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1 Department of Microbiology and Molecular Genetics, University of California 92697-4025; 2 Department of Anatomy and Neurobiology, University of California, Irvine, California 92697-1280
Submitted 13 October 2003; accepted in final form 29 December 2003
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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2 subunit gene (GBRG2). The biophysical characterization of 3 mutations (T875M, W1204R, and R1648H) in SCN1A, the gene encoding the CNS voltage-gated sodium channel 
subunit Nav1.1, demonstrated a variety of functional effects. The T875M mutation enhanced slow inactivation, the W1204R mutation shifted the voltage dependency of activation and inactivation in the negative direction, and the R1648H mutation accelerated recovery from inactivation. To determine how these changes affect neuronal firing, we used the NEURON simulation software to design a computational model based on the experimentally determined properties of each GEFS+ mutant sodium channel and a delayed rectifier potassium channel. The model predicted that W1204R decreased the threshold, T875M increased the threshold, and R1648H did not affect the threshold for firing a single action potential. Despite the different effects on the threshold for firing a single action potential, all of the mutations resulted in an increased propensity to fire repetitive action potentials. In addition, each mutation was capable of driving repetitive firing in a mixed population of mutant and wild-type channels, consistent with the dominant nature of these mutations. These results suggest a common physiological mechanism for epileptogenesis resulting from sodium channel mutations that cause GEFS+. |
INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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; Singh et al. 1999). The disease is inherited in an autosomal dominant manner with incomplete penetrance (Scheffer and Berkovic 1997; Singh et al. 1999), and it is caused by mutations in one of 3 voltage-gated sodium channel genes (SCN1B, SCN1A, and SCN2A) or the GABAA receptor 2 subunit gene (GBRG2) (Abou-Khalil et al. 2001; Annesi et al. 2003; Baulac et al. 2001; Escayg et al. 2000, 2001; Harkin et al. 2002; Meisler et al. 2001; Sugawara et al. 2001; Wallace et al. 1998, 2001, 2002). Numerous additional mutations in SCN1A cause intractable childhood epilepsy with generalized tonic-clonic seizures (ICEGTC) and severe myoclonic epilepsy of infancy (SMEI), a more severe form of GEFS+ (Claes et al. 2001, 2003; Fujiwara et al. 2003; Gennaro et al. 2003; Scheffer et al. 2001; Sugawara et al. 2002; Veggiotti et al. 2001; Wallace et al. 2003).
SCN1A encodes the CNS voltage-gated sodium channel subunit Nav1.1, which is a 260-kDa transmembrane protein with 4 homologous domains, each with 6 transmembrane segments. Nav1.1 is one of 3 primary sodium channel subunits (along with Nav1.2 and Nav1.6) responsible for initiation and propagation of action potentials in the CNS. Nav1.1 mRNA is expressed during postnatal development predominantly in hippocampal pyramidal neurons, cerebellar Purkinje neurons, and spinal motor neurons (Black et al. 1994; Brysch et al. 1991; Furuyama et al. 1993; Novakovic et al. 2001), with the channel protein localized in a somatic distribution (Kaplan et al. 2001; Westenbroek et al. 1989).
We previously analyzed the effects of 3 Nav1.1 mutations that cause GEFS+ and we observed different biophysical effects on channel function for each mutation (Spampanato et al. 2001, 2003). T875M, located in the 4th transmembrane segment of the second domain, caused a negative shift in the voltage dependency of slow inactivation and a rapid entry into the slow inactivated state. W1204R, located in the cytoplasmic region between the 2nd and 3rd domains, caused a negative shift in the voltage dependency of both activation and inactivation. R1648H, located in the 4th transmembrane segment of the 4th domain, dramatically accelerated recovery from inactivation. To determine how these very different changes in sodium channel function affected neuronal activity, we designed a computational model using the experimentally defined characteristics of the mutant sodium channels and a generic delayed rectifier potassium channel. The computer simulations demonstrate that each mutation results in a greater propensity for the neuron to fire repetitive action potentials at a given stimulus intensity compared with neurons expressing the wild-type sodium channel.
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METHODS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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To study the effect of changes in sodium channel kinetics in GEFS+ mutations, Hodgkin–Huxley type conductance-based models of spiking neurons were constructed using the NEURON simulation software (Hines and Carnevale 1997). We constructed single-compartment models of neuronal soma that contained sodium channels and delayed rectifier potassium channels. Passive parameters similar to the passive properties of hippocampal principal cells (Spruston and Johnston 1992; Staley and Mody 1992) were adapted from previous models (Aradi and Soltesz 2002). The input resistance of the soma was 100 M
and the resting membrane potential was –60 mV.
The model neurons included either control sodium channels (Nav1.1) or one of the 3 mutations T875M, W1204R, or R1648H, for which we had previously characterized the electrophysiological properties (Spampanato et al. 2001, 2003). In all cases, the modeled sodium channel kinetics represented those that were determined during coexpression of the 
1 subunit. The model also included delayed rectifier potassium channels with kinetics similar to those used previously (Aradi and Holmes 1999). Although the interaction of the wild-type and mutant sodium channels with other potassium channels could vary depending on the type of potassium channels, we have chosen to use a simplified model in which only delayed rectifier channels are present so that any differences in the firing of action potentials between the mutant and wild-type cells could be attributed exclusively to changes in the sodium channel conductances. The sodium currents were described with activation and fast and slow inactivation as follows
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The steady-state activation and inactivation curves were fitted with Boltzmann functions as described previously (Spampanato et al. 2001, 2003) and the parameters of the fits are shown in Table 1. The fast and slow inactivation kinetics were fitted with the 3-parameter Gaussian function
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m, h, and s were used to provide time dependency to the conductance (Johnston and Wu 1995).
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The T875M mutation altered the parameters for steady-state slow inactivation and the time constant of slow inactivation, as follows (Fig. 1, A and B)
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The R1648H mutation altered the time constant of fast inactivation, as follows (Fig. 1D)
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In all simulations, the noninactivating potassium channel kinetics were the same as those used previously (Aradi and Soltesz 2002; Yuen and Durand 1991)
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mS/cm2, and
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Use-dependent sodium currents were recorded from the model neurons at 40 Hz using a 17.5 ms depolarizing potential from a holding potential of –100 mV to –10 mV. The protocol lasted for 1.5 s, and the currents were normalized to the initial peak current amplitude. This protocol is identical to the experimental procedure used to originally determine the effects of each GEFS+ mutation on sodium channel use dependency in Xenopus oocytes (Spampanato et al. 2001, 2003). Current-clamp simulations were carried out to study action potential (AP) threshold, AP shape, and repetitive firing properties in control and mutant model neurons.
Electrophysiological recording
Mutant channel characteristics were determined as described previously (Spampanato et al. 2001, 2003) by expression in Xenopus oocytes followed by electrophysiological analysis using both the 2-electrode voltage clamp and the cut-open oocyte voltage clamp. Wild-type and mutant subunits were coexpressed with the 1 subunit to produce faster channel kinetics that more closely resembled those observed in neurons. Use dependency was analyzed at a frequency of about 40 Hz using 17.5 ms depolarizations to –10 mV from a holding potential of –100 mV. The protocol was carried out for more than 1.5 s, which was longer than necessary for the current to reach an equilibrium value in each case. Data were analyzed using a baseline subtraction method in which the average current amplitude recorded during the last 1 ms of the final test pulse was subtracted from the peak current amplitude of each test pulse before normalization. Peak current amplitudes were normalized to the peak current amplitude during the first depolarization and plotted against time.
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RESULTS |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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The properties that are altered by each of the 3 GEFS+ mutations (T875M, W1204R, and R1648H) are shown in Fig. 1. The graphs show the fits to the experimental data (Spampanato et al. 2001, 2003), as described in METHODS. The voltage dependencies of activation [m(V)], fast inactivation [h(V)], and slow inactivation [s(V)] were fitted with a 2-state Boltzmann equation and the kinetics of fast inactivation (h) and slow inactivation (s) were fit with a 3-parameter Gaussian function. T875M produced a hyperpolarized shift in the voltage dependency of slow inactivation (V1/2 of –62 mV compared with –46 mV for wild-type Nav1.1) and accelerated the rate of entry into the slow-inactivated state (Fig. 1, A and B). W1204R shifted the V1/2 of steady-state activation to –26 mV and the V1/2 of steady-state inactivation to –45 mV compared with –21 and –40 mV, respectively, for wild-type Nav1.1 (Fig. 1C). R1648H dramatically accelerated recovery from inactivation (Fig. 1D).
To test the model's ability to accurately predict sodium channel behavior, we simulated a rapid series of depolarizations similar to the use-dependency protocol that we used to acquire data in our previous studies (Spampanato et al. 2001, 2003). The model neuron was rapidly depolarized from a holding potential of –100 mV to a test potential of –10 mV at a frequency of 40 Hz to elicit use-dependent sodium currents. The pulse train was maintained for about 1.5 s and the recorded sodium currents during each depolarization were normalized to the current amplitude during the first depolarization and plotted against time (Fig. 2). In each panel, the train of currents was generated using the model and the inset shows the first and last (after 1.5 s) traces recorded experimentally from the mutant channels. The W1204R channels displayed a level of use dependency that was similar to that of the wild-type channel, with the peak current reaching an equilibrium level <60% of the initial peak current. The T875M mutant displayed the largest use-dependent decrease with an equilibrium level <40% of the initial peak current. The R1648H channels displayed the least use dependency with an equilibrium level <80% of the initial peak current. In each case, the model correctly predicted the experimentally determined results (Spampanato et al. 2001, 2003), verifying the design of the model and validating its use in predicting the effects of the mutations on neuronal properties that we cannot experimentally determine at this time.
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Changes that result in neuronal hyperexcitability, such as a decrease in the threshold for generating action potentials, can be the primary cause of seizure activity. It seemed likely that one or more of the changes in voltage-dependent activation, fast inactivation, and slow inactivation could alter the action potential threshold. To determine the minimum stimulus that could initiate an action potential, model neurons expressing pure populations of either mutant or wild-type channels were injected with increasing amplitudes of current using the current-clamp feature of the NEURON simulator. A 50 ms adjustment period was applied first to allow the membrane conductance to settle to a steady state, after which a stimulus of 100 pA was applied and maintained for 200 ms. The resulting membrane potential of the neuron was calculated and plotted against time (Fig. 3). The amplitude of the injected current was increased by 25 pA each successive time until the cell fired an action potential. The model neuron expressing the wild-type Nav1.1 channel fired an action potential after injection of 250 pA of current. This threshold level was not significantly altered by the R1648H mutation. In contrast, the W1204R mutation produced the most excitable model neuron, with an action potential generated in response to a 175 pA current injection, and the T875M mutation produced the least excitable model neuron, requiring 275 pA of current to elicit a single action potential.
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Neurons fire repetitively in response to larger incoming stimuli, and an increased frequency of firing in response to a given stimuli can result in hyperexcitability and seizures. Neuronal burst firing is a known physiological mechanism of seizure generation (Dichter 1991) and antiepileptic drugs that target sodium channels are known to reduce the capability of a neuron to fire repetitive action potentials (Dichter 1991; Köhling 2002). Therefore we evaluated the effects of each of the mutations on repetitive neuronal firing. The amount of current injected was increased stepwise beyond threshold for each model neuron and the number of action potentials generated during the 200 ms stimulus was counted and plotted against the stimulus strength (Fig. 4). The wild-type Nav1.1 model neuron, which generated a single-action potential at 250 pA, required 375 pA to fire repetitively. The large window for a single action potential may be a mechanism by which the neuron can buffer its output without firing multiple action potentials in relation to varying intensities of incoming stimuli. All 3 of the mutations decreased the window. The T875M mutant generated repetitive action potentials in response to a lower stimulus of 350 pA compared with wild-type Nav1.1, despite the fact that this mutant had an elevated threshold for firing a single action potential (Fig. 4, up triangles). The W1204R mutant, which displayed the lowest single action potential threshold, also generated repetitive action potentials in response to the lowest stimuli (225 pA; Fig. 4, squares). The R1648H mutant, which demonstrated the same threshold for single action potential firing as the wild-type channel, generated repetitive action potentials in response to a lower stimulus (325 pA; Fig. 4, down triangles).
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). To determine which of these 2 alterations resulted in the faster and larger action potentials, separate simulations in which each of these changes was individually incorporated were performed. The negative shift in steady-state slow inactivation had little effect on the rate of action potential generation over the 100 ms time period shown and had no effect on the height of the action potentials (Fig. 5B). In contrast, the more rapid entry into the slow-inactivated state resulted in larger and faster action potentials in the model neuron (Fig. 5C).
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). To determine what effect each of these properties had on the generation of action potentials, 2 separate models were generated. The negative shift in the voltage dependency of activation produced a large increase in the rate of action potential firing and a slight increase in the magnitude of each action potential (Fig. 6B). In contrast, the negative shift in steady-state inactivation slowed the rate of action potential generation and reduced the height of the action potentials (Fig. 6C). The shift in inactivation had a much smaller effect on the firing properties of the neuron then did the shift of the same magnitude in activation, suggesting that the shift in activation is more significant with respect to AP firing.
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).
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Although the mutant channels were studied as homogeneous populations to determine their functional characteristics, neurons contain a heterogeneous mixture of wild-type and mutant channels because GEFS+ is an autosomal dominant disorder (Scheffer and Berkovic 1997; Singh et al. 1999). Therefore it is important to determine how a heterogeneous population of channels affects the physiology of a neuron to mimic the in vivo situation. The computational model makes it possible to assign both mutant and wild-type channels to a single neuron and thus examine the behavior of a mixed population of channels. Figure 8A shows trace overlays of the first 3 action potentials generated in response to a 200 ms injection of 400 pA for neurons containing all mutant channels (gray lines), a 50/50 mix of mutant and wild-type channels (+/–, dashed black lines), and pure wild-type channels (solid black lines).
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In the previous experiments, the ratio of GEFS+ mutant channels to wild-type Nav1.1 channels was fixed at 1:1. However, a real neuron may not uniformly express an equal number of wild-type and mutant channels, and slight variations in the ratio between mutant and wild-type channels could alter neuronal excitability. Therefore we examined the effects of different ratios of GEFS+ mutant channels to wild-type Nav1.1 channels on neuronal excitability by analyzing repetitive firing after a 350 pA stimulus that does not elicit repetitive firing for the wild-type channels alone (Fig. 8B). Action potentials generated during a 200 ms stimulus were counted and plotted against the percentage of mutant channels in the total population. Each of the GEFS+ mutant channels was capable of driving the model neuron into a state of repetitive firing when the mutant channels made up 
40% of the total population. The W1204R mutant channels were the most effective, requiring only 5% mutant channels for the model neuron to fire repetitively (squares). The W1204R mutant also produced an "all-or-nothing" effect in that the model neuron fired either a single action potential or a repetitive burst of action potentials at close to the maximum rate, with little change from 5 to 100% of the sodium channels being mutant. Both the T875M (up triangles) and R1648H (down triangles) channels began to drive repetitive firing when the mutant channels represented 20% of the total population. These 2 mutants produced a gradual shift from single action potential generation to repetitive firing as more mutant sodium channels were added to the total population, with the maximum effect occurring at 30% for R1648H and 40% for T875M. These data suggest that a neuron expressing GEFS+ mutant channels would demonstrate the mutant phenotype unless a large percentage of those channels were specifically eliminated from the membrane.
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DISCUSSION |
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TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONACKNOWLEDGMENTSREFERENCES |
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, 2003), prompting the question of how these diverse differences in sodium channel function could result in the same clinical epileptic syndrome. To address this question, we used the model neuron to determine how the different biophysical changes affected action potential threshold, shape, size, and frequency. The effects of the mutations on the threshold for action potential initiation were generally consistent with predictions based on the biophysical properties of the mutant channels. A negative shift in the voltage dependency of slow inactivation combined with an increased entry into the slow-inactivated state produced by the T875M mutation resulted in a model neuron with an increased threshold for generation of a single action potential. This is easily explained by the fact that the T875M mutation shifted the V1/2 of slow inactivation to –62 mV (from –46 mV for wild-type Nav1.1), causing more channels to be slow inactivated at the model neuron's resting potential of –60 mV and thus resulting in fewer channels available to fire an action potential. The opposite was true for the W1204R mutation, which produced a model neuron with a decreased threshold for action potential generation as a result of a negative shift in both the voltage dependency of activation and fast inactivation. The negative shift in activation produced a much greater effect on channel excitability than the equal shift in inactivation and would account for the decreased threshold. Not surprisingly, the increased rate of recovery produced by the R1648H mutation had no effect on the model neuron's single action potential threshold.
All 3 of the GEFS+ mutations increased the tendency for the model neuron to fire action potentials repetitively in response to an incoming stimulus that produced a single action potential only in the wild-type Nav1.1 model neuron. The wild-type model neuron produced a single action potential in response to a 250 pA stimulus and continued to fire a single action potential until a stimulus of 375 pA or greater was applied. This large buffer between single action potential generation and repetitive firing was not present in the GEFS+ model neurons and may play an important role in modulating the excitability of the soma. The mutation with the most dramatic effect, W1204R, produced a model neuron that fired a single action potential in response to a 175 pA stimulus and quickly entered into a repetitive firing mode when the stimulus was 225 pA. This decrease and shift of the single action potential window to smaller stimuli can be attributed entirely to the shift in the voltage dependency of activation. The R1648H mutation also increased the propensity for the model neuron to fire repetitively in response to a stimulus of 325 pA, resulting in a smaller window for single action potential generation. This result is consistent with previously published data suggesting that broad changes in sodium channel inactivation and recovery can shift the firing properties of spider mechanoreceptor neurons from single action potential generation to repetitive firing (Torkkeli and French 2002). The T875M mutation had the smallest effect but still resulted in a model neuron that fired repetitively at a stimulus of 350 pA with a smaller window for single action potential generation.
An increase in the firing of repetitive action potentials as a cause of seizure activity is consistent with the effects of antiepileptic drugs used to treat generalized tonic-clonic seizures, such as valproate (Pugsley et al. 1999; Vreugdenhil and Wadman 1999; Vreugdenhil et al. 1998), lamotrigine (Kuo 1998; Kuo and Lu 1997; Siep et al. 2002; Xie et al. 1995; Zona and Avoli 1997), and carbamazepine (Kuo 1998; Kuo et al. 1997; Pugsley et al. 1999; Reckziegel et al. 1999; Vreugdenhil and Wadman 1999). These drugs increase the use dependency of sodium channel activity resulting in a decrease in repetitive action potential firing (Köhling 2002). We predict that application of these drugs to the GEFS+ mutant neurons would result in an elimination of their repetitive firing behavior.
The increased action potential frequency in the T875M mutant model neuron was unexpected because that mutation enhanced slow inactivation. The repetitive firing in our model resulted from rapid entry into the slow-inactivated state, which was modeled as a Gaussian function along with recovery from slow inactivation. The rates of recovery from slow inactivation and entry into slow inactivation were defined to be the same at potentials at which these 2 properties could not be experimentally separated. Therefore it is possible that the prediction of repetitive firing in the T875M mutant model neuron may not reflect the behavior of a real neuron. Alternatively, it is possible that the rapid entry into the slow-inactivated state gave the T875M mutant channels that were slow inactivated a "jumpstart" on recovery, which occurred rapidly and similarly to wild-type in the first few seconds (Spampanato et al. 2001). Experimental recordings from neurons expressing the T875M mutant will be necessary to distinguish between these 2 possibilities.
The model that we used included 2 simplifying assumptions. First, the model neuron represented only the neuronal soma without any processes. Second, Nav1.1 was the only sodium channel that was included, even though neurons often express more than one sodium channel isoform. We believe that these assumptions are a good first approximation because Nav1.1 is predominantly expressed in the soma of neurons (Kaplan et al. 2001; Westenbroek et al. 1989), with the other 2 CNS sodium channel isoforms (Nav1.2 and Nav1.6) present at the axon hillock and nodes of Ranvier (Boiko et al. 2003; Caldwell et al. 2000; Kaplan et al. 2001; Schaller and Caldwell 2003). In addition, Nav1.1 is expressed in regions that are likely to be involved in epileptogenesis, including hippocampal pyramidal, dentate granule, cerebellar Purkinje, and spinal motor neurons with expression generally beginning during postnatal development and increasing into adulthood (Black et al. 1994; Brysch et al. 1991; Furuyama et al. 1993; Novakovic et al. 2001; Schaller and Caldwell 2003).
Although action potential initiation in neurons of the CNS occurs outside of the soma (Colbert and Johnston 1996; Colbert and Pan 2002; Stuart and Sakmann 1994; Stuart et al. 1997), the reduction in action potential threshold produced by the W1204R mutation may enable the soma of affected neurons to initiate an action potential. The action potential would result from an otherwise subthreshold dendritic depolarization, resulting in a hyperexcitable neuron or one that could possibly initiate synchronization of a network of neurons, causing seizure activity. This hypothesis is supported by previous experimental and computational studies showing that axonal initiation of action potentials in pyramidal neurons occurs because of a 7 mV negative shift in the V1/2 of sodium channel activation in axonal channels compared with those in the soma (Colbert and Johnston 1996; Colbert and Pan 2002). This shift resulted in the axonal sodium channels being more sensitive to incoming membrane depolarizations than those in the soma. With the W1204R mutant channels in the soma activating at a V1/2 about 5 mV more negative than that of the wild-type channels, these neurons may experience a shift from axonal action potential initiation to somatic action potential initiation, resulting in premature action potential initiation in response to otherwise subthreshold stimuli.
In summary, we have shown that 3 sodium channel mutations that produce different biophysical effects on channel function all result in a lower threshold for the firing of repetitive action potentials in model neurons. This result suggests that, although there may be a number of different biophysical effects on sodium channel function produced by GEFS+ mutations, there may still be a similar physiological mechanism that produces neuronal hyperexcitability and seizure activity. If this prediction is correct, it suggests that a common therapeutic approach might be effective in treating patients with GEFS+, regardless of the specific underlying mutation.
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ACKNOWLEDGMENTS |
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GRANTS
This research was supported by National Institute of Neurological Disorders and Stroke Grants NS-38580 to I. Soltesz and NS-26729 and NS-48336 to A. L. Goldin.
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FOOTNOTES |
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The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Address for reprint requests and other correspondence: A. L. Goldin, Dept. of Microbiology & Molecular Genetics, Univ. of California, Irvine, CA 92697-4025 (E-mail: agoldin{at}uci.edu).
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