Transition rate constants for IKs models
Model . | α(0) (ms−1) . | β(0) (ms−) . | δ(0) (ms−1) . | γ(0) (ms−1) . | κ(0) (ms−1) . | λ(0) (ms−1) . | Zα (e0) . | Zβ (e0) . | Zδ (e0) . | Zγ (e0) . | Zκ (e0) . | Zλ (e0) . |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (1) EQ*QQ*Q* + E1 Whole-cell patch clamp | 2.38e-5 | 1.48e-4 | 7.45e-1 | −9.0e-1 | ||||||||
| (2) EQ*QQ*Q* + E1 Optimized for Scheme 1 C model | 2.678e-5 | 9.704e-5 | 8.68e-1 | −8.56e-1 | ||||||||
| (3) Scheme 1 B, EQ*Q+E1 model, optimized | 1.201e-4 | 9.527e-5 | 4.860e-1 | 9.195e-1 | ||||||||
| (4) Scheme 1 A, wt EQ model, optimized | 2.567e-4 | 8.227e-5 | 4.636e-1 | 9.161e-1 | ||||||||
| (5) G219C psQ+E1Voltage clamp fluorimetry | 4.817e-3 | 1.596e-4 | 3.354e-4 | 3.895e-4 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | ||||
| (6) G219C psQQ*+E1 Voltage clamp fluorimetry | 4.255e-3 | 1.6e-4 | 1.363e-4 | 3.895e-4 | 4.863e-1 | −4.50e-1 | 6.99e-1 | −5.38e-1 | ||||
| (7) Scheme 2 A, psQ+E1, optimized | 9.63e-4 | 3.19e-5 | 1.34e-4 | 1.56e-4 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | ||||
| (8) Scheme 2 B, psQQ*+E1, optimized | 8.51e-4 | 3.19e-5 | 5.45e-5 | 1.558e-4 | 4.863e-1 | −4.50e-1 | 6.99e-1 | −5.38e-1 | ||||
| (9) Scheme 4 allosteric models, optimized, D = 1.357 | 8.71e-4 | 2.43e-5 | 2.88e-5 | 6.92e-5 | 4.75e-1 | −4.34e-1 | 6.52e-1 | −5.07e-1 | ||||
| Mean rates, n = 5 ± SEM | 9.23e-4 ± 4.92e-5 | 2.60e-5 ± 1.32e-6 | 4.42e-5 ± 1.03e-5 | 1.54e-4 ± 5.73e-5 | 4.87e-1 ± 0.009 | −4.64e-1 ± 0.007 | 6.89e-1 ± 0.011 | −5.62e-1 ± 0.042 | ||||
| (10) Scheme 5 allosteric models, optimized | 9.64e-4 | 3.19e-5 | 1.042e-4 | 1.298e-4 | 6.053e-5 | 7.79e-5 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | 5.38e-1 | −5.38e-1 |
| Mean rates, n = 4 ± SEM | 9.55e-4 ± 1.84e-5 | 3.29e-5 ± 3.90e-7 | 1.152e-4 ± 1.27e-5 | 1.214e-4 ± 9.486e-6 | 7.455e-5 ± 5.41e-6 | 5.844e-5 ± 8.84e-6 | 4.76e-1 ± 0.011 | −4.61e-1 ± 0.004 | 5.96e-1 ± 0.024 | −6.15e-1 ± 0.038 | 6.03e-1 ± 0.030 | −5.67e-1 ± 0.013 |
| (11) Scheme 5 B, τact and Δt optimized | 2.89e-3 | 9.57e-5 | 5.21e-5 | 6.49e-5 | 1.82e-4 | 2.34e-4 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | 3.23e-1 | −5.38e-1 |
| (12) Scheme 5 C, τact and Δt optimized | 3.85e-3 | 1.28e-4 | 3.473e-5 | 4.33e-5 | 3.03e-4 | 3.89e-4 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | 4.30e-1 | −5.38e-1 |
Model . | α(0) (ms−1) . | β(0) (ms−) . | δ(0) (ms−1) . | γ(0) (ms−1) . | κ(0) (ms−1) . | λ(0) (ms−1) . | Zα (e0) . | Zβ (e0) . | Zδ (e0) . | Zγ (e0) . | Zκ (e0) . | Zλ (e0) . |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (1) EQ*QQ*Q* + E1 Whole-cell patch clamp | 2.38e-5 | 1.48e-4 | 7.45e-1 | −9.0e-1 | ||||||||
| (2) EQ*QQ*Q* + E1 Optimized for Scheme 1 C model | 2.678e-5 | 9.704e-5 | 8.68e-1 | −8.56e-1 | ||||||||
| (3) Scheme 1 B, EQ*Q+E1 model, optimized | 1.201e-4 | 9.527e-5 | 4.860e-1 | 9.195e-1 | ||||||||
| (4) Scheme 1 A, wt EQ model, optimized | 2.567e-4 | 8.227e-5 | 4.636e-1 | 9.161e-1 | ||||||||
| (5) G219C psQ+E1Voltage clamp fluorimetry | 4.817e-3 | 1.596e-4 | 3.354e-4 | 3.895e-4 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | ||||
| (6) G219C psQQ*+E1 Voltage clamp fluorimetry | 4.255e-3 | 1.6e-4 | 1.363e-4 | 3.895e-4 | 4.863e-1 | −4.50e-1 | 6.99e-1 | −5.38e-1 | ||||
| (7) Scheme 2 A, psQ+E1, optimized | 9.63e-4 | 3.19e-5 | 1.34e-4 | 1.56e-4 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | ||||
| (8) Scheme 2 B, psQQ*+E1, optimized | 8.51e-4 | 3.19e-5 | 5.45e-5 | 1.558e-4 | 4.863e-1 | −4.50e-1 | 6.99e-1 | −5.38e-1 | ||||
| (9) Scheme 4 allosteric models, optimized, D = 1.357 | 8.71e-4 | 2.43e-5 | 2.88e-5 | 6.92e-5 | 4.75e-1 | −4.34e-1 | 6.52e-1 | −5.07e-1 | ||||
| Mean rates, n = 5 ± SEM | 9.23e-4 ± 4.92e-5 | 2.60e-5 ± 1.32e-6 | 4.42e-5 ± 1.03e-5 | 1.54e-4 ± 5.73e-5 | 4.87e-1 ± 0.009 | −4.64e-1 ± 0.007 | 6.89e-1 ± 0.011 | −5.62e-1 ± 0.042 | ||||
| (10) Scheme 5 allosteric models, optimized | 9.64e-4 | 3.19e-5 | 1.042e-4 | 1.298e-4 | 6.053e-5 | 7.79e-5 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | 5.38e-1 | −5.38e-1 |
| Mean rates, n = 4 ± SEM | 9.55e-4 ± 1.84e-5 | 3.29e-5 ± 3.90e-7 | 1.152e-4 ± 1.27e-5 | 1.214e-4 ± 9.486e-6 | 7.455e-5 ± 5.41e-6 | 5.844e-5 ± 8.84e-6 | 4.76e-1 ± 0.011 | −4.61e-1 ± 0.004 | 5.96e-1 ± 0.024 | −6.15e-1 ± 0.038 | 6.03e-1 ± 0.030 | −5.67e-1 ± 0.013 |
| (11) Scheme 5 B, τact and Δt optimized | 2.89e-3 | 9.57e-5 | 5.21e-5 | 6.49e-5 | 1.82e-4 | 2.34e-4 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | 3.23e-1 | −5.38e-1 |
| (12) Scheme 5 C, τact and Δt optimized | 3.85e-3 | 1.28e-4 | 3.473e-5 | 4.33e-5 | 3.03e-4 | 3.89e-4 | 4.50e-1 | −4.50e-1 | 5.38e-1 | −5.38e-1 | 4.30e-1 | −5.38e-1 |
Rate constants obtained directly from fits to experimental data and modified rate constants obtained after model optimization, as indicated. For Schemes 4 and 5 models, the single best optimization result as determined by “fval” (MATLAB), the minimum value of the objective function at the solution, is shown, as well as mean data from a number of optimization runs starting from different initial parameter values. The best solution was used to generate plots for Schemes 4 and 5 models. Optimizing transition kinetics used G-V, F-V, tact-V, Δt -V experimental data, and the F2/F1 ratio (see Materials and methods).