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PubMed2005

Brownian dynamics simulations of the self- and collective rotational diffusion coefficients of rigid long thin rods.

Recently a microscopic theory for the dynamics of suspensions of long thin rigid rods was presented, confirming and expanding the well-known theory by Doi and Edwards [The Theory of Polymer Dynamics (Clarendon, Oxford, 1986)] and Kuzuu [J. Phys. Soc. Jpn. 52, 3486 (1983)]. Here this theory is put to the test by comparing it against computer simulations. A Brownian dynamics simulation program was developed to follow the dynamics of the rods, with a length over a diameter ratio of 60, on the Smoluchowski time scale. The model accounts for excluded volume interactions between rods, but neglects hydrodynamic interactions. The self-rotational diffusion coefficients D(r)(phi) of the rods were calculated by standard methods and by a new, more efficient method based on calculating average restoring torques. Collective decay of orientational order was calculated by means of equilibrium and nonequilibrium simulations. Our results show that, for the currently accessible volume fractions, the decay times in both cases are virtually identical. Moreover, the observed decay of diffusion coefficients with volume fraction is much quicker than predicted by the theory, which is attributed to an oversimplification of dynamic correlations in the theory.

Journal Article↗
PubMed2005

Relaxation of the distribution function tails for systems described by Fokker-Planck equations.

We study the formation and the evolution of velocity distribution tails for systems with weak long-range interactions. In the thermal bath approximation, the evolution of the distribution function of a test particle is governed by a Fokker-Planck equation where the diffusion coefficient depends on the velocity. We extend the theory of Potapenko et al [Phys. Rev. E 56, 7159 (1997)] developed for power-law diffusion coefficients to the case of an arbitrary form of diffusion coefficient and friction force. We study how the structure and the progression of the front depend on the behavior of the diffusion coefficient and friction force for large velocities. Particular emphasis is given to the case where the velocity dependence of the diffusion coefficient is Gaussian. This situation arises in Fokker-Planck equations associated with one dimensional systems with long-range interactions such as the Hamiltonian mean field (HMF) model and in the kinetic theory of two-dimensional point vortices in hydrodynamics. We show that the progression of the front is extremely slow (logarithmic) in that case so that the convergence towards the equilibrium state is peculiar. Our general formalism can have applications for other physical systems such as optical lattices.

Journal Article↗
PubMed1976

Kinetics of permeation of nucleotide through oil/water interface in the interaction of nucleotide with octadecylamine and dodecyl guanidine.

The transports of tritiated ATP, ADP and AMP from the aqueous to scintillator phase with and without octadecylamine (or dodecyl guanidine) have been studied by the layered scintillation method and a theory suitable for an explanation of the results has been presented. (1) Transport processes were all expressed by the first order kinetics. (2) For the simple partitioning of ATP, the reciprocal of the rate constant of the backward permeation was linear with respect to the square of the partition coefficient. (3) For the transport of nucleotide with chemical reaction, the reciprocal of the rate constant of the backward permeation was linear against the overall partition coefficient of nucleotide. (4) A theory was presented on the basis of a general diffusion equation by assuming the two-film model with potential energy near the interface. (5) The theory could explain the dependences of the permeation rates on the partition coefficients. (6) From the finding that the ratio of the apparent diffusion coefficient in aqueous to scintillator phase was much smaller than unity, the occurrence of an energy barrier at interface was suggested. For the simple partitioning of ATP, the energy barrier was not significant.

Adenine Nucleotides↗
PubMed1990

Identity status and self-construct systems: process X structure interactions.

This study investigated the relationship between identity status and structural dimensions of individuals' self-theories or personal construct systems. The sample was composed of 31 Achievers, 31 Moratoriums, 30 Foreclosures, and 26 Diffusions. Participants completed a modified version of Kelly's (1955) Role Construct Repertory test designed to assess their personal sense of integrative continuity over time. Status differences in self-construct differentiation, integration, and self-certainty were analyzed. Results indicated that Moratoriums and Diffusions had the highest self-construct differentiation. Achievers were the most self-certain in their ratings, Diffusions the least. Status differences in self-theory integration were found, but only when a qualitative, structural analysis of levels of self-construct differentiation and integration was performed. No sex effects were found. Results are discussed as replicating and extending previous work in the area, and future research directions are noted.

Adolescent↗
PubMedDate not supplied

[Dynamics of electron-conformational transitions in proteins and physical mechanisms of biomacromolecule function].

The proteins can be considered as a microheterogeneous structured media possessing memory and feedback properties. The conformational energy surface depends on the chemical states of protein groups. Conformational motions are local diffusion with relaxation times much longer than vibrational relaxation times in condensed media. Owing to the hierarchy of relaxation times chemical reaction rates depend on conformation parametrically. Regulation of functional activity by conformational mobility is accomplished via transmission of information in the form of changes in the distribution functions of separate groups along the conformational substates. The interpretation of drastic effects on conformational mobility needs super-stochastic approaches. A possible mechanism of sharp conformational change are discussed in terms of the catastrophe theory.

Diffusion↗
PubMed2006

Non-equilibrium theory of the allele frequency spectrum.

A forward diffusion equation describing the evolution of the allele frequency spectrum is presented. The influx of mutations is accounted for by imposing a suitable boundary condition. For a Wright-Fisher diffusion with or without selection and varying population size, the boundary condition is lim(x downward arrow0)xf(x,t)=thetarho(t), where f(.,t) is the frequency spectrum of derived alleles at independent loci at time t and rho(t) is the relative population size at time t. When population size and selection intensity are independent of time, the forward equation is equivalent to the backwards diffusion usually used to derive the frequency spectrum, but this approach allows computation of the time dependence of the spectrum both before an equilibrium is attained and when population size and selection intensity vary with time. From the diffusion equation, a set of ordinary differential equations for the moments of f(.,t) is derived and the expected spectrum of a finite sample is expressed in terms of those moments. The use of the forward equation is illustrated by considering neutral and selected alleles in a highly simplified model of human history. For example, it is shown that approximately 30% of the expected total heterozygosity of neutral loci is attributable to mutations that arose since the onset of population growth in roughly the last 150,000 years.

Gene Frequency↗
PubMed2005

Diffuse optical tomography using intensity measurements and the a priori acquired regions of interest: theory and simulations.

Light transmission data collected around an object show large variation with source-detector separation owing to the presence of single or multiple inhomogeneous regions in the object. This variation in the measured intensity is made use of to reconstruct regions of the inhomogeneous inclusions. In addition, it is possible to select a set of data from the above which is most likely least affected by the presence of the inhomogeneity, and estimate reasonably accurately the background optical properties from it. The reconstructed region is found to always contain the inhomogeneity and is of size approximately 140% by area of the inhomogeneity. With the regions to be reconstructed a priori known, a model-based iterative reconstruction procedure for reconstructing the optical properties of the region converged five times faster than without such information. It is also shown that whereas for the full object, a view-based propagation-backpropagation reconstruction procedure failed to converge, owing to large underdeterminacy of the problem, a smaller problem attempting to reconstruct a priori specified regions of interest converged and did so faster than a non-view-based approach for similar objects. Reconstruction results are presented from simulated transmitted intensity data from the following objects with regions of inhomogeneity in both absorption and scattering: (i) single centrally located inhomogeneity, (ii) two off-centred inhomogeneous regions of equal size and contrast (iii) two off-centred inhomogeneous regions of unequal size and equal contrast and (iv) two off-centred inhomogeneous regions of unequal size and contrast. Whereas the model-based iterative image reconstruction procedure gave good convergence in the first, second and third cases, in the fourth case the reconstructions failed to recover the exact numerical value of the optical properties in the higher contrast region.

Algorithms↗
PubMed2004

Theory of dust and dust-void structures in the presence of the ion diffusion.

A dust void is a dust-free region inside the dust cloud that often develops for conditions relevant to plasma processing discharges and complex plasma experiments. A distinctive feature of the void is a sharp boundary between the dust and dust-free regions; this is manifested especially clear when dissipation in the plasma is small and discontinuity of the dust number density appear. Here, the structure of the dust void boundary and the distribution of the dust and plasma parameters in the dust structure bordering the void is analyzed taking into account effects of dissipation due to the ion diffusion on plasma neutrals. The sharp boundary between the dust and void regions exists also in the presence of the ion diffusion; however, only derivatives of the dust density, dust charge, electron density and electric field are discontinuous at the void boundaries, while the functions themselves as well as derivatives of the ion drift velocity and the ion density are continuous. Numerical calculations demonstrate various sorts of diffusive dust void structures; the possibility of singularities in the balance equations caused by the diffusion process inside the dust structures is investigated. These singularities can be responsible for a new type of shocklike structures. Other structures are typically self-organized to eliminate the singularities. Numerical computations in this case demonstrate a set of thin dust layers separated by high density thin dust clouds similar to the multiple-layer dust structures observed in the laboratory and in the upper ionosphere. The possibility for existence of a few equilibrium positions of the void boundary is discussed.

Journal Article↗
PubMed2002

Stability of nanodispersions: a model for kinetics of aggregation of nanoparticles.

In the course of aggregation of very small colloid particles (nanoparticles) the overlap of the diffuse layers is practically complete, so that one cannot apply the common DLVO theory. Since nanopoarticles are small compared to the extent of the diffuse layer, the process is considered in the same way as for two interacting ions. Therefore, the Brønsted concept based on the Transition State Theory was applied. The charge of interacting nanoparticles was calculated by means of the Surface Complexation Model and decrease of effective charge of particles was also taken into account. Numerical simulations were performed using the parameters for hematite and rutile colloid systems. The effect of pH and electrolyte concentration on the stability coefficient of nanosystems was found to be more pronounced but similar to that for regular colloidal systems. The effect markedly depends on the nature of the solid which is characterized by equilibrium constants of surface reactions responsible for surface charge, i.e., by the point of zero charge, while the specificity of counterions is described by their association affinity, i.e., by surface association equilibrium constants. The most pronounced is the particle size effect. It was shown that extremely small particles cannot be stabilized by an electrostatic repulsion barrier. Additionally, at the same mass concentration, nanoparticles aggregate more rapidly than ordinary colloidal particles due to thier higher number concentration.

Journal Article↗
PubMedDate not supplied

Sieving coefficients for small solutes during experimental peritoneal dialysis in rats.

A single 4-hour experimental peritoneal dialysis was performed in 6 normal Sprague-Dawley rats to investigate sieving coefficients (S) for small solutes during peritoneal dialysis. A modified 3.86% Dianeal solution with approximately the same concentrations of urea, sodium, and potassium as in the rat plasma (isochratic solution) was used to avoid diffusion of investigated solutes and to achieve sufficient ultrafiltration. As a control, a 4-hour peritoneal dialysis in 7 normal Sprague-Dawley rats was performed using the conventional 3.86% Dianeal solution. The infusion volume was 30 ml. A dilution of radioiodinated serum albumin was used to determine the intraperitoneal dialysate volume. S was calculated (1) from the mass and volume balances for the initial 30 min of the exchange with the isochratic solution (SI, isochratic method) and (2) by using a membrane model based on the thermodynamic theory of mass transport (SM). The diffusive mass transport coefficient KBD for the solutes investigated was estimated using the membrane model. The SI values for urea, sodium, and potassium were similar with the isochratic solution. For urea and sodium, the S values were within the physiological range 0-1, whereas the S values for glucose were close to 0 and for potassium were negative. SM for glucose, urea, and sodium using the conventional solution did not differ from the values obtained with the isochratic solution; however, SM for potassium was significantly lower than with the isochratic solution. SI and SM for potassium and sodium were correlated. The KBD values for glucose, urea, and sodium using the isochratic solution did not differ from the values obtained with the conventional solution, whereas the KBD values for potassium were significantly higher with the isochratic solution as compared with the conventional solution. We conclude that the net sieving coefficients SI and SM for urea and sodium were lower than unity in the rats dialyzed with the two solutions and did not differ from the previously reported S values measured in continuous ambulatory peritoneal dialysis patients with the isochratic solution. However, the transport of potassium was abnormal with the isochratic solution, suggesting mechanisms other than passive diffusive and convective potassium transport.

Animals↗
PubMed2001

Release kinetics of acyclovir from a suspension of acyclovir incorporated in a cubic phase delivery system.

Acyclovir is a widely used agent in the treatment of herpes virus infections of the skin, but owing to its poor physicochemical properties in terms of bioavailability and suboptimal formulations, the treatment is far from optimal. The liquid crystalline cubic phase system has been reported to act as a bioadhesive drug delivery system. In the present study, acyclovir was suspended in a cubic phase of glycerol monooleate (GMO) and water 65%:35% w/w, and the phase behavior and release kinetics were examined. X-ray diffraction and differential scanning calorimetry (DSC) measurements demonstrated that the cubic phase containing 1%-10% (w/w) acyclovir retains its phase condition in the temperature range investigated (20 degrees C-70 degrees C). Acyclovir can be incorporated in high amounts (approximately 40% w/w) without causing phase transition, as is shown in polarized light. This is probably because of its low solubility (approximately 0.11% w/w) in the cubic phase. The release characteristics of acyclovir incorporated as a suspension (1%-5% w/w) into a cubic phase were investigated using Franz diffusion cells. Acyclovir was quantified by high-performance liquid chromatography (HPLC). The drug was readily released from the system, and the release increased with the initial drug load concentration. About 25%-50% was released after 24 h. The release is dependent on the square root of time, and the kinetics can be described by the Higuchi theory. The rate-limiting step in the release process is most likely diffusion. The suggested theory is further supported by identical release data obtained for micronized and nonmicronized acyclovir. The fluxes for 1% and 5% w/w were 380 and 900 microg/h(1/2), respectively. Comparison of the release rates of acyclovir delivered from a cubic phase and from the commercial product, Zovir cream, showed the rate to be six times faster from the cubic phase. The results indicate that the cubic phase is a promising drug delivery system for acyclovir.

Acyclovir↗
PubMed2006

Conformational studies of cyclopropylmethyl isothiocyanate from temperature-dependent FT-IR spectra of rare gas solutions and ab initio calculations.

Variable temperature (-55 to -150 degrees C) studies of the infrared spectra (3200-100 cm(-1)) of cyclopropylmethyl isothiocyanate, c-C(3)H(5)CH(2)NCS, dissolved in liquefied rare gases (Xe and Kr), have been carried out. The infrared spectra of the gas and solid, as well as the Raman spectrum of the liquid, have also been recorded from 3200 to 100 cm(-1). By analyzing six conformer pairs in xenon solutions, a standard enthalpy difference of 228 +/- 23 cm(-1) (2.73 +/- 0.27 kJ.mol(-1)) was obtained with the gauche-cis (the first designation indicates the orientation of the CNCS group with respect to the three-membered ring, the second designation indicates the relative orientation of the NCS group with respect to the bridging C-C bond) rotamer the more stable form, and it is also the only form present in polycrystalline solid. Given statistical weights of 2:1 for the gauche-cis and cis-trans forms (the only stable conformers predicted); the abundance of cis-trans conformer present at ambient temperature is 14 +/- 2%. The potential surface describing the conformational interchange has been analyzed, and the corresponding two-dimensional Fourier coefficients were obtained. From MP2 ab initio calculations utilizing various basis sets with diffuse functions, the gauche-cis conformer is predicted to be more stable by 159-302 cm(-1), which is consistent with the experimental results. However, without diffuse functions, the conformational energy differences are nearly zero even with large basis sets. For calculations with density functional theory by the B3LYP method, basis sets without diffuse functions also predict smaller energy differences between the conformers, although not nearly as small as the MP2 results. A complete vibrational assignment for the gauche-cis conformer is proposed, and several fundamentals for the cis-trans conformer have been identified. The structural parameters, dipole moments, conformational stability, vibrational frequencies, and infrared and Raman intensities have been predicted from ab initio calculations and compared to the experimental values when applicable; the r(0) structural parameters are also estimated. The energies for the linear CNCS moiety were calculated. These experimental and theoretical results are compared to the corresponding quantities of some similar molecules.

Journal Article↗
PubMed1981

Analytical modeling for the optical properties of the skin with in vitro and in vivo applications.

Analytical modeling that interrelates the optical properties of multilayered structures is applied to the skin. The mathematical approach is based on relations of diffuse reflectance and transmittance of a multilayered system and the diffuse reflectance and transmittance of each component layer. The formula can also be derived from the Kubelka-Munk theory of radiation transfer. Using both collimated and diffuse incident irradiance, the applicability of the model to human epidermis over the UV and visible region has been verified. The model has been applied to calculate to absorption and scattering coefficients of human epidermis in vitro, and to estimate the epidermal transmittance under simulated in vivo condition.

Humans↗
PubMed1997

Kinetic theory of fibrillogenesis of amyloid beta-protein.

Prior quasielastic light scattering (QLS) studies of fibrillogenesis of synthetic amyloid beta-protein (Abeta)-(1-40) at low pH have suggested a kinetic model in which: (i) fibrillogenesis requires a nucleation step; (ii) nuclei are produced by Abeta micelles in addition to seeds initially present; and (iii) fibril elongation occurs by irreversible binding of Abeta monomers to the fibril ends. Here we present the full mathematical formulation of this model. We describe the temporal evolution of the concentrations of Abeta monomers and micelles as well as the concentration and size distribution of fibrils. This formulation enables deduction of the fundamental parameters of the model-e.g., the nucleation and elongation rate constants kn and ke-from the time dependency of the apparent diffusion coefficient measured by QLS. The theory accurately represents the experimental observations for Abeta concentrations both below and above c*, the critical concentration for Abeta micelle formation. We suggest that the method of QLS in combination with this theory can serve as a powerful tool for understanding the molecular factors that control Abeta plaque formation.

Amyloid beta-Peptides↗
PubMed2001

Reduction of ion thermal diffusivity associated with the transition of the radial electric field in neutral-beam-heated plasmas in the large helical device.

Recent large helical device experiments revealed that the transition from ion root to electron root occurred for the first time in neutral-beam-heated discharges, where no nonthermal electrons exist. The measured values of the radial electric field were found to be in qualitative agreement with those estimated by neoclassical theory. A clear reduction of ion thermal diffusivity was observed after the mode transition from ion root to electron root as predicted by neoclassical theory when the neoclassical ion loss is more dominant than the anomalous ion loss.

Journal Article↗
PubMed2003

Mathematical model of the spatio-temporal dynamics of second messengers in visual transduction.

A model describing the role of transversal and longitudinal diffusion of cGMP and Ca(2+) in signaling in the rod outer segment of vertebrates is developed. Utilizing a novel notion of surface-volume reaction and the mathematical theories of homogenization and concentrated capacity, the diffusion of cGMP and Ca(2+) in the inter-disc spaces is shown to be reducible to a one-parameter family of diffusion processes taking place on a single rod cross section; whereas the diffusion in the outer shell is shown to be reducible to a diffusion on a cylindrical surface. Moreover, the exterior flux of the former serves as a source term for the latter, alleviating the assumption of a well-stirred cytosol. A previous model of visual transduction that assumes a well-stirred rod outer segment cytosol (and thus contains no spatial information) can be recovered from this model by imposing a "bulk" assumption. The model shows that upon activation of a single rhodopsin, cGMP changes are local, and exhibit both a longitudinal and a transversal component. Consequently, membrane current is also highly localized. The spatial spread of the single photon response along the longitudinal axis of the outer segment is predicted to be 3-5 microm, consistent with experimental data. This approach represents a tool to analyze point-wise signaling dynamics without requiring averaging over the entire cell by global Michaelis-Menten kinetics.

Animals↗