Common folding processes of mini‐proteins: Partial formations of secondary structures initiate the immediate protein folding

The folding processes of mini‐proteins (FSD‐EY/FBPWW28 domain) were computationally investigated by an enhanced conformational sampling method. Through the analyses of trajectories, these mini‐proteins had multiple folding pathways different from a simple two‐state folding, and the multiple folding processes were initiated by partial formations of secondary structures. These findings can be used to understand the folding of large proteins, that is, which secondary structures are partially folded in the early process, and how the remaining parts are sequentially folded. It is found that FSD‐EY (α/β topology) folds by a simple diffusion‐collision mechanism, while the folding process of the FBPWW28 domain (all‐β topology) requires a modification of the diffusion‐collision theory to adequately treat the coil‐sheet transition for the β sheet formation. © 2017 Wiley Periodicals, Inc.     

Reversible peptide folding: Dependence on molecular force field used

Temperature‐dependent nuclear magnetic resonance (NMR) and CD spectra of methanol solutions of a β‐heptapeptide have been interpreted in such a way that the secondary structure, a 3₁₄‐helix, is assumed to be stable in a temperature range of between 298 and 393 K. This is in contrast to the results of a 50‐ns molecular dynamics simulation using the GROMOS 96 force field, which found a melting temperature of about 340 K. This discrepancy is addressed by further computational studies using the OPLS‐AA force field. The conformational energetics of N‐formyl‐3‐aminobutanamide in vacuo are obtained using ab initio and density functional quantum‐mechanical calculations at the HF/6‐31G*, B3LYP/6‐31G*, and B3LYP/6‐311+G* levels of theory. The results permit development of torsional parameters for the OPLS‐AA force field that reproduce the conformational energetics of the monomer. By varying the development procedure, three parameter sets are obtained that focus on reproducing either low‐energy or high‐energy conformations. These parameter sets are tested by simulating the reversible folding of the β‐heptapeptide in methanol. The melting temperature of the helix formed (>360 K) is found to be higher than the one obtained from simulations using the GROMOS 96 force field (∼340 K). Differences in the potential energy functions of the latter two force fields are evaluated and point to the origins of the difference in stability. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 774–787, 2000     

Temperature‐shuffled parallel cascade selection molecular dynamics accelerates the structural transitions of proteins

Parallel cascade selection molecular dynamics (PaCS‐MD) is an enhanced conformational sampling method for searching structural transition pathways from a given reactant to a product. Recently, a temperature‐aided PaCS‐MD (Vinod et al., Eur. Biophys. J. 2016, 45, 463) has been proposed as its extension, in which the temperatures were introduced as additional parameters in conformational resampling, whereas the temperature is fixed in the original PaCS‐MD. In the present study, temperature‐shuffled PaCS‐MD is proposed as a further extension of temperature‐aided PaCS‐MD in which the temperatures are shuffled among different replicas at the beginning of each cycle of conformational resampling. To evaluate their conformational sampling efficiencies, the original, temperature‐aided, and temperature‐shuffled PaCS‐MD were applied to a protein‐folding process of Trp‐cage, and their minimum computational costs to identify the native state were addressed. Through the evaluation, it was confirmed that temperature‐shuffled PaCS‐MD remarkably accelerated the protein‐folding process of Trp‐cage compared with the other methods. © 2017 Wiley Periodicals, Inc.     

Dynamic folding pathway models of the villin headpiece subdomain (HP‐36) structure

We have investigated the folding pathway of the 36‐residue villin headpiece subdomain (HP‐36) by action‐derived molecular dynamics simulations. The folding is initiated by hydrophobic collapse, after which the concurrent formation of full tertiary structure and α‐helical secondary structure is observed. The collapse is observed to be associated with a couple of specific native contacts contrary to the conventional nonspecific hydrophobic collapse model. Stable secondary structure formation after the collapse suggests that the folding of HP‐36 follows neither the framework model nor the diffusion‐collision model. The C‐terminal helix forms first, followed by the N‐terminal helix positioned in its native orientation. The short middle helix is shown to form last. Signs for multiple folding pathways are also observed. © 2009 Wiley Periodicals, Inc. J Comput Chem 2010     

Influence of variation of a side chain on the folding equilibrium of a β‐peptide: Limitations of one‐step perturbation

In a recent study (Lin et al., Helv. Chim. Acta 2011, 94 , 597), the one‐step perturbation method was applied to tackle a challenging computational problem, that is, the calculation of the folding free enthalpies ΔG_F,U of six hepta‐β‐peptides with different, Ala, Val, Leu, Ile, Ser, or Thr, side chains in the fifth residue. The ΔG_F,U values obtained using one‐step perturbation based on a single molecular dynamics simulation of a judiciously chosen reference state with soft‐core atoms in the side chain of the fifth residue showed an overall accuracy of about k_BT for the four peptides with nonpolar side chains, but twice as large deviations were observed for the peptides with polar side chains. Here, alternative reference‐state Hamiltonians that better cover the conformational space relevant to these peptides are investigated, and post simulation rotational sampling of the χ₁ and χ₂ torsional angles of the fifth residue is carried out to sample different orientations of the side chain. A reference state with rather soft atoms yields accurate ΔG_F,U values for the peptides with the Ser and Thr side chains, but it failed to correctly predict the folding free enthalpy for one peptide with a nonpolar side chain, that is, Leu. Based on the results and those of earlier studies, possible ways to improve the accuracy of the efficient one‐step perturbation technique to compute free enthalpies of folding are discussed. © 2013 Wiley Periodicals, Inc.     

Sparsity‐weighted outlier FLOODing (OFLOOD) method: Efficient rare event sampling method using sparsity of distribution

As an extension of the Outlier FLOODing (OFLOOD) method [Harada et al., J. Comput. Chem. 2015, 36, 763], the sparsity of the outliers defined by a hierarchical clustering algorithm, FlexDice, was considered to achieve an efficient conformational search as sparsity‐weighted “OFLOOD.” In OFLOOD, FlexDice detects areas of sparse distribution as outliers. The outliers are regarded as candidates that have high potential to promote conformational transitions and are employed as initial structures for conformational resampling by restarting molecular dynamics simulations. When detecting outliers, FlexDice defines a rank in the hierarchy for each outlier, which relates to sparsity in the distribution. In this study, we define a lower rank (first ranked), a medium rank (second ranked), and the highest rank (third ranked) outliers, respectively. For instance, the first‐ranked outliers are located in a given conformational space away from the clusters (highly sparse distribution), whereas those with the third‐ranked outliers are nearby the clusters (a moderately sparse distribution). To achieve the conformational search efficiently, resampling from the outliers with a given rank is performed. As demonstrations, this method was applied to several model systems: Alanine dipeptide, Met‐enkephalin, Trp‐cage, T4 lysozyme, and glutamine binding protein. In each demonstration, the present method successfully reproduced transitions among metastable states. In particular, the first‐ranked OFLOOD highly accelerated the exploration of conformational space by expanding the edges. In contrast, the third‐ranked OFLOOD reproduced local transitions among neighboring metastable states intensively. For quantitatively evaluations of sampled snapshots, free energy calculations were performed with a combination of umbrella samplings, providing rigorous landscapes of the biomolecules. © 2015 Wiley Periodicals, Inc.     

Improvements of network approach for analysis of the folding free‐energy surface of peptides and proteins

Folding network is an effective approach to investigate the high‐dimensional free‐energy surface of peptide and protein folding, and it can avoid the limitations of the projected free‐energy surface based on two‐order parameters. In this article, we present improvements of the effectiveness and accuracy of the folding network analysis based on Markov cluster (MCL) algorithm. We used this approach to investigate the folding free‐energy surface of the beta‐hairpin peptide trpzip2 and found the folding network is able to determine the basins and folding paths of trpzip2 more clearly and accurately than the two‐dimensional free‐energy surface. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Quantum topology phase diagrams for the cis‐ and trans‐isomers of the cyclic contryphan‐Sm peptide

Within the quantum theory of atoms in molecules (QTAIM) framework we present a quantum topology phase diagram (QTPD) using the Poincaré–Hopf relation of a total of 17 all new QTAIM topologies of the cis‐ and trans‐isomers of the cyclic contryphan‐Sm peptide. The resultant QTPD consists of separate regions for the cis‐ and trans‐isomers that only overlap for topologies associated with the lowest energy minima of the cis‐ and trans‐isomers. We determine the QTAIM topologies of 29 “missing” isomers. A new, contracted formulation of the QTPD is presented, this contracted formulation includes the interamino acid bond critical points (BCPs) that link together the amino acid units, the disulphide bridge “pivot” BCP and side chain bonding interactions. The seven interamino acid BCPs linking the amino acid units coincide with the so‐called peptide backbone, the conventional qualitative approach to reduce the complexity of the peptide. We expand the interpretation of ellipticity to include the associated eigenvectors and find that higher values of the ellipticity ? are associated with a greater preference to conserve folding states. We quantify previous qualitative findings that suggested the disulfide bond is central to the folding behavior of the cyclic contryphan‐Sm peptide and why the cis‐isomer is the major form of the cyclic contryphan‐Sm peptide. © 2014 Wiley Periodicals, Inc.     

Isomerization‐ and Temperature‐Jump‐Induced Dynamics of a Photoswitchable β‐Hairpin

Conformational changes in proteins and peptides can be initiated by diverse processes. This raises the question how the variation of initiation mechanisms is connected to differences in folding or unfolding processes. In this work structural dynamics of a photoswitchable β‐hairpin model peptide were initiated by two different mechanisms: temperature jump (T‐jump) and isomerization of a backbone element. In both experiments the structural changes were followed by time‐resolved IR spectroscopy in the nanosecond to microsecond range. When the photoisomerization of the azobenzene backbone switch initiated the folding reaction, pronounced absorption changes related to folding into the hairpin structure were found with a time constant of about 16 μs. In the T‐jump experiment kinetics with the same time constant were observed. For both initiation processes the reaction dynamics revealed the same strong dependence of the reaction time on temperature. The highly similar transients in the microsecond range show that the peptide dynamics induced by T‐jump and isomerization are both determined by the same mechanism and exclude a downhill‐folding process. Furthermore, the combination of the two techniques allows a detailed model for folding and unfolding to be presented: The isomerization‐induced folding process ends in a transition‐state reaction scheme, in which a high energetic barrier of 48 kJ mol^?1 separates unfolded and folded structures.     

3D superposition of chemical fragments for N‐membered rings: application to conformational analysis

In this paper a procedure is suggested for the 3D superposition of chemical fragments, which is specifically designed for rings molecules and can be combined with statistical multivariate procedures to extract useful conformational information. The procedure relies on the plane introduced by Cremer and Pople ‘A general definition of ring puckering coordinates. J. Am. Chem. Soc. 1975; 97 (6): 1354–1358’ to define the celebrated puckering coordinates, and provides a measure of distance between two geometrical conformations. Real datasets are analyzed to illustrate how it can be used as input to agglomerative clustering methods, multidimensional scaling analysis and allows to compute the centroid of a group of fragments. Copyright © 2010 John Wiley & Sons, Ltd.     

Collapse‐expansion transition of elastic shell induced by grafted polymer chains

A coarse‐grained model for an elastic shell grafted with polymer chains is investigated by molecular dynamics methods. With increasing the number of grafted polymer chains (GPCs), it is found that the conformation of the shell undergoes from expansion to collapse and back to the expansion. By varying the density of the GPCs, the phase transition of the elastic shell can be successfully controlled at moderate bending energy of the shell and at moderate binding energy between the shell and GPCs. Furthermore, the self‐assembly structures of the GPCs are also affected by the elastic shell in certain conditions. In the case of a few GPCs on the shell, the chains tend to be adsorbed on the shell surface unfolded at high value of bending energy. However, when the bending energy is small, the chains can be folded several times easily. This may be an important step toward a deeper understanding of how to control the microstructure in the production of biocomposites. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Force field‐dependant structural divergence revealed during long time simulations of Calbindin d9k

The structural and the dynamic features of the Calbindin (CaB) protein in its holo and apo states are compared using molecular dynamics simulations under nine different force fields (FFs) (G43a1, G53a6, Opls‐AA, Amber94, Amber99, Amber99p, AmberGS, AmberGSs, and Amber99sb). The results show that most FFs reproduce reasonably well the majority of the experimentally derived features of the CaB protein. However, in several cases, there are significant differences in secondary structure properties, root mean square deviations (RMSDs), root mean square fluctuations (RMSFs), and S² order parameters among the various FFs. What is more, in certain cases, these parameters differed from the experimentally derived values. Some of these deviations became noticeable only after 50 ns. A comparison with experimental data indicates that, for CaB, the Amber94 shows overall best agreement with the measured values, whereas several others seem to deviate from both crystal and nuclear magnetic resonance data. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

1H‐Azepine‐4‐amino‐4‐carboxylic Acid: A New α,α‐Disubstituted Ornithine Analogue Capable of Inducing Helix Conformations in Short Ala‐Aib Pentapeptides

A very efficient synthesis of orthogonally protected 1H‐azepine‐4‐amino‐4‐carboxylic acid, abbreviated as Azn, a conformationally restricted analogue of ornithine, was realized. It was obtained on a gram scale in good overall yield in five steps, three of which did not require isolation of the intermediates, starting from the readily available 1‐amino‐4‐oxo‐cyclohexane‐4‐carboxylic acid. Both enantiomers were used for the preparation of pentapeptide models containing Ala, Aib, and Azn. Conformational studies using both spectroscopic techniques (NMR, CD) and molecular dynamics on model 5‐mer peptides showed that the (R)‐Azn isomer possesses a marked helicogenic effect.     

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.     

Conformational dynamics of bis(BF2)‐2,2′‐bidipyrrins revealed by through‐space 13C?19F and 19F?19F couplings

The conformation of [bis‐(N,N′‐difluoroboryl)]‐3,3′‐diethyl‐4,4′,8,8′,9,9′,10,10′‐octamethyl‐2,2′‐bidipyrrin (1) in solution was studied by analyzing the ¹³C? ¹⁹F and ¹⁹F? ¹⁹F through‐space spin–spin couplings. The ¹H and ¹³C NMR spectra were assigned on the basis of nuclear Overhauser effect spectroscopy (NOESY), heteronuclear single‐quantum correlation (HSQC), and heteronuclear multiple‐bond correlation (HMBC) experiments. The ¹⁹F spectrum of 1 was compared with that of 2‐ethyl‐1,3,5,6,7‐pentamethyl‐4,4‐difluoro‐4‐bor‐3a,4a‐diaza‐s‐indacen (2). The ¹⁹F? ¹⁹F through‐space spin? spin coupling in 1 was thus assigned and the coupling constant was obtained by simulating the coupling patterns. The obtained conformation of 1 was compared with those of the known complexes [bis‐(N,N′‐difluoroboryl)]‐3,3′,8,8′,9,9′‐hexaethyl‐4,4′,10,10′‐tetramethyl‐6,6′‐(4‐methylphenyl)‐2,2′‐bidipyrrin (3)and [bis‐(N,N′‐difluoroboryl)]‐9,9′‐diethyl‐4,4′,8,8′,10,10′‐hexamethyl‐3,3′‐bis(methoxycarbonylethyl)‐2,2′‐bidipyrrin (4). The conformational dynamics of 1, 3, and 4 was surveyed by observing the temperature dependence of the through‐space coupling constants between 253 and 333 K. The ¹³C? ¹⁹F and ¹⁹F? ¹⁹F through‐space spin–spin couplings thus confirm similar conformations of different BisBODIPYs in solution in contrast to earlier findings in the solid state. Copyright © 2009 John Wiley & Sons, Ltd.     

Insight into the structural requirements of benzimidazole derivatives as interleukin‐2 inducible t‐cell kinase inhibitors by computational explorations

In the present work, a set of ligand‐ and receptor‐based 3D‐QSAR models were developed to explore the structure–activity relationship of 109 benzimidazole‐based interleukin‐2‐inducible T‐cell kinase (ITK) inhibitors. In order to reveal the requisite 3D structural features impacting the biological activities, a variety of in silico modeling approaches including the comparative molecular field analysis (CoMFA), comparative molecular similarity indices analysis (CoMSIA), docking, and molecular dynamics were applied. The results showed that the ligand‐based CoMFA model (Q² = 0.552, R²_ncv = 0.908, R²_pred = 0.787, SEE = 0.252, SEP = 0.558) and CoMSIA model (Q² = 0.579, R²_ncv = 0.914, R²_pred = 0.893, SEE = 0.240, SEP = 0.538) were superior to other models with greater predictive power. In addition, a combined analysis between the 3D contour maps and docking results showed that: (1) Compounds with bulky or hydrophobic substituents near ring D and electropositive or hydrogen acceptor groups around rings C and D could increase the activity. (2) The key amino acids impacting the receptor–ligand interactions in the binding pocket are Met438, Asp500, Lys391, and Glu439. The results obtained from this work may provide helpful guidelines in design of novel benzimidazole analogs as inhibitors of ITK. © 2013 Wiley Periodicals, Inc.     

Atomistic detailed free‐energy landscape of intrinsically disordered protein studied by multi‐scale divide‐and‐conquer molecular dynamics simulation

Calcineurin (CaN) is a eukaryotic serine/threonine protein phosphatase activated by both Ca²⁺ and calmodulin (CaM), including intrinsically disordered region (IDR). The region undergoes folding into an α‐helix form in the presence Ca²⁺‐loaded CaM. To sample the ordered structure of the IDR by conventional all atom model (AAM) molecular dynamics (MD) simulation, the IDR and Ca²⁺‐loaded CaM must be simultaneously treated. However, it is time‐consuming task because the coupled folding and binding should include repeated binding and dissociation. Then, in this study, we propose novel multi‐scale divide‐and‐conquer MD (MSDC‐MD), which combines AAM‐MD and coarse‐grained model MD (CGM‐MD). To speed up the conformation sampling, MSDC‐MD simulation first treats the IDR by CGM to sample conformations from wide conformation space; then, multiple AAM‐MD in a limited area is initiated using the resultant CGM conformation, which is reconstructed by homology modeling method. To investigate performance, we sampled the ordered conformation of the IDR using MSDC‐MD; the root‐mean‐square distance (RMSD) with respect to the experimental structure was 2.23 Å.