A tensegrity model of the cytoskeleton in spread and round cells.

Measurements on adherent cells have shown that spreading affects their mechanics. Highly spread cells are stiffer than less spread cells. The stiffness increases approximately linearly with increasing applied stress and more so in highly spread cells than in less spread cells. In this study, a six-strut tensegrity model of the cytoskeleton is used to analyze the effect of spreading on cellular mechanics. Two configurations are considered: a "round" configuration where a spherically shaped model is anchored to a flat rigid surface at three joints, and a "spread" configuration, where three additional joints of the model are attached to the surface. In both configurations a pulling force is applied at a free joint, distal from the anchoring surface, and the corresponding deformation is determined from equations of equilibrium. The model stiffness is obtained as the ratio of applied force to deformation. It is found that the stiffness changes with spreading consistently with the observations in cells. These findings suggest the possibility that the spreading-induced changes of the mechanical properties of the cell are the result of the concomitant changes in force distribution and microstructural geometry of the cytoskeleton.     

On periodicities in metabolizing systems

Following a previous study by A. Weinberg, the author investigates periodical diffusion phenomena produced in a spherical cell by a simple coupled set of chemical reactions. The general solution even for a spherical cell does not possess spherical symmetry. It is found that periodic oscillations are possible with a frequency spectrum determined by a set of “eigenvalues”. However, these oscillations are all damped even if the system of coupled reactions which is responsible for them has non-damped solutions. Therefore, although very complex and highly asymmetrical configurations of concentrations may be thus produced in the cell, none of those configurations, except some possible centrally symmetric ones, is lasting.     

Diffusion of water in skeletal muscle tissue is not influenced by compression in a rat model of deep tissue injury

Sustained mechanical loading of skeletal muscle may result in the development of a severe type of pressure ulcer, referred to as deep tissue injury. Recently it was shown that the diffusion of large molecules (10–150 kDa) is impaired during deformation of tissue-engineered skeletal muscle, suggesting a role for impaired diffusion in the aetiology of deep tissue injury. However, the influence of deformation on diffusion of smaller molecules on its aetiology is less clear. This motivated the present study designed to investigate the influence of deformation of skeletal muscle on the diffusion of water, which can be measured with diffusion tensor magnetic resonance imaging (MRI). It could be predicted that this approach will provide valuable information on the diffusion of small molecules. Additionally the relationship between muscle temperature and diffusion was investigated. During deformation of the tibialis anterior a decrease of the apparent diffusion coefficient (ADC) was observed (7.2±3.9%). The use of a finite element model showed that no correlation existed between the maximum shear strain and the decrease of the ADC. The ADC in the uncompressed gastrocnemius muscle decreased with 5.9±3.7%. In an additional experiment a clear correlation was obtained between the decrease of the ADC and the relative temperature change of skeletal muscle tissue as measured by MRI. Taken together, it was concluded that (1) the decreased diffusion of water was not a direct effect of tissue deformation and (2) that it is likely that the observed decreased ADC during deformation was a result of a decreased muscle temperature. The present study therefore provides evidence that diffusion of small molecules, particularly oxygen and carbon dioxide, is not impaired during deformation of skeletal muscle tissue.     

Elongation and constriction in cell division

The deformation of a constant reaction ellipsoidal cell by diffusion and constant surface tension forces is studied. The critical size of a spherical cell at which it becomes unstable to ellipsoidal deformations is found to be the same as that obtained previously by N. Rashevsky from energy considerations. It is shown that such a cell once unstable will elongate to a finite amount, and that it will tend to constrict in the center and round up at the poles.     

Coupling bending and shear effects on liposome deformation

Cell membrane deformation induced by external mechanical stimuli has been studied extensively over the past three decades. The present study focuses on the coupling of in-plane shear H and out-of-plane bending B of liposome membrane and its influences on the deformation of a single vesicle subjected to (i) external compressive load via two parallel platens and (ii) contact forces caused by a rigid substrate. Our results show that the increase of membrane resultant stress in both loading configurations causes the liposome to become more rigid and the degree of vesicle deformation decreases when the in-plane shearing effect is dominant. A theoretical approach is developed to facilitate cell membrane characterization under different biomechanical stimuli.     

Microfluidic biofuel cells: the influence of electrode diffusion layer on performance

Microfluidic biofuel cells exploit the lack of convective mixing at low Reynolds number to eliminate the need for a physical membrane to separate fuel from oxidant. This paper demonstrates how the length and spacing of electrodes within a microchannel, and thus thickness of the diffusion layer, affects the performance of a microfluidic biofuel cell. It was found that splitting a single electrode into two (or more) smaller electrodes and separating them by a distance equal to three times their length prevents the continuous increase in thickness of a diffusion layer. This change results in a 25% increase in maximum power density compared to a single electrode device with identical electroactive area. Furthermore, we found that the maximum current density of a microfluidic biofuel cell operated with different electrode configurations (i.e., length of cathode) closely matches that predicted by theory.     

Interaction of the fibrinogen-binding tetrapeptide Gly-Pro-Arg-Pro with fine clots and oligomers of alpha-fibrin; comparisons with alpha beta-fibrin

The tetrapeptide Gly-Pro-Arg-Pro(GPRP) was introduced by diffusion into fine unligated clots formed from human fibrinogen at pH 8.5 and ionic strength 0.45 by batroxobin (αβ-fibrin) and by thrombin (α-fibrin). The α-fibrin clots were essentially liquefied at GPRP concentrations above 1 mM and αβ-fibrin clots above 15 mM, and the degree of polymerization of the resulting oligomers decreased progressively with increasing GPRP concentration as shown by γ-γ ligation with factor XIIIa and subsequent gel electrophoresis. Much smaller concentrations of GPRP, when introduced into unligated clots by diffusion, were sufficient to modify their mechanical properties profoundly. The shear modulus of elasticity G₂₅ measured 25 s after imposition of stress fell, for example, by a factor of 0.4 at 0.1 mM GPRP in α-fibrin and at 1.1 mM in αβ-fibrin. The rate of shear creep under constant stress and the proportion of irrecoverable deformation also increased enormously. This behavior, and the corresponding decrease in steady flow viscosity, may be interpreted in terms of competition of GPRP with A sites on the E domains of fibrin monomers for bidning to “a” sites on the D domains, resulting in a moderate increase with increasing GPRP concentration of the average proportion of severed network strands and an enormous increase in the rate at which all strands dissociate and reassociate. Reassociation of severed strands in new configurations is a necessary corollary since the differential modulus or compliance remains constant during creep and creep recovery. The greater susceptibility of α-fibrin clots to interaction with GPRP is attributed to stabilization of contacts between monomer units by Bb associations in αβ-fibrin. Ligated clots, with or without GPRP, exhibited essentially no time-dependent creep and no irrecoverable deformation, corresponding to an absence of any severance of network strands.     

To Hop or not to Hop: Exceptions in the FCS Diffusion Law

Diffusion obstacles in membranes have not been directly visualized because of fast membrane dynamics and the occurrence of subresolution molecular complexes. To understand the obstacle characteristics, mobility-based methods are often used as an indirect way of assessing the membrane structure. Molecular movement in biological plasma membranes is often characterized by anomalous diffusion, but the exact underlying mechanisms are still elusive. Imaging total internal reflection fluorescence correlation spectroscopy (ITIR-FCS) is a well-established mobility-based method that provides spatially resolved diffusion coefficient maps and is combined with FCS diffusion law analysis to examine subresolution membrane organization. In recent years, although FCS diffusion law analysis has been instrumental in providing new insights into the membrane structure below the optical diffraction limit, there are certain exceptions and anomalies that require further clarification. To this end, we correlate the membrane structural features imaged by atomic force microscopy (AFM) with the dynamics measured using ITIR-FCS. We perform ITIR-FCS measurements on supported lipid bilayers (SLBs) of various lipid compositions to characterize the anomalous diffusion of lipid molecules in distinct obstacle configurations, along with the high-resolution imaging of the membrane structures with AFM. Furthermore, we validate our experimental results by performing simulations on image grids with experimentally determined obstacle configurations. This study demonstrates that FCS diffusion law analysis is a powerful tool to determine membrane heterogeneities implied from dynamics measurements. Our results corroborate the commonly accepted interpretations of imaging FCS diffusion law analysis, and we show that exceptions happen when domains reach the percolation threshold in a biphasic membrane and a network of domains behaves rather like a meshwork, resulting in hop diffusion.     

Circular closed DNA. Topology, energy, and stress at different equilibrium configurations and deformation conditions

The topology of circular closed DNA in different equilibrium configurations and deformation conditions has been investigated. The distribution of twisting and bending energy and stress has been assessed. It is shown that the twisting/bending stiffness ratio qualitatively influences the deformation of a circular DNA molecule.     

Volume osmotic flows of non-homogeneous electrolyte solutions through horizontally mounted membrane

Results of an experimental study of volume osmotic flows in a single-membrane osmotic-diffusive cell, which contains a horizontal, microporous, symmetrical polymer membrane separating water and binary or ternary electrolyte solutions are presented. In the experimental set-up, water was placed on one side of the membrane. The opposite side of the membrane was exposed to binary or ternary solutions. As binary solutions, aqueous potassium chloride or ammonia solutions were used, whereas potassium chloride in 0.25 mol x l(-1) aqueous ammonia solution or ammonia in 0.1 mol x l(-1) aqueous potassium chloride solution were used as ternary solutions. Two (A and B) configurations of a single-membrane osmotic-diffusive cell in a gravitational field were studied. In configuration A, water was placed in a compartment above the membrane and the solution below the membrane. In configuration B the position of water and solution was reversed. Furthermore, the effect of amplification of volume osmotic flows of electrolyte solutions in the single-membrane osmotic-diffusive electrochemical cell was demonstrated. The thermodynamic models of the flux graviosmotic and amplification effects were developed, and the volume flux graviosmotic effect for configurations A and B of a single-membrane osmotic-diffusive cell was calculated. The results were interpreted within the conventional instability category, increasing the diffusion permeability coefficient value for the system: concentration boundary layer/membrane/concentration boundary layer.     

Diffusion Microscopist Simulator: A General Monte Carlo Simulation System for Diffusion Magnetic Resonance Imaging

This article describes the development and application of an integrated, generalized, and efficient Monte Carlo simulation system for diffusion magnetic resonance imaging (dMRI), named Diffusion Microscopist Simulator (DMS). DMS comprises a random walk Monte Carlo simulator and an MR image synthesizer. The former has the capacity to perform large-scale simulations of Brownian dynamics in the virtual environments of neural tissues at various levels of complexity, and the latter is flexible enough to synthesize dMRI datasets from a variety of simulated MRI pulse sequences. The aims of DMS are to give insights into the link between the fundamental diffusion process in biological tissues and the features observed in dMRI, as well as to provide appropriate ground-truth information for the development, optimization, and validation of dMRI acquisition schemes for different applications. The validity, efficiency, and potential applications of DMS are evaluated through four benchmark experiments, including the simulated dMRI of white matter fibers, the multiple scattering diffusion imaging, the biophysical modeling of polar cell membranes, and the high angular resolution diffusion imaging and fiber tractography of complex fiber configurations. We expect that this novel software tool would be substantially advantageous to clarify the interrelationship between dMRI and the microscopic characteristics of brain tissues, and to advance the biophysical modeling and the dMRI methodologies.     

Coupled Protein Diffusion and Folding in the Cell

When a protein unfolds in the cell, its diffusion coefficient is affected by its increased hydrodynamic radius and by interactions of exposed hydrophobic residues with the cytoplasmic matrix, including chaperones. We characterize protein diffusion by photobleaching whole cells at a single point, and imaging the concentration change of fluorescent-labeled protein throughout the cell as a function of time. As a folded reference protein we use green fluorescent protein. The resulting region-dependent anomalous diffusion is well characterized by 2-D or 3-D diffusion equations coupled to a clustering algorithm that accounts for position-dependent diffusion. Then we study diffusion of a destabilized mutant of the enzyme phosphoglycerate kinase (PGK) and of its stable control inside the cell. Unlike the green fluorescent protein control''s diffusion coefficient, PGK''s diffusion coefficient is a non-monotonic function of temperature, signaling ‘sticking’ of the protein in the cytosol as it begins to unfold. The temperature-dependent increase and subsequent decrease of the PGK diffusion coefficient in the cytosol is greater than a simple size-scaling model suggests. Chaperone binding of the unfolding protein inside the cell is one plausible candidate for even slower diffusion of PGK, and we test the plausibility of this hypothesis experimentally, although we do not rule out other candidates.     

Molecular dynamics study of the KcsA potassium channel

The structural, dynamical, and thermodynamic properties of a model potassium channel are studied using molecular dynamics simulations. We use the recently unveiled protein structure for the KcsA potassium channel from Streptomyces lividans. Total and free energy profiles of potassium and sodium ions reveal a considerable preference for the larger potassium ions. The selectivity of the channel arises from its ability to completely solvate the potassium ions, but not the smaller sodium ions. Self-diffusion of water within the narrow selectivity filter is found to be reduced by an order of magnitude from bulk levels, whereas the wider hydrophobic section of the pore maintains near-bulk self-diffusion. Simulations examining multiple ion configurations suggest a two-ion channel. Ion diffusion is found to be reduced to approximately (1)/(3) of bulk diffusion within the selectivity filter. The reduced ion mobility does not hinder the passage of ions, as permeation appears to be driven by Coulomb repulsion within this multiple ion channel.     

Numerical Simulation of CO2 Flooding of Coalbed Methane Considering the Fluid-Solid Coupling Effect

CO₂ flooding of coalbed methane (CO₂-ECBM) not only stores CO₂ underground and reduces greenhouse gas emissions but also enhances the gas production ratio. This coupled process involves multi-phase fluid flow and coal-rock deformation, as well as processes such as competitive gas adsorption and diffusion from the coal matrix into fractures. A dual-porosity medium that consists of a matrix and fractures was built to simulate the flooding process, and a mathematical model was used to consider the competitive adsorption, diffusion and seepage processes and the interaction between flow and deformation. Due to the effects of the initial pressure and the differences in pressure variation during the production process, permeability changes caused by matrix shrinkage were spatially variable in the reservoir. The maximum value of permeability appeared near the production well, and the degree of rebound decreased with increasing distance from the production well.     

Single-particle tracking: the distribution of diffusion coefficients.

In single-particle tracking experiments, the diffusion coefficient D may be measured from the trajectory of an individual particle in the cell membrane. The statistical distribution of single-trajectory diffusion coefficients is examined by Monte Carlo calculations. The width of this distribution may be useful as a measure of the heterogeneity of the membrane and as a test of models of hindered diffusion in the membrane. For some models, the distribution of the short-range diffusion coefficient is much narrower than the observed distribution for proteins diffusing in cell membranes. To aid in the analysis of single-particle tracking measurements, the distribution of D is examined for various definitions of D and for various trajectory lengths.     

Diffusion approximation of the stochastic process of microtubule assembly

Microtubules are protein polymers that guide intracellular motility. Stochastic switching of a microtubule between states of elongation, shortening, and pause is described in detail by the dynamic instability (DI) model. Recently we have described the dynamics of microtubules phenomenologically as generalized diffusion of their ends. Genesis of the diffusion dynamics and accuracy of diffusion model are studied in this work. It is shown that wandering of the end of a microtubule undergoing DI asymptotically approaches the Wiener diffusion process. Accuracy of the diffusion approximation is evaluated by comparing its predictions with results of simulation of DI. Stationary distributions of microtubule length and lifetime that are predicted by both models differ qualitatively between two cell types considered. However, predictions of the diffusion model are in each case practically identical to predictions of the DI model being also consistent with experimental data. The peculiar stochastic process of microtubule assembly thus converges at cell scale to a kind of widespread-in-nature diffusion process. This result is considered an example of qualitative change in dynamical properties in transition from the molecular to cellular level of biological organization. Additionally, it suggests employment of diffusion process theory in studying functions of microtubules in the cell.     

Effects of Dragonfly Wing Structure on the Dynamic Performances

The configurations of dragonfly wings, including the corrugations of the chordwise cross-section, the microstructure of the longitudinal veins and membrane, were comprehensively investigated using the Environmental Scanning Electron Microscopy (ESEM). Based on the experimental results reported previously, the multi-scale and multi-dimensional models with different structural features of dragonfly wing were created, and the biological dynamic behaviors of wing models were discussed through the Finite Element Method (FEM). The results demonstrate that the effects of different structural features on dynamic behaviors of dragonfly wing such as natural frequency/modal, bending/torsional deformation, reaction force/torque are very significant. The corrugations of dragonfly wing along the chordwise can observably improve the flapping frequency because of the greater structural stiffness of wings. In updated model, the novel sandwich microstructure of the longitudinal veins remarkably improves the torsional deformation of dragonfly wing while it has a little effect on the flapping frequency and bending deformation. These integrated structural features can adjust the deformation of wing oneself, therefore the flow field around the wings can be controlled adaptively. The fact is that the flights of dragonfly wing with sandwich microstructure of longitudinal veins are more efficient and intelligent.     

Transport of neutral solute in articular cartilage: effect of microstructure anisotropy

Due to the avascular nature of articular cartilage, solute transport through its extracellular matrix is critical for the maintenance and the functioning of the tissue. What is more, diffusion of macromolecules may be affected by the microstructure of the extracellular matrix in both undeformed and deformed cartilage and experiments demonstrate diffusion anisotropy in the case of large solute. However, these phenomena have not received sufficient theoretical attention to date. We hypothesize here that the diffusion anisotropy of macromolecules is brought about by the particular microstructure of the cartilage network. Based on this hypothesis, we then propose a mathematical model that correlates the diffusion coefficient tensor with the structural orientation tensor of the network. This model is shown to be successful in describing anisotropic diffusion of macromolecules in undeformed tissue and is capable of clarifying the effects of network reorientation as the tissue deforms under mechanical load. Additionally, our model explains the anomaly that at large strain, in a cylindrical plug under unconfined compression, solute diffusion in the radial direction increases with strain. Our results indicate that in cartilage the degree of diffusion anisotropy is site specific, but depends also on the size of the diffusing molecule. Mechanical loading initiates and/or further exacerbates this anisotropy. At small deformation, solute diffusion is near isotropic in a tissue that is isotropic in its unstressed state, becoming anisotropic as loading progresses. Mechanical loading leads to an attenuation of solute diffusion in all directions when deformation is small. However, loading, if it is high enough, enhances solute transport in the direction perpendicular to the load line, instead of inhibiting it.