A novel and robust automated docking method that predicts the bound conformations of flexible ligands to macromolecular targets has been developed and tested, in combination with a new scoring function that estimates the free energy change upon binding. Interestingly, this method applies a Lamarckian model of genetics, in which environmental adaptations of an individual's phenotype are reverse transcribed into its genotype and become . heritable traits sic . We consider three search methods, Monte Carlo simulated annealing, a traditional genetic algorithm, and the Lamarckian genetic algorithm, and compare their performance in dockings of seven protein)ligand test systems having known three-dimensional structure. We show that both the traditional and Lamarckian genetic algorithms can handle ligands with more degrees of freedom than the simulated annealing method used in earlier versions of AUTODOCK, and that the Lamarckian genetic algorithm is the most efficient, reliable, and successful of the three. The empirical free energy function was calibrated using a set of 30 structurally known protein)ligand complexes with experimentally determined binding constants. Linear regression analysis of the observed binding constants in terms of a wide variety of structure-derived molecular properties was performed. The final model had a residual standard y1 y1 .

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Automated docking using a Lamarckian genetic algorithm and an empirical binding free energy function

We report re-optimization of a recently proposed long-range corrected (LC) hybrid density functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom–atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-corrected density functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.

/pdf/long-range-corrected-hybrid-density-functionals-with-damped-44ti6za9f3.pdf

Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections

Inference of macromolecular assemblies from crystalline state.

Unlike other methods for docking ligands to the rigid 3D structure of a known protein receptor, Glide approximates a complete systematic search of the conformational, orientational, and positional space of the docked ligand In this search, an initial rough positioning and scoring phase that dramatically narrows the search space is followed by torsionally flexible energy optimization on an OPLS-AA nonbonded potential grid for a few hundred surviving candidate poses The very best candidates are further refined via a Monte Carlo sampling of pose conformation; in some cases, this is crucial to obtaining an accurate docked pose Selection of the best docked pose uses a model energy function that combines empirical and force-field-based terms Docking accuracy is assessed by redocking ligands from 282 cocrystallized PDB complexes starting from conformationally optimized ligand geometries that bear no memory of the correctly docked pose Errors in geometry for the top-ranked pose are less than 1 A in nearly ha

/pdf/glide-a-new-approach-for-rapid-accurate-docking-and-scoring-lnxrmd5zbm.pdf

Glide: a new approach for rapid, accurate docking and scoring. 1. Method and assessment of docking accuracy.

Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections Jeng-Da Chai ∗ and Martin Head-Gordon † Department of Chemistry, University of California and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA (Dated: June 14, 2008) We report re-optimization of a recently proposed long-range corrected (LC) hybrid density func- tionals [J.-D. Chai and M. Head-Gordon, J. Chem. Phys. 128, 084106 (2008)] to include empirical atom-atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent sys- tems, ωB97X-D shows slight improvement over other empirical dispersion-corrected density func- tionals, while for covalent systems and kinetics, it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is signiﬁcantly superior for non-bonded interactions, and very similar in performance for bonded interactions. I. INTRODUCTION Due to its favorable cost-to-performance ratio, Kohn- Sham density-functional theory (KS-DFT) [1, 2] has be- come the most popular electronic structure theory for large-scale ground-state systems [3–5]. Its extension for treating excited-state systems [6, 7], time-dependent den- sity functional theory (TDDFT), has also been developed to the stage where it is now very widely used. The essential ingredient of KS-DFT, the exchange- correlation energy functional E xc , remains unknown and needs to be approximated. Semi-local gradient-corrected density functionals, though successful in many applica- tions, lead to qualitative failures in some circumstances, where the accurate treatment of non-locality of exchange- correlation hole becomes crucial. These situations occur mostly in the asymptotic regions of molecular systems, such as spurious self-interaction eﬀects upon dissociation [8, 9] and dramatic failures for long-range charge-transfer excitations [10–12]. Widely used hybrid density function- als, like B3LYP [13, 14], do not qualitatively resolve these problems. These self-interaction errors can be qualitatively re- solved using the long-range corrected (LC) hybrid density functionals [15, 16, 18], which employ 100% Hartree-Fock (HF) exchange for long-range electron-electron interac- tions. This is accomplished by a partition of unity, using erf(ωr)/r for long-range (treated by HF exchange) and erfc(ωr)/r for short-range (treated by an exchange func- tional), with the parameter ω controlling the partition- ing. Over the past ﬁve years, the LC hybrid scheme has been attracting increasing attention [15] since its compu- tational cost is comparable with standard hybrid func- tionals [13]. However, LC functionals have tended to be inferior to the best hybrids for properties such as ther- mochemistry. ∗ Electronic † Author address: jdchai@berkeley.edu to whom correspondence should be addressed. Electronic address: mhg@cchem.berkeley.edu Recently we have improved the overall accuracy at- tainable with the LC functionals by using a systematic optimization procedure [18]. One important conclusion is that optimizing LC and hybrid functionals with identical numbers of parameters in their GGA exchange and cor- relation terms leads to noticeably better results for all properties using the LC form. The resulting LC func- tional is called ωB97. Further statistically signiﬁcant improvement results from re-optimizing the entire func- tional with one extra parameter corresponding to an ad- justable fraction of short-range exact exchange, deﬁning the ωB97X functional. Independent test sets covering thermochemistry and non-covalent interactions support these conclusions. However, problems associated with the lack of non-locality of the correlation hole, such as the lack of dispersion interactions (London forces), still remain, as the semi-local correlation functionals cannot capture long-range correlation eﬀects [19, 20]. There have been signiﬁcant eﬀorts to develop a frame- work that can account for long-range dispersion eﬀects within DFT. Zaremba and Kohn (ZK) [21] derived an exact expression for the second-order dispersion energy in terms of the exact density-density response functions of the two separate systems. To obtain a tractable non- local dispersion functional, Dobson and Dinite (DD) [22] made local density approximations to the ZK response functions. DD’s non-local correlation functional was ob- tained independently [23] by modifying the eﬀective den- sity deﬁned in the earlier work of Rapcewicz and Ashcroft Starting from the formally exact expression of KS- DFT, the adiabatic connection ﬂuctuation-dissipation theorem (ACFDT), for the ground-state exchange- correlation energy, Langreth and co-workers [25] devel- oped a so-called van der Waals density functional (vdW- DF) by making a series of reasonable approximations to yield a computationally tractable scheme. Recently, Becke and Johnson (BJ) developed a series of post-HF correlation models with a novel treatment for dispersion interactions based on the exchange-hole dipole moment [26]. The origin of dispersion claimed in the BJ models was recently questioned by Alonso, and A.

Long-Range Corrected Hybrid Density Functionals with Damped Atom-Atom Dispersion Corrections

The Chemscore function was implemented as a scoring function for the protein-ligand docking program GOLD, and its performance compared to the original Goldscore function and two consensus docking protocols, "Goldscore-CS" and "Chemscore-GS," in terms of docking accuracy, prediction of binding affinities, and speed. In the "Goldscore-CS" protocol, dockings produced with the Goldscore function are scored and ranked with the Chemscore function; in the "Chemscore-GS" protocol, dockings produced with the Chemscore function are scored and ranked with the Goldscore function. Comparisons were made for a "clean" set of 224 protein-ligand complexes, and for two subsets of this set, one for which the ligands are "drug-like," the other for which they are "fragment-like." For "drug-like" and "fragment-like" ligands, the docking accuracies obtained with Chemscore and Goldscore functions are similar. For larger ligands, Goldscore gives superior results. Docking with the Chemscore function is up to three times faster than docking with the Goldscore function. Both combined docking protocols give significant improvements in docking accuracy over the use of the Goldscore or Chemscore function alone. "Goldscore-CS" gives success rates of up to 81% (top-ranked GOLD solution within 2.0 A of the experimental binding mode) for the "clean list," but at the cost of long search times. For most virtual screening applications, "Chemscore-GS" seems optimal; search settings that give docking speeds of around 0.25-1.3 min/compound have success rates of about 78% for "drug-like" compounds and 85% for "fragment-like" compounds. In terms of producing binding energy estimates, the Goldscore function appears to perform better than the Chemscore function and the two consensus protocols, particularly for faster search settings. Even at docking speeds of around 1-2 min/compound, the Goldscore function predicts binding energies with a standard deviation of approximately 10.5 kJ/mol.

Improved protein-ligand docking using GOLD.

This paper describes the development of a simple empirical scoring function designed to estimate the free energy of binding for a protein-ligand complex when the 3D structure of the complex is known or can be approximated. The function uses simple contact terms to estimate lipophilic and metal-ligand binding contributions, a simple explicit form for hydrogen bonds and a term which penalises flexibility. The coefficients of each term are obtained using a regression based on 82 ligand-receptor complexes for which the binding affinity is known. The function reproduces the binding affinity of the complexes with a cross-validated error of 8.68 kJ/mol. Tests on internal consistency indicate that the coefficients obtained are stable to changes in the composition of the training set. The function is also tested on two test sets containing a further 20 and 10 complexes, respectively. The deficiencies of this type of function are discussed and it is compared to approaches by other workers.

Empirical scoring functions: I. The development of a fast empirical scoring function to estimate the binding affinity of ligands in receptor complexes

We present a large test set of protein–ligand complexes for the purpose of validating algorithms that rely on the prediction of protein–ligand interactions. The set consists of 305 complexes with protonation states assigned by manual inspection. The following checks have been carried out to identify unsuitable entries in this set: (1) assessing the involvement of crystallographically related protein units in ligand binding; (2) identification of bad clashes between protein side chains and ligand; and (3) assessment of structural errors, and/or inconsistency of ligand placement with crystal structure electron density. In addition, the set has been pruned to assure diversity in terms of protein–ligand structures, and subsets are supplied for different protein-structure resolution ranges. A classification of the set by protein type is available. As an illustration, validation results are shown for GOLD and SuperStar. GOLD is a program that performs flexible protein–ligand docking, and SuperStar is used for the prediction of favorable interaction sites in proteins. The new CCDC/Astex test set is freely available to the scientific community (http://www.ccdc.cam.ac.uk). Proteins 2002;49:457–471. © 2002 Wiley-Liss, Inc.

A new test set for validating predictions of protein–ligand interaction

Fragment screening offers an alternative to traditional screening for discovering new leads in drug discovery programs. This paper describes a fragment screening methodology based on high throughput X-ray crystallography. The method is illustrated against five proteins (p38 MAP kinase, CDK2, thrombin, ribonuclease A, and PTP1B). The fragments identified have weak potency (>100 microM) but are efficient binders relative to their size and may therefore represent suitable starting points for evolution to good quality lead compounds. The examples illustrate that a range of molecular interactions (i.e., lipophilic, charge-charge, neutral hydrogen bonds) can drive fragment binding and also that fragments can induce protein movement. We believe that the method has great potential for the discovery of novel lead compounds against a range of targets, and the companion paper illustrates how lead compounds have been identified for p38 MAP kinase starting from fragments such as those described in this paper.

Fragment-Based Lead Discovery Using X-ray Crystallography

This article describes the implementation of a new docking approach. The method uses a Tabu search methodology to dock flexibly ligand molecules into rigid receptor structures. It uses an empirical objective function with a small number of physically based terms derived from fitting experimental binding affinities for crystallographic complexes. This means that docking energies produced by the searching algorithm provide direct estimates of the binding affinities of the ligands. The method has been tested on 50 ligand-receptor complexes for which the experimental binding affinity and binding geometry are known. All water molecules are removed from the structures and ligand molecules are minimized in vacuo before docking. The lowest energy geometry produced by the docking protocol is within 1.5 A root-mean square of the experimental binding mode for 86% of the complexes. The lowest energies produced by the docking are in fair agreement with the known free energies of binding for the ligands.

Christopher W. Murray

Papers

Improved protein-ligand docking using GOLD.

Empirical scoring functions: I. The development of a fast empirical scoring function to estimate the binding affinity of ligands in receptor complexes

A new test set for validating predictions of protein–ligand interaction

Fragment-Based Lead Discovery Using X-ray Crystallography

Flexible docking using tabu search and an empirical estimate of binding affinity