Here, the first three principal components that accounts for 68.3%
of the total variance, as shown on the scree plot, are plotted against
each other (Fig.2)(seeNotes 12and 13 ).
After aligning trajectories from each method, we observe that
the conformational spaces explored by cMD and aMD are partially
overlapped. Interestingly, aMD simulation explores larger and
more distant conformational space from the starting point than
the cMD. This result is particularly relevant since it includes most
of the experimental structures.Reweighting the aMD
Results
The last step of analysis will be reweighting the aMD distribution to
recover the original free energy profile.
In an aMD simulation of an observable ensembleA(r), the
canonical ensemble distributionhAican be calculated from the
ensemble-averaged Boltzmann factor ofΔV(r) in the aMD (heβΔV
(r)i*) as follows:hiA ¼ArðÞeβΔVrðÞ(^) ∗
hieβΔVrðÞ
∗
Whereβ¼1/kBTandΔV(r) is the boost potential of each
frame.
There are several available scripts that perform 1D and 2D
aMD reweight. We recommend the available scripts and tutorials
at:https://mccammon.ucsd.edu/computing/amdReweighting/.
For the reweighting procedure, we perform a PCA of the
backbone on the last 100 ns of the aMD simulation and the
22 crystallographic structures. The results from PCA were
reweighted using a modified method called “Maclaurin series
expansion algorithm” to thekth order [39] that greatly suppresses
the energetic noise. In this algorithm, the reweighting factorheβΔVi
is approximated by summation of the Maclaurin series to the tenth
order as follows:
eβΔV
¼
X^1
k¼ 0
βk
k!
ΔVk
The results of the reweighting were projected on PC1–PC2
plot (Fig.3)(seeNote 14).
The projection of the crystallographic structures on the 2D free
energy surface shows that the crystal structures are located in
low-energy region but not in the lowest ones.
416 Sonia Ziada et al.