conformational entropy as function of the vibration modes where DOFs are modeled as a set of simple harmonic oscillators, vibrating independently [246], but with
the growing understanding of the nature of vibrational modes of biomolecules, it
was realized that NMA is not the most suitable theory [247] for understanding
entropy. Thus, methods utilizing internal coordinates for molecular description in
conjunction with approximations representing full dimensional probability density
function as a series of marginal PDFs of fluctuation of DOFs got attention of
research community. This theory has been successfully applied to estimate entropy
for small molecules [248], peptides [249, 250], to protein–peptide binding study
with at least qualitative insight, while quantitative aspect still remains to be
debatable [251, 252]. In some case, even for the set of ligands binding to the same
receptor, entropic components are surprisingly quite different and play a crucial role
in deciding the rank/affinity order of ligands.
As mentioned above, we found out that for a set of experimentally known
ligands binding to the P. falciparum protein kinase PfPK5, docking scores yielded
very poor correlation with experimental affinity, even inclusion of end-state free
energy using MM-PBSA [253] method using 3 ls simulation data for each of the
ligands, no significant improvement in computed affinity was observed. However,
when configurational entropy for the ligands was included with the MM-PBSA
estimates, a significant improvement in the bonding affinity was observed (manuscript in preparation).
As shown in (Fig. 13), achieving convergence to reduce error in estimation of
entropy takes longer trajectories i.e., covering larger configuration space. Using a
distance cutoff-based adaptation of Maximum Information Spanning Tree (MIST)
called Neighbor Approximated Maximum Information Spanning Tree (A-MIST)
Fig. 13 Binding configurational entropy estimated using A-MIST methods with a distance cutoff
of 14 Å and convergence of estimate with simulation time is shown. a Convergence of first order
(assuming DOFs are uncorrelated) is shown. b Convergence of second order (accounting pair-wise
correlations DOFs) is shown
156
S. K. Panday and I. Ghosh
the growing understanding of the nature of vibrational modes of biomolecules, it
was realized that NMA is not the most suitable theory [247] for understanding
entropy. Thus, methods utilizing internal coordinates for molecular description in
conjunction with approximations representing full dimensional probability density
function as a series of marginal PDFs of fluctuation of DOFs got attention of
research community. This theory has been successfully applied to estimate entropy
for small molecules [248], peptides [249, 250], to protein–peptide binding study
with at least qualitative insight, while quantitative aspect still remains to be
debatable [251, 252]. In some case, even for the set of ligands binding to the same
receptor, entropic components are surprisingly quite different and play a crucial role
in deciding the rank/affinity order of ligands.
As mentioned above, we found out that for a set of experimentally known
ligands binding to the P. falciparum protein kinase PfPK5, docking scores yielded
very poor correlation with experimental affinity, even inclusion of end-state free
energy using MM-PBSA [253] method using 3 ls simulation data for each of the
ligands, no significant improvement in computed affinity was observed. However,
when configurational entropy for the ligands was included with the MM-PBSA
estimates, a significant improvement in the bonding affinity was observed (manuscript in preparation).
As shown in (Fig. 13), achieving convergence to reduce error in estimation of
entropy takes longer trajectories i.e., covering larger configuration space. Using a
distance cutoff-based adaptation of Maximum Information Spanning Tree (MIST)
called Neighbor Approximated Maximum Information Spanning Tree (A-MIST)
Fig. 13 Binding configurational entropy estimated using A-MIST methods with a distance cutoff
of 14 Å and convergence of estimate with simulation time is shown. a Convergence of first order
(assuming DOFs are uncorrelated) is shown. b Convergence of second order (accounting pair-wise
correlations DOFs) is shown
156
S. K. Panday and I. Ghosh