Rotational diffusion coefficients of a small,spherical subunit flexibly tethered to a larger sphere

The rotational diffusion coefficients of a small spherical particle, which is flexibly anchored to the surface of a much larger sphere, are calculated using the hydrodynamic theory of segmentally flexible particles. The model is intended for representing the rotational mobility of a small residue or chromophore in the surface of a globular macromolecule. The coefficients are found to be essentially independent, or to vary slowly with the relative dispositions of the spheres. They are also insensitive to the size ratio when this ratio is high enough. These findings support the use of an approximative treatment proposed by Wegener in which the small conformation dependence is averaged out. The resulting averages are tentatively used in the Lipari-Szabo model for restricted rotational diffusion in a cone. It is concluded that the rotational relaxation of the small sphere has three components: (i) a torsional rotation with the same diffusion coefficient as the free sphere; (ii) a perpendicular wobbling with a diffusion coefficient several (five in a typical case) times smaller; and (iii) an overall rotation of the whole macromolecule, that will appear in a much longer time scale if the two spheres have quite distinct sizes.     

A diffusion model for mesoderm induction in amphibian embryos

In this paper we try to answer the question whether diffusion is a possible mechanism to explain mesoderm induction in Amphibians. First the embryological data are discussed and a hypothesis for mesoderm formation is set forth. The blastula being essentially a hollow sphere, we assume that the induction mechanism in an embryo at the blastula stage can be simulated by diffusion-reaction processes on spherical surfaces. A model is constructed for the simple case when the source is held constant with respect to time, the decay proportional to the concentration and the diffusion coefficient a constant, From simulation we find a (best) value for the decay constant to be 6 × 10^–5/sec and for the diffusion constant to be 0.24 × 10^{– 6} cm²/sec. The relation between the parameters is derived from an analytic solution for the diffusion process on a spherical surface with a continuously producing point source and the concentration proportional to the decay. The form and regulative properties of the steady concentration gradient are discussed.     

Lateral diffusion of cholesterol and dimyristoylphosphatidylcholine in a lipid bilayer measured by pulsed field gradient NMR spectroscopy

The pulsed field gradient NMR method for measuring self-diffusion has been used for a direct determination of the lateral diffusion coefficient of cholesterol, fluorine labeled at the 6-position, for an oriented lamellar liquid-crystalline phase of dimyristoylphosphatidylcholine (DMPC)/cholesterol/water. It is found that the diffusion coefficients of DMPC and cholesterol are equal over a large temperature interval. The apparent energy of activation for the diffusion process (58 kJ/mol) is about the same as for a lamellar phase of DMPC/water, whereas the phospholipid lateral diffusion coefficient is approximately four times smaller in the presence of cholesterol.     

Anisotropic diffusion in mitral cell dendrites revealed by fluorescence correlation spectroscopy

Fluorescence correlation spectroscopy (FCS) can be used to measure kinetic properties of single molecules in drops of solution or in cells. Here we report on FCS measurements of tetramethylrhodamine (TMR)-dextran (10 kDa) in dendrites of cultured mitral cells of Xenopus laevis tadpoles. To interpret such measurements correctly, the plasma membrane as a boundary of diffusion has to be taken into account. We show that the fluorescence data recorded from dendrites are best described by a model of anisotropic diffusion. As compared to diffusion in water, diffusion of the 10-kDa TMR-dextran along the dendrite is slowed down by a factor 1.1-2.1, whereas diffusion in lateral direction is 10-100 times slower. The dense intradendritic network of microtubules oriented parallel to the dendrite is discussed as a possible basis for the observed anisotropy. In somata, diffusion was found to be isotropic in three dimensions and 1.2-2.6 times slower than in water.     

Intracellular diffusion of water

Self-diffusion of cell water has been measured at diffusion times ranging from 0.3 ms to 1.0 s for human red cells, yeast, and brine shrimp using various pulsed gradient NMR methods. Intracellular diffusion coefficients and membrane permeabilities are calculated from these data with the aid of previous theoretical results for regularly spaced permeable planar barriers. The intracellular diffusion coefficients of water range from 1.2 X 10(-6) to 6 X 10(-6) cm2/s for the various samples. Outer-membrane permeabilities to water range from 0.0001 to 0.01 cm/s. The self-diffusion coefficient of lipid in a sample of human breast adipose tissue was found to be 1.5 X 10(-7) cm2/s.     

Anomalous diffusion due to binding: a Monte Carlo study.

In classical diffusion, the mean-square displacement increases linearly with time. But in the presence of obstacles or binding sites, anomalous diffusion may occur, in which the mean-square displacement is proportional to a nonintegral power of time for some or all times. Anomalous diffusion is discussed for various models of binding, including an obstruction/binding model in which immobile membrane proteins are represented by obstacles that bind diffusing particles in nearest-neighbor sites. The classification of binding models is considered, including the distinction between valley and mountain models and the distinction between singular and nonsingular distributions of binding energies. Anomalous diffusion is sensitive to the initial conditions of the measurement. In valley models, diffusion is anomalous if the diffusing particles start at random positions but normal if the particles start at thermal equilibrium positions. Thermal equilibration leads to normal diffusion, or to diffusion as normal as the obstacles allow.     

Random genetic drift and selection in a triallelic locus: a continuous diffusion model.

The Kolmogorov forward diffusion equation is used to examine the evolution of three alleles at one locus under viability selection and random genetic drift. Separation of variables and Chebyschev approximations are employed to solve this equation for long times. As an example, one artificial viability set is examined in detail; its general implications for the evolution at a triallelic locus are discussed.     

Singular solutions of the diffusion equation of population genetics

The forward diffusion equation for gene frequency dynamics is solved subject to the condition that the total probability is conserved at all times. This can lead to solutions developing singular spikes (Dirac delta functions) at the gene frequencies 0 and 1. When such spikes appear in solutions they signal gene loss or gene fixation, with the "weight" associated with the spikes corresponding to the probability of loss or fixation. The forward diffusion equation is thus solved for all gene frequencies, namely the absorbing frequencies of 0 and 1 along with the continuous range of gene frequencies on the interval (0,1) that excludes the frequencies of 0 and 1. Previously, the probabilities of the absorbing frequencies of 0 and 1 were found by appeal to the backward diffusion equation, while those in the continuous range (0,1) were found from the forward diffusion equation. Our unified approach does not require two separate equations for a complete dynamical treatment of all gene frequencies within a diffusion approximation framework. For cases involving mutation, migration and selection, it is shown that a property of the deterministic part of gene frequency dynamics determines when fixation and loss can occur. It is also shown how solution of the forward equation, at long times, leads to the standard result for the fixation probability.     

Lateral diffusion coefficients in membranes measured by resonance energy transfer and a new algorithm for diffusion in two dimensions

We describe measurements of lateral diffusion in membranes using resonance energy transfer. The donor was a rhenium (Re) metal-ligand complex lipid, which displays a donor decay time near 3 micros. The long donor lifetime resulted in an ability to measure lateral diffusion coefficient below 10(-8) cm(2)/s. The donor decay data were analyzed using a new numerical algorithm for calculation of resonance energy transfer for donors and acceptors randomly distributed in two dimensions. An analytical solution to the diffusion equation in two dimensions is not known, so the equation was solved by the relaxation method in Laplace space. This algorithm allows the donor decay in the absence of energy transfer to be multiexponential. The simulations show that mutual lateral diffusion coefficients of the donor and acceptor on the order of 10(-8) cm(2)/s are readily recovered from the frequency-domain data with donor decay times on the microsecond timescale. Importantly, the lateral diffusion coefficients and acceptor concentrations can be recovered independently despite correlation between these parameters. This algorithm was tested and verified using the donor decays of a long lifetime rhenium lipid donor and a Texas red-lipid acceptor. Lateral diffusion coefficients ranged from 4.4 x 10(-9) cm(2)/s in 1,2-dimyristoyl-sn-glycero-3-[phospho-rac-(1-glycerol)] (DMPG) at 10 degrees C to 1.7 x 10(-7) cm(2)/s in 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) at 35 degrees C. These results demonstrated the possibility of direct measurements of lateral diffusion coefficients using microsecond decay time luminophores.     

External diffusion in solid-phase immunoassays

Calculations are presented describing the influence of external diffusion in the kinetics of solid-phase immunoassays. The analysis is concerned with systems where one reactant is immobilized at the surface of a sphere of arbitrary radius. The solution for a plane surface is found as a limiting case. The factors determining whether the reaction is diffusion or reaction controlled are found to be sphere radius, surface concentration of binding sites, forward reaction rate and diffusion constant of reacting species. Means of determining whether the reaction is diffusion or reaction controlled from observable quantities are described. When applied to heterogeneous antibody-antigen binding it is found that normally the binding to cell-size spheres is not limited by external diffusion. However, when applied to solid-phase assays with high surface concentrations of binding sites immobilized at plane surfaces or macroscopic spheres the binding is found to be diffusion limited. The importance of a mass transfer analysis in this case is also discussed.     

Transient solute diffusion in articular cartilage

The one-dimensional transient diffusion of glucose, inulin and dextran into adult bovine knee articular cartilage was determined for transport times of 1, 5, 15 and 60 min, and 4, 12, 24 and 48 h. The apparent diffusion coefficient and apparent interface partition coefficient were calculated from the concentration-depth profiles within the tissue using a theoretical model for non-steady state solute diffusion. The diffusion coefficient was found to decrease with both solute size and transport time. The partition coefficient also decreased with solute size but increased with transport time. Neither coefficient was dependent on normal tissue fluid or proteoglycan content variations.     

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.     

Measurement of normal and anomalous diffusion of dyes within protein structures fabricated via multiphoton excited cross-linking

We demonstrate microscale spatial and chemical control of diffusion within protein matrixes created through the use of nonlinear multiphoton excited photochemistry. The mobility of fluorescent dyes of different mass and composition within controlled cross-linked environments has been measured using two-photon excited fluorescence recovery after photobleaching (FRAP). The diffusion times for several rhodamine and sulforhodamine dyes within these fabricated structures were found to be approximately 3-4 orders of magnitude slower than in free solution. The precise diffusion times can be tuned by varying the laser exposure during the fabrication of the matrix, and the diffusion can be correlated with the mesh size determined by TEM and Flory-Rehner analysis. We find that the hydrophobic Texas Red dyes (sulforhodamines) exhibit diffusion that is highly anomalous, indicative of a strong interaction with the hydrophobic cross-linked protein matrix. These results suggests the use of these cross-linked protein matrixes as ideal model systems in which to systematically study anomalous diffusion. Finally, the diffusion can be tuned within a multilayered protein matrix, and this in conjunction with slow diffusion also suggests the use of these structures in controlled release applications.     

Analysis of diffusion and relaxation behavior of water in apple parenchymal cells

It has been demonstrated by an example of apple parenchymal cells that NMR spectroscopy can be used to analyze the relaxation and diffusion of water molecules in plant cells. With small diffusion times, three relaxation components have been distinguished, which correspond to water in a vacuole, in the cytoplasm, and in intercellular liquid. The coefficient of self-diffusion corresponding to these components have been determined. With large diffusion times, it is possible to distinguish two components. For the slowly relaxing component (which corresponds to water in a vacuole), the regime of restricted diffusion was observed. For a quickly relaxing component, an anomalous increase in the coefficient of self-diffusion with the time of diffusion took place.     

Effective diffusion rate through a polymer network: influence of nonspecific binding and intersegment transfer

The effective diffusion rate of a tracer molecule through a polymer network can be influenced by nonspecific binding. If such binding occurs, the local density fluctuations (segmental diffusion) of the network molecules will contribute to the net displacements of tracer molecules. If the network is strongly interconnected by entanglement or cross-linking, these local motions will only carry the tracer molecules over a small region, and effective transport would require dissociation and reassociation of the tracer molecule to another part of the network. Alternatively, tracer molecules could be transferred directly (intersegment transfer) between different parts of the network whenever they are brought sufficiently close by the density fluctuations. A wormlike-chain model for the segmental diffusion of a polymer is used to describe the network motions and to derive the effective diffusion rate for a tracer molecule as a function of network density and binding constant with or without intersegment transfer contributing. It is found that the density dependence for the effective diffusion of ethidium bromide through dense DNA solutions studied by photobleaching recovery [R. D. Icenogle and E. L. Elson (1983) Biopolymers 22 , 1949–1966] agrees with an intersegment-transfer mechanism limited by the segmental DNA motions. The calculations are also applied to a model for the intracellular diffusion of molecules loosely bound to the cytomatrix. If intersegment transfer dominates it can account for the observed size independence for the intracellular diffusion rates of various injected macromolecules.     

Protein diffusion in mammalian cell cytoplasm

We introduce a new method for mesoscopic modeling of protein diffusion in an entire cell. This method is based on the construction of a three-dimensional digital model cell from confocal microscopy data. The model cell is segmented into the cytoplasm, nucleus, plasma membrane, and nuclear envelope, in which environment protein motion is modeled by fully numerical mesoscopic methods. Finer cellular structures that cannot be resolved with the imaging technique, which significantly affect protein motion, are accounted for in this method by assigning an effective, position-dependent porosity to the cell. This porosity can also be determined by confocal microscopy using the equilibrium distribution of a non-binding fluorescent protein. Distinction can now be made within this method between diffusion in the liquid phase of the cell (cytosol/nucleosol) and the cytoplasm/nucleoplasm. Here we applied the method to analyze fluorescence recovery after photobleach (FRAP) experiments in which the diffusion coefficient of a freely-diffusing model protein was determined for two different cell lines, and to explain the clear difference typically observed between conventional FRAP results and those of fluorescence correlation spectroscopy (FCS). A large difference was found in the FRAP experiments between diffusion in the cytoplasm/nucleoplasm and in the cytosol/nucleosol, for all of which the diffusion coefficients were determined. The cytosol results were found to be in very good agreement with those by FCS.     

The impact of diffusion and stirring on the dynamics of interacting populations

We investigate the combined effects of diffusion and stirring on the dynamics of interacting populations which have spatial structure. Specifically we consider the marine phytoplankton and zooplankton populations, and model them as an excitable medium. The results are applicable to other biological and chemical systems. Under certain conditions the combination of diffusion and stirring is found to enhance the excitability, and hence population growth of the system. Diffusion is found to play an important role: too much and initial perturbations are smoothed away, too little and insufficient mixing takes place before the reaction is over. A key time-scale is the mix-down time, the time it takes for the spatial scale of a population to be reduced to that of a diffusively controlled filament. If the mix-down time is short compared to the reaction time-scale, then excitation of the system is suppressed. For intermediate values of the mix-down time the peak population can attain values many times that of a population without spatial structure. We highlight the importance of the spatial scale of the initial disturbance to the system.     

Hyaluronate diffusion in semidilute solutions

Analysis of the mutual diffusion coefficient of hyaluronate reveals that it rapidly increases with increasing concentration or decreasing ionic strength. The mutual diffusion coefficients analyzed by boundary relaxation in the analytical ultracentrifuge by either Raleigh interference optics or absorption optics (through the use of fluorescein-labeled hyaluronate) yielded similar values. The theoretical treatment of the mutual diffusion coefficient has been analyzed in terms of experimentally measured intradiffusion coefficients and thermodynamic virial coefficients. Only approximate agreement between theory and experiment was found. The concept of formation of transient statistical network structures in semidilute solutions of hyaluronate was applied to evaluate a critical concentration at which network formation occurs. This has been discussed in relation to the marked decrease in the intradiffusion coefficient of hyaluronate with concentration. The formation of network structures in hyaluronate was found not to preclude the hyaluronate undergoing extremely rapid rates of mutual diffusion (with diffusion coefficients ～30 × 10^?11 m² s¹) under conditions of relatively large initial chemical potential gradients. Measurements of the unidirectional flux of hyaluronate for nonzero gradients demonstrated their marked sensitivity to the magnitude of the concentration difference across the boundary. An experimental feature of the unidrectional diffusion coefficients of hyaluronate is that they may be analyzed purely in terms of mutual and intradiffusion processes. The backflux diffusion coefficient (describing the flux against the imposed concentration gradient) appeared identical with the intradiffusion coefficient. The analysis of the various sources of errors made in this study suggests that the magnitude of the diffusion coefficients measured may be regarded only as approximate.     

Distribution and diffusion of alamethicin in a lecithin/water model membrane system

Summary Attenuated total reflection infrared spectroscopy has been used to determine the equilibrium distribution of the peptide antibiotic alamethicinR _F30 between dipalmitoyl phosphatidylcholine bilayers and the aqueous environment. The distribution coefficientK=c _eq ^W /c _eq ^M turned out to be concentration dependent, pointing to alamethicin association in the membrane with increasing concentration in the aqueous phase (c _eq ^W ). This concentration was varied within 28 and 310nm, i.e., in a range typical for black film experiments. Furthermore, diffusion coefficients of alamethicin in the hydrophobic phase of the membrane (D _M) and across the membrane/water interface (D _I) have been estimated from the time course of the equilibration process. It was found that the diffusion rate of the uncharged analogueR _F50 is about 10 times higher than that of theR _F30 component, exhibiting one negative charge at theC-terminus. The time constants for transmembrane diffusion of alamethicinR _F30 varied between 2.2 hr at low concentration and 3.2 hr at higher concentration. The corresponding low concentration value of theR _F50 component was found to be 0.25 hr.     

The effect of diffusion,depolymerization and nucleation promoting factors on actin gel growth

In eukaryotic cells, localized actin polymerization is able to deform the plasma membrane and push the cell forward. Depolymerization of actin filaments and diffusion of actin monomers ensure the availability of monomers at sites of polymerization, and therefore these processes must play an active role in cellular actin dynamics. Here we reveal experimental evidence that actin gel growth can be limited by monomer diffusion, consistent with theoretical predictions. We study actin gels formed on beads coated with ActA (and ActA fragments), the bacterial factor responsible for actin-based movement of Listeria monocytogenes. We observe a saturation of gel thickness with increasing bead radius, the signature of diffusion control. Data analysis using an elastic model of actin gel growth gives an estimate of 2×10^–8 cm^–2 s^–1 for the diffusion coefficient of actin monomers through the gel, ten times less than in buffer, and in agreement with literature values in bulk cytoskeleton, providing corroboration of our model. The depolymerization rate of actin filaments and the elastic modulus of the gel are also evaluated. Furthermore, we qualitatively examine the different actin gels produced when ActA fragments interact with either VASP or the Arp2/3 complex.