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Comparison of enveloping distribution sampling and thermodynamic integration to calculate binding free energies of phenylethanolamine N-methyltransferase inhibitors
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10.1063/1.3604534
/content/aip/journal/jcp/135/2/10.1063/1.3604534
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/2/10.1063/1.3604534

Figures

Image of FIG. 1.
FIG. 1.

Pictorial representation of the effect of the smoothness parameter s and the energy offset for a two state system with V A (black, dashed-dotted), V B (black, dashed), and the reference state V R (s; E R ) (black, solid). The vertical gray dashed line and the gray crosses indicate to what end state energy V A or V B a specific reference state energy V R (s; E R ) corresponds to. The black dots indicate which reference state energies are sampled. The gray solid line corresponds to the energy threshold E thres . (a) too small, therefore, only state B is sampled. (b) and (c) optimal, but s too large, therefore, only one end state is sampled (depending on the starting structure). (d) s parameter and energy offsets are optimal, both end states are sampled equally. (e) and (f) optimal, but s too small, thus undersampling occurs and the important configurations of the end states are no longer sampled. V(x) and x are in arbitrary units.

Image of FIG. 2.
FIG. 2.

Schematic representation of the new parameter update procedure (2). s n and are the EDS parameters at step n, 〈V X 〉 is the average potential energy of H X in state X, while N X is the number of configurations belonging to state X. The energy offsets are updated at each step n using Eq. (12).

Image of FIG. 3.
FIG. 3.

Crystal structure of human PNMT complexed with the cofactor S-adenosyl-L-homocysteine (red) and the inhibitor 7-sulfamoyl-1,2,3,4-tetrahydroisoquinolinium (orange) (ligand 7 in Fig. 4) (RCSB protein data bank entry: 1HNN) (Ref. 36), which was used as initial structure in this study. Molecular graphics made with visual molecular dynamics (VMD) (Ref. 42).

Image of FIG. 4.
FIG. 4.

Ten different tetrahydroisoquinoline derivates which act as inhibitors for PNMT.

Image of FIG. 5.
FIG. 5.

Comparison of free enthalpy differences ΔG BA = G B - G A obtained from EDS and TI for the ligands in water at 298 K and 1 atm. Results using a dual topology are shown in the upper row and those using a single topology in the lower. ΔG BA estimated with reference state parameters obtained using the original update scheme 1 are shown in the left column and those obtained using the new update scheme 2 in the right column.

Image of FIG. 6.
FIG. 6.

Comparison of the potential energy distributions of the EDS end states A (blue) and B (orange) and of the TI simulations at λ-values λ A = 0 (black) and λ B = 1 (red) for the ligands in water. EDS simulations were performed using dual topology and either the original parameter update scheme 1 (left column) or the new parameter update scheme 2 (right column). Simulations were done at 298 K and 1 atm.

Image of FIG. 7.
FIG. 7.

Comparison of the potential energy distributions of the EDS end states A (blue) and B (orange) and of the TI simulation at λ-values λ A = 0 (black) and λ B = 1 (red) for the ligands in water. EDS simulations were performed using single topology and either the original parameter update scheme 1 (left column) or the new parameter update scheme 2 (right column). Simulations were done at 298 K and 1 atm.

Image of FIG. 8.
FIG. 8.

RDF g(r) of the nitro group of ligand 5 (Fig. 4), N, O1, and O2, with respect to the oxygen atom of water. Data is shown for the end state simulation of ligand 5 (dashed line), the EDS simulation between ligand 1 and ligand 5 using parameters obtained from the original update scheme 1 (circles), and the EDS simulation between ligand 1 and ligand 5 using parameters obtained from the new update scheme 2 (thick, solid line).

Image of FIG. 9.
FIG. 9.

RDF g(r) of the sulfonamide group of ligand 7 (Fig. 4), S, O1, O2, N, H1, and H2, with respect to the oxygen atom of water. Data is shown for the end state simulation of ligand 7 (dashed line), the EDS simulation between ligand 1 and ligand 7 using parameters obtained from the original update scheme 1 (circles), and the EDS simulation between ligand 1 and ligand 7 using parameters obtained from the new update scheme 2 (thick, solid line).

Image of FIG. 10.
FIG. 10.

EDS smoothness parameter s as a function of the difference in energy offset parameters obtained from the original update scheme 1 (filled symbols) and the new update scheme 2 (open symbols). Both topology approaches were used. The values from the original update scheme were fitted with a reciprocal function.

Image of FIG. 11.
FIG. 11.

Comparison of free enthalpy differences ΔG BA = G B - G A obtained from EDS and TI for the ligand-protein complexes at 298 K and 1 atm. The EDS simulation were performed with the single topology approach. ΔG BA estimated with reference state parameters obtained using the original update scheme 1 are shown in the left panel and those obtained using the new update scheme 2 in the right panel.

Image of FIG. 12.
FIG. 12.

Comparison of potential energy distributions of the TI and EDS simulations using the new update scheme 1 for the ligands 1, 5, and 6 for the ligands in water and in the complex at 298 K and 1 atm. The distributions from perturbation 1-5 are shown in black, dashed lines for EDS and in black, solid lines for TI. The distributions from perturbation 1-6 are shown in red, dashed lines for EDS and in red, solid lines for TI. The distributions from perturbation 5-6 are shown in blue, dashed lines for EDS and in blue, solid lines for TI.

Image of FIG. 13.
FIG. 13.

Superimposed structures of ligand 6 inside the binding pocket of PNMT observed during the perturbations 1–5 and 5–6. The carbon atoms are yellow in the conformation of perturbation 1–5 and orange in the conformation of perturbation 5–6. The nitrogen atoms are in both cases blue, the hydrogen atoms white, and the oxygen atom red. The hydrogen atoms bound to carbons are not shown. Molecular graphics made with VMD (Ref. 42).

Tables

Generic image for table
Table I.

Comparison of free enthalpy differences ΔG BA = G B - G A from TI and EDS simulations of the 10 ligands (Fig. 4) in water at 298 K and 1 atm. EDS simulations were performed with parameters obtained from two different parameter update schemes 1 and 2 using a single or a dual topology. The results from TI are the averages between both perturbation directions. The errors given for the EDS results are statistical uncertainties (Ref. 11). The error estimated for the TI results was obtained by block averaging (Ref. 41).

Generic image for table
Table II.

Comparison of the reference state parameters s and energy offsets (in kJ mol−1) obtained from two different parameter update schemes using either a single or a dual topology for EDS simulations of the 10 ligands (Fig. 4) in water at 298 K and 1 atm.

Generic image for table
Table III.

Comparison of some free enthalpy differences ΔG BA = G B - G A from TI and EDS simulations of the ligands bound to PNMT at 298 K and 1 atm. EDS simulations were performed with parameters obtained from two different parameter update schemes 1 and 2 using a single topology. The results from TI are the averages between both perturbation directions, except the ones marked with a star. The errors given for the EDS results are statistical uncertainties (Ref. 11). The error estimated for the TI results was obtained by block averaging (Ref. 41).

Generic image for table
Table IV.

Experimental and computed relative binding free enthalpies from TI and EDS simulations at 298 K and 1 atm. EDS simulations were performed with parameters obtained from two different parameter update schemes 1 and 2 using a single topology. The errors of the EDS results are the sum of the errors of and . The experimental values were calculated from binding constants measured at room temperature (298 K) using Eqs. (3) and (2). Data for ligand 1 and 8 was taken from Ref. 27, for ligand 3, 4, 9, and 10 from Ref. 30, and for ligand 5, 6, and 7 from Ref. 28. In Ref. 30, bovine PNMT was used (marked with a star).

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2011-07-11
2014-04-19
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Comparison of enveloping distribution sampling and thermodynamic integration to calculate binding free energies of phenylethanolamine N-methyltransferase inhibitors
http://aip.metastore.ingenta.com/content/aip/journal/jcp/135/2/10.1063/1.3604534
10.1063/1.3604534
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