Table 1.

Summary of the results of free-energy calculations

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	$\mathrm{\Delta }{G}_{r_{\mathrm{L}},r_{\mathrm{P}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ = −17.7 ± 1.0	$\mathrm{\Delta }{G}_{\Omega ,r_{\mathrm{L}},r_{\mathrm{P}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ = −17.0 ± 0.5
Orientation correction (kcal mol−1)	NA	ΔUΩ(xB) = 4.4 ± 0.3	NA	$\mathrm{\Delta }{U}_{\Omega ,r_{\mathrm{L}},r_{\mathrm{P}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ = 4.6 ± 0.3
Ligand RMSD correction (kcal mol−1)	NA	N/A	$\mathrm{\Delta }{U}_{r_{\mathrm{L}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ = 0.6 ± 0.1	$\mathrm{\Delta }{U}_{r_{\mathrm{L}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ = 0.6 ± 0.1
Protein RMSD correction (kcal mol−1)	NA	NA	$\mathrm{\Delta }{U}_{r_{\mathrm{P}}}^{r_{\mathrm{L}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ = 0.3 ± 0.1	$\mathrm{\Delta }{U}_{r_{\mathrm{P}}}^{r_{\mathrm{L}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ = 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

We are comparing the ΔG° of four different restraining methods (see ‘BEUS simulations’ in Methods for details).

^aAll error estimates are based on 1 s.d.

^bEquilibrium dissociation constant (K_d) values are determined directly from mean absolute binding-free-energy (ΔG°) values using relation (2).

^cK_d range is determined from the lower and upper limits of ΔG° values (mean ± s.d.) using relation (2). The experimentally determined K_d 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 (r_P), RMSD of heparin (r_L), and the contribution of the difference between the volume of the binding pocket and the bulk to the binding free energy (ΔG_V). ΔG(x_B), ΔG_Ω(x_B), $\mathrm{\Delta }{G}_{r_{\mathrm{L}},r_{\mathrm{P}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ and $\mathrm{\Delta }{G}_{\Omega ,r_{\mathrm{L}},r_{\mathrm{P}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ 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. ΔU_Ω(x_B), $\mathrm{\Delta }{U}_{\Omega }^{r_{\mathrm{L}},r_{\mathrm{P}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$, $\mathrm{\Delta }{U}_{r_{\mathrm{L}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ and $\mathrm{\Delta }{U}_{r_{\mathrm{P}}}^{r_{\mathrm{L}}}\left({\mathbf{x}}_{\mathrm{B}}\right)$ are correction terms associated with restraints (see ‘Theoretical foundation’ in Methods for details).