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PubMed1999

Diffusion of macromolecules in agarose gels: comparison of linear and globular configurations.

The diffusion coefficients (D) of different types of macromolecules (proteins, dextrans, polymer beads, and DNA) were measured by fluorescence recovery after photobleaching (FRAP) both in solution and in 2% agarose gels to compare transport properties of these macromolecules. Diffusion measurements were conducted with concentrations low enough to avoid macromolecular interactions. For gel measurements, diffusion data were fitted according to different theories: polymer chains and spherical macromolecules were analyzed separately. As chain length increases, diffusion coefficients of DNA show a clear shift from a Rouse-like behavior (DG congruent with N0-0.5) to a reptational behavior (DG congruent with N0-2.0). The pore size, a, of a 2% agarose gel cast in a 0.1 M PBS solution was estimated. Diffusion coefficients of the proteins and the polymer beads were analyzed with the Ogston model and the effective medium model permitting the estimation of an agarose gel fiber radius and hydraulic permeability of the gels. Not only did flexible macromolecules exhibit greater mobility in the gel than did comparable-size rigid spherical particles, they also proved to be a more useful probe of available space between fibers.

Animals↗
PubMed2006

Transport and localization amongst coupled substructures.

The dynamics of the transport of the mean-square diffuse wave amplitude among coupled substructures is examined. Applications include coupled quantum dots, reverberation rooms, and chaotic billiards. A self-consistent theory is found to predict classical diffusive behavior at strong coupling, but to predict localization when coupling times are comparable to or greater than Heisenberg times. Predictions are compared to an exact result, to the Vollhardt-Wolfle self-consistent theory for multiply scattering continua, and to direct numerical simulations.

Journal Article↗
PubMed1992

Extending the stochastic two-stage model of carcinogenesis to include self-regulation of the nonmalignant cell population.

One of the challenges of introducing greater biological realism into stochastic models of cancer induction is to find a way to represent the homeostatic control of the normal cell population over its own size without complicating the analysis too much to obtain useful results. Current two-stage models of carcinogenesis typically ignore homeostatic control. Instead, a deterministic growth path is specified for the population of "normal" cells, while the population of "initiated" cells is assumed to grow randomly according to a birth-death process with random immigrations from the normal population. This paper introduces a simple model of homeostatically controlled cell division for mature tissues, in which the size of the nonmalignant population remains essentially constant over time. Growth of the nonmalignant cell population (normal and initiated cells) is restricted by allowing cells to divide only to fill the "openings" left by cells that die or differentiate, thus maintaining the constant size of the nonmalignant cell population. The fundamental technical insight from this model is that random walks, rather than birth-and-death processes, are the appropriate stochastic processes for describing the kinetics of the initiated cell population. Qualitative and analytic results are presented, drawn from the mathematical theories of random walks and diffusion processes, that describe the probability of spontaneous extinction and the size distribution of surviving initiated populations when the death/differentiation rates of normal and initiated cells are known. The constraint that the nonmalignant population size must remain approximately constant leads to much simpler analytic formulas and approximations, flowing directly from random walk theory, than in previous birth-death models.(ABSTRACT TRUNCATED AT 250 WORDS)

Cell Death↗
PubMed2000

Resolving heterogeneity on the single molecular level with the photon-counting histogram.

The diffusion of fluorescent particles through a small, illuminated observation volume gives rise to intensity fluctuations caused by particle number fluctuations in the open observation volume and the inhomogeneous excitation-beam profile. The intensity distribution of these fluorescence fluctuations is experimentally captured by the photon-counting histogram (PCH). We recently introduced the theory of the PCH for diffusing particles (Chen et al., Biophys. J., 77:553-567), where we showed that we can uniquely describe the distribution of photon counts with only two parameters for each species: the molecular brightness of the particle and the average number of particles within the observation volume. The PCH is sensitive to the molecular brightness and thus offers the possibility to separate a mixture of fluorescent species into its constituents, based on a difference in their molecular brightness alone. This analysis is complementary to the autocorrelation function, traditionally used in fluorescence fluctuation spectroscopy, which separates a mixture of species by a difference in their diffusion coefficient. The PCH of each individual species is convoluted successively to yield the PCH of the mixture. Successful resolution of the histogram into its components is largely a matter of the signal statistics. Here, we discuss the case of two species in detail and show that a concentration for each species exists, where the signal statistics is optimal. We also discuss the influence of the absolute molecular brightness and the brightness contrast between two species on the resolvability of two species. A binary dye mixture serves as a model system to demonstrate that the molecular brightness and the concentration of each species can be resolved experimentally from a single or from several histograms. We extend our study to biomolecules, where we label proteins with a fluorescent dye and show that a brightness ratio of two can be resolved. The ability to resolve a brightness ratio of two is very important for biological applications.

Alcohol Dehydrogenase↗
PubMed2001

Determination of genuine diffusivities in heterogeneous media using stimulated echo pulsed field gradient NMR.

Pulsed field gradient (PFG) NMR diffusion measurements in heterogeneous media may lead to erroneous results due to the disturbing influence of internal magnetic field gradients. Here, we present a simple theoretical model which allows one to interpret data obtained by stimulated spin echo PFG NMR in the presence of spatially varying internal field gradients. Using the results of this theory, the genuine self-diffusion coefficients in heterogeneous media may be extrapolated from the dependence of the apparent diffusivities on the dephasing time of the simulated echo PFG NMR sequence. Experimental evidence that such extrapolation yields satisfactory results for self-diffusion of hexadecane in natural sediments (sand) and of n-octanol in doped MgO pastes is provided.

Journal Article↗
PubMed1989

Lateral diffusion of membrane proteins in protein-rich membranes. A simple hard particle model for concentration dependence of the two-dimensional diffusion coefficient.

A model for the effect of protein concentration on the rate of lateral diffusion of integral membrane proteins is presented, in which the proteins are represented by equivalent hard circular particles on a surface. As the density of particles increases, the probability of finding a vacancy immediately adjacent to a tracer particle into which it may diffuse decreases, resulting in a concomitant reduction of the tracer diffusion coefficient. Using scaled particle theory to calculate the concentration-dependent probabilities, a simple approximate result is obtained in closed form, that is compared with the results of previously published Monte Carlo lattice simulations and experimental observations.

Diffusion↗
PubMed1988

Effect of flow on O2 consumption during progressive hypoxemia.

Rabbit hindlimb preparations perfused with blood from donor rabbits were used to determine whether O2 consumption (VO2) during hypoxemia is limited by total O2 transport (TO2) or by capillary O2 driving pressure, as reflected by the venous PO2 (PVO2). The preparations were randomized into two groups: low flow (LF) and high flow (HF), perfused at 18 and 32 ml.min-1.kg of preparation wt-1, respectively. After a 1-h base-line period with arterial PO2 (PaO2) greater than 100 Torr, both groups were exposed to progressive decrements in PaO2 to less than 10 Torr. Sequential sets of arterial and venous blood gases were obtained, and VO2, TO2, and O2 extraction ratio (ERO2) were calculated. A plot of PVO2 vs. TO2 showed higher levels of PVO2 (P less than 0.05) in LF than HF, when compared at similar levels of TO2. Therefore the experimental protocol allowed the comparison of the separate effects of TO2 or PVO2 on VO2. Plotting VO2 as a function of TO2 revealed two distinct curves (P less than 0.05), with LF having a greater VO2 than HF at a given TO2. Conversely, a plot of VO2 as a function of PVO2 did not show a difference between the groups. The ERO2 of LF was greater than HF when compared at similar levels of TO2 (P less than 0.05). We conclude from these data that during progressive hypoxemia VO2 appears to be primarily limited by factors that determine capillary O2 diffusion. This conclusion supports the Kroghian theory of capillary O2 exchange.

Animals↗
PubMed1997

Myoglobin and hemoglobin rotational diffusion in the cell.

The detection of the 1H NMR signal of myoglobin (Mb) in tissue opens an opportunity to examine its cellular diffusion property, which is central to its purported role in facilitating oxygen transport. In perfused myocardium the field-dependent transverse relaxation analysis of the deoxy Mb proximal histidyl NdeltaH indicates that the Mb rotational correlation time in the cell is only approximately 1.4 times longer than it is in solution. Such a mobility is consistent with the theory that Mb facilitates oxygen diffusion from the sarcoplasm to the mitochondria. The microviscosities of the erythrocyte and myocyte environment are different. The hemoglobin (Hb) rotational correlation time is 2.2 longer in the cell than in solution. Because both the overlapping Hb and Mb signals are visible in vivo, a relaxation-based NMR strategy has been developed to discriminate between them.

Animals↗
PubMed1986

Structure and mobility of actin filaments as measured by quasielastic light scattering, viscometry, and electron microscopy.

Actin filaments of different lengths were prepared by polymerizing actin in the presence of various concentrations of gelsolin, a protein which accelerates actin polymerization by stabilizing nuclei from which filaments grow and which binds to their fast growing ends. The lengths of the actin filaments following polymerization were measured by electron microscopy and showed that the number-average filament length agreed with the predicted length if each gelsolin molecule acted as a seed for the growth of an actin filament. The distribution of lengths was independent of the actin:gelsolin ratio and was similar to that of actin filaments polymerized in the absence of gelsolin (Lw/Ln = 1.8). The mobility of these filaments in solution was studied by quasielastic light scattering and by viscometry. The translational diffusion constant determined by quasielastic light scattering was in agreement with the infinite dilution values calculated from the dimensions and the distribution of lengths determined by electron microscopy for relatively short filament lengths. Under conditions where overlap of the rotational domains of the filaments would be expected to occur, the measured diffusion rates deviated from their predicted dilute solution values and the solution viscosity increased abruptly. The dependence of the diffusion constant and the solution viscosity on the length of the actin filaments can be explained in terms of a theory that describes the restraints on diffusion of independent rigid rods in semi-dilute solution. The results suggest that the rheology of actin filaments can be accounted for by steric restraints. The length of cytoplasmic actin filaments in some cell types is such that these steric constraints are significant and could produce large changes in physical properties with small changes in filament length.

Actins↗
PubMed2000

A unifying theory of refractive error development.

While retinal defocus is believed to be myopigenic in nature, the underlying mechanism has remained elusive. We recently constructed a theory of refractive error development to investigate its fundamental properties. Our Incremental Retinal-Defocus Theory is based on the principle that the change in retinal-defocus magnitude during an increment of genetically-programmed ocular growth provides the requisite sign for the appropriate alteration in subsequent environmentally-induced ocular growth. This theory was tested under five experimental conditions: lenses, diffusers, occlusion, crystalline lens removal, and prolonged nearwork. Predictions of the theory were consistent with previous animal and human experimental findings. In addition, simulations using a MATLAB/SIMULINK model supported our theory by demonstrating quantitatively the appropriate directional changes in ocular growth rate. Thus, our Incremental Retinal-Defocus Theory provides a simple and logical unifying concept underlying the mechanism for the development of refractive error.

Computer Simulation↗
PubMed2005

Magnetization and spin-spin energy diffusion in the XY model: a diagrammatic approach.

It is shown that the diagrammatic cluster expansion technique for equilibrium averages of spin operators may be straightforwardly extended to the calculation of time-dependent correlation functions of spin operators. We use this technique to calculate exactly the first two non-vanishing moments of the spin-spin and energy-energy correlation functions of the XY model with arbitrary couplings, in the long-wavelength, infinite temperature limit appropriate for spin diffusion. These moments are then used to estimate the magnetization and spin-spin energy diffusion coefficients of the model using a phenomenological theory of Redfield. Qualitative agreement is obtained with recent experiments measuring diffusion of dipolar energy in calcium fluoride.

Journal Article↗
PubMed2005

Diffusion-influenced excited-state reversible transfer reactions, A* + Bright harpoon over left harpoonC* + D, with two different lifetimes: theories and simulations.

We report accurate Brownian simulation results for the kinetics of the pseudo-first-order diffusion-influenced excited-state reversible transfer reaction A(*) + Bright harpoon over left harpoonC(*) + D with two different lifetimes using two different propagation algorithms. The results are used to test approximate solutions for this many-particle problem. Available theories fail when one of the two reactions or (decay) rate constants is large. To remedy this situation, we develop two uniform approximations, which are based on introducing a generalized Smoluchowski term into the relaxation-time approximation. The best of these is the extended unified theory of reversible target reactions, which reduces correctly in all limits and exhibits superior agreement with simulations.

Journal Article↗
PubMed1991

The validation of freely diffusible tracer methods with NMR detection for measurement of blood flow.

While the general theory of measuring organ perfusion using exogenously administered freely diffusible tracers was originally formulated over 40 years ago, the application of NMR techniques for tracer detection is a recent development. A brief theoretical review and discussion of the literature validating the use of deuterium and fluorine as NMR-detectable tracers is provided.

Blood Circulation↗
PubMed2000

Dimension of fractal growth patterns as a dynamical exponent

We consider a conformal theory of fractal growth patterns in two dimensions, including diffusion limited aggregation (DLA) as a particular case. In this theory the fractal dimension of the asymptotic cluster manifests itself as a dynamical exponent observable already at very early growth stages. Using a renormalization relation we show from early stage dynamics that the dimension D of DLA can be estimated, 1.69<D<1.72. We explain why traditional numerical estimates converged so slowly. We discuss similar computations for other fractal growth processes in two dimensions.

Journal Article↗
PubMed1991

Gas diffusion in the middle ear.

The ex vacuo theory, claiming that in cases of middle ear underaeration air enters the middle ear through the Eustachian tube in diminished amounts while oxygen continues to leave it into the blood by diffusion as in normal condition, does not provide a complete explanation for the aeration problems encountered in middle ear pathology. This study shows that when atelectatic ears are politzerized (hyperinflated) with different gases, these gases disappear with a speed that correspond to the diffusion coefficient of the different gases. This finding together with the fact that the composition of middle ear gases is very similar to that found in the venous circulation suggests that it is a diffusional process of several gases from the middle ear into the blood and in the opposite direction that mainly determines the middle ear pressure.

Adolescent↗
PubMed2006

Cooperative hydrogen bonds of macromolecules. 2. Two-dimensional cooperativity in the binding of poly(4-vinylpyridine) to poly(4-vinylphenol).

The hydrogen bond interaction of poly(4-vinylphenol) (PVF), ligated by a 20 mol/mol excess of pyridine-d(5) (PD) in tetrahydrofuran-d(8), with poly(4-vinylpyridine) (PVP) was studied using liquid and solid-state NMR and quantum mechanical calculations. Because of its cooperative interaction, PVP substitutes PD in its hydrogen bond with PVF, thus forming a PVF-PVP complex, which gradually precipitates from solution. On the basis of the 1H/13C NMR spin-diffusion experiments and density functional theory quantum calculations, the complex is shown to have the fairly regular structure of a polymer sheet with intermittent H-bond links between PVF and PVP chains. The cooperativity of PVP interaction with PVF was studied by measuring the dependence of the binding degree alpha of PVP on its polymerization degree (P(n), being 10, 17, 30, 36, 48, 65, and 84) at various PVP/PVF molar ratios. The value of alpha was established indirectly by measuring the fraction of liberated PD using its 2H quadrupolar relaxation and pulsed field-gradient spin-echo measurement of self-diffusion. The cooperativity is shown to be of a higher order and two-dimensional, that is, dependent on both the polymerization degree of PVP and its ratio to PVF. A mathematical model of such two-dimensional cooperativity based chiefly on a proximity effect is suggested.

Journal Article↗
PubMed2003

Diffusion in a generalized Rubinstein-Duke model of electrophoresis with kinematic disorder.

Using a generalized Rubinstein-Duke model, we prove rigorously that kinematic disorder leaves the prediction of the standard reptation theory for the scaling of the diffusion constant in the limit for long polymer chains D proportional to L(-2) unaffected. Based on an analytical calculation as well as on Monte Carlo simulations, we predict kinematic disorder to affect the center-of-mass diffusion constant of an entangled polymer in the limit for long chains by the same factor as single particle diffusion in a random barrier model.

Journal Article↗
PubMed1994

Diffusion measurement in sandstone core: NMR determination of surface-to-volume ratio and surface relaxivity.

Recent theoretical work has shown that the time dependence of the effective diffusion constant in porous media contains information about the surface to pore volume ratio, the tortuosity and other petrophysical information. We have measured the effective diffusion constant in a water saturated core of Fontainebleau sandstone as a function of diffusion time. From the short time behavior, we are able to extract the surface to pore volume ratio. This value can be combined with the spin-lattice relaxation rate measured on the same core under identical conditions to yield the surface relaxivity rho = 1.6 x 10(-5)m/s. Measurements at 25.0 degrees C and 40.0 degrees C demonstrate that the effect of surface relaxation on the measured diffusion coefficient is small, as predicted by theory.

Diffusion↗