Http://www.abbs.info e-mail:[email protected]

ISSN 0582-9879                 ACTA BIOCHIMICA et BIOPHYSICA SINICA 2003, 35(9): 806-810                  CN 31-1300/Q

 

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

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 time course of membrane potential and ISI series of parabolic bursting

Fig.3       The discharge pattern of a neuron exhibiting beating was transformed into parabolic bursting after addition of 5 μmol/L veratridine

 

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 course of membrane potential of parabolic bursting

Fig.5       ISI versus series number

 

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]