Full kinetic model of NPPB effects on CFTR gating and permeation. (A; left) Two-tiered kinetic model of NPPB gating effects (cube). States C

_{1}, O

_{1}, O

_{2}, and C

_{2} (red) correspond to the four states depicted in the cartoons in – and represent states in which NPPB is not bound at its “gating site.” The C

_{2}↔C

_{1} transition, which reflects exchange of ADP for ATP at site 2, is modeled as a single step, with a K

_{d} of 50 µM for ATP. For simplicity, a single voltage-independent K

_{d} of 80 µM is used to characterize rapid binding/unbinding of NPPB to the gating site in all four conformational states (vertical transitions; gray arrows). States C

_{1}*, O

_{1}*, O

_{2}*, and C

_{2}* (blue) are conformational states analogous to C

_{1}, O

_{1}, O

_{2}, and C

_{2}, but with NPPB bound at the gating site. In 0 or 210 µM NPPB, the full model (cube) reduces to the four-state models to its left (red) and right (blue), respectively; states

in the blue reduced model are compound states (

= {C

_{1}; C

_{1}*},

= {O

_{1}; O

_{1}*}, etc.), and printed rates are apparent rates of transition between them. (Right) Voltage and dose dependence of pore block by NPPB is modeled as an instantaneous effect on apparent unitary conductance (

*g*) and is approximated by the Boltzmann equation with parameters printed (

*g*_{0}, control unitary conductance;

*T*, temperature in Kelvin;

*R* = 8.31 J · mol

^{−1} · K

^{−1}; F = 96,500 C · mol

^{−1}). (B–L) Predictions of the model in A for the experimental protocols and analysis results obtained in this study. Macroscopic current time courses for the experimental protocols in B–E and I–L were calculated, whereas single-channel traces for F–H were simulated using standard Q-matrix techniques (). Rate O

_{1}*→O

_{2}* was tentatively set to zero. Gating effects of the K1250A mutation were modeled by setting rate O

_{1}→O

_{2} to zero while increasing the K

_{d} for ATP to 5 mM (), those of the ΔF508 mutation were modeled by decreasing rate C

_{1}→O

_{1} 30-fold while increasing rate O

_{1}→C

_{1} threefold (; ). Analysis of macroscopic currents was done as described in –, , , and . For F and H, five independent events lists, containing 100 open events each, were simulated for each condition; bar charts show mean ± SEM of obtained mean open and closed times. Open duration histograms in G were created from 3,000 simulated open events for both conditions and fitted by maximum likelihood as described for .

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