Calculation of binding free energies for non-zinc chelating pyrimidine dicarboxamide inhibitors with MMP-13

All-atom molecular dynamics (MD) simulations in both explicit and implicit solvent, followed by MM-GBSA energy analysis, have been used to estimate binding free energies of four pyrimidine dicarboxamide inhibitors with human collagenase-3 (MMP-13) for comparison with experimental activities. Energetic analysis reveals that affinity is driven primarily by favorable van der Waals interactions and burial of total surface area. The computed effects of desolvation, as a function of ligand structure, quantitatively show that hydrophilic derivatives pay greater penalties upon binding than their related more hydrophobic analogs.     

Computing van der Waals energies in the context of the rotamer approximation

The rotamer approximation states that protein side-chain conformations can be described well using a finite set of rotational isomers. This approximation is often applied in the context of computational protein design and structure prediction to reduce the complexity of structural sampling. It is an effective way of reducing the structure space to the most relevant conformations. However, the appropriateness of rotamers for sampling structure space does not imply that a rotamer-based energy landscape preserves any of the properties of the true continuous energy landscape. Specifically, because the energy of a van der Waals interaction can be very sensitive to small changes in atomic separation, meaningful van der Waals energies are particularly difficult to calculate from rotamer-based structures. This presents a problem for computational protein design, where the total energy of a given structure is often represented as a sum of precalculated rigid rotamer self and pair contributions. A common way of addressing this issue is to modify the van der Waals function to reduce its sensitivity to atomic position, but excessive modification may result in a strongly nonphysical potential. Although many different van der Waals modifications have been used in protein design, little is known about which performs best, and why. In this paper, we study 10 ways of computing van der Waals energies under the rotamer approximation, representing four general classes, and compare their performance using a variety of metrics relevant to protein design and native-sequence repacking calculations. Scaling van der Waals radii by anywhere from 85 to 95% gives the best performance. Linearizing and capping the repulsive portion of the potential can give additional improvement, which comes primarily from getting rid of unrealistically large clash energies. On the other hand, continuously minimizing individual rotamer pairs prior to evaluating their interaction works acceptably in native-sequence repacking, but fails in protein design. Additionally, we show that the problem of predicting relevant van der Waals energies from rotamer-based structures is strongly nonpairwise decomposable and hence further modifications of the potential are unlikely to give significant improvement.     

Understanding beta-hairpin formation by molecular dynamics simulations of unfolding

We have studied the mechanism of formation of a 16-residue beta-hairpin from the protein GB1 using molecular dynamics simulations in an aqueous environment. The analysis of unfolding trajectories at high temperatures suggests a refolding pathway consisting of several transient intermediates. The changes in the interaction energies of residues are related with the structural changes during the unfolding of the hairpin. The electrostatic energies of the residues in the turn region are found to be responsible for the transition between the folded state and the hydrophobic core state. The van der Waals interaction energies of the residues in the hydrophobic core reflect the behavior of the radius of gyration of the core region. We have examined the opposing influences of the protein-protein (PP) energy, which favors the native state, and the protein-solvent (PS) energy, which favors unfolding, in the formation of the beta-hairpin structure. It is found that the behavior of the electrostatic components of PP and PS energies reflects the structural changes associated with the loss of backbone hydrogen bonding. Relative changes in the PP and PS van der Waals interactions are related with the disruption of the hydrophobic core of a protein. The results of the simulations support the hydrophobic collapse mechanism of beta-hairpin folding.     

Role of non-covalent interactions for determining the folding rate of two-state proteins

Understanding the factors influencing the folding rate of proteins is a challenging problem. In this work, we have analyzed the role of non-covalent interactions for the folding rate of two-state proteins by free-energy approach. We have computed the free-energy terms, hydrophobic, electrostatic, hydrogen-bonding and van der Waals free energies. The hydrophobic free energy has been divided into the contributions from different atoms, carbon, neutral nitrogen and oxygen, charged nitrogen and oxygen, and sulfur. All the free-energy terms have been related with the folding rates of 28 two-state proteins with single and multiple correlation coefficients. We found that the hydrophobic free energy due to carbon atoms and hydrogen-bonding free energy play important roles to determine the folding rate in combination with other free energies. The normalized energies with total number of residues showed better results than the total energy of the protein. The comparison of amino acid properties with free-energy terms indicates that the energetic terms explain better the folding rate than amino acid properties. Further, the combination of free energies with topological parameters yielded the correlation of 0.91. The present study demonstrates the importance of topology for determining the folding rate of two-state proteins.     

Energetic analysis of binding of progesterone and 5 beta-androstane-3,17-dione to anti-progesterone antibody DB3 using molecular dynamics and free energy calculations.

Molecular dynamics simulations and molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) free energy calculations were used to study the energetics of the binding of progesterone (PRG) and 5 beta-androstane-3,17-dione (5AD) to anti-PRG antibody DB3. Although the two steroids bind to DB3 in different orientations, their binding affinities are of the same magnitude, 1 nM for PRG and 8 nM for 5AD. The calculated relative binding free energy of the steroids, 8.8 kJ/mol, is in fair agreement with the experimental energy, 5.4 kJ/mol. In addition, computational alanine scanning was applied to study the role of selected amino acid residues of the ligand-binding site on the steroid cross-reactivity. The electrostatic and van der Waals components of the total binding free energies were found to favour more the binding of PRG, whereas solvation energies were more favourable for the binding of 5AD. The differences in the free energy components are due to the binding of the A rings of the steroids to different binding pockets: PRG is bound to a pocket in which electrostatic antibody-steroid interactions are dominating, whereas 5AD is bound to a pocket in which van der Waals and hydrophobic interactions dominate.     

Adhesive and conformational behaviour of mycolic acid monolayers

We have studied the pH-dependent interaction between mycolic acid (MA) monolayers and hydrophobic and hydrophilic surfaces using molecular (colloidal probe) force spectroscopy. In both cases, hydrophobic and hydrophilic monolayers (prepared by Langmuir-Blodgett and Langmuir-Schaefer deposition on silicon or hydrophobized silicon substrates, respectively) were studied. The force spectroscopy data, fitted with classical DLVO (Derjaguin, Landau, Verwey, and Overbeek) theory to examine the contribution of electrostatic and van der Waals forces, revealed that electrostatic forces are the dominant contribution to the repulsive force between the approaching colloidal probe and MA monolayers. The good agreement between data and the DLVO model suggest that beyond a few nm away from the surface, hydrophobic, hydration, and specific chemical bonding are unlikely to contribute to any significant extent to the interaction energy between the probe and the surface. The pH-dependent conformation of MA molecules in the monolayer at the solid-liquid interface was studied by ellipsometry, neutron reflectometry, and with a quartz crystal microbalance. Monolayers prepared by the Langmuir-Blodgett method demonstrated a distinct pH-responsive behaviour, while monolayers prepared by the Langmuir-Schaefer method were less sensitive to pH variation. It was found that the attachment of water molecules plays a vital role in determining the conformation of the MA monolayers.     

Regulation of channel function due to physical energetic coupling with a lipid bilayer

Regulation of membrane protein functions due to hydrophobic coupling with a lipid bilayer has been investigated. An energy formula describing interactions between lipid bilayer and integral ion channels with different structures, which is based on the screened Coulomb interaction approximation, has been developed. Here the interaction energy is represented as being due to charge-based interactions between channel and lipid bilayer. The hydrophobic bilayer thickness channel length mismatch is found to induce channel destabilization exponentially while negative lipid curvature linearly. Experimental parameters related to channel dynamics are consistent with theoretical predictions. To measure comparable energy parameters directly in the system and to elucidate the mechanism at an atomistic level we performed molecular dynamics (MD) simulations of the ion channel forming peptide–lipid complexes. MD simulations indicate that peptides and lipids experience electrostatic and van der Waals interactions for short period of time when found within each other’s proximity. The energies from these two interactions are found to be similar to the energies derived theoretically using the screened Coulomb and the van der Waals interactions between peptides (in ion channel) and lipids (in lipid bilayer) due to mainly their charge properties. The results of in silico MD studies taken together with experimental observable parameters and theoretical energetic predictions suggest that the peptides induce ion channels inside lipid membranes due to peptide–lipid physical interactions. This study provides a new insight helping better understand of the underlying mechanisms of membrane protein functions in cell membrane leading to important biological implications.     

De novo protein design. I. In search of stability and specificity.

We have developed a fully automated protein design strategy that works on the entire sequence of the protein and uses a full atom representation. At each step of the procedure, an all-atom model of the protein is built using the template protein structure and the current designed sequence. The energy of the model is used to drive a Monte Carlo optimization in sequence space: random moves are either accepted or rejected based on the Metropolis criterion. We rely on the physical forces that stabilize native protein structures to choose the optimum sequence. Our energy function includes van der Waals interactions, electrostatics and an environment free energy. Successful protein design should be specific and generate a sequence compatible with the template fold and incompatible with competing folds. We impose specificity by maintaining the amino acid composition constant, based on the random energy model. The specificity of the optimized sequence is tested by fold recognition techniques. Successful sequence designs for the B1 domain of protein G, for the lambda repressor and for sperm whale myoglobin are presented. We show that each additional term of the energy function improves the performance of our design procedure: the van der Waals term ensures correct packing, the electrostatics term increases the specificity for the correct native fold, and the environment solvation term ensures a correct pattern of buried hydrophobic and exposed hydrophilic residues. For the globin family, we show that we can design a protein sequence that is stable in the myoglobin fold, yet incompatible with the very similar hemoglobin fold.     

Protein docking using continuum electrostatics and geometric fit

The computer program DOT quickly finds low-energy docked structures for two proteins by performing a systematic search over six degrees of freedom. A novel feature of DOT is its energy function, which is the sum of both a Poisson-Boltzmann electrostatic energy and a van der Waals energy, each represented as a grid-based correlation function. DOT evaluates the energy of interaction for many orientations of the moving molecule and maintains separate lists scored by either the electrostatic energy, the van der Waals energy or the composite sum of both. The free energy is obtained by summing the Boltzmann factor over all rotations at each grid point. Three important findings are presented. First, for a wide variety of protein-protein interactions, the composite-energy function is shown to produce larger clusters of correct answers than found by scoring with either van der Waals energy (geometric fit) or electrostatic energy alone. Second, free-energy clusters are demonstrated to be indicators of binding sites. Third, the contributions of electrostatic and attractive van der Waals energies to the total energy term appropriately reflect the nature of the various types of protein-protein interactions studied.     

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

A network cell with molecular agents that divides from centrosome signals

A novel model of network artificial chemistry (NAC) in which molecular agents with assembler programs move through the network is presented. By the execution of the agent programs, nodes rewire edges according to their own types (either hydrophilic or hydrophobic), and as a consequence, a global topological structure is created in the network. Using numerical experiments equipped with three agent types (centrosome, hydrogen, and van der Waals), it is demonstrated that the revised NAC is able to emulate the organization of a pseudo-lattice structure between hydrophilic nodes, repulsion between hydrophilic and hydrophobic nodes, and the division of a network cell actualized as a hydrophilic cluster.     

Locomotion and adhesion of polymorphonuclear leukocytes effects of the supporting substratum

Contact angle measurements have been used to correlate surface hydrophobicity of a supporting substratum with adhesion and locomotion of polymorphonuclear leukocytes. The binding of human serum albumin, a well-known chemokinetic substance, to hydrophilic glass slides gave rise to hydrophobic surfaces with adhesive properties conducive, to cell polarization thus allowing cell locomotion. Parallel contact angle and cell adhesion measurements suggested that albumin modified the cellsubstratum interaction by increasing the van der Waals forces of attraction and reducing the electrostatic forces. By allowing cells to adhere to a hydrophobic surface (siliconized glass), it was found that protein could be omitted from in vitro test systems for leukocyte locomotion. It is suggested that quantitatively equal cell adhesion values may, depending on the type of attraction forces working in adhesion to the substratum, result in different locomotion patterns.     

Locomotion and adhesion of polymorphonuclear leukocytes. Effects of the supporting substratum

Contact angle measurements have been used to correlate surface hydrophobicity of a supporting substratum with adhesion and locomotion of polymorphonuclear leukocytes. The binding of human serum albumin, a well-known chemokinetic substance, to hydrophilic glass slides gave rise to hydrophobic surfaces with adhesive properties conductive to cell polarization, thus allowing cell locomotion. Parallel contact angle and cell adhesion measurements suggested that albumin modified the cell-substratum interaction by increasing the van der Waals forces of attraction and reducing the electrostatic forces. By allowing cells to adhere to a hydrophobic surface (siliconized glass), it was found that protein could be omitted from in vitro test systems for leukocyte locomotion. It is suggested that quantitatively equal cell adhesion values may, depending on the type of attraction forces working in adhesion to the substratum, result in different locomotion patterns.     

Antifreeze proteins: an unusual receptor-ligand interaction

Antifreeze proteins (AFPs) help organisms to survive below 0 degrees C by inhibiting ice growth. Although AFPs are structurally diverse, they typically present a large proportion of their surface area for binding to ice. Whereas earlier proposed binding mechanisms relied almost entirely on a hydrogen bond match between the AFP and ice, it now seems probable that van der Waals and hydrophobic interactions make a significant contribution to the enthalpy of adsorption. These interactions require intimate surface-surface complementarity between the receptor (AFP) and its ligand (ice).     

Protein-nucleic acid recognition: statistical analysis of atomic interactions and influence of DNA structure

We analyzed structural features of 11,038 direct atomic contacts (either electrostatic, H-bonds, hydrophobic, or other van der Waals interactions) extracted from 139 protein-DNA and 49 protein-RNA nonhomologous complexes from the Protein Data Bank (PDB). Globally, H-bonds are the most frequent interactions (approximately 50%), followed by van der Waals, hydrophobic, and electrostatic interactions. From the protein viewpoint, hydrophilic amino acids are over-represented in the interaction databases: Positively charged amino acids mainly contact nucleic acid phosphate groups but can also interact with base edges. From the nucleotide point of view, DNA and RNA behave differently: Most protein-DNA interactions involve phosphate atoms, while protein-RNA interactions involve more frequently base edge and ribose atoms. The increased participation of DNA phosphate involves H-bonds rather than salt bridges. A statistical analysis was performed to find the occurrence of amino acid-nucleotide pairs most different from chance. These pairs were analyzed individually. Finally, we studied the conformation of DNA in the interaction sites. Despite the prevalence of B-DNA in the database, our results suggest that A-DNA is favored in the interaction sites.     

Quantification of helix-helix binding affinities in micelles and lipid bilayers

A theoretical approach for estimating association free energies of alpha-helices in nonpolar media has been developed. The parameters of energy functions have been derived from DeltaDeltaG values of mutants in water-soluble proteins and partitioning of organic solutes between water and nonpolar solvents. The proposed approach was verified successfully against three sets of published data: (1) dissociation constants of alpha-helical oligomers formed by 27 hydrophobic peptides; (2) stabilities of 22 bacteriorhodopsin mutants, and (3) protein-ligand binding affinities in aqueous solution. It has been found that coalescence of helices is driven exclusively by van der Waals interactions and H-bonds, whereas the principal destabilizing contributions are represented by side-chain conformational entropy and transfer energy of atoms from a detergent or lipid to the protein interior. Electrostatic interactions of alpha-helices were relatively weak but important for reproducing the experimental data. Immobilization free energy, which originates from restricting rotational and translational rigid-body movements of molecules during their association, was found to be less than 1 kcal/mole. The energetics of amino acid substitutions in bacteriorhodopsin was complicated by specific binding of lipid and water molecules to cavities created in certain mutants.     

Temperature-dependent van der Waals forces

Biological systems can experience a strong van der Waals interaction involving electromagnetic fluctuations at the low frequency limit. In lipid-water mixtures the free energy of this interaction is proportional to temperature, primarily involves an entropy change, and has qualitative features of a “hydrophobic bond.” Protein-protein attraction in dilute solution is due as much to low frequency proton fluctuation (Kirkwood-Shumaker forces) and permanent dipole forces as to high frequency (infrared and UV) van der Waals intreactions. These conclusions are described in terms of numerical calculations via the Lifshitz theory of van der Waals forces.     

Innate non-specific cell substratum adhesion

Adhesion of motile cells to solid surfaces is necessary to transmit forces required for propulsion. Unlike mammalian cells, Dictyostelium cells do not make integrin mediated focal adhesions. Nevertheless, they can move rapidly on both hydrophobic and hydrophilic surfaces. We have found that adhesion to such surfaces can be inhibited by addition of sugars or amino acids to the buffer. Treating whole cells with αlpha-mannosidase to cleave surface oligosaccharides also reduces adhesion. The results indicate that adhesion of these cells is mediated by van der Waals attraction of their surface glycoproteins to the underlying substratum. Since glycoproteins are prevalent components of the surface of most cells, innate adhesion may be a common cellular property that has been overlooked.