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The Journal of Chemical Physics Apr 2015In this paper, we study biased diffusion of point Brownian particles in a three-dimensional comb-like structure formed by a main cylindrical tube with identical periodic...
In this paper, we study biased diffusion of point Brownian particles in a three-dimensional comb-like structure formed by a main cylindrical tube with identical periodic cylindrical dead ends. It is assumed that the dead ends are thin cylinders whose radius is much smaller than both the radius of the main tube and the distance between neighboring dead ends. It is also assumed that in the main tube, the particle, in addition to its regular diffusion, moves with a uniform constant drift velocity. For such a system, we develop a formalism that allows us to derive analytical expressions for the Laplace transforms of the first two moments of the particle displacement along the main tube axis. Inverting these Laplace transforms numerically, one can find the time dependences of the two moments for arbitrary values of both the drift velocity and the dead-end length, including the limiting case of infinitely long dead ends, where the unbiased diffusion becomes anomalous at sufficiently long times. The expressions for the Laplace transforms are used to find the effective drift velocity and diffusivity of the particle as functions of its drift velocity in the main tube and the tube geometric parameters. As might be expected from common-sense arguments, the effective drift velocity monotonically decreases from the initial drift velocity to zero as the dead-end length increases from zero to infinity. The effective diffusivity is a more complex, non-monotonic function of the dead-end length. As this length increases from zero to infinity, the effective diffusivity first decreases, reaches a minimum, and then increases approaching a plateau value which is proportional to the square of the particle drift velocity in the main tube.
Topics: Algorithms; Diffusion; Models, Chemical; Motion
PubMed: 25854222
DOI: 10.1063/1.4916310 -
Magnetic Resonance in Medical Sciences... Apr 2024Diffusion MRI is a physical measurement method that quantitatively indicates the displacement of water molecules diffusing in voxels. However, there are insufficient...
PURPOSE
Diffusion MRI is a physical measurement method that quantitatively indicates the displacement of water molecules diffusing in voxels. However, there are insufficient data to characterize the diffusion process physically in a uniform structure such as a phantom. This study investigated the transitional relationship between structure scale, temperature, and diffusion time for simple restricted diffusion using a capillary phantom.
METHODS
We performed diffusion-weighted pulsed-gradient stimulated-echo acquisition mode (STEAM) MRI with a 9.4 Tesla MRI system (Bruker BioSpin, Ettlingen, Germany) and a quadrature coil with an inner diameter of 86 mm (Bruker BioSpin). We measured the diffusion coefficients (radial diffusivity [RD]) of capillary plates (pore sizes 6, 12, 25, 50, and 100 μm) with uniformly restricted structures at various temperatures (10ºC, 20ºC, 30ºC, and 40ºC) and multiple diffusion times (12-800 ms). We evaluated the characteristics of scale, temperature, and diffusion time for restricted diffusion.
RESULTS
The RD decayed and became constant depending on the structural scale. Diffusion coefficient fluctuations with temperature occurred mostly under conditions of a large structural scale and short diffusion time. We obtained data suggesting that temperature-dependent changes in the diffusion coefficients follow physical laws.
CONCLUSION
No water molecules were observed outside the glass tubes in the capillary plates, and the capillary plates only reflected a restricted diffusion process within the structure.We experimentally evaluated the characteristics of simple restricted diffusion to reveal the transitional relationship of the diffusion coefficient with diffusion time, structure scale, and temperature through composite measurement.
Topics: Temperature; Magnetic Resonance Imaging; Diffusion Magnetic Resonance Imaging; Diffusion; Biological Transport; Phantoms, Imaging; Water
PubMed: 36754420
DOI: 10.2463/mrms.mp.2022-0103 -
Environmental Technology Feb 2019Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the...
Surface diffusion coefficients may be estimated by fitting solutions of a diffusion model to batch kinetic data. For non-linear systems, a numerical solution of the diffusion model's governing equations is generally required. We report here the application of the classic Langmuir kinetics model to extract surface diffusion coefficients from batch kinetic data. The use of the Langmuir kinetics model in lieu of the conventional surface diffusion model allows derivation of an analytical expression. The parameter estimation procedure requires determining the Langmuir rate coefficient from which the pertinent surface diffusion coefficient is calculated. Surface diffusion coefficients within the 10 to 10cm/s range obtained by fitting the Langmuir kinetics model to experimental kinetic data taken from the literature are found to be consistent with the corresponding values obtained from the traditional surface diffusion model. The virtue of this simplified parameter estimation method is that it reduces the computational complexity as the analytical expression involves only an algebraic equation in closed form which is easily evaluated by spreadsheet computation.
Topics: Adsorption; Diffusion; Kinetics
PubMed: 29072126
DOI: 10.1080/09593330.2017.1397767 -
Electrophoresis Aug 2016We explored the feasibility of using confocal fluorescence correlation spectroscopy to study small nanoparticle diffusion in hundred-nanometer-sized cylindrical pores....
We explored the feasibility of using confocal fluorescence correlation spectroscopy to study small nanoparticle diffusion in hundred-nanometer-sized cylindrical pores. By modeling single particle diffusion in tube-like confined three-dimensional space aligned parallel to the confocal optical axis, we showed that two diffusion dynamics can be observed in both original intensity traces and the autocorrelation functions (ACFs): the confined two-dimensional lateral diffusion and the unconfined one-dimensional (1D) axial diffusion. The separation of the axial and confined lateral diffusion dynamics provides an opportunity to study diffusions in different dimensions separately. We further experimentally studied 45 nm carboxylated polystyrene particles diffusing in 300 nm alumina pores. The experimental data showed consistency with the simulation. To extract the accurate axial diffusion coefficient, we found that a 1D diffusion model with a Lorentzian axial collection profile needs to be used to analyze the experimental ACFs. The diffusion of the 45 nm nanoparticles in polyethyleneglycol-passivated 300 nm pores slowed down by a factor of ∼2, which can be satisfactorily explained by hydrodynamic frictions.
Topics: Diffusion; Hydrodynamics; Models, Theoretical; Molecular Dynamics Simulation; Nanoparticles; Porosity; Spectrometry, Fluorescence
PubMed: 27196052
DOI: 10.1002/elps.201600158 -
Biophysical Journal Jun 2023Previous studies have documented the formation of a heterodimer between the two protein kinases PDK1 and PKCα on a lipid bilayer containing their target lipids. This...
Previous studies have documented the formation of a heterodimer between the two protein kinases PDK1 and PKCα on a lipid bilayer containing their target lipids. This work investigates the association-dissociation kinetics of this PDK1:PKCα heterodimer. The approach monitors the two-dimensional diffusion of single, membrane-associated PDK1 molecules for diffusivity changes as PKCα molecules bind and unbind. In the absence of PKCα, a membrane-associated PDK1 molecule exhibits high diffusivity (or large diffusion constant, D) because its membrane-contacting PH domain binds the target PIP lipid headgroup with little bilayer penetration, yielding minimal frictional drag against the bilayer. In contrast, membrane-associated PKCα contacts the bilayer via its C1A, C1B, and C2 domains, which each bind at least one target lipid with significant bilayer insertion, yielding a large frictional drag and low diffusivity. The present findings reveal that individual fluor-PDK1 molecules freely diffusing on the membrane surface undergo reversible switching between distinct high and low diffusivity states, corresponding to the PDK1 monomer and the PDK1:PKCα heterodimer, respectively. The observed single-molecule diffusion trajectories are converted to step length time courses, then subjected to two-state, hidden Markov modeling and dwell time analysis. The findings reveal that both the PDK1 monomer state and the PDK1:PKCα heterodimer state decay via simple exponential kinetics, yielding estimates of rate constants for state switching in both directions. Notably, the PDK1:PKCα heterodimer has been shown to competitively inhibit PDK1 phosphoactivation of AKT1, and is believed to play a tumor suppressor role by limiting excess activation of the highly oncogenic PDK1/AKT1/mTOR pathway. Thus, the present elucidation of the PDK1:PKCα association-dissociation kinetics has important biological and medical implications. More broadly, the findings illustrate the power of single-molecule diffusion measurements to reveal the kinetics of association-dissociation events in membrane signaling reactions that yield a large change in diffusive mobility.
Topics: Protein Kinase C-alpha; Lipid Bilayers; Signal Transduction; Protein Binding; Diffusion
PubMed: 36733254
DOI: 10.1016/j.bpj.2023.01.041 -
Journal of Contaminant Hydrology Jun 2022Diffusion is the main transport process of water and solutes in clay-rich porous media owing to their very low permeability, so they are widely used as barriers against...
Diffusion is the main transport process of water and solutes in clay-rich porous media owing to their very low permeability, so they are widely used as barriers against contaminant spreading. However, the prediction of contaminant mobility can be very complicated when these media are partially water-saturated. We conducted diffusion experiments for water (HTO and HDO) and ions (Na and I) through partially water saturated compacted kaolinite, a weakly charged clay material, to quantify the distinct diffusive behavior of these species. The osmosis method was used to set kaolinite samples at 67, 86 and 100% saturation. The results showed that desaturation led to a sharp decrease in diffusive rates by factors of 6.5, 18 and 35 for HTO, I and Na, respectively, from 100 to 67% of the degree of saturation. Thus, to interpret water diffusivities, we proposed a model taking into account the diffusion of water in both gas and liquid phases, using diffusion data obtained for ions, considered as inert species. This model was capable of properly predicting water diffusive flux, especially at a low degree of saturation (67% saturation), for which the assumption made for the occurrence of air phase continuity throughout the sample appears to be more relevant than at 86% saturation.
Topics: Clay; Diffusion; Gases; Kaolin; Water
PubMed: 35306324
DOI: 10.1016/j.jconhyd.2022.103989 -
Physical Review Letters Apr 2015Standard game theory cannot describe microbial interactions mediated by diffusible molecules. Nevertheless, we show that one can still model microbial dynamics using...
Standard game theory cannot describe microbial interactions mediated by diffusible molecules. Nevertheless, we show that one can still model microbial dynamics using game theory with parameters renormalized by diffusion. Contrary to expectations, greater sharing of metabolites reduces the strength of cooperation and leads to species extinction via a nonequilibrium phase transition. We report analytic results for the critical diffusivity and the length scale of species intermixing. Species producing slower public good is favored by selection when fitness saturates with nutrient concentration.
Topics: Diffusion; Ecosystem; Extinction, Biological; Microbial Interactions; Models, Biological
PubMed: 25955075
DOI: 10.1103/PhysRevLett.114.168102 -
The Journal of Cell Biology Dec 1982Diffusion of the complex consisting of low density lipoprotein (LDL) bound to its receptor on the surface of human fibroblasts has been measured with the help of an...
Diffusion of the complex consisting of low density lipoprotein (LDL) bound to its receptor on the surface of human fibroblasts has been measured with the help of an intensely fluorescent, biologically active LDL derivative, dioctadecylindocarbocyanine LDL (dil(3)-LDL). Fluorescence photobleaching recovering and direct video observations of the Brownian motion of individual LDL-receptor complexes yielded diffusion coefficients for the slow diffusion on cell surfaces and fast diffusion on membrane blebs, respectively. At 10 degrees C, less that 20 percent of the LDL-receptor complex was measurably diffusible either on normal human fibroblasts GM-3348 or on LDL-receptor- internalization-defective J.D. cells GM-2408A. At 21 degrees and 28 degrees C, the diffusion fractions of approximately 75 and 60 percent, respectively, on both cell lines. The lipid analog nitrobenzoxadiazolephosphatidylcholine (NBD-PC) diffused in the GM-2408A cell membrane at 1.5x10(-8) cm(2)/sec at 22 degrees C. On blebs induced in GM-2408A cell membranes, the dil(3)-LDL receptor complex diffusion coefficient increased to approximately 10(-9) cm(2)/s, thus approaching the maximum theoretical predictions for a large protein in the viscous lipid bilayer. Cytoskeletal staining of blebs with NBD- phallacidin, a fluorescent probe specific for F-actin, indicated that loss of the bulk of the F-actin cytoskeleton accompanied the release of the natural constraints on later diffusion observed on blebs. This work shows that the internalization defect of J.D. is not due to immobilization of the LDL-receptor complex since its diffusibility is sufficient to sustain even the internalization rates observed in the native fibroblasts. Nevertheless, as with many other cell membrane receptors, the diffusion coefficient of the LDL-receptor complex is at least two orders of magnitude slower on native membrane than the viscous limit approached on cell membrane blebs where it is released from lateral constraints. However, LDL-receptor diffusion may not limit LDL internalization in normal human fibroblasts.
Topics: Actins; Cell Line; Cell Membrane; Diffusion; Fibroblasts; Fluorescent Dyes; Humans; Lipoproteins, LDL; Receptors, Cell Surface; Receptors, LDL; Temperature
PubMed: 6296157
DOI: 10.1083/jcb.95.3.846 -
The Journal of Physical Chemistry. B Jul 2021We present here a model for multivalent diffusive transport whereby a central point-like hub is coupled to multiple feet, which bind to complementary sites on a...
We present here a model for multivalent diffusive transport whereby a central point-like hub is coupled to multiple feet, which bind to complementary sites on a two-dimensional landscape. The available number of binding interactions is dependent on the number of feet (multivalency) and on their allowed distance from the central hub (span). Using Monte Carlo simulations that implement the Gillespie algorithm, we simulate multivalent diffusive transport processes for 100 distinct walker designs. Informed by our simulation results, we derive an analytical expression for the diffusion coefficient of a general multivalent diffusive process as a function of multivalency, span, and dissociation constant . Our findings can be used to guide the experimental design of multivalent transporters, in particular, providing insight into how to overcome trade-offs between diffusivity and processivity.
Topics: Algorithms; Computer Simulation; Diffusion; Monte Carlo Method
PubMed: 34151560
DOI: 10.1021/acs.jpcb.1c02821 -
IEEE Transactions on Visualization and... 2007This paper proposes an image-based painterly rendering algorithm for automatically synthesizing an image with color ink diffusion. We suggest a mathematical model with a...
This paper proposes an image-based painterly rendering algorithm for automatically synthesizing an image with color ink diffusion. We suggest a mathematical model with a physical base to simulate the phenomenon of color colloidal ink diffusing into absorbent paper. Our algorithm contains three main parts: a feature extraction phase, a Kubelka-Munk (KM) color mixing phase, and a color ink diffusion synthesis phase. In the feature extraction phase, the information of the reference image is simplified by luminance division and color segmentation. In the color mixing phase, the KM theory is employed to approximate the result when one pigment is painted upon another pigment layer. Then, in the color ink diffusion synthesis phase, the physically-based model that we propose is employed to simulate the result of color ink diffusion in absorbent paper using a texture synthesis technique. Our image-based ink diffusing rendering (IBCIDR) algorithm eliminates the drawback of conventional Chinese ink simulations, which are limited to the black ink domain, and our approach demonstrates that, without using any strokes, a color image can be automatically converted to the diffused ink style with a visually pleasing appearance.
Topics: Algorithms; Color; Coloring Agents; Computer Graphics; Computer Simulation; Diffusion; Image Interpretation, Computer-Assisted; Ink; Models, Chemical; Paintings; Paper; User-Computer Interface
PubMed: 17218741
DOI: 10.1109/TVCG.2007.41