Fast- or slow-inactivated state preference of Na+ channel inhibitors: a simulation and experimental study

Abstract

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.

Figure 1. Effectiveness of two simulated drugs in “steady-state fast inactivation” and “steady-state slow inactivation” protocols.

A typical example showing that state preference of drugs cannot reliably be deduced from these protocols (see Figure 2). Drug 1 has preferential affinity to fast inactivated state, while Drug 2 prefers slow inactivated state. A, “steady-state fast inactivation” protocol. B, “steady-state slow inactivation” protocol.

Figure 2. Protocols used in experiments and simulations.

For explanation see text.

Figure 3. Results of simulations with the tetracube model using the four prototypical mechanisms.

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). A, Concentration response curves. B, Effect of simulated “drugs” on “steady-state fast inactivation” (left panel) and “steady-state slow inactivation” (right panel) protocols. C, Effect of simulated “drugs” on the slow inactivation onset curve. D, Effect of simulated “drugs” on the recovery curve. E, Dependence of the effect of simulated “drugs” on the duration of the hyperpolarizing gap. The effect was quantified by calculating the areas between curves from the semilogarithmic plots. Box indicates data calculated from curves seen in Figure 3C.

Figure 4. Results of 100 simulations with random parameters of the tetracube model.

Measures of the potency of the four prototypical “drugs” are plotted against the difference between V_1/2 values for fast and slow inactivation. A, Leftward shift of the V_1/2 of “FInact_V” and “SInact_V” curves, caused by “FI_sb.” B, Effect of all four “drugs” on the “SInact_t” curve. The effect was quantified by calculating the sum of differences between control and drug curves (see Figure 3C). C, Effect of all four “drugs” on the “Rec_t” curve. Sum of differences between the curves in control conditions, and during drug application. (see Figure 3D).

Figure 5. Different effectiveness of “FI” and “SI” drugs in two voltage protocols.

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 (CF or CS) and concentration are connected. A, Distribution of 100 simulated drugs with different state preference factors and binding kinetics, applied in their IC₅₀ (−90 mV) concentration. B, The effect of different state preference factors. Simulated drugs were applied in 14 µM concentrations in the case of fast inactivation preferring, and in 81.75 µM concentrations in the case of slow inactivation preferring drugs. C, The effect of different concentrations. The state preference factor was set to 10 in case of both fast and slow inactivation preferring drugs. D, All simulated drugs plotted on one figure. The areas of fast- and slow-inactivated preferring drugs were determined using all data points simulated. E, Prototypical drugs (“FI_fb,” “FI_sb,” “SI_fb,” and “SI_sb”) simulated using the 100 channel models from the Monte Carlo simulation. The two areas were defined based on the points shown in panel D. F, Effect of increasing the hyperpolarizing gap in the “SInact_t” protocol from 10 ms to 1 s. The 100 simulated drugs from panel A were applied in their IC₅₀ (−90 mV) concentration.

Figure 6. The effect of five SCIs in different voltage protocols.

The following drugs were investigated: 30 µM fluoxetine (FLX, black squares), 30 µM desipramine (DMI, black diamonds), 300 µM carbamazepine (CBZ, gray squares), 300 µM phenytoin (PHE, gray diamonds) and 300 µM lidocaine (LID, gray circles). A, “FInact_V” protocol. Pre-pulse duration was set to 2 s. All drugs produced a similar voltage shift. B, “SInact_t” protocol. Carbamazepine and phenytoin induced only a minor modification compared to the control. Fluoxetine and desipramine produced a definite shift. Lidocaine caused inhibition even in the time range of fast inactivation. C, “Rec_t” protocol. Unlike fluoxetine and desipramine, carbamazepine, phenytoin and lidocaine only affected the first phase of the curve, which corresponds with recovery from the fast-inactivated state. D, The nSOD(Rec_t) – nSOD(SInact_t) plots for the drugs that were studied. Fluoxetine and desipramine occupied the overlapping area; plots of carbamazepine, phenytoin and lidocaine fell into the area of fast-inactivated state stabilization.

Figure 7. Topology of states in our models, as described in the text.

A, Tetracube model of the drug-free channel. The position of the three gates is illustrated as a section of a circle. (This arrangement makes no reference to the structure of sodium channels.) B, Formation of the tetracube: Introduction of drug-bound states into the model. Drug association to all states was allowed. C, “Multi-step activation” (MSA) model of the drug-free channel.