperpolarization and
afterhyperpolarization, the muscle fiber force began
to decrease. The minimum point in every oscillation
was not zero but still exceeded this value. When the
motor neuron was depolarized again, the muscle fiber
force assumed higher values once more. In about
9000 msec, the motoneuron became resting and did not
fire anymore, and the muscle fiber force decreased to
zero gradually. These results indicate that the muscle
fiber force depends on the membrane potential in the
motoneuron, while the potential in this neuron is in
the phase of depolarization and hyperpolarization.
Oscillations of the muscle fiber force are related to
the excitation-contraction coupling in the muscle. As
the subgraph in Fig. 5A shows, the increasing change
in the muscle fiber force could lead to the contraction
of the entire muscle. On the contrary, the relaxation
phase in the muscle fiber is the result of the muscle
fiber force decreasing [12].
Synaptic Plasticity in the Tail-Withdrawal
Reflex Circuit Model. Synaptic plasticity is an
important mechanism for regulation of reflexes,
learning and memory. To understand how activation
of synaptic connections influences the output of
the network model, we used a series of simulation
tests for modulating the parameters in the synapse
(Fig. 6).
T h e c o n d u c t a n c e o f t h e d e c r e a s e d -
conductance synapse is given by the equation
gsyn(ij) = gmax(ij) / (1+αDC Asyn(ij)). A increment in αDC caused
the duration of the long-lasting response of the motor
neuron to rise regularly, which caused the conductance
to decrease correspondingly at the same time
(Fig. 6D). When αDC was 8, the duration of the long-
lasting response was 7264.9 msec, and this response
caused the muscle fiber force to vary correspondingly
(Fig. 6A). By increasing αDC to 100, the duration of the
long-lasting response showed an obvious increment,
increasing to 28,911.8 msec. When αDC reached 1000,
the duration of the long-lasting response reached
44,914.4 msec (Fig. 6C). In these procedures, the
muscle fiber force oscillated with variations of the
potential in the motor neuron and became zero, while
the motor neuron turned into resting. Figure 6D shows
a positive correlation between αDC and the duration
of the long-lasting response. When αDC was less than
300, the duration of such response rose rapidly. After
that, the rate of increment changes entered a plateau
period, and this process became relatively slow. When
αDC was greater than 5000, the long-lasting response
approached a stable state. Variations of the synaptic
conductance induced regular outputs in both motor
neuron and muscle fiber, which may imply that there
is some synaptic plasticity in the synapse between the
interneuron and motor neuron.
DISCUSSION
The SFA phenomenon is a frequently observed feature
of sensory neurons [13, 14]. It plays an important
role in the tuning of sensory responses to specific
features, which is considered a significant modulatory
mechanism. This feature emphasizes the fact that
sensory neurons in the tail-withdrawal reflex are
involved in the regulation of the firing pattern of the
entire circuit and transmission of specific electrical
signals. Another feature of the sensory neuron is that
the minimum of the AP number changes regularly.
With increments in the stimulus strength, the minimum
of the AP number shows pattern looking like a period-
NEUROPHYSIOLOGY / НЕЙРОФИЗИОЛОГИЯ.—2013.—T. 45, № 6512
W. YE, S.Q. LIU, and Y.J. ZENG
adding bifurcation. It is a mathematical characteristic
that reveals a variation of the firing patterns.
Initially, the strength of stimulation correlated
positively with the number of spikes at the output of
the network model. When the stimulating strength
exceeded 1.1 nA, the correlation between the stimulus
intensity and the number of APs acquired a negative
sign. This regularity may be relevant to the fatigue
phenomenon, which is frequently manifested in motor
reflex activity [15]. Fatigue can induce a suppression
of the response when the stimulus strength exceeds
a certain threshold. Thus, changes in the number of
APs in the model network may be connected with the
fatigue-related decrease in the magnitude of the tail-
withdrawal reflex.
The data obtained using our model network agree
in general with the statement that not only the mean
firing rate but also the number of sensory neurons
involved affect the information encoding in the tail-
withdrawal reflex [16, 17].
Muscles of the “tail” are the effector of the tail-
withdrawal reflex in Aplysia. The muscle force
induced by the stimulus makes the tail perform the
corresponding movements. Our results show that a
positive correlation exists between the muscle fiber
force and characteristics of AP bursts generated by
the network. Increases in the number of spikes in a
burst provide a summation effect that increases the
muscle fiber force. While APs generated by the motor
neuron are coming to the muscle fiber, the muscle
fiber force increases correspondingly. This increment
leads to more intense contraction of the muscle fiber.
Then, when the motor neuron is after-hyperpolarized,
this induces relaxation of the muscle fiber. Such fiber
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F i g. 6. Synaptic plasticity in the network model. A–C) Outputs of the motor neuron in the network model and muscle fiber model when
αDC is 8, 100, and 1000, respectively. In each panel, the upper trace is the response of the motor neuron, and the lower one is the force (gram
force, gf) developed by the muscle fiber. D) Diagram of the relationship between αDC and duration of long-lasting response after cessation
of stimulation.
Р и с. 6. Синаптична пластичність у моделі мережі.
A
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D
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PECULIARITIES OF THE TAIL-WITHDRAWAL REFLEX CIRCUIT
does not relax entirely but still maintains a certain
degree of muscle contraction force. These effects
provide persistent withdrawal of the tail. When the
motor neuron turns into the resting state, the motor
fiber relaxes entirely. However, our model allowed us
to stimulate only one motor unit, while the real tail-
withdrawal reflex circuit in Aplysia includes a number
of motor units. More complete simulation is needed
to combine a comparable number of motor units for
studying how the muscle force varies.
In many studies, it was reported that synapses
between interneurons and motor neurons of Aplysia
is a key site of plasticity [1, 2, 4, 5]. The relationship
between αDC and the duration of the long-lasting
responses indicates that the plasticity phenomenon in
synapses between interneurons and motor neuron in
the tail-withdrawal reflex network is manifested rather
clearly. Although the mechanisms of many aspects of
synaptic plasticity are unknown, some assumptions
with respect to this plasticity can be made according
to our results. Long-lasting responses of the motor
neuron can provide sustained contraction of the tail
muscles [18]. Changes in the characteristics of activity
generated by units of the network can modulate
sustained contraction of muscle fiber of the “tail.”
It appears that Aplysia has a possibility to alter the
duration of muscle contractions due to changes in the
conductance of synapses between neurons forming the
respective network.
The authors, W. Ye, S.Q. Liu, and Y.J. Zeng, confirm that they
have no conflict of interest.
В. Йє 1, Ш. Лью1, Я. Зенг2
ОСОБЛИВОСТІ МЕРЕЖІ РЕФЛЕКСУ ВІДСМИКУВАННЯ
„ХВОСТА” В АПЛІЗІЇ (МОДЕЛЬНЕ ДОСЛІДЖЕННЯ)
1 Південнокитайський технологічний університет,
Гуанчжоу (Китай).
2 Центр біологічної інженерії Пекінського технологічного
університету (Китай).
Р е з ю м е
Організація нервової мережі відсмикування „хвоста” в аплі-
зії дозволяє побудувати модельну систему, за допомогою
якої можна ефективно досліджувати прості форми навчання
та пам’яті. Використовуючи інтерфейс Python та програм-
ний засіб NEURON, ми змоделювали даний рефлекс та до-
слідили декілька властивостей модельної мережі. Феноме-
ни адаптації частоти розряду (SFA) та біфуркації з доданням
періоду при мінімумі частоти спостерігалися в сенсорних
нейронах в умовах стимуляції прямокутними стимулами.
В усіх нейронах мережі зміни сили стимуляції призводи-
ли спочатку до збільшення числа піків у пачках, а потім до
його зменшення. Окрім того, при зменшенні кількості сти-
мульованих сенсорних нейронів на виходах інтернейронів
та моторного нейрона з’являлася підпорогова кайма, що від-
різнялася від такої в інтактних пачок. Більш того, потенціа-
ли, продуковані моторним нейроном, індукували відповідні
осциляції сили, розвинутої м’язовим волокном, що свідчило
про сполучення процесів збудження/скорочення у хвостовій
частині аплізії. Нарешті, при змінах провідності синапсів
між інтернейронами та мотонейронами тривалість „довгих”
імпульсних відповідей закономірно збільшувалася, що вка-
зувало на прояви синаптичної пластичності.
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