Low-frequency motions in protein molecules. Beta-sheet and beta-barrel.

Low-frequency internal motions in protein molecules play a key role in biological functions. Based on previous work with alpha-helical structure, the quasi-continuum model is extended to the beta-structure, another fundamental element in protein molecules. In terms of the equations derived here, one can easily calculate the low-frequency wave number of a beta-sheet in an accordionlike motion, and the low-frequency wave number of a beta-barrel in a breathing motion. The calculated results for immunoglobulin G and concanavalin A agree well with the observations. These findings further verify that the observed low-frequency motion (or the so-called dominant low-frequency mode) in a protein molecule is essentially governed by the collective fluctuations of its weak bonds, especially hydrogen bonds, and the internal displacement of the massive atoms therein, as described by the quasi-continuum model.     

Origin of low-frequency motions in biological macromolecules. A view of recent progress in the quasi-continuity model

The recent progress in the quasi-continuity model and its applications in studying the low-frequency internal motions of biological macromolecules have been surveyed. Emphasis is placed on revealing the origin of this kind of internal collective motion, which involves many atoms and has significant biological functions. In light of such a line, the low-frequency motions in alpha-helix structure, beta-structure (including beta-sheet and beta-barrel), and DNA double-helix structure, the three most fundamental component elements in biological macromolecules, are discussed, and the corresponding physical pictures described. It turns out that the low-frequency motion in biological macromolecules originates from their two common intrinsic characteristics, i.e., they possess a series of weak bonds, such as hydrogen bonds and salt bridges, and a substantial mass distributed over the region containing those weak bonds.     

Low-frequency vibrations of DNA molecules.

A model for calculating the low-frequency modes in DNA molecules is presented. The present model is associated with the 'breathing' of a DNA molecule as well as its complementary hydrogen bonds. The calculated results show excellent agreement with the observed low-frequency wavenumber (30 cm-1). Consequently, such an internal motion as reflected in the proposed model might be the origin of the observed low-frequency vibration in DNA molecules. This is helpful for investigating the relevant biological functions, which so far have been discussed by many scientists.     

Identification of low-frequency modes in protein molecules.

It is demonstrated that the observed low-frequency motions with wave numbers of 22 cm-1 and 25 cm-1 for insulin and lysozyme respectively originate from the accordion-like motions of the principal helices therein. The calculated results based on such a model are in good agreement with the observed values. During calculations the role of the internal microenvironment upon the low-frequency motion is naturally revealed, so as to elucidate as well why this kind of low-frequency motion is so sensitive to the conformations of proteins observed.     

Helical water wires

A helitetrahedral model has been proposed to help explain reports of low-frequency oscillations in pure water following electromagnetic excitation at the hydronium ion cyclotron resonance frequency. The Lorentz force and the intrinsic structure constrain the motion of the H₃O⁺ ion so that it enjoys a unique form of proton-hopping, one whose path is helical. This model may also explain the numerous previously observed cyclotron resonance (ICR) biological couplings for cations other than hydronium by merely substituting hydrogen-bonded versions of these for hydronium in the tetrahedral structure. Thus the effectiveness of resonance stimulation in biological systems is explained in terms of the enhanced conductivity and reduced scattering associated with proton-hopping. It is further shown that the addition of charge-balancing hydroxyl ions act to enable oscillatory electric dipole moments that propagate along the helical axis, giving rise to weak power (≈ femtoWatts) radiation patterns. It is conceivable that the radiation associated with this process may play a role in the interactions at the interface between water and living matter.     

Modulation of Ca2+ dependent protease activity in fish and invertebrates by weak low-frequency magnetic fields

Results of experiments addressing the effects of weak low-frequency magnetic fields on intracellular Ca²⁺ dependent proteinases (calpains) from invertebrates and fish are discussed. Exposure of live animals to weak low-frequency magnetic fields with parameters chosen to induce the resonance of Ca²⁺ ions led to a significant decrease of calpain activity in the animals investigated. The physical factor studied also caused partial loss of activity in preparations of Ca²⁺ dependent proteinases obtained from invertebrates and fish. The phenomenon discovered is in accordance with the interference model of the effect of weak low-frequency magnetic fields on biological objects.     

Low-frequency Raman scattering study of six nucleosides

Raman spectroscopy was used to study the low-frequency (?200?cm^?1) vibrations in crystalline samples of six naturally occurring nucleosides: deoxythymidine (dT), deoxycytidine (dC), deoxyadenosine (dA), uridine (rU), cytidine (rC), and adenosine (rA). Such low-frequency vibrations are important for biological processes in which the conformation of a nucleic acid molecule changes. These experiments also provide a test for the low-frequency vibrational modes of dT, dC, and dA predicted by Shishkin et al.     

An Effective Enzyme Interacting with Poly (dT-dA)· Poly (dT-dA): A Dynamic Enhancer-Repressor Action

Abstract

The Green function technique is used to study the open hydrogen bond probability of poly(dT-dA)·poly(dT-dA) when an effective enzyme is attached to the helix. The DNA interstrand hydrogen bond mean motion and probability of fluctuating to an open state depends on the internal vibrational frequency of the enzyme. An enzyme with internal frequency of 80 cm ^?1 reduces hydrogen bond motion and the resulting probability of hydrogen bond fluctuational opening. An enzyme with internal frequency of 72 cm ^?1 increases hydrogen bond motion and the probability of hydrogen bond breaking.     

Low-frequency Raman spectra of lysozyme.

New techniques in laser Raman spectroscopy are used to obtain spectra of aqueous solutions of lysozylme for frequency shifts as small as 5 cm^?1. In addition, Raman measurements are made on two crystalline forms of hen egg white lysozyme. The spectra obtained from the solution and from the crystal are found to be similar for frequencies above 100 cm^?1. However, a low-frequency band at 25 cm^?1 observed in crystalline lysozyme is not found in the solution, indicating that this band cannot be attributed to an internal molecular vibration.     

The biological functions of low-frequency vibrations (phonons). 4. Resonance effects and allosteric transition

Based on the internal structure of oligoprotein as well as the basic physical characteristics+ of vibrations, it is deduced that the low-frequency vibrations possess some exceptional functions in transmitting biological information at the molecular level. In particular, according to the viewpoint of energy exchange and intramolecular displacement, it is demonstrated that the low-frequency resonance plays a very significant role during the dynamic process of allosterism of an oligomeric protein molecule. Furthermore, the cooperative reaction between hemoglobins and ligands is taken as an example, through which it is seen that some observed phenomena, whose dynamic principle has thus far been unclear, can be explicitly interpreted in terms of the concept of low-frequency resonance.     

Coherent Neutron Scattering and Collective Dynamics in the Protein,GFP

Collective dynamics are considered to be one of the major properties of soft materials, including biological macromolecules. We present coherent neutron scattering studies of the low-frequency vibrations, the so-called boson peak, in fully deuterated green fluorescent protein (GFP). Our analysis revealed unexpectedly low coherence of the atomic motions in GFP. This result implies a low amount of in-phase collective motion of the secondary structural units contributing to the boson peak vibrations and fast conformational fluctuations on the picosecond timescale. These observations are in contrast to earlier studies of polymers and glass-forming systems, and suggest that random or out-of-phase motions of the β-strands contribute greater than two-thirds of the intensity to the low-frequency vibrational spectra of GFP.     

Neutron Spin-Echo Studies of Hemoglobin and Myoglobin: Multiscale Internal Dynamics

Neutron spin-echo spectroscopy was used to study structural fluctuations that occur in hemoglobin (Hb) and myoglobin (Mb) in solution. Using neutron spin-echo data up to a very high momentum transfer q (∼ 0.62 Å^− 1), we characterized the internal dynamics of these proteins at the levels of dynamic pair correlation function and self-correlation function in the time range of several picoseconds to a few nanoseconds. In the same protein solution, data transition from pair correlation motion to self-correlation motion as the momentum transfer q increases. At low q, coherent scattering dominates; at high q, observations are largely due to incoherent scattering. The low q data were interpreted in terms of an effective diffusion coefficient; on the other hand, the high q data were interpreted in terms of mean square displacements. Comparison of data from the two homologous proteins collected at different temperatures and protein concentrations was used to assess the contributions made by translational and rotational diffusion and internal modes of motion to the data. The temperature dependence of decay times can be attributed to changes in the viscosity and temperature of the solvent, as predicted by the Stokes-Einstein relationship. This is true for contributions from both diffusive and internal modes of motion, indicating an intimate relationship between the internal dynamics of the proteins and the viscosity of the solvent. Viscosity change associated with protein concentration can account for changes in diffusion observed at different concentrations, but is apparently not the only factor involved in the changes in internal dynamics observed with change in protein concentration. Data collected at high q indicate that internal modes in Mb are generally faster than those in Hb, perhaps due to the greater surface-to-volume ratio of Mb and the fact that surface groups tend to exhibit faster motion than buried groups. Comparison of data from Hb and data from Mb at low q indicates an unexpectedly rapid motion of Hb αβ dimers relative to one another. Dynamic motion of subunits is increasingly perceived as important to the allosteric behavior of Hb. Our data demonstrate that this motion is highly sensitive to protein concentration, temperature, and solvent viscosity, indicating that great care needs to be exercised in interpreting its effect on protein function.     

Coherent Neutron Scattering and Collective Dynamics in the Protein,GFP

Collective dynamics are considered to be one of the major properties of soft materials, including biological macromolecules. We present coherent neutron scattering studies of the low-frequency vibrations, the so-called boson peak, in fully deuterated green fluorescent protein (GFP). Our analysis revealed unexpectedly low coherence of the atomic motions in GFP. This result implies a low amount of in-phase collective motion of the secondary structural units contributing to the boson peak vibrations and fast conformational fluctuations on the picosecond timescale. These observations are in contrast to earlier studies of polymers and glass-forming systems, and suggest that random or out-of-phase motions of the β-strands contribute greater than two-thirds of the intensity to the low-frequency vibrational spectra of GFP.     

Understanding DNA Conformational Dynamics: Answering Questions and Questioning Answers

Abstract

Phosphorus-31 and especially Carbon-13 NMR measurements have recently become primary input to the understanding of DNA solution dynamics. While the ³¹P measurements are inherently easier, the quality of ³¹P dynamics information is suspect and therefore ¹³C measurements are preferred. In fact, it is necessary to obtain several kinds of ¹³C data (T₁s, NOE's, linewidths, integrated peak intensities) over a wide range of magnetic fields (¹³C NMR frequencies) in order to identify major features of DNA internal motions. Further information comes from variation of temperature and DNA fragment length and/or concentration. Most of our ¹³C measurements have been performed at 37.7–90.6 MHz on fully double stranded monomer size (147 base pair) DNA at concentrations in phosphate buffer of < 10 to > 200 mg ml^?1; temperatures studied range from 6 to 55°C. Other measurements have been performed on monomer-size single-stranded DNA at 85 and 92°.

The large data set we have acquired appears to answer some important questions about the nature and extent of DNA overall and internal motional dynamics. However, the picture remains incomplete and a number of questions arise from these results:

1. Overall motion of the double stranded DNA fragments follows expected hydrodynamic behavior;

2. Restricted but rapid internal motion along the DNA structure is well represented by a spaghetti-like wobbling-in-a-cone model;

3. DNA-DNA Interactions and solvent ordering, present at relatively low DNA concentrations, partially quench the internal motion, consistent with hinge-model structural changes (and the spaghetti model above) but not as compatible with in-plane torsional motion models;

4. The deoxyribose C-2′ sites undergo additional motion which is partially uncoupled from the internal wobbling motions;

5. At high DNA concentrations, a phase transition occurs, resulting in ordered structures which drastically affect DNA internal dynamics;

6. DNA interacting with ethidium does not greatly change its conformational mobility;

7. DNA interacting with Hg²⁺ ions shows less than anticipated change in internal DNA dynamics.

The remaining challenge is to interpret our current results in terms of specific conformational processes and to understand why the conformational mobility of double stranded DNA is relatively unhindered by major structural perturbants such as intercalating ethidium and mercury ion.     

A critical evaluation of models for complex molecular dynamics: application of NMR studies of double- and single-stranded DNA

The nature of internal and overall motions in native (double-stranded) and denatured (single-stranded) DNA fragments 120–160 base pairs (bp) long is examined by molecular-dynamics modeling using ¹³C-nmr spin-relaxation data obtained over the frequency range of 37–125 MHz. The broad range of ¹³C frequencies is required to differentiate among various models. Relatively narrow linewidths, large nuclear Overhauser enhancements (NOEs), and short T₁ values all vary significantly with frequency and indicate the presence of rapid, restricted internal motions on the nanosecond time scale. For double-stranded DNA monomer fragments (147 bp, 24 Å diam at 32°C), the overall motion is that of an axially symmetric cylinder (τ_x = ～10^?6 s;τ_Z = ～1.8 × 10^?8s), which is in good agreement with values calculated from hydrodynamic theory (τ_x = ～1.8 × 10^?6 s; τ_Z = ～2.7 × 10^?8 s). The DNA internal motion can be modeled as restricted amplitude internal diffusion of individual C? H vectors of deoxyribose methine carbons C1′, C3′, and C4′, either with conic boundary conditions (τ_w = ～4 × 10^?9 s, θ_cone = ～21°) or as a bistable jump (τ_A = τ_B = ～2 × 10^?9 s, θ = ～15°). We discuss the critical role in molecular-dynamics modeling played by the angle (β) that individual C? H vectors make with the long axis of the DNA helix. Heat denaturation brings about increases in both the rate and amplitude of the internal motion (described by the wobble model with τ_W = ～0.2 × 10^?9 s, θ_cone = ～50°), and overall motion is affected by becoming essentially isotropic (τ_x = τ_Z = ～5 × 10^?8 s) for the single-stranded molecules. Since ¹³C-nmr data obtained at various DNA concentrations for C2′ of the deoxyribose ring is not described well by the above models, a new model incorporating an additional internal motion is proposed to take into account the rapid, extensive, and weakly coupled motion of C2′.     

Conserved nucleotides in an RNA essential for hepatitis B virus replication show distinct mobility patterns

The number of regulatory RNAs with identified non-canonical structures is increasing, and structural transitions often play a role in their biological function. This stimulates interest in internal motions of RNA, which can underlie structural transitions. Heteronuclear NMR relaxation measurements, which are commonly used to study internal motion, only report on local motions of few sites within the molecule. Here we have studied a 27-nt segment of the human hepatitis B virus (HBV) pregenomic RNA, which is essential for viral replication. We combined heteronuclear relaxation with the new off-resonance ROESY technique, which reports on internal motions of H,H contacts. Using off-resonance ROESY, we could for the first time detect motion of through-space H,H contacts, such as in intra-residue base-ribose contacts or inter-nucleotide contacts, both essential for NMR structure determination. Motions in non-canonical structure elements were found primarily on the sub-nanosecond timescale. Different patterns of mobility were observed among several mobile nucleotides. The most mobile nucleotides are highly conserved among different HBV strains, suggesting that their mobility patterns may be necessary for the RNA’s biological function.     

Diagonalization in a mixed basis: A method to compute low-frequency normal modes for large macromolecules

Low-frequency collective motions in proteins are generally very important for their biological functions. To study such motions, harmonic dynamics proved most useful since it is a straightforward method; it consists of the diagonalization of the Hessian matrix of the potential energy, yielding the vibrational spectrum and the directions of internal motions. Unfortunately, the diagonalization of this matrix requires a large computer memory, which is a limiting factor when the protein contains several thousand atoms. To circumvent this limitation we have developed three methods that enable us to diagonalize large matrices using much less computer memory than the usual harmonic dynamics. The first method is approximate; it consists of diagonalizing small blocks of the Hessian matrix, followed by the coupling of the low-frequency modes obtained for each block. It yields the low-frequency vibrational spectrum with a maximum error of 20%. The second method consists, after diagonalizing small blocks, of coupling the high- and low-frequency modes using an iterative procedure. It yields the exact low-frequency normal modes, but requires a long computational time with convergence problems. The third method, DIMB (Diagonalization in a Mixed Basis), which has the best performance, consists of coupling the approximate low-frequency modes with the mass-weighted cartesian coordinates, also using an iterative procedure. It reduces significantly the required computer memory and converges rapidly. The eigenvalues and eigenvectors obtained by this method are without significant error in the chosen frequency range. Moreover, it is a general method applicable to any problem of diagonalization of a large matrix. We report the application of these methods to a deca-alanine helix, trypsin inhibitor, a neurotoxin, and lysozyme. © 1993 John Wiley & Sons, Inc.     

Normal mode refinement: crystallographic refinement of protein dynamic structure. I. Theory and test by simulated diffraction data.

A dynamic structure refinement method for X-ray crystallography, referred to as the normal mode refinement, is proposed. The Debye-Waller factor is expanded in terms of the low-frequency normal modes whose amplitudes and eigenvectors are experimentally optimized in the process of the crystallographic refinement. In this model, the atomic fluctuations are treated as anisotropic and concerted. The normal modes of the external motion (TLS model) are also introduced to cover the factors other than the internal fluctuations, such as the lattice disorder and diffusion. A program for the normal mode refinement (NM-REF) has been developed. The method has first been tested against simulated diffraction data for human lysozyme calculated by a Monte Carlo simulation. Applications of the method have demonstrated that the normal mode refinement has: (1) improved the fitting to the diffraction data, even with fewer adjustable parameters; (2) distinguished internal fluctuations from external ones; (3) determined anisotropic thermal factors; and (4) identified concerted fluctuations in the protein molecule.