Hydrodynamic resistance and diffusion coefficients of a freely hinged rod

The seven-dimensional hydrodynamic resistance and diffusion tensors are evaluated for a rod which is freely hinged at its center and immersed in a viscous fluid. The hydrodynamic resistance tensor is first determined at the hinge, then transformed to other points and inverted to obtain the diffusion tensor. Hydrodynamic interactions between rod halves are neglected, which is asymptotically correct for long rods. In the long-rod limit, the diffusion coefficient characterizing translations over macroscopic distances is decreased by 3–6% from that for a rigid straight rod of same total length, while the average end-over-end rotational diffusion coefficient for each rod half is increased 4.67 times.     

Models for boundary effects on molecular rotation in membranes

Rotational and wobbling diffusion coefficients for spherical and long-chain molecules in membranes are calculated using a simple hydrodynamic model. Estimates of the contributions to the diffusion coefficients arising from hydrodynamic interactions between molecules and membrane interfaces are obtained and found to be small. For molecules containing polar head groups, we show that the presence of a membrane interface can produce a significant reduction in the wobbling diffusion coefficient over what would be obtained in an isotropic fluid.     

Simulation of the response of the inner hair cell stereocilia bundle to an acoustical stimulus

Mammalian hearing relies on a cochlear hydrodynamic sensor embodied in the inner hair cell stereocilia bundle. It is presumed that acoustical stimuli induce a fluid shear-driven motion between the tectorial membrane and the reticular lamina to deflect the bundle. It is hypothesized that ion channels are opened by molecular gates that sense tension in tip-links, which connect adjacent stepped rows of stereocilia. Yet almost nothing is known about how the fluid and bundle interact. Here we show using our microfluidics model how each row of stereocilia and their associated tip links and gates move in response to an acoustical input that induces an orbital motion of the reticular lamina. The model confirms the crucial role of the positioning of the tectorial membrane in hearing, and explains how this membrane amplifies and synchronizes the timing of peak tension in the tip links. Both stereocilia rotation and length change are needed for synchronization of peak tip link tension. Stereocilia length change occurs in response to accelerations perpendicular to the oscillatory fluid shear flow. Simulations indicate that nanovortices form between rows to facilitate diffusion of ions into channels, showing how nature has devised a way to solve the diffusive mixing problem that persists in engineered microfluidic devices.     

Influence of hydrophobic mismatching on membrane protein diffusion

The observation of membrane domains in vivo and in vitro has triggered a renewed interest in the size-dependent diffusion of membrane inclusions (e.g., clusters of transmembrane proteins and lipid rafts). Here, we have used coarse-grained membrane simulations to quantify the influence of a hydrophobic mismatch between the inclusion's transmembrane portion and the surrounding lipid bilayer on the diffusive mobility of the inclusion. Our data indicate only slight changes in the mobility (<30%) when altering the hydrophobic mismatch, and the scaling of the diffusion coefficient D is most consistent with previous hydrodynamic predictions, i.e., with the Saffman-Delbruck relation and the edgewise motion of a thin disk in the limit of small and large radii, respectively.     

Hydrodynamic thickening of lubricating fluid layer beneath sliding mesothelial tissues

The delicate mesothelial surfaces of the pleural space and other serosal cavities slide relative to each, lubricated by pleural fluid. In the absence of breathing motion, differences between lung and chest wall shape could eventually cause the lungs and chest wall to come into contact. Whether sliding motion keeps lungs and chest wall separated by a continuous liquid layer is not known. To explore the effects of hydrodynamic pressures generated by mesothelial sliding, we measured the thickness of the liquid layer beneath the peritoneal surface of a 3-cm disk of rat abdominal wall under a normal stress of 2 cm H2O sliding against a glass plate rotating at 0-1 rev/s. Thickness of the lubricating layer was determined microscopically from the appearance of fluorescent microspheres adherent to the tissue and glass. Usually, fluid thickness near the center of the tissue disk increased with the onset of glass rotation, increasing to 50-200 microm at higher rotation rates, suggesting hydrodynamic pumping. However, thickness changes often differed substantially among tissue samples and between clockwise and counter-clockwise rotation, and sometimes thickness decreased with rotation, suggesting that topographic features of the tissue are important in determining global hydrodynamic effects. We conclude that mesothelial sliding induces local hydrodynamic pressure gradients and global hydrodynamic pumping that typically increases the thickness of the lubricating fluid layer, moving fluid against the global pressure gradient. A similar phenomenon could maintain fluid continuity in the pleural space, reducing frictional force and shear stress during breathing.     

On the relative contribution of viscous flow vs. diffusional (frictional) flow to the stationary state flow of water through a "tight" membrane

The practice of calculating the diffusion contribution to the total pressure-driven flow of water through a tight membrane by using the self-diffusion coefficient for tritiated water is examined by a theoretical analysis. Equations of motion for water and membrane in pressure-driven water flow and water, membrane, and tritiated water in self-diffusion of tritiated water are adapted from Bearman and Kirkwood (1958). These equations of motion are used to develop an equation for the pressure-driven flow of water. Because of the lack of specific information about the detailed structure of most membranes, as well as considerations of the need to eliminate some of the mathematical difficulties, an "equivalent capillary" model is used to find a solution to the equation of motion. The use of the equivalent capillary model and possible ambiguities in distinctions between diffusion and hydrodynamic flow are discussed     

Molecular dynamics study of the lauryl alcohol-laurate model bilayer

Molecular dynamics (MD) calculation of the fluid phase lauryl alcohol-laurate bilayer has been executed based on Berendsen's surface-constrained model. Structure and dynamics of the bilayer have been investigated by analyzing the trajectories of the chain configurations. Newly defined correlation functions as well as the conventional ones showed that the tilt and bend of the chain play an important role in the bilayer structure, including behavior of the order parameter. Interpenetration of the layers as well as formation of collectively ordered small domains was also found. The calculated lateral diffusion coefficient was in satisfactory agreement with the experimental one. Successive jumps of the head group, rather than the hydrodynamic continuous motion, were observed. Between the jumps, the molecule librated in a local site. Time-dependent autocorrelation functions showed evidence of several different modes of the chain motion, whose time constant ranged from a few tenths of picoseconds to several tens of picoseconds.     

Numerical simulation of the electrophoretic transport of a biopolymer through a synthetic nano-pore

We employed a hybrid approach to study numerically the translocation of a biopolymer through an artificial nano-pore driven by an external electric field in the presence of an explicit solvent. The motion of the polymer is simulated by the 3D Langevin dynamics technique. The hydrodynamic interactions (HI) between the polymer and the fluid are taken into account by the lattice Boltzmann equation. Our polymer chain model representing the double-stranded DNA was first validated by comparing the diffusion coefficient obtained from the numerical results with the experimental and theoretical results. Then, we conducted numerical simulations of the biopolymer's translocation process by applying a theoretical formula for the net electrophoretic force acting on the part of the polymer residing in the pore. We compared quantitatively the translocation times and the velocities of different DNA lengths with the corresponding experimental results. Our simulation results are in good agreement with the experimental ones when the HI are considered explicitly.     

对地贫红细胞的显微激光散射和图象分析

应用显微准弹性激光散射(MQLS)技术与显微生物医学图象分析技术对地中海贫血红细胞及胞内血红蛋白动态特性进行了研究.在实验中,比较了正常人及地贫患者红细胞胞内血红蛋白聚集体的平均流体力学半径、平均平动扩散系数及红细胞膜的搏动频率等动态特性参数,以及细胞的截面积、规化形状因子、长径、短径、灰度等图象分析数据,发现地贫红细胞的血红蛋白聚合物平均流体力学半径远远大于正常人红细胞的,其大小变异亦较正常人大,且其膜搏动频率也较为缓慢,细胞的截面积也变小.这反映了地贫红细胞内有较大的蛋白质聚合物存在和红细胞变形能力差的特性.研究还表明,显微准弹性激光散射技术结合图象分析技术,可使测量的可比性和准确性大大提高,预期可广泛适用于各种活细胞动态特性的研究.     

Transport properties of particles with segmental flexibility. I. Hydrodynamic resistance and diffusion coefficients of a freely hinged particle

Expressions are derived for the hydrodynamic resistance tensor and the diffusion tensor of a particle consisting of two rigid subunits connected by a free hinge. No restrictions are placed on the shapes of the subunits. The resistance tensor is obtained by using two independent approaches: first, from the Rayleigh dissipation function and, second, from an examination of the generalized forces for the appropriate seven-dimensional coordinate system. For the derivation of the generalized Einstein equation connecting the diffusion and resistance tensors, the Brownian motion is treated as a stochastic process. That derivation is based on the assumption that the restoring force for bending is negligible, and the Einstein relation holds instantaneously only if that assumption is true. The relationship between these tensors and the macroscopically observable parameters is discussed, and it is shown that the separate measurement of resistance and diffusion coefficients can be used to detect macromolecular flexibility. One example is treated, the diffusion of a particle composed of two long rods joined at a free hinge. Those calculations are carried out with the first-order assumption of negligible hydrodynamic interactions between the subunits. For the hinged rod, the bending degree of freedom produces a 34% increase in the translational diffusion coefficient over that of a stiff rod of the same total length, while the rotational diffusion coefficient about the axis perpendicular to the plane of bending is increased by 125%.     

Transient relative motion of two cells in a channel flow

The hydrodynamic interaction of a red blood cell and a white blood cell in microvessels is studied, by use of a two-dimensional numerical model. The red blood cell, modeled as a small rigid circular cylinder, and the white blood cell, modeled as a larger rigid circular cylinder, are immersed in an incompressible Newtonian fluid in a two-dimensional channel. It is assumed that no external force or moment acts on the model cells, and the effect of inertia forces on the motion of the fluid and the cells is neglected. The velocity field of the suspending fluid and the instantaneous velocities of the two model cells are computed by the finite element method. Using the translational velocities of the model cells obtained, the trajectories of their relative motion are determined, for various initial positions. It is shown that the cells may or may not pass each other or separate, depending on the initial positions. The present results compare well to the experimental results.     

Environmental modulation of M13 coat protein tryptophan fluorescence dynamics

The effects of detergent [deoxycholate (DOC) and phospholipid [dimyristoylphosphatidylcholine (DMPC)] environments on the rotational dynamics of the single tryptophan residue 26 of bacteriophage M13 coat protein have been investigated by using time-resolved single photon counting measurements of the fluorescence intensity and anisotropy decay. The total fluorescence decay of tryptophan-26 is complex but rather similar in DOC as compared to DMPC when analyzed in terms of a lifetime distribution (exponential series method). This similarity, in conjunction with the almost identical steady-state fluorescence spectra, indicates only minor differences between the tryptophan environments in DOC and DMPC. The reorientational dynamics of tryptophan-26 are dominated by slow rotation of the entire protein in both detergent and phospholipid environments. The resolved anisotropy decay in DOC can be approximated by a simple hydrodynamic model of protein/detergent micelle rotational diffusion, although the data indicative slightly greater complexity in the rotational motion. The tryptophan fluorescence anisotropy is not sensitive to protein conformational changes in DOC detected by nuclear magnetic resonance on the basis of pH independence in the range 7.5-9.1. In DMPC bilayers, restricted tryptophan motion with a correlation time of approximately 2 ns is observed together with a second very slow reorientational component. Resolution of the time constant for this slow rotation is obscured by the tryptophan fluorescence time window being too short to clearly locate its anisotropic limit. The possible contribution made by axial rotational diffusion of the protein to this slow rotational process is discussed.(ABSTRACT TRUNCATED AT 250 WORDS)     

Fluid Forces Enhance the Performance of an Aspirant Leader in Self-Organized Living Groups

In this paper, the performance of an individual aiming at guiding a self-organized group is numerically investigated. A collective behavioural model is adopted, accounting for the mutual repulsion, attraction and orientation experienced by the individuals. Moreover, these represent a set of solid particles which are supposed to be immersed in a fictitious viscous fluid. In particular, the lattice Boltzmann and Immersed boundary methods are used to predict the fluid dynamics, whereas the effect of the hydrodynamic forces on particles is accounted for by solving the equation of the solid motion through the time discontinuous Galerkin scheme. Numerical simulations are carried out by involving the individuals in a dichotomous process. On the one hand, an aspirant leader (AL) additional individual is added to the system. AL is forced to move along a prescribed direction which intersects the group. On the other hand, these tend to depart from an obstacle represented by a rotating lamina which is placed in the fluid domain. A numerical campaign is carried out by varying the fluid viscosity and, as a consequence, the hydrodynamic field. Moreover, scenarios characterized by different values of the size of the group are investigated. In order to estimate the AL''s performance, a proper parameter is introduced, depending on the number of individuals following AL. Present findings show that the sole collective behavioural equations are insufficient to predict the AL''s performance, since the motion is drastically affected by the presence of the surrounding fluid. With respect to the existing literature, the proposed numerical model is enriched by accounting for the presence of the encompassing fluid, thus computing the hydrodynamic forces arising when the individuals move.     

The effect of turbulent motion on the diffusion of microorganisms

The effect of turbulent fluid motion on the diffusion of simple organisms is discussed. The net reproduction rate and the turbulent flow are assumed to be Gaussian-correlated random variables. For homogeneous istropic turbulence, simple equations for the average concentration of the organisms are derived in terms of the energy density of the fluid. It is shown that the effective diffusivity generated by the motion is positive-definite, and is independent of the helicity of the flow.     

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.     

Anomalous versus Slowed-Down Brownian Diffusion in the Ligand-Binding Equilibrium

Measurements of protein motion in living cells and membranes consistently report transient anomalous diffusion (subdiffusion) that converges back to a Brownian motion with reduced diffusion coefficient at long times after the anomalous diffusion regime. Therefore, slowed-down Brownian motion could be considered the macroscopic limit of transient anomalous diffusion. On the other hand, membranes are also heterogeneous media in which Brownian motion may be locally slowed down due to variations in lipid composition. Here, we investigate whether both situations lead to a similar behavior for the reversible ligand-binding reaction in two dimensions. We compare the (long-time) equilibrium properties obtained with transient anomalous diffusion due to obstacle hindrance or power-law-distributed residence times (continuous-time random walks) to those obtained with space-dependent slowed-down Brownian motion. Using theoretical arguments and Monte Carlo simulations, we show that these three scenarios have distinctive effects on the apparent affinity of the reaction. Whereas continuous-time random walks decrease the apparent affinity of the reaction, locally slowed-down Brownian motion and local hindrance by obstacles both improve it. However, only in the case of slowed-down Brownian motion is the affinity maximal when the slowdown is restricted to a subregion of the available space. Hence, even at long times (equilibrium), these processes are different and exhibit irreconcilable behaviors when the area fraction of reduced mobility changes.     

Investigation of hydrodynamic focusing in a microfluidic coulter counter device

The Coulter technique enables rapid analysis of particles or cells suspended in a fluid stream. In this technique, the cells are suspended in an electrically conductive solution, which is hydrodynamically focused by nonconducting sheath flows. The cells produce a characteristic voltage signal when they interrupt an electrical path. The population and size of the cells can be obtained through analyzing the voltage signal. In a microfluidic Coulter counter device, the hydrodynamic focusing technique is used to position the conducting sample stream and the cells and also to separate close cells to generate distinct signals for each cell and avoid signal jam. The performance of hydrodynamic focusing depends on the relative flow ratio between the sample stream and sheath stream. We use a numerical approach to study the hydrodynamic focusing in a microfluidic Coulter counter device. In this approach, the flow field is described by solving the incompressible Navier-Stokes equations. The sample stream concentration is modeled by an advection-diffusion equation. The motion of the cells is governed by the Newton-Euler equations of motion. Particle motion through the flow field is handled using an overlapping grid technique. A numerical model for studying a microfluidic Coulter counter has been validated. Using the model, the impact of relative flow rate on the performance of hydrodynamic focusing was studied. Our numerical results show that the position of the sample stream can be controlled by adjusting the relative flow rate. Our simulations also show that particles can be focused into the stream and initially close particles can be separated by the hydrodynamic focusing. From our study, we conclude that hydrodynamic focusing provides an effective way to control the position of the sample stream and cells and it also can be used to separate cells to avoid signal jam.     

Diffusion control in reversible enzyme reactions. Applications to carbonic anhydrase.

The limit to the possible rate of reversible enzymatic reactions set by the diffusional motion has been considered. It is found that not only the diffusion of the reactants to the enzyme but also the diffusion away of the products can be rate limiting. To avoid assumptions about the detailed nature of the enzyme only diffusion in the bulk aqueous medium is treated. By such an approach one obtains an upper limit to the possible rate. In the latter half of the paper the derived general equations are applied to the possible suggested reaction schemes for the enzyme carbonic anhydrase. It is found that a scheme involving HCO3- as substrate for the dehydration process and a direct reaction between buffer and enzyme is comsistent with the limits set by the diffusional motion, while several other possibilities can be ruled out.     

A study of bacterial flagellar bundling

Certain bacteria, such as Escherichia coli (E. coli) and Salmonella typhimurium (S. typhimurium), use multiple flagella often concentrated at one end of their bodies to induce locomotion. Each flagellum is formed in a left-handed helix and has a motor at the base that rotates the flagellum in a corkscrew motion.We present a computational model of the flagellar motion and their hydrodynamic interaction. The model is based on the equations of Stokes flow to describe the fluid motion. The elasticity of the flagella is modeled with a network of elastic springs while the motor is represented by a torque at the base of each flagellum. The fluid velocity due to the forces is described by regularized Stokeslets and the velocity due to the torques by the associated regularized rotlets. Their expressions are derived. The model is used to analyze the swimming motion of a single flagellum and of a group of three flagella in close proximity to one another. When all flagellar motors rotate counterclockwise, the hydrodynamic interaction can lead to bundling. We present an analysis of the flow surrounding the flagella. When at least one of the motors changes its direction of rotation, the same initial conditions lead to a tumbling behavior characterized by the separation of the flagella, changes in their orientation, and no net swimming motion. The analysis of the flow provides some intuition for these processes.