Brownian dynamics simulation of electrostatically interacting proteins

Brownian dynamics simulation software has been developed to study the dynamics of proteins as a whole in solution. The proteins were modelled as spheres with point dipoles embedded in the centre of sphere. A set of Brownian dynamics simulations at different values of the dipole moments, protein concentration and translational diffusion coefficient was performed to investigate the influence of interprotein electrostatic interactions on dynamic protein behaviour in solution. It was shown that these interactions led to the slowing down of protein rotation and a complex non-exponential shape of the rotational correlation function. Analysis of the correlation functions was performed within the frame of the model of electrostatic interprotein interactions advanced earlier on the basis of NMR and dielectric spectroscopy data. This model assumes that, due to electrostatic interactions, protein Brownian rotation becomes anisotropic. The lifetime of this anisotropy is controlled mainly by translational diffusion of proteins. Thus, the correlation function can be decomposed into two components corresponding to anisotropic Brownian rotation and an isotropic motion of an external electric field vector produced by the surrounding proteins.     

Bacterial chemotaxis: A survey

Chemotactic bacteria likeE. coli respond to chemical gradients. The translational movements of individual cells can be traced. These are coupled to the rotation of the cell body. Both types of motions are regular in temporal attractant or repellent gradients. A corresponding regularity is observed for bacterial populations in spatial gradients. The distribution of a bacterial population is space and time may be described by a diffusion equation linked to the motions of single cells.     

A Depolarized Dynamic Light Scattering Method to Calculate Translational and Rotational Diffusion Coefficients of Nanorods

A new analysis of depolarized dynamic light scattering data is presented, which allows the unambiguous determination of rotational and translational diffusions coefficients of nanorods in suspension. By visualizing data scaling, purely translational diffusive motions can be isolated from vertically polarized scattering, allowing the unique determination of rotational diffusion from the depolarized scattering. The method is applied to nanorods with four different aspect ratios, and compared with theoretical predictions. Diffusion coefficients obtained show good agreement with calculations based on the direct measurements of rod length and diameter. Where the theories are shown to be valid, the method allows the measurement of statistically meaningful particle sizes and aspect ratios.     

Dipole moment and far infra-red absorption of quinuclidine (1-aza-bicyclo-[2-2-2]-octane)

Incoherent quasi-elastic neutron-scattering spectra have been measured on powder samples of D-BPBAC in its smectic E, B and A phases using the high-resolution backscattering technique. The data have been analysed in terms of translational diffusion and a localized rotational motion. It has been found that the apparent translational diffusion constant has a temperature dependent value of ～1 × 10^-6 cm² s^-1 in the smectic A phase but is smaller by at least an order of magnitude in the smectic B and E phases. Comparison of the widths of the rotational components of the spectra with other measurements suggests that simple rotational models are not adequate to explain the experimental data.     

The statistical correlation of intermolecular coriolis and centrifugal forces

Correlation functions are computed in the laboratory frame for the molecular coriolis and centrifugal forces with respect to a frame of reference static in the laboratory. The molecular Coriolis and centrifugal forces in this laboratory frame result from a combination of the molecule's rotational and translational motion, and correlate statistically these two types of motion. They are not usually considered in the theory of decoupled rotational or translational diffusion. Correlation functions are computed for the enantiomers and racemic mixture of liquid bromochlorofluoromethane, and for dichloromethane liquid subjected to a strong, uniaxial, electric field of force in the z axis of the laboratory frame.     

Evaluation of the translational and rotational diffusion coefficients of a cubic particle (for the application to Brownian dynamics simulations)

By estimating the force and torque acting on the cube for the two cases of a uniform flow field and a rotational flow field, we have discussed whether or not there is a coupling between the translational and the rotational motion. From the characteristics of the friction coefficients, we may understand that there is no coupling between the translation motion and the rotational motion in the situation of the Reynolds number being sufficiently smaller than unity. In contrast, in the case of a non-slow flow field with the Reynolds number larger than unity, the coupling characteristics of the motion of a cube is certainly recognised and therefore the interaction with the ambient fluid is characterised by a variety of friction coefficients including friction coefficients that relate the forces acting on the cube to the angular velocities of the rotational motion. Hence, the employment of these translational and rotational diffusion coefficients for a cube enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles in order to analyse the dynamic characteristics of a cubic particle suspension.

Highlights

1. We have considered a flow problem around a cube in order to numerically clarify the characteristics of the translational and rotational friction or diffusion coefficients.

2. In a slow flow field the motion of the cube need only to be characterised by two friction coefficients, i.e. the translational and rotational friction coefficients.

3. In the case of a non-slow flow field, the coupling characteristics between the translational motion and the rotational motion are recognised.

4. Employment of these diffusion coefficients enables the implementation of Brownian dynamics simulations for a suspension composed of cubic particles.

     

Translational and rotational diffusion of an anisotropic particle in a molecular liquid: Long-time tails and Brownian limit

Formally exact equations are written down, describing the translational and rotational diffusion of an anisotropic tagged particle in a fluid of anisotropic particles. These equations are tractable in the long-time limit, and reduce to the solution of ordinary hydrodynamic equations supplemented by slip boundary conditions in the Brownian limit for a smooth tagged particle. No rotational viscosities or spin-diffusion constants appear in these results. The relation to other work is discussed.     

The effects of chain segment motion on ionic diffusion in solid polymer electrolytes

The “vehicular effects” of chain segment motion on ionic diffusion in solid polymer electrolytes have been investigated via numerical simulation on a two-dimensional square lattice where the dynamical variation of chain configuration is presented by translational or rotational bond movement. It is found that (a) both types of bond motion promote continuous diffusion when the fraction (p) of available bonds is below the static percolation threshold of p=0.5 in two dimensions; (b) translational motion of bonds parallel to the direction of diffusion produces larger diffusion coefficients (D) than that by random renewal of the dynamic bond percolation model (DBPM), while the perpendicular motion or rotational motion gives smaller values of D; (c) Smooth lines instead of “stair-case like” curves generated by DBPM are obtained in the mean-squared displacement versus time plot, when bonds are shifting along the diffusion route. The dependence of diffusion coefficients on the variation of motion patterns of bonds is expected to be related to the temperature change under which these patterns are excited accordingly, such that VTF behavior of certain polymer electrolytes may be deduced.     

Simultaneous measurement of rotational and translational diffusion of anisotropic colloids with a new integrated setup for fluorescence recovery after photobleaching

This paper describes an integrated setup for fluorescence recovery after photobleaching (FRAP) for determining translational and rotational Brownian diffusion simultaneously, ensuring that these two quantities are measured under exactly the same conditions and at the same time in dynamic experiments. The setup is based on translational-FRAP with a fringe pattern of light for both the bleaching and monitoring of fluorescently labeled particles, and rotational-FRAP, which uses the polarization of a short bleach light pulse to create a polarization anisotropy. The fringe pattern of the probe beam is modulated in conjunction with a synchronized lock-in amplifier giving a fast, sensitive, ensemble-averaged measurement compared to microscope-image based techniques. The experimental polarization geometry we used ensures that the fluorescence emission is collected without polarization bias. Therefore, only the orientation of the absorption dipole moment of the fixed dye in the particles is measured, which simplifies interpretation of the data. The polarization is modulated rapidly between two orthogonal polarization states, giving the polarization anisotropy in one, single measurement. The rotational and translational Brownian diffusion of anisotropic colloids is measured for ellipsoids of revolution. This experiment shows that in this case the rotational correlation function matches a three-exponential decay in accordance with theoretical predictions.     

Theory of phonon linewidth in orientationally disordered crystals

The dynamics of coupled translational (T) and rotational (R) modes is studied with special reference to the experimental situation in the alkali cyanides. The dynamic equations are extended and, in addition to the bilinear T-R coupling, anharmonic interactions of the form T-T-R are considered. These interactions lead to additional friction coefficients for translational and rotational motion. Transport coefficients are evaluated with mode-mode coupling theory. The validity of orientational relaxation models coupled to lattice vibration is confirmed as a particular case of the present theory at low frequencies. An extension to the high frequency regime is proposed.Dedicated to Prof. Dr. H.E. Müser ob the occasion of his 60th birthday     

Microrheology from rotational diffusion of colloidal particles

The microrheology of viscoelastic fluids is obtained from rotational diffusion of optically anisotropic spherical colloidal probes, measured by depolarized dynamic light scattering. The storage and loss moduli obtained from the rotational mean squared displacement is in excellent agreement with those obtained from translational diffusion and by mechanical measurements. We also show that this method is applicable to samples with strong light scattering components. This extends the capabilities of the microrheological methods based on the diffusional motion of colloidal probes.     

X‐ray microtomographic visualization of Escherichia coli by metalloprotein overexpression

This paper reports X‐ray microtomographic visualization of the microorganism Escherichia coli overexpressing a metalloprotein ferritin. The three‐dimensional distribution of linear absorption coefficients determined using a synchrotron radiation microtomograph with a simple projection geometry revealed that the X‐ray absorption was homogeneously distributed, suggesting that every E. coli cell was labeled with the ferritin. The ferritin‐expressing E. coli exhibited linear absorption coefficients comparable with those of phosphotungstic acid stained cells. The submicrometer structure of the ferritin‐expressing E. coli cells was visualized by Zernike phase contrast using an imaging microtomograph equipped with a Fresnel zone plate. The obtained images revealed curved columnar or bunching oval structures corresponding to the E. coli cells. These results indicate that the metalloprotein overexpression facilitates X‐ray visualization of three‐dimensional cellular structures of biological objects.     

Rotational viscosity coefficients of nematic and smecticC liquid crystals: Statistical theory

Summary The rotational diffusion of a rodlike molecule in a nematic and smecticC liquid crystal is considered in the molecular-field approximation. The microscopic friction constant, which determines the molecular rotation drag, possesses an exponential temperature dependence with the activation energy determined by the isotropic part of the intermolecular interaction energy. The rotational viscous coefficients,γ ₁ andγ _⊥ are obtained by averaging of the corresponding microscopic stress tensor with the nonequilibrium distribution function. The additional activation energy, proportional to the corresponding order parameter, appears in the expressions for the rotational viscosity coefficients both in nematics andC smectics. Work presented at the second USSR-Italy Bilateral Meeting on Liquid Crystals held in Moscow, September 15–21, 1988.     

Dynamic Light Scattering Measurement of Nanometer Particles in Liquids

Dynamic light scattering (DLS) techniques for studying sizes and shapes of nanoparticles in liquids are reviewed. In photon correlation spectroscopy (PCS), the time fluctuations in the intensity of light scattered by the particle dispersion are monitored. For dilute dispersions of spherical nanoparticles, the decay rate of the time autocorrelation function of these intensity fluctuations is used to directly measure the particle translational diffusion coefficient, which is in turn related to the particle hydrodynamic radius. For a spherical particle, the hydrodynamic radius is essentially the same as the geometric particle radius (including any possible solvation layers). PCS is one of the most commonly used methods for measuring radii of submicron size particles in liquid dispersions. Depolarized Fabry-Perot interferometry (FPI) is a less common dynamic light scattering technique that is applicable to optically anisotropic nanoparticles. In FPI the frequency broadening of laser light scattered by the particles is analyzed. This broadening is proportional to the particle rotational diffusion coefficient, which is in turn related to the particle dimensions. The translational diffusion coefficient measured by PCS and the rotational diffusion coefficient measured by depolarized FPI may be combined to obtain the dimensions of non-spherical particles. DLS studies of liquid dispersions of nanometer-sized oligonucleotides in a water-based buffer are used as examples.     

Rotational and Translational Mobility of Nitroxide Spin Probes in Ionic Liquids and Molecular Solvents

Rotational and translational movements of 1-oxyl-2,2,6,6-tetramethyl-4-oxypiperidine (TEMPOL) spin probe in the room temperature ionic liquid (RTIL) 1-octyl-3-methylimidazolium tetrafluoroborate (omimBF₄) and in two molecular solvents, 1-propanol and isopropyl benzene (cumene), have been studied by X-band electron paramagnetic resonance (EPR) spectroscopy. Rotational correlation times τ _c of spin probes and the intermolecular spin exchange rate constants k _e were measured from EPR spectra at different temperatures and TEMPOL concentrations, and compared with the published data. The τ _c values were calculated both by known equations and from the EPR spectra simulation. Rotation movements of TEMPOL in omimBF₄ cannot be described by the model of the isotropic Brownian diffusion, which is valid for conventional solvents. The correct modeling of EPR spectra in RTIL can be achieved with the assumption of different rotational mobility of the spin probe around different molecular axes. The rotational, D _rot, and translational, D _tr, diffusion coefficients were calculated from τ _c and k _e values. The Debye–Stokes–Einstein law is valid in all three solvents while the dependence of D _tr on T/η is not linear in Stokes–Einstein coordinates. The effective activation energy E _rot^a of the rotational movements in omimBF₄ is noticeably higher than the corresponding values for conventional solvents, while the effective activation energies E _tr^a of the translational movements are comparable in all solvents studied.     

Estimation of diffusion coefficients by a capillary method in the presence of oppositely directed convection of the melt

The paper presents a theoretical analysis of linear diffusion in the presence of convection with a constant flow rate for an instantaneous plane source and for diffusion in infinite capillary. A conclusion can be drawn that diffusion in the melt moving at the ratev together with the source is described, with respect to the system of coordinates connected with the capillary, by a superposition of molecular diffusion and translational motion of the melt. Self-diffusion of⁵¹Cr in Fe-Cr-O systems of different compositions and self-diffusion of⁵⁹Fe in molten iron at 1860 K have been investigated experimentally. The results of theoretical analysis have been applied in the evaluation of diffusion coefficients in the presence of convection.     

Computer simulation investigation of diffusion selectivity in graphite slit pores

Equilibrium molecular dynamics simulations are reported of oxygen and nitrogen molecules confined in graphite slit pores. Self- and collective diffusion coefficients have been calculated as a function of pore width, temperature and density for each pure component in the pore space. The aim of this study was to elucidate the mechanism by which oxygen and nitrogen are kinetically separated when air is passed over an adsorbent bed consisting of molecular sieving carbon in the commercial production of oxygen. It was found that a critical pore width exists for each species at which there is a sharp drop in the rate of diffusion (both self- and collective diffusion) of each fluid. The critical pore width is one for which the individual molecules are prevented from rotating freely about one of their axes. The greater length of a nitrogen molecule means that the critical pore width is higher for this species than for oxygen. Consequently, oxygen molecules diffuse substantially faster than nitrogen molecules in the vicinity of the nitrogen critical pore width. From an analysis of correlation functions and their corresponding power spectra it is shown that the restricted rotations, which occur at or below the critical pore width, cause a decoupling of translational and rotational modes, with the net result being a lowering of translational diffusion. The nitrogen critical pore width lies within the range of the mean pore size of most commercial molecular sieving carbons, and so this mechanism may help to explain the high oxygen selectivities reported in the literature.     

Confocal zero-angle dynamic depolarized light scattering

We present a novel Dynamic Depolarized Scattering method based on a tight confocal, zero scattering angle, heterodyne scheme. The method is highly immune from parasitic multiple-scattering contributions, so that it can operate with non-index-matched samples presenting large turbidity. It provides measurements of both rotational and translational diffusion coefficients, the latter via number fluctuation spectroscopy. In addition, the amplitude ratio between the two baselines for the fast rotational mode and the slow translational mode can be used to determine the particles intrinsic birefringence.     

Influence of rotational diffusion of the Mössbauer spectrum of ultrafine particles in a supercooled liquid

The theory of the Mössbauer line shape of ultrafine particles in a liquid has been developed taking into account both translational and rotational diffusion of the particles. A simple analytical expression has been found for the line shape in the limiting case of fast rotational diffusion. In this limit the line shape appears to be independent of the rotational diffusion constant apart from a constant and a scaling factor. The quadrupole splitting remains visible even in this limiting case in contrast to the case of molecular rotation diffusion spectra. The predictions of the theory are compared with experimental spectra of nanosize iron oxide particles dispersed in supercooled decalin where a rapid decrease of the total area with increasing temperature has been found. The present theory can account for a part of the observed loss of spectral area. It is also demonstrated that the uncertainty in the determination of the total area and diffusion constants from the Mössbauer spectra increases significantly when the rotational diffusion is taken into account.     

Strain effects on optical polarisation properties in （11^-22） plane GaN films

We present the theoretical results of the electronic band structure of wurtzite GaN films under biaxial strains in the （11^-22）-plane. The calculations are performed by the k.p perturbation theory approach through using the effectivemass Hamiltonian for an arbitrary direction. The results show that the transition energies decrease with the biaxial strains changing from -0.5% to 0.5%. For films of （11^-22）-plane, the strains are expected to be anisotropic in the growth plane. Such anisotropic strains give rise to valence band mixing which results in dramatic change in optical polarisation property. The strain can also result in optical polarisation switching phenomena. Finally, we discuss the applications of these properties to the （1132） plane GaN-based light-emitting diode and lase diode.