Calculation of Molecular Configuration Integrals

Chang, Chia‐en A.; Potter, Michael J.; Gilson, Michael K.

doi:10.1021/jp027149c

Cited by 80 publications

(129 citation statements)

References 24 publications

(44 reference statements)

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“…Each local configuration integral z j is estimated via an enhanced version of the harmonic approximation (39), in which the second derivative matrix of the energy at the energy minimum is diagonalized, and numerical integrals are evaluated along the eigenvectors with low force constants. If the numerical integral deviates from the harmonic approximation by Ͼ1 kcal/mol, then the numerical integral along that mode is substituted for the harmonic approximation.…”

Section: [13]mentioning

confidence: 99%

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Ligand configurational entropy and protein binding

Chang

Chen

Gilson

2007

Proc. Natl. Acad. Sci. U.S.A.

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379

424

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The restriction of a small molecule's motion on binding to a protein causes a loss of configurational entropy, and thus a penalty in binding affinity. Some energy models used in computer-aided ligand design neglect this entropic penalty, whereas others account for it based on an expected drop in the number of accessible rotamers upon binding. However, the validity of the physical assumptions underlying the various approaches is largely unexamined. The present study addresses this issue by using Mining Minima calculations to analyze the association of amprenavir with HIV protease. The computed loss in ligand configurational entropy is large, contributing ϳ25 kcal/mol (4.184 kJ/kcal) to ⌬G°. Most of this loss results from narrower energy wells in the bound state, rather than a drop in the number of accessible rotamers. Coupling among rotation/translation and internal degrees of freedom complicates the decomposition of the entropy change into additive terms. The results highlight the potential to gain affinity by designing conformationally restricted ligands and have implications for the formulation of energy models for ligand scoring.drug design ͉ translation ͉ rotamer ͉ affinity ͉ rotation A drug-like molecule that binds a protein becomes less mobile, and the resulting loss in configurational entropy opposes the attractive forces that drive binding. A number of empirical energy models used in virtual ligand screening include a term to account for this entropic penalty, but the underlying physics is not well characterized and hence merits critical examination. For example, most energy models assume that the ligand's entropy change can be decomposed into additive components, although correlated motions could lead to nonadditivity (see, e.g., refs. 1 and 2). Also, energy models often account for changes in torsional entropy with a term related to the number of rotatable bonds in the ligand, based on reasoning about the number of rotamers each bond can adopt (e.g., refs. 3-8) and a computational analysis of changes in vibrational and conformational entropy on protein folding (9). However, the physical rationale and accuracy of this approach is largely unexamined, especially in the context of protein-ligand binding. Similarly, the common assumption that changes in rotational and translational entropy are constant from one ligand to another appears to be unsupported.Recent calculations with the second-generation Mining Minima algorithm (M2) have provided insight into changes in configurational entropy upon binding for small host-guest systems (10, 11). The computed entropic penalty was found to range as high as ϳ20 kcal/mol, considerably more than typically assumed in ligandprotein scoring functions. The validity of these results is supported by the fact that the computed binding free energies were accurate to within ϳ1 kcal/mol. The entropy change was furthermore found to vary significantly across complexes of the same ligand with different receptors and even across different bound conformations of the same ligand and...

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Section: [13]mentioning

confidence: 99%

“…The calculations use a coordinate system consisting of bond lengths, bond angles, and bond torsions (36,39). The position and orientation of the ligand are specified via the coordinates of three ''root'' atoms, here numbered 1, 2, and 3 for convenience, where atoms 1 and 2 are connected by a covalent bond, as are atoms 2 and 3.…”

Section: [13]mentioning

confidence: 99%

Ligand configurational entropy and protein binding

Chang

Chen

Gilson

2007

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

379

424

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“…The present method uses an internal coordinate system comprising bond-lengths, bond-angles, and dihedrals, rather than Cartesian coordinates 38,39,41,[47][48][49] . For a molecule with N atoms, a system of 3N -6 bond-angle-torsion (BAT) coordinates can be defined as follows (see Figure 1).…”

Section: B Bond-angle-torsion Coordinatesmentioning

confidence: 99%

Extraction of configurational entropy from molecular simulations via an expansion approximation

Killian¹,

Kravitz²,

Gilson³

2007

The Journal of Chemical Physics

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183

394

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A method is presented for extracting the configurational entropy of solute molecules from molecular dynamics simulations, in which the entropy is computed as an expansion of multi-dimensional mutual information terms, which account for correlated motions amongst the various internal degrees of freedom of the molecule. The mutual information expansion is demonstrated to be equivalent to estimating the full-dimensional configurational probability density function (pdf) using the Generalized Kirkwood Superposition Approximation (GKSA). While the mutual information expansion is derived to the full dimensionality of the molecule, the current application uses a truncated form of the expansion in which all fourth-and higher-order mutual information terms are neglected. Truncation of the mutual information expansion at the nth-order is shown to be equivalent to approximating the full-dimensional pdf using joint pdfs with dimensionality of n or smaller by successive application of the GKSA. The expansion method is used to compute the absolute (classical) configurational entropy in a basis of bond-angle-torsion internal coordinates for several small molecules as well as the change in entropy upon binding for a small host-guest system. Convergence properties of the computed entropy values as a function of simulation time are investigated and comparisons are made with entropy values from the second generation Mining Minima software. These comparisons demonstrate a deviation in -TS of no more than about 2 kcal/ mol for all cases in which convergence has been obtained.

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“…Nevertheless, such MINTA errors and neglect of the rotational and translational contributions to the configuration integral by default in MINTA appear not to be that critical here. 38,39 Indeed, neglect of the rotational and translational contributions were not problematic in all other MINTA computations of DDG values for enantiomeric separation published to date.…”

Section: S6mentioning

confidence: 99%

Theoretical reassessment of Whelk-O1 as an enantioselective receptor for 1-(4-halogeno-phenyl)-1-ethylamine derivatives

Río

Hayes²,

Stein³

et al. 2004

Chirality

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A combination of molecular mechanics and first principles calculations was used to explore the enantioselectivity of receptors, taking into account experimental data from the CHIRBASE database. Interactions between the Whelk-O1 HPLC chiral stationary phase with the complete series of 1-(4-halogeno-phenyl)-1-ethylamine derivative racemates were studied. The objective was to extract information from the interactions between the chiral Whelk-O1 stationary phase and the enantiomers, hence probing the origin of the enantioselective behavior. Calculations correctly reproduce the elution orders and reasonably describe the experimental enantioselectivities and retention factors. Different binding modes were observed for the first eluted enantiomer complexes, whereas the second eluted show only one prevalent diastereomeric binding fashion. Natural bond orbital (NBO) analysis was used on the global minima bound-complexes to quantify donor-acceptor interactions among chiral stationary phase and ligand moieties. Intermolecular hydrogen bonding was found to be the essential energetic interaction for all systems studied. CH-pi, aromatic stacking and various charge transfer interactions were found to be smaller in magnitude but still important for the global enantioselective behavior. The three-point interaction model is discussed, pointing out the difficulty of its application for the qualitative prediction of elution orders (absolute configurations).

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Calculation of Molecular Configuration Integrals

Cited by 80 publications

References 24 publications

Ligand configurational entropy and protein binding

Ligand configurational entropy and protein binding

Extraction of configurational entropy from molecular simulations via an expansion approximation

Theoretical reassessment of Whelk-O1 as an enantioselective receptor for 1-(4-halogeno-phenyl)-1-ethylamine derivatives

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