Cavities and Atomic Packing in Protein Structures and Interfaces

A comparative analysis of cavities enclosed in a tertiary structure of proteins and interfaces formed by the interaction of two protein subunits in obligate and non-obligate categories (represented by homodimeric molecules and heterocomplexes, respectively) is presented. The total volume of cavities increases with the size of the protein (or the interface), though the exact relationship may vary in different cases. Likewise, for individual cavities also there is quantitative dependence of the volume on the number of atoms (or residues) lining the cavity. The larger cavities tend to be less spherical, solvated, and the interfaces are enriched in these. On average 15 ų of cavity volume is found to accommodate single water, with another 40–45 ų needed for each additional solvent molecule. Polar atoms/residues have a higher propensity to line solvated cavities. Relative to the frequency of occurrence in the whole structure (or interface), residues in β-strands are found more often lining the cavities, and those in turn and loop the least. Any depression in one chain not complemented by a protrusion in the other results in a cavity in the protein–protein interface. Through the use of the Voronoi volume, the packing of residues involved in protein–protein interaction has been compared to that in the protein interior. For a comparable number of atoms the interface has about twice the number of cavities relative to the tertiary structure.     

Cavities and packing at protein interfaces.

An analysis of internal packing defects or "cavities" (both empty and water-containing) within protein structures has been undertaken and includes 3 cavity classes: within domains, between domains, and between protein subunits. We confirm several basic features common to all cavity types but also find a number of new characteristics, including those that distinguish the classes. The total cavity volume remains only a small fraction of the total protein volume and yet increases with protein size. Water-filled "cavities" possess a more polar surface and are typically larger. Their constituent waters are necessary to satisfy the local hydrogen bonding potential. Cavity-surrounding atoms are observed to be, on average, less flexible than their environments. Intersubunit and interdomain cavities are on average larger than the intradomain cavities, occupy a larger fraction of their resident surfaces, and are more frequently water-filled. We observe increased cavity volume at domain-domain interfaces involved with shear type domain motions. The significance of interfacial cavities upon subunit and domain shape complementarity and the protein docking problem, as well as in their structural and functional role in oligomeric proteins, will be discussed. The results concerning cavity size, polarity, solvation, general abundance, and residue type constituency should provide useful guidelines for protein modeling and design.     

Lattice models, packing density, and Boltzmann-like distribution of cavities in proteins

A model reproducing the experimental Boltzmann-like distribution of empty cavity sizes in proteins is introduced. Proteins are represented by lattices of different dimensionalities, corresponding to different numbers of nearest neighbor contacts. Small cavities emerge and join into larger ones in a random process that can be related to random mutations. Simulations of cavity creation are performed under the constraint of a limiting total packing density. Cavities sufficiently large (20 A(3) or more), that they might accommodate at least one additional methyl group produced by a mutation, are counted and compared to the distribution of cavities according to their sizes from protein statistics. The distributions calculated with this very simple model within a realistic range of packing densities are in good agreement with the empirical cavity distribution. The results suggest that the Boltzmann-like distribution of cavities in proteins might be affected by a mechanism controlled by limiting packing density and maximum allowed protein destabilization. This supports an earlier suggestion that the agreement between the free energies of cavity formation from the mutational experiments and from the statistics of the empty cavity distribution in X-ray protein structures is nonfortuitous. A possible relation of the suggested model to the Boltzmann hypothesis is discussed.     

Buried waters and internal cavities in monomeric proteins

We have analyzed the buried water molecules and internal cavities in a set of 75 high-resolution, nonhomologous, monomeric protein structures. The number of hydrogen bonds formed between each water molecule and the protein varies from 0 to 4, with 3 being most common. Nearly half of the water molecules are found in pairs or larger clusters. Approximately 90% are shown to be associated with large cavities within the protein, as determined by a novel program, PRO_ACT. The total volume of a protein's large cavities is proportional to its molecular weight and is not dependent on structural class. The largest cavities in proteins are generally elongated rather than globular. There are many more empty cavities than hydrated cavities. The likelihood of a cavity being occupied by a water molecule increases with cavity size and the number of available hydrogen bond partners, with each additional partner typically stabilizing the occupied state by 0.6 kcal/mol.     

Protein-ligand dynamics. A 96 picosecond simulation of a myoglobin-xenon complex

A 96 picosecond dynamics trajectory of myoglobin with five xenon-probe ligands in internal cavities is examined to study the effect of protein motions on ligand motion and internal cavity fluctuations. Average structural and energetic properties indicate that the simulation is well behaved. The average protein volume is similar to the volume of the X-ray model and the main-chain atom root-mean-square deviation between the X-ray model and the average dynamical structure is 1.25 A. The protein volume oscillates 3 to 4% around the volume of the X-ray structure. These fluctuations lead to changes in the internal free volume and in the size, shape and location of atom-sized cavity features. Transient cavities produced in the simulation have a crucial role in the movement of two of the ligands. One of the ligands escapes to the protein surface, whilst a second ligand travels through the protein interior. Complex gating processes involving several protein residues are responsible for producing the necessary pores through which the ligand passes between transient cavities or packing defects.     

A review about nothing: Are apolar cavities in proteins really empty?

Cavities within proteins that are strictly apolar typically appear to be empty. It has been suggested, however, that water molecules may be present within such cavities but are too disordered to be seen in conventional crystallographic analyses. In contrast, it is argued here that solvent mobility will be limited by the size of the cavity and for this reason high‐occupancy solvent in cavities of typical volume should be readily detectable using X‐ray crystallography. Recent experimental studies of cavity hydration are reviewed. Such studies are consistent with theoretical predictions that it is energetically unfavorable to have a single water molecule in an apolar cavity. As apolar cavities become larger, a point is reached where it is favorable to have the cavity occupied by a cluster of mutually H‐bonded water molecules. The exact size of such a cavity in a protein is yet to be verified.     

Molecular dynamics simulation of a synthetic four-alpha-helix bundle that binds the anesthetic halothane.

The structural features of binding sites for volatile anesthetics are examined by performing a molecular dynamics simulation study of the synthetic four-alpha-helix bundles (Aalpha2)2, which are formed by association of two 62-residue di-alpha-helical peptides. The peptide bundle (Aalpha2)2 was designed by Johansson et al. [Biochemistry 37 (1998) 1421-1429] and was shown experimentally to have a high affinity for the binding of the anesthetic halothane (CF3CBrCIH) in a hydrophobic cavity. Since (Aalpha2)2 can exhibit either the anti or syn topologies, the two distinct bundles are simulated both in the presence and in the absence of halothane. Nanosecond length molecular dynamics trajectories were generated for each system at room temperature (T = 298 K). The structural and dynamic effects of the inclusion of halothane are compared, illustrating that the structures are stable over the course of the simulation; that the (Aalpha2)2 bundles have suitable pockets that can accommodate halothane; that the halothane remains in the designed hydrophobic cavity in close proximity to the Trp residues with a preferred orientation; and that the dimensions of the peptide are perturbed by the inclusion of an anesthetic molecule.     

Topography of cyclodextrin inclusion complexes : Part I. Classification of crystallographic data of α-cyclodextrin inclusion complexes

The crystallographic and stoichiometric data obtained for 17 different inclusion complexes of α-cyclodextrin are reported. The cell dimensions and space-group symmetries reflect the packing arrangement of the torus-shaped host molecules and are largely determined by the size and ionic character of the guest molecules.In the series acetic acid, propionic acid, butyric acid, valeric acid, the first three complexes with α-cyclodextrin crystallize in a cage-type structure with space group P2₁2₁2₁, which is characteristic or small, non-ionic guest molecules. The valeric acid molecule seems to be too long to be accommodated in a cage structure; thus, the α-cyclodextrin molecules are arranged such that a structure consisting of parallel channels is formed. This packing is typical for the inclusion of long, thin, or ionic guest molecules. A third class of complexes with structures differing from the two described was also observed.A correlation exists between the type of inclusion complex and the volume required for a complex molecule: 1200–≈ 1400 ų for molecular guests, and 1400–1500 ų for ionic guests.     

Internal cavities and buried waters in globular proteins

A fast algorithm that detects internal cavities in proteins and predicts the positions of buried water molecules is described. The cavities are characterized in terms of volume, surface area, polarity, and the presence of bound waters. The algorithm is applied to 12 proteins whose structures are known to high resolution and successfully predicts the locations of over 80% of internal water molecules. Most proteins are found to have a number of internal cavities ranging in volume from 10 to 180 A3. Some of these cavities contain water and some do not, with the probability of containing a buried water increasing with cavity size. However, many large cavities are found to be empty (i.e., they do not contain a crystallographically determined water). For multidomain proteins over half of the total cavity volume is at the interdomain interface. Possible implications for the energetics of cavity formation and for the functional role of internal cavities are discussed.     

Cavities in proteins: structure of a metmyoglobin-xenon complex solved to 1.9 A

X-ray crystallographic data to 1.9-A resolution were collected on sperm whale metmyoglobin equilibrated with 7 atm of xenon gas. The results indicate four xenon sites of occupancy from 0.45 to 1.0. These sites are located in interior spaces or packing defects of the myoglobin molecule. The effects of the bound xenon on the protein structure are minor, and we observe a small overall reduction in refined isotropic atomic protein temperature factors. We interpret the results as a confirmation that, on a time-averaged basis, cavities exist within the myoglobin molecule and suggest that the binding of small ligands in these cavities affects the internal motions and conformational substrates of the protein.     

A molecular dynamics study of thermodynamic and structural aspects of the hydration of cavities in proteins.

The structure and activity of a protein molecule are strongly influenced by the extent of hydration of its cavities. This is, in turn, related to the free energy change on transfer of a water molecule from bulk solvent into a cavity. Such free energy changes have been calculated for two cavities in a sulfate-binding protein. One of these cavities contains a crystallographically observed water molecule while the other does not. Thermodynamic integration and perturbation methods were used to calculate free energies of hydration for each of the cavities from molecular dynamics simulations of two separate events: the removal of a water molecule from pure water, and the introduction of a water molecule into each protein cavity. From the simulations for the pure water system, the excess chemical potential of water was computed to be -6.4 +/- 0.4 kcal/mol, in accord with experiment and with other recent theoretical calculations. For the protein cavity containing an experimentally observed water molecule, the free energy change on hydrating it with one water molecule was calculated as -10.0 +/- 1.3 kcal/mol, indicating the high probability that this cavity is occupied by a water molecule. By contrast, for the cavity in which no water molecules were experimentally observed, the free energy change on hydrating it with one water molecule was calculated as 0.2 +/- 1.5 kcal/mol, indicating its low occupancy by water. The agreement of these results with experiment suggests that thermodynamic simulation methods may become useful for the prediction and analysis of internal hydration in proteins.     

The structure of human microsomal cytochrome P450 3A4 determined by X-ray crystallography to 2.05-A resolution

The structure of P450 3A4 was determined by x-ray crystallography to 2.05-A resolution. P450 3A4 catalyzes the metabolic clearance of a large number of clinically used drugs, and a number of adverse drug-drug interactions reflect the inhibition or induction of the enzyme. P450 3A4 exhibits a relatively large substrate-binding cavity that is consistent with its capacity to oxidize bulky substrates such as cyclosporin, statins, taxanes, and macrolide antibiotics. Family 3A P450s also exhibit unusual kinetic characteristics that suggest simultaneous occupancy by smaller substrates. Although the active site volume is similar to that of P450 2C8 (PDB code: 1PQ2), the shape of the active site cavity differs considerably due to differences in the folding and packing of portions of the protein that form the cavity. Compared with P450 2C8, the active site cavity of 3A4 is much larger near the heme iron. The lower constraints on the motions of small substrates near the site of oxygen activation may diminish the efficiency of substrate oxidation, which may, in turn, be improved by space restrictions imposed by the presence of a second substrate molecule. The structure of P450 3A4 should facilitate a better understanding of the substrate selectivity of the enzyme.     

Studies in werner clathrates. Part 3. Structures of bis(isothiocyanato)tetra(4-vinylpyridine)nickel(lI) and its clathrates with ortho-, meta- and para-xylenes

The crystal structures of the α-phase Ni(NCS)₂-(4ViPy)₄ (I) Werner complex and of its β-phase clathrates with p-xylene (II), m-xylene (III), and o-xylene (IV) have been elucidated. The Ni(NCS)₂-(4ViPy)₄ molecules in all four structures have octahedral coordination and 'propeller' conformation. The shape of a typical channel in a β-phase structure is portrayed by potential energy calculations. The potential energy of each xylene in its respective cavity is calculated. A comparison of packing efficiencies in all four structures is discussed. Results of packing modes and energy calculations both imply that matching the symmetry of the cavity in the β-phase with a prospective guest is favoured.     

Crystal structure of the cyclomaltohexaose (alpha-cyclodextrin) complex with isosorbide dinitrate. Guest-modulated channel-type structure

The crystal structure of the 2:1 complex of cyclomaltohexaose (alpha-cyclodextrin, alpha-CD) with isosorbide dinitrate was determined by single-crystal X-ray analysis. In the crystal with the space group C2, two cyclomaltohexaose molecules form a head-to-head dimer with the secondary hydroxy-group sides facing each other. The dimer unit is stacked along the crystallographic c-axis to form a channel-type structure. The isosorbide dinitrate molecule is encapsulated in the cylindrical cavity of the cyclomaltohexaose dimer. The dimeric structure exhibits pseudo twofold symmetry, and the guest molecule is disordered on the local symmetry axis. The isosorbide moiety is located at the center of the dimer cavity, and the nitrate groups penetrate into the cyclomaltohexaose rings. The guest molecule modulates the dimer structure to attain the most stable accommodation into the cavity. The cyclomaltohexaose molecules are laterally shifted away from each other to create the cavity fitted to the shape of the guest molecule. As the result, the intermolecular hydrogen bonds between secondary hydroxy-groups are not fully formed, but the dimeric structure is stabilized by the interaction with the guest molecule.     

Thermodynamics of water mediating protein-ligand interactions in cytochrome P450cam: a molecular dynamics study.

Ordered water molecules are observed by crystallography and nuclear magnetic resonance to mediate protein-ligand interactions. Here, we examine the energetics of hydrating cavities formed at protein-ligand interfaces using molecular dynamics simulations. The free energies of hydrating two cavities in the active site of two liganded complexes of cytochrome P450cam were calculated by multiconfigurational thermodynamic integration. The complex of cytochrome P450cam with 2-phenyl-imidazole contains a crystallographically well defined water molecule mediating hydrogen bonds between the protein and the inhibitor. We calculate that this water molecule is stabilized by a binding free energy of -11.6 +/- kJ/mol. The complex of cytochrome P450cam with its natural substrate, camphor, contains a cavity that is empty in the crystal structure although a water molecule in it could make a hydrogen bond to camphor. Here, solvation of this cavity is calculated to be unfavorable by +15.8 +/- 5.0 kJ/mol. The molecular dynamics simulations can thus distinguish a hydrated interfacial cavity from an empty one. They also provide support for the notion that protein-ligand complexes can accommodate empty interfacial cavities and that such cavities are likely to be unhydrated unless more than one hydrogen bond can be made to a water molecule in the cavity.     

The crystal structure of the 1:1 inclusion complex of beta-cyclodextrin with squaric acid.

The crystal and molecular structure of the 1:1 inclusion complex of beta-cyclodextrin (cyclomaltoheptaose) with squaric acid (3,4-dihydroxycyclobutene-1,2-dione) was determined by X-ray diffraction. The complex crystallizes in the monoclinic P2(1) space group and belongs to the monomeric cage-type, characterized by a herringbone-like packing motif. Co-crystallized water molecules are present on seven sites, of which six are fully occupied. The guest molecule is placed inside the beta-cyclodextrin cavity, perpendicular to the plane defined by the glycosidic O-4n atoms, and held in place by direct and water-mediated hydrogen bonds mainly involving symmetry-related beta-cyclodextrin molecules. The accommodation of the planar guest molecule into the beta-cyclodextrin cavity determines a significant distortion of the latter from the sevenfold symmetry.     

Standard atomic volumes in double-stranded DNA and packing in protein--DNA interfaces

Standard volumes for atoms in double-stranded B-DNA are derived using high resolution crystal structures from the Nucleic Acid Database (NDB) and compared with corresponding values derived from crystal structures of small organic compounds in the Cambridge Structural Database (CSD). Two different methods are used to compute these volumes: the classical Voronoi method, which does not depend on the size of atoms, and the related Radical Planes method which does. Results show that atomic groups buried in the interior of double-stranded DNA are, on average, more tightly packed than in related small molecules in the CSD. The packing efficiency of DNA atoms at the interfaces of 25 high resolution protein-DNA complexes is determined by computing the ratios between the volumes of interfacial DNA atoms and the corresponding standard volumes. These ratios are found to be close to unity, indicating that the DNA atoms at protein-DNA interfaces are as closely packed as in crystals of B-DNA. Analogous volume ratios, computed for buried protein atoms, are also near unity, confirming our earlier conclusions that the packing efficiency of these atoms is similar to that in the protein interior. In addition, we examine the number, volume and solvent occupation of cavities located at the protein-DNA interfaces and compared them with those in the protein interior. Cavities are found to be ubiquitous in the interfaces as well as inside the protein moieties. The frequency of solvent occupation of cavities is however higher in the interfaces, indicating that those are more hydrated than protein interiors. Lastly, we compare our results with those obtained using two different measures of shape complementarity of the analysed interfaces, and find that the correlation between our volume ratios and these measures, as well as between the measures themselves, is weak. Our results indicate that a tightly packed environment made up of DNA, protein and solvent atoms plays a significant role in protein-DNA recognition.     

Monte Carlo study of sI hydrogen hydrates

In this study, we perform grand canonical Monte Carlo simulations to evaluate the hydrogen storage capacity of structure I (sI) hydrogen hydrates at pressures up to 500 MPa. Initially, we calculate the upper limit of H₂ content of sI hydrates by studying the hypothetical sI hydrate, where H₂ is the single guest component. It is found that the storage capacity of the hypothetical pure H₂ sI hydrate could reach 3.5 wt% at 500 MPa and 274 K. Depending on pressure, the large cavities of the pure H₂ hydrate can accommodate up to three H₂ molecules while the small ones are singly occupied at most, even at pressures as high as 500 MPa, without any double occupancy being observed. Subsequently, the binary H₂–ethylene oxide (EO) hydrate is examined. In this case, the large cavities are occupied by a single EO molecule while the small cavities can accommodate at most a single H₂ molecule. Such configuration results in a maximum H₂ content of only 0.37 wt%. The hydrogen storage capacity does not improve significantly even in case when EO is replaced by a component with smaller molecular weight.     

Structure of the complex of beta-cyclodextrin with beta-naphthyloxyacetic acid in the solid state and in aqueous solution

The structure of the complex of beta-cyclodextrin (cyclomaltoheptaose) with beta-naphthyloxyacetic acid was studied in solid state by X-ray diffraction and in aqueous solution by 1H NMR spectroscopy. The complex crystallizes in the channel mode, space group C2, with a stoichiometry of 2:1; two beta-cyclodextrin molecules related by a twofold crystal axis form dimers, in the cavity of which one guest molecule is found on average. The above stoichiometry indicates one guest per beta-CD dimer statistically oriented over two positions or two guest molecules in pi-pi interactions in half of the beta-CD dimers and the rest of the beta-CD dimers empty. In addition, occupancy of 0.5 for the guest per every beta-CD dimer is in accord with the occupancy of the two disordered primary hydroxyls. These two hydroxyl groups, to which the carboxylic oxygen atoms of the guest are hydrogen bonded, point towards the interior of the beta-CD cavity. In aqueous solution, the 1H NMR spectroscopic study indicated that there is a mixture of complexes with host-guest stoichiometries both 1:1 and 2:1.     

A procedure for detection and quantitation of cavity volumes proteins. Application to measure the strength of the hydrophobic driving force in protein folding

Accurate identification of cavities is important in the study of protein structure, stability, design, and ligand binding. Identification and quantitation of cavities is a nontrivial problem because most cavities are connected to the protein exterior. We describe a computational procedure for quantitating cavity volumes and apply this to derive an estimate of the hydrophobic driving force in protein folding. A grid-based Monte Carlo procedure is used to position water molecules on the surface of a protein. A Voronoi procedure is used to identify and quantitate empty space within the solvated protein. Additional cavities not detected by other existing procedures can be identified. Most of these are close to surface concavities. Residue volumes for both the interior and the surface residues as well as cavity volumes are in good agreement with volumes calculated from fully hydrated protein structures obtained from molecular dynamic simulations. We show that the loss of stability because of cavity-creating mutations correlates better with cavity volumes determined by this procedure than with cavity volumes determined by other methods. Available structural and thermodynamic data for a number of cavity-containing mutants were analyzed to obtain estimates of 26.1 cal x mol(-1) x A(-3) and 18.5 cal x mol(-1) x A(-2) for the relative contributions of cavity formation and the hydrophobic effect to the observed stability changes. The present estimate for the hydrophobic driving force is at the lower end of estimates derived from model compound studies and considerably lower than previous estimates of approximately 50 cal x mol(-1) x A(-2) derived from protein mutational data. In the absence of structural rearrangement, on average, deletion of a single methylene group is expected to result in losses in stability of 0.41 and 0.70 kcal x mol(-1) resulting from decrease in hydrophobicity and packing, respectively.