Protein diffusion probed by the transient grating method with a new type of photochromic molecule

A new type of photochromic molecule that can be used for diffusion coefficient (D) measurements of various proteins in solution is described. The absorption spectrum of this molecule is changed upon photoexcitation by the trans-cis isomerization reaction. Target proteins were labeled by this photochromic molecule in the dark and the translational motion of the proteins was detected by the transient grating (TG) method. The TG signal was simple enough to determine D accurately and was stable even for long-time irradiation by the laser light. The TG method using this probe molecule improves many drawbacks of the other techniques.     

Effects of the bead-bead potential on the restricted rotational diffusion of nonrigid macromolecules

The influence of the bead-bead interaction on the rotational dynamics of macromolecules which are immersed into a solution has been investigated by starting from the microscopic theory of the macromolecular motion, i.e., from a Fokker-Planck equation for the phase-space distribution function. From this equation, we then derived an explicit expression for the configuration-space distribution function of a nonrigid molecule which is immobilized on a surface. This function contains all the information about the interaction among the beads as well as the effects from the surrounding solvent particles and from the surface. For the restricted rotational motion, the dynamics of the macromolecules can now be characterized in terms of a rotational diffusion coefficient as well as a radial distribution functions. Detailed computations for the rotational diffusion coefficient and the distribution functions have been carried out for HOOKEAN, finitely extensible nonlinear elastic, and a DNA type bead-bead interaction.     

Biased diffusion in tubes formed by spherical compartments

We study the effect of the driving force on brownian motion of a point particle in a tube formed by identical spherical compartments, which create periodic entropy potential for the motion along the tube axis. The focus is on (i) the effective mobility and diffusion coefficient of the particle as functions of the driving force, (ii) localization of the particle in the central part of the tube induced by the driving force, and (iii) transit time of the particle between the openings connecting neighboring compartments. Some of the results at very small and large driving force are obtained analytically, while the majority of the results are obtained from brownian dynamics simulations.     

Simultaneous investigation of sedimentation and diffusion of a single colloidal particle near an interface

We describe here a new procedure for the simultaneous investigation of sedimentation and diffusion of a colloidal particle in close proximity to a solid, planar wall. The measurements were made using the optical technique of total internal reflection microscopy, coupled with optical radiation pressure, for dimensionless separation distances (gap width/radius of particle) ranging from 0.01 to 0.05. In this region, the hydrodynamic mobility and diffusion coefficient are substantially reduced below bulk values. The procedure involved measuring the mean and the variance of vertical displacements of a Brownian particle settling under gravity toward the plate. The spatially varying diffusion coefficient was calculated from the displacements at small times (where diffusive motion was dominant). The mobility relationship for motion normal to a flat plate was tested by measuring the average distance of travel versus time as the particle settled under the constant force of gravity. For the simple Newtonian fluid used here (aqueous salt solution), the magnitude of the diffusion coefficient and mobility, plus their dependence on separation distance, showed excellent agreement with predictions. This new technique could be of great value in measuring the mobility and diffusion coefficient for near-contact motion in more complex fluids for which the hydrodynamic correction factors are not known a priori, such as shear-thinning fluids.     

Kinetics of the Photodimerization of Anthracene in an Inhomogeneous Polymer Matrix

The photodimerization of anthracene in polyethylene was investigated. It was shown that the kinetics of photodimerization are not described in terms of nonstationary diffusion. A method is proposed for determining the probability of the existence a volume of inhomogeneous polymer layer with a specific diffusion coefficient of the impurity anthracene molecule. An equation describing the kinetics of photodimerization is derived, and the limiting values of the diffusion coefficient (minimum and maximum) are obtained. A probability distribution for the existence of regions of polymer layer with diffusion coefficient between D and D + dD is also obtained.     

Coupling of the overall molecular motion with the conformational transitions. II. The full rotational problem

The method proposed in the companion paper for analysing the coupling between overall and internal dynamics is applied to the study of the full rotational motion of a molecule with one internal degree of freedom. For systems characterized by a finite set of stable conformers determined by the minima of the intramolecular potential, a simplified time evolution operator of mixed type is derived, with the continuous diffusion equation and the generalized random walk operator representing the overall rotation and the internal dynamics, respectively. The dependence on the conformational state of the rotational diffusion tensor is one source of coupling between these two types of motion. Another source is represented by the recoil rotations acting on each subunit during a conformational transition. Both conformational-dependent rotational diffusion tensors and recoil rotations can be calculated from a model for the friction exerted by the solvent. Some applications of the theory are presented in relation to the butane molecule and the molecules having the structure of biphenyl, with particular emphasis on the calculation of the experimental observables in NMR and dielectric relaxation measurements.     

Combined atomic force microscopy and fluorescence correlation spectroscopy measurements to study the dynamical structure of interfacial fluids

We have studied the dynamic structure of thin (approximately a few nanometers) liquid films of a nearly spherical, nonpolar molecule tetrakis(2-ethylhexoxy)silane (TEHOS) by using a combination of atomic force microscopy (AFM) and fluorescence correlation spectroscopy (FCS). Ultra-sensitive interferometer-based AFM was used to determine the stiffness (force gradient) and the damping coefficient of the liquid film. The experiments show oscillations in the damping coefficient with a period of approximately 1 nm, which is consistent with the molecular dimension of TEHOS as well as previous X-ray reflectivity measurements. Additionally, we performed FCS experiments for direct determination of the molecular dynamics within the liquid film. From the fluctuation autocorrelation curve, we measured the translational diffusion of the probe molecule embedded within the fluid film formed on a solid substrate. The autocorrelation function was best fitted with two components, which indicate that the dynamics are heterogeneous in nature. However, the heterogeneity is not as pronounced as had been previously observed for molecularly thin liquid films sandwiched between two solid substrates.     

Analysis of the transverse and the longitudinal pseudodiffusion of CO2 in sub- and supercritical states: a molecular-dynamics analysis

We have performed molecular-dynamics simulations of CO(2) system along the gas-liquid coexistence curve and on the isochore 94.22 cm(3) mol(-1) (which corresponds to the critical isochore). The calculation has been carried out in order to analyze the diffusion of CO(2) and particularly to figure out how the diffusion coefficient may be decomposed along the molecular axes. This makes it possible to analyze the anisotropy of the diffusion along these axes and to shed light on the microscopic changes which accompany such behavior. This anisotropy is traced back to the effect of the translation-rotation coupling (TRC) along the molecular axes. Along the liquid-gas coexistence curve, the pseudolongitudinal diffusion is found to be more rapid than the transverse one. The opposite trend is found along the isochore 94.22 cm(3) mol(-1). The role of the local structure was explored by calculating intermediate scattering function and the autocorrelation functions for the forces acting along the molecular axes. It is shown that the strength of the TRC effect is correlated to the difference between the relaxation times of the local structure, that of the reorientation along the molecular axes, and that of the translational motion. The analysis of the correlation time and the average mean square force along the longitudinal and transverse directions confirms the anisotropy of the local environment that determines the translational dynamics of a molecule.     

Langevin dynamics simulations of the diffusion of molecular knots in tensioned polymer chains

Motivated by recent experiments, in which knots have been tied in individual biopolymer molecules, we use Langevin dynamics simulations to study the diffusion of a knot along a tensioned polymer chain. We find that the dependence of the knot diffusion coefficient on the tension can be non-monotonic. This behavior can be explained by the model, in which the motion of the knot involves cooperative displacement of a local knot region. At low tension, the overall viscous drag force that acts on the knot region is proportional to the number N of monomers that participate in the knot, which decreases as the tension is increased, leading to faster diffusion. At high tension the knot becomes tight and its dynamics are dominated by the chain's internal friction, which increases with the increasing tension, thereby slowing down the knot diffusion. This model is further supported by the observation that the knot diffusion coefficient measured across a set of different knot types is inversely proportional to N. We propose that the lack of tension dependence of the knot diffusion coefficients measured in recent experiments is due to the fact that the experimental values of the tension are close to the turnover between the high- and low-force regimes.     

On the friction coefficient of straight-chain aggregates

A methodology to calculate the friction coefficient of an aggregate in the continuum regime is proposed. The friction coefficient and the monomer shielding factors, aggregate-average or individual, are related to the molecule-aggregate collision rate that is obtained from the molecular diffusion equation with an absorbing boundary condition on the aggregate surface. Calculated friction coefficients of straight chains are in very good agreement with previous results, suggesting that the friction coefficients may be accurately calculated from the product of the collision rate and an average momentum transfer, the latter being independent of aggregate morphology. Langevin-dynamics simulations show that the diffusive motion of straight-chain aggregates may be described either by a monomer-dependent or an aggregate-average random force, if the shielding factors are appropriately chosen.     

Single-molecule motions of oligoarginine transporter conjugates on the plasma membrane of Chinese hamster ovary cells

To explore the real-time dynamic behavior of molecular transporters of the cell-penetrating-peptide (CPP) type on a biological membrane, single fluorescently labeled oligoarginine conjugates were imaged interacting with the plasma membrane of Chinese hamster ovary (CHO) cells. The diffusional motion on the membrane, characterized by single-molecule diffusion coefficient and residence time (tau R), defined as the time from the initial appearance of a single-molecule spot on the membrane (from the solution) to the time the single molecule disappears from the imaging focal plane, was observed for a fluorophore-labeled octaarginine (a model guanidinium-rich CPP) and compared with the corresponding values observed for a tetraarginine conjugate (negative control), a lipid analogue, and a fluorescently labeled protein conjugate (transferrin-Alexa594) known to enter the cell through endocytosis. Imaging of the oligoarginine conjugates was enabled by the use of a new high-contrast fluorophore in the dicyanomethylenedihydrofuran family, which brightens upon interaction with the membrane at normal oxygen concentrations. Taken as a whole, the motions of the octaarginine conjugate single molecules are highly heterogeneous and cannot be described as Brownian motion with a single diffusion coefficient. The observed behavior is also different from that of lipids, known to penetrate cellular membranes through passive diffusion, conventionally involving lateral diffusion followed by membrane bilayer flip-flop. Furthermore, while the octaarginine conjugate behavior shares some common features with transferrin uptake (endocytotic) processes, the two systems also exhibit dissimilar traits when diffusional motions and residence times of single constructs are compared. Additionally, pretreatment of cells with cytochalasin D, a known actin filament disruptor, produces no significant effect, which further rules out unimodal endocytosis as the mechanism of uptake. Also, the involvement of membrane potential in octaarginine-membrane interaction is supported by significant changes in the motion with high [K(+)] treatment. In sum, this first study of single transporter motion on the membrane of a living cell indicates that the mode by which the octaarginine transporter penetrates the cell membrane appears to either be a multimechanism uptake process or a mechanism different from unimodal passive diffusion or endocytosis.     

Probing the interplay between chain diffusion and polymer crystal growth under nanoscale confinement: a study by single molecule fluorescence microscopy

Motions of single poly(ε-caprolactone) (PCL) molecules during the formation of the dendrite crystals in ultrathin films are captured by single molecule fluorescence microscopy. The relationship of single molecule diffusion coefficient with the crystal growth rate, together with radius curvature, side-branch spacing of dendrite crystal and morphology are examined. The results support Mullins-Sekerka (MS) instability as the origin of lamellar branching induced by a diffusion field generated by a gradient of polymer segment density ahead of the crystal. Further analysis of the molecular trajectories has recognized different types of motions, depending on the distance to the crystal front: Fickian diffusion in regions far away from the crystal, sub-diffusion in regions adjacent to the crystal, and directed motion between these two regions. Anti-correlation of successive steps is discovered accompanying the sub-diffusion, providing a clear signature of macromolecule crowding at the crystal growth front. This anomalous diffusion process in polymer ultrathin films presents a new insight into the understanding of the retarded dynamics of interfacial mass transport towards the crystal front. It is considered to play a decisive role in controlling the crystal growth and evolution of crystal morphology.     

Drag of a Solid Particle Trapped in a Thin Film or at an Interface: Influence of Surface Viscosity and Elasticity

We propose a theoretical model for the motion of a spherical particle entrapped in a thin liquid film or in a monolayer of insoluble surfactant at the air/water interface. Both surface shear and dilational viscosity, surface diffusion, and elasticity of the film are taken into consideration. The drag force acting on the particle is analytically calculated and asymptotic expressions of the problem are provided. The relevance of the model is discussed by comparing the calculated "viscoelastic" drag, gamma(vel), to the one predicted by Saffman's theory, gamma(S), for cylindrical inclusions in membranes. Numerical analyses are performed to evaluate the contributions of the surface viscosity and the diffusion coefficient of the layer on the hydrodynamical resistance experienced by the particle. Copyright 2000 Academic Press.     

Diffusion-Editing NMR Spectroscopy for Mixtures

According to the Stokes-Einstein equation, the diffusion coefficient of a molecule is inversely proportional to the molecular radius, therefore translational diffusion coefficients are different for various molecular sizes. The aim of this work was to develop a diffusion-editing NMR method that allows to directly observe the individual components in mixtures without the need of physical separation.     

Analytical treatment of biased diffusion in tubes with periodic dead ends

Effective mobility and diffusion coefficient of a particle in a tube with identical periodic dead ends characterize the motion on large time scale, when the particle displacement significantly exceeds the tube period. We derive formulas that show how these transport coefficients depend on the driving force and the geometric parameters of the system. Numerical tests show that values of the transport coefficients obtained from Brownian dynamics simulations are in excellent agreement with our theoretical predictions.     

Motion of star‐branched chains in polymer networks: a Monte Carlo study

A simple model of branched polymers in confined space is developed. Star‐branched polymer molecules are built on a simple cubic lattice with excluded volume and no attractive interactions (good solvent conditions). A single star molecule is trapped in a network of linear polymer chains of restricted mobility. The simulations are carried out using the classical Metropolis algorithm. Static and dynamic properties of the star‐branched polymer are determined using various networks. The dependence of the longest relaxation time and the self‐diffusion coefficient on chain length and network properties are discussed and the proper scaling laws formulated. The possible mechanism of motion is discussed. The differences between the motion of star‐branched polymers in such a network are compared with the cases of a dense matrix of linear chains and regular rod‐like obstacles.     

A study of the gas barrier properties of highly oriented polyethylene

Measurements of permeability and diffusivity have been undertaken for the gases helium and oxygen in a range of highly oriented polyethylene films. The solubilities deduced for both gases are proportional to the amorphous volume fraction, showing that the noncrystalline regions are the transport medium in all instances. The changes in diffusion coefficient are more complex. A large reduction in diffusion coefficient is observed with increasing draw ratio, and this is particularly marked in the case of the larger oxygen molecule, where significant differences are also observed for different grades of polymer and different drawing conditions. These changes in diffusion coefficient are discussed in the light of previous studies of diffusion in polymers and present knowledge of the changes in structure produced by drawing.     

Calculating slow-motional electron paramagnetic resonance spectra from molecular dynamics using a diffusion operator approach

A number of groups have utilized molecular dynamics (MD) to calculate slow-motional electron paramagnetic resonance (EPR) spectra of spin labels attached to biomolecules. Nearly all such calculations have been based on some variant of the trajectory method introduced by Robinson, Slutsky and Auteri (J. Chem. Phys. 1992,96, 2609-2616). Here we present an alternative approach that is specifically adapted to the diffusion operator-based stochastic Liouville equation (SLE) formalism that is also widely used to calculate slow-motional EPR line shapes. Specifically, the method utilizes MD trajectories to derive diffusion parameters such as the rotational diffusion tensor, diffusion tilt angles, and expansion coefficients of the orienting potential, which are then used as direct inputs to the SLE line shape program. This approach leads to a considerable improvement in computational efficiency over trajectory-based methods, particularly for high frequency, high field EPR. It also provides a basis for deconvoluting the effects of local spin label motion and overall motion of the labeled molecule or domain: once the local motion has been characterized by this approach, the label diffusion parameters may be used in conjunction with line shape analysis at lower EPR frequencies to characterize global motions. The method is validated by comparison of the MD predicted line shapes to experimental high frequency (250 GHz) EPR spectra.