Quantification of protein surfaces,volumes and atom-atom contacts using a constrained Voronoi procedure

MOTIVATION: Geometric representations of proteins and ligands, including atom volumes, atom-atom contacts and solvent accessible surfaces, can be used to characterize interactions between and within proteins, ligands and solvent. Voronoi algorithms permit quantification of these properties by dividing structures into cells with a one-to-one correspondence with constituent atoms. As there is no generally accepted measure of atom-atom contacts, a continuous analytical representation of inter-atomic contacts will be useful. Improved geometric algorithms will also be helpful in increasing the speed and accuracy of iterative modeling algorithms. RESULTS: We present computational methods based on the Voronoi procedure that provide rapid and exact solutions to solvent accessible surfaces, volumes, and atom contacts within macromolecules. Furthermore, we define a measure of atom-atom contact that is consistent with the calculation of solvent accessible surfaces, allowing the integration of solvent accessibility and inter-atomic contacts into a continuous measure. The speed and accuracy of the algorithm is compared to existing methods for calculating solvent accessible surfaces and volumes. The presented algorithm has a reduced execution time and greater accuracy compared to numerical and approximate analytical surface calculation algorithms, and a reduced execution time and similar accuracy to existing Voronoi procedures for calculating atomic surfaces and volumes.     

Variation of folded polypeptide surface area with probe size

Three types of polypeptide surface area (contact, accessible, and molecular) have been studied as a function of the radius of a probe sphere used to map the surface. The surfaces are: (1) three alpha-helices, the H-helix of myoglobin, the E-helix of leghemoglobin, and an artificial polyalanine helix, each with 26 residues; (2) two globins, myoglobin and leghemoglobin, each with 153 residues; and (3) a two-center model system for which the three types of surface area have been calculated analytically. The two globin helices have almost identical surface areas as a function of probe size as do the two globins. The polyalanine helix surface area is smaller but similar in shape to the globin helix areas. All three helix contact areas tend to the same limit as the probe size increases, and the globin contact areas behave similarly. Fractal dimensions were calculated for the helix and globin contact and molecular surfaces. All fractal dimensions showed strong dependence on probe size. The contact fractal dimension peaks at larger values for both the helices and globins. Most residues do not make contact with large probes (15 A).     

Determination of the accessible surface of lysozyme and human serum albumin molecules by the total tritium labeling method

Amino acids composing an accessible surface of lysozyme and human serum albumin (HSA) globules were determined by the total tritium labelling method. A good correlation between our data on the distribution of the tritium label for the lysozyme molecule and X-ray data on the tertiary structure for this macromolecule was received. Lysozyme was used as a standard for determining the accessible surface of the globule albumin. It was shown that the accessible surface of the albumin globule is substantially more hydrophobic (average accessible surface area of hydrophobic amino acids is 130 A2 in HSA and 20 A2 in lysozyme) than in lysozyme. The HSA molecule is characterized by high values of: the accessible surface area, the ratio of extended area to the folded one, and the surface roughness index. These data indicate that the HSA molecule is less compactly packed than lysozyme.     

CASTp: Computed Atlas of Surface Topography of proteins

Computed Atlas of Surface Topography of proteins (CASTp) provides an online resource for locating, delineating and measuring concave surface regions on three-dimensional structures of proteins. These include pockets located on protein surfaces and voids buried in the interior of proteins. The measurement includes the area and volume of pocket or void by solvent accessible surface model (Richards' surface) and by molecular surface model (Connolly's surface), all calculated analytically. CASTp can be used to study surface features and functional regions of proteins. CASTp includes a graphical user interface, flexible interactive visualization, as well as on-the-fly calculation for user uploaded structures. CASTp is updated daily and can be accessed at http://cast.engr.uic.edu.     

Fast accurate evaluation of protein solvent exposure

Protein solvation energies are often taken to be proportional to solvent-accessible surface areas. Computation of these areas is numerically demanding and may become a bottleneck for folding and design applications. Fast graph-based methods, such as dead-end elimination (DEE), become possible if all energies, including solvation energies, are expressed as single-residue and pair-residue terms. To this end, Street and Mayo originated a pair-residue approximation for solvent-accessible surface areas (Street AG, Mayo SL. Pairwise calculation of protein solvent accessible surface areas. Fold Des 1998;3:253-258). The dominant source of error in this method is the overlapping burial of side-chain surfaces in the protein core. Here we report a new pair-residue approximation, which greatly reduces this overlap error by the use of optimized generic side-chains. We have tested the generic-side-chain method for the ten proteins studied by Street and Mayo and for 377 single-domain proteins from the CATH database (Orengo CA, Michie AD, Jones S, Jones DT, Swindells MB, Thornton JM. CATH-A hierarchic classification of protein domain structures. Structure 1997;5:1093-1108). With little additional cost in computation, the new method consistently reduces error for total areas and residue-by-residue areas by more than a factor of two. For example, the residue-by-residue error (for buried area) is reduced from 7.42 A(2) to 3.70 A(2). This difference translates into a solvation energy difference of approximately 0.2 kcal/mol per residue, amounting to a reduction in root-mean-square energy error of 2 kcal/mol for a 100 residue chain, a potentially critical difference for both protein folding and design applications.     

Surface, subunit interfaces and interior of oligomeric proteins

The solvent-accessible surface area (As) of 23 oligomeric proteins is calculated using atomic co-ordinates from high-resolution and well-refined crystal structures. As is correlated with the protein molecular weight, and a power law predicts its value to within 5% on average. The accessible surface of the average oligomer is similar to that of monomeric proteins in its hydropathy and amino acid composition. The distribution of the 20 amino acid types between the protein surface and its interior is also the same as in monomers. Interfaces, i.e. surfaces involved in subunit contacts, differ from the rest of the subunit surface. They are enriched in hydrophobic side-chains, yet they contain a number of charged groups, especially from Arg residues, which are the most abundant residues at interfaces except for Leu. Buried Arg residues are involved in H-bonds between subunits. We counted H-bonds at interfaces and found that several have none, others have one H-bond per 200 A2 of interface area on average (1 A = 0.1 nm). A majority of interface H-bonds involve charged donor or acceptor groups, which should make their contribution to the free energy of dissociation significant, even when they are few. The smaller interfaces cover about 700 A2 of the subunit surface. The larger ones cover 3000 to 10,000 A2, up to 40% of the subunit surface area in catalase. The lower value corresponds to an estimate of the accessible surface area loss required for stabilizing subunit association through the hydrophobic effect alone. Oligomers with small interfaces have globular subunits with accessible surface areas similar to those of monomeric proteins. We suggest that these oligomers assemble from preformed monomers with little change in conformation. In oligomers with large interfaces, isolated subunits should be unstable given their excessively large accessible surface, and assembly is expected to require major structural changes.     

Calculation of the partial specific volumes of proteins in concentrated salt, sugar, and amino acid solutions

A method for calculating the isopotential partial specific volumes of proteins in concentrated salt, sugar, and amino acid solutions has been developed. It is based on the finding that the preferential hydration of the protein in these solutions is relatively independent of the concentration of the additive and is proportional to the specific surface area of the proteins, i.e., to the ratio of the total accessible surface area to molecular weight. Agreement between the calculated and experimental values was satisfactory, indicating the reliability of the proposed method. These calculations show that the isopotential partial specific volume increases greatly with the concentration of the additive, in particular in the case of Na2SO4, (NH4)2SO4 and sucrose, and for smaller proteins.     

Protein Molecular Surface Mapped at Different Geometrical Resolutions

Many areas of biochemistry and molecular biology, both fundamental and applications-orientated, require an accurate construction, representation and understanding of the protein molecular surface and its interaction with other, usually small, molecules. There are however many situations when the protein molecular surface gets in physical contact with larger objects, either biological, such as membranes, or artificial, such as nanoparticles. The contribution presents a methodology for describing and quantifying the molecular properties of proteins, by geometrical and physico-chemical mapping of the molecular surfaces, with several analytical relationships being proposed for molecular surface properties. The relevance of the molecular surface-derived properties has been demonstrated through the calculation of the statistical strength of the prediction of protein adsorption. It is expected that the extension of this methodology to other phenomena involving proteins near solid surfaces, in particular the protein interaction with nanoparticles, will result in important benefits in the understanding and design of protein-specific solid surfaces.     

The molecular surface package

The Molecular Surface Package is a reimplementation, in C, of a set of earlier FORTRAN programs for computing analytical molecular surfaces, areas, volumes, polyhedral molecular surfaces, and surface curvatures. The software does not do interactive molecular graphics, but it will produce pixel maps of smooth molecular surfaces. The polyhedral molecular surfaces are suited to display on graphics systems with real-time rendering of polyhedra.     

Medium reorganization energy and enzymatic reaction activation energy

Reorganization and activation energies for charge transfer reactions occurring inside a dielectric sphere have been calculated by solving the problem of polar medium reorganization within and outside a dielectric sphere placed in another infinite dielectric. The dielectric sphere is assumed to simulate a protein globule, i.e. an enzyme molecule. It has been shown that for some reaction types the activation energy tends to decrease as the globule radius increases and that for each of the reaction types considered there is an optimal globule radius an increase of which does not bring about any tangible activation energy reduction. The calculated optimal radii for different processes are in good agreement with the increasing molecular sizes in the series: ribonuclease less than or equal to lysozyme less than serine proteinases approximately equal to cysteine proteinases less than NAD-dependent dehydrogenases. The calculated radii are usually about 1.5 to 1.7 times (and molecular masses about 4-5 times) smaller than the experimental ones. The reasons for this discrepancy are discussed and it has been suggested that the approximate nature of the treatment of a protein globule as a structureless dielectric is the main reason. It is shown that charge transfer at an acute angle to the globule surface is the optimum process. For endoergonic reaction stages it is the net charge transfer towards the periphery and for exoergonic ones that in the reverse direction which are advantageous. These conclusions are consistent with the data about the structure of the above-mentioned enzymes.     

Analysis of accessible surface of residues in proteins

We analyzed the total, hydrophobic, and hydrophilic accessible surfaces (ASAs) of residues from a nonredundant bank of 587 3D structure proteins. In an extended fold, residues are classified into three families with respect to their hydrophobicity balance. As expected, residues lose part of their solvent-accessible surface with folding but the three groups remain. The decrease of accessibility is more pronounced for hydrophobic than hydrophilic residues. Amazingly, Lysine is the residue with the largest hydrophobic accessible surface in folded structures. Our analysis points out a clear difference between the mean (other studies) and median (this study) ASA values of hydrophobic residues, which should be taken into consideration for future investigations on a protein-accessible surface, in order to improve predictions requiring ASA values. The different secondary structures correspond to different accessibility of residues. Random coils, turns, and beta-structures (outside beta-sheets) are the most accessible folds, with an average of 30% accessibility. The helical residues are about 20% accessible, and the difference between the hydrophobic and the hydrophilic residues illustrates the amphipathy of many helices. Residues from beta-sheets are the most inaccessible to solvent (10% accessible). Hence, beta-sheets are the most appropriate structures to shield the hydrophobic parts of residues from water. We also show that there is an equal balance between the hydrophobic and the hydrophilic accessible surfaces of the 3D protein surfaces irrespective of the protein size. This results in a patchwork surface of hydrophobic and hydrophilic areas, which could be important for protein interactions and/or activity.     

Study of the structure of human serum albumin, liberated from fatty acids, by a tritium marker method]

To elucidate the natural fatty acids effect on the human serum albumin (HSA) structure a new method of tritium labelling was used. The main peculiarity of the method consists in the possibility to get information on the qualitative and quantitative amino acid composition of the surface layer of the protein globule at different conformational states of the globule. Defatted HSA was shown to be characterized a higher accessibility of Asx, Glx, Thr, Ser, Gly, Pro, Ile, Tyr residues while the other residues remain unchanged. Asx residues are characterized by the largest changes (about 8 folds). Full accessible protein surface during defatting increases from 39,000 to 48,000 A2. Fatty acids connected with albumin in the relation 1-3 moles/mol of protein are noted to be the factor increasing the globule compactness and stipulating for the conformational protein stability to warmth, urine and guanidine salts effect.     

Microwave dielectric study on bound water of globule proteins in aqueous solution

A dielectric relaxation peak due to bound water of globule proteins in aqueous solution was observed at first by the use of a time domain reflectometry. This peak locates around 100 MHz as well as that of the aqueous DNA solution and the moist collagen, and has a relaxation strength in proportion to surface of the globule protein except for trypsin and pepsin of hydrolase. It is suggested that this peak is caused by orientation of bound water molecules on the protein surface. The number of bound water molecules estimated is in good agreement with that obtained by other method such as x-ray analysis. The solution exhibits another peak below 100 MHz, which is caused by the rotation of globule protein supplemented by migration of the counterion. Its relaxation time is completely proportional to the molecular weight of the protein. © 1994 John Wiley & Sons, Inc.     

Improved technique for calculating X-ray scattering intensity of biopolymers in solution: Evaluation of the form,volume, and surface of a particle

An improved cube method has been developed for calculating the intensity of diffuse x-ray scattering of macromolecules in solution using a certain set of their atomic coordinates. The technique is based on the ideas of B. Lee and F. M. Richards [(1971) J. Mol. Biol. 55 , 374–400] and Richards [(1977) Annu. Rev. Biophys. Bioeng. 6 , 151–176] on the possibility of estimating the molecular and accessible surface of a particle by “rolling” a sphere, simulating a water molecule, on its molecular surface. It is shown that this technique is more advantageous than earlier versions of the cube methods. The improved technique for calculating scattering curves was utilized for several globular proteins, and for the first time, reliable scattering curves were obtained for protein-“bound” water complexes. In the case of globular proteins and tRNA, this technique has permitted a strict evaluation of their accessible surfaces, their volumes, and, apparently for the first time, their complete molecular surfaces.     

Approximation and characterization of molecular surfaces

The representation and characterization of molecular surfaces are important in many areas of molecular modeling. Parametric representations of protein molecular surfaces are a compact way to describe a surface, and are useful for the evaluation of surface properties such as the normal vector, principal curvatures, and principal curvature directions. Simplified representations of molecular surfaces are useful for efficient rendering and for the display of large-scale surface features. Several techniques for representing surfaces by expansions of spherical harmonic functions have been reported, but these techniques require that the radius function is single valued, that is, each ray from an origin inside the surface intersects the surface at one and only one point. A new technique is described that removes this limitation and can be used to compute surface shape properties. © 1993 John Wiley & Sons, Inc.     

Macromolecular solvation energies derived from small molecule crystal morphology.

The morphology of small molecule crystals provides a model for evaluating surface solvation energies in a system with similar packing density to that observed for amino acid residues in proteins. The solvation energies associated with the transfer of methylene and carboxyl groups between vacuum and aqueous phases are estimated to be approx. $40 and -260 cal/A2, respectively, from an analysis of the morphology of succinic acid crystals. These solvation energies predict values for contact angles in reasonable agreement with measurements determined from macroscopic monolayer surfaces. Transfer free energies between vapor and water phases for a series of carboxylic acids are also predicted reasonably well by these solvation energies, provided the surface exposure of different groups is quantitated with the molecular surface area rather than the more traditional accessible surface area. In general, molecular surfaces and molecular surface areas are seen to have important advantages for characterizing the structure and energetics of macromolecular surfaces. Crystal faces of succinic acid with the lowest surface energies in aqueous solution are characteristically smooth. Increasing surface roughness and apolarity are associated with higher surface energies, which suggests an approach for modifying the surface properties of proteins and other macromolecules.     

Sorption immobilization of NAD-dependent enzyme systems. I. Influence of electrostatic interactions on the orientation of alcohol dehydrogenase on the sorbent surface

The model calculation of interactions between the horse liver alcoholdehydrogenase-globule and the charged surface of sorbents and electrodes was performed. It has been shown that due to the discrete distribution of charges the enzyme globula can sorb on the surfaces having the same sign of charge as the total globule charge. In case of alcoholdehydrogenase the anion sorption can occur at pH greater than pI. Also, the orientation and therefore the catalytic activity of the immobilized system can be optimal.     

自然氨基酸的溶剂可及性标准

提出一种新的计算蛋白质溶剂可及面积的方法.利用该方法计算了二十个氨基酸在三肽模型中的可及面积,与他人的结果作了比较.提供了一套在分子模建中很有用的数据.