Davydov Soliton Dynamics in Proteins: III. Applications and Calculation of Vibrational Spectra

The mechanism for energy and signal transport in proteins as suggested by Davydov is discussed. The idea is based on a coupling of amide-I oscillators to acoustic phonons in a hydrogen bonded chain. Results as obtained with the usually used ansätze are discussed. The quality of these states for an approximate solution of the time-dependent Schrödinger equation is investigated. It is found that the semiclassical ansatz is a poor approximation, while the more sophisticated |D₁> state seems to represent the exact dynamics quite well. This was shown by extensive calculations, both analytically and numerically in the two preceding papers. Calculations at a temperature of 300K for one chain, as well as for three coupled ones (as they are present in an -helix) are presented and discussed. From the calculations it is evident, that Davydov solitons are stable for reasonable parameter values at 300K for special initial excitations close to the terminal sites of the chain. Further vibrational spectra are presented and discussed. Our results suggest, that due to their strong dependence on the initial state, the Davydov |D₁> model system might be a (quantum) chaotic one.     

Davydov Soliton Dynamics in Proteins: II. The General Case

We performed long time simulations using the |D₁> approximation for the solution of the Davydov Hamiltonian. In addition we computed expectation values of the relevant operators with the state (_D/J)|D₁> and the deviation |> from the exact solution over long times, namely 10 ns. We found that in the very long time scale the |D₁> ansatz is very close to an exact solution, showing expectation values of the relevant physical observables in the state (_D/J)|D₁> being about 5-6 orders of magnitudes larger than in the deviation state |>. In the intermediate time scale of the ps range such errors, as known from our previous work, are somewhat larger, but still more or less negligibly. Thus we also report results from an investigation of the very short time (in the range 0-0.4 ps) behaviour of the |D₁> state compared with that of an expansion of the exact solution in powers of time t. This expansion is reliable for about 0.12 ps for special cases as shown in the previous paper. However, the accuracy of the exactly known value of the norm and the expectation value of the Hamiltonian finally indicates up to what time a given expansion is valid, as also shown in the preceding paper. The comparison of the expectation values of the operators representing the relevant physical observables, formed with the third order wave function and with the corresponding results of |D₁> simulations has shown, that our expansion is valid up to a time of roughly 0.10-0.15 ps. Within this time the second and third order corrections turned out to be not very important. This is due to the fact that our first order state contains already some terms of the expansion, summed up to inifinite order. Further we found good agreement of the results obtained with our expansion and those from the corresponding |D₁> simulations within the time of about 0.10 ps. At later times, the factors with explicit powers of t in second and third order become dominant, making the expansion meaningless. Possibilities for the use of such expansions for larger times are described. Alltogether we have shown (together with previous work on medium times), that the |D₁> state, although of approximative nature, is very close to an exact solution of the Davydov model on time scales from some femtoseconds up to nanoseconds. Especially the very small time region is of importance, because in this time a possible soliton formation from the initial excitation would start.     

Davydov Soliton Dynamics in Proteins: I. Initial States and Exactly Solvable Special Cases

For the Davydov Hamiltonian several special cases are known which can be solved analytically. Starting from these cases we show that the initial state for a simulation using Davydovs |D₁> approximation has to be constructed from a given set of initial lattice displacements and momenta in form of a coherent state with its amplitudes independent of the lattices site, corresponding to Davydovs |D₂> approximation. In the |D₁> ansatz the coherent state amplitudes are site dependent. The site dependences evolve from this initial state exclusively via the equations of motion. Starting the |D₁> simulation from an ansatz with site dependent coherent state amplitudes leads to an evolution which is different from the analytical solutions for the special cases. Further we show that simple construction of such initial states from the expressions for displacements and momenta as functions of the amplitudes leads to results which are inconsistent with the expressions for the lattice energy. The site-dependence of coherent state amplitudes can only evolve through the exciton-phonon interactions and cannot be introduced already in the initial state. Thus also in applications of the |D₁> ansatz to polyacetylene always |D₂> type initial states have to be used in contrast to our previous suggestion [W. Förner, J. Phys.: Condens. Matter 1994, 6, 9089-9151, on p. 9105]. Further we expand the known exact solutions in Taylor serieses in time and compare expectation values in different orders with the exact results. We find that for an approximation up to third order in time (for the wave function) norm and total energy, as well as displacements and momenta are reasonably correct for a time up to 0.12-0.14 ps, depending somewhat on the coupling strengh for the transportless case. For the oscillator system in the decoupled case the norm is correct up to 0.6-0.8 ps, while the expectation values of the number operators for different sites are reasonably correct up to roughly 0.6 ps, when calculated from the third order wave function. The most important result for the purpose to use such expansions for controlling the validity of ansatz states is, however, that the accuracy of S(t) and H(t) (constant in time, exact values known in all cases) is obviously a general indicator for the time region in which a given expansion yields reliable values also for the other, physically more interesting expectation values.     

Ab initio Calculation of the Conformations and Vibrational Spectra of 2-Phenylbutane

Molecules with internal degrees of rotation are of particular interest to understand the behavior of synthetic or natural polymers. With the extremely rapid increase in floating point performance of modern computers we are able to calculate a subspace of the Born-Oppenheimer hypersphere for quite large molecules with ab initio methods. We choose 2-Phenylbutane as an elementary model for Polystyrene (PS), because it possesses two internal degrees of freedom, that are highly relevant for PS. These are the rotation of the benzene ring and the chain like motion of the ethylgroup.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1007/s0089460020373     

The Davydov/Scott Model for Energy Storage and Transport in Proteins

The current status of the Davydov/Scott model for energy transfer in proteins is reviewed. After a brief introduction to the theoretical framework and to the basic results, the problems of finite temperature dynamics and of the full quantum and mixed quantum-classical approximations are described, as well as recent results obtained within each of these approximations. A short survey of experimental evidence in support of the Davydov/Scott model is made and absorption spectra are calculated that show the same temperature dependence as that measured in crystalline acetanilide. Future applications of the Davydov/Scott model to protein folding and function and to misfolding diseases are outlined.     

FTIR Emission Spectra of Bacteriorhodopsin in a Vibrational Excited-State

Vibrational IR-emission spectra of bacteriorhodopsin (bR) were recorded under continuous illumination with visible light at room temperature. They contain selective information about the chromophore, Schiff base, and opsin. The spectral bands were identified by comparing the data with resonance Raman and IR absorption data. The IR-emission spectra were shown to contain a set of bands characteristic for both all-trans (bR₅₆₈) and 13-cis conformations (K₆₁₀-like intermediate) simultaneously. Variation of spectral composition and the intensity of visible light illumination influenced the spectral traces and intensity distribution between them. Greater intensity of deformational vibrations suggests distorted retinal structure in the vibrationally excited ground electronic state. The origin of the emitting species of bR is discussed.     

Rotamer Dynamics: Analysis of Rotamers in Molecular Dynamics Simulations of Proteins

Given by χ torsional angles, rotamers describe the side-chain conformations of amino acid residues in a protein based on the rotational isomers (hence the word rotamer). Constructed rotamer libraries, based on either protein crystal structures or dynamics studies, are the tools for classifying rotamers (torsional angles) in a way that reflect their frequency in nature. Rotamer libraries are routinely used in structure modeling and evaluation. In this perspective article, we would like to encourage researchers to apply rotamer analyses beyond their traditional use. Molecular dynamics (MD) of proteins highlight the in silico behavior of molecules in solution and thus can identify favorable side-chain conformations. In this article, we used simple computational tools to study rotamer dynamics (RD) in MD simulations. First, we isolated each frame in the MD trajectories in separate Protein Data Bank files via the cpptraj module in AMBER. Then, we extracted torsional angles via the Bio3D module in R language. The classification of torsional angles was also done in R according to the penultimate rotamer library. RD analysis is useful for various applications such as protein folding, study of rotamer-rotamer relationship in protein-protein interaction, real-time correlation between secondary structures and rotamers, study of flexibility of side chains in binding site for molecular docking preparations, use of RD as guide in functional analysis and study of structural changes caused by mutations, providing parameters for improving coarse-grained MD accuracy and speed, and many others. Major challenges facing RD to emerge as a new scientific field involve the validation of results via easy, inexpensive wet-lab methods. This realm is yet to be explored.     

Prediction of methyl-side Chain Dynamics in Proteins

A simple analytical model is presented for the prediction of methyl-side chain dynamics in comparison with S(2) order parameters obtained by NMR relaxation spectroscopy. The model, which is an extension of the local contact model for backbone order parameter prediction, uses a static 3D protein structure as input. It expresses the methyl-group S(2) order parameters as a function of local contacts of the methyl carbon with respect to the neighboring atoms in combination with the number of consecutive mobile dihedral angles between the methyl group and the protein backbone. For six out of seven proteins the prediction results are good when compared with experimentally determined methyl-group S(2) values with an average correlation coefficient r = 0.65+/-0.14. For the unusually rigid cytochrome c(2) no significant correlation between prediction and experiment is found. The presented model provides independent support for the reliability of current side-chain relaxation methods along with their interpretation by the model-free formalism.     

去垢剂在膜蛋白研究中的应用

去垢剂是同时具有亲水极性基团和疏水非极性基团的双极性分子,能够使脂膜解体释放膜蛋白,并在溶液中为去膜状态下的膜蛋白提供疏水环境,维持和保护膜蛋白的疏水跨膜结构,在膜蛋白的结构和功能研究中有重要的意义。去垢剂的双极性和理化特性,如临界胶束浓度能够极大影响去垢剂和膜蛋白间的相互作用。在膜蛋白研究中,需要充分利用去垢剂的结构和特性:一方面,需要利用去垢剂代替脂质分子支持和稳定去膜状态下膜蛋白的结构和功能;另一方面,需要控制去垢剂和膜蛋白的相互作用,以满足膜蛋白结构研究如蛋白质结晶试验的要求。简要介绍了去垢剂在膜蛋白研究中的最新应用进展,涉及去垢剂在膜蛋白离体表达、分离和纯化、以及结构研究中的应用。     

Fragmentation of Ar 3 + : The Role of Rotational and Vibrational Predissociation Dynamics

The quantum study of the fragmentation dynamics of argon trimer ions has been carried out using two different ab-initio potential energy surfaces. Different computational methods have been employed and the effects of the total angular momentum of the system have been evaluated. It is found that the observed metastability can be explained with the lengthening of the lifetimes produced by the centrifugal barrier.     

蛋白纤维作为优质蛋白的新技术和应用

蛋白纤维是构成生命的基本结构单元,它在细胞、组织和生物体的游动性、弹性、稳定性、骨架保护方面有重要作用。讨论了蛋白纤维在生物学、工业和医药上的应用,以及蛋白纤维的装配、控制和模仿蛋白纤维装配的进展。     

Weak Interactions between Salmonella enterica FlhB and Other Flagellar Export Apparatus Proteins Govern Type III Secretion Dynamics

The bacterial flagellum contains its own type III secretion apparatus that coordinates protein export with assembly at the distal end. While many interactions among export apparatus proteins have been reported, few have been examined with respect to the differential affinities and dynamic relationships that must govern the mechanism of export. FlhB, an integral membrane protein, plays critical roles in both export and the substrate specificity switching that occurs upon hook completion. Reported herein is the quantitative characterization of interactions between the cytoplasmic domain of FlhB (FlhB_C) and other export apparatus proteins including FliK, FlhA_C and FliI. FliK and FlhA_C bound with micromolar affinity. K_D for FliI binding in the absence of ATP was 84 nM. ATP-induced oligomerization of FliI induced kinetic changes, stimulating fast-on, fast-off binding and lowering affinity. Full length FlhB purified under solubilizing, nondenaturing conditions formed a stable dimer via its transmembrane domain and stably bound FliH. Together, the present results support the previously hypothesized central role of FlhB and elucidate the dynamics of protein-protein interactions in type III secretion.     

Ab Initio Calculations of Vibrational Frequencies,Potential Functions of Internal Rotations and Vibrational Infrared and Raman Spectra for 3,3,3-Trifluoropropanal

The conformational behavior and structure of 3,3,3,-trifluoropropal have been investigated by utilizing ab initio calculations with the 6-31G^** basis set (valence double zeta basis with polarization functions on all atoms) at the restricted Hartree Fock (RHF), second-order Møller-Plesset perturbation (MP2), and Density Functional (B3LYP) levels. The molecule is predicted to have a cis Û gauche conformational equilibrium. Full optimization of the transition states was performed and the rotational barriers of both the CHO and CF₃ rotors were calculated. Vibrational frequencies were computed at the three levels and the zero-point corrections were included into the calculated asymmetric CHO rotational barrier. Complete vibrational assignments were made on the basis of normal coordinate calculations for both stable conformers of the molecule.     

Nitric Oxide Dynamics in Truncated Hemoglobin: Docking Sites, Migration Pathways, and Vibrational Spectroscopy from Molecular Dynamics Simulations

Atomistic simulations of nitric oxide (NO) dynamics and migration in the trHbN of Mycobacterium tuberculosis are reported. From extensive molecular dynamics simulations (48 ns in total), the structural and energetic properties of the ligand docking sites in the protein have been characterized and a connectivity network between the ligand docking sites has been built. Several novel migration and exit pathways are found and are analyzed in detail. The interplay between a hydrogen-bonding network involving residues Tyr³³ and Gln⁵⁸ and the bound O₂ ligand is discussed and the role of Phe⁶² residue in ligand migration is examined. It is found that Phe⁶² is directly involved in controlling ligand migration. This is reminiscent of His⁶⁴ in myoglobin, which also plays a central role in CO migration pathways. Finally, infrared spectra of the NO molecule in different ligand docking sites of the protein are calculated. The pocket-specific spectra are typically blue-shifted by 5-10 cm⁻¹, which should be detectable in future spectroscopic experiments.