Normal modes of vibration in bovine pancreatic trypsin inhibitor and its mechanical property

The normal mode analysis of conformational fluctuation is carried out for a small globular protein, bovine pancreatic trypsin inhibitor. Results are analyzed mainly to reveal the mechanical construction of the protein molecule. We take dihedral angles, including peptide omega angles, as independent variables for the normal mode analysis. There are 306 such angles in this molecule. Motions in modes with frequencies lower than 120 cm-1 are shown to involve atoms in the whole protein molecule, and spatial change of displacement vectors is continuous, i.e., those of atoms near in space are similar. To quantitate the observation of the continuity, a correlation function of direction vectors of atomic displacements is calculated. From this function we define a quantity that is interpreted as the wave length of an equivalent elastic plane wave. From this quantity we deduce effective Young's modulus for each mode. For the mode with the lowest frequency 4.4 cm-1, it turned out to be 0.8 x 10(9) dyn cm-2, the value two orders of magnitude softer than, for instance, alpha-helices. Prompted by this observation, the four lowest frequency modes and also the harmonic motions in the thermal equilibrium are analyzed further mainly to detect relatively rigid structural elements in the molecule. From this analysis emerges a mechanical picture of the protein molecule that is made up of relatively rigid elements held together by very soft parts.     

Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory

A theory of elastic normal modes is described for the exploration of global distortions of biological structures and their assemblies based upon low-resolution image data. Structural information at low resolution, e.g. from density maps measured by cryogenic electron microscopy (cryo-EM), is used to construct discrete multi-resolution models for the electron density using the techniques of vector quantization. The elastic normal modes computed based on these discretized low-resolution models are found to compare well with the normal modes obtained at atomic resolution. The quality of the normal modes describing global displacements of the molecular system is found to depend on the resolution of the synthetic EM data and the extent of reductionism in the discretized representation. However, models that reproduce the functional rearrangements of our test set of molecules are achieved for realistic values of experimental resolution. Thus large conformational changes as occur during the functioning of biological macromolecules and assemblies can be elucidated directly from low-resolution structural data through the application of elastic normal mode theory and vector quantization.     

Simplified normal mode analysis of conformational transitions in DNA-dependent polymerases: the elastic network model

The Elastic Network Model is used to investigate the open/closed transition in all DNA-dependent polymerases whose structure is known in both forms. For each structure the model accounts well for experimental crystallographic B-factors. It is found in all cases that the transition can be well described with just a handful of the normal modes. Usually, only the lowest and/or the second lowest frequency normal modes deduced from the open form give rise to calculated displacement vectors that have a correlation coefficient larger than 0.50 with the observed difference vectors between the two forms. This is true for every structural class of DNA-dependent polymerases where a direct comparison with experimental structural data is available. In cases where only one form has been observed by X-ray crystallography, it is possible to make predictions concerning the possible existence of another form in solution by carefully examining the vector displacements predicted for the lowest frequency normal modes. This simple model, which has the advantage to be computationally inexpensive, could be used to design novel kind of drugs directed against polymerases, namely drugs preventing the open/closed transition from occurring in bacterial or viral DNA-dependent polymerases.     

Deoxymyoglobin studied by the conformational normal mode analysis. II. The conformational change upon oxygenation

The conformational change taking place in myoglobin concomitantly with the observed geometrical change at the heme-His(F8) linkage upon oxygenation is studied by normal mode analysis, which is based on the quadratic approximation of the conformational energy function. The heme-globin interaction energy increases for this change by 8.114 kcal/mol when both the heme group and the globin molecule are held rigid. When they are permitted flexibility, the interaction energy relaxes by 7.038 kcal/mol, and the difference (1.076 kcal/mol) is distributed as strain energy within the molecule. This increase is the work necessary for the heme group to move against the force exerted by the globin. If the force is assumed to be invariable during this move, the work is small, 0.276 kcal/mol, meaning that the force is strongly variable. Furthermore, this means that the heme group is located near the equilibrium point of the potential energy of the heme-globin interaction. The change in the localized strain energy stored in the force field at the linkage between the heme and the imidazole of HisF8 is estimated to be of the same order of magnitude as the distributed energy. The largest atomic displacements are observed at the region from the F helix to the beginning of the G helix, and secondary large displacements occur at several regions, i.e, the A helix, from the C helix to the CD corner, the E helix, and the C-terminal side of the H helix. All of these regions have strong dynamic interactions with the heme group, either directly or indirectly. Their secondary structures show complex deformations. In other parts, relatively rigid segments undergo rotational and/or bending changes in a way consistent with the large changes described above and close atomic packing within the molecule. The calculated conformational change is decomposed to vibrational normal modes of deoxymyoglobin. The magnitude of the conformational change, measured by the mass-weighted mean-square atomic displacement, is accounted for up to 92.0% by the 151 normal modes with frequencies lower than 40 cm-1. In descending order of contribution, the first six modes, each of which has a frequency lower than 12 cm-1, account for up to 57.4%. This means that the functionally important conformational change can well be expressed in terms of a relatively small number of collective low frequency normal modes.     

Sequence Dependencies of DNA Deformability and Hydration in the Minor Groove

DNA deformability and hydration are both sequence-dependent and are essential in specific DNA sequence recognition by proteins. However, the relationship between the two is not well understood. Here, systematic molecular dynamics simulations of 136 DNA sequences that differ from each other in their central tetramer revealed that sequence dependence of hydration is clearly correlated with that of deformability. We show that this correlation can be illustrated by four typical cases. Most rigid basepair steps are highly likely to form an ordered hydration pattern composed of one water molecule forming a bridge between the bases of distinct strands, but a few exceptions favor another ordered hydration composed of two water molecules forming such a bridge. Steps with medium deformability can display both of these hydration patterns with frequent transition. Highly flexible steps do not have any stable hydration pattern. A detailed picture of this correlation demonstrates that motions of hydration water molecules and DNA bases are tightly coupled with each other at the atomic level. These results contribute to our understanding of the entropic contribution from water molecules in protein or drug binding and could be applied for the purpose of predicting binding sites.     

High-frequency electric field and radiation characteristics of cellular microtubule network

Microtubules are important structures in the cytoskeleton, which organizes the cell. Since microtubules are electrically polar, certain microtubule normal vibration modes efficiently generate oscillating electric field. This oscillating field may be important for the intracellular organization and intercellular interaction. There are experiments which indicate electrodynamic activity of variety of cells in the frequency region from kHz to GHz, expecting the microtubules to be the source of this activity. In this paper, results from the calculation of intensity of electric field and of radiated electromagnetic power from the whole cellular microtubule network are presented. The subunits of microtubule (tubulin heterodimers) are approximated by elementary electric dipoles. Mechanical oscillation of microtubule is represented by the spatial function which modulates the dipole moment of subunits. The field around oscillating microtubules is calculated as a vector superposition of contributions from all modulated elementary electric dipoles which comprise the cellular microtubule network. The electromagnetic radiation and field characteristics of the whole cellular microtubule network have not been theoretically analyzed before. For the perspective experimental studies, the results indicate that macroscopic detection system (antenna) is not suitable for measurement of cellular electrodynamic activity in the radiofrequency region since the radiation rate from single cells is very low (lower than 10?2? W). Low noise nanoscopic detection methods with high spatial resolution which enable measurement in the cell vicinity are desirable in order to measure cellular electrodynamic activity reliably.     

The vibrational normal modes of beta-barrels in an IgG antibody molecule.

Based on the quasi-continuity model, and using the method of group theory, we studied the normal vibrations of the VL- and the CHL-beta-barrels in an IgG molecule. We put emphasis on the Raman- and the infrared-active normal modes. The Raman modes we obtained include both the breathing motion mode (or the dominant low-frequency mode) which corresponds to the maximum peak in the Raman spectrum, and the normal modes that correspond to the lower peaks. Our calculated vibration frequencies are found to be in good agreement with the experimental results observed by Painter et al. (Biopolymers 20 (1981) 243). The method and work presented in this paper may improve Chou's quasi-continuity theory in calculating the vibrational modes of a beta-barrel protein.     

Intrinsic viscoelasticity of blood cell suspensions: effects of erythrocyte deformability

The intrinsic viscoelasticity of erythrocyte suspensions holds great potential for specifying the deformability of the individual, noninteracting cells in an oscillatory shear flow field. In order to extrapolate to zero cell concentration, the complex viscoelastic modulus was measured as a function of hematocrit using 2 Hertz oscillatory flow and a shear rate of 10/sec. This was done for both normal cells and cells with severely reduced deformability when hardened with glutaraldehyde. Suspension media were blood plasma, isotonic saline, and Dextran solutions. The real parts of the complex intrinsic visco-elasticities were obtained by an extrapolation using a regression fit to Huggins' equation. For normal cells in native plasma the values ranged from 1.7 to 2, increasing to the range 2.4 to 3.1 when the plasma was diluted with isotonic saline solution. For hardened cells the value obtained was near 3.5. These results are compared with theories for suspensions of both rigid and deformable particles. Several theories for deformable particles predict an increase in intrinsic viscoelasticity with increases in the ratio of the viscosity of the interior of the particle to that of the suspending medium. This ratio controls the balance between rotational and deformational response of the cell in the flow field. The trends of these theories were observed in the measurements.     

Hydration force and bilayer deformation: a reevaluation

The hydration repulsive force between lipid bilayers and the deformability of both gel and liquid-crystalline bilayers have been quantitated by an X-ray diffraction analysis of osmotically stressed liposomes. Both sampling theorem reconstructions and electron density distributions were calculated from diffraction data obtained from multilayers with applied osmotic pressures of 0-50 atm. The bilayer thickness and area per lipid molecule remain nearly constant (to within about 4%) in this pressure range, as adjacent bilayers move from their equilibrium separation in excess water to within 2-4 A of each other. This analysis indicates that the bilayers are relatively incompressible. This results differs from previously published X-ray diffraction studies of bilayer compressibility but agrees with direct mechanical measurements of the bilayer compressibility modulus. It is also found that the hydration repulsive force decays exponentially with separation between bilayers with a decay constant of 1.4 A for gel-state dipalmitoylphosphatidylcholine and 1.7 A for liquid-crystalline egg phosphatidylcholine bilayers. This implies that the exponential decay constant is not necessarily equal to the diameter of a water molecule, as has been previously suggested on experimental and theoretical grounds.     

Enhanced susceptibility of erythrocytes deficient in glucose-6-phosphate dehydrogenase to alloxan/glutathione-induced decrease in red cell deformability

It has been hypothesized that enhanced oxidant sensitivity of glucose-6-phosphate dehydrogenase (G6PD) deficient red cells(RBCs) is the underlying mechanism for drug- or chemical-induced hemolytic crises in G6PD-deficiency. To further test this hypothesis, we used an alloxanglutathione system to mimic oxidative stress and see how oxidative damage might affect RBC deformability. RBC deformability, a major determinant of RBC survival in vivo, was monitored by a laser viscodiffractometer. Under our experimental conditions, GSH alone had very little effect on the deformability of either normal or G6PD-deficient RBCs. In contrast, alloxan alone induced a small but significant decrease in the deformability of either normal or G6PD-deficient RBCs. Interestingly, alloxan and GSH together induced a further decrease in the deformability of either normal or G6PD-deficient RBCs. The decrease in deformability in G6PD-deficient RBCs was much more profound than in normal RBCs. In addition, an alloxan-vitamin C system produced a similar deleterious effect on RBC deformability as that produced by the alloxan-GSH system. Appreciable amount of hydroxyl radicals was generated by both alloxan-GSH and alloxan-vitamin C systems as evidenced by the production of hydroxylated products of salicylate which was used as a radical trap. Moreover, salicylate could ameliorate the deleterious effect of the alloxan system on the deformability of RBCs. Taken together, our results demonstrated that G6PD-deficient RBCs were particularly susceptible to oxidant-induced damage leading to a dramatic decrease in their deformability and thus provided strong support for the hypothesis that enhanced oxidant sensitivity of G6PD-deficient RBCs is the underlying mechanism for accelerated destruction of these RBCs in vivo.     

Pressure-induced correlation field splitting of vibrational modes: structural and dynamic properties in lipid bilayers and biomembranes.

Correlation field splittings of the vibrational modes of methylene chains in lipid bilayers, isolated lipid molecules in perdeuterated lipid bilayers, crystalline lipid, and interdigitated lipid bilayers have been investigated by pressure-tuning Fourier-transform infrared spectroscopy. The correlation field splittings of these modes are originating from the vibrational coupling interactions between the fully extended methylene chains with different site symmetry along each bilayer leaflet. The interchain-interactions of the methylene chains with the same site symmetry only contribute to frequency shift of the vibrational modes. The magnitude of the correlation field splitting is a measure of the strength of the interchain-interactions, and the relative intensities of the correlation field component bands provide information concerning the relative orientation of the zig-zag planes of the interacting methylene chains. It has been demonstrated in the present work that the correlation field splitting of the CH2 bending and rocking modes commonly observed in the vibrational spectra of lipid bilayers is the result of the intermolecular interchain-interactions among the methylene chains of the neighboring molecules. The intramolecular interchain-interactions between the sn-1 and sn-2 methylene chains within each molecule are weak. The correlation field splitting resulting from the intramolecular interchain-interactions exhibits a much smaller magnitude than that from the intermolecular interchain-interactions and is observed only at very high pressure. Interdigitation of the opposing bilayer leaflets disturbs significantly the intermolecular interchain-interactions and results in dramatic changes in the pressure profiles of the correlation field component bands of both the CH2 bending and rocking modes. The relative intensities of the correlation field component bands of these modes and the magnitude of the splitting are also altered significantly. These results provide further evidence that the correlation field splitting of the CH2 bending and rocking modes in the vibrational spectra of lipid bilayers is due to the intermolecular interchain-interactions. The present work has also demonstrated that the correlation field splitting of the vibrational modes in lipid bilayers is mainly contributed by the intermolecular interchain-interactions among the nearest neighboring molecules and that the long-range correlation interactions beyond the second neighboring molecules are insignificant.     

Myosin molecule packing within the vertebrate skeletal muscle thick filaments. A complete bipolar model

Computer modelling related to the real dimensions of both the whole filament and the myosin molecule subfragments has revealed two alternative modes for myosin molecule packing which lead to the head disposition similar to that observed by EM on the surface of the cross-bridge zone of the relaxed vertebrate skeletal muscle thick filaments. One of the modes has been known for three decades and is usually incorporated into the so-called three-stranded model. The new mode differs from the former one in two aspects: (1) myosin heads are grouped into asymmetrical cross-bridge crowns instead of symmetrical ones; (2) not the whole myosin tail, but only a 43-nm C-terminus of each of them is straightened and near-parallel to the filament axis, the rest of the tail is twisted. Concurrent exploration of these alternative modes has revealed their influence on the filament features. The parameter values for the filament models as well as for the building units depicting the myosin molecule subfragments are verified by experimental data found in the literature. On the basis of the new mode for myosin molecule packing a complete bipolar structure of the thick filament is created.     

Discriminating small molecule DNA binding modes by single molecule force spectroscopy

Drugs may interact with double stranded DNA via a variety of binding modes, each mode giving rise to a specific pharmacological function. Here we demonstrate the ability of single molecule force spectroscopy to discriminate between different interaction modes by measuring the mechanical properties of DNA and their modulation upon the binding of small molecules. Due to the unique topology of double stranded DNA and due to its base pair stacking pattern, DNA undergoes several well-characterised structural transitions upon stretching. We show that small molecule binding markedly affects these transitions in ways characteristic to the binding mode and that these effects can be detected at the level of an individual molecule. The minor groove binder berenil, the crosslinker cisplatin and the intercalator ethidium bromide are compared.     

Influence of sickle hemoglobin polymerization and membrane properties on deformability of sickle erythrocytes in the microcirculation.

The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In sickle cell disease, the intracellular polymerization of sickle hemoglobin upon deoxygenation leads to a marked increase in intracellular viscosity and elastic stiffness as well as having indirect effects on the cell membrane. To estimate the components of abnormal cell rheology due to the polymerization process and that due to the membrane abnormalities, we have developed a simple mathematical model of whole cell deformability in narrow vessels. This model uses hydrodynamic lubrication theory to describe the pulsatile flow in the gap between a cell and the vessel wall. The interior of the cell is modeled as a Voigt viscoelastic solid with parameters for the viscous and elastic moduli, while the membrane is assigned an elastic shear modulus. In response to an oscillatory fluid shear stress, the cell--modeled as a cylinder of constant volume and surface area--undergoes a conical deformation which may be calculated. We use published values of normal and sickle cell membrane elastic modulus and of sickle hemoglobin viscous and elastic moduli as a function of oxygen saturation, to estimate normalized tip displacement, d/ho, and relative hydrodynamic resistance, Rr, as a function of polymer fraction of hemoglobin for sickle erythrocytes. These results show the transition from membrane to internal polymer dominance of deformability as oxygen saturation is lowered. More detailed experimental data, including those at other oscillatory frequencies and for cells with higher concentrations of hemoglobin S, are needed to apply fully this approach to understanding the deformability of sickle erythrocytes in the microcirculation. The model should be useful for reconciling the vast and disparate sets of data available on the abnormal properties of sickle cell hemoglobin and sickle erythrocyte membranes, the two main factors that lead to pathology in patients with this disease.     

Particle interaction effects on blood cell sedimentation and separations

Experiments with a continuous centrifuge reveal that the separation of leukocytes (WBCs) and platelets from erythrocytes (RBCs) is maximized at a lower than normal RBC concentration or hematocrit (HCT). Conventional hindered settling models are unsatisfactory in the explanation of this behavior because they do not adequately account for differences in cell size, density, deformability and electrical charge on the membrane surface. In this paper a new approach is taken where an effective porosity is used to account for the differences in the micro-environment of each particle type. Introduction of effective porosities into various sedimentation equations is useful in allowing better prediction of the optimum separation conditions observed in experimental data. Further adjustment of parameters is necessary for some models to shift optimums in settling curves to align with experimental trends.     

Vibrational dynamics and heat capacity in polyglycine II

The earlier works on the vibrational dynamics of polyglycine II (PG II) suffer from several infirmities, which not only suppress the dynamical nature of normal modes, but also lead to several incorrect assignments and interactive constants of the potential field. In this study, we have re-examined the phonon dispersion profiles of PG II using Higgs method for evaluation of phase-related normal modes and have attempted to remove the infirmities, as far as possible. The Wilson's GF matrix method combined with the Urey-Bradley force field has been used for normal mode analysis. This potential field leads to correct assignments of Raman, infrared and inelastic neutron scattering frequencies. Characteristic features of the dispersion curve (v versus delta/pi plot), such as repulsion and regions of high density-of-states have been interpreted. In addition, the heat capacity as a function of temperature has been obtained via density-of-states. It agrees well with the experimental data and is being reported for the first time.     

92 Novel interpretation of the isotherms of multimodal ligands binding with DNA

The binding of ligands with DNA is a key moment in a whole range of cellular processes that provide not only the normal cell vital activity but also the development of some pathological processes. Depending on ligand type, structure of DNA adsorption centers, and physical–chemical conditions of the surrounding, the ligand may bind to DNA by several modes [1]. Particularly, adsorption isotherm of multimodal ligands binding to DNA in Scatchard’s coordinates has a concave shape with two brightly expressed linear areas in the region of small fillings. The analysis of such type of adsorption isotherm for determining of important binding parameters such as binding constant and number of adsorption centers (the part of DNA polymer with which one ligand molecule binds) presents difficulties. Practically in all cases, the analysis of such adsorption isotherm is carried out by linear parts of curves. Such analysis mode of experimental points is approximate method, since all registered of experimental points are roughly divided into two groups and they are treated by linear binding isotherm and therefore the binding parameters are determined. In the present work, the non-linear adsorption isotherm in Scatchard‘s coordinates is obtained which allowed, provided, the more precise treatment of all experimental points by unique curve which includes linear regions as well. Such mode of treatment of experimental points makes more precise the determination of not only binding constant and number of adsorption centers that correspond to the one ligand molecule binding, but also additional binding parameter – a proportion of adsorption centers of each binding to DNA type of multimodal ligand.     

Separation and characterization of red blood cells with different membrane deformability using steric field-flow fractionation

Human red blood cells were treated in different ways to alter their membrane deformability, and the hydrodynamic behavior of these altered cells was studied using the steric field-flow fractionation (FFF) technique. The relationships between cell retention in the FFF channel, flow-rate of the carrier fluid and the applied field strength were studied for normal and glutaraldehyde-fixed human red cells, and separation conditions were optimized. The effect of flow-induced hydrodynamic lift forces on red cell retention in the steric FFF channel was studied, and the results suggest that the membrane deformability of the red cell is an important factor contributing to the lift force, besides other previously described effects due to density and flow velocity. Using steric FFF, a mixture of normal and glutaraldehyde-fixed human red cells was completely separated with a resolution twice that found in published d ata from gel permeation, another hydrodynamic separation technique. Partial loss of membrane deformability, induced by different degrees of glutaraldehyde-fixation, by diamide, or by a thermal treatment, has also been studied. Steric FFF is thus shown to have potential for rapid separation and differentiation of red cells with different density and membrane deformability, conditions known to be associated with, e.g., cell senescence and certain hematological diseases.     

DNA sequence-dependent deformability--insights from computer simulations

The article reviews some recent developments in studying DNA sequence-dependent deformability, with emphasis on computer modeling. After a brief outline of available experimental techniques, we proceed to computational methods and focus on atomic-resolution molecular dynamics (MD) simulations. A sequence-dependent local (base-pair step) force field inferred from MD is compared with force fields obtained by other techniques. Various methods for establishing global (flexible-rod) DNA elastic constants are reviewed, including an approach based on atomic resolution MD. The problem of defining the global deformation variables, as well as the question of anisotropy and nonlocal effects, are discussed. As an example, both local and global deformability calculations from atomic-resolution MD of EcoRI dodecamer are presented.