Construction of a Triangle‐Shaped Trimer and a Tetrahedron Using an α‐Helix‐Inserted Circular Permutant of Cytochrome c555

Highly‐ordered protein structures have gained interest for future uses for biomaterials. Herein, we constructed a building block protein (BBP) by the circular permutation of the hyperthermostable Aquifex aeolicus cytochrome (cyt) c₅₅₅, and assembled BBP into a triangle‐shaped trimer and a tetrahedron. The angle of the intermolecular interactions of BBP was controlled by cleaving the domain‐swapping hinge loop of cyt c₅₅₅ and connecting the original N‐ and C‐terminal α‐helices with an α‐helical linker. We obtained BBP oligomers up to ≈40 mers, with a relatively large amount of trimers. According to the X‐ray crystallographic analysis of the BBP trimer, the N‐terminal region of one BBP molecule interacted intermolecularly with the C‐terminal region of another BBP molecule, resulting in a triangle‐shaped structure with an edge length of 68 Å. Additionally, four trimers assembled into a unique tetrahedron in the crystal. These results demonstrate that the circular permutation connecting the original N‐ and C‐terminal α‐helices with an α‐helical linker may be useful for constructing organized protein structures.     

Influence of the Helical Backbone in the Behavior of a Simple Model for Dimeric Coiled‐Coil Proteins

Using computer simulations as a tool for thought experiments, we investigate the influence of the helical backbone geometry in the association process and the final structures of a simple model which mimics parallel, two‐stranded coiled‐coil proteins. We define three types of helices: two of them have straight helical axes and 3.5 or 3.6 residues per helical turn; the third type presents a coiled helical axis, according to the canonical scheme defined by Crick. By using a Monte Carlo simulation algorithm, we observe that the three models exhibit different transition temperatures for the formation of the dimeric structure from two independent peptides, and a different behavior concerning the appearance of out‐of‐register structures. The energy minimized dimer structures present strong deviations from the correct association for straight helices with 3.6 residues/turn, especially for long peptides, deviations which are absent for the other two types when only the burial of hydrophobic residues is considered. A careful analysis of the energies for the out‐of‐register configurations and the contact maps reveals also differences between dimers resulting from the model with Crick parameterization and with 3.5 residues/turn. The results presented in this paper may be relevant for the design of simple models which use rigid α‐helices built from predicted elements of secondary structure.

Top views of the helical models used in this work.     

Alpha- and beta-polypeptides show a different stability of helical secondary structure

β-Polypeptides are known to adopt helical secondary structure in organic solvents, even for rather short chain lengths. It is investigated whether a short α-polypeptide with amino-acid side chains that enable β-peptides to adopt helical structures, can maintain or adopt stable helical structure in methanol or in water. The molecular dynamics simulations do not predict a particular fold, which indicates an essential role for the additional methylene moiety in the backbone of β-peptides regarding helix stability.     

Structural dissimilarity sampling with dynamically self‐guiding selection

Structural dissimilarity sampling (SDS) has been proposed as an enhanced conformational sampling method for reproducing the structural transitions of a given protein. SDS consists of cycles of two steps: (1) Selections of initial structures with structural dissimilarities by referring to a measure. (2) Conformational resampling by restarting short‐time molecular dynamics (MD) simulations from the initial structures. In the present study, an efficient measure is proposed as a dynamically self‐guiding selection to accelerate the structural transitions from a reactant state to a product state as an extension to the original SDS. In the extended SDS, the inner product (IP ) between the reactant and the snapshots generated by short‐time MD simulations are evaluated and ranked according to the IP s at every cycle. Then, the snapshots with low IP s are selected as initial structures for the short‐time MD simulations. This scheme enables one to choose dissimilar and distant initial structures from the reactant, and thus the initial structures dynamically head towards the product, promoting structural transitions from the reactant. To confirm the conformational sampling efficiency, the extended SDS was applied to maltodextrin binding protein (MBP), and we successfully reproduced the structural transition from the open to closed states with submicrosecond‐order simulation times. However, a conventional long‐time MD simulation failed to reproduce the same structural transition. We also compared the performance with that obtained by the ordinary SDS and other sampling techniques that have been developed by us to characterize the possible utility of the extended SDS for actual applications. © 2017 Wiley Periodicals, Inc.     

Molecular dynamics simulations of monodisperse/bidisperse polymer melt crystallization

We use large scale coarse‐grained molecular dynamics simulations to study the kinetics of polymer melt crystallization. For monodisperse polymer melts of several chain lengths under various cooling protocols, we show that short chains have a higher terminal crystallinity value compared to longer ones. They align at the early stages and then cease evolving. Long chains, however, align, fold into lamella structures and then slowly optimize their dangling ends for the remaining simulation time. We then identify the mechanism behind bidisperse blend crystallization. To this end, we introduce a new algorithm (called Individual Chain Crystallinity) that allows the calculation of the crystallinity separately for short and long chains in the blend. We find that, in general, bidispersity hinders crystallization significantly. At first the crystallinity of the long chain components exceeds that of the monodisperse melt, but subsequently falls below the corresponding monodisperse melt curve after a certain “crossover time.” The time of the crossover can be attributed to the time required for the full crystallization of the short chains. This indicates that at the early stages the short chains are helping long chains to crystallize. However, after all short chains have crystallized they start to hinder the crystallization of the long chains by obstructing their motion. Lastly, polymer crystallization upon various thermodynamic protocols is studied. Slower cooling is found to increase the crystallinity value. Upon an instantaneous deep quench and subsequent isothermal relaxation, the crystallinity grows rapidly with time at early stages and subsequently saturates. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2318–2326     

Compactization of rigid-chain amphiphilic macromolecules with local helical structure

Conformational characteristics of amphiphilic macromolecules with secondary local helical structuring are studied by the method of molecular dynamics for different properties of a helix (bending angles between neighboring vectors of the bond and internal rotation angle) and different rigidities of its fixation. Extended helices with high distances between helical turns and dense helices in which neighboring turns directly adjoin each other are studied. As the quality of a solvent deteriorates, extended helices experience a well-pronounced coil-globule transition, whose amplitude increases with an increase in chain rigidity, while the dimensions of dense helices gradually change. In a poor solvent, extended helices formed “collagen-like” structures, flexible chains of dense helices produce hairpin structures, and rigid macromolecules of dense helices form rodlike globules with an almost ideal local helical order. Independently of helix parameters, a deterioration in solvent quality leads to stabilization of the local secondary structure.     

Temperature dependence of molecular conformation in uniaxially deformed isotactic polypropylene investigated by combination of polarized FTIR spectroscopy and 2D correlation analysis

Evolution of molecular conformation in uniaxially deformed isotactic polypropylene (iPP) as a function of temperature is investigated by time‐resolved polarized Fourier‐transform infrared spectroscopy. It is observed that oriented crystals (microfibrils) induced by deformation possess better thermal stability compared with isotropic spherulites. 2D correlation analysis reveals that the relaxation process of ordered helices in deformed iPP could be divided into two regions referring to the melting of different crystalline structures. No obvious sequential change of ordering conformations observed in low temperature region is attributed to melting of defective or destructed crystals. However, notable sequential changes of helices occur in the high temperature region; interestingly, long helices are more thermally stable than short helices. The central region of microfibrils is suggested to consist of a large amount of long helical bundles, and the short ordering segments are primarily located in the outer lateral surfaces. A physical picture of the conformational distribution in deformation‐induced microfibrils is thus gained. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2015 , 53, 673–684     

Influences of Quantum Mechanically Mixed Electronic and Vibrational Pigment States in 2D Electronic Spectra of Photosynthetic Systems: Strong Electronic Coupling Cases

In 2D electronic spectroscopy studies, long‐lived quantum beats have recently been observed in photosynthetic systems, and several theoretical studies have suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic‐vibrational quantum mixtures, the impact of protein‐induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with the Franck‐Condon active vibrational modes in the resonant condition [Fujihashi et al., J. Chem. Phys.­ 2015 , 142, 212403.]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter‐pigment electronic coupling. In this study, we explore the impact of the fluctuations on electronic‐vibrational quantum mixtures in a strongly coupled dimer with an off‐resonant vibrational mode. Toward this end, we calculate energy transfer dynamics and 2D electronic spectra of a model dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna‐Matthews‐Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein‐induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the energy transfer dynamics are demonstrated to be dominated by the environment and coupling between the 0 0 vibronic transitions as long as the Huang‐Rhys factor of the vibrational mode is small. The electronic‐vibrational quantum mixtures do not necessarily play a significant role in electronic energy transfer dynamics despite contributing to the enhancement of long‐lived quantum beating in the 2D spectra.     

Crystallization of helical oligomers with chirality selection. I. A molecular dynamics simulation for bare helix

Helical polymers often exhibit pronounced chirality recognition during crystallization. By molecular dynamics simulation, we have already shown that the helical polymers crystallize with or without marked chirality selection depending on structural details of the polymer molecules. We have there classified the helical polymers into two categories: the bare helices made of only backbone atoms which show rather tolerant chirality selection, and the general helices with large side groups showing strict chirality recognition. Polymer crystallization is in general largely hampered and retarded by slow dynamics of the entangled chains, and therefore short helical oligomers are very suitable models for studying the chiral crystallization. We here report on molecular simulations of crystallization in the bare helical oligomer molecules by the use of Monte Carlo and molecular dynamics simulations. First we confirm the low temperature chiral crystal phase and the reversible order-disorder transition. We also observe frequent inversions of the helical sense, and the helix reversal defects propagating along the chains. Then we investigate crystallization from the melt into the chiral crystal phase. We find that the crystallization rate depends very sensitively on the degree of undercooling. The crystallization is found to be the first order transition that conforms well to the traditional picture of crystal growth in small molecules. Even when the crystallization directly into the chiral crystal phase is conducted, marked chirality selections are not observed at the early stage of crystallization; the chains adhere to the crystal surfaces selecting their helical senses rather at random resulting in racemic crystallites. The isothermal crystallization for a sufficiently long time, however, yields lamellar crystals composed of well-developed chiral domains, the growth of which seems to be accomplished through the transition back into the ordered chiral crystal phase.     

Visualization and characterization of the infrared active amide I vibrations of proteins

To facilitate the analysis of frequency-structure correlations in the amide I vibrational spectroscopy of proteins, we investigate visualization methods and spatial correlation functions that describe delocalized vibrations of proteins and protein secondary structures. To study those vibrational modes revealed in infrared spectroscopy, we characterize frequency-dependent bright states obtained from doorway mode analysis. Our visualization methods pictorially color code amplitude and phase of each oscillator within the structure to reveal spatially varying patterns characteristic of excitations within sheets and helices. Spatial correlation functions in the amplitude and phase of amide I oscillators quantitatively address the extent of delocalization and the alpha helical and beta sheet character of these modes. Specifically, we investigate the vibrations of idealized antiparallel beta sheets and alpha helices and perform case studies on three proteins: concanavalin A, myoglobin, and ubiquitin.     

Selective adsorption behavior of polymer at the polymer–nanoparticle interface

Coarse‐grained molecular dynamics simulations are used to investigate the adsorption behavior of monodisperse and bidisperse polymer chains on the nanoparticle (NP) surface at various polymer–NP interactions, chain lengths, and stiffness. At a strong polymer–NP interaction, long chains preferentially occupy interfacial region and squeeze short chains out of the interfacial region. Semiflexible chains with proper stiffness wrap NPs dominantly in a helical fashion, whereas fully flexible chains constitute the surrounding matrix. As chain stiffness increases, the results of the preferential adsorption are the opposite. The chain‐length or chain‐stiffness‐induced selective adsorption behavior of polymer chains in the polymer–NP interfacial region relies on a delicate competition between entropic and enthalpic contributions to the total free energy. These results could provide insights into polymer–NP interfacial adsorption behavior and guide the design of high‐performance nanocomposites. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1829–1837     

Temperature dependence of pitch and twist elastic constant in a cholesteric to smectic A phase transition

To understand chirality in cholesteric (Ch) liquid crystals, we performed an experimental study on the Ch-smetic A (SmA) transition of a cholesteric liquid crystal. By studying the reflection spectrum at zero field and at the critical electric field used to unwind the helical structure, we were able to measure the helical pitch P and the twist elastic constant K ²² in the Ch phase. As the temperature was lowered toward the Ch-TGB phase transition, the helical pitch and twist elastic constant diverged. The results support the model that short range SmA forms in the Ch phase. When the results were fitted by power-law temperature dependence, the exponent for P was 0.78 and the exponent for K ²² was 1.36.     

An insight into molecular motions and phase composition of gliadin/glutenin glycerol blends studied by 13C solid‐state and 1H time‐domain NMR

Monitoring of the molecular motions and secondary structures of gliadin (Gli) and glutenin (Glu) in blends with 10, 20, 30, and 40% glycerol was performed by solid‐state (SS) and time domain (TD) NMR spectroscopy. Increasing the glycerol content increased the relative amount of β‐sheets and disordered structures, while decreasing α‐helices in Gli/Glu–glycerol blends studied by ¹³C CPMAS NMR. For ≥20% glycerol samples, the protein side‐chain mobility increased similarly for Gli and Glu. A higher proportion of α‐helices versus β‐sheets was found in Gli‐glycerol blends compared with Glu–glycerol blends. Glycerol acted as “immobilized” in 10–20% glycerol Gli samples and was found mainly “free” in 30 and 40% glycerol Gli/Glu samples. During temperature experiments, 30 and 40% glycerol amounts impacted the dynamic molecular behavior of the Gli and Glu proteins differently than lipids, as observed by TD‐NMR. The combination of TD‐NMR together with SS‐NMR showed details of the dynamic molecular variations in Gli/Glu protein structure and are promising techniques to monitor the molecular dynamics of plasticized proteins. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2018 , 56, 739–750     

Helical DNA Origami Tubular Structures with Various Sizes and Arrangements

We developed a novel method to design various helical tubular structures using the DNA origami method. The size‐controlled tubular structures which have 192, 256, and 320 base pairs for one turn of the tube were designed and prepared. We observed the formation of the expected short tubes and unexpected long ones. Detailed analyses of the surface patterns of the tubes showed that the short tubes had mainly a left‐handed helical structure. The long tubes mainly formed a right‐handed helical structure and extended to the directions of the double helical axes as structural isomers of the short tubes. The folding pathways of the tubes were estimated by analyzing the proportions of short and long tubes obtained at different annealing conditions. Depending on the number of base pairs involved in one turn of the tube, the population of left‐/right‐handed and short/long tubes changed. The bending stress caused by the stiffness of the bundled double helices and the non‐natural helical pitch determine the structural variety of the tubes.     

Understanding the Signatures of Secondary‐Structure Elements in Proteins with Raman Optical Activity Spectroscopy

A prerequisite for the understanding of functional molecules like proteins is the elucidation of their structure under reaction conditions. Chiral vibrational spectroscopy is one option for this purpose, but provides only indirect access to this structural information. By first‐principles calculations, we investigate how Raman optical activity (ROA) signals in proteins are generated and how signatures of specific secondary‐structure elements arise. As a first target we focus on helical motifs and consider polypeptides consisting of twenty alanine residues to represent α‐helical and 3₁₀‐helical secondary‐structure elements. Although ROA calculations on such large molecules have not been carried out before, our main goal is the stepwise reconstruction of the ROA signals. By analyzing the calculated ROA spectra in terms of rigorously defined localized vibrations, we investigate in detail how total band intensities and band shapes emerge. We find that the total band intensities can be understood in terms of the reconstructed localized vibrations on individual amino acid residues. Two different basic mechanisms determining the total band intensities can be established, and it is explained how structural changes affect the total band intensities. The band shapes can be rationalized in terms of the coupling between the localized vibrations on different residues, and we show how different band shapes arise as a consequence of different coupling patterns. As a result, it is demonstrated for the chiral variant of Raman spectroscopy how collective vibrations in proteins can be understood in terms of well‐defined localized vibrations. Based on our calculations, we extract characteristic ROA signatures of α helices and of 3₁₀‐helices, which our analysis directly relates to differences in secondary structure.     

Steered molecular dynamics simulations for uncovering the molecular mechanisms of drug dissociation and for drug screening: A test on the focal adhesion kinase

Drug‐binding kinetics could play important roles in determining the efficacy of drugs and has caught the attention of more drug designers. Using the dissociation of 1H‐pyrrolo[2,3‐b]‐pyridines from the focal adhesion kinase as an example, this work finds that steered molecular dynamics simulations could help screen compounds with long‐residence times. It also reveals a two‐step mechanism of ligand dissociation resembling the release of ADP from protein kinase A reported earlier. A phenyl group attaching to the pyrrole prolongs residence time by creating a large activation barrier for transition from the bound to the intermediate state when it becomes exposed to the solvent. Principal component analysis shows that ligand dissociation does not couple with large‐scale collective motions of the protein involving many of its amino acids. Rather, a small subset of amino acids dominates. Some of these amino acids do not contact the ligands directly along the dissociation pathways and could exert long‐range allosteric effects. © 2018 Wiley Periodicals, Inc.     

A Disulfide Switch Providing Absolute Handedness Control in Double Helices via Conversion from the Antiparallel to Parallel Helical Pattern

A strategy to reversibly switch the parallel/antiparallel helical conformation of aromatic double helices through the formation/breakage of a disulfide bond is presented. Single-crystal X-ray structures, NMR, and circular dichroism spectroscopy demonstrate that the double helices with terminal thiol groups favor an antiparallel helical arrangement both in the solid state and in solution, while the P/M bias of helicity induced by chiral segments from another extremity of the sequence is weak in this structural motif. The antiparallel helices can be rearranged to parallel helices through the disulfide connection of the sequences. This change enhances the bias of helical handedness and results in absolute chirality control of the double helices. The handedness-mediated process can be governed by the oxidation-reduction cycle, thereby switching the structural arrangement and the enhancement of chiral bias. In addition, we find that the sequences can dimerize into an intermolecular double helix with the disulfide connection. And the helical handedness is also fully controlled due to the head-to-head structural motif.     

Phase behavior of a single polyethylene chain confined between two adsorption walls

The phase behavior of a single polyethylene chain confined between two adsorption walls is investigated by using molecular dynamics simulations. In the free space, it is confirmed in our calculation that the isolated polymer chain exhibits a disordered coil state at high temperatures, and collapses into a condensed state at low temperatures, that is, the coil‐to‐globule transition, and the finite chain length effects are considered since the critical region depends on chain lengths. When the chain is confined between two attractive walls, however, the equilibrium properties not only depend on the chain length but also depend on the adsorption energy and the confinement. Mainly, we focus on the influence of polymer chain length, confinement, and adsorption interaction on the equilibrium thermodynamic properties of the polyethylene chains. Chain lengths of N = 40, 80, and 120 beads, distances between the two walls of D = 10, 20, 30, 50, and 90 Å, and adsorption energies of w = 1.5, 2.5, 3.5, 6.5, and 8.5 kcal/mol are considered here. By considering the confinement–adsorption interactions, some new folding structures are found, that is, the hairpin structure for short chain of N = 40 beads, and the enhanced hairpin or crystal like structures for long chains of N = 80 and 120 beads. The results obtained in our simulations may provide some insights into the phase behaviors of confined polymers, which can not be obtained by previous studies without considering confinement–adsorption interactions. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 370–387, 2008     

Quasi-Hamiltonian equations of motion for internal coordinate molecular dynamics of polymers

Conventional molecular dynamics simulations of macromolecules require long computational times because the most interesting motions are very slow compared to the fast oscillations of bond lengths and bond angles that limit the integration time step. Simulation of dynamics in the space of internal coordinates, that is, with bond lengths, bond angles, and torsions as independent variables, gives a theoretical possibility of eliminating all uninteresting fast degrees of freedom from the system. This article presents a new method for internal coordinate molecular dynamics simulations of macromolecules. Equations of motion are derived that are applicable to branched chain molecules with any number of internal degrees of freedom. Equations use the canonical variables and they are much simpler than existing analogs. In the numerical tests the internal coordinate dynamics are compared with the traditional Cartesian coordinate molecular dynamics in simulations of a 56 residue globular protein. For the first time it was possible to compare the two alternative methods on identical molecular models in conventional quality tests. It is shown that the traditional and internal coordinate dynamics require the same time step size for the same accuracy and that in the standard geometry approximation of amino acids, that is, with fixed bond lengths, bond angles, and rigid aromatic groups, the characteristic step size is 4 fs, which is 2 times higher than with fixed bond lengths only. The step size can be increased up to 11 fs when rotation of hydrogen atoms is suppressed. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18 : 1354–1364, 1997     

The Helix to Super‐Helix Transition in the Self‐Assembly of π‐Systems: Superseding of Molecular Chirality at Hierarchical Level

Higher‐order super‐helical structures derived from biological molecules are known to evolve through opposite coiling of the initial helical fibers, as seen in collagen protein. A similar phenomenon is observed in a π‐system self‐assembly of chiral oligo(phenyleneethylene) derivatives (S )‐ 1 and (R )‐ 1 that explains the unequal formation of both left‐ and right‐handed helices from molecule having a specific chiral center. Concentration‐ and temperature‐dependent circular dichroism (CD) and UV/Vis spectroscopic studies revealed that the initial formation of helical aggregates is in accordance with the molecular chirality. At the next level of hierarchical self‐assembly, coiling of the fibers occurs with opposite handedness, thereby superseding the command of the molecular chirality. This was confirmed by solvent‐dependent decoiling of super‐helical structures and concentration‐dependent morphological analysis.