Fig 1.
Moreno et al. [4] model of Na+ channel-lidocaine interactions.
(A) The drug-free Na+ channel model. The O state represents the conducting state, while C3, C2, and C1 correspond to 3 closed states. The IC3, IC2, and IF states represent conformational states in which the “fast” inactivation gate is closed, and the IS state represents a state in which a “slow” inactivation gate is closed. Arrows indicate possible conformational state transitions with corresponding voltage-dependent rate constants labeled (e.g., α13 and β13 are the rate constants for transitions from C1 to O and O to C1, respectively). (B) The full lidocaine-Na+ channel interaction model. The drug-free model from (A) is depicted in black. Red (D+ prefix) and blue (D prefix) states represent conformational states where charged and neutral drug is bound, respectively. Charged drug can only bind to non-inactivated states (C3, C2, C1, and O), while neutral drug can bind to any state. Drug binding and unbinding rates are state-dependent, as indicated by the binding and unbinding rates of charged drug to the open state (kon and koff) and closed states (kcon and kcoff), and neutral drug to the open state (k_on and k_off), closed states (kc_on and kc_off), and inactivated states (ki_on and ki_off). For clarity, blue (black) circles as opposed to arrows were used to indicate neutral drug binding (unbinding) to the fast inactivated states with a rate constant ki_on (ki_off).
Fig 2.
The low-dimensional Na+ conductance model is fit to experimental data from steady state availability (A; sum squared errors (SSE) of 0.038 and 0.035 for the Moreno et al. and low-dimensional models, respectively), steady state activation (B; SSE of 0.042 and 7.0×10−4 for the Moreno et al. and low-dimensional models, respectively), time to half inactivation (C; SSE of 197 and 17 for the Moreno et al. and low-dimensional models, respectively), and time constant of activation (D; SSE of 1.4×10−3 for the low-dimensional model) voltage-clamp experiments [17–19]. In all subfigures, filled circles indicate experimental data points, blue curves represent output from the Moreno et al. model [4], orange curves represent output from the low-dimensional Na+ conductance model. t1/2 at -80 mV in the Moreno et al. model is not indicated in the figure as it is substantially larger (48.8 ms) than the other t1/2 values. For the low-dimensional model in (D), , n is total number of data points, {yi} are the model output, and {xi} are the experimental data values.
Fig 3.
Experimental voltage-clamp data (filled circles), Moreno et al. 2011 model fit (solid blue curves), low-dimensional model output (solid orange curves) for lidocaine effects on the Na+ conductance. V-clamp data for control, i.e. no drug, experiments (open circles), Moreno et al. (blue dashed curves), and low-dimensional model with no drug (orange dashed curves) are included for appropriate protocols. (A) Steady state availability with SSE of 3.6×10−3 and 2.9×10−3 for the Moreno et al. and low-dimensional lidocaine models, respectively. (B) Frequency dependence of block with SSE of 8.8×10−4 and 1.7×10−3 for the Moreno et al. and low-dimensional lidocaine models, respectively. (C) Tonic block with SSE of 3.1×10−3 and 0.033 for the Moreno et al. and low-dimensional lidocaine models, respectively. (D) Dose-dependence of use-dependent block with SSE of 1.3×10−3 and 1.1×10−2 for the Moreno et al. and low-dimensional lidocaine models, respectively. (E) Recovery from use-dependent block with SSE of 2.3×10−3 and 5.0×10−3 for the Moreno et al. and low-dimensional lidocaine models, respectively. n is total number of data points, {yi} are the model output, and {xi} are the experimental data values [9,10,17].
Fig 4.
Rate-Dependent Effects of Lidocaine.
Normalized peak upstroke velocity (A), conduction velocity (B), and fraction of channels not bound to drug during the upstroke (C) plotted against BCL for the ten Tusscher et al. human ventricular myocyte model [22,23] with the Moreno et al. model (blue curves) or low-dimensional model (orange curves) of the Na+ conductance. Peak upstroke and conduction velocities for 5 μM (solid curves) and 20 μM (dashed curves) concentrations of lidocaine are normalized by peak upstroke and conduction velocities at the same BCL in the corresponding drug-free model. In C, predictions from an analytically derived expression for fraction of channels bound to drug during the upstroke (b*) in our low-dimensional model are also plotted (yellow curves; see Eq (5)) and were shifted up slightly to make them visible as they overlap the output of the ten Tusscher et al. model with our low-dimensional Na+ conductance model.
Fig 5.
Mechanism of lidocaine rate-dependent effects.
(A) Simulated action potentials of our modified ten Tusscher et al. model paced at a BCL of 750 ms with 20 μM lidocaine (blue) and a square wave approximation of the action potential (orange) that alternates between -85 mV and 20 mV. (B) Dynamics of the fraction of channels bound to drug, b, with 20 μM lidocaine present in our modified ten Tusscher et al. model (blue) and low-dimensional Na+ conductance model stimulated by the square wave approximation (orange). (C) Voltage dependence of 1−h∞ (dashed green) and b∞ for 20 μM (yellow) and 5 μM (purple) lidocaine. (D) Voltage dependence of τb for 20 μM (yellow) and 5 μM (purple) lidocaine.
Fig 6.
Cardiac electrophysiological properties and lidocaine binding.
(A) APD90 restitution curve for our modified ten Tusscher et al. model with 20 μM of lidocaine (blue curve) and a steeper, hypothetical restitution curve (black circles). (B) Time course of transmembrane potential for our modified ten Tusscher et al. model paced at a BCL of 750 ms and the square wave approximation of V (dashed blue line) as well as hypothetical alterations: VAP decreased to -20 mV (dashed yellow curve), VDI decreased to -95 mV (dashed purple curve), and VDI increased to -75 mV (dashed orange curve). (C) Fraction of channels bound to lidocaine during the upstroke (b*(BCL)) in the presence of 20 μM lidocaine, as given by Eq (5), for our modified ten Tusscher et al. model and the various shifts in cardiac electrophysiological characteristics in (A) and (B).