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Grid-Search Molecular Accessible Surface Algorithm for Solving the Protein Docking Problem
Abstract
An algorithm for solving the protein docking problem is presented. Many tentative dockings are first generated by requiring a hole on the surface of one protein to match a knob on the surface of the other. All the tentative dockings are then applied. The initial configurations thus generated are further optimized. The optimization is facilitated by giving a discrete representation to the protein interior and a double-layer discrete representation to the protein surface. The algorithm presented correctly predicts the association of trypsin with its inhibitor as well as that of the α and β subunits in hemoglobin.
... In a similar scheme Wang (1991) succeeded in docking these same two examples. Wang used an almost identical definition of critical points, requiring however, only one pair of complementary critical points to effect a match between the two protein molecules. ...
... It has long been recognized that shape complementarity is essential for molecular recognition (Kuntz et al., 1982; Connolly, 1986, 1992, Wang, 1991; Jiang & Kim, 1991; Shoichet & Kuntz, 1991; Katchalski-Katzir et al., 1992; Kasinos et al., 1992; Norel et al., 1994b; Lin et al., 1994; Fischer et al., 1995). A variety of geometrically-based schemes have thus been devised, attempting to represent the surface adequately, and to match the surface descriptors. ...
... It has long been recognized that shape complementarity is essential for molecular recognition (Kuntz et al., 1982; Connolly, 1986, 1992, Wang, 1991 Jiang & Kim, 1991; Shoichet & Kuntz, 1991; Katchalski-Katzir et al., 1992; Kasinos et al., 1992; Norel et al., 1994b; Lin et al., 1994; Fischer et al., 1995). A variety of geometrically-based schemes have thus been devised, attempting to represent the surface adequately, and to match the surface descriptors. ...
Rigid-body docking of two molecules involves matching of their surfaces. A successful docking methodology considers two key issues: molecular surface representation, and matching. While approaches to the problem differ, they all employ certain surface geometric features. While surface normals are routinely created with molecular surfaces, their employment has surprisingly been almost completely overlooked. Here we show how the normals to the surface, at specific, well placed points, can play a critical role in molecular docking. If the points for which the normals are calculated represent faithfully and accurately the molecular surfaces, the normals can substantially ameliorate the efficiency of the docking in a number of ways. The normals can drastically reduce the combinatorial complexity of the receptor-ligand docking. Furthermore, they can serve as a powerful filter in screening for quality docked conformations. Below we show how deploying such a straight forward device, which is easy to calculate, large protein-protein molecules are docked with unparalleled short times and with a manageable number of potential solutions. Considering the facts that here we dock (1) two large protein molecules, including several large immunoglobulin-lysozyme complexes; (2) that we use the entire molecular surfaces, without a predefinition of the active sites, or of the epitopes, of neither the ligand nor the receptor; that (3) the docking is completely automated, without any labelling, or pre-specification, of the input structural database, and (4) with a single set of parameters, without any further tuning whatsoever, such results are highly desirable. This approach is specifically geared towards matching of the surfaces of large protein molecules and is not applicable to small molecule drugs.
... Most of the research in shape complementarity analysis is indebted to computational attempts in ab initio protein docking, extensively studied among computer scientists and computational biologists [42]. The earlier techniques ranged from geometric hashing [35,14], to detection and matching of 'knobs and holes' [53,47,33], and other signature features [23,18,14] on the surfaces of the binding proteins. More recent methods characterize the topography of cavities and protrusions of the surface by means of a so-called 'elevation function' [1], and compare the maxima of this function for geometric alignment of protein surfaces [54]. ...
... A relatively successful and contemporary formulation is based on the double-skin layer (DSL) approach, illustrated in Figure 3 (a). It was first introduced in [12,53] in 2D and 3D, respectively, implemented using grid-based equispaced FFTs in [26], generalized to complex affinities in [8], and evolved to a grid-free nonequispaced FFT-based algorithm in [7,4]. Two skin regions are defined implicitly: 1) the grown skin region of the receptor, formed by an additional layer of pseudo-atoms populated over the solvent accessible surface (SAS); and 2) the surface skin region of the ligand, formed by the original solvent accessible atoms. ...
The basic problem of shape complementarity analysis appears fundamental to applications as diverse as mechanical design, assembly automation, robot motion planning, micro- and nano-fabrication, protein-ligand binding, and rational drug design. However, the current challenge lies in the lack of a general mathematical formulation that applies to objects of arbitrary shape. We propose that a measure of shape complementarity can be obtained from the extent of approximate overlap between shape skeletons. A space-continuous implicit generalization of the skeleton, called the skeletal density function (SDF) is defined over the Euclidean space that contains the individual assembly partners. The SDF shape descriptors capture the essential features that are relevant to proper contact alignment, and are considerably more robust than the conventional explicit skeletal representations. We express the shape complementarity score as a convolution of the individual SDFs. The problem then breaks down to a global optimization of the score over the configuration space of spatial relations, which can be efficiently implemented using fast Fourier transforms (FFTs) on nonequispaced samples. We demonstrate the effectiveness of the scoring approach for several examples from 2D peg-in-hole alignment to more complex 3D examples in mechanical assembly and protein docking. We show that the proposed method is reliable, inherently robust against small perturbations, and effective in steering gradient-based optimization.
... A knob and hole detection and matching algorithm [16] was used to successfully redock the α, β subunits of hemoglobin. This was extended in [62] to allow for a further sampling along the axis containing the matched knob and hole. He performs an optimization using a grid-based double skin layer approach in 2D. ...
... Surface atoms Pseudo atoms Skin For shape based docking we will try to maximize the overlap of the surface of protein B with the complementary space of A. The double skin layer approach is used here. It was introduced in [62] for 2D, [32] for 3D, sped up using Fast Fourier Transforms in [35], and extended to complex space in [11]. We define two skin regions: 1). ...
The functions of proteins is often realized through their mutual interactions. Determining a relative transformation for a pair of proteins and their conformations which form a stable complex, reproducible in nature, is known as docking. It is an important step in drug design, structure determination and understanding function and structure relationships. We provide a model for rigid docking and error-bounded approximation algorithms to solve the model and predict docking sites. Translational search is sped up using the Fourier domain. Shape based interactions is shown to give good results for a large range of pairs of proteins.
... In [19] the combinatorial search was reduced to a clique finding problem by considering pairwise distances among atoms. A knob and hole detection and matching algorithm was used in [20], [21] where an optimization is performed using a grid-based double skin layer approach in 2D. We shall further discuss this double skin layer approach later as we use a variation of it in our algorithm. ...
... shape based docking we maximize the overlap of the surface of protein B with the complementary space of A. The double skin layer approach is used here. It was introduced in [21] for 2D, [22] for 3D, sped up using Fast Fourier Transforms in [47], and extended to complex space in [29]. We define two skin regions: ...
The functions of proteins are often realized through their mutual interactions. Determining a relative transformation for a pair of proteins and their conformations which form a stable complex, reproducible in nature, is known as docking. It is an important step in drug design, structure determination, and understanding function and structure relationships. In this paper, we extend our nonuniform fast Fourier transform-based docking algorithm to include an adaptive search phase (both translational and rotational) and thereby speed up its execution. We have also implemented a multithreaded version of the adaptive docking algorithm for even faster execution on multicore machines. We call this protein-protein docking code F2Dock (F2 = Fast Fourier). We have calibrated F2Dock based on an extensive experimental study on a list of benchmark complexes and conclude that F2Dock works very well in practice. Though all docking results reported in this paper use shape complementarity and Coulombic-potential-based scores only, F2Dock is structured to incorporate Lennard-Jones potential and reranking docking solutions based on desolvation energy .
... Therefore restrictions were formulated and applied, like interactively specifying a binding site in (Wodak & Janin 1978). Alternatively, in (Connolly 1986;Wang 1991;Norel et al. 1994) "critical points" were computed. Among these only small subsets were compared in search for the correct docking position. ...
... Thus, the grids we use have only 163 up to 323 grid points, reducing computational complexity by a factor O(10) -O(100) compared (Katchalski-Katzir et al. 1992). On the other hand we avoid a complete sampling of the rotational parameter space, which usually is the major draw back of grid based evaluations of protein docking positions (Wang 1991;Katchalski-Katzir et al. 1992). ...
With the growing number of known 3D protein structures, computing systems, that can predict where two protein molecules interact with each other is becoming of increasing interest. A system is presented, integrating preprocessing like the computation of molecular surfaces, segmentation, and searching for complementarity in the general framework of a pattern analyzing semantic network (ERNEST). The score of coarse symbolic computations is used by the problem independent control strategy of ERNEST to guide a more detailed analysis considering steric clash and judgements based on grid-based surface representations. Successful examples of the docking system are discussed that compare well with other approaches.
... It has to be pointed out that none of them includes explicit solvent molecules. The target functions range from surface complementarity, 1,2 to surface area burial, 3 to total molecular mechanics energy, 4 to free energy calculations. 5,6 When only rigid receptors are taken into account, the computational effort can be reduced by pre-computing the potential energy of the receptor so that the ligand energy has only to be evaluated for any specific ligand. ...
In this paper, a method of simulating the docking of small flexible ligands to flexible receptors in water is reported. The method is based on molecular dynamics simulations and is an extension of an algorithm previously reported by Di Nola et al. (Di Nola et al., Proteins 1994;19:174–182). The method allows a fast exploration of the receptor surface, using a high temperature of the center of mass translational motion, while the ligand internal motions, the solvent, and the receptor are simulated at room temperature. In addition, the method allows a fast center of mass motion of the ligand, even in solution. The dampening effect of the solvent can be overcome by applying different weights to the interactions between system subsets (solvent, receptor, and ligand). Specific ligand–receptor distances have been used to compare the results of the simulations with the crystal structure. The method is applied, as a test system, to the docking of the phosphocholine to the immunoglobulin McPC603. The results show the similarity of structure between the complex in solution and in the crystal. Proteins 1999;35:153–162. © 1999 Wiley-Liss, Inc.
... Les solutions données correspondentà une concordance de groupes de quatre points critiques, laquelle est identifiée grâceà une triangulation de surface comme définie par M. Connolly en 1985 [56]. Cette méthode aété beaucoup améliorée en 1991 par H. Wang, avec la modélisation de la surfaceà l'aide d'une grille [255]. ...
My thesis shows results for the prediction of protein-RNA interactions with machine learning. An international community named CAPRI (Critical Assessment of PRedicted Interactions) regularly assesses in silico methods for the prediction of the interactions between macromolecules. Using blindpredictions within time constraints, protein-protein interactions and more recently protein-RNA interaction prediction techniques are assessed.In a first stage, we worked on curated protein-RNA benchmarks, including 120 3D structures extracted from the non redundant PRIDB (Protein-RNA Interface DataBase). We also tested the protein-RNA prediction method we designed using 40 protein-RNA complexes that were extracted from state-ofthe-art benchmarks and independent from the non redundant PRIDB complexes. Generating candidates identical to the in vivo solution with only a few 3D structures is an issue we tackled by modelling a candidate generation strategy using RNA structure perturbation in the protein-RNAcomplex. Such candidates are either near-native candidates – if they are close enough to the solution– or decoys – if they are too far away. We want to discriminate the near-native candidates from thedecoys. For the evaluation, we performed an original cross-validation process we called leave-”onepdb”-out, where there is one fold per protein-RNA complex and each fold contains the candidates generated using one complex. One of the gold standard approaches participating in the CAPRI experiment as to date is RosettaDock. RosettaDock is originally optimized for protein-proteincomplexes. For the learning step of our scoring function, we adapted and used an evolutionary algorithm called ROGER (ROC-based Genetic LearnER) to learn a logistic function. The results show that our scoring function performs much better than the original RosettaDock scoring function. Thus,we extend RosettaDock to the prediction of protein-RNA interactions. We also evaluated classifier based and metaclassifier-based approaches, which can lead to new improvements with further investigation.In a second stage, we introduced a new way to evaluate candidates using a multi-scale protocol. A candidate is geometrically represented on an atomic level – the most detailed scale – as well as on a coarse-grained level. The coarse-grained level is based on the construction of a Voronoi diagram over the coarse-grained atoms of the 3D structure. Voronoi diagrams already successfully modelled coarsegrained interactions for protein-protein complexes in the past. The idea behind the multi-scale protocolis to first find the interaction patch (epitope) between the protein and the RNA before using the time consuming and yet more precise atomic level. We modelled new scoring terms, as well as new scoring functions to evaluate generated candidates. Results are promising. Reducing the number of parameters involved and optimizing the explicit solvent model may improve the coarse-grained level predictions.
... D'autres types d'algorithmes, utilisant la complémentarité de surface, ont été mis en oeuvre à partir d'une description en points critiques définis comme « trous et bosses » (knobs and holes) [53,128,235], les solutions données correspondant à une concordance de groupes de quatre points critiques, laquelle est identifiée grâce à une triangulation de surface comme définie par M. Connolly en 1985 [52]. Cette méthode a été beaucoup améliorée en 1991 par H. Wang, avec la modélisation de la surface à l'aide d'une grille [222]. ...
The function of a protein is often subordinated to its interaction with one or many partners. Yet, the tridimensional structure study of this complexes, that can't be done experimentally, would permit the understanding of many cellular processes. This work contains two parts. The first part concerns the setting up of a scoring function for protein-protein docking and the second part concerns the crystallographic structure study of a tetrameric protein : the Paramecium Bursaria Chlorella Virus thymidylate synthase X, a potential antibacterial target. Docking of protein-protein complexes consists in two successive steps : first a large number of putative conformations are generated, then a scoring function is applied to rank them. This scoring function has to take into account both geometric complementarity of the two molecules and physico-chemical properties of surfaces in interaction. We addressed the second step of this problem through the development of a quick and reliable scoring function. This was done using Voronoi tessellation of the tridimensional structure of the proteins. Voronoi or Laguerre tessellations were shown to be good mathematical models of protein structure. In particular, this formalization leads to a good description of structural properties of the residues. This modeling illustrates the packing of the residues at the interface between two proteins. Thus, it is possible to measure a set of parameters, on protein-protein complexes whose structure is known, and on decoys. These parameters are frequencies of residues and pair frequencies of the residues at the interface, volumes of Voronoi cells, distances between residues at the interface, interface area and number of residues at the interface. They were used as input in statistical machine learning procedures (logistic learning, support vector machines (SVM) and genetic algorithms). These led to efficient scoring functions, able to separate native structures from decoys. In the second part, I describe the experimental determination of thymidylate synthase X tridimensionnal structure, an interesting antibacterial target. Thymidylate synthase X is a flavoprotein discovered recently. It plays a key role in the synthesis of dTMP in most of the prokaryotic organisms, but does not exist in superior eukaryotic organisms. This protein catalyses the methyl transfer from tetrahydrofolate to dUMP using FAD as a cofactor and NADPH as substrate. The tridimensional structure of ThyX homotetramer with its cofactor, FAD, was solved at 2.4Å by molecular replacement. As shown in the Thermotoga maritima and Mycobacterium tuberculosis ThyX structures, the monomer contains a core of β sheets and two α helices at its extremity. The active site is at the interface between three monomers, the isoalloxazine part of FAD being accessible to the solvent and close to a long flexible loop. FAD binding in this structure is a little different from those already observed, especially its the adenine part. This structure, in association with directed mutagenesis experiments made by our collabora- tors, revealed residues playing a key role during the catalysis.
... According to [4], "protein surface comparison is a hard computational challenge and evaluated methods allowing the comparison of protein surfaces are difficult to find". Past implementations for the representation and study of protein surfaces include approaches such as triangulation, Voronoi tessellations, lattice modeling, geometric hashing etc [5]- [8]. Another approach is the convex hull [9] -defined as the smallest convex polyhedron enclosing all atom centers and is a subset of the Delauney triangulation. ...
... His procedure correctly docked the alpha and beta subunits of hemoglobin but failed to dock the smaller trypsin/trypsin inhibitor complex. Connolly's procedure was successfully extended by Wang to dock the trypsin/trypsin inhibitor, again using selected points on the surface, but incorporating a grid-based fine structure search as a second step [27]. Jiang and Kim implemented a "soft-docking" approach whereby the molecular surfaces are transformed into collections of cubes that are then matched, allowing for the effects of minor conformational changes [14]. ...
Protein-protein interactions are essential to all cellular processes. Given the recent increase in protein structural information, mostly of monomeric proteins, the need to understand protein-protein interactions from a computational approach is increasing. Previous attempts at docking proteins generate a multitude of answers that have similarly high scores for both correctly and incorrectly docked complexes. We have developed an algorithm that successfully predicts the re-docking of known protein-protein complexes without any false positives. Our algorithm is based on matching shape complementarity alone and involves an exhaustive search of all possible docking conformations in the 6-dimensional space of translations and rotations. Using the barnase/barstar protein complex (1BRS) as a test case, we explore the additional input parameters such as the number of allowed overlaps and the optimal distance between surface residues. We tested our method using a test set of 20 different protein complexes and our re-docking procedure succeeds without reporting false positives, even with larger proteins containing larger and flatter interfaces.
... The original version of F 2 Dock [31] used the traditional double skin layer approach for shape comple- mentarity [41]. Two skin regions are defined (Figure 2): a grown skin region around A, and the surface skin of B, which consists of the surface atoms of B. The atoms of A and the inner atoms of B form core regions. ...
Motivation:
Computational simulation of protein-protein docking can expedite the process of molecular modeling and drug discovery. This paper reports on our new F(2) Dock protocol which improves the state of the art in initial stage rigid body exhaustive docking search, scoring and ranking by introducing improvements in the shape-complementarity and electrostatics affinity functions, a new knowledge-based interface propensity term with FFT formulation, a set of novel knowledge-based filters and finally a solvation energy (GBSA) based reranking technique. Our algorithms are based on highly efficient data structures including the dynamic packing grids and octrees which significantly speed up the computations and also provide guaranteed bounds on approximation error.
Results:
The improved affinity functions show superior performance compared to their traditional counterparts in finding correct docking poses at higher ranks. We found that the new filters and the GBSA based reranking individually and in combination significantly improve the accuracy of docking predictions with only minor increase in computation time. We compared F(2) Dock 2.0 with ZDock 3.0.2 and found improvements over it, specifically among 176 complexes in ZLab Benchmark 4.0, F(2) Dock 2.0 finds a near-native solution as the top prediction for 22 complexes; where ZDock 3.0.2 does so for 13 complexes. F(2) Dock 2.0 finds a near-native solution within the top 1000 predictions for 106 complexes as opposed to 104 complexes for ZDock 3.0.2. However, there are 17 and 15 complexes where F(2) Dock 2.0 finds a solution but ZDock 3.0.2 does not and vice versa; which indicates that the two docking protocols can also complement each other.
Availability:
The docking protocol has been implemented as a server with a graphical client (TexMol) which allows the user to manage multiple docking jobs, and visualize the docked poses and interfaces. Both the server and client are available for download. Server: http://www.cs.utexas.edu/~bajaj/cvc/software/f2dock.shtml. Client: http://www.cs.utexas.edu/~bajaj/cvc/software/f2dockclient.shtml.
... According to Via et al [9], " protein surface comparison is a hard computational challenge and evaluated methods allowing the comparison of protein surfaces are difficult to find " . Many implementations are available as of current and these include approaches such as triangulation, Voronoi tessellations, lattice modeling, multi-resolution modeling, geometric hashing etc [10]-[13]. One of the more commonly used geometric-based methods is the convex hull which is a subset of the Delauney triangulation and is defined as the smallest convex polyhedron enclosing all atom centers. ...
Formed of amino acids combinations, proteins are
essential components of living beings which participate in the
regulation of bodily functions. Each protein is assigned specific
function(s) and reacts to external agents of the best fits. Most
binding activities take place on surfaces specifically in regions
of high complementarity. The structure and chemical
composition of each site are defined by the arrangement of
residues and their corresponding atoms. As such the extraction
of protein surface atoms provides a good listing for
investigation of surface properties as well as aids in reducing
the amount of processing required in computer-aided drug
design (CADD) programs. Many algorithms are available for
the analysis of protein surfaces including but not limited to
methods of probe or geometrical nature, calculation of hot spots
and energy functions, triangulation and Voronoi tessellations
etc. Grid units have been used for locating potential cavities in
early programs such as POCKET and LIGSITE but the role of
voxels in the extraction of surface atoms has not been
thoroughly investigated. A method is presented here which
enlists voxels as its main experimental tool with constraints
applied. These constraints come in the form of voxel occupancy
as well as the degree of belonging of an atom to the voxel.
Application of these rules to the voxels lead to considerable
improvements in the extracts, with further enhancements made
through the implementation of a ‘peeling’ method for removing
internal atoms found in the output. The study was carried out
on sets of proteins with the results visualised and compared to
output from the MSMS and Surface Racer programs.
... [11][12][13][14] Ab initio matching of the protein surfaces without a priori knowledge about the binding sites is also possible, but the molecular surfaces have to be represented by a manageable number of points which retain the critical geometric features of surfaces. 15,16 With a reduced surface representation, surface match can be identified by using the simple ''knob-hole'' pairing algorithms 17,18,19,20 or more sophisticated algorithms which draw on ideas from computer vision. 16,[21][22][23][24][25] Algorithms designed to search for geometric complementarity usually produce a large number of candidate structures. ...
We present a rapidly executable minimal binding energy model for molecular docking and use it to explore the energy landscape in the vicinity of the binding sites of four different enzyme inhibitor complexes. The structures of the complexes are calculated starting with the crystal structures of the free monomers, using DOCK 4.0 to generate a large number of potential configurations, and screening with the binding energy target function. In order to investigate possible correlations between energy and variation from the native structure, we introduce a new measure of similarity, which removes many of the difficulties associated with root mean square deviation. The analysis uncovers energy gradients, or funnels, near the binding site, with decreasing energy as the degree of similarity between the native and docked structures increases. Such energy funnels can increase the number of random collisions that may evolve into productive stable complex, and indicate that short-range interactions in the precomplexes can contribute to the association rate. The finding could provide an explanation for the relatively rapid association rates that are observed even in the absence of long-range electrostatic steering. Proteins 1999; 34:255–267. © 1999 Wiley-Liss, Inc.
... It has to be pointed out that none of them includes explicit solvent molecules. The target functions range from surface complementarity, 1,2 to surface area burial, 3 to total molecular mechanics energy, 4 to free energy calculations. 5,6 When only rigid receptors are taken into account, the computational effort can be reduced by pre-computing the potential energy of the receptor so that the ligand energy has only to be evaluated for any specific ligand. ...
In this paper, a method of simulating the docking of small flexible ligands to flexible receptors in water is reported. The method is based on molecular dynamics simulations and is an extension of an algorithm previously reported by Di Nola et al. (Di Nola et al., Proteins 1994;19:174–182). The method allows a fast exploration of the receptor surface, using a high temperature of the center of mass translational motion, while the ligand internal motions, the solvent, and the receptor are simulated at room temperature. In addition, the method allows a fast center of mass motion of the ligand, even in solution. The dampening effect of the solvent can be overcome by applying different weights to the interactions between system subsets (solvent, receptor, and ligand). Specific ligand–receptor distances have been used to compare the results of the simulations with the crystal structure. The method is applied, as a test system, to the docking of the phosphocholine to the immunoglobulin McPC603. The results show the similarity of structure between the complex in solution and in the crystal. Proteins 1999;35:153–162. © 1999 Wiley-Liss, Inc.
... The requirement to determine consistently and rapidly the global free energy minimum on the binding energy landscape addresses a kinetic aspect in computational studies of ligand–protein binding. Recent advances in computational structure prediction of ligand–protein complexes utilize a diverse range of energetic models, based on either surface complementarity (Shoichet and Kuntz, 1991; Wang, 1991; Jiang and Kim, 1991; Walls and Sternberg, 1992; Katchalski-Katzir et al., 1992; Stoddard and Koshland, 1993; Desjarlais and Dixon, 1994; Vakser and Aflalo, 1994; Lin et al., 1994; Jackson and Sternberg, 1995; Fisher et al., 1995; Norel et al., 1995; Sobolev et al., 1996) or atom–atom representations of the intermolecular interactions (Friedman et al., 1994; Gehlhaar et al., 1995; Luty et al., 1995; Rarey et al., 1996 Rarey et al., , 1997 Welch et al., 1996). These energetic models combined with stochastic optimization techniques (Goodsell and Olson, 1990; Yue, 1990; Cherfils et al., 1991; Caflish et al., 1992; Hart and Read, 1992; Di Nola et al., 1994; Clark and Ajay, 1995; Oshiro et al., 1995; Gehlhaar et al., 1995; Jones et al., 1997; Westhead et al., 1997; Apostolakis et al., 1998) have led to a number of powerful strategies for computational structure prediction of ligand–protein complexes. ...
The thermodynamic and kinetic aspects of molecular recognition for the methotrexate (MTX)-dihydrofolate reductase (DHFR) ligand-protein system are investigated by the binding energy landscape approach. The impact of 'hot' and 'cold' errors in ligand mutations on the thermodynamic stability of the native MTX-DHFR complex is analyzed, and relationships between the molecular recognition mechanism and the degree of ligand optimization are discussed. The nature and relative stability of intermediates and thermodynamic phases on the ligand-protein association pathway are studied, providing new insights into connections between protein folding and molecular recognition mechanisms, and cooperativity of ligand-protein binding. The results of kinetic docking simulations are rationalized based on the thermodynamic properties determined from equilibrium simulations and the shape of the underlying binding energy landscape. We show how evolutionary ligand selection for a receptor active site can produce well-optimized ligand-protein systems such as MTX-DHFR complex with the thermodynamically stable native structure and a direct transition mechanism of binding from unbound conformations to the unique native structure.
... These purely geometric algorithms (e.g. [20, 125, 33, 32]) were successful for a large number of examples. It was soon recognized, that geometric complementarity alone is not sufficient to identify the binding site. ...
In the first part of this work, we propose new methods for protein docking. First, we present two approaches to protein docking with flexible side chains. The first approach is a fast greedy heuristic, while the second is a branch
-&-cut algorithm that yields optimal solutions. For a test set of protease-inhibitor complexes, both approaches correctly predict the true complex structure. Another problem in protein docking is the prediction of the
binding free energy, which is the the final step of many protein docking
algorithms. Therefore, we propose a new approach that avoids the expensive and difficult calculation of the binding free energy and, instead, employs a
scoring function that is based on the similarity of the proton nuclear magnetic resonance spectra of the tentative complexes with the experimental spectrum.
Using this method, we could even predict the structure of a very difficult protein-peptide complex that could not be solved using any energy-based
scoring functions.
The second part of this work presents BALL (Biochemical ALgorithms Library), a framework for Rapid Application Development in the field of Molecular Modeling.
BALL provides an extensive set of data structures as well as classes for Molecular Mechanics, advanced solvation methods, comparison and analysis of
protein structures, file import/export, NMR shift prediction, and visualization. BALL has been carefully designed to be robust, easy to use, and open to extensions. Especially its extensibility, which results from an object-oriented and generic programming approach, distinguishes it from other
software packages.
... Investigating molecular recognition in such a relayed mode can be far more efficient than ab initio methods for larger molecular systems. Docking methods have emerged during the last few years that are able to reproduce near-native conformations on the basis of geometri- Present address: D. Fischer, Laboratory of Mathematical Biology, NCI-FCRF, Bldg 469, Rm 151, Frederick, MD 21702, U.S.A. cal complementarity (Fischer et al., 1993; Lin et al., 1994; Norel et al., 1994a,b; Connoll}¢ 1986; Cherfils et al., 1991; Jiang & Kim, 1991; Shoichet & Kuntz, 1991; Wang, 1991; Bacon & Moult, 1992; KatchalskiKatzir et al., 1992; Walls & Sternberg, 1992). Geometric docking is exceedingly complex, due to the fact that computational costs increase exponentially with the degrees of freedom of the molecular system. ...
We have developed a geometry-based suite of processes for molecular docking. The suite consists of a molecular surface representation, a docking algorithm, and a surface inter-penetration and contact filter. The surface representation is composed of a sparse set of critical points (with their associated normals) positioned at the face centers of the molecular surface, providing a concise yet representative set. The docking algorithm is based on the Geometric Hashing technique, which indexes the critical points with their normals in a transformation invariant fashion preserving the multi-element geometric constraints. The inter-penetration and surface contact filter features a three-layer scoring system, through which docked models with high contact area and low clashes are funneled. This suite of processes enables a pipelined operation of molecular docking with high efficacy. Accurate and fast docking has been achieved with a rich collection of complexes and unbound molecules, including protein-protein and protein-small molecule associations. An energy evaluation routine assesses the intermolecular interactions of the funneled models obtained from the docking of the bound molecules by pairwise van der Waals and Coulombic potentials. Applications of this routine demonstrate the goodness of the high scoring, geometrically docked conformations of the bound crystal complexes.
This chapter focuses on the use of molecular surfaces for the comparison of molecules. These molecular surfaces provide a description of the spatial or three-dimensional (3D) characteristics of a molecule. This is important since molecular recognition, the binding of a drug to its target receptor, is inherently a 3D phenomenon. Hence, the comparison of molecular surfaces is a search for the similarity (or complementarity) of the 3D properties of molecules. Because of their 3D nature, these comparisons will be sensitive to changes in the geometry or conformation, and to the relative orientation of the molecules being compared. While simple steric or geometrical surfaces are often used in the search for surface similarity or surface complementarity, other chemical properties such as electrostatic or hydrophobic properties are important and have also been used in surface comparisons.
A number of challenging computational problems arise in the field of structure-based drug design, including the estimation of ligand binding affinity and the de novo design of novel ligands. An important step toward solutions of these problems is the consistent and rapid prediction of the thermodynamically most favorable structure of a ligand—protein complex from the three-dimensional structures of its unbound ligand and protein components. This fundamental problem in molecular recognition is commonly known as the docking problem [1–3]. To solve this problem, two distinct conditions must be satisfied. The first is a thermodynamic requirement: the energy function used to describe ligand—protein binding must have the crystal structure of ligand—protein complexes as its global energy minimum. The second is a kinetic requirement: it must be possible to locate consistently and rapidly the global energy minimum on the ligand—protein binding energy landscape. While the first condition is necessary for successful structure prediction, it is by no means sufficient. Without kinetic accessibility, the global minimum cannot be reached during docking simulations, and computational structure prediction will fail. Here we review approaches to address both the kinetic and thermodynamic aspects of the docking problem.
The three-dimensional (3D) structure of most protein complexes reveals a close geometric match between those parts of the respective surfaces of the protein and the ligand that are in contact. In many cases the 3D structure of the components in the complex closely resembles that of the molecules in their free, native state. Geometric matching thus appears to play an important role in determining the structure of a complex. A geometric recognition algorithm was developed to identify molecular surface complementarity. It is based on a purely geometric approach and takes advantage of techniques applied in the field of pattern recognition. The algorithm provides a list of correlation values indicating the extent of geometric match between the surfaces of the molecules. The procedure is equivalent to a six-dimensional search, but is much faster by design, and the computations are only moderately dependent on the molecular size. The procedure was tested and validated by using five known complexes for which the relative position of the molecules in the respective adducts was successfully predicted. The molecular pairs were the α, β subunits of deoxy-hemoglobin and methemoglobin, tRNA synthetase-tyrosinyl adenylate, aspartate proteinase-peptide inhibitor, and trypsin-trypsin inhibitor. The algorithm developed is being extended to include electrostatic match and hydrophobic interactions. In view of the above findings, the parameters determining biological specificity on the molecular level are discussed and evaluated.
Giulio Vistoli was born in 1968. He received his Laurea degree in medicinal chemistry at University of Milan in 1994. During his PhD studies with Prof L Villa, he spent a period in Lausanne under the supervision of Prof B Testa with whom he has fruitfully collaborated since 1996. In 1999, he became assistant professor in medicinal chemistry at University of Milan. His recent research focuses on developing the property space concept to explore the dynamic profile of molecular fields, deriving fertile descriptors for dynamic 4D-QSAR analyses.
Proteins specifically interact with other proteins and nucleic acids to form a wide variety of assemblies, from binary complexes to the elaborate multicomponent machines that perform many of the cellular functions. This chapter describes how Critical Assessment of PRedicted Interactions (CAPRI) is organized, summarizes the results of protein-protein recognition, and shows how CAPRI has fostered progress during the past 12 years. Protein-protein docking may be defined as the search for stable modes of association between two preformed protein structures. In single-cell organisms, more than half of the proteins are part of protein complexes, which may contain tens of subunits. CAPRI has taken on the evaluation of scoring functions and more recently that of affinity predictions. The CAPRI community has responded to new challenges arising from exciting new protein design endeavors. Genome-wide analyses are currently in the process of charting the landscape of protein-protein interactions in many organisms including human.
The completion of the Human Genome Project has launched the post-sequencing phase of genome research. Once a genome information is identified, protein structures become most important in life sciences. Drug design is one immediate example, and docking, a computational method to understand molecular binding between protein and compound, is one of its fundamental implementation methods. This chapter presents a docking problem between a receptor and a ligand in the framework of combinatorial optimization and is an effort to formalize the problem into a mathematically and computationally rigorous theory so that follow-up studies can safely rely on the concepts presented in this chapter. Docking problem is a mathematical and computational problem and a highly complicated, intractable problem. In addition, this problem is very much interdisciplinary encompassing biology, biochemistry, biophysics, medicinal chemistry, and computational disciplines such as optimization, mathematics, and geometric computations. Therefore, it is desirable to develop a common language. To accomplish this objective, this chapter is based on geometric constructs called the beta-complex and beta-shape of molecules.
Molecular docking explores the binding modes of two interacting molecules. The technique is increasingly popular for studying protein-ligand interactions and for drug design. A fundamental problem problem with molecular docking is that orientation space is very large and grows combinatorially with the number of degrees of freedom of the interacting molecules. Here, we describe and evaluate algorithms that improve the efficiency and accuracy of a shape-based docking method. We use molecular organization and sampling techniques to remove the exponential time dependence on molecular size in docking calculations. The new techniques allow us to study systems that were prohibitively large for the original method. The new algorithms are tested in 10 different protein-ligand systems, including 7 systems where the ligand is itself a protein. In all cases, the new algorithms successfully reproduce the experimentally determined configurations of the ligand in the protein.
IntroductionProtein-Protein InteractionsProtein-DNA InteractionsConclusion
References
The growing number of known 3D protein structures asks for computing systems predicting whether and where two molecules interact with each other. This requires search for possible docking sites of proteins. Based on results of preprocessing techniques like computation of molecular surfaces and segmentation, a knowledge based control algorithm implemented with the semantic network ERNEST searches for geometrical and chemical complementarity on molecular surfaces, computes coarse docking positions considering steric clash and simple geometric judgement functions. Additionally, ERNEST guides a more detailed analysis of finer calcultations including correlation of geometry and hydro- phobicity. The proposed hierarchical system allows to predict completely automatically and in reasonable short computing times possible docking sites for two given proteins. A set of 18 representative examples is discussed. © GBF (Gesellschaft für Biotechnologische Forschung mbH), 1995.
IntroductionBiological Specificity as Revealed by a Single ReceptorAnalysis of Systems Consisting of a Repertoire of ReceptorsThe Geometric Fit between Proteins and their LigandsAdditivity and Nonadditivity in Protein-Ligand InteractionsConcluding Remarks
Here we carry out an examination of shape complementarity as a criterion in protein--protein docking and binding. Specifically, we examine the quality of shape complementarity as a critical determinant not only in the docking of 26 protein--protein "bound", complexed cases, but in particular, of 19 "unbound" protein--protein cases, where the structures have been determined separately. In all cases, entire molecular surfaces are utilized in the docking, with no consideration of the location of the active site, or of particular residues/atoms in either the receptor or the ligand which participate in the binding. To evaluate the goodness of the strictly geometry-based shape complementarity in the docking process as compared to the main favorable and unfavorable energy components, we study systematically a potential correlation between each of these components and the RMSD of the "unbound" protein--protein cases. Specifically, we examine the non-polar buried surface area, polar b...
The authors first outline the basics of the deterministic global optimization approach, αBB, which has been used extensively to study the protein structure prediction, dynamics of protein-protein folding, and protein docking problems. This is followed by a comprehensive study of ab initio modeling for structure prediction of single-chain polypeptides in Section III. An extensive comparison of energy modeling, including solvation, entropic effects, and free energy calculations, is provided for the oligopeptides. The related problem of restrained structure refinement in the presence of sparse experimen-tally derived restraints is also discussed. Section IV moves beyond the static structure prediction problem toward an understanding of the dynamics of protein folding. An in-depth analysis of the coil-to-helix transition is provided for the alanine tetrapeptide. This analysis includes the elucidation of folding pathways and the identification of plausible reaction coordinates. Section V addresses the peptide docking problem. First, an approach for the determination of binding site structure is introduced. This is followed by a decomposition-based approach for the prediction of relative binding affinities. Both approaches are applied to peptide docking in HLA molecules.
Computer aided design methods are starting to gain acceptance in the field of life sciences and drug discovery, thus giving rise to a discipline coined Computer Aided Drug Discovery (CADD). This trend is accompanied by a larger interest in 3-dimensional methods. Traditionally for many applications chemical entities such as proteins and molecules have been regarded as either 2D graphs or sequences of letters (proteins and genome). This survey article will give an overview and historical perspective of the state of the art of geometric modeling as it relates to drug discovery.
An extended dynamic programming algorithm is presented that is applicable to the fragment assembly phase of the site mapping fragment assembly approach to peptide docking. After constructing a free energy map of the receptor using each of the amino acids in the peptides to be docked, we apply the algorithm to two systems: HIV-1 protease complexed with a synthetic hexameric inhibitor, and MHC HLA-A2 complexed with a nonameric peptide. The all atom root mean square deviation between the predicted and crystal structures was 1.7 and 2.0 Å, respectively. While these results are reasonable considering the relatively coarse level of mapping, the more important result is that the structures are probably very close to the best obtainable by an exhaustive search through the entire data map, and yet are obtained with a reduction of 3–5 orders of magnitude in the number of computations. We also outline a prescription for an iterative procedure which finds the global minimum with increasing confidence. © 1996 by John Wiley & Sons, Inc.
This paper presents an approach and a software, BetaDock, to the docking problem by putting the priority on shape complementarity between a receptor and a ligand. The approach is based on the theory of the β-complex. Given the Voronoi diagram of the receptor whose topology is stored in the quasi-triangulation, the β-complex corresponding to water molecule is computed. Then, the boundary of the β-complex defines the β-shape which has the complete proximity information among all atoms on the receptor boundary. From the β-shape, we first compute pockets where the ligand may bind. Then, we quickly place the ligand within each pocket by solving the singular value decomposition problem and the assignment problem. Using the conformations of the ligands within the pockets as the initial solutions, we run the genetic algorithm to find the optimal solution for the docking problem. The performance of the proposed algorithm was verified through a benchmark test and showed that BetaDock is superior to a popular docking software AutoDock 4.
This chapter describes the α-helical form of M13 major coat protein and its properties in relation to the in vivo biological processes. M13 bacteriophage and the closely related phages, fl and fd, are Escherichia coli-specific filamentous phages belonging to the genus, Inovirus. The chapter discusses the molecular properties of the membrane-bound bacteriophage disassembly and assembly processes by studying the structural and functional behavior of the major coat protein of bacteriophage M13 and related phages, when incorporated into model membrane systems. Various spectroscopic techniques have been applied that provide detailed information about these reconstituted systems, whereas biochemical separation techniques allow purifying and characterizing these systems. The chapter discusses the role of M13 coat protein in the infection process, leading to conditions to reconstitute the protein in its native state into model membrane systems. In addition, the structure of the coat protein and protein–lipid interactions is discussed in the chapter.
A geometric recognition algorithm was developed to identify molecular surface complementarity. It is based on a purely geometric approach and takes advantage of techniques applied in the field of pattern recognition. The algorithm involves an automated procedure including (i) a digital representation of the molecules (derived from atomic coordinates) by three-dimensional discrete functions that distinguishes between the surface and the interior; (ii) the calculation, using Fourier transformation, of a correlation function that assesses the degree of molecular surface overlap and penetration upon relative shifts of the molecules in three dimensions; and (iii) a scan of the relative orientations of the molecules in three dimensions. The algorithm provides a list of correlation values indicating the extent of geometric match between the surfaces of the molecules; each of these values is associated with six numbers describing the relative position (translation and rotation) of the molecules. The procedure is thus equivalent to a six-dimensional search but much faster by design, and the computation time is only moderately dependent on molecular size. The procedure was tested and validated by using five known complexes for which the correct relative position of the molecules in the respective adducts was successfully predicted. The molecular pairs were deoxyhemoglobin and methemoglobin, tRNA synthetase-tyrosinyl adenylate, aspartic proteinase-peptide inhibitor, and trypsin-trypsin inhibitor. A more realistic test was performed with the last two pairs by using the structures of uncomplexed aspartic proteinase and trypsin inhibitor, respectively. The results are indicative of the extent of conformational changes in the molecules tolerated by the algorithm.
We have added a chemical filter to the ligand placement algorithm of the molecular docking program DOCK. DOCK places ligands
in receptors using local shape features. Here we label these shape features by chemical type and insist on complementary matches.
We find fewer physically unrealistic complexes without reducing the number of complexes resembling the known ligand–receptor
configurations. Approximately 10-fold fewer complexes are calculated and the new algorithm is correspondingly 10-fold faster
than the previous shape-only matching. We tested the new algorithm's ability to reproduce three known ligand–receptor complexes:
methotrexate in dihydrofolate reductase, deoxyuridine monophosphate in thymidylate synthase and pancreatic trypsin inhibitor
in trypsin. The program found configurations within 1 AÅ of the crystallographic mode, with fewer non-native solutions compared
with shape-only matching. We also tested the program's ability to retrieve known inhibitors of thymidylate synthase and dihydrofolate
reductase by screening molecular databases against the enzyme structures. Both algorithms retrieved many known inhibitors
preferentially to other compounds in the database. The chemical matching algorithm generally ranks known inhibitors better
than does matching based on shape alone.
Docking and design are the major computational steps toward understanding and affecting receptor-ligand interactions. The flexibility of many ligands makes these calculations difficult and requires the development and use of special methods. The need for such tools is illustrated by two examples: the design of protease inhibitors and the analysis and design of peptide antigens binding to specific MHC receptors. We review the computational concepts that have been extended from rigid-body to flexible docking, as well as the following important strategies for flexible docking and design: (a) Monte Carlo/molecular dynamics docking, (b) in-site combinatorial search, (c) ligand build-up, and (d) site mapping and fragment assembly. The use of empirical free energy as a target function is discussed. Due to the rapid development of the methodology, most new methods have been tested on only a limited number of applications and are likely to improve results obtained by more traditional computational or graphic tools.
An algorithm has been developed that can be used to divide triangulated molecular surfaces into distinct domains on the basis of physical and topographical molecular properties. Domains are defined by a certain degree of homogeneity concerning one of these properties. The method is based on fuzzy logic strategies, thus taking into consideration the smooth changes of the properties considered along complex macromolecular surfaces. Scalar qualities assigned to every node point on a triangulated surface are translated into linguistic variables, which can then be processed using a special fuzzy dissimilarity operator. Possible applications are demonstrated using surface segmentation for properties like electrostatic potential, lipophilicity and shape for the analysis of serine proteinase substrate/inhibitor specificity.
A matching algorithm using surface complementarity between receptor and ligand protein molecules is outlined. The molecular surfaces are represented by "critical points," describing holes and knobs. Holes (maxima of a shape function) are matched with knobs (minima). This simple and appealing surface representation has been previously described by Connolly [(1986) Biopolymers, Vol. 25, pp. 1229-1247]. However, attempts to implement this description in a docking scheme have been unsuccessful (e.g., Connolly, ibid.). In order to decrease the combinatorial complexity, and to make the execution time affordable, four critical hole/knob point matches were sought. This approach failed since some bound interfaces are relatively flat and do not possess four critical point matches. On the otherhand, matchings of fewer critical points require a very time-consuming, full conformational (grid) space search [Wang, (1991) Journal of Computational Chemistry, Vol. 12, pp. 746-750]. Here we show that despite the initial failure of this approach, with a simple and straightforward modification in the matching algorithm, this surface representation works well. Out of the 16 protein-protein complexes we have tried, 15 were successfully docked, including two immunoglobulins. The entire molecular surfaces were considered, with absolutely no additional information regarding the binding sites. The whole process is completely automated, with no manual intervention, either in the input atomic coordinate data, or in the matching. We have been able to reach this level of performance with the hole/knob surface description by using pairs of critical points along with their surface normals in the calculation of the transformation matrix. The success of this approach suggests that future docking methods should use geometric docking as the first screening filter.(ABSTRACT TRUNCATED AT 250 WORDS)
We have defined a molecular surface representation that describes precisely and concisely the complete molecular surface. The representation consists of a limited number of critical points disposed at key locations over the surface. These points adequately represent the shape and the important characteristics of the surface, despite the fact that they are modest in number. We expect the representation to be useful in areas such as molecular recognition and visualization. In particular, using this representation, we are able to achieve accurate and efficient protein-protein and protein-small molecule docking.
A method is described to dock a ligand into a binding site in a protein on the basis of the complementarity of the intermolecular atomic contacts. Docking is performed by maximization of a complementarity function that is dependent on atomic contact surface area and the chemical properties of the contacting atoms. The generality and simplicity of the complementarity function ensure that a wide range of chemical structures can be handled. The ligand and the protein are treated as rigid bodies, but displacement of a small number of residues lining the ligand binding site can be taken into account. The method can assist in the design of improved ligands by indicating what changes in complementarity may occur as a result of the substitution of an atom in the ligand. The capabilities of the method are demonstrated by application to 14 protein-ligand complexes of known crystal structure.
Energy landscapes of molecular recognition are explored by performing "semi-rigid" docking of FK-506 and rapamycin with the Fukisawa binding protein (FKBP-12), and flexible docking simulations of the Ro-31-8959 and AG-1284 inhibitors with HIV-1 protease by a genetic algorithm. The requirements of a molecular recognition model to meet thermodynamic and kinetic criteria of ligand-protein docking simultaneously are investigated using a family of simple molecular recognition energy functions. The critical factor that determines the success rate in predicting the structure of ligand-protein complexes is found to be the roughness of the binding energy landscape, in accordance with a minimal frustration principle. The results suggest that further progress in structure prediction of ligand-protein complexes can be achieved by designing molecular recognition energy functions that generate binding landscapes with reduced frustration.
Fueled by advances in molecular structure determination, tools for structure-based drug design are proliferating rapidly. Lead discovery through searching of ligand databases with molecular docking techniques represents an attractive alternative to high-throughout random screening. The size of commercial databases imposes severe computational constraints on molecular docking, compromising the level of calculational detail permitted for each putative ligand. We describe alternative philosophies for docking which effectively address this challenge. With respect to the dynamic aspects of molecular recognition, these strategies lie along a spectrum of models bounded by the Lock-and-Key and Induced-Fit theories for ligand binding. We explore the potential of a rigid model in exploiting species specificity and of a tolerant model in predicting absolute ligand binding affinity. Current molecular docking methods are limited primarily by their ability to rank docked complexes; we therefore place particular emphasis on this aspect of the problem throughout our validation of docking strategies.
We present a rapidly executable minimal binding energy model for molecular docking and use it to explore the energy landscape in the vicinity of the binding sites of four different enzyme inhibitor complexes. The structures of the complexes are calculated starting with the crystal structures of the free monomers, using DOCK 4.0 to generate a large number of potential configurations, and screening with the binding energy target function. In order to investigate possible correlations between energy and variation from the native structure, we introduce a new measure of similarity, which removes many of the difficulties associated with root mean square deviation. The analysis uncovers energy gradients, or funnels, near the binding site, with decreasing energy as the degree of similarity between the native and docked structures increases. Such energy funnels can increase the number of random collisions that may evolve into productive stable complex, and indicate that short-range interactions in the precomplexes can contribute to the association rate. The finding could provide an explanation for the relatively rapid association rates that are observed even in the absence of long-range electrostatic steering.
In this work, we present an algorithm developed to handle biomolecular structural recognition problems, as part of an interdisciplinary research endeavor of the Computer Vision and Molecular Biology fields. A key problem in rational drug design and in biomolecular structural recognition is the generation of binding modes between two molecules, also known as molecular docking. Geometrical fitness is a necessary condition for molecular interaction. Hence, docking a ligand (e.g., a drug molecule or a protein molecule), to a protein receptor (e.g., enzyme), involves recognition of molecular surfaces. Conformational transitions by "hinge-bending" involves rotational movements of relatively rigid parts with respect to each other. The generation of docked binding modes between two associating molecules depends on their three dimensional structures (3-D) and their conformational flexibility. In comparison to the particular case of rigid-body docking, the computational difficulty grows considerably when taking into account the additional degrees of freedom intrinsic to the flexible molecular docking problem. Previous docking techniques have enabled hinge movements only within small ligands. Partial flexibility in the receptor molecule is enabled by a few techniques. Hinge-bending motions of protein receptors domains are not addressed by these methods, although these types of transitions are significant, e.g., in enzymes activity. Our approach allows hinge induced motions to exist in either the receptor or the ligand molecules of diverse sizes. We allow domains/subdomains/group of atoms movements in either of the associating molecules. We achieve this by adapting a technique developed in Computer Vision and Robotics for the efficient recognition of partially occluded articulated objects. These types of objects consist of rigid parts which are connected by rotary joints (hinges). Our method is based on an extension and generalization of the Hough transform and the Geometric Hashing paradigms for rigid object recognition. We show experimental results obtained by the successful application of the algorithm to cases of bound and unbound molecular complexes, yielding fast matching times. While the "correct" molecular conformations of the known complexes are obtained with small RMS distances, additional, predictive good-fitting binding modes are generated as well. We conclude by discussing the algorithm's implications and extensions, as well as its application to investigations of protein structures in Molecular Biology and recognition problems in Computer Vision.
In this paper, a method of simulating the docking of small flexible ligands to flexible receptors in water is reported. The method is based on molecular dynamics simulations and is an extension of an algorithm previously reported by Di Nola et al. (Di Nola et al., Proteins 1994;19:174-182). The method allows a fast exploration of the receptor surface, using a high temperature of the center of mass translational motion, while the ligand internal motions, the solvent, and the receptor are simulated at room temperature. In addition, the method allows a fast center of mass motion of the ligand, even in solution. The dampening effect of the solvent can be overcome by applying different weights to the interactions between system subsets (solvent, receptor, and ligand). Specific ligand-receptor distances have been used to compare the results of the simulations with the crystal structure. The method is applied, as a test system, to the docking of the phosphocholine to the immunoglobulin McPC603. The results show the similarity of structure between the complex in solution and in the crystal.
Here we carry out an examination of shape complementarity as a criterion in protein-protein docking and binding. Specifically, we examine the quality of shape complementarity as a critical determinant not only in the docking of 26 protein-protein "bound" complexed cases, but in particular, of 19 "unbound" protein-protein cases, where the structures have been determined separately. In all cases, entire molecular surfaces are utilized in the docking, with no consideration of the location of the active site, or of particular residues/atoms in either the receptor or the ligand that participate in the binding. To evaluate the goodness of the strictly geometry-based shape complementarity in the docking process as compared to the main favorable and unfavorable energy components, we study systematically a potential correlation between each of these components and the root mean square deviation (RMSD) of the "unbound" protein-protein cases. Specifically, we examine the non-polar buried surface area, polar buried surface area, buried surface area relating to groups bearing unsatisfied buried charges, and the number of hydrogen bonds in all docked protein-protein interfaces. For these cases, where the two proteins have been crystallized separately, and where entire molecular surfaces are considered without a predefinition of the binding site, no correlation is observed. None of these parameters appears to consistently improve on shape complementarity in the docking of unbound molecules. These findings argue that simplicity in the docking process, utilizing geometrical shape criteria may capture many of the essential features in protein-protein docking. In particular, they further reinforce the long held notion of the importance of molecular surface shape complementarity in the binding, and hence in docking. This is particularly interesting in light of the fact that the structures of the docked pairs have been determined separately, allowing side chains on the surface of the proteins to move relatively freely. This study has been enabled by our efficient, computer vision-based docking algorithms. The fast CPU matching times, on the order of minutes on a PC, allow such large-scale docking experiments of large molecules, which may not be feasible by other techniques. Proteins 1999;36:307-317.
Here we examine the recognition of small molecules by their protein and DNA receptors. We focus on two questions: First, how well does the solid angle molecular surface representation perform in fitting together the surfaces of small ligands, such as drugs and cofactors to their corresponding receptors; And second, in particular, to what extent does the shape complementarity play a role in the matching (recognition) process of such small molecules. Both questions have been investigated in protein-protein binding: "Critical Points" based on solid angle calculations have been shown to perform well in the matching of large protein molecules. They are robust, may be few in numbers, and capture satisfactorily the molecular shape. Shape complementarity has been shown to be a critical factor in protein-protein recognition, but has not been examined in drug-receptor recognition. To probe these questions, here we dock 185 receptor-small ligand molecule pairs. We find that such a representation performs adequately for the smaller ligands too, and that shape complementarity is also observed. These issues are important, given the large databases of drugs that routinely have to be scanned to find candidate, lead compounds. We have been able to carry out such large scale docking experiments owing to our efficient, computer-vision based docking algorithms. Its fast CPU matching times, on the order of minutes on a PC, allows such large scale docking experiments.
The formation of the protein-protein interface by the insulin dimer, the trypsin-PTI complex and the alphabeta oxyhaemoglobin dimer removes 1,130-1,720 A2 of accessible surface from contact with water. The residues forming the interface are close packed: each occupies the same volume as it does in crystals of amino acids. These results indicate that hydrophobicity is the major factor stabilising protein-protein association, while complementarily plays a selective role in deciding which proteins may associate.
A computational method for attempting to predict protein complexes from the coordinates of the individual proteins has been developed. It is based on matching complementary patterns of knobs and holes. The computer algorithm correctly and uniquely predicts the association of the alpha and beta subunits to form the αβ dimer corresponding to the α1β1 interface in the hemoglobin tetramer. It fails to correctly dock trypsin inhibitor onto trypsin. Nevertheless, this lone success is still a significant advance over previous protein-docking algorithms. The method is also important because it introduces several ways to measure the shape of protein surface regions.
A computer algorithm is presented for calculating the part of the van der Waals surface of molecule that is accessible to solvent. The solvent molecule is modeled by a sphere. This sphere is, in effect, rolled over the molecule to generate a smooth outer-surface contour. This surface contour is made up of pieces of spheres and tori that join at circular arcs. The spheres, tori and arcs are defined by analytical expressions in terms of the atomic coordinates, van der Waals radii and the probe radius. The area of each surface piece may be calculated analytically and the surface may be displayed on either vector or raster computer-graphics systems. These methods are useful for studying the structure and interactions of proteins and nucleic acids.
The three-dimensional refined high resolution structures of 20 proteins were examined for the presence of packing defects of atomic size or larger. Of the proteins examined, 12 had no such packing defects, 6 proteins had just 1 packing defect, and 2 proteins had 2 or 3 packing defects. These results confirm earlier studies on smaller samples of proteins which demonstrated that proteins are well packed. The atoms that surround the packing defects are almost always hydrophobic (carbon or sulfur). This study also tabulated the number of internal waters in each protein, which varied from 0 to 28.
A program is described for drawing the van der Waal's surface of a protein molecule. An extension of the program permits the accessibility of atoms, or groups of atoms, to solvent or solute molecules of specified size to be quantitatively assessed. As defined in this study, the accessibility is proportional to surface area. The accessibility of all atoms in the twenty common amino acids in model tripeptides of the type Ala-X-Ala are given for defined conformation. The accessibilities are also given for all atoms in ribonuclease-S, lysozyme and myogoblin. Internal cavities are defined and discussed. Various summaries of these data are provided. Forty to fifty per cent of the surface area of each protein is occupied by non-polar atoms. The actual numerical results are sensitive to the values chosen for the van der Waal's radii of the various groups. Since there is uncertainty over the correct values for these radii, the derived numbers should only be used as a qualitative guide at this stage.The average change in accessibility for the atoms of all three proteins in going from a hypothetical extended chain to the folded conformation of the native protein is about a factor of 3. This number applies to both polar (nitrogen and oxygen) and non-polar (carbon and sulfur) atoms considered separately. The larger non-polar amino acids tend to be more “buried” in the native form of all three proteins. However, for all classes and for residues within a given class the accessibility changes on folding tend to be highly variable.
We describe a method to explore geometrically feasible alignments of ligands and receptors of known structure. Algorithms are presented that examine many binding geometries and evaluate them in terms of steric overlap. The procedure uses specific molecular conformations. A method is included for finding putative binding sites on a macromolecular surface.Results are reported for two systems: the heme-myoglobin interaction and the binding of thyroid hormone analogs to prealbumin. In each case the program finds structures within 1 Å of the X-ray results and also finds distinctly different geometries that provide good steric fits. The approach seems well-suited for generating starting conformations for energy refinement programs and interactive computer graphics routines.