A modeling study predicts the presence of voltage gated Ca2+ channels on myelinated central axons

Computer Methods and Programs in Biomedicine 71 (2003) 25 – 31 www.elsevier.com/locate/cmpb

A modeling study predicts the presence of voltage gated Ca2 + channels on myelinated central axons Angus M. Brown * Department of Neurology, Box 356465, Uni6ersity of Washington School of Medicine, Seattle, WA 98195, USA Received 17 July 2001; received in revised form 13 March 2002; accepted 21 March 2002

Abstract The objective of this current study was to investigate whether voltage gated Ca2 + channels are present on axons of the adult rat optic nerve (RON). Simulations of axonal excitability using a Hodgkin– Huxley based one-compartment model incorporating INa, IK and leak currents were used to predict conditions under which the potential contribution of a Ca2 + current to an evoked action potential could be measured. Under control conditions the inclusion of a high threshold Ca2 + current (ICa) in the model had a negligible effect on the action potential. Reducing IK, by decreasing the value of gK, elongated the repolarizing phase of the action potential, increasing its duration. Subsequent incorporation of ICa in the model revealed a significant ICa contribution to the repolarizing phase of the action potential. The simulation thus suggests that Ca2 + channels may be present on RON axons, but that pharmacological intervention is required to unmask their presence. Experiments based on the simulations revealed that there was no significant contribution of ICa to the control action potential. However, as predicted by the simulation, reducing the repolarizing effect of IK by adding the K+ channel blocker 4-AP revealed a Ca2 + component on the repolarizing phase of the action potential that was blocked by the Ca2 + channel inhibitor nifedipine. © 2002 Elsevier Science Ireland Ltd. All rights reserved. Keywords: ICa; Action potential; Nifedipine; Hodgkin Huxley model; Simulation

1. Introduction This article is an extension of two previous studies that described in detail the implementation

* Tel.: +1-206-616-8278; fax: +1-206-685-8100. E-mail address: [email protected] Brown).

(A.M.

and execution of simulating biological systems using a Microsoft Excel spreadsheet [1,2]. The focus of this current study was to use the simulation to predict whether voltage gated Ca2 + channels could be present on axons of the adult rat optic nerve (RON). The presence of voltage gated Ca2 + channels on RON axons has been in doubt for the last 20 years [3–5]. Electrophysiological evidence suggested that high threshold Ca2 + channels were absent from axons due to the inef-

0169-2607/02/$ - see front matter © 2002 Elsevier Science Ireland Ltd. All rights reserved. PII: S 0 1 6 9 - 2 6 0 7 ( 0 2 ) 0 0 0 3 1 - 7

26

A.M. Brown / Computer Methods and Programs in Biomedicine 71 (2003) 25–31

fectiveness of Ca2 + channel blockers to alter the stimulus evoked compound action potential (CAP) shape under control conditions [3,4], Imaging studies, however, have shown increases in intracellular [Ca2 + ] evoked by axon stimulation [6–8], but it is difficult to say with any degree of certainty that the Ca2 + signals originated in axons rather than surrounding glial cells. In addition, the fact that inhibitors of voltage gated Ca2 + channels reduced anoxic injury in adult RON suggested a Ca2 + channel presence [3], although a similar study found no evidence of Ca2 + channels [9]. While Ca2 + channels are located on peripheral [10,11] and central [8,12,13] unmyelinated axons, no study to date has convincingly shown Ca2 + channels on adult central myelinated axons. This is not an academic point, as both anoxic [14] and hypoglycemic injury [15] in the adult RON are dependent upon extracellular Ca2 + , and the presence of Ca2 + channels on axons would offer a direct pathway for toxic Ca2 + flux into axons during anoxia and/ or hypoglycemia, implicating the use of Ca2 + channel blockers as potential neuroprotective agents of white matter during anoxic/hypoglycemic insults such as lacunar infarcts (white matter stroke) or secondary spinal cord trauma. To investigate the presence of Ca2 + channels on axons a simulation based on the Hodgkin– Huxley model [16] was carried out using a onecompartment model containing INa, IK and leak currents. The contribution of a high threshold Ca2 + current was investigated by including ICa in the model. The simulation data suggested that under control conditions the contribution of ICa to an evoked action potential was negligible, explaining why previous electrophysiological studies have been inconclusive. However, increasing the duration of the repolarizing phase of the action potential by decreasing IK unmasked a contribution by ICa to the action potential. Experiments based on the simulations indicated that under normal conditions the Ca2 + current contribution to the action potential was negligible, but when IK was reduced

by the K+ channel blocker 4-AP, a Ca2 + component of the action potential was unmasked.

2. Methods

2.1. Simulation Full details of the methodology and its implementation are described in detail elsewhere [1,2].

2.2. Preparation All experiments were carried out in accordance with the guidelines for Animal Care of the University of Washington. Long Evans rats, aged 45+ days, were deeply anesthetized with 80% CO2/20% O2 in an enclosed chamber then decapitated. The optic nerves were removed and placed in an interface perfusion chamber (Medical Systems Corp, Greenvale, NY, USA). RONs were maintained at 37 °C and perfused with artificial cerebrospinal fluid (aCSF) bubbled with 95% O2, 5% CO2 (pH 7.45), which contained (in mM): 153 Na+, 3 K+, 2 Mg2 + , 2− 2 Ca2 + , 143 Cl−, 26 HCO− and 3 , 1.25 HPO4 10 glucose. Nerves were constantly aerated with humidified gas mixture supplied at 2 l min − 1. Nerves were allowed to equilibrate for 60 min before recording commenced. A stock solution of 10 mM nifedipine was dissolved in 100% ethanol and added to aCSF to give a final concentration of 10 mM. All experiments using nifedipine were carried out in reduced ambient light. A suction electrode back-filled with aCSF was attached to the distal end of the nerve and stimulated every 30 s (WPI, Sarasota, FL, USA: Isostim 130). A recording suction electrode filled with aCSF was attached to the proximal end of the nerve to record the CAP, which was evoked by a 125% supramaximal stimulus (50 vs duration). CAPs were recorded using a suction electrode connected to an Axoclamp 2A amplifier; the signal was amplified 500× , filtered at 30 kHz and acquired at 25 kHz. Data were acquired online (Axon Instru-

A.M. Brown / Computer Methods and Programs in Biomedicine 71 (2003) 25–31

ments, Digidata 1200A) using proprietary software (Axon Instruments, Axotape).

3. Results

3.1. Simulation In order to simulate action potential conduction of an RON axon a one-compartment model containing a Na+ current, a K+ current and leak currents based closely on the model described in squid giant axon [16] was utilized, although the rate constants were based on data from mammalian preparations, rather than squid giant axon. The current clamp simulation illustrated in Fig. 1 shows the changes in membrane potential in response to a constant current pulse injection. In current clamp mode the change in membrane potential with respect to time is described by; dV (Iinj + INa +IK +INaleak +IKleak) = Cn dt

(1)

27

where Iinj is injected current; INa describes the transient Na+ current that underlies action potential generation; IK describes the delayed rectifier K+ current that repolarizes the action potential; INaleak and IKleak are linear leak conductances. Cn was 1 mF cm − 2; dt was set at 10 ms. The transient Na+ current is described by the following equations [16]; vA cm − 2

INa = g*Na (Vm − ENa)

(2)

where Vm is the membrane potential, ENa is the equilibrium potential for Na+ (+ 45 mV), and gNa is the maximal conductance and is described by; gNa = 20* m3h

S cm − 2

(3)

m and h are the activation and inactivation parameters, respectively. In all Hodgkin–Huxley style descriptions, the steady state (in)activation variable is described by; m(h)=

h h+i

(4)

The rate constants for INa (in)activation [17] are;



0.091*(V+ 38) − (V+ 38) 1− exp 5 − 0.062*(V+ 38) im= (V+38) 1 − exp 5 (− 55− V) hh= 0.016*exp 15

hm=



ih= Fig. 1. Model of axonal action potential. (A) An axon containing INa, IK and leak currents displays an action potential in response to injected current of 8 nA for 1 ms (see bottom trace for current injection profile) Scale bars are 1 ms; 50 mV and apply to B and C. Including a high threshold Ca2 + current in the model did not significantly affect the action potential although it resulted in a slight increase in the repolarizing phase. (B) Reducing IK to simulate the addition of a K+ channel blocker resulted in a prolonged action potential compared with control. (C) Inclusion of the high threshold Ca2 + current in the model with reduced IK reveals a Ca2 + current contribution to the action potential.



n

n



(5)

(6)

n

2.07 17−V exp +1 21

n

(7) (8)

The delayed rectifier is described by; IK = g*K (Vm − EK)

vA cm − 2

(9)

where gK is the maximal conductance and is described by; gK = 2*n 4

S cm − 2

(10)

EK is the equilibrium potential for K+ (− 105 mV). n is the activation variable, where

A.M. Brown / Computer Methods and Programs in Biomedicine 71 (2003) 25–31

28

n=

hn hn + in

(11)

and the rate constants [18] are;



0.01*(−45−V) −45−V exp −1 5 exp(− 50− V) in = 0.17* 40 hn =

n

(12)

(13)

ICa is a high threshold Ca2 + current modeled using the Goldman Hodgkin Katz constant field equation [19]; VmF 2 RT

ICa = m2Pz2*

− zFVm RT −zFVm 1− exp RT

[Ca2 + ]i − [Ca2 + ]*exp 0 ×

vA cm − 2 (14)

where P is the maximum permeability (80×10 − 6 cm3 s − 1), F =96480 C mol − 1, R =8.315 J K − 1, T= 295 K and z= + 2. The activation parameter is described by; m=

hm hm+ im

(15)

and the rate constants [20] are; hm=

1.6 1+ exp[− 0.072*(V −5.0)]



(16)

0.02*(V −1.31) (17) (V−1.31) exp −1 5.36 Finally the leak conductances are linear functions [21] described by; im =

n

IKleak = 0.007*(Vm +105) INaleak =0.00265*(Vm −45)

vA cm − 2

(18)

vA cm

(19)

−2

The simulation was carried out using the method of Brown [2] and verified using the CCLAMP simulation program [22]. A simulated action potential containing INa, IK and the leak currents evoked by current injection of 8 nA for 1 ms from a resting membrane potential (Em) of −70 mV is illustrated in Fig. 1A. The

action potential takes about 1 ms to peak at + 30 mV and a further 1 ms to repolarize to Em. Incorporating a high threshold Ca2 + current (ICa) with a permeability of 80× 10 − 6 cm3 s − 1 in the model did not affect the rising phase of the action potential, but slightly delayed the repolarizing phase resulting in a small increase in the action potential duration. Reducing IK, which causes membrane repolarization, by decreasing gK to 0.5 from 2, had no effect on the rising phase of the action potential but significantly delayed the repolarizing phase, almost doubling the action potential duration (Fig. 1B). When ICa was incorporated into the model in addition to reduction of IK, ICa had a much greater effect on the action potential then under control conditions (Fig. 1C). There was no effect on the depolarizing phase of the action potential but there was a distinct increase in action potential duration due to the increased repolarizing phase. Thus reducing the repolarizing effect of IK unmasked a contribution of ICa to the action potential. There are obvious differences between modeling a single action potential and using extracellular recording techniques to record a CAP in the RON, which is the summed contribution of 100 000 axons. However, prior modeling studies have shown that compound action potentials can be accurately reconstructed from experimentally recorded single axon fiber properties [23]. Thus, the simulation was an encouraging springboard from which to embark upon experimental analysis of the potential role of Ca2 + currents in RON axons.

3.2. Experiments In the RON perfused with control aCSF, the evoked CAP had the characteristic three peaks previously described with a total duration of 2 ms (Fig. 2A, [4]). The CAP area was unchanged by addition of 10 mM nifedipine, an L-type Ca2 + channel blocker (Fig. 2A). Ca2 + influx, therefore, has a negligible role in axonal conduction under normal conditions. In several mammalian unmyelinated preparations, blockade of a delayed rectifier K+ current is required before the Ca2 + contribution to an action potential is revealed [11,13]. Addition of 1 mM 4-aminopyridine (4-AP) increased CAP duration

A.M. Brown / Computer Methods and Programs in Biomedicine 71 (2003) 25–31

Fig. 2. Stimulus evoked CAP from rat optic nerve. (A) Addition of 10 mM nifedipine had no significant effect on the evoked CAP (control and treated CAPs overlap). Scale bars are 1 ms and 1 mV. (B) Addition of 1 mM 4-AP resulted in augmentation of CAP area and prolonged the duration of the CAP from 2 ms to 20 ms. Scale bars are 2 ms and 1 mV. (C) Exposure of 4-AP treated nerves to 10 mM nifedipine caused a decrease in the repolarizing phase of the CAP. Scale bars are 2 ms and 1 mV.

from 2 ms to over 20 ms, the effect being greater on the slower third peak than on the faster, first peaks (Fig. 2B, see [4]). Experiments were conducted to determine if inhibition of IK revealed a Ca2 + contribution to the CAP. Addition of 10 mM nifedipine, an L-type Ca2 + channel blocker, to a 4-AP treated nerve resulted in a reversible reduction in the repolarizing phase of the action potential (Fig. 2C). These results suggested that there is a Ca2 + contribution to the action potential, and that at least part of the Ca2 + current contributing to the CAP occurred via nifedipine-sensitive L-type Ca2 + channels.

4. Discussion The present data are consistent with the presence of Ca2 + channels on axons of the adult RON, although it is clear that Ca2 + channels play no role in action potential conduction under control conditions [3,4], In other nerve preparations the apparent absence of a Ca2 + current contribution the control

29

action potential has been demonstrated, only for subsequent pharmacological intervention to unmask a Ca2 + component of the action potential [8,10,13]. Reduction of the delayed rectifier (IK) by addition of IK channel blockers greatly enhances the action potential duration by increasing the repolarizing phase of the action potential, and it is during this repolarizing phase that the Ca2 + current contribution is seen. This is logical for several reasons. First, the Na+ channels would be inactivated and closed by this stage. Given their high density and rapid activation kinetics they would tend to mask any contribution of Ca2 + channels during the depolarizing phase. Second, the time constant for Na+ channel activation tends to be more rapid than for Ca2 + channels, thus Na+ channels would tend to have activated and inactivated before Ca2 + channel activation occurred [19]. Third, the nifedipine-sensitive Ca2 + channel does not have rapid inactivation kinetics and once activated remains in the open state for comparatively long periods of time. Thus, the Ca2 + current would remain open during the prolonged repolarization phase of a 4-AP treated nerve resulting in sustained Ca2 + influx. The present results support previous experimental evidence suggesting the presence of Ca2 + channels on axons on adult RON [3,6–8]. If Ca2 + channels are present on axons they would surely act as a route for toxic Ca2 + influx into axons during anoxia and hypoglycemia, as the axonal membrane depolarization required to activate the high threshold Ca2 + channels occurs during both of these insults [24,25]. What role the Ca2 + channels play under physiological conditions is unknown, but Ca2 + influx via the L-type channels may act to down-regulate excitability by inactivating ion channels [26,27] or by affecting gene translation [28]. The data presented in this paper suggested that Ca2 + channels were present on the axons of RON and a more detailed study was carried out that utilized both electrophysiological and immunocytochemistry techniques [14]. The electrophysiological data demonstrated a reduction in the repolarizing phase of the action potential from a 4-AP treated RON by both low Ca2 + containing aCSF and cadmium. These data suggested that a voltage gated Ca2 + channel was contributing to the repolarizing phase of the action potential. Inhibition of the repolarizing phase by

30

A.M. Brown / Computer Methods and Programs in Biomedicine 71 (2003) 25–31

nifedipine, an L-type Ca2 + channel blocker, indicated the presence of L-type Ca2 + channels. Indeed the fact that nifedipine produced the same degree of inhibition as cadmium suggested that solely L-type Ca2 + channels were present. Immunocytochemical evidence supported this by showing that only antibodies that specifically recognize the al subunits of classes C and D (specific for L-type channels) stained the RON [14]. In addition we have subsequently shown that axonal L-type Ca2 + channels are a route of Ca2 + influx into axons during both anoxia [14] and hypoglycemia [15]. This suggests that Ca2 + channel blockers may be used as neuroprotective agents to attenuate injury in white matter that occurs during anoxia and/or hypoglycemia, such as lacunar infarcts or secondary spinal cord trauma. In summary, while perhaps the most important aspect of modeling biological systems is that the model accurately reproduces the behavior of the system, the data in this paper indicates that another important function of modeling is the ability of the model to predict unexpected behavior of the system upon which the model is based.

Acknowledgements This research was supported by the Eastern Paralyzed Veterans Association (AMB and BRR).

References [1] A.M. Brown, A methodology for simulating biological systems using Microsoft Excel, Comp. Meth. Prog. Biomed. 58 (1999) 181 –190. [2] A.M. Brown, Simulation of axonal excitability using a spreadsheet template created in Microsoft Excel, Comp. Meth. Prog. Biomed. 63 (2000) 47 –54. [3] R. Fern, B.R. Ransom, S.G. Waxman, Voltage-gated calcium channels in CNS white matter; role in anoxic injury, J. Neurophysiol. 74 (1995) 369 – 377. [4] R.E. Foster, B.W. Connors, S.G. Waxman, Rat optic nerve: electrophysiological, pharmacological and anatomical studies during development, Dev. Brain Res. 3 (1982) 371 – 386. [5] P.K. Stys, Anoxic and ischemic injury of myelinated axons in CNS white matter; From mechanistic concepts to therapeutics, J. Cereb. Blood Flow Metab. 18 (1998)

2 – 25. [6] S. Kriegler, S.Y. Chiu, Calcium signaling of glial cells along mammalian axons, J. Neurosci. 13 (1993) 4229 – 4245. [7] V. Lev-Ram, A. Grinvald, Activity-dependent calcium transients in central nervous system myelinated axons revealed by the calcium indicator Fura-2, Biophys. J. 52 (1987) 571 – 576. [8] B.B. Sun, S.Y. Chiu, N-type calcium channels and their regulation by GABAB receptors in axons of neonatal rat optic nerve, J. Neurosci. 19 (1999) 5185 –5194. [9] P.K. Stys, B.R. Ransom, S.G. Waxman, Effects of polyvalent cations and dihydropyridine calcium channel blockers on recovery of CNS white matter from anoxia, Neurosci. Lett. 115 (1990) 293 – 299. [10] P. Elliott, S.J. Marsh, D.A. Brown, Inhibition of Caspikes in rat preganglionic cervical sympathetic nerves by sympathomimetic amines, Br. J. Pharmacol. 96 (1989) 65 – 76. [11] J. Wachtler, C. Mayer, P. Grafe, Activity-dependent intracellular Ca2 + transients in unmyelinated nerve fibres of the isolated adult rat vagus nerve, Pflu¨ gers. Archiv. 435 (1998) 678 – 686. [12] G. Callewaert, J. Eilers, A. Konnerth, Axonal calcium entry during fast ‘sodium’ action potentials in rat cerebellar Purkinje neurones, J. Physiol. 495 (1996) 641 – 647. [13] C.N. Scholfield, Presynaptic Na/Ca action potentials in unmyelinated axons of olfactory cortex, Pflu¨ gers. Archiv. 411 (1988) 180 – 187. [14] A.M. Brown, R.E. Westenbroek, W.A. Catterall, B.R. Ransom, Axonal L-type Ca2 + channels and anoxic injury in rat CNS white matter, J. Neurophysiol. 85 (2001) 900 – 911. [15] A.M. Brown, R. Wender, B.R. Ransom, Ionic mechanisms of aglycemic axon injury in mammalian central white matter, J. Cereb. Blood Flow Met. 21 (2001) 385 – 395. [16] A.L. Hodgkin, A.F. Huxley, A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117 (1952) 500 – 544. [17] J.R. Huguenard, O.P. Hamill, D.A. Prince, Developmental changes in Na+ conductances in rat neocortical neurons: appearance of a slowly inactivating component, J. Neurophysiol. 59 (1988) 778 – 795. [18] D.A. McCormick, J.R. Huguenard, A model of the electrophysiological properties of thalamocortical relay neurons, J. Neurophysiol. 68 (1992) 1384 – 1400. [19] B. Hille, Ionic Channels of Excitable Membranes, Sinauer Associates Inc, Sunderland, MA, USA, 2001. [20] A.R. Kay, R.K. Wong, Calcium current activation kinetics in isolated pyramidal neurones of the CA1 region of the mature guinea-pig hippocampus, J. Physiol. 392 (1987) 603 – 616. [21] D.A. McCormick, D.A. Prince, Post-natal development of electrophysiological properties of rat cerebral cortical pyramidal neurones, J. Physiol. 393 (1987) 743 – 762. [22] J.P. Huguenard, D.A. McCormick, Electrophysiology of the Neuron: An Interactive Tutorial, Oxford University Press, New York, 1994.

A.M. Brown / Computer Methods and Programs in Biomedicine 71 (2003) 25–31 [23] K.L. Cummins, D.H. Perkel, L.J. Dorfman, Nerve fiber conduction-velocity distributions. I. Estimation based on the single-fiber and compound action potentials, Electroencephalogr. Clin. Neurophysiol. 46 (1979) 634 –646. [24] L. Leppanen, P.K. Stys, Ion transport and membrane potential in CNS myelinated axons. II. Effects of metabolic inhibition, J. Neurophysiol. 78 (1997) 2095 – 2107. [25] P.K. Stys, H. Sontheimer, B.R. Ransom, S.G. Waxman, Noninactivating, tetrodotoxin-sensitive Na+ conductance in rat optic nerve axons, Proc. Natl. Acad. Sci. USA 90 (1993) 6976 – 6980.

31

[26] I. Deschenes, N. Neyroud, D. DiSilvestre, E. Marban, D.T. Yue, G.F. Tomaselli, Isoform-specific modulation of voltage-gated Na+ channels by calmodulin, Circ. Res. 90 (2002) E49 – E57. [27] G.S. Pitt, R.D. Zuhlke, A. Hudmon, H. Schulman, H. Reuter, R.W. Tsien, Molecular basis of calmodulin tethering and Ca2 + -dependent inactivation of L-type Ca2 + channels, J. Biol. Chem. 276 (2001) 30794 – 30802. [28] G.E. Hardingham, S. Chawla, C.M. Johnson, H. Bading, Distinct functions of nuclear and cytoplasmic calcium in the control of gene expression, Nature 385 (1997) 260 – 265.