Effect Of Rotational Diffusion Research Articles

Strongly enhanced dynamics of a charged Rouse dimer by an external magnetic field.

While the dynamics of dimers and polymer chains in a viscous solvent is well understood within the celebrated Rouse model, the effect of an external magnetic field on the dynamics of a charged chain is much less understood. Here, we generalize the Rouse model for a charged dimer to include the effect of an external magnetic field. Our analytically solvable model allows a fundamental insight into the magneto-generated dynamics of the dimer in the overdamped limit as induced by the Lorentz force. Surprisingly, for a dimer of oppositely charged particles, we find an enormous enhancement of the dynamics of the dimer center, which exhibits even a transient superballistic behavior. This is highly unusual in an overdamped system for there is neither inertia nor any internal or external driving. We attribute this to a significant translation and rotation coupling due to the Lorentz force. We also find that magnetic field reduces the mobility of a dimer along its orientation and its effective rotational diffusion coefficient. In principle, our predictions can be tested by experiments with colloidal particles and complex plasmas.

Microscopic diffusion coefficients of dumbbell- and spherocylinder-shaped colloids and their application in simulations of crowded monolayers.

We explore the diffusion properties of colloidal particles with dumbbell and spherocylinder shapes using a hydrodynamic bead-shell approach and additional Brownian dynamics (BD) simulations. By applying the bead-shell method, we determine empirical formulas for the microscopic diffusion coefficients. A comparison of these formulas and established experimental and theoretical results shows remarkable agreement. For example, the maximum relative discrepancy found for dumbbells is less than 5%. As an application example of the empirical formulas, we perform two-dimensional (2D) BD simulations based on a single dumbbell or spherocylinder in a suspension of spheres and calculate the resulting effective long-time diffusion coefficients. The performed BD simulations can be compared to quasi-2D systems such as colloids confined at the interface of two fluids. We find that the effective diffusion coefficient of translation mostly depends on the sphere area fraction ϕ, while the effective diffusion coefficient of rotation is influenced by the aspect ratio and ϕ. Furthermore, the effective rotational diffusion constant seems to depend on the particle shape with the corresponding implementation of the interactions. In the resolution limit of our methods, the shape-dependent differences of the microscopic diffusion coefficients and the long-time diffusion constant of translation are negligible in the first approximation. The determined empirical formulas for the microscopic diffusion coefficients add to the knowledge of the diffusion of anisotropic particles, and they can be used in countless future studies.

Diffusion of skyrmions: the role of topology and anisotropy

We study the diffusive motion of metastable localized spin structures with various topological charges by combining atomistic spin model simulations with an extension to the Thiele equation taking into account translational and rotational degrees of freedom. The Brownian motion of skyrmions is shown to obey markedly different diffusion laws depending on their topological properties. We demonstrate that skyrmions with topological charges Q = −1 and Q = 0 exhibit anisotropic translational diffusion due to their non-circular shape. The coupling between rotational and translational Brownian motion, however, causes memory of the initial orientation to be lost on a timescale governed by the effective rotational diffusion coefficient, ultimately leading to isotropic diffusion in the long time limit.

Active particles with fractional rotational Brownian motion

We study the two-dimensional overdamped motion of an active particle whose orientational dynamics is subject to fractional Brownian noise, whereas its position is affected by self-propulsion and Brownian fluctuations. From a Langevin-like model of active motion with constant swimming speed, we derive the corresponding Fokker–Planck equation, from which we find the angular probability density of the particle orientation for arbitrary values of the Hurst exponent that characterizes the fractional rotational noise. We provide analytical expressions for the velocity autocorrelation function and the translational mean-squared displacement, which show that active diffusion effectively emerges in the long-time limit for all values of the Hurst exponent. The corresponding expressions for the active diffusion coefficient and the effective rotational diffusion time are also derived. Our results are compared with numerical simulations of active particles with rotational motion driven by fractional Brownian noise, with which we find an excellent agreement.

EPR SPECTROSCOPY STUDIES OF CHANGES IN ERYTHROCYTE MEMBRANES IN PATIENTS WITH LARYNGEAL CANCER

To evaluate microviscosity and sorption capacity of erythrocyte membranes (SCEM) from patients with laryngeal cancer (LC). Samples from 35 patients with LC of stages II and III and 20 healthy volunteers were investigated by electron paramagnetic resonance with Bis(1-oxyl-2,2,6,6-tetramethylpiperidinyl-4)-ester of 5,7-dimethyladamantane-1,3-dicarbonic acid (AdTEMPO) probe. SCEM was evaluated by amount of unabsorbed methylene blue. Microviscosity of erythrocyte membranes was determined by the effective rotational diffusion correlation times (τeff) and a decrease in radical spectrum signal intensity per hour. The most apparent decrease in mobility of the AdTEMPO in erythrocytes was observed prior to washing of erythrocytes with 0.9% NaCl for 5 min after probe insertion. The deceleration after 60 min was observed only in stage II LC. τeff was at control values after washing of erythrocytes of stage II LC 5 min after probe insertion and was significantly reduced in stage III LC in comparison to control. Radical spectrum signal intensity per hour in samples of stage II and III patients prior to and after washing of erythrocytes was on average 1.5-fold higher than that of control. SCEM in samples of stage II and III LC was found in 40 and 33% cases, respectively and was on average significantly reduced in comparison to control. The initial interaction of AdTEMPO with erythrocyte membranes of stage II and III LC patients is accompanied by an increase in τeff, indicating deceleration of probe rotation. τeff of the probe in membranes remains unchanged in 60 min, indicating changes in the structural organization of lipid bilayer and its associated proteins in particular. The similarity of SCEM for both studied groups reflects the pathological changes in function of erythrocyte membranes.

Anomalous dielectric relaxation with linear reaction dynamics in space-dependent force fields.

The anomalous dielectric relaxation of disordered reaction with linear reaction dynamics is studied via the continuous time random walk model in the presence of space-dependent electric field. Two kinds of modified reaction-subdiffusion equations are derived for different linear reaction processes by the master equation, including the instantaneous annihilation reaction and the noninstantaneous annihilation reaction. If a constant proportion of walkers is added or removed instantaneously at the end of each step, there will be a modified reaction-subdiffusion equation with a fractional order temporal derivative operating on both the standard diffusion term and a linear reaction kinetics term. If the walkers are added or removed at a constant per capita rate during the waiting time between steps, there will be a standard linear reaction kinetics term but a fractional order temporal derivative operating on an anomalous diffusion term. The dielectric polarization is analyzed based on the Legendre polynomials and the dielectric properties of both reactions can be expressed by the effective rotational diffusion function and component concentration function, which is similar to the standard reaction-diffusion process. The results show that the effective permittivity can be used to describe the dielectric properties in these reactions if the chemical reaction time is much longer than the relaxation time.

Dynamics of Self-Propelled Janus Particles in Viscoelastic Fluids.

We experimentally investigate active motion of spherical Janus colloidal particles in a viscoelastic fluid. Self-propulsion is achieved by a local concentration gradient of a critical polymer mixture which is imposed by laser illumination. Even in the regime where the fluid's viscosity is independent of the deformation rate induced by the particle, we find a remarkable increase of up to 2 orders of magnitude of the rotational diffusion with increasing particle velocity, which can be phenomenologically described by an effective rotational diffusion coefficient dependent on the Weissenberg number. We show that this effect gives rise to a highly anisotropic response of microswimmers in viscoelastic media to external forces, depending on its orientation.

Spin-Labeled Small Unilamellar Vesicles with the T 1-Sensitive Saturation-Recovery EPR Display as an Oxygen-Sensitive Analyte for Measurement of Cellular Respiration

This study validated the use of small unilamellar vesicles (SUVs) made of 1-palmitoyl-2-oleoylphosphatidylcholine with 1 mol% spin label of 1-palmitoyl-2-(16-doxylstearoyl)phosphatidylcholine (16-PC) as an oxygen sensitive analyte to study cellular respiration. In the analyte the hydrocarbon environment surrounds the nitroxide moiety of 16-PC. This ensures high oxygen concentration and oxygen diffusion at the location of the nitroxide as well as isolation of the nitroxide moiety from cellular reductants and paramagnetic ions that might interfere with spin-label oximetry measurements. The saturation-recovery EPR approach was applied in the analysis since this approach is the most direct method to carry out oximetric studies. It was shown that this display (spin-lattice relaxation rate) is linear in oxygen partial pressure up to 100% air (159 mmHg). Experiments using a neuronal cell line in suspension were carried out at X-band for closed chamber geometry. Oxygen consumption rates showed a linear dependence on the number of cells. Other significant benefits of the analyte are: the fast effective rotational diffusion and slow translational diffusion of the spin-probe is favorable for the measurements, and there is no cross reactivity between oxygen and paramagnetic ions in the lipid bilayer.

Effect of rotational diffusion in an orientational potential well on the point spread function of electric dipole emitters.

A study is presented of the point spread function (PSF) of electric dipole emitters that go through a series of absorption-emission cycles while the dipole orientation is changing due to rotational diffusion within the constraint of an orientational potential well. An analytical expression for the PSF is derived valid for arbitrary orientational potential wells in the limit of image acquisition times much larger than the rotational relaxation time. This framework is used to study the effects of the direction of incidence, polarization, and degree of coherence of the illumination. In the limit of fast rotational diffusion on the scale of the fluorescence lifetime the illumination influences only the PSF height, not its shape. In the limit of slow rotational diffusion on the scale of the fluorescence lifetime there is a significant effect on the PSF shape as well, provided the illumination is (partially) coherent. For oblique incidence, illumination asymmetries can arise in the PSF that give rise to position offsets in localization based on Gaussian spot fitting. These asymmetries persist in the limit of free diffusion in a zero orientational potential well.

Random walk patterns of a soil bacterium in open and confined environments

We used microfluidic tools and high-speed time-lapse microscopy to record trajectories of the soil bacterium Pseudomonas putida in a confined environment with cells swimming in close proximity to a glass-liquid interface. While the general swimming pattern is preserved, when compared to swimming in the bulk fluid, our results show that cells in the presence of two solid boundaries display more frequent reversals in swimming direction and swim faster. Additionally, we observe that run segments are no longer straight and that cells swim on circular trajectories, which can be attributed to the hydrodynamic wall effect. Using the experimentally observed parameters together with a recently presented analytic model for a run-reverse random walker, we obtained additional insight on how the spreading behavior of a cell population is affected under confinement. While on short time scales, the mean square displacement of confined swimmers grows faster as compared to the bulk fluid case, our model predicts that for large times the situation reverses due to the strong increase in effective rotational diffusion.

Modeling E. coli Tumbles by Rotational Diffusion. Implications for Chemotaxis

The bacterium Escherichia coli in suspension in a liquid medium swims by a succession of runs and tumbles, effectively describing a random walk. The tumbles randomize incompletely, i.e. with a directional persistence, the orientation taken by the bacterium. Here, we model these tumbles by an active rotational diffusion process characterized by a diffusion coefficient and a diffusion time. In homogeneous media, this description accounts well for the experimental reorientations. In shallow gradients of nutrients, tumbles are still described by a unique rotational diffusion coefficient. Together with an increase in the run length, these tumbles significantly contribute to the net chemotactic drift via a modulation of their duration as a function of the direction of the preceding run. Finally, we discuss the limits of this model in propagating concentration waves characterized by steep gradients. In that case, the effective rotational diffusion coefficient itself varies with the direction of the preceding run. We propose that this effect is related to the number of flagella involved in the reorientation process.

Rotational diffusion may govern the rheology of magnetic suspensions

This paper is focused on the theoretical modeling of the rheological properties of the magnetic suspensions in shear flows under an external magnetic field aligned with the streamlines. The conventional theory postulates that the field-induced aggregates of magnetic particles are highly anisotropic and aligned with the flow direction. Therefore, no substantial variation in suspension viscosity would be expected in the presence of field. However, experiments reveal a strong Bingham rheological behavior of the suspensions with a dynamic yield stress of the same order of magnitude that the one measured in the magnetic fields perpendicular to the flow. We explain the high level of shear stress, generated in longitudinal magnetic fields, by stochastic rotary oscillations of the aggregates caused by many-body magnetic interactions with neighboring aggregates. The interaggregate interactions are accounted for by an effective rotational diffusion process with a diffusion constant proportional to the mean square interaction torque—a net magnetic torque exerted to a given aggregate by all the neighboring aggregates. Using the equations for the orientation tensors coupled with the balance of forces acting on aggregates, we find the orientation distribution and size of the aggregates as function of the magnetic field intensity and shear rate. Our theory, developed for semidilute regime, reproduces the Bingham behavior observed experimentally and fits the experimental data reasonably well in a wide range of particle concentrations. We find that the yield stress increases quadratically with the magnetic field strength and exhibits a cubic growth with respect to the particle volume fraction. A part from resolving a particular rheological problem, the new concept of magnetically induced diffusion reveals the importance of long-range nonhydrodynamic interactions in the rotary diffusion process and could probably contribute to the understanding of this process in other concentrated systems subject to nonhydrodynamic interactions.

Magnetoviscosity of dilute suspensions of magnetic ellipsoids obtained through rotational Brownian dynamics simulations

The magnetic field dependent viscosity (magnetoviscosity) of dilute suspensions of magnetic tri-axial ellipsoidal particles suspended in a Newtonian fluid and under applied shear and magnetic fields was studied numerically. Brownian dynamics simulations were performed to compute the intrinsic magnetoviscosity of the suspension. Results are presented for the response of dilute suspensions of ellipsoidal particles to constant magnetic and shear flow fields. Suspensions of ellipsoidal particles show a significant effect of aspect ratio on the intrinsic magnetoviscosity of the suspension, and this effect is more pronounced as the aspect ratio becomes more extreme. The use of an effective rotational diffusion coefficient D r , eff collapses the normalized intrinsic magnetoviscosity of all suspensions to a master curve as a function of Péclet number with the Langevin parameter α = ( μ 0 μ H ) / ( k B T ) as parameter, up to a critical value of α for which the results for suspensions of spherical particles deviate from those of suspensions of ellipsoids. This discrepancy is attributed to the action of the shear-torque on the ellipsoidal particles, which tends to orient these particles in the direction of maximum deformation of the simple shear flow, and which does not act on spherical particles.

Study of the rotational diffusivity coefficient of fibres in planar contracting flows with varying turbulence levels

The Fokker–Planck equation is solved by describing the evolution of a 3D fibre orientation state along a planar contraction. A constant value of the effective rotational diffusion coefficient was determined for four different turbulent flow cases in planar contractions, reported experimentally in the literature. Two hypotheses for the non-dimensional rotational diffusivity are presented, each based on two different turbulent time scales, i.e. the Kolmogorov time scales and the time scale associated with large energy bearing eddies. These hypotheses are dependent on either the Reynolds number, based on the Taylor micro-scale, and/or a non-dimensional fibre length. The hypothesis, based on the assumption of long fibres, L f / η ≳ 25 , compared to the Kolmogorov scale and in the limit of large Re λ seems to capture the basic trends presented in the literature. This hypothesis has also the feature of predicting effects of varying fibre length within certain limits. Accordingly, by modeling the variation of turbulent quantities along the contraction in a CFD analysis, local values of rotational diffusivity can be evaluated with the mentioned hypothesis, based on either Kolmogorov time scale or Eulerian integral time scale.

Glass transition in systems without static correlations: a microscopictheory

We present a first step toward a microscopic theory for the glass transition insystems with trivial static correlations. As an example we have chosenN infinitely thin hardrods with length L,fixed with their centres on a periodic lattice with lattice constanta. Startingfrom the N-rodSmoluchowski equation we derive a coupled set of equations for fluctuations of reducedk-roddensities. We approximate the influence of the surrounding rods on the dynamics of a pairof rods by introduction of an effective rotational diffusion tensor D(Ω1, Ω2)and in this way we obtain a self-consistent equation for D.This equation exhibits a feedback mechanism leading to a slowing down ofthe relaxation. It involves as an input the Laplace transform υ0 (l/r)at z = 0,l = L/a,of a torque–torque correlator of an isolated pair of rods with distanceR = ar. Ourequation predicts the existence of a continuous ergodicity-breaking transition at a criticallength lc = Lc /a.To estimate the critical length we perform an approximate analytical calculation of υ0 (l/r)based on a variational approach and obtain lcvar ∼ = 5.68,4.84 and 3.96 for an sc, bcc and fcc lattice. We also evaluate υ0 (l/r) numericallyexactly from a two-rod simulation. The latter calculation leads to lcnum ∼ = 3.45,2.78 and 2.20 for the corresponding lattices. Close tolcthe rotational diffusion constant decreases as D(l) ∼ (lc − l)γ withγ = 1and a diverging timescale tϵ ∼ |lc − l|−δ, δ = 2, appears. Onthis timescale the t-and l-dependenceof the one-rod density is determined by a master function depending only on t/tϵ. Incontrast to present microscopic theories our approach predicts a glass transitiondespite the absence of any static correlations.

Segmental Rotational Diffusion of Spin-Labeled Polystyrene in Dilute Toluene Solution by 9 and 250 GHz ESR

A copolymer of styrene containing less than 5 mol % of chain units spin-labeled by attachment of the nitroxide via a short tether has been synthesized. ESR spectra of dilute toluene solution of the copolymer have been obtained using 9 and 250 GHz ESR. Parameters characterizing polystyrene segmental rotational diffusion in toluene solution over a broad temperature range have been determined from nonlinear least-squares fits of theoretical ESR spectra to the experimental ESR spectra. The model used was that of relatively fast internal rotation of the nitroxide about its tether, with slower polymer chain segmental motion. Together they lead to effective rotational diffusion with an anisotropic diffusion tensor. In addition, constraints in the form of an orientational potential restrict the range of angles over which this diffusion occurs relative to the polymer backbone, and the latter is assumed to reorient on an ultraslow time scale. This is referred to as a model of microscopic order but macroscopic disorder (MOMD). Rates for the slower polymer chain segmental motion (from the 250 GHz spectra) ranged from 3.6 × 108 s-1 at 311 K to 0.15 × 108 s-1 at 215 K, with a substantial orientational potential of about 2kT over this temperature range. Although there was reasonable agreement between the results obtained at 9 and 250 GHz, there were systematic discrepancies such that the orienting potentials obtained from the 250 GHz spectra were about twice (or more) those from the 9 GHz spectra, and the rotational diffusion tensor components from the 250 GHz spectra were at least twice those from the 9 GHz spectra. This implies a breakdown of the MOMD model for the 9 GHz spectra presumably due to their sensitivity to the slower overall tumbling motion at this low spectral frequency. For the faster “time scale” of the 250 GHz spectra, such a slow motion is “frozen out”, rendering these spectra consistent with the MOMD model. Nevertheless, the results at both frequencies yielded a common activation energy, Eexp = 20.7 ± 1.5 kJ/mol, which, when corrected for the viscous flow contribution, yielded an Ea = 11.9 ± 1.5 kJ/mol, which is in good agreement with recent results from fluorescence studies.

The structure of streptonigrin semiquinone in solution

Streptonigrin semiquinone (SQ ·), a free radical intermediate implicated in the biological functioning of the antitumor antibiotic streptonigrin has been prepared and its structural properties in solution have been characterized. Through the use of electron paramagnetic resonance spectroscopy, the spin densities of the unpaired electron have been determined, indicating that the unpaired electron is largely confined to the quinolinesemiquinone moiety of the antibiotic. Unambiguous assignment of the hyperfine coupling constants was achieved employing isotopically labeled semiquinone radical, INDO molecular orbital calculations, and the study of unsubstituted 5,8-quinolinesemiquinone as a reference system. The assignments point to a negative spin density at the carbon para to the pyridine nitrogen in the radicals derived from both streptonigrin and the unsubstituted 5,8-quinolinequinone. Characterization of the properties of the streptonigrin semiquinone in solution indicate that the radical is stable in solution: it can be conveniently studied in 0.1 M methanolic lithium hydroxide or in aqueous organic solvent mixtures buffered with 0.06 M K 3PO 4 at pH 12.0. Under these conditions, the semiquinone shows completely reversible spectral changes between −10 to 60°C. Lowering the pH from 12.0 to 7.0 in aqueous DMSO decreases the lifetime of the radical from two weeks to a few minutes. Changes in structural properties of streptonigrin semiquinone in solution have been found to occur mainly due to variation in solvation and freedom of rotation of the amino group. Decreasing the temperature of SQ · solution in methanol from 60 to −10°C leads to an increase in the hyperfine coupling constant to the amino nitrogen from 1.28 to 1.40 G, and those of the two amino protons from 0.73 and 0.73 to 1.02 and 1.11 G respectively, while the other coupling constants change less than 3%. Greater electron spin delocalization onto the -NH 2 group has been found throughout the solvent systems examined, yet the temperature at which the two amino protons become equivalent changes with the nature of the solvent (e.g., from 25°C in MeOH to 40°C in aq. DMSO). The effective rotational diffusion constant as measured from EPR spectra in a series of solvents with fixed polarity ( E T) follows the Stokes–Einstein equation only in solvent mixtures of low to moderate viscosities (10–12.4 cP) suggesting that in addition to the viscosity of the medium a more specific mechanism (e.g., hydrogen bonding to the solvent) restricts the motion of the amino group. This hydrogen bonding mechanism is further supported by the fact that the degree of inequivalence in the amino proton hyperfine coupling constants varies monotonically with the spin density at the amino nitrogen. Studies of SQ · in aqueous micellar dispersions using neutral, cationic, and anionic sufractants indicate that SQ · is located at the surface of these aggregates. The structure of SQ · changes little at neutral and anionic micellar surfaces; however, more severe structural changes occur in cationic micelles which appear to be consistent with a conformational change induced by the positively charged surface.

Observation of Lateral Diffusion in Biomembranes by Excitation Transfer 31P NMR: Estimation of Vesicle Size Distributions

An excitation transfer 31P NMR experiment is described which directly measures translationally induced rotation of lipid molecules in large membrane vesicles. The experiment involves selective excitation of a small subset of the lipid molecules whose axially symmetric chemical shift tensors are oriented at approximately 90° to the magnetic field. Line shapes due only to the selected molecules are then recorded as a function of the mixing time. The spectra directly reflect the time dependent orientational distribution of lipid molecules and may be analyzed in terms of the distribution of effective rotational diffusion constants, related analytically to the distribution of vesicle radii. Employing this 31P NMR method, size distributions have been evaluated for multilamellar vesicles of dimyristoylphosphatidylcholine (DMPC) and DMPC/1.12% (mol/mol) bovine rhodopsin. In both cases the radius distributions are extremely broad, spanning more than 2 orders of magnitude in the case of the pure DMPC vesicles.

Fluctuations in rotation rate of the flagellar motor of Escherichia coli

The purpose of this work was to study the changes in rotation rate of the bacterial motor and to try to discriminate between various sources of these changes with the aim of understanding the mechanism of force generation better. To this end Escherichia coli cells were tethered and videotaped with brief stroboscopic light flashes. The records were scanned by means of a computerized motion analysis system, yielding cell size, radius of rotation, and accumulated angle of rotation as functions of time for each cell selected. In conformity with previous studies, fluctuations in the rotation rate of the flagellar motor were invariably found. Employing an exclusively counterclockwise rotating mutant ("gutted" RP1091 strain) and using power spectral density, autocorrelation and residual mean square angle analysis, we found that a simple superposition of rotational diffusion on a steady rotary motion is insufficient to describe the observed rotation. We observed two additional rotational components, one fluctuating (0.04-0.6 s) and one oscillating (0.8-7 s). However, the effective rotational diffusion coefficient obtained after taking these two components into account generally exceeded that calculated from external friction by two orders of magnitude. This is consistent with a model incorporating association and dissociation of force-generating units.

Continuum model of voltage-dependent gating. Macroscopic conductance, gating current, and single-channel behavior

It is assumed that the conformational change of the voltage-gated channel is continuous, characterized by movement along a generalized one-dimensional reaction coordinate, x, varying from 0 to 1. This large conformational change is coupled to the movement of most of the gating charge. Superimposed on this large movement is a smaller, very fast conformational change that opens or closes the channel. The large conformational change perturbs the channel so that opening is favored near x = 1 and closing is favored near x = 0. The movement along the x axis is described by a generalized Nernst-Planck equation, whereas the open-close transition is modeled as a discrete reaction-rate process. The macroscopic conductance, gating current, and single-channel behavior of a simple, linearized version of the model is described. Although the model has only seven adjustable constants (about the same as would be required for a conventional three-state model), it can mimic the behavior of the delayed rectified K+ channel with 12 or more closed states. The single-channel behavior of the model can have bursts of rapid openings and closings, separated by long closed times. If the conformational change is assumed to correspond to the rotation and translation of charged helices, then this model can be used to estimate the effective rotational diffusion coefficient of the helix. Such calculations for the delayed rectifier K+ channel indicate that the motion must be very restricted.