TABLE II

Scheme . | 2 (EC_{50} free). | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Df | 6 | 6 | 13 | 15 | 7 | 15 | 15 | |||||

SS (pA^{2}) | 90, 512 | 960, 362 | 83,500 | 47,205 | 324,371 | 51,071 | 53,187 | |||||

Macroscopic parameters | ||||||||||||

EC_{50} (μM) | 44.9 | Constrained to 9.8 μM | ||||||||||

pO_{max} | 0.0145 | 0.0032 | 0.109 | 0.158 | 0.985 | 0.54 | 0.92 | |||||

pO_{min} | 0 | 0 | 0 | 0 | 7 × 10^{−6} | 0.004 | 0.0004 | |||||

Kinetic rates | ||||||||||||

k_{on} (s^{−1}μM^{−1}) | 10.2 ± 11% | 7.90 ± 12% | 18.0 ± 81% | 15.98 ± 120% | 5.85 ± 11% | 9.28 ± 17% | 12.0 ± 24% | |||||

k_{on2} (s^{−1}μM^{−1}) | 16.8 ± 64% | 16.3 ± 85% | ||||||||||

k_{on3} (s^{−1}μM^{−1}) | 8.42 ± 52% | 11.6 ± 120% | ||||||||||

k_{off} (s^{−1}) | 1,869 ± 39% | 121 ± 24% | 0.017 ± 250% | 0.019 ± 560% | 190 ± 10% | 1,871 ± 62% | 6,731 ± 65% | |||||

k_{off2} (s^{−1}) | 175 ± 56% | 380 ± 120% | ||||||||||

k_{off3} (s^{−1}) | 4,541 ± 30% | 6,822 ± 61% | ||||||||||

γ (s^{−1}) | 27.9 ± 9% | 42.1 ± 23% | 43.54 ± 98% | 1.07 ± 105% | 242 ± 75% | |||||||

δ (s^{−1}) | 3,491 ± 17% | 632 ± 9% | 3,718 ± 17% | 3,875 ± 33% | 9,035 ± 11% | |||||||

α (s^{−1}) | 1,829 ± 9% | 110,104 ± ∞% | 29.0 ± 13% | 1,088 ± 33% | 10.2 ± 53% | 776 ± 120% | 110 ± 66% | |||||

α_{2} (s^{−1}) | 1,189 ±410% | 0.246 ±123% | ||||||||||

β (s^{−1}) | 27.3 ± 14% | 382 ± ∞% | 24.08 ± ∞% | 540 ± 99% | 769 ± 7% | 914 ± 110% | 1,380 ± 9% | |||||

β_{2} (s^{−1}) | 3,198 ± 18% | 0.033 ± 160% | ||||||||||

ε_{1} (s^{−1}) | 1,936 ± 7% | 79.0 ± 84% | ||||||||||

ε_{2} (s^{−1}) | 8.48 ± 822% | 3.20 ± 491% | ||||||||||

ζ_{1} (s^{−1}) | 0.298 ± 680% | 31.16 ± 123% | ||||||||||

ζ_{2} (s^{−1}) | 5.9*10^{7} ± 490% | 4.53 ± 113% | ||||||||||

Allosteric factors | ||||||||||||

A_{koff} | 49.6 ± 17% | 1.00 ± 34% | 0.309 ± 316% | |||||||||

A_{kon} | 4.51 ± 31% | 1.77 ± 31% | 1.00 ± 182% | |||||||||

A_{α} | 48.9 ± 19% | 2.30 ± 103% | 1.00 ± 106% | |||||||||

A_{β} | 4.58 ± 41% | 0.77 ± 121% | 0.309 ± 226% | |||||||||

B_{koff} | 65.1 ± 72% | 4,295 ± 270% | ||||||||||

B_{kon} | 1.15 ± 110% | 1.00 ± 520% | ||||||||||

B_{δ} | 33.3 ± 115% | 4,300 ± 260% | ||||||||||

B_{γ} | 2.25 ± 33% | 1.00 ± 300% | ||||||||||

C_{α} | 0.19 ± 230% | 10.1 ± 240% | ||||||||||

C_{β} | 635 ± ∞% | 62.1 ± 380% | ||||||||||

C_{δ} | 1.00 ± ∞% | 5.31 ± 440% | ||||||||||

C_{γ} | 123 ± 300% | 118 ± 250% |

Scheme . | 2 (EC_{50} free). | 2 . | 3 . | 4 . | 5 . | 6 . | 7 . | |||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Df | 6 | 6 | 13 | 15 | 7 | 15 | 15 | |||||

SS (pA^{2}) | 90, 512 | 960, 362 | 83,500 | 47,205 | 324,371 | 51,071 | 53,187 | |||||

Macroscopic parameters | ||||||||||||

EC_{50} (μM) | 44.9 | Constrained to 9.8 μM | ||||||||||

pO_{max} | 0.0145 | 0.0032 | 0.109 | 0.158 | 0.985 | 0.54 | 0.92 | |||||

pO_{min} | 0 | 0 | 0 | 0 | 7 × 10^{−6} | 0.004 | 0.0004 | |||||

Kinetic rates | ||||||||||||

k_{on} (s^{−1}μM^{−1}) | 10.2 ± 11% | 7.90 ± 12% | 18.0 ± 81% | 15.98 ± 120% | 5.85 ± 11% | 9.28 ± 17% | 12.0 ± 24% | |||||

k_{on2} (s^{−1}μM^{−1}) | 16.8 ± 64% | 16.3 ± 85% | ||||||||||

k_{on3} (s^{−1}μM^{−1}) | 8.42 ± 52% | 11.6 ± 120% | ||||||||||

k_{off} (s^{−1}) | 1,869 ± 39% | 121 ± 24% | 0.017 ± 250% | 0.019 ± 560% | 190 ± 10% | 1,871 ± 62% | 6,731 ± 65% | |||||

k_{off2} (s^{−1}) | 175 ± 56% | 380 ± 120% | ||||||||||

k_{off3} (s^{−1}) | 4,541 ± 30% | 6,822 ± 61% | ||||||||||

γ (s^{−1}) | 27.9 ± 9% | 42.1 ± 23% | 43.54 ± 98% | 1.07 ± 105% | 242 ± 75% | |||||||

δ (s^{−1}) | 3,491 ± 17% | 632 ± 9% | 3,718 ± 17% | 3,875 ± 33% | 9,035 ± 11% | |||||||

α (s^{−1}) | 1,829 ± 9% | 110,104 ± ∞% | 29.0 ± 13% | 1,088 ± 33% | 10.2 ± 53% | 776 ± 120% | 110 ± 66% | |||||

α_{2} (s^{−1}) | 1,189 ±410% | 0.246 ±123% | ||||||||||

β (s^{−1}) | 27.3 ± 14% | 382 ± ∞% | 24.08 ± ∞% | 540 ± 99% | 769 ± 7% | 914 ± 110% | 1,380 ± 9% | |||||

β_{2} (s^{−1}) | 3,198 ± 18% | 0.033 ± 160% | ||||||||||

ε_{1} (s^{−1}) | 1,936 ± 7% | 79.0 ± 84% | ||||||||||

ε_{2} (s^{−1}) | 8.48 ± 822% | 3.20 ± 491% | ||||||||||

ζ_{1} (s^{−1}) | 0.298 ± 680% | 31.16 ± 123% | ||||||||||

ζ_{2} (s^{−1}) | 5.9*10^{7} ± 490% | 4.53 ± 113% | ||||||||||

Allosteric factors | ||||||||||||

A_{koff} | 49.6 ± 17% | 1.00 ± 34% | 0.309 ± 316% | |||||||||

A_{kon} | 4.51 ± 31% | 1.77 ± 31% | 1.00 ± 182% | |||||||||

A_{α} | 48.9 ± 19% | 2.30 ± 103% | 1.00 ± 106% | |||||||||

A_{β} | 4.58 ± 41% | 0.77 ± 121% | 0.309 ± 226% | |||||||||

B_{koff} | 65.1 ± 72% | 4,295 ± 270% | ||||||||||

B_{kon} | 1.15 ± 110% | 1.00 ± 520% | ||||||||||

B_{δ} | 33.3 ± 115% | 4,300 ± 260% | ||||||||||

B_{γ} | 2.25 ± 33% | 1.00 ± 300% | ||||||||||

C_{α} | 0.19 ± 230% | 10.1 ± 240% | ||||||||||

C_{β} | 635 ± ∞% | 62.1 ± 380% | ||||||||||

C_{δ} | 1.00 ± ∞% | 5.31 ± 440% | ||||||||||

C_{γ} | 123 ± 300% | 118 ± 250% |

The EC_{50} was forced to be 9.8 μM for all fits except for the version of Scheme 2 indicated as EC_{50} free. The data set is the same illustrated in Fig. 11. Df indicates the number of free parameters to be optimized by the nonlinear algorithm. SS indicates the sum of squared residuals. Except for Scheme 2 there was very little increase in the SS as a result of fixing the EC_{50}. The macroscopic parameters pOmax (maximum open probability for a saturating pulse of ATP) and pOmin (the open probability with no ATP present) were calculated based on the microscopic rates from each fit shown below. The EC_{50} was also calculated for Model 2. Standard errors of the estimated kinetic rates and allosteric constants were calculated on a logarithmic scale and presented as percentages. They were obtained using a bootstrap approach (Kraushaar and Jonas, 2000).

The kinetic rates of the fits are defined as follows. For Schemes 2, 5, 6, and 7 there was a single binding rate (k_{on}) and unbinding rate (k_{off}), while for Schemes 3 and 4 there were three independent rates designated as k_{on}, k_{on2}, and k_{on3} for binding and k_{off}, k_{off2}, and k_{off3} for unbinding. When flipping was present, the flipping rate was designated as δ and the unflipping rate as γ. β is the opening rate and α the closing rate from the fully liganded (and if relevant, fully flipped) state. For Schemes 3 and 4, additional values are provided for the opening to (β_{2}) and closing from (α_{2}) a second open state. For models 3 and 4 in which there are two open states, *ζ* is the rate of closing to, and *ε* the rate of opening from, a final closed state from which only opening is possible. The subscript 1 or 2 indicates the identity of the open state involved in the transition.

Allosteric factors of Schemes 5–7 are designated as follows. Binding–gating coupling factors start with an A. A_{kon} indicates the factor of increase in the binding rate produced by each ligand. A_{koff} indicates the factor of decrease in the unbinding rate per ligand. A_{α} indicates the factor of decrease in the closing rate per ligand and A_{β} the factor of increase in the opening rate per ligand. Binding–flipping coupling factors start with a B. B_{kon} is factor of increase in the binding rate to the binding domain produced by flipping of the whole channel (Scheme 6) or by the flipping of the same domain referred by the binding rate. B_{koff} is the factor of decrease in the unbinding rate produced by the flipping of the whole channel or of the relevant domain. B_{γ} and B_{δ} in Scheme 6 are the factor of increase and decrease of the flipping and unflipping rate produced by each ligand. In Scheme 7 they are the factor of increase and decrease of the flipping and unflipping rates produced at the ligand domain by the presence of a bound ligand. Flipping–gating coupling factors start with a C. C_{δ} and C_{γ} indicate the factor of increase in flipping rate and decrease in unflipping rate produced by the opening of the channels, whereas C_{β} and C_{α} indicate the factor of increase in opening and of decrease in closing produced by the flipping either of the whole channel (Scheme 6) or by each flipping domain (Scheme 7).

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