Enhanced conformational sampling method for proteins based on the TaBoo SeArch algorithm: Application to the folding of a mini‐protein,chignolin

The conformational samplings are indispensible for obtaining reliable canonical ensembles, which provide statistical averages of physical quantities such as free energies. However, the samplings of vast conformational space of biomacromolecules by conventional molecular dynamics (MD) simulations might be insufficient, due to their inadequate accessible time‐scales for investigating biological functions. Therefore, the development of methodologies for enhancing the conformational sampling of biomacromolecules still remains as a challenging issue in computational biology. To tackle this problem, we newly propose an efficient conformational search method, which is referred as TaBoo SeArch (TBSA) algorithm. In TBSA, an inverse energy histogram is used to select seeds for the conformational resampling so that states with high frequencies are inhibited, while states with low frequencies are efficiently sampled to explore the unvisited conformational space. As a demonstration, TBSA was applied to the folding of a mini‐protein, chignolin, and automatically sampled the native structure (C_α root mean square deviation < 1.0 Å) with nanosecond order computational costs started from a completely extended structure, although a long‐time 1‐µs normal MD simulation failed to sample the native structure. Furthermore, a multiscale free energy landscape method based on the conformational sampling of TBSA were quantitatively evaluated through free energy calculations with both implicit and explicit solvent models, which enable us to find several metastable states on the folding landscape. © 2015 Wiley Periodicals, Inc.     

LigDockCSA: protein-ligand docking using conformational space annealing

Protein–ligand docking techniques are one of the essential tools for structure‐based drug design. Two major components of a successful docking program are an efficient search method and an accurate scoring function. In this work, a new docking method called LigDockCSA is developed by using a powerful global optimization technique, conformational space annealing (CSA), and a scoring function that combines the AutoDock energy and the piecewise linear potential (PLP) torsion energy. It is shown that the CSA search method can find lower energy binding poses than the Lamarckian genetic algorithm of AutoDock. However, lower‐energy solutions CSA produced with the AutoDock energy were often less native‐like. The loophole in the AutoDock energy was fixed by adding a torsional energy term, and the CSA search on the refined energy function is shown to improve the docking performance. The performance of LigDockCSA was tested on the Astex diverse set which consists of 85 protein–ligand complexes. LigDockCSA finds the best scoring poses within 2 Å root‐mean‐square deviation (RMSD) from the native structures for 84.7% of the test cases, compared to 81.7% for AutoDock and 80.5% for GOLD. The results improve further to 89.4% by incorporating the conformational entropy. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

A comparison of distance geometry and molecular dynamics simulation techniques for conformational analysis of β-cyclodextrin

Distance geometry and molecular dynamics simulation techniques were compared in their ability to search the conformational potential energy surface of β-cyclodextrin. Structures generated by the DISGEO program were minimized using three different atomic point charge sets. Some of these structures were used as starting points for molecular dynamics simulation in vacuo at 298K. The distance geometry results showed that the global features of the conformational potential energy surface were generally independent of the point charge set. The distance geometry technique was able to find structures of lower energy than those obtained by direct minimization of the X-ray or neutron diffraction structures. However, the molecular dynamics simulation technique was consistently able to find structures of lower energy than those generated by distance geometry. Root mean square fit of the trajectory structures to the starting structure showed that the simulation allowed the molecule to explore regions of the potential energy surface in the neighborhood of the starting structure. Both the distance geometry and molecular dynamics simulation techniques showed that β-cyclodextrin can adopt a wide range of conformations in the gas phase and that these conformations are much less symmetrical than the crystalline structure.     

UV resonance Raman measurements of poly-L-lysine's conformational energy landscapes: dependence on perchlorate concentration and temperature

UV resonance Raman spectroscopy has been used to determine the conformational energy landscape of poly-L-lysine (PLL) in the presence of NaClO4 as a function of temperature. At 1 degree C, in the presence of 0.83 M NaClO4, PLL shows an approximately 86% alpha-helix-like content, which contains alpha-helix and pi-bulge/helix conformations. The high alpha-helix-like content of PLL occurs because of charge screening due to strong ion-pair formation between ClO4- and the lysine side chain -NH3+. As the temperature increases from 1 to 60 degrees C, the alpha-helix and pi-bulge/helix conformations melt into extended conformations (PPII and 2.51-helix). We calculate the Psi Ramachandran angle distribution of the PLL peptide bonds from the UV Raman spectra which allows us to calculate the PLL (un)folding energy landscapes along the Psi reaction coordinate. We observe a basin in the Psi angle conformational space associated with alpha-helix and pi-bulge/helix conformations and another basin for the extended PPII and 2.51-helical conformations.     

Surface modification by substitution: Changing topology of conformational potential energy surfaces

It is shown for compounds XS-CHCH-CHO that chemical substitution (X = H → F and X = H → Li) results in the change of conformational potential energy surfaces not only in the quantitative but in the qualitative sense as well. Qualitative change always implied a modified surface topology, i.e. critical points are either created by “split-ups” or annihilated by “collapse”. It appears that some kind of “selection rule” might be operative in the “creation” and “annihilation” of critical points during the change of surface topology as the result of chemical substitution.     

Theoretical analysis on changes in thermodynamic quantities upon protein folding: essential role of hydration

The free energy change associated with the coil-to-native structural transition of protein G in aqueous solution is calculated by using the molecular theory of solvation, also known as the three-dimensional reference interaction site model theory, to uncover the molecular mechanism of protein folding. The free energy is decomposed into the protein intramolecular energy, the hydration energy, and the hydration entropy. The folding is accompanied with a large gain in the protein intramolecular energy. However, it is almost canceled by the correspondingly large loss in the hydration energy due to the dehydration, resulting in the total energy gain about an order of magnitude smaller than might occur in vacuum. The hydration entropy gain is found to be a substantial driving force in protein folding. It is comparable with or even larger than the total energy gain. The total energy gain coupled with the hydration entropy gain is capable of suppressing the conformational entropy loss in the folding. Based on careful analysis of the theoretical results, the authors present a challenging physical picture of protein folding where the overall folding process is driven by the water entropy effect.     

Hidden protein folding pathways in free-energy landscapes uncovered by network analysis

A network analysis is used to uncover hidden folding pathways in free-energy landscapes usually defined in terms of such arbitrary order parameters as root-mean-square deviation from the native structure, radius of gyration, etc. The analysis has been applied to molecular dynamics (MD) trajectories of the B-domain of staphylococcal protein A, generated with the coarse-grained united-residue (UNRES) force field in a broad range of temperatures (270K ≤ T ≤ 325K). Thousands of folding pathways have been identified at each temperature. Out of these many folding pathways, several most probable ones were selected for investigation of the conformational transitions during protein folding. Unlike other conformational space network (CSN) methods, a node in the CSN variant implemented in this work is defined according to the nativelikeness class of the structure, which defines the similarity of segments of the compared structures in terms of secondary-structure, contact-pattern, and local geometry, as well as the overall geometric similarity of the conformation under consideration to that of the reference (experimental) structure. Our previous findings, regarding the folding model and conformations found at the folding-transition temperature for protein A (Maisuradze et al., J. Am. Chem. Soc. 132, 9444, 2010), were confirmed by the conformational space network analysis. In the methodology and in the analysis of the results, the shortest path identified by using the shortest-path algorithm corresponds to the most probable folding pathway in the conformational space network.     

Mesoscopic analysis of conformational and entropic contributions to nonspecific adsorption of HP copolymer chains using dynamic Monte Carlo simulations

Dynamic Monte Carlo simulations of short linear HP-type copolymers exhibiting proteinlike characteristics are used to investigate both chain dynamics and changes in chain conformational entropy and their contributions to the energetics of adsorption onto a solid-liquid interface. The dMC results show that the conformations and energies of adsorbed chains are highly degenerate. The ensemble-averaged energy of the adsorbed state is dependent on temperature, chain sequence, native-state stability, and sorbent surface geometry and hydrophobicity. Mesoscopic thermodynamic analyses reveal that, although increased chain conformational entropy contributes to the driving force for adsorption in certain cases, many conditions exist where the change in conformational entropy is either negligible or unfavorable due to constraints imposed by the need to form a large and specific number of favorable intra- and intermolecular contacts and by the impenetrable nature of the sorbent surface. Step-number-averaged energy trajectories, based on sampling of a large number of energy trajectories and thus conformational states at each step number, suggest that the search for a global energy minimum is gradual, so that adsorption is first reversible but becomes apparently irreversible with longer exposure to the sorbent. These results appear to be connected to the conformational adaptability of the chain both on the surface and in solution, and an adsorption model taking chain conformational dynamics into account is proposed.     

Exit-channel dynamics in barrierless unimolecular reactions: criteria of vibrational adiabaticity

Conversion of translational into vibrational energy during the last step of a unimolecular reaction is brought about by the curvature of the reaction path. The corresponding coupling is analyzed by an angle-action reaction path Hamiltonian (RPH). The accuracy of the vibrational adiabatic approximation is found to be completely independent of the shape of the potential energy Vs. Vibrations are adiabatic when two independent dimensionless parameters are small. The first one, denoted as sigma, controls the dynamic coupling. The physical significance of the condition sigma<1 is that the amplitude of the vibrations normal to the reaction path should be much smaller than the radius of curvature of the reaction path. The second parameter, denoted as mu, governs the static coupling. It results from the dependence of the vibrational frequency omega on the reaction coordinate s. The higher omega, the lower its derivative with respect to s and, more unexpectedly, the higher the translational energy epsilon, the lower mu is. A criterion for locating a particular dividing surface in barrierless reactions is proposed. This surface separates two regions of space: one where energy flows freely, and one where energy conversion between translation and vibration is hindered by adiabatic invariance. The nature of the dynamical constraint that prevents the product translational energy distribution from being fully statistical can be identified by a maximum entropy analysis. The constraint is found to bear on the translational momentum ps, i.e., on the square root of the translational energy epsilon1/2. This can be understood by applying Jacobi's form of the least action principle to the vibrationally adiabatic RPH.     

Estimation of protein folding rate from Monte Carlo simulations and entropy capacity

The problem of protein self-organization is one of the most important problems of molecular biology nowadays. Despite the recent success in the understanding of general principles of protein folding, details of this process are yet to be elucidated. Moreover, the prediction of protein folding rates has its own practical value due to the fact that aggregation directly depends on the rate of protein folding. The time of folding has been calculated for 67 proteins with known experimental data at the point of thermodynamic equilibrium between unfolded and native states using a Monte Carlo model where each residue is considered to be either folded as in the native state or completely disordered. The times of folding for 67 proteins which reach the native state within the limit of 10(8) Monte Carlo steps are in a good correlation with the experimentally measured folding rate at the mid-transition point (the correlation coefficient is -0.82). Theoretical consideration of a capillarity model for the process of protein folding demonstrates that the difference in the folding rate for proteins sharing more spherical and less spherical folds is the result of differences in the conformational entropy due to a larger surface of the boundary between folded and unfolded phases in the transition state for proteins with more spherical fold. The capillarity model allows us to predict the folding rate at the same level of correlation as by Monte Carlo simulations. The calculated model entropy capacity (conformational entropy per residue divided by the average contact energy per residue) for 67 proteins correlates by about 78% with the experimentally measured folding rate at the mid-transition point.     

Predissociation via conformational change: photodissociation of N,N-dimethylnitrosamine in the S(1) state

We investigated the photodissociation mechanism of N,N-dimethylnitrosamine (CH(3))(2)NNO (DMN) by ab intio quantum chemical methods. Inspired by an earlier study we calculated two-dimensional potential energy surfaces of the S(1) state of DMN in its planar and pyramidal conformations. While the planar molecular geometry appears to possess no direct dissociation channel, the pyramidal configuration is dissociative yielding the products NO + (CH(3))(2)N. Using wave packet dynamics on the planar S(1) potential energy surface the experimental absorption spectrum was well reproduced which gives indirect but strong support for the nondissociative nature of this surface. The transition from the planar to the pyramidal conformation of DMN was then investigated by an ab initio molecular dynamics method which revealed the time evolution of the geometrical parameters of the molecule up to the dissociation of the N-N bond. This occurs about 90 fs after photon excitation. The calculated minimum energy path along the N-N coordinate and the structural changes of the molecule along this coordinate provided a detailed picture of this indirect dissociation or, more specific, predissociation process via conformational change.     

Steepest descent reaction path integration using a first-order predictor-corrector method

The theoretical treatment of chemical reactions inevitably includes the integration of reaction pathways. After reactant, transition structure, and product stationary points on the potential energy surface are located, steepest descent reaction path following provides a means for verifying reaction mechanisms. Accurately integrated paths are also needed when evaluating reaction rates using variational transition state theory or reaction path Hamiltonian models. In this work an Euler-based predictor-corrector integrator is presented and tested using one analytic model surface and five chemical reactions. The use of Hessian updating, as a means for reducing the overall computational cost of the reaction path calculation, is also discussed.     

Metadynamics in essential coordinates: free energy simulation of conformational changes

We propose an approach that combines an extraction of collective motions of a molecular system with a sampling of its free energy surface. A recently introduced method of metadynamics allows exploration of the free energy surface of a molecular system by means of coarse-grained dynamics with flooding of free energy minima. This free energy surface is defined as a function of a set of collective variables (e.g., interatomic distances, angles, torsions, and others). In this study, essential coordinates determined by essential dynamics (principle component analysis) were used as collective variables in metadynamics. First, dynamics of the model system (explicitly solvated alanine dipeptide, Ace-Ala-Nme) was simulated by a classical molecular dynamics simulation. The trajectory (1 ns) was then analyzed by essential dynamics to obtain essential coordinates. The free energy surface as a function of the first and second essential coordinates was then explored by metadynamics. The resulting free energy surface is in agreement with other studies of this system. We propose that a combination of these two methods (metadynamics and essential dynamics) has great potential in studies of conformational changes in peptides and proteins.     

Conformational transition free energy profiles of an adsorbed, lattice model protein by multicanonical Monte Carlo simulation

Proteins often undergo changes in internal conformation upon interacting with a surface. We investigate the thermodynamics of surface induced conformational change in a lattice model protein using a multicanonical Monte Carlo method. The protein is a linear heteropolymer of 27 segments (of types A and B) confined to a cubic lattice. The segmental order and nearest neighbor contact energies are chosen to yield, in the absence of an adsorbing surface, a unique 3x3x3 folded structure. The surface is a plane of sites interacting either equally with A and B segments (equal affinity surface) or more strongly with the A segments (A affinity surface). We use a multicanonical Monte Carlo algorithm, with configuration bias and jump walking moves, featuring an iteratively updated sampling function that converges to the reciprocal of the density of states 1/Omega(E), E being the potential energy. We find inflection points in the configurational entropy, S(E)=k ln Omega(E), for all but a strongly adsorbing equal affinity surface, indicating the presence of free energy barriers to transition. When protein-surface interactions are weak, the free energy profiles F(E)=E-TS(E) qualitatively resemble those of a protein in the absence of a surface: a free energy barrier separates a folded, lowest energy state from globular, higher energy states. The surface acts in this case to stabilize the globular states relative to the folded state. When the protein surface interactions are stronger, the situation differs markedly: the folded state no longer occurs at the lowest energy and free energy barriers may be absent altogether.     

A line integral reaction path approximation for large systems via nonlinear constrained optimization: application to alanine dipeptide and the beta hairpin of protein G

A variation of the line integral method of Elber with self-avoiding walk has been implemented using a state of the art nonlinear constrained optimization procedure. The new implementation appears to be robust in finding approximate reaction paths for small and large systems. Exact transition states and intermediates for the resulting paths can easily be pinpointed with subsequent application of the conjugate peak refinement method [S. Fischer and M. Karplus, Chem. Phys. Lett. 194, 252 (1992)] and unconstrained minimization, respectively. Unlike previous implementations utilizing a penalty function approach, the present implementation generates an exact solution of the underlying problem. Most importantly, this formulation does not require an initial guess for the path, which makes it particularly useful for studying complex molecular rearrangements. The method has been applied to conformational rearrangements of the alanine dipeptide in the gas phase and in water, and folding of the beta hairpin of protein G in water. In the latter case a procedure was developed to systematically sample the potential energy surface underlying folding and reconstruct folding pathways within the nearest-neighbor hopping approximation.     

Consistent free energy landscapes and thermodynamic properties of small proteins based on a single all-atom force field employing an implicit solvation

We have attempted to improve the PARAM99 force field in conjunction with the generalized Born (GB) solvation model with a surface area correction for more consistent protein folding simulations. For this purpose, using an extended alphabeta training set of five well-studied molecules with various folds (alpha, beta, and betabetaalpha), a previously modified version of PARAM99/GBSA is further refined, such that all native states of the five training species correspond to their lowest free energy minimum states. The resulting modified force field (PARAM99MOD5/GBSA) clearly produces reasonably acceptable conformational free energy surfaces of the training set with correct identifications of their native states in the free energy minimum states. Moreover, due to its well-balanced nature, this new force field is expected to describe secondary structure propensities of diverse folds in a more consistent manner. Remarkably, temperature dependent behaviors simulated with the current force field are in good agreement with the experiment. This agreement is a significant improvement over the existing standard all-atom force fields. In addition, fundamentally important thermodynamic quantities, such as folding enthalpy (DeltaH) and entropy (DeltaS), agree reasonably well with the experimental data.     

Homogeneous human complex-type oligosaccharides in correctly folded intact glycoproteins: evaluation of oligosaccharide influence on protein folding, stability, and conformational properties

The N-glycosylation of proteins is generated at the consensus sequence NXS/T (where X is any amino acid except proline) by the biosynthetic process, and occurs in the endoplasmic reticulum and Golgi apparatus. In order to investigate the influence of human complex-type oligosaccharides on counterpart protein conformation, crambin and ovomucoide, which consist of 46 and 56 amino acid residues, respectively, were selected for synthesis of model glycoproteins. These small glycoproteins were intentionally designed to be glycosylated at the α-helix (crambin: 8?position), β-sheet (crambin: 2?position) and loop position between the antiparallel β-sheets (ovomucoide: 28?position), and were synthesized by using a peptide-segment coupling strategy. After preparation of these glycosylated polypeptide chains, protein folding experiments were performed under redox conditions by using cysteine-cystine. Although the small glycoproteins bearing intentional glycosylation at the α-helix and β-sheet exhibited a suitable folding process, glycosylation at the loop position between the antiparallel β-strands caused multiple products. The conformational differences in the isolated homogeneous glycoproteins compared with non-glycosylated counterparts were evaluated by circular dichroism (CD) and NMR spectroscopy. These analyses suggested that this intentional N-glycosylation did not result in large conformational changes in the purified protein structures, including the case of glycosylation at the loop position between the antiparallel β-strands. In addition to these experiments, the conformational properties of three glycoproteins were evaluated by CD spectroscopy under different temperatures. The oligosaccharides on the protein surface fluctuated considerably; this was dependent on the increase in the solution temperature and was thought to disrupt the protein tertiary structure. Based on the measurement of the CD spectra, however, the glycoproteins bearing three disulfide bonds did not exhibit any change in their protein tertiary structure. These results suggest that the oligosaccharide conformational fluctuations were not disruptive to protein tertiary structure, and the tertiary structure of glycoproteins might be stabilized by the disulfide bond network.