3.2.2 Fitting
to Experimental Binding
Free Energies
Experimental binding free energies were available for 44 complexes
[44]. Four very weak binders were excluded. To obtain relative
values, the free energies were compared to either the WT:Sdc1
value or the QM:Caspr4 value, depending on which X-ray structure
was used to model each variant. This left 38 independent ΔG
values. Three involving the neurexin peptide were left aside and
the remaining 35 were used to fit the adjustable constants α, β, and
γ. Extensive cross-validation was done, where subsets of the data
were excluded from the fit; this gave similar fitted values and errors.
3.3 Selected Results
3.3.1 Mean Errors
For the 35 complexes with experimental ΔG values, the mean
unsigned and rms errors were 0.43 and 0.55 kcal/mol. The Pearson correlation between the experimental and computed values was
R ¼ 0.64. The three largest errors were 1.31, 1.13, and 1.09 kcal/
mol and included two Caspr4 complexes. Thus, there were no very
large errors and the mean error is very small, and corresponds to
chemical accuracy (less than the thermal energy kT).
3.3.2 Scoring Sequences
from CPD
From the top 30 peptide variants predicted by CPD to be the
tightest binders, we chose 14 for medium-throughput study.
Results (reported here) are given in Table 1. The adaptive MC
results are also given. MC predicted that several variants should
bind more strongly than Sdc1. PB/LIE, on the other hand, predicts that 12 of the variants bind less strongly, with ΔGs that are
between 0.1 and 0.6 kcal/mol less favorable than Sdc1. Two are
predicted to bind as strongly as Sdc1. None show improved binding. Since the mean PB/LIE error is around 0.5 kcal/mol, we
conclude that at best, the high-throughput design may have produced a few peptides with weakly improved affinities. It may be
possible to improve binding by designing other peptide positions
or allowing ncAAs.
3.4 Other Variants
of the Model
3.4.1 GB Instead of PB
Claims are sometimes made that PB is a better electrostatic model
than GB for binding and other properties. Here, switching to GB
gave very slight increases of mue and rmse, to 0.55 and 0.66 kcal/
mol, respectively. Notice that we used GB for CPD.
3.4.2 Lazaridis–Karplus
Instead of SA
The Lazaridis–Karplus solvent model was parameterized elsewhere
for nonpolar solvation effects [32]. It was applied to the PDZ–
peptide complexes without any reparameterization, in combination
with the GB electrostatic term. The mue and rmse values were 0.59
and 0.69 kcal/mol, respectively, almost the same as with GB + SA.
3.4.3 Two-Trajectory
Model for Peptide Flexibility
The flexibility of the unbound peptide is in principle sequencedependent, which could influence relative affinities. Therefore, we
also considered a model where the binding process is divided into
two steps. In the first, we apply restraints to the peptide, forcing it
to be close to its bound conformation; in the second it binds
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to Experimental Binding
Free Energies
Experimental binding free energies were available for 44 complexes
[44]. Four very weak binders were excluded. To obtain relative
values, the free energies were compared to either the WT:Sdc1
value or the QM:Caspr4 value, depending on which X-ray structure
was used to model each variant. This left 38 independent ΔG
values. Three involving the neurexin peptide were left aside and
the remaining 35 were used to fit the adjustable constants α, β, and
γ. Extensive cross-validation was done, where subsets of the data
were excluded from the fit; this gave similar fitted values and errors.
3.3 Selected Results
3.3.1 Mean Errors
For the 35 complexes with experimental ΔG values, the mean
unsigned and rms errors were 0.43 and 0.55 kcal/mol. The Pearson correlation between the experimental and computed values was
R ¼ 0.64. The three largest errors were 1.31, 1.13, and 1.09 kcal/
mol and included two Caspr4 complexes. Thus, there were no very
large errors and the mean error is very small, and corresponds to
chemical accuracy (less than the thermal energy kT).
3.3.2 Scoring Sequences
from CPD
From the top 30 peptide variants predicted by CPD to be the
tightest binders, we chose 14 for medium-throughput study.
Results (reported here) are given in Table 1. The adaptive MC
results are also given. MC predicted that several variants should
bind more strongly than Sdc1. PB/LIE, on the other hand, predicts that 12 of the variants bind less strongly, with ΔGs that are
between 0.1 and 0.6 kcal/mol less favorable than Sdc1. Two are
predicted to bind as strongly as Sdc1. None show improved binding. Since the mean PB/LIE error is around 0.5 kcal/mol, we
conclude that at best, the high-throughput design may have produced a few peptides with weakly improved affinities. It may be
possible to improve binding by designing other peptide positions
or allowing ncAAs.
3.4 Other Variants
of the Model
3.4.1 GB Instead of PB
Claims are sometimes made that PB is a better electrostatic model
than GB for binding and other properties. Here, switching to GB
gave very slight increases of mue and rmse, to 0.55 and 0.66 kcal/
mol, respectively. Notice that we used GB for CPD.
3.4.2 Lazaridis–Karplus
Instead of SA
The Lazaridis–Karplus solvent model was parameterized elsewhere
for nonpolar solvation effects [32]. It was applied to the PDZ–
peptide complexes without any reparameterization, in combination
with the GB electrostatic term. The mue and rmse values were 0.59
and 0.69 kcal/mol, respectively, almost the same as with GB + SA.
3.4.3 Two-Trajectory
Model for Peptide Flexibility
The flexibility of the unbound peptide is in principle sequencedependent, which could influence relative affinities. Therefore, we
also considered a model where the binding process is divided into
two steps. In the first, we apply restraints to the peptide, forcing it
to be close to its bound conformation; in the second it binds
248
Nicolas Panel et al.