Efficient Sampling of High-Dimensional …
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directly. Overall, in systems like these where ions and peptides have competing slow
degrees of freedom, PBMetaD is shown to be the most accurate sampling scheme as
it takes both these effects into account.
This is a choice example of a system, where PBMetaD-PF could find application,
due to the degeneracy in free energy profiles of each “family” of ions. For example,
in the highly concentrated system, the PBMetaD simulation was used to bias the
distances between the COM of the peptide, 25 sodium, and 26 chloride ions to the
surface, for a total of 51 CVs. Alternatively, since the profile of each class of ions
is degenerate, a PF simulation would bias only three CVs: (1) the peptide, (2) the
family of sodium ions, and (3) the family of chloride ions.
Example 5 Sampling structural ensembles of peptides without force fields
Löhr et al. show that the M and M approach implemented with PBMetaD studies can
effectively explore the conformational space of a disordered peptide, with sufficient
experimental data, independent of the forcefield [86]. They simulated a disordered
peptide with the sequence EGAAWAASS incorporating three sources of experimental data which included: NMR chemical shifts (CS), J-couplings (JC), and
Residual Dipolar Couplings (RDCs). They simulated three variations of M and M:
unrestrained (no experimental data), using CS and JC data, and using all the data
(CS, JC, and RDCs), while also comparing two forcefield/water model combinations
(CHARMM22/TIP3P vs AMBER99SB/TIP4P-D). Additionally, they compared the
results of an implicit water model (EEF1-SB) using the CHARMM36 forcefield
for the unrestrained and full data (CS, JC, and RDCs) cases. This gave a total of
eight simulation ensembles to be compared. For the metadynamics calculations, they
biased the following CVs: backbone and dihedral angles; E1-S9 Cα–Cα distance;
W5 χ
1 and W5 χ
2 angles; and similarities between ϕ 3 and ϕ 6 , as well as ψ 3 and ψ 6 ,
dihedral angles. Upon reweighting the simulations for the equilibrium distribution,
their results indicate that regardless of the forcefield, quality of results from M and
M simulations was more similar to the reference data, with the addition of more
experimental information into the system. This method allowed for results using two
forcefields that were not only in good agreement with each other, but the experimental data as well. To push the limits of this method, they looked at simulations of
the protein in implicit solvent and compared them to results from the explicit water
models. Compared to the unrestrained models, they noted an increase in agreement
with experiments, similar to results obtained for the explicit model. A summary
of these results is included in Fig. 7. Figure 7c demonstrates that in the M and M
simulations the results for two different forcefields are indistinguishable from the
experimental results, which are not observed without the M and M scheme implemented. The power of this approach is demonstrated by its ability to elucidate an
ensemble of data with different priors that share a common solution.
Example 6 Seven-particle Lennard–Jones system
Prakash et al. employed PBMetaD-PF to describe the system consisting of 7 LJ
particles constrained in two dimensions [79]. All 21 inter-atomic distances were
135
directly. Overall, in systems like these where ions and peptides have competing slow
degrees of freedom, PBMetaD is shown to be the most accurate sampling scheme as
it takes both these effects into account.
This is a choice example of a system, where PBMetaD-PF could find application,
due to the degeneracy in free energy profiles of each “family” of ions. For example,
in the highly concentrated system, the PBMetaD simulation was used to bias the
distances between the COM of the peptide, 25 sodium, and 26 chloride ions to the
surface, for a total of 51 CVs. Alternatively, since the profile of each class of ions
is degenerate, a PF simulation would bias only three CVs: (1) the peptide, (2) the
family of sodium ions, and (3) the family of chloride ions.
Example 5 Sampling structural ensembles of peptides without force fields
Löhr et al. show that the M and M approach implemented with PBMetaD studies can
effectively explore the conformational space of a disordered peptide, with sufficient
experimental data, independent of the forcefield [86]. They simulated a disordered
peptide with the sequence EGAAWAASS incorporating three sources of experimental data which included: NMR chemical shifts (CS), J-couplings (JC), and
Residual Dipolar Couplings (RDCs). They simulated three variations of M and M:
unrestrained (no experimental data), using CS and JC data, and using all the data
(CS, JC, and RDCs), while also comparing two forcefield/water model combinations
(CHARMM22/TIP3P vs AMBER99SB/TIP4P-D). Additionally, they compared the
results of an implicit water model (EEF1-SB) using the CHARMM36 forcefield
for the unrestrained and full data (CS, JC, and RDCs) cases. This gave a total of
eight simulation ensembles to be compared. For the metadynamics calculations, they
biased the following CVs: backbone and dihedral angles; E1-S9 Cα–Cα distance;
W5 χ
1 and W5 χ
2 angles; and similarities between ϕ 3 and ϕ 6 , as well as ψ 3 and ψ 6 ,
dihedral angles. Upon reweighting the simulations for the equilibrium distribution,
their results indicate that regardless of the forcefield, quality of results from M and
M simulations was more similar to the reference data, with the addition of more
experimental information into the system. This method allowed for results using two
forcefields that were not only in good agreement with each other, but the experimental data as well. To push the limits of this method, they looked at simulations of
the protein in implicit solvent and compared them to results from the explicit water
models. Compared to the unrestrained models, they noted an increase in agreement
with experiments, similar to results obtained for the explicit model. A summary
of these results is included in Fig. 7. Figure 7c demonstrates that in the M and M
simulations the results for two different forcefields are indistinguishable from the
experimental results, which are not observed without the M and M scheme implemented. The power of this approach is demonstrated by its ability to elucidate an
ensemble of data with different priors that share a common solution.
Example 6 Seven-particle Lennard–Jones system
Prakash et al. employed PBMetaD-PF to describe the system consisting of 7 LJ
particles constrained in two dimensions [79]. All 21 inter-atomic distances were