Table 1 Summary of the results of free-energy calculations

From: Binding affinity estimation from restrained umbrella sampling simulations

Quantity

No restraints

Ω restraint

rL and rP restraint

Ω, rL and rP restraint

Grid PMF difference (kcal mol−1)

ΔG(xB) = −19.7 ± 1.1a

ΔGΩ(xB) = −13.2 ± 0.3

\({{\Delta }}G_{r_{\mathrm{L}},r_{\mathrm{P}}}( {{{{\boldsymbol{x}}}}_{\mathrm{B}}})\) = −17.7 ± 1.0

\({{\Delta }}G_{{\varOmega},{r_{\mathrm{L}},r_{\mathrm{P}}}}( {{{{\boldsymbol{x}}}}_{\mathrm{B}}})\) = −17.0 ± 0.5

Orientation correction (kcal mol−1)

NA

ΔUΩ(xB) = 4.4 ± 0.3

NA

\({{\Delta }}U_{{\varOmega},{r_{\mathrm{L}},r_{\mathrm{P}}}}( {{{{\boldsymbol{x}}}}_{\mathrm{B}}})\) = 4.6 ± 0.3

Ligand RMSD correction (kcal mol−1)

NA

N/A

\({{\Delta }}U_{r_{\mathrm{L}}}( {{{{\boldsymbol{x}}}}_{\mathrm{B}}})\) = 0.6 ± 0.1

\({{\Delta }}U_{r_{\mathrm{L}}}( {{{{\boldsymbol{x}}}}_{\mathrm{B}}})\) = 0.6 ± 0.1

Protein RMSD correction (kcal mol−1)

NA

NA

\({{\Delta }}U_{{{r}}_{{{\mathrm{P}}}}}^{r_{\mathrm{L}}}\left( {{{{\boldsymbol{x}}}}_{\mathrm{B}}} \right)\) = 0.3 ± 0.1

\({{\Delta }}U_{{{r}}_{{{\mathrm{P}}}}}^{r_{\mathrm{L}}}\left( {{{{\boldsymbol{x}}}}_{\mathrm{B}}} \right)\) = 0.3 ± 0.1

ΔGV (kcal mol−1)

3.7 ± 0.2

2.5 ± 0.2

2.3 ± 0.2

2.7 ± 0.2

ΔG°(kcal mol−1)

−16.0 ± 1.2

−6.3 ± 0.5

−14.5 ± 1.0

−8.7 ± 0.7

Kd (μM)b

O(10−6)

25

O(10−5)

0.5

Kd range (μM)c

10−7–10−5

11–58

10−6–10−4

0.2−2.0

  1. We are comparing the ΔG° of four different restraining methods (see ‘BEUS simulations’ in Methods for details).
  2. aAll error estimates are based on 1 s.d.
  3. bEquilibrium dissociation constant (Kd) values are determined directly from mean absolute binding-free-energy (ΔG°) values using relation (2).
  4. cKd range is determined from the lower and upper limits of ΔG° values (mean ± s.d.) using relation (2). The experimentally determined Kd and ΔG° were 1.68 ± 0.03 μM and −7.88 ± 0.01 kcal mol−1, respectively (see Fig. 4). The orientation angle of heparin with respect to the protein (Ω), RMSD of the protein (rP), RMSD of heparin (rL), and the contribution of the difference between the volume of the binding pocket and the bulk to the binding free energy (ΔGV). ΔG(xB), ΔGΩ(xB), \({{\Delta }}G_{r_{\mathrm{L}},r_{\mathrm{P}}}\left( {{{{\boldsymbol{x}}}}_{\mathrm{B}}} \right)\) and \({{\Delta }}G_{{{\varOmega }},r_{\mathrm{L}},r_{\mathrm{P}}}\left( {{{{\boldsymbol{x}}}}_{\mathrm{B}}} \right)\) are the PMF difference between the binding pocket center and the bulk associated with respective restraints. NA means the data are not applicable in the corresponding section. ΔUΩ(xB), \({{\Delta }}U_{{\varOmega }}^{r_{\mathrm{L}},r_{\mathrm{P}}}\left( {{{{\boldsymbol{x}}}}_{\mathrm{B}}} \right)\), \({{\Delta }}U_{{{r}}_{{{\mathrm{L}}}}}\left( {{{{\boldsymbol{x}}}}_{\mathrm{B}}} \right)\) and \({{\Delta }}U_{{{r}}_{{{\mathrm{P}}}}}^{r_{\mathrm{L}}}\left( {{{{\boldsymbol{x}}}}_{\mathrm{B}}} \right)\) are correction terms associated with restraints (see ‘Theoretical foundation’ in Methods for details).
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