Transport properties and hydrodynamic centers of rigid macromolecules with arbitrary shapes

A general formalism, which includes translation–rotation coupling, is proposed for calculating translational and rotational transport properties, as well as intrinsic viscosities, of rigid macromolecules with an arbitrary shape. This formalism is based on Brenner's theory of translational–rotational dynamics and on methods for the calculation of hydrodynamic properties that have been already presented, and can be regarded as a generalization of the one proposed by Nakajima and Wada. The calculated transport properties depend on the origin as predicted by Brenner's theory, but in a disagreement with him, the center of resistance and the center of diffusion do not coincide. As one can define several hydrodynamic centers, which in practice turn out to be located at different points, the influence of the choice of the center on the calculated transport properties is discussed. An analysis of the translation–rotation coupling effects in translational diffusion reveals that they arise exclusively from hydrodynamic interactions and are rather small in some cases of interest. Finally, we present a study of the rotational diffusion of rigid bent rods with a fixed length-to-diameter ratio. The diffusion coefficients obtained can be useful to estimate changes with respect to a straight rod.     

Viscoelasticity of rigid macromolecules with irregular shapes in the limit of overwhelming Brownian motion

We consider viscoelastic properties of complex rigid macromolecules in fluids undergoing steady or sinusoidal linear shearing. An arbitrary body is hydrodynamically described by six tensors to allow for irregular shapes that couple rotational and translational motions to each other and to the shear field. The viscosity increment ν is obtained for infinitely dilute suspensions in the limit of overwhelming Brownian motion by balancing drag forces and torques with entropic forces and torques. For sinusoidal shearing, ν is a complex number that exhibits five resonances at frequencies matching the j = 2 eigenvalues of the rotational diffusion equation for a stationary fluid. The resonance amplitudes are conveniently expressed in terms of a second-rank body-fixed tensor χ that characterizes alignment by the shear field, and special cases of symmetry are considered which reduce the number of contributing terms. Steadyshear methods, which assume a body matches the translational and rotational motions of the fluid element it replaces, are shown to slightly overestimate ν when complex shapes are involved. An algebraic criterion is found to locate the center of viscosity needed in these other methods although our treatment is independent of the choice of position in the body used for calculations. Bead-model expressions are derived in order to provide numerical treatments of complicated structures. As an example, we examine a long bent rod.     

Quasielastic light scattering from solutions of filamentous viruses. II. Comparison between theories and experiments

We have compared four theoretical effects of rodlike macromolecules with the fast components, i.e., components other than translational diffusion, of our experimental data, which are presented as amplitude autocorrelation functions of electric field scattered from dilute solutions of monodisperse rodlike viruses with lengths from 3300 Å for tobacco mosaic virus to 20,000 Å for Pf1. The four effects are (1) the optic anisotropy treated by Aragón and Pecora, (2) coupled translational–rotational diffusion due to anisotropy in translational mobility recently reformulated by Gierke, (3) anisotropic rotational diffusion with respect to the direction of translational displacement first discussed by Berne and Pecora, and (4) the bending mode of a rod by Fujime and Maruyama. We show that both the first and second effects are required to explain the enhancement of amplitude of the translational diffusion at the expense of fast components. The experimental decay rates of the fast component exceed that of the rotational diffusions. In order to explain the excessive decay rate in the fast component, we need to include a minute amount (～1%) of bending mode of rodlike viruses, especially in longer viruses such as M13 and Pf1.     

A rotational diffusion coefficient of the 70S ribosome determined by depolarized laser light scattering

We have obtained a rotational diffusion coefficient of the 70S ribosome isolated from Escherichia-coli (MRE-600), from the depolarized light scattering spectrum measured by photon correlation spectroscopy. The intensity correlation function of depolarized scattered light contains contributions due to multiple scattered and anisotropy scattered light from the ribosomal particle. We discuss extensively the subtraction procedure used to obtain the rotational correlation time from the experimental correlation function. We have also obtained the translational diffusion coefficient from the same sample by determining the polarized correlation function. The hydrodynamic radius determined from the rotational diffusion coefficient is only slightly larger than the radius obtained from the translational diffusion coefficient. Therefore the ribosomal particle has a non-spherical shape. This conclusion, however, could be impaired by the effect of free draining of the ribosome.     

A rotational diffusion coefficient of the 70S ribosome determined by depolarized laser light scattering.

We have obtained a rotational diffusion coefficient of the 70S ribosome isolated from Escherichia-coli (MRE-600), from the depolarized light scattering spectrum measured by photon correlation spectroscopy. The intensity correlation function of depolarized scattered light contains contributions due to multiple scattered and anisotropy scattered light from the ribosomal particle. We discuss extensively the subtraction procedure used to obtain the rotational correlation from the time from the experimental correlation function. We have also obtained the translational diffusion coefficient from the same sample by determining the polarized correlation function. The hydrodynamic radius determined from the rotational diffusion coefficient is only slightly larger than the radius obtained from the translational diffusion coefficient. Therefore the ribosomal particle has a non-spherical shape. This conclusion, however, could be impaired by the effect of free draining of the ribosome.     

Whole-field integration, not detailed analysis, is used by the crab optokinetic system to separate rotation and translation in optic flow

For optimal visual control of compensatory eye movements during locomotion it is necessary to distinguish the rotational and translational components of the optic flow field. Optokinetic eye movements can reduce the rotational component only, making the information contained in the translational flow readily available to the animal. We investigated optokinetic eye rotation in the marble rock crab, Pachygrapsus marmoratus, during translational movement, either by displacing the animal or its visual surroundings. Any eye movement in response to such stimuli is taken as an indication that the system is unable to separate the translational and the rotational components in the optic flow in a mathematically perfect way. When the crabs are translated within a pseudo-natural environment, eye movements are negligible, especially during sideways translation. When, however, crabs were placed in a gangway between two elongated rectangular sidewalls carrying dotted patterns which were translated back and forth, marked eye movements were elicited, depending on the translational velocity. To resolve this discrepancy, we tested several hypotheses about mechanisms using detailed analysis of the optic flow or whole-field integration. We found that the latter are sufficient to explain the efficient separation of translation and rotation of crabs in quasi-natural situations. Accepted: 6 May 1997     

Protein effective rotational correlation times from translational self-diffusion coefficients measured by PFG-NMR

Molecular rotational correlation times are of interest for many studies carried out in solution, including characterization of biomolecular structure and interactions. Here we have evaluated the estimates of protein effective rotational correlation times from their translational self-diffusion coefficients measured by pulsed-field gradient NMR against correlation times determined from both collective and residue-specific (15)N relaxation analyses and those derived from 3D structure-based hydrodynamic calculations. The results show that, provided the protein diffusive behavior is coherent with the Debye-Stokes-Einstein model, translational diffusion coefficients provide rapid estimates with reasonable accuracy of their effective rotational correlation times. Effective rotational correlation times estimated from translational diffusion coefficients may be particularly beneficial in cases where i) isotopically labelled material is not available, ii) collective backbone (15)N relaxation rates are difficult to interpret because of the presence of flexible termini or loops, or iii) a full relaxation analysis is practically difficult because of limited sensitivity owing to low protein concentration, high molecular mass or low temperatures.     

Separation of translational and rotational contributions in solution studies using fluorescence photobleaching recovery

Although fluorescence photobleaching recovery (FPR) experiments are usually interpreted in terms of the translational motions of a fluorescently labeled species, rotational motions can also modulate recovery through the cosine-squared laws for dipolar absorption and emission processes. In a complex interacting system, translational and rotational contributions may both be simultaneously present. We show how these contributions can be separated in solution studies using an FPR setup in which (a) the linear polarization of the low-intensity observation beam and the high-intensity photobleaching pulse can be varied independently, and (b) all emitted fluorescent photons are counted equally. The fluorescence recovery signal obtained with the observation beam polarized at the magic angle, 54.7 degrees, from the bleach polarization direction is independent of label orientation, whereas the anisotropy function formed from a combination of parallel and perpendicular polarizations isolates the orientational recovery. The anisotropy function is identical to that in fluorescence correlation spectroscopy and, for rigid-body rotational diffusion, can be expressed as a sum of five exponential terms.     

Diffusive properties of water in Artemia cysts as determined from quasi-elastic neutron scattering spectra.

Results have been obtained on the quasi-elastic spectra of neutrons scattered from pure water, a 20% agarose gel (hydration four grams H2O per gram of dry solid) and cysts of the brine shrimp Artemia for hydrations between 0.10 and 1.2 grams H2O per gram of dry solids. The spectra were interpreted using a two-component model that included contributions from the covalently bonded protons and the hydration water, and a mobile water fraction. The mobile fraction was described by a jump-diffusion correlation function for the translation motion and a simple diffusive orientational correlation function. The results for the line widths gamma (Q2) for pure water were in good agreement with previous measurements. The agarose results were consistent with NMR measurements that show a slightly reduced translational diffusion for the mobile water fraction. The Artemia results show that the translational diffusion coefficient of the mobile water fraction was greatly reduced from that of pure water. The line width was determined mainly by the rotational motion, which was also substantially reduced from the pure water value as determined from dielectric relaxation studies. The translational and rotational diffusion parameters were consistent with the NMR measurements of diffusion and relaxation. Values for the hydration fraction and the mean square thermal displacement [u2] as determined from the Q-dependence of the line areas were also obtained.     

Integration of Semi-Circular Canal and Otolith Cues for Direction Discrimination during Eccentric Rotations

Humans are capable of moving about the world in complex ways. Every time we move, our self-motion must be detected and interpreted by the central nervous system in order to make appropriate sequential movements and informed decisions. The vestibular labyrinth consists of two unique sensory organs the semi-circular canals and the otoliths that are specialized to detect rotation and translation of the head, respectively. While thresholds for pure rotational and translational self-motion are well understood surprisingly little research has investigated the relative role of each organ on thresholds for more complex motion. Eccentric (off-center) rotations during which the participant faces away from the center of rotation stimulate both organs and are thus well suited for investigating integration of rotational and translational sensory information. Ten participants completed a psychophysical direction discrimination task for pure head-centered rotations, translations and eccentric rotations with 5 different radii. Discrimination thresholds for eccentric rotations reduced with increasing radii, indicating that additional tangential accelerations (which increase with radius length) increased sensitivity. Two competing models were used to predict the eccentric thresholds based on the pure rotation and translation thresholds: one assuming that information from the two organs is integrated in an optimal fashion and another assuming that motion discrimination is solved solely by relying on the sensor which is most strongly stimulated. Our findings clearly show that information from the two organs is integrated. However the measured thresholds for 3 of the 5 eccentric rotations are even more sensitive than predictions from the optimal integration model suggesting additional non-vestibular sources of information may be involved.     

Negative Geotactic Behavior of Paramecium Caudatum is Completely Described by the Mechanism of Buoyancy-Oriented Upward Swimming

This paper presents evidence that the negative geotactic behavior of Paramecium caudatum takes place by the mechanism of buoyancy-oriented upward swimming. Photographs of swimming pathways of the organisms were completely described by two dynamic equations for the translational motion of the center of gravity of the organism's body and for the rotational motion of the organism's body about its center of gravity, where the rotational torque is induced by a slight difference in position between the center of gravity and the center of buoyancy. It now seems unlikely that complicated mechanisms such as the statocyst mechanism and the gravity-propulsion mechanism, which have been proposed by many investigators, need be considered for other protozoa since preliminary observation and analysis of other ciliates such as Paramecium multimicronucleatum, Paramecium tetraurelia, and Tetrahymena pyriformis also strongly suggested that their negative geotaxis is due to buoyancy-oriented upward swimming.     

Translational and Rotational Diffusion Constants of Tobacco Mosaic Virus from Rayleigh Linewidths

The translational and rotational diffusion constants of tobacco mosaic virus (TMV) have been determined from homodyne and heterodyne measurements of the spectrum of laser light scattered from dilute aqueous solutions of TMV. Our results for the translational and rotational constants respectively, reduced to 20 degrees C, are: D(T) = 0.280 +/- 0.006 x 10(-7) cm(2)/sec, and D(R) = 320 +/- 18 sec(-1). We include a theoretical derivation of the spectrum of light scattered from rod-shaped molecules which reproduces results obtained previously by Pecora, but which is specialized at the outset to the problem of dilute solutions so that simple single-particle correlation functions may be utilized. An analysis of the photocurrent spectrum for both the homodyne and heterodyne detection schemes is given. Various data reduction schemes utilized in the analysis of our spectra are described in some detail, and our results are compared with values of the diffusion constants obtained from other experiments.     

Contribution of changes in translational, rotational, and vibrational degrees of freedom to the energy of complex formation of aromatic ligands with DNA

A method for calculation and analysis of the contribution of changes in translational, rotational, and vibrational degrees of freedom to the energy of complex formation of aromatic compounds with DNA duplex has been developed. The results of calculations of the thermodynamic parameters (ΔG, ΔH, ΔS) indicate that changes in the translational and rotational degrees of freedom destabilize, and changes in the vibrational degree of freedom stabilize the complexes, the energy contribution from the movements under consideration being predominantly of entropic character. It is shown that the energy components of changes in translational, rotational, and vibrational degrees of freedom are in the main comparable with the experimentally determined thermodynamic parameters, which requires consideration of these components in the energy analysis of complex formation of aromatic molecules with DNA. It has been found that the total contribution of changes in translational, rotational, and vibrational degrees of freedom to the Gibbs energy of complexing of aromatic molecules with DNA can be assumed to be on the average the same for different ligands and equal to 8.2 kcal/mol.     

Bending and flexibility of kinetoplast DNA

We have evaluated the extent of bending at an anomalous locus in DNA restriction fragments from the kinetoplast body of Leishmania tarentolae using transient electric dichroism to measure the rate of rotational diffusion of DNA fragments in solution. We compare the rate of rotational diffusion of two fragments identical in sequence except for circular permutation, which places the bend near the center in one case and near one end of the molecule in the other. Hydrodynamic theory was used to conclude that the observed 20% difference in rotational relaxation times is a consequence of an overall average bending angle of 84 +/- 6 degrees between the end segments of the fragment that contains the bending locus near its center. If it is assumed that bending results from structural dislocations at the junctions between oligo(dA).oligo(dT) tracts and adjacent segments of B DNA, a bend angle of 9 +/- 0.5 degrees at each junction is required to explain the observations. The extent of bending is little affected by ionic conditions and is weakly dependent on temperature. Comparison of one of the anomalous fragments with an electrophoretically normal control fragment leads to the conclusion that they differ measurably in apparent stiffness, consistent with a significantly increased persistence length or contour length in the kinetoplast fragments.     

Kinetics of nanochain formation in a simplified model of amelogenin biomacromolecules

We show that the kinetics of nanochain formation of amelogenin molecules is well described by a combination of translational and rotational diffusion of a simplified anisotropic bipolar model consisting of hydrophobic spherical colloid particles and a point charge located on each particle surface. The colloid particles interact via a standard depletion attraction whereas the point charges interact through a screened Coulomb repulsion. We study the kinetics via a Brownian dynamics simulation of both translational and rotational motions and show that the anisotropy brought in by the charge dramatically affects the kinetic pathway of cluster formation and our simple model captures the main features of the experimental observations.     

Theory of the rotational contribution to facilitated diffusion

Gros and others have recently shown experimentally that the facilitated diffusion of protons carried by a form of haemoglobin is enhanced by rotational diffusion of the carrier, whereas facilitated diffusion of oxygen by the same carrier is not. In this paper the theory of facilitated transport by rotating carriers is developed from first principles. The theory confirms Gros's findings that (i) the rotational contribution appears only when the angle of rotational diffusion over the average time the proton remains bound is small and (ii) under these conditions rotation enhances the normal translational contribution by a factor 1/2 at the lowest carrier concentrations. The theory also shows that there must be a rotational boundary layer.     

Orientational exchange approach to fluorescence anisotropy decay.

Fluorescence depolarization is a powerful technique in resolving dynamics of molecular systems. Data obtained in fluorescence depolarization experiments are highly complex. Mathematical models for analyzing data from depolarization due to rotational motion have been largely based on the rotational diffusion equation. These results have been verified by Monte Carlo simulations. It has been implicitly stated that a 90 degrees jump model between predefined orientations such as presented by G. Weber (1971. J. Chem. Phys. 55:2399-2411) should, for the specific case of fluorescence depolarization, give the same answer as the diffusion equation. Since the highly symmetric cases considered by G. Weber gave the same result as the diffusion equation, it has been desirable to use this method in cases where depolarization arises from both discrete processes and rotational diffusion. We have derived, in a compartmental formalism, the general result for excitation and emission dipoles not necessarily coincident with any of the principal rotational axes of the fluorophore from this exchange model, and have found it to be different from that of the diffusion equation approach. We have also verified this difference with a Monte Carlo simulation of our exchange model. This derivation allows us to define the limits of validity of the 90 degrees exchanges to model rotational diffusion. Also, for systems where movements may be jumps between a few preferred orientations, the actual physical mechanism of depolarization may not be accurately represented by continuous diffusion. The compartmental formalism developed here can be used to easily combine rotational motions with discrete position jumps or other level kinetics.(ABSTRACT TRUNCATED AT 250 WORDS)     

Temporal Statistics of Natural Image Sequences Generated by Movements with Insect Flight Characteristics

Many flying insects, such as flies, wasps and bees, pursue a saccadic flight and gaze strategy. This behavioral strategy is thought to separate the translational and rotational components of self-motion and, thereby, to reduce the computational efforts to extract information about the environment from the retinal image flow. Because of the distinguishing dynamic features of this active flight and gaze strategy of insects, the present study analyzes systematically the spatiotemporal statistics of image sequences generated during saccades and intersaccadic intervals in cluttered natural environments. We show that, in general, rotational movements with saccade-like dynamics elicit fluctuations and overall changes in brightness, contrast and spatial frequency of up to two orders of magnitude larger than translational movements at velocities that are characteristic of insects. Distinct changes in image parameters during translations are only caused by nearby objects. Image analysis based on larger patches in the visual field reveals smaller fluctuations in brightness and spatial frequency composition compared to small patches. The temporal structure and extent of these changes in image parameters define the temporal constraints imposed on signal processing performed by the insect visual system under behavioral conditions in natural environments.