Tiam1. The first free energy contribution is deduced from the
fraction of bound conformations in MD simulations of the
unbound peptide. The second is computed from the PB/LIE
model as before. Hence, two trajectories are used (per peptide
variant). In practice, the first contribution is small and noisy, and
several 100 ns are needed for convergence. Its sequencedependence is weak. With this model, the rms error did not
improve.
3.4.4 Three-Trajectory
Model
For two complexes, WT:Sdc1 and QM:Caspr4, we performed
much longer MD simulations and applied a 3-trajectory method
to the PB free energy component. The unbound peptides were
simulated for 400 ns, the two complexes for 500 ns, and the
unbound proteins for 1000 ns each. The binding free energy
difference between the two variants was in excellent agreement
with the single-trajectory value.
Table 1
Relative Tiam1 binding free energies ΔΔG of designed peptides from PB/LIE
ΔΔG
Sequence
a
PB
b
vdW
b
SA
b
c
ΔG
c PB/LIE
d Proteus
ETMNA
À3.25
À48.10
À1310.1
3.46
À0.05
À1.2
EEMNA
À2.99
À49.48
À1307.6
3.49
À0.02
À1.1
EEFYA
À2.84
À58.67
À1349.3
3.51
0.00
0.0
YECEA
À3.01
À55.62
À1371.0
3.61
0.11
À1.3
YTCDA
À2.26
À50.67
À1313.2
3.77
0.16
À1.3
ESMTA
À2.24
À48.65
À1305.9
3.70
0.18
À1.2
YSCDA
À1.88
À49.70
À1295.0
3.71
0.20
À1.3
ETMTA
À2.50
À49.47
À1331.0
3.71
0.20
À1.1
ETMEA
À1.06
À46.81
À1247.8
3.79
0.28
À1.1
EEMSA
À1.64
À49.27
À1329.5
3.92
0.41
À1.2
YNCTA
+1.20
À38.10
À1111.0
3.98
0.47
À1.3
YTCVA
À1.87
À57.31
À1398.6
3.98
0.47
À1.3
YTCTA
À0.93
À50.07
À1321.8
4.05
0.54
À1.5
YNCYA
À1.56
À57.28
À1401.7
4.07
0.56
À1.3
YSCTA
À0.46
À49.27
À1311.0
4.14
0.63
À1.4
PB/LIE binding free energies ΔG (Eq. 4) for selected peptide sequences, in kcal/mol. ΔΔG values are relative to Sdc1
(in bold, “EEFYA”)
a
The five C-terminal amino acids are listed. The N-terminal ones are always TKQ
b
Specific ΔG contributions, in kcal/mol or Å
2 (SA)
c
Component weights (Eq. 4) were α ¼ 0.02 (vdw), β ¼ 0.25 (elec), and γ ¼ À4 cal/mol/Å
2
d
CPD values (adaptive MC with Proteus)
Computational Design of Binding
249
fraction of bound conformations in MD simulations of the
unbound peptide. The second is computed from the PB/LIE
model as before. Hence, two trajectories are used (per peptide
variant). In practice, the first contribution is small and noisy, and
several 100 ns are needed for convergence. Its sequencedependence is weak. With this model, the rms error did not
improve.
3.4.4 Three-Trajectory
Model
For two complexes, WT:Sdc1 and QM:Caspr4, we performed
much longer MD simulations and applied a 3-trajectory method
to the PB free energy component. The unbound peptides were
simulated for 400 ns, the two complexes for 500 ns, and the
unbound proteins for 1000 ns each. The binding free energy
difference between the two variants was in excellent agreement
with the single-trajectory value.
Table 1
Relative Tiam1 binding free energies ΔΔG of designed peptides from PB/LIE
ΔΔG
Sequence
a
PB
b
vdW
b
SA
b
c
ΔG
c PB/LIE
d Proteus
ETMNA
À3.25
À48.10
À1310.1
3.46
À0.05
À1.2
EEMNA
À2.99
À49.48
À1307.6
3.49
À0.02
À1.1
EEFYA
À2.84
À58.67
À1349.3
3.51
0.00
0.0
YECEA
À3.01
À55.62
À1371.0
3.61
0.11
À1.3
YTCDA
À2.26
À50.67
À1313.2
3.77
0.16
À1.3
ESMTA
À2.24
À48.65
À1305.9
3.70
0.18
À1.2
YSCDA
À1.88
À49.70
À1295.0
3.71
0.20
À1.3
ETMTA
À2.50
À49.47
À1331.0
3.71
0.20
À1.1
ETMEA
À1.06
À46.81
À1247.8
3.79
0.28
À1.1
EEMSA
À1.64
À49.27
À1329.5
3.92
0.41
À1.2
YNCTA
+1.20
À38.10
À1111.0
3.98
0.47
À1.3
YTCVA
À1.87
À57.31
À1398.6
3.98
0.47
À1.3
YTCTA
À0.93
À50.07
À1321.8
4.05
0.54
À1.5
YNCYA
À1.56
À57.28
À1401.7
4.07
0.56
À1.3
YSCTA
À0.46
À49.27
À1311.0
4.14
0.63
À1.4
PB/LIE binding free energies ΔG (Eq. 4) for selected peptide sequences, in kcal/mol. ΔΔG values are relative to Sdc1
(in bold, “EEFYA”)
a
The five C-terminal amino acids are listed. The N-terminal ones are always TKQ
b
Specific ΔG contributions, in kcal/mol or Å
2 (SA)
c
Component weights (Eq. 4) were α ¼ 0.02 (vdw), β ¼ 0.25 (elec), and γ ¼ À4 cal/mol/Å
2
d
CPD values (adaptive MC with Proteus)
Computational Design of Binding
249