Supplementary Material of "Assessment and acceleration of binding energy calculations for
protein-ligand complexes by fragment molecular orbital method"
Takao Otsuka, Noriaki Okimoto, and Makoto Taiji
Laboratory for Computational Molecular Design, Computational Biology Research Core,
RIKEN Quantitative Biology Center (QBiC), 1-6-5 Minatojima Minamimachi, Chuo-ku,
Kobe, Hyogo 650-0047, Japan
Corresponding to: totsuka@riken.jp and okimoto@gsc.riken.jp
Supporting data for the FMO calculations discussed in the main article are provided
in Sections 1 to 3 in this document. In our article, we described a scheme for predicting
binding affinities using the QSAR model with binding energies obtained by FMO calculations.
We showed that the binding energy from the FMO calculation is an important factors in the
prediction scheme. In the supplementary material, we present detailed binding energy results
for various FMO calculation conditions.
S1. Fragmentation size dependency and FMO three-body expansion binding energy
results calculated by the FMO method
Here, we describe the dependence of binding energy on fragmentation size and
three-body expansion in the FMO calculations. The total number of fragments is shown in
Table S-1. Table S1-2 shows the binding energies calculated by FMO2-MP2/6-31G(d) with
various fragmentation sizes. Figure S1-A also shows the correlation between the experimental
binding affinities and the calculated binding energies for various fragmentation sizes. As seen
in Table S1-2 and Figure S1-A, the 2res/1frg and 3res/1frg fragmentation sizes exhibit nearly
similar tendencies and overestimate the binding energy compared to the case of 1res/1frg. The
differences in binding energies between 2res/1frg and 3res/1frg are very small. The binding
energies calculated by FMO2-HF (2res/1frg and 3res/1frg) exhibit no correlation (R =
0.18-0.19) with the experimental binding affinity, whereas those calculated by
FMO2-MP2/6-31G(d) show slightly higher correlation coefficients (R = 0.79) for 2res/1frg
and 3res/1frg.
Table S1-3 shows the binding energies calculated by FMO3-HF/6-31G(d) and
FMO3-MP2/6-31G(d) with 1res/1frg fragmentation size. Figure S1-B also shows the
correlation
between
experimental
binding
affinities
and
values
computed
by
FMO3-MP2/6-31G(d). From Table S1-3 and Figure S1-B, the FMO3-MP2/6-31G(d) results
show higher correlation coefficients (R = 0.80) compared to FMO2-MP2/6-31G(d). Generally,
the FMO3 scheme can better describe local molecular interactions such as covalent and/or
hydrogen bonds compared to FMO2. Recently, it has been reported that the FMO three or
four-body expansions provide improved descriptions of the interactions between the
fragments in the inter-fragment interaction energy analysis [1,2]. Therefore, the FMO3
scheme can be expected to provide an improved description of the intermolecular interactions
for a wide range of protein and ligand molecules, owing to the inclusion of the three-residue
interaction effects.
Table S-1. Total number of fragments, Nfrg, for the FKBP molecule only, obtained by the
fragmentation of one amino-acid residue per fragment (1res/1frg), two amino-acid residues
per fragment (2res/1frg), and three-amino acid residues per fragment (3res/1frg). The numbers
in parentheses refer to the corresponding number of fragments for the FKBP-ligand complex
molecule.
Nfrg
1res/1frg
2res/1frg
3res/1frg
106 (107)
54 (55)
37 (38)
Table S1-2. Fragmentation size dependence of binding energies (in kcal/mol) calculated by
FMO2−HF
FMO2−MP2
FMO2-HF (∆𝐸𝑏𝑖𝑛𝑑
) and FMO2-MP2 (∆𝐸𝑏𝑖𝑛𝑑
) with one amino-acid residue, two
amino-acid residues, and three amino-acid residues per fragment (1res/1frg, 2res/1frg, and
3res/1frg, respectively). 6-31G(d) is used as the basis set. The correlation coefficients (R) and
the squared values (R2) are also shown.
FMO2−HF
∆𝐸𝑏𝑖𝑛𝑑
Expa
FMO2−MP2
∆𝐸𝑏𝑖𝑛𝑑
1res/1frg
2res/1frg
3res/1frg
1res/1frg
2res/1frg
3res/1frg
Lig2
-7.8
-18.56
-19.80
-19.68
-58.85
-60.67
-60.58
Lig3
-8.4
-14.62
-15.94
-15.65
-55.40
-57.27
-57.01
Lig5
-9.5
-12.29
-14.65
-14.39
-61.83
-65.13
-64.99
Lig6
-10.8
-16.30
-18.12
-17.94
-71.66
-74.03
-74.16
Lig8
-10.9
-12.07
-13.94
-13.59
-66.37
-69.12
-69.05
Lig9
-11.1
-13.07
-15.28
-14.99
-63.76
-67.08
-66.75
Lig12
-10.3
-17.99
-19.14
-18.88
-62.18
-64.01
-64.00
Lig13
-9.5
-17.91
-19.01
-18.69
-66.09
-68.18
-68.13
Lig14
-12.3
-13.55
-15.59
-15.27
-66.69
-69.80
-69.61
Lig20
-12.8
-23.52
-24.67
-24.36
-89.49
-92.01
-92.06
R2
0.019
0.036
0.031
0.593
0.630
0.625
R
0.136
0.190
0.177
0.770
0.794
0.790
a
is taken from Ref. [12].
Table S1-3. FMO three-body expansion of binding energies (in kcal/mol) calculated by
FMO3−HF
FMO3−MP2
FMO3-HF (∆𝐸𝑏𝑖𝑛𝑑
) and FMO3-MP2 (∆𝐸𝑏𝑖𝑛𝑑
) with one amino-acid residue per
fragment (1res/1frg). 6-31G(d) is used as the basis set. The correlation coefficients (R) and the
squared values (R2) are also shown.
FMO2
∆𝐸𝑏𝑖𝑛𝑑
Expa
HF
FMO3
∆𝐸𝑏𝑖𝑛𝑑
MP2
HF
MP2
Lig2
-7.8
-18.56
-58.85
-19.25
-62.84
Lig3
-8.4
-14.62
-55.40
-15.32
-59.04
Lig5
-9.5
-12.29
-61.83
-14.57
-68.09
Lig6
-10.8
-16.30
-71.66
-18.09
-77.54
Lig8
-10.9
-12.07
-66.37
-13.46
-72.16
Lig9
-11.1
-13.07
-63.76
-15.25
-70.29
Lig12
-10.3
-17.99
-62.18
-17.65
-65.09
Lig13
-9.5
-17.91
-66.09
-17.48
-69.43
Lig14
-12.3
-13.55
-66.69
-15.06
-72.77
Lig20
-12.8
-23.52
-89.49
-23.04
-94.28
R2
0.019
0.593
0.034
0.654
R
0.136
0.770
0.184
0.808
a
is taken from Ref. [12].
Figure S1-A. Correlation between the experimental binding affinities and binding energies
calculated by (a) FMO2-HF/6-31G(d) and (b) FMO2-MP2/6-31G(d) with various
fragmentation sizes: one amino-acid residue (1res/1frg, black circle), two amino-acid residues
(2res/1frg, red open triangle), and three amino-acid residues (3res/1frg, green open square)
per fragment. The regression lines for each fragmentation size (black dashed line: 1res/1frg,
red solid line: 2res/1frg, green solid line: 3res/1frg) are also drawn in the diagrams.
Experimental (kcal/mol)
(a)
-6
1res/1frg (R=0.136)
2res/1frg (R=0.190)
3res/1frg (R=0.177) Lig2
-8
Lig3
Lig13
-10
Lig5
Lig12
Lig8
Lig6
-12
Lig9
Lig14
Lig20
-14
-30
-25
-20
-15
-10
Calculated (kcal/mol)
Experimental (kcal/mol)
(b)
-6
1res/1frg (R=0.770)
2res/1frg (R=0.794)
3res/1frg (R=0.790) Lig2
-8
Lig13
-10
-12
Lig5
Lig3
Lig12
Lig6
Lig8
Lig9
Lig20
Lig14
-14
-100 -90 -80 -70 -60 -50 -40 -30
Calculated (kcal/mol)
Figure S1-B. Correlation between the experimental binding affinities and binding energies
calculated by FMO3-MP2/6-31G(d) (inverted open triangle). In the diagrams, the
FMO2-MP2/6-31G(d) results (black circle) are also shown for reference. The regression lines
for each calculation condition (dashed line: FMO2-MP2, solid line: FMO3-MP2) are also
Experimental (kcal/mol)
drawn in the diagram.
-6
FMO2-MP2 (R=0.770)
FMO3-MP2 (R=0.808)
Lig2
-8
Lig3
Lig5
Lig13
Lig6
-10
-12
Lig8
Lig12
Lig9
Lig20
Lig14
-14
-100 -90 -80 -70 -60 -50 -40 -30
Calculated (kcal/mol)
S2. Dependence of the binding energies calculated by the FMO method on empirical
MP2 corrections
We also report the effects of the empirically modified MP2 corrections
(spin-component-scaling correction of MP2 (SCS-MP2)) [3].
Table S2-1 shows the binding energies calculated by FMO2 with 6-31G(d) basis sets
with SCS-MP2 corrections. Figure S2-A shows the correlation between the experimental
binding affinities and binding energies calculated by FMO2-SCS-MP2. We can see that the
correlation coefficient in the case of FMO2-SCS-MP2/6-31G(d) (R = 0.74) is slightly lower
compared to conventional FMO2-MP2/6-31G(d) (R = 0.77). The slope of the regression line
for the binding energies calculated by FMO2-SCS-MP2/6-31G(d) exhibit a slightly different
tendency than those calculated by conventional FMO methods, as shown in Figure S2-A.
Based on studies on high-level quantum chemistry calculations using some small molecular
systems, it is known that the SCS-MP2 scheme with appropriate parameters provides
significant improvement in describing non-covalent or stacking interactions [10]. In the
present study, we were unable to obtain such drastic improvements in the descriptions of
protein-ligand interactions, although we used the original SCS-MP2 parameter set proposed
by Grimme [3].
Table S2-1. Comparison of binding energies (in kcal/mol) calculated by FMO2-MP2
FMO2−MP2
FMO2−SCS−MP2
(∆𝐸𝑏𝑖𝑛𝑑
) and FMO2-SCS-MP2 (∆𝐸𝑏𝑖𝑛𝑑
) with one amino-acid residue per
fragment (1res/1frg). 6-31G(d) is used as the basis set. The correlation coefficients (R) and the
squared values (R2) are also shown.
FMO2−MP2
∆𝐸𝑏𝑖𝑛𝑑
Expa
FMO2−SCS−MP2
∆𝐸𝑏𝑖𝑛𝑑
Lig2
-7.8
-58.85
-49.77
Lig3
-8.4
-55.40
-46.27
Lig5
-9.5
-61.83
-50.80
Lig6
-10.8
-71.66
-59.37
Lig8
-10.9
-66.37
-54.36
Lig9
-11.1
-63.76
-52.51
Lig12
-10.3
-62.18
-52.36
Lig13
-9.5
-66.09
-55.36
Lig14
-12.3
-66.69
-54.86
Lig20
-12.8
-89.49
-74.25
R2
0.593
0.544
R
0.770
0.738
a
is taken from Ref. [12].
Figure S2-A. Correlation between the experimental binding affinities and binding energies
calculated
by
FMO2-SCS-MP2/6-31G(d)
(open
circle).
In
the
diagrams,
the
FMO2-MP2/6-31G(d) results (black circle) are also shown for reference. The regression lines
for the two calculation conditions (dashed line: FMO2-MP2, solid line: FMO2-SCS-MP2) are
Experimental (kcal/mol)
also shown in the diagram.
-6
FMO2-MP2 (R=0.770)
FMO2-SCS-MP2 (R=0.738)
Lig2
-8
Lig13
-10
Lig12
Lig6
-12
Lig3
Lig5
Lig8
Lig9
Lig20
Lig14
-14
-100 -90 -80 -70 -60 -50 -40 -30
Calculated (kcal/mol)
S3. Incorporation of the solvation effect obtained by the PCM method in the FMO
binding energy calculations
Here, we also report detailed information on the FMO calculations considering
solvation effects. Following the previous study on the binding energy calculations by the
combination of FMO and PCM methods [11], we utilized the FMO/PCM [1(2)] method,
which was shown to be the most practical method. Table S3-1 and Figure S3-A show the
binding energy results obtained by combining FMO2-MP2 with the PCM method. The
correlation coefficient in this case is drastically improved (R = 0.91) compared to the values
calculated by FMO-MP2 without PCM. The slope of the regression line in the case of
FMO2-MP2/PCM[1(2)] exhibits a different tendency compared to the conventional
FMO2-MP2 without PCM method. The binding energies calculated by including the solvation
effect better correlate with the experimental affinity values.
Table S3-1. Comparison of binding energies (in kcal/mol) calculated by FMO2-MP2
FMO2−MP2/PCM
FMO2−MP2
(∆𝐸𝑏𝑖𝑛𝑑
) and FMO2-MP2/PCM (∆𝐸𝑏𝑖𝑛𝑑
) with one amino-acid residue per
fragment (1res/1frg). 6-31G(d) is used as the basis set. The correlation coefficients (R) and the
squared values (R2) are also shown.
FMO2−MP2
∆𝐸𝑏𝑖𝑛𝑑
Expa
FMO2−MP2/PCM
∆𝐸𝑏𝑖𝑛𝑑
Lig2
-7.8
-58.85
-39.34
Lig3
-8.4
-55.40
-40.52
Lig5
-9.5
-61.83
-45.42
Lig6
-10.8
-71.66
-51.33
Lig8
-10.9
-66.37
-53.24
Lig9
-11.1
-63.76
-50.45
Lig12
-10.3
-62.18
-47.84
Lig13
-9.5
-66.09
-50.02
Lig14
-12.3
-66.69
-54.73
Lig20
-12.8
-89.49
-69.03
R2
0.593
0.827
R
0.770
0.910
a
is taken from Ref. [12].
Figure S3-A. Correlation between the experimental binding affinities and binding energies
calculated by FMO2-MP2/6-31G(d)/PCM[1(2)] (open rhombus). In the diagrams, the
FMO2-MP2/6-31G(d) results (black circle) are also shown for reference. The regression lines
for
the
two
calculation
conditions
(dashed
line:
FMO2-MP2,
Experimental (kcal/mol)
FMO2-MP2/PCM[1(2)]) are also drawn in the diagram.
-6
FMO2-MP2 (R=0.770)
FMO2-MP2/PCM (R=0.910)
Lig2
-8
Lig3
Lig13
-10
-12
Lig6
Lig20
Lig8
Lig14
Lig5
Lig12
Lig9
-14
-100 -90 -80 -70 -60 -50 -40 -30
Calculated (kcal/mol)
solid
line:
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