Conceived and designed the experiments: RK ESV AM. Performed the experiments: RK NL. Analyzed the data: RK NL AOJ AM. Contributed reagents/materials/analysis tools: AOJ. Wrote the paper: RK AM.
The authors have declared that no competing interests exist.
Sodium channels are one of the most intensively studied drug targets. Sodium channel inhibitors (e.g., local anesthetics, anticonvulsants, antiarrhythmics and analgesics) exert their effect by stabilizing an inactivated conformation of the channels. Besides the fast-inactivated conformation, sodium channels have several distinct slow-inactivated conformational states. Stabilization of a slow-inactivated state has been proposed to be advantageous for certain therapeutic applications. Special voltage protocols are used to evoke slow inactivation of sodium channels. It is assumed that efficacy of a drug in these protocols indicates slow-inactivated state preference. We tested this assumption in simulations using four prototypical drug inhibitory mechanisms (fast or slow-inactivated state preference, with either fast or slow binding kinetics) and a kinetic model for sodium channels. Unexpectedly, we found that efficacy in these protocols (e.g., a shift of the “steady-state slow inactivation curve”), was not a reliable indicator of slow-inactivated state preference. Slowly associating fast-inactivated state-preferring drugs were indistinguishable from slow-inactivated state-preferring drugs. On the other hand, fast- and slow-inactivated state-preferring drugs tended to preferentially affect onset and recovery, respectively. The robustness of these observations was verified: i) by performing a Monte Carlo study on the effects of randomly modifying model parameters, ii) by testing the same drugs in a fundamentally different model and iii) by an analysis of the effect of systematically changing drug-specific parameters. In patch clamp electrophysiology experiments we tested five sodium channel inhibitor drugs on native sodium channels of cultured hippocampal neurons. For lidocaine, phenytoin and carbamazepine our data indicate a preference for the fast-inactivated state, while the results for fluoxetine and desipramine are inconclusive. We suggest that conclusions based on voltage protocols that are used to detect slow-inactivated state preference are unreliable and should be re-evaluated.
Sodium channels are the key proteins for action potential firing in most excitable cells. Inhibitor drugs prevent excitation (local anesthetics), regulate excitability (antiarrhythmics), or prevent overexcitation (antiepileptic, antispastic and neuroprotective drugs) by binding to the channel and keeping it in one of the inactivated channel conformations. Sodium channels have one fast- and several slow-inactivated conformations (states). The specific stabilization of slow-inactivated states have been proposed to be advantageous in certain therapeutic applications. The question of whether individual drugs stabilize the fast or the slow-inactivated state is studied using specific voltage protocols. We tested the reliability of conclusions based on these protocols in simulation experiments using a model of sodium channels, and we found that fast- and slow-inactivated state-stabilizing drugs could not be differentiated. We suggested a method by which the state preference of at least a subset of individual drugs could be determined and tried the method in electrophysiology experiments with five individual drugs. Three of the drugs (lidocaine, phenytoin and carbamazepine) were classified as fast-inactivated state-stabilizers, while the state preference of fluoxetine and desipramine was found to be undeterminable by this method.
Sodium channels are the key proteins in action potential firing for most excitable cells. They exhibit a complex, membrane potential-dependent gating behavior
Thus far only a single drug binding site is established unequivocally on sodium channels, the “local anesthetic receptor”, located within the inner vestibule, its key residue being the phenylalanine located right below the selectivity filter, on domain 4 segment 6
The major mechanism of SCIs is stabilization of an inactivated channel conformational state as a result of a preferential affinity for that state. The question of which inactivated state is preferred is under debate for many SCI drugs (e.g.
Special voltage protocols are used to evoke and study the slow-inactivated state. Availability of channels is studied after a prolonged depolarization (to induce slow inactivation), followed by a hyperpolarizing gap (to allow recovery from fast, but not slow inactivation). Because availability in such protocols is solely determined by the extent of slow inactivation, a drug that decreases availability is considered to be slow-inactivated state-preferring. However, gating rates (the rate of inactivation and rate of recovery from inactivation) are altered by drug binding. A fast-inactivated state-preferring drug stabilizes this state by delaying recovery. A delayed recovery does not necessarily indicate actual modification of the gating rate. For example if the bound drug prevents recovery from inactivation, then recovery will appear to be slowed because the drug needs first to dissociate
With the help of simulations, we intended to understand the interactions between binding and gating rates and wanted to test the major prototypical inhibitor mechanisms in commonly used protocols. We wanted to explore what could be deduced from these data, and wanted to find the right protocols that could help to determine the inhibition mechanisms.
Our data suggest that conclusions based on conventional protocols are not reliable. For example, the fact that one drug preferentially shifts the “steady-state slow inactivation curve” as compared to another drug does not necessarily mean that the drug prefers the slow-inactivated state.
A typical example showing that state preference of drugs cannot reliably be deduced from these protocols (see
For explanation see text.
Using patch-clamp experiments, we tested three classic SCIs (lidocaine, phenytoin and carbamazepine) and two antidepressants (fluoxetine and desipramine). Properties of inhibition by classic SCIs were consistent with fast-inactivated state preference with fast binding kinetics. Inhibition by antidepressants was distinctly different. Whether the difference was caused by slow binding kinetics or slow-inactivated state preference could not be determined.
For simulations two different kinds of models were used: a phenomenological Hodgkin-Huxley type model and a state model similar to the one published by Kuo and Bean
To compare simulated data with experimental results, we used similar voltage protocols in both the simulations and experiments (
“
“
“
“
Concentration-response curves were simulated using single depolarizations to 0 mV from holding potentials of −150, −90 and −60 mV.
In order to address the problem of fast- vs. slow-inactivated state preference and the interaction between the dynamics of binding and gating, we simulated four prototypical mechanisms: either the fast- or the slow-inactivated state was preferred by the drug (“FI” and “SI”, respectively), and the drug had either fast or slow binding kinetics (“fb” and “sb”, respectively). Fast-inactivated state preference was introduced by setting
Simulations with the tetracube model, obtained under control conditions and in the continuous presence of 30 µM of any of the four prototypical “drugs,” are shown in
The mechanisms were: “FI_fb” (fast-inactivated state is stabilized, with fast binding kinetics), “FI_sb” (fast-inactivated state is stabilized, with slow binding kinetics), “SI_fb” (slow-inactivated state is stabilized, with fast binding kinetics) and “SI_sb” (slow-inactivated state is stabilized, with slow binding kinetics).
No difference in the concentration-response curves between the drugs with fast and slow association rates was found at very negative holding potentials (−150 mV), at which there is no significant inactivation (
If a drug has no effect on the “steady-state fast inactivation curve”, but it shifts the “steady-state slow inactivation” curve substantially, one might think that the reason for this must be slow-inactivated state preference. To test this argument, we simulated both “steady-state fast inactivation” and “steady-state slow inactivation” curves. For the “FInact_V” curve, a 100 ms long conditioning pulse (ranging from −120 mV to −30 mV) preceded the test pulse (
In the “SInact_t” protocol, the four drugs shifted the curve in clearly dissimilar patterns (
In the “Rec_t” protocol, “FI_fb” behaved as expected, affecting only the part of the curve that is responsible for recovery from the fast-inactivated state. However, drug “FI_sb” was as effective as slow-inactivated state-preferring drugs. In experiments using this protocol, the recovery from inhibition is slowed down for two reasons: i) the slow dissociation rate of the drug; and ii) drug-bound channels display a slowed gating. In the case of “FI_sb,” the former seems to be the rate-limiting step and, if dissociation is slow enough, the curve is shifted, whichever state is preferred (
Although recovery from fast inactivation is almost complete (95%) within the 10 ms gap, some studies used longer gaps (100 ms to 1 s) in “steady-state slow inactivation” (“SInact_V”) or onset of slow inactivation (“SInact_t”) protocols in order to make sure that even drug-bound fast-inactivated channels had time to recover. However, this time is still insufficient for drugs with slow dissociation kinetics. To test how the relative potency of the four drugs depends on gap duration, we made simulations with different gap durations ranging from 1 ms to 10 s. The curves shown in
In summary, conventional voltage protocols failed to reliably distinguish between drugs “FI_sb” and “SI_fb.”In particular, results of the “SInact_t” protocol are not only unreliable, but are clearly misleading as “FI_sb” caused a much larger shift than “SI_fb.”
We made three major observations in the simulations described above: 1) A shift of the “SInact_V” curve does not necessarily reflect a slow-inactivated state preference; 2) Fast-inactivated state-stabilizing drugs caused a larger shift of the “SInact_t” curve than slow-inactivated state-preferring drugs; and 3) Slow-inactivated state-preferring drugs are not necessarily more effective than fast-inactivated state-preferring ones in delaying recovery in the “Rec_t” protocol.
In order to judge the reliability of these observations, we first repeated the experiments using the MSA model, an allosteric model where inactivation processes draw their voltage-dependencies from the voltage-dependence of the activation process. Results of the simulations are shown in
We also tested the consistency of our observations by varying parameters of the tetracube model. We wanted to test at which part of the parameter space they were true and under what conditions they failed. To this end, we performed Monte Carlo simulations. All 18 parameters were randomized between the constraints shown in
Measures of the potency of the four prototypical “drugs” are plotted against the difference between
The first question was how the observation that “FI_sb” can cause a shift of the “SInact_V” (“steady-state slow inactivation”) curve depends on model parameters. Out of the 100 simulations, 23 random sets of parameters did not result in substantial slow inactivation, so the shift of V1/2 could not be determined. In 50 out of the remaining 77 simulations, the shift was larger than −5 mV (
To verify the second and third observations, the effect of all four prototypical drugs was tested in protocols “SInact_t” and “Rec_t.” The extent of the shift caused by individual drugs was quantified by calculating the sum of differences (SOD) between the curves in the control conditions and during drug application. Because the sampling points were evenly distributed on the logarithmic scale, the SOD was proportional to the area between the curves displayed on a semi logarithmic plot. For the sake of comparability, we calculated the normalized sum of differences (nSOD) by dividing SOD values by the sum of the control values (i.e., the full “area” under the control curve). The value of nSOD varied between 0 and 1; nSOD equaled 0 if the drug had no effect on slow inactivation or recovery, and equaled 1 if the current was completely abolished by the drug. Values of nSOD for the four prototypical drugs are shown in
Summarizing the results of the Monte Carlo simulations, all three observations were verified for all models. We have demonstrated that “FI_sb” type drugs can behave like “SI” type drugs in “FInact_V” and “SInact_V” protocols. Therefore these protocols cannot be used for distinguishing “FI” and “SI” drugs. Nevertheless, we also observed definite tendencies, e.g., “FI” drugs tend to be more effective in “SInact_t” protocols than in “Rec_t” protocols, or “FI_sb” drugs tend to be the most effective in “Rec_t” protocols (
We plotted the nSOD values of the “Rec_t” protocol as a function of the nSOD values of the “SInact_t” protocol. (
Plots of effectiveness (quantified as nSOD, as described in text) in the “Rec_t” protocol plotted against effectiveness (nSOD) in the “SInact_t” protocol for various simulated drugs. Drugs with the same state preference factor (
When
When all simulation results were plotted on the nSOD(Rec_t) – nSOD(SInact_t) plane, we observed that fast- and slow-inactivated state-stabilizing drugs were confined to limited but overlapping areas of the plane (
In summary, localization on the nSOD(Rec_t) – nSOD(SInact_t) plane can reveal the state preference of a drug if it falls on one of the non-overlapping areas. However, many “SI_fb” and “FI_sb” type drugs are expected to fall in the overlapping section and, therefore, their state preference cannot be determined.
The following SCI drugs were used: the local anesthetic and antiarrhythmic lidocaine (300 µM), the anticonvulsants phenytoin (300 µM) and carbamazepine (300 µM), and the antidepressants fluoxetine (30 µM) and desipramine (30 µM). The concentrations were chosen to be similarly effective in causing a hyperpolarizing shift (−10 to −18 mV) of the “steady-state inactivation” curve (“FInact_V” – 2 s pre-pulse) (
The following drugs were investigated: 30 µM fluoxetine (FLX,
In the “SInact_t” protocol (
In the “Rec_t” protocol (
We created the nSOD(Rec_t) – nSOD(SInact_t) plots for all five drugs (
Slow-inactivated state preference has been proposed to be a therapeutic advantage
A shift of the “steady-state slow inactivation curve” (“SInact_V” protocol), a shift of the “slow inactivation onset” curve (“SInact_t” protocol) and a shift of the recovery curve (“Rec_t” protocol) could all be caused by both fast- or slow-inactivated state stabilization. This conclusion was confirmed both by testing whether our observations were true for the entire parameter space and by applying a different type of model. We found that, with all combinations of parameters (within the reasonable range), our observations held true. Furthermore, both the phenomenological tetracube model and the MSA state model gave qualitatively similar results.
Nevertheless, the four prototypical mechanisms behaved appreciably differently. For this reason, we investigated the extent to which the two major mechanisms (“FI” and “SI”) could be distinguished using the combined information from different voltage protocols. Based on the nSOD(Rec_t) – nSOD(SInact_t) plots, we concluded that “FI” type drugs can be recognized, provided that their binding kinetics are fast enough. However, “FI” drugs with slower binding kinetics will overlap with “SI” drugs. Determination of the state preference would only be possible if we could measure the binding kinetics of individual drugs. However, distinguishing slow association from association to a slow-inactivated state is not trivial. In order to separate gating kinetics from binding kinetics, a rapid pulse application of the drug is necessary
We investigated three well-known SCI drugs (lidocaine, phenytoin and carbamazepine) and two antidepressants (fluoxetine and desipramine). The uniquely high incidence of SCI activity among antidepressants
The experimental behavior of the five drugs was remarkably similar to the behavior of prototypical drugs in simulations. We suggest that lidocaine, phenytoin and carbamazepine stabilize the fast-inactivated state, and that they have fast binding kinetics. Their nSOD(Rec_t) – nSOD(SInact_t) plot clearly fell into the “fast area.” Furthermore, their effect on the “Rec_t” curve was similar to the effect of “FI_fb.” Lidocaine behaved similarly to “FI_fb” in the “SInact_t” protocol as well. We hypothesized that the moderate effect of phenytoin and carbamazepine was due to their extra fast dissociation kinetics. This hypothesis was verified in the case of carbamazepine, which produced the characteristic “FI_fb” type effect on “SInact_t” curves upon minor modifications to the protocol.
The nSOD(Rec_t) – nSOD(SInact_t) plots of fluoxetine and desipramine fell into the overlapping area. Thus, their state preference could not be unambiguously determined. However, their properties of inhibition definitely differed from those of classic SCIs.
Patch clamp electrophysiology was done on native sodium channels in cultured hippocampal neurons. Cell culture preparation and electrophysiology were performed as published previously
All experimental procedures were approved by the Animal Care and Experimentation Committee of the Institute of Experimental Medicine, and as stated by the decision of the Animal Health and Food Control Department of the Ministry of Agriculture and Regional Development, were in accordance with 86/609/EEC/2 Directives of European Community.
The simulation was based on a set of differential equations with the occupancy of each state (i.e., the fraction of the ion channel population in that specific state) given by the following equation:
Differential equations were solved during simulations using a fourth-order Runge-Kutta method. We used either Berkeley Madonna v8.0.1 (
The model in itself, not including drug effects, is equivalent to a modified Hodgkin-Huxley model of sodium channels; the gates were assumed to move independently but in a voltage-dependent manner. One modification is that, besides activation and fast inactivation gates, we included a slow inactivation gate. (The structural correlate of slow inactivation is thought to be a collapse of the outer pore region
Because we supposed that drug association to all states is possible, we connected a drug-bound state to each vacant state, thus forming the tetracube (tesseract) topology of the model (
In order to describe the specific drug effects on the channels, we have defined five “drug-specific” parameters:
While the affinity of the drug to resting channels is determined by the
Although the tetracube model reproduces the voltage-dependent kinetics of major gating transitions (activation, deactivation, fast and slow inactivation, as well as recovery from both inactivated states) fairly well, it obviously oversimplifies the gating mechanisms. Most notably, unlike in real sodium channels, activation is a single-step process, both types of inactivation are voltage-dependent in themselves, and the gating transitions are independent. A model in which activation is a multi-step process with several intermediate states could better reproduce channel behavior. In addition, using such a model, both fast and slow inactivation themselves can be made voltage-independent (deriving their voltage-dependence from the movement of voltage sensors), which is a more correct approximation of real channel behavior. Furthermore, using this type of model would enable researchers to test alternative state preferences, such as the preference for intermediate states
We used the model described by Kuo and Bean
In the model (
Reproductions of the currents, “steady-state inactivation” (“FInact_V”) and activation curves, as well as the “SInact_t” and “Rec_t” curves by both the tetracube and MSA models, are shown in
We added drug-bound states, following the same principle as described for the tetracube model (see
In order to test the robustness of our findings, we performed simulations with the tetracube model using random parameters. The program was written in C++. The constraints used for random number generation are given in
Evaluation of the goodness of fit during optimization of the models
(0.39 MB TIF)
Results of simulations with the MSA model using the four prototypical mechanisms
(0.78 MB TIF)
The effect of drug binding on rate constants
(0.03 MB DOC)
Calculation of association and dissociation rate constants
(0.03 MB DOC)
Ion channel-specific parameters of the tetracube model
(0.03 MB DOC)
Ion channel-specific parameters of the MSA model
(0.03 MB DOC)
IC50 values for simulated drugs with different CF or CS factors
(0.03 MB DOC)
Detailed description of the “tetracube” and “MSA” models
(0.09 MB DOC)