A new perspective on analysis of helix-helix packing preferences in globular proteins

For many years, statistical analysis of protein databanks has led to the belief that the steric compatibility of helix interfaces may be the source of observed preferences for particular angles between neighboring helices. Several elegant models describing how side chains on helices can interdigitate without steric clashes were able to account quite reasonably for the observed distributions. However, it was later recognized that the 'bare' measured angle distribution should be corrected to avoid statistical bias.12 Disappointingly, the rescaled distributions dramatically lost their similarity with theoretical predictions, casting doubts on the validity of the geometrical assumptions and models. In this article, we elucidate a few points concerning the proper choice of a random reference distribution. In particular we demonstrate the need for corrections induced by unavoidable uncertainties in determining whether two helices are in face-to-face contact or not and their relative orientations. By using this new rescaling, we show that 'true' packing angle preferences are well described by regular packing models, thus proving that preferential angles between contacting helices do exist.     

Residue packing in globular and intrinsically disordered proteins

Intrinsically disordered proteins (IDPs)/regions do not have well‐defined secondary and tertiary structures, however, they are functional and it is critical to gain a deep understanding of their residue packing. The shape distributions methodology, which is usually utilized in pattern recognition, clustering, and classification studies in computer science, may be adopted to study the residue packing of the proteins. In this study, shape distributions of the globular proteins and IDPs were obtained to shed light on the residue packing of their structures. The shape feature that was used is the sphericity of tetrahedra obtained by Delaunay Tessellation of points of Cα coordinates. Then the sphericity probability distributions were compared by using Principal Component Analysis. This computational structural study shows that the set of IDPs constitute a more diverse set than the set of globular proteins in terms of the geometrical properties of their network structures.     

Side-chain entropy and packing in proteins.

What role does side-chain packing play in protein stability and structure? To address this question, we compare a lattice model with side chains (SCM) to a linear lattice model without side chains (LCM). Self-avoiding configurations are enumerated in 2 and 3 dimensions exhaustively for short chains and by Monte Carlo sampling for chains up to 50 main-chain monomers long. This comparison shows that (1) side-chain degrees of freedom increase the entropy of open conformations, but side-chain steric exclusion decreases the entropy of compact conformations, thus producing a substantial entropy that opposes folding; (2) there is a side-chain “freezing” or ordering, i.e., a sharp decrease in entropy, near maximum compactness; and (3) the different types of contacts among side chains (s) and main-chain elements (m) have different frequencies, and the frequencies have different dependencies on compactness. mm contacts contribute significantly only at high densities, suggesting that main-chain hydrogen bonding in proteins may be promoted by compactness. The distributions of mm, ms, and ss contacts in compact SCM configurations are similar to the distributions in protein structures in the Brookhaven Protein Data Bank. We propose that packing in proteins is more like the packing of nuts and bolts in a jar than like the pairwise matching of jigsaw puzzle pieces.     

Disulfide bonds and the stability of globular proteins.

An understanding of the forces that contribute to stability is pivotal in solving the protein-folding problem. Classical theory suggests that disulfide bonds stabilize proteins by reducing the entropy of the denatured state. More recent theories have attempted to expand this idea, suggesting that in addition to configurational entropic effects, enthalpic and native-state effects occur and cannot be neglected. Experimental thermodynamic evidence is examined from two sources: (1) the disruption of naturally occurring disulfides, and (2) the insertion of novel disulfides. The data confirm that enthalpic and native-state effects are often significant. The experimental changes in free energy are compared to those predicted by different theories. The differences between theory and experiment are large near 300 K and do not lend support to any of the current theories regarding the stabilization of proteins by disulfide bonds. This observation is a result of not only deficiencies in the theoretical models but also from difficulties in determining the effects of disulfide bonds on protein stability against the backdrop of numerous subtle stabilizing factors (in both the native and denatured states), which they may also affect.     

Thermodynamics of the temperature-induced unfolding of globular proteins.

The heat capacity, enthalpy, entropy, and Gibbs energy changes for the temperature-induced unfolding of 11 globular proteins of known three-dimensional structure have been obtained by microcalorimetric measurements. Their experimental values are compared to those we calculate from the change in solvent-accessible surface area between the native proteins and the extended polypeptide chain. We use proportionality coefficients for the transfer (hydration) of aliphatic, aromatic, and polar groups from gas phase to aqueous solution, we estimate vibrational effects, and we discuss the temperature dependence of each constituent of the thermodynamic functions. At 25 degrees C, stabilization of the native state of a globular protein is largely due to two favorable terms: the entropy of non-polar group hydration and the enthalpy of interactions within the protein. They compensate the unfavorable entropy change associated with these interactions (conformational entropy) and with vibrational effects. Due to the large heat capacity of nonpolar group hydration, its stabilizing contribution decreases quickly at higher temperatures, and the two unfavorable entropy terms take over, leading to temperature-induced unfolding.     

Understanding the determinants of stability and folding of small globular proteins from their energetics

The results of minimal model calculations indicate that the stability and the kinetic accessibility of the native state of small globular proteins are controlled by few "hot" sites. By means of molecular dynamics simulations around the native conformation, which describe the protein and the surrounding solvent at the all-atom level, an accurate and compact energetic map of the native state of the protein is generated. This map is further simplified by means of an eigenvalue decomposition. The components of the eigenvector associated with the lowest eigenvalue indicate which hot sites are likely to be responsible for the stability and for the rapid folding of the protein. The comparison of the results of the model with the findings of mutagenesis experiments performed for four small proteins show that the eigenvalue decomposition method is able to identify between 60% and 80% of these (hot) sites.     

A large scale test of computational protein design: folding and stability of nine completely redesigned globular proteins

A previously developed computer program for protein design, RosettaDesign, was used to predict low free energy sequences for nine naturally occurring protein backbones. RosettaDesign had no knowledge of the naturally occurring sequences and on average 65% of the residues in the designed sequences differ from wild-type. Synthetic genes for ten completely redesigned proteins were generated, and the proteins were expressed, purified, and then characterized using circular dichroism, chemical and temperature denaturation and NMR experiments. Although high-resolution structures have not yet been determined, eight of these proteins appear to be folded and their circular dichroism spectra are similar to those of their wild-type counterparts. Six of the proteins have stabilities equal to or up to 7kcal/mol greater than their wild-type counterparts, and four of the proteins have NMR spectra consistent with a well-packed, rigid structure. These encouraging results indicate that the computational protein design methods can, with significant reliability, identify amino acid sequences compatible with a target protein backbone.     

Ideal architecture of residue packing and its observation in protein structures.

A simple model of sphere packing has been investigated as an ideal model for long-range interactions for the packing of non-bonded residues in protein structures. By superposing all residues, the geometry of packing around a central residue is investigated. It is found that all residues conform almost perfectly to this lattice model for sphere packing when a radius of 6.5 A is used to define non-bonded (virtual) interacting residues. Side-chain positions with respect to sequential backbone segments are relatively regular as well. This lattice can readily be used in conformation simulations to reduce the conformational space.     

Thermodynamics of globular proteins

The analysis of temperature-induced unfolding of proteins in aqueous solutions was performed. Based on the data of thermodynamic parameters of protein unfolding and using the method of semi-empirical calculations of hydration parameters at reference temperature 298 K, we obtained numerical values of enthalpy, free energy, and entropy which characterize the unfolding of proteins in the ‘gas phase’. It was shown that specific values of the energy of weak intramolecular bonds (?H^int), conformational free energy (?G^conf) and entropy (?S^conf) are the same for proteins with molecular weight 7–25 kDa. Using the energy value (?H^int) and the proposed approach for estimation of the conformational entropy of native protein (S^NC), numerical values of the absolute free energy (G^NC) were obtained.     

Structural principles of alpha/beta barrel proteins: the packing of the interior of the sheet

Alpha/beta barrel structures very similar to that first observed in triose phosphate isomerase are now known to occur in 14 enzymes. To understand the origin of this fold, we analyzed in three of these proteins the geometry of the eight-stranded beta-sheets and the packing of the residues at the center of the barrel. The packing in this region is seen in its simplest form in glycolate oxidase. It consists of 12 residues arranged in three layers. Each layer contains four side chains. The packing of RubisCO and TIM can be understood in terms of distortions of this simple pattern, caused by residues with small side chains at some of the positions inside the barrel. Two classes of packing are found. In one class, to which RubisCO and TIM belong, the central layer is formed by a residue from the first, third, fifth, and seventh strands; the upper and lower layers are formed by residues from the second, fourth, sixth, and eighth strands. In the second class, to which GAO belongs, this is reversed: it is side chains from the even-numbered strands that form the central layer, and side chains from the odd-numbered strands that form the outer layers. Our results suggest that not all proteins with this fold are related by evolution, but that they represent a common favorable solution to the structural problems involved in the creation of a closed beta barrel.     

Dynamic polyhedral models of globular proteins

We have devised several mechanical models of globular proteins by approximating them to various polyhedra (dodecahedron, truncated octahedron, icosahedron, truncated icosahedron). The models comprise hollow blocks linked together in a flexible chain. Between blocks there is a set of several reversible, weak magnetic interactions such that when the chain is agitated, it will fold into a stable polyhedral structure about the size of a hand. Folding may be followed in real time with a video camera. Key to the success of the folding process is the lightness of the chain. Several side chains may also be added to the blocks such that they come together to create a polyhedral core when the chain folds. The models have a number of similarities to globular proteins: each chain folds into a unique, but dynamic, three-dimensional structure; the instructions that determine this structure are built into the configuration of blocks; and it is difficult to predict this structure given the unfolded block configuration. Furthermore, the chains fold quickly, generally in less than a minute, several pathways are involved, and these pathways progress through elements of "native" structure. In particular, the models emphasize the importance of restricted conformational mobility in assisting the chain to fold, and also in eliminating undesirable interactions. Because of these similarities to globular proteins, we believe that the polyhedral models will, with continued development, be helpful in understanding the protein folding process, while at the same time acting as valuable educational visual aids. They might also inspire the construction of new types of microscopic, self-assembling devices.     

Characterization of dry globular proteins and protein fibrils by synchrotron radiation vacuum UV circular dichroism

Circular dichroism using synchrotron radiation (SRCD) can extend the spectral range down to approximately 130 nm for dry proteins, potentially providing new structural information. Using a selection of dried model proteins, including alpha-helical, beta-sheet, and mixed-structure proteins, we observe a low-wavelength band in the range 130-160 nm, whose intensity and peak position is sensitive to the secondary structure of the protein and may also reflect changes in super-secondary structure. This band has previously been observed for peptides but not for globular proteins, and is compatible with previously published theoretical calculations related to pi-orbital transitions. We also show that drying does not lead to large changes in the secondary structure and does not induce orientational artifacts. In combination with principal component analysis, our SRCD data allow us to distinguish between two different types of protein fibrils, highlighting that bona fide fibrils formed by lysozyme are structurally more similar to the nonclassical fibrillar aggregates formed by the SerADan peptide than with the amyloid formed by alpha-synuclein. Thus, despite the lack of direct structural conclusions, a comprehensive SRCD-based database of dried protein spectra may provide a useful method to differentiate between various types of supersecondary structure and aggregated protein species.     

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.     

The molecular stoichiometric hydration model (SHM) as applied to tendon/collagen, globular proteins and cells

This report describes and documents the presence of multiple water-of-hydration fractions on proteins and in cells. Initial studies of hydration fractions in g of water/g of DM (dry mass) for tendon/collagen led to the development of the molecular SHM (stoichiometric hydration model) and the development of methods for calculating the size of hydration fractions on a number of different proteins of known amino acid composition. The water fractions have differences in molecular motion and other physical properties due to electrostatic interactions of polar water molecules with electric fields generated by covalently bound pairs of opposite partial charge on the protein backbone. The methods allow calculation of the size of four hydration fractions: single water bridges, double water bridges, dielectric water clusters over polar-hydrophilic surfaces and water clusters over hydrophobic surfaces. These four fractions provide monolayer water coverage. The predicted SHM hydration fractions match closely measured hydration fraction values for collagen and for globular proteins. This report also presents water sorption findings that support the SHM. The SHM is applicable for cell systems where it has been studied. In seven cell systems studied, more than half of all of the cell water had properties unlike those of bulk water. The SHM predicts and explains the commonly cited and measured bound water fraction of 0.2-0.4 g of water/g of DM on proteins. The commonly accepted concept that water beyond this bound water fraction can be considered bulk-like water in its physical properties is unwarranted.     

Novel approach for alpha-helical topology prediction in globular proteins: generation of interhelical restraints

The protein folding problem represents one of the most challenging problems in computational biology. Distance constraints and topology predictions can be highly useful for the folding problem in reducing the conformational space that must be searched by deterministic algorithms to find a protein structure of minimum conformational energy. We present a novel optimization framework for predicting topological contacts and generating interhelical distance restraints between hydrophobic residues in alpha-helical globular proteins. It should be emphasized that since the model does not make assumptions about the form of the helices, it is applicable to all alpha-helical proteins, including helices with kinks and irregular helices. This model aims at enhancing the ASTRO-FOLD protein folding approach of Klepeis and Floudas (Journal of Computational Chemistry 2003;24:191-208), which finds the structure of global minimum conformational energy via a constrained nonlinear optimization problem. The proposed topology prediction model was evaluated on 26 alpha-helical proteins ranging from 2 to 8 helices and 35 to 159 residues, and the best identified average interhelical distances corresponding to the predicted contacts fell below 11 A in all 26 of these systems. Given the positive results of applying the model to several protein systems, the importance of interhelical hydrophobic-to-hydrophobic contacts in determining the folding of alpha-helical globular proteins is highlighted.     

Analysis of anisotropic side-chain packing in proteins and application to high-resolution structure prediction

pi-pi, Cation-pi, and hydrophobic packing interactions contribute specificity to protein folding and stability to the native state. As a step towards developing improved models of these interactions in proteins, we compare the side-chain packing arrangements in native proteins to those found in compact decoys produced by the Rosetta de novo structure prediction method. We find enrichments in the native distributions for T-shaped and parallel offset arrangements of aromatic residue pairs, in parallel stacked arrangements of cation-aromatic pairs, in parallel stacked pairs involving proline residues, and in parallel offset arrangements for aliphatic residue pairs. We then investigate the extent to which the distinctive features of native packing can be explained using Lennard-Jones and electrostatics models. Finally, we derive orientation-dependent pi-pi, cation-pi and hydrophobic interaction potentials based on the differences between the native and compact decoy distributions and investigate their efficacy for high-resolution protein structure prediction. Surprisingly, the orientation-dependent potential derived from the packing arrangements of aliphatic side-chain pairs distinguishes the native structure from compact decoys better than the orientation-dependent potentials describing pi-pi and cation-pi interactions.     

Solvation energetics and conformational change in EF-hand proteins

Calmodulin and other members of the EF-hand protein family are known to undergo major changes in conformation upon binding Ca(2+). However, some EF-hand proteins, such as calbindin D9k, bind Ca(2+) without a significant change in conformation. Here, we show the importance of a precise balance of solvation energetics to conformational change, using mutational analysis of partially buried polar groups in the N-terminal domain of calmodulin (N-cam). Several variants were characterized using fluorescence, circular dichroism, and NMR spectroscopy. Strikingly, the replacement of polar side chains glutamine and lysine at positions 41 and 75 with nonpolar side chains leads to dramatic enhancement of the stability of the Ca(2+)-free state, a corresponding decrease in Ca(2+)-binding affinity, and an apparent loss of ability to change conformation to the open form. The results suggest a paradigm for conformational change in which energetic strain is accumulated in one state in order to modulate the energetics of change to the alternative state.     

The energetics of specific binding of AT-hooks from HMGA1 to target DNA

The interaction of the second and third AT-hooks of HMGA1 (formerly HMGI/Y), which bind selectively in the minor groove of an AT-rich DNA sequence, was studied at different temperatures and ionic strengths by spectropolarimetry, spectrofluorimetry, isothermal titration calorimetry and differential scanning calorimetry. The data show that binding of the ten amino acid core element of the two AT-hooks, which penetrates deep into the minor groove, is entropically driven: both the entropy and enthalpy of association of the peptides to the target DNA are positive up to 50 degrees C. The seven amino acid extension of the core in the second AT-hook, which extends out from the minor groove and loops over the phosphodiester backbone, adds a substantial negative enthalpic component into the binding of the 17 residue DBD2 peptide to DNA that corresponds in magnitude to the enthalpy of formation of two hydrogen bonds. The ionic strength dependence of the association constant allowed an estimation of the electrostatic component of binding and, by subtraction, the contribution of the non-electrostatic component, which results from dehydration of the contacting surfaces and makes up almost 70% of the total energy of complex formation. The exceptionally large positive entropy and enthalpy of association of the core AT-hook peptides with target DNA suggest that the water, which is removed from the minor groove of DNA upon binding, is in a highly ordered state. Acetylation of the lysine residue in the second AT-hook, which corresponds to Lys65 of HMGA1, has little effect on the DNA binding; so it appears that repression of the hIFNbeta gene, which follows this modification, is not a direct result of the abrogation of DNA binding.