Effective protein conformational sampling based on predicted torsion angles

Protein structure prediction is a long‐standing problem in molecular biology. Due to lack of an accurate energy function, it is often difficult to know whether the sampling algorithm or the energy function is the most important factor for failure of locating near‐native conformations of proteins. This article examines the size dependence of sampling effectiveness by using a perfect “energy function”: the root‐mean‐squared distance from the target native structure. Using protein targets up to 460 residues from critical assessment of structure prediction techniques (CASP11, 2014), we show that the accuracy of near native structures sampled is relatively independent of protein sizes but strongly depends on the errors of predicted torsion angles. Even with 40% out‐of‐range angle prediction, 2 Å or less near‐native conformation can be sampled. The result supports that the poor energy function is one of the bottlenecks of structure prediction and predicted torsion angles are useful for overcoming the bottleneck by restricting the sampling space in the absence of a perfect energy function. © 2015 Wiley Periodicals, Inc.     

ZIBgridfree: efficient conformational analysis by partition-of-unity coupling

Obtaining a sufficient sampling of conformational space is a common problem in molecular simulation. We present the implementation of an umbrella-like adaptive sampling approach based on function-based meshless discretization of conformational space that is compatible with state of the art molecular dynamics code and that integrates an eigenvector-based clustering approach for conformational analysis and the computation of inter-conformational transition rates. The approach is applied to three example systems, namely $n$ -pentane, alanine dipeptide, and a small synthetic host-guest system, the latter two including explicitly modeled solvent.     

New formulation for derivatives of torsion angles and improper torsion angles in molecular mechanics: Elimination of singularities

A new set of formulae is developed for the derivatives of torsion angle energy terms and is introduced into the program CHARMM. These formulae, which are based on derivatives of the torsion angle itself, avoid the singularities introduced by use of the derivatives of the torsion angle cosine. The potential energy can include any differentiable function of the torsion angle and there is no need for a special treatment for cases where planar conformations are not extrema. The resulting code is simpler than the original version and yields correct derivatives in all practical situations. Because the minimum of the torsion energy can be at any angle, the functionality of the existing energy routines is generalized. © 1996 by John Wiley & Sons, Inc.     

Compare-Conformer: a program for the rapid comparison of molecular conformers based on interatomic distances and torsion angles.

A computer program for comparison of the conformations of a number of related molecular structures is described. The comparisons are performed on either interatomic distances or torsion angles. The comparisons are accomplished on ordered pairs of distances or torsion angles, and the distance comparisons can be performed in a manner that allows permutation of the distance pairs being compared. The algorithm utilizes bit-string Boolean operations that allow the comparisons to be performed rapidly. The program should be useful for computer-assisted molecular modeling studies in which the viable conformers of bioactive analogues are compared in order to locate those conformers that place key substituents in the same spatial orientation.     

Fragment growing induces conformational changes in acetylcholine-binding protein: a structural and thermodynamic analysis

Optimization of fragment hits toward high-affinity lead compounds is a crucial aspect of fragment-based drug discovery (FBDD). In the current study, we have successfully optimized a fragment by growing into a ligand-inducible subpocket of the binding site of acetylcholine-binding protein (AChBP). This protein is a soluble homologue of the ligand binding domain (LBD) of Cys-loop receptors. The fragment optimization was monitored with X-ray structures of ligand complexes and systematic thermodynamic analyses using surface plasmon resonance (SPR) biosensor analysis and isothermal titration calorimetry (ITC). Using site-directed mutagenesis and AChBP from different species, we find that specific changes in thermodynamic binding profiles, are indicative of interactions with the ligand-inducible subpocket of AChBP. This study illustrates that thermodynamic analysis provides valuable information on ligand binding modes and is complementary to affinity data when guiding rational structure- and fragment-based discovery approaches.     

Gold nanoparticles as a colorimetric sensor for protein conformational changes

Spherical gold nanoparticles and flat gold films are prepared in which yeast iso-1-cytochrome c (Cyt c) is covalently bound to the gold surface by a thiol group in the cystein 102 residue. Upon exposure to solutions of different pH, bound Cyt c unfolds at low pH and refolds at high pH. This conformational change causes measurable shifts in the color of the coated nanoparticle solutions detected by UV-VIS absorption spectroscopy and in the refractive index (RI) of the flat gold films detected by surface plasmon resonance (SPR) spectroscopy. Both experiments demonstrate the same trend with pH, suggesting the use of protein-covered gold nanoparticles as a simple colorimetric sensor for conformational change.     

Interpretation of protein adsorption: surface-induced conformational changes

Protein adhesion plays a major role in determining the biocompatibility of materials. The first stage of implant integration is the adhesion of protein followed by cell attachment. Surface modification of implants (surface chemistry and topography) to induce and control protein and cell adhesion is currently of great interest. This communication presents data on protein adsorption (bovine serum albumin and fibrinogen) onto model hydrophobic (CH(3)) and hydrophilic (OH) surfaces, investigated using a quartz crystal microbalance (QCM) and grazing angle infrared spectroscopy. Our data suggest that albumin undergoes adsorption via a single step whereas fibrinogen adsorption is a more complex, multistage process. Albumin has a stronger affinity toward the CH(3) compared to OH terminated surface. In contrast, fibrinogen adheres more rapidly to both surfaces, having a slightly higher affinity toward the hydrophobic surface. Conformational assessment of the adsorbed proteins by grazing angle infrared spectroscopy (GA-FTIR) shows that after an initial 1 h incubation few further time-dependent changes are observed. Both proteins exhibited a less organized secondary structure upon adsorption onto a hydrophobic surface than onto a hydrophilic surface, with the effect observed greatest for albumin. This study demonstrates the ability of simple tailor-made monochemical surfaces to influence binding rates and conformation of bound proteins through protein-surface interactions. Current interest in biocompatible materials has focused on surface modifications to induce rapid healing, both of implants and for wound care products. This effect may also be of significance at the next stage of implant integration, as cell adhesion occurs through the surface protein layer.     

Pyrene: a probe to study protein conformation and conformational changes

The review focuses on the unique spectral features of pyrene that can be utilized to investigate protein structure and conformation. Pyrene is a fluorescent probe that can be attached covalently to protein side chains, such as sulfhydryl groups. The spectral features of pyrene are exquisitely sensitive to the microenvironment of the probe: it exhibits an ensemble of monomer fluorescence emission peaks that report on the polarity of the probe microenvironment, and an additional band at longer wavelengths, the appearance of which reflects the presence of another pyrene molecule in spatial proximity (~10 ?). Its high extinction coefficient allows us to study labeled proteins in solution at physiologically relevant concentrations. The environmentally- and spatially-sensitive features of pyrene allow monitoring protein conformation, conformational changes, protein folding and unfolding, protein-protein, protein-lipid and protein-membrane interactions.     

Automated conformational analysis: Algorithms for the efficient construction of low-energy conformations

Summary The method of constructing low-energy conformations using template joining can provide an efficient means of searching the conformational space of molecules. The simplest algorithm to perform this task would construct each potential conformation from scratch. However, new algorithms, some of which use techniques from Artificial Intelligence, have been developed which can greatly improve the efficiency of this approach.     

Application of torsion angle molecular dynamics for efficient sampling of protein conformations

We investigate the application of torsion angle molecular dynamics (TAMD) to augment conformational sampling of peptides and proteins. Interesting conformational changes in proteins mainly involve torsional degrees of freedom. Carrying out molecular dynamics in torsion space does not only explicitly sample the most relevant degrees of freedom, but also allows larger integration time steps with elimination of the bond and angle degrees of freedom. However, the covalent geometry needs to be fixed during internal coordinate dynamics, which can introduce severe distortions to the underlying potential surface in the extensively parameterized modern Cartesian-based protein force fields. A "projection" approach (Katritch et al. J Comput Chem 2003, 24, 254-265) is extended to construct an accurate internal coordinate force field (ICFF) from a source Cartesian force field. Torsion crossterm corrections constructed from local molecular fragments, together with softened van der Waals and electrostatic interactions, are used to recover the potential surface and incorporate implicit bond and angle flexibility. MD simulations of dipeptide models demonstrate that full flexibility in both the backbone phi/psi and side chain chi1 angles are virtually restored. The efficacy of TAMD in enhancing conformational sampling is then further examined by folding simulations of small peptides and refinement experiments of protein NMR structures. The results show that an increase of several fold in conformational sampling efficiency can be reliably achieved. The current study also reveals some complicated intrinsic properties of internal coordinate dynamics, beyond energy conservation, that can limit the maximum size of the integration time step and thus the achievable gain in sampling efficiency.     

Rapid identification of oxidation-induced conformational changes by kinetic analysis

Protein oxidation by reactive oxygen species is known to result in changes in the structure and function of the oxidized protein. Many proteins can tolerate multiple oxidation events before altering their conformation, while others suffer gross changes in conformation after a single oxidation event. Additionally, reactive oxygen species have been used in conjunction with mass spectrometry to map the accessible surface of proteins, often after verification that the oxidations do not alter the conformation. However, detection of oxidation-induced conformational changes by detailed kinetic oxidation analysis of individual proteolytic peptides or non-mass spectrometric analysis is labor-intensive and often requires significant amounts of sample. In this work, we describe a methodology to detect oxidation-induced conformational changes in proteins via direct analysis of the intact protein. The kinetics of addition of oxygen to unmodified protein are compared with the kinetics of addition of oxygen to the mono-oxidized protein. These changes in the rate of oxidation of the oxidized versus the non-oxidized protein are strongly correlated with increases in the random coil content as measured by the molar ellipticity at 198 nm. This methodology requires only small amounts of protein, and can be done rapidly without additional sample handling or derivatization.     

Small-amplitude protein conformational dynamics: Second-order analytic relation between cartesian coordinates and dihedral angles

An analytic expression for protein atomic displacements in Cartesian coordinate space (CCS) against small changes in dihedral angles is derived. To study time-dependent dynamics of a native protein molecule in CCS from dynamics in the internal coordinate space (ICS), it is necessary to convert small changes of internal coordinate variables to Cartesian coordinate variables. When we are interested in molecular motion, six degrees of freedom for translational and rotational motion of the molecule must be eliminated in this conversion, and this conversion is achieved by requiring the Eckart condition to hold. In this article, only dihedral angles are treated as independent internal variables (i.e., bond angles and bond lengths are fixed), and Cartesian coordinates of atoms are given analytically by a second-order Taylor expansion in terms of small deviations of variable dihedral angles. Coefficients of the first-order terms are collected in the K matrix obtained previously by Noguti and Go (1983) (see ref. 2). Coefficients of the second-order terms, which are for the first time derived here, are associated with the (newly termed) L matrix. The effect of including the resulting quadratic terms is compared against the precise numerical treatment using the Eckart condition. A normal mode analysis (NMA) in the dihedral angle space (DAS) of the protein bovine pancreatic trypsin inhibitor (BPTI) has been performed to calculate shift of mean atomic positions and mean square fluctuations around the mean positions. The analysis shows that the second-order terms involving the L matrix have significant contributions to atomic fluctuations at room temperature. This indicates that NMA in CCS involves significant errors when applied for such large molecules as proteins. These errors can be avoided by carrying out NMA in DAS and by considering terms up to second order in the conversion of atomic motion from DAS to CCS. © 1995 by John Wiley & Sons, Inc.     

Generate: a program for 3-D structure generation and conformational analysis of peptides and peptidomimetics

The program Generate, aimed at generating 3-D structures for peptides and peptidomimetics, is presented. The algorithm is based on a build-up procedure, using a library of conformations of amino acid residues. This library is built from conformational analysis of amino acids placed in a di- or tripeptide environment to mimic the surroundings of the amino acid in a true peptide, considering different positions of the residue in the peptide chain (peptidyl fragment, NH(+)(3)-terminus or COO(-)-terminus). Cis-trans isomerism in the amide bonds is taken into account by construction of rotamer libraries for different isomers. Water solvation is included through the GB/SA model. New amino acid residues can easily be added to the libraries, making it possible to generate conformations of peptidomimetics.     

Systematic conformational analysis. torsion constraint evaluation in cyclic systems

In connection with a general procedure for manual systematic conformational analysis, a method for the evaluation of torsion constraint in cyclic systems is reported. Torsion constraining structural features presently include fusions and bridgings. Starting from the two-dimensional structure of the molecule, where stereocenters are indicated by the conventional wedged/hashed stereobond notation, the method allows for the ready determination of allowed endocyclic torsion angle magnitudes and signs at constrained bonds. The method rests on the analysis of the torsion angles related to a cyclic fragment. The limitations of the method are discussed and its scope is exemplified by the analysis of the required geometry of a key reaction in the total synthesis of quadrone.     

pH-dependent protein conformational changes in albumin:gold nanoparticle bioconjugates: a spectroscopic study

The conformational changes of bovine serum albumin (BSA) in the albumin:gold nanoparticle bioconjugates were investigated in detail by various spectroscopic techniques including UV-vis absorption, fluorescence, circular dichroism, and Fourier transform infrared spectroscopies. Our studies suggested that albumin in the bioconjugates that was prepared by the common adsorption method underwent substantial conformational changes at both secondary and tertiary structure levels. BSA was found to adopt a more flexible conformational state on the boundary surface of gold nanoparticles as a result of the conformational changes in the bioconjugates. The conformational changes at pH 3.8, 7.0, and 9.0, which corresponded to different isomeric forms of albumin, were investigated, respectively, to probe the pH effect on the conformational changes of BSA in the bioconjugates. The results showed that the pH of the medium influenced the changes greatly and that fluorescence and circular dichroism studies further indicated that the changes were larger at higher pH.     

Determination of an empirical energy function for protein conformational analysis by energy embedding

It is quite easy to propose an empirical potential for conformational analysis such that given crystal structures lie near local minima. What is much more difficult, is to devise a function such that the native structure lies near a relatively deep local minimum, at least in some neighborhood of the native in conformation space. An algorithm is presented for finding such a potential acting on proteins where each amino acid residue is represented by a single point. When the given structure is either an α-helical, β-strand, or hairpin bend segment of pancreatic trypsin inhibitor, the resulting potential function in each case possesses a deep minimum within 0.10 Å of the native conformation. The improved energy embedding algorithm locates a marginally better minimum in each case only 0.1–1.3 Å away from the respective native state. In other words, this potential function guides a conformational search toward structures very close to the native over a wide range of conformation space.     

Simulation of conformational changes occurring when a protein interacts with its receptor

In order to simulate the conformational changes occurring when a protein interacts with its receptor, we firstly evaluated the structural differences between the experimental unbound and bound conformations for selected proteins and created theoretical complexes by replacing, in each experimental complex, the protein-bound with the protein-unbound chain. The theoretical models were then subjected to additional modeling refinements to improve the side chain geometry. Comparing the theoretical and experimental complexes in term of structural and energetic factors is resulted that the refined theoretical complexes became more similar to the experimental ones. We applied the same procedure within an homology modeling experiment, using as templates the experimental structures of human interleukin-1beta (IL-1beta) unbound and bound with its receptor, to build models of the homologous proteins from mouse and trout in unbound and bound conformations and to simulate the interaction with the related receptors. Our results suggest that homology modeling techniques are sensitive to differences between bound and unbound conformations, and that modeling with accuracy the side chains in the complex improves the interaction and molecular recognition. Moreover, our refinement procedure could be used in protein-protein interaction studies and, also, applied in conjunction with rigid-body docking when is not available the protein-bound conformation.     

Hydrophobic interaction chromatography of proteins: Thermodynamic analysis of conformational changes

For BSA and β-lactoglobulin adsorption to hydrophobic interaction chromatography (HIC) stationary phases leads to conformational changes. In order to study the enthalpy (ΔH_ads), entropy (ΔS_ads), free energy (ΔG_ads) and heat capacity (Δc_p,ads) changes associated with adsorption we evaluated chromatographic data by the non-linear van’t Hoff model. Additionally, we performed isothermal titration calorimetry (ITC) experiments. van’t Hoff analysis revealed that a temperature raise from 278 to 308 K increasingly favoured adsorption seen by a decrease of ΔG_ads from −12.9 to −20.5 kJ/mol for BSA and from −6.6 to −13.2 kJ/mol for β-lactoglobulin. Δc_p,ads values were positive at 1.2 m (NH₄)₂SO₄ and negative at 0.7 m (NH₄)₂SO₄. Positive Δc_p,ads values imply hydration of apolar groups and protein unfolding. These results further corroborate conformational changes upon adsorption and their dependence on mobile phase (NH₄)₂SO₄ concentration. ITC measurements showed that ΔH_ads is dependent on surface coverage already at very low loadings. Discrepancies between ΔH_ads determined by van’t Hoff analysis and ITC were observed. We explain this with protein conformational changes upon adsorption which are not accounted for by van’t Hoff analysis.