Parabolic Bursting Induced by Veratridine in
Rat Injured Sciatic Nerves
XIE Yong*, DUAN Yu-Bin1, XU
Jian-Xue, KANG Yan-Mei, HU San-Jue2
(
State Key Laboratory of Mechanical Structural Strength and Vibration, Xi′an
Jiaotong University, Xi′an 710049, China; 1Department of Physiology,
The Fourth Military Medical University, Xi′an 710032, China; 2Institute
of Neuroscience, The Fourth Military Medical University, Xi′an 710032, China)
Abstract
A specific bursting, parabolic bursting induced by veratridine, has been
observed in rat injured sciatic nerve. With the help of Plant model, the
biophysical mechanism for such a phenomenon is revealed from the viewpoint of
nonlinear dynamical theory. The slow sodium influx educed by veratridine and
the calcium-dependent potassium outflux are regarded as the two slow variables,
which are responsible for the parabolic bursting. Furthermore, the roles that
veratridine plays in the emergence of the parabolic bursting, namely inhibiting
the inactivation of sodium channels and eliciting the slow sodium influx, are
clarified.
Key words parabolic bursting;
interspike interval; Plant model; ionic channel; bifurcation
Excitable cells, such as nerve cells, cardiac cells and
pancreatic beta-cells, etc, frequently exhibit the activity of bursting, which
means the membrane potential changes periodically between an active phase of
rapid spike oscillations and a phase of quiescence. Most recently, it is
believed that bursting is information-rich , and can be reliably transmitted to
postsynaptic targets[1]. Therefore, bursting may play a special role in neural
signaling. Theoretically, the bursting is generated as the evolution of the
slow variables switches the fast dynamics between steady state and oscillatory
dynamics. According to a number of experimental phenomena, numerous theoretical
models of bursting have been developed[2－5], and they all require at least two different time scales, one on
the scale of slow modulations and the other on the scale of individual action
potentials. However, bursting has distinct types. A formal classification
scheme was first described by Rinzel[6]. After that, Bertram et al.[7]
classified bursting into several types in detail from the viewpoint of topology
and phenomenology; the advantage of this scheme consists in its directness and
visualization. Izhikevich[8] proposed another scheme from the bifurcation
mechanism for producing bursting, which is more reasonable from the viewpoint
of nonlinear dynamics. In this study, we will concern ourselves with a specific
type of bursing called parabolic bursting according to the second scheme, but
circle/circle bursting following the third scheme. To our knowledge, this
phenomenon, parabolic bursting induced by veratridine is observed in neurons of
rat injured sciatic nerve, has never been reported before. This discharge
pattern has a significent feature, that is, the instantaneous spike frequency
is low at both the beginning and the end of a bursting, and high at the middle
section of the bursting. Therefore, the series of interspike interval(ISI),
which denotes the time elapsed between two successive spikes, looks like a
parabolic curve, and thus the discharge pattern is named parabolic bursing.
Nowadays, it is widely considered that the information detected by sensory
neurons from external enviroment is contained in the ISI series[9].
Consequently, we take great interest in both the time course of membrane
potential and ISIs in experimental recording and numerical analysis of a
theoretical model.
From a number of
physiological experiments about rat injured peripheral nerves, it has been
found that experimental ectopic pacemakers, which generate spontaneous
discharges in various rhythms, are formed at the injured site of the rat
sciatic nerve subjected to chronic injury[10－12]. Such spontaneous discharges are inputted into the central
nervous system and recongnized as afferent message from the receptive field of
the injured nerve, causing abnormal sensations, such as hyperalgesia,
spontaneous pain and paraesthesia[10,13,14]. Recent study suggests that sodium
channels, potassium channels and calcium channels as well as calcium-dependent
potassium channels were involved in the generation of the spontaneous discharges.
The discharge frequency and pattern play an important role in determing the
property and intensity of sensation. Latest work[15, 16] shows that discharge
pattern is connected with the distribution of sodium channels and the variation
in their activity. However, there are still some problems, such as what role
the inactivation gate of sodium channels plays in producing a discharge pattern
and how it affects the discharge pattern and so on, remaining unclear. The
studies on these problems may give us some hints to understand the relationship
between the inactivation gate of sodium channels and the discharge pattern, and
further to explore the mechanism for neural encoding. Therefore, veratridine,
an inhibitor of the inactivation gate of sodium channels, was applied to the
injured sciatic nerve in order to observe the changes in the ISI series and
time course of membrane potental. To our surprise, parabolic bursting was
observed after the application of veratridine. We use Plant model to account
for the mechanism for parabolic bursting from the perspective of nonlinear
dynamics and further clarify the role of veratridine and the reason for the
emergence of the parabolic bursting in our experiments based on ionic channels.
Although Plant model is to describe an invertebrate neuron, its firing pattern
is the same as that of our experimental pacemaker. Hence, the model is
effective for our purpose. We expect the analysis method in this study can
provide a new path to explore the pharmacodynamics of drugs.
1 Materials
and Methods
and Methods
Experimental pacemakers were formed at the injured
site of a rat sciatic nerve subjected to chronic compression operated as
described by Bennett et al.[10]. Adult Sprague-Dawley rats of both sexes,
weighing 200－300 g, were anesthetized with
pentobarbital sodium (40 mg/kg, i.p.). Under aseptic condition, the right
sciatic nerve was exposed at mid-high level and approximately 1 cm of the nerve
was freed of connective tissue. 3 or 4 ligatures were tied so as to loosely
constrict the sciatic nerve. The muscle and skin were then closed in layers and
the animals allowed 7－12 days to recover
from surgery before electrophysiological recordings.
The recording method was described in
references[10－12]. The membrane potential and
interspike intervals were recorded. Our experimental setup was shown in Fig.
1(A) and Fig. 1(B).
Fig.1 The experimental setup
(A)
Schematic diagram of the experimental setup; (B) Enlargement of the operational
area of the injured sciatic nerve.
2 Results
2.1 Parabolic
bursting in pacemakers
Experimental
results are illustrated in Fig. 2 and Fig. 3. Fig. 2 exhibits a periodic
parabolic bursting inthe pacemaker after the addition of 5 μmol/L veratridine.
The upper trace is the time course of membrane potential, and mainly exhibits
the active phase of one burst; while the ISI as a function of time is shown in
the lower trace. It can be seen clearly that parabolic bursting is
characterized by a spike frequency which is low at the beginning, high in the
middle, and low again near the end of the active phase. ISI series looks like a
family of parabolic curves, as seen in the lower trace.
|
Fig.2 The |
Fig.3 The |
A neuron
displaying beating was chosen as our experimental object at the injured site of
sciatic nerve, as shown in the upper trace of Fig. 3. It can be seen that the
ISI of the neuron decreases gradually at the beginning of the addition of 5
μmol/L veratridine in the lower trace of Fig.3, and then shows small amplitude
oscillation without discontinuity, and finally parabolic bursting occurs.
2.2 Parabolic
bursting in Plant model
To make clear
how the parabolic bursting is induced by 5 μmol/L veratridine in rat injured
sciatic nerve, the discharge pattern of parabolic bursting was represented in
the Plant model to illustrate the underlying mechanism.
Actually, many
scholars investigated parabolic bursting and proposed some theoretical
models[17－23]. Here,
Plant model[24], which was motivated by experimental data from the R-15
pacemaker neurons of Aplysia, is analyzed numerically. Our intention is not to
explore the bifurcation mechanism for parabolic bursting in this model, but to
illustrate the necessary condition for parabolic bursting.
Plant’s model
takes the form:
With the above
equations integrated numerically, it can be clearly seen that the time course
of membrane potential displays bursting from Fig.4, and spike frequency is low
at the beginning and the end of bursting. Namely, the model exhibits parabolic
bursting. The ISI series looks like a family of parabolic curves, as shown in
Fig.5.
|
Fig.4 Time |
Fig.5 ISI
|
Existing
theoretical results show that a model requires at least two slow variables in
order to produce parabolic bursting[7, 17－23]. This point is different from other types of bursting, such as
square-wave bursting, which can occur with only one slow variable. Parabolic
bursting is due to passage of the bursting trajectory through a saddle-node on
an invariant circle bifurcation both at the beginning and at the end of the
active phase[7, 8, 22]. The two slow variables interact with the fast subsystem
to generate an oscillation on a slow time scale, driving the fast subsystem
back and forth through a silent and an active phase.
In Plant model,
V, h and n are regarded as fast variables and form the fast subsystem, while x
and Ca are regarded as slow variables and constitute the slow subsystem[22].
Biophysically, x is a conductance with slow change for an inward calcium
current; Ca is dominated by slow kinetics and represents the slowly changing
concentration of intracellular free calcium, which activates an outward
potassium current[22]. Parabolic bursting is due to these two slow variables
with opposing effects.
3 Discussion
3.1 Mechanism for spontaneous firing
of pacemakers
To our
knowledge, a large number of ion channels accumulate in the nerve membrane at
the injured area following the nerve injury, and make the ionic permeability
increase greatly, and thus form ectoptic pacemaker, where the spontaneous
afferent discharges occur. The further research indicates that sodium,
potassium and calcium current all participated in spontaneous discharge.
Existence of calcium-dependent potassium channels has been confirmed in the
injured sciatic nerve in the previous physiological experiments[25].
Our experimental
studies on the mechanism for the spontaneous discharge of bursting in rat
injured nerve show the onset of quiescence relates to calcium influx and
calcium-dependent potassium current. When calcium influx is facilitated, the
period of quiescence will shorten and even disappear; whereas the blockage of
calcium-dependent outward potassium current can reverse the action of promoting
the calcium influx and result in the onset of quiescence. This suggests that
when the calcium infux becomes stronger or the rate of calcium clearance
becomes slower in the pacemaker of spontaneous discharge in the injured nerve,
the concentration of intracelluar free calcium increases gradually, and leads to
the enhancement of calcium-dependent outward potassium current, and thus
promotes the action of repolarization. With the increase of the action of
repolarization to a certain degree, it can terminate the underlying oscillation
which is on the basis of sodium infux and potassium outflux, and then results
in the cessation of spike. In this way, the calcium influx decays, and the
concentration of intracelluar free calcium goes down to rest level.
Accordingly, the calcium-dependent outward potassium current weakens, and
finally repolarization becomes neglectable.
3.2
Role of veratridine
It is evident
that the calcium-dependent outward potassium current is a slow variable and
participates in the emergence of bursting in our experiments. According to the
analysis for Plant model, a system for parabolic bursting requires at least two
slow variables. In order to obtain the slow oscillation that underlies
parabolic bursting we need yet another slow variable so that there are opposing
influences of slow positive and slow negative feedback.
Since the
discharge pattern of a neuron can be transformed from beating into parabolic
bursting only when 5 μmol/L veratridine is applied, there is a reason to
believe that a slow inward current is induced by veratridine. This point is
deduced by making use of the above prerequisite for parabolic bursting. It is
well known that veratridine is a depolarizing agent that causes sodium channels
to stay open a sustained membrane depolarization by abolishing inactivation. As
for the detailed action of veratridine, it is not completely clear for us.
However, there are two points known for us. One is that a slow variable can be
elicited by veratridine, the other is that veratridine is an inhibitor of
inactivation gate of sodium channels. According to the two points, we can draw
a conclusion that a slow inward sodium current is induced by veratridine. It is
the slow inward sodium current and the slow outward calcium-dependent potassium
current that have opposing effects and govern the slow dynamics of the neuronal
firing and result in parabolic bursting in rat injured sciatic nerve. This
opnion that the slow sodium influx is induced by veratridine is in good
agreement with that of the documents[26, 27], although our experimental objects
are different from those used in these documents, where the objects are rat
hippocampal CA1 pyramidal neurons and human neuroblastoma cells, respectively.
As a result, role of veratridine is uncovered in the experimental pacemaker.
Note that there
is no corresponding theoretical model to describe the activities of
experimental pacemakers in rat injured sciatic nerve because the role of the
inactivation gate of sodium channels is unclear yet. Hence, we can make merely
such qualitative analyses.The role of drug can be revealed from the viewpoint
of nonlinear dynamics. For example, If the change in the discharge pattern is
observed after the application of a drug, it is probably a bifurcation
phenomenon that has been uncovered in a nonlinear dynamical system. And then,
we can return to experimental phenomenon to understand the action of the drug.
Here, we have made parabolic bursting induced by veratridine related to its
emergence in Plant model, and make use of this model and existing conclusions
to reveal the role of veratridine from the perspective of nonlinear dynamics.
This may provide a new method to analyze pharmacodynamics of drugs.
Acknowledgements We would
like to thank Dr. HE Dai-Hai and WANG Ye-Hong for helpful discussion.
References
1 Lisman
JE. Bursts as a unit of neural information: Making unreliable synapses
reliable. TINS, 1997, 20(1): 38－43
2 Chay
TR, Rinzel J. Bursting, beating, and chaos in an excitable membrane model.
Biophys J, 1985, 47: 357－366
3 Fan
YS, Chay TR. Generation of periodic and chaotic bursting in an excitable cell
model. Biol Cybern, 1994, 71: 417－431
4 Av-Ron
E, Parnas H, Segel LA. A basic biophysical model for bursting neurons. Biol
Cybern, 1993, 69: 87－95
5 Chay
TR, Keizer J. Minimal model for membrane oscillations in the pancreatic β-cell.
Biophys J, 1983, 42: 181－190
6 Rinzel
J. A formal classification of bursting mechanisms in excitable systems. In:
Mathematical Topics in Population Biology, Morphogenesis and Neurosciences,
Teramoto E and Yamoguti M eds， Lecture Notes in Biomathematics, 1987, 71: 267－281
7 Bertram
R, Butte MJ, Kiemel T, Sherman A. Topological and phenomenological
classification of bursting oscillations. Bull Math Biol, 1995, 57(3): 413－439
8 Izhikevich
EM. Neural excitability, spiking, and bursting. Int J Bifur Chaos, 2000, 10:
1171－1266
9 Gong
PL, Xu JX, Long KP, Hu SJ. Chaotic interspike intervals with multipeaked
histogram in neurons. Int J Bifur Chaos, 2002, 12(2): 319－328
10 Bennett
GT, Xie YK. A peripheral mononeuropathy in rat that produces disorders of pain
sensation like those seen in man. Pain, 1988, 33: 87－107
11 Ren
W, Hu SJ, Zhang BJ, Wang FZ, Wang FZ, Gong YF, Xu JX. Period-adding bifurcation
with chaos in the interspike intervals generated by an experimental neural
pacemaker. Int J Bifur Chaos, 1997, 7(8): 1867－1872
12 Duan
YB, Hu SJ, Jian Z, Duan JH. Three types of induced bursting rhythm in rat
injured nerves. Acta Physiologica Sinica, 2002, 54(4): 329－332
13 Hu
SJ, Xing JL. An experimental model for chronic compression of dorsal root
ganglion produced by intervertebral foramen stenosis in the rat. Pain, 1998,
77: 15－23
14 Song
XJ, Hu SJ, Greenquist KW, Zhang JM, LaMotte RH. Mechanical and thermal
hyperalgesia and ectopic neuronal discharge after chronic compression of dorsal
root ganglion. J Neurophysiol, 1999, 82(6): 3347－3358
15 Duan
JH, Duan YB, Han S, Hu SJ. Slow wave oscillation induced by veratridine in
injured dorsal root ganglion neurons. Acta Biophysical Sinica, 2002, 18(1): 49－52
16 Duan
JH, Duan YB, Xing JL, Hu SJ. Triggered oscillations in type A dorsal ganglion
neurons induced by veratridine. Acta Physiologica Sinica, 2002, 54(3): 208－212
17 Rinzel
J, Ermentrout G.B. Analysis of neural excitability and oscillations. In:
Methods in Neuronal Modeling: From Synapses to Networks, Koch C and Segev I
eds, 1989, MIT Press, Cambridge MA
18 Terman
D, Rubin J. Geometric singular perturbation analysis of neuronal dynamics. In:
Handbook of Dynamical Systems II, Fiedler B ed. 2002, Elsevier, Amsterdam
19 Baer
SM, Rinzel J, Carrillo H. Analysis of an autonomous phase model for neuronal
parabolic bursting. J Math Biol, 1995, 33: 309－333
20 Ermentrout
GB, Kopell N. Parabolic bursting in an excitable system coupled with a slow oscillation.
Siam J Appl Math, 1986, 46(2): 233－253
21 Soto-TreviJ
Math Biol, 1996, 35(1): 114－128
22 Rinzel
J, Lee YS. Dissection of a model for neuronal parabolic bursting. J Math Biol,
1987, 25: 653－675
23 Chay
TR, Cook DL. Endogenous bursting patterns in excitable cells. Math Biosci,
1988, 90: 139－153
24 Plant
RE. Bifurcation and resonance in a model for bursting nerve cells. J Math Biol,
1981, 11: 15－32
25 Duan
YB. Nonlinear dynamics in interspike intervals of an experimental neural
pacemaker. PhD dissertation, 2002, Fourth Military Medical University
26 Alkadhi
KA, Tian LM. Veratridine-enhanced slow sodium current induces epileptiform
discharge in the hippocampus. Neuroscience, 1996, 71(3): 625－632
27 Patt
S, Wlasak R, Kraft R. Influence of voltage-activated sodium channels on growth
and motility of human neuroblastoma cells in vitro. Fourteenth International
Congress of Neuropathology in Birmingham, 2000, England
Received:
April 14, 2003 Accepted:
June 16, 2003
This work was
supported by a grant from the National Natural Science Foundation of China (No.
30030040)
*Corresponding
author: Tel, 86-29-2668751; Fax, 86-29-3237910; e-mail, [email protected]