Exact analytic solutions for diffusion impeded by an infinite array of partially permeable barriers

Powles, J.G.; Mallett, M. J. D.; Rickayzen, G.; Evans, W. T.

doi:10.1098/rspa.1992.0025

Cited by 90 publications

(60 citation statements)

References 3 publications

(3 reference statements)

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“…The movies were recorded on a digital videotape (PDV-184ME; Sony). Quantitative analysis of ABCA1 movement was performed based on mean square displacement (MSD) methods described previously (39)(40)(41)(42)(43). For each trajectory of a particle, MSD, <(Δr(Δt)) 2 >, every time interval was calculated according to the equation (41,44) …”

Section: Methodsmentioning

confidence: 99%

ABCA1 dimer–monomer interconversion during HDL generation revealed by single-molecule imaging

Nagata

Nakada

Kasai

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

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The generation of high-density lipoprotein (HDL), one of the most critical events for preventing atherosclerosis, is mediated by ATPbinding cassette protein A1 (ABCA1). ABCA1 is known to transfer cellular cholesterol and phospholipids to apolipoprotein A-I (apoA-I) for generating discoidal HDL (dHDL) particles, composed of 100-200 lipid molecules surrounded by two apoA-I molecules; however, the regulatory mechanisms are still poorly understood. Here we observed ABCA1-GFP and apoA-I at the level of single molecules on the plasma membrane via a total internal reflection fluorescence microscope. We found that about 70% of total ABCA1-GFP spots are immobilized on the plasma membrane and estimated that about 89% of immobile ABCA1 molecules are in dimers. Furthermore, an ATPase-deficient ABCA1 mutant failed to be immobilized or form a dimer. We found that the lipid acceptor apoA-I interacts with the ABCA1 dimer to generate dHDL and is followed by ABCA1 dimermonomer interconversion. This indicates that the formation of the ABCA1 dimer is the key for apoA-I binding and nascent HDL generation. Our findings suggest the physiological significance of conversion of the ABCA1 monomer to a dimer: The dimer serves as a receptor for two apoA-I molecules for dHDL particle generation.membrane protein | transporter P lasma high-density lipoprotein (HDL) is critical for preventing coronary artery disease (1). A member of the ATPdependent transporter family of ABC proteins, ATP-binding cassette protein A1 (ABCA1) initiates the generation of discoidal HDL (dHDL), a bilayer fragment consisting of 100-200 lipids wrapped by two molecules of apolipoprotein A-I (apoA-I) (2-4), by exporting cholesterol and phospholipids to lipid-free apoA-I in serum (5). More than 70 mutations have been identified in the ABCA1 gene. Indeed, mutations in ABCA1 lead to Tangier disease, which is characterized by plasma HDL deficiency (6-10). ABCA1 has two large extracellular domains (ECDs), and the two intramolecular disulfide bonds between them are necessary for apoA-I binding and HDL formation (11-13) (Fig. 1A). Two pieces of evidence suggest that apoA-I interacts with a specific conformation of the ECDs in an ATP-dependent manner: Chemical cross-linkers can cross-link apoA-I with ABCA1, and ATPasedeficient ABCA1 mutants fail to mediate apoA-I binding and crosslinking. However, the importance of direct binding of ABCA1-apoA-I in HDL formation is still controversial and, furthermore, how a dHDL particle containing two molecules of apoA-I is formed from lipid-free apoA-I monomers and membrane lipids is unknown.To address these issues, we performed single-molecule fluorescence imaging (14, 15) of ABCA1 and apoA-I on the plasma membrane (PM) via a total internal reflection fluorescence (TIRF) microscope in living cells. We examined the dynamic behaviors of ABCA1 as well as the interaction of ABCA1 with apoA-I, and found that ABCA1 forms an immobile dimer on the PM; the ABCA1 dimer then dissociates into diffusing monomers upon interaction with apoA-I, finally gen...

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Section: Methodsmentioning

confidence: 99%

ABCA1 dimer–monomer interconversion during HDL generation revealed by single-molecule imaging

Nagata

Nakada

Kasai

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

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“…Our observations are consistent with momentary trapping of the beads in the pores formed by the agarose fibres, in which case one expects a cross-over from simple to anomalous diffusion to occur, at or slightly above the characteristic pore size. Different analytical models have been proposed to describe the cross-over in the MSD for arrays of cages [96][97][98] . For simplicity's sake, we have fitted our data using a model developed for a simplified system with a single pore size, L 98 .…”

Section: The Caged Diffusion Of Beads In Agarose Gelsmentioning

confidence: 99%

Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

et al. 2016

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The diffusion of macromolecules in cells and in complex fluids is often found to deviate from simple Fickian diffusion. One explanation offered for this behavior is that molecular crowding renders diffusion anomalous, where the mean-squared displacement of the particles scales as r 2 ∝ t α with α < 1. Unfortunately, methods such as fluorescence correlation spectroscopy (FCS) or fluorescence recovery after photobleaching (FRAP) probe diffusion only over a narrow range of lengthscales and cannot directly test the dependence of the mean-squared displacement (MSD) on time. Here we show that variable-lengthscale FCS (VLS-FCS), where the volume of observation is varied over several orders of magnitude, combined with a numerical inversion procedure of the correlation data, allows retrieving the MSD for up to five decades in time, bridging the gap between diffusion experiments performed at different lengthscales. In addition, we show that VLS-FCS provides a way to assess whether the propagator associated with the diffusion is Gaussian or non-Gaussian. We used VLS-FCS to investigate two systems where anomalous diffusion had been previously reported. In the case of dense cross-linked agarose gels, the measured MSD confirmed that the diffusion of small beads was anomalous at short lengthscales, with a cross-over to simple diffusion around ≈ 1 µm, consistent with a caged diffusion process. On the other hand, for solutions crowded with marginally entangled dextran molecules, we uncovered an apparent discrepancy between the MSD, found to be linear, and the propagators at short lengthscales, found to be non-Gaussian. These contradicting features call to mind the "anomalous, yet Brownian" diffusion observed in several biological systems, and the recently proposed "diffusing diffusivity" model.

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“…Similar equations can describe molecular diffusion between two media across semipermeable membranes [3,4]. In that case, u(x, t) represents the (normalized) concentration of molecules, while Eqs.…”

Section: Introductionmentioning

confidence: 99%

“…For any physical setting of heat or molecular diffusion, there would be an intermediate layer between two media in which the material properties would change rapidly but continuously. When the thickness of this intermediate layer is much smaller than the size of the domain, the physical problem with continuously varying parameters can be approximated by the heat problem (1)- (4). Such an approximation is applicable starting from a small cut-off time while understanding the heat exchange at smaller time scales would need either restituting an intermediate layer, or introducing nonlinear terms into the heat equation.…”

Section: Introductionmentioning

confidence: 99%

“…In fact, u(x, t) can describe how the distribution of (normalized) temperature evolves with time. The transmission boundary conditions (3), (4) impose the continuity of the temperature flux across the boundary, and relate this flux to the temperature drop at the boundary due to thermal isolation. The growth rate of the heat content with time characterizes the efficiency of thermal isolation.…”

Section: Introductionmentioning

confidence: 99%

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Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions

Bardos

Rozanova-Pierrat

2015

Math. Models Methods Appl. Sci.

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We consider a heat problem with discontinuous diffusion coefficients and discontinuous transmission boundary conditions with a resistance coefficient. For all compact (ǫ, δ) -domains Ω ⊂ R n with a d -set boundary (for instance, a self-similar fractal), we find the first term of the small-time asymptotic expansion of the heat content in the complement of Ω , and also the second-order term in the case of a regular boundary. The asymptotic expansion is different for the cases of finite and infinite resistance of the boundary. The derived formulas relate the heat content to the volume of the interior Minkowski sausage and present a mathematical justification to the de Gennes' approach. The accuracy of the analytical results is illustrated by solving the heat problem on prefractal domains by a finite elements method.

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Exact analytic solutions for diffusion impeded by an infinite array of partially permeable barriers

Cited by 90 publications

References 3 publications

ABCA1 dimer–monomer interconversion during HDL generation revealed by single-molecule imaging

ABCA1 dimer–monomer interconversion during HDL generation revealed by single-molecule imaging

Characterizing anomalous diffusion in crowded polymer solutions and gels over five decades in time with variable-lengthscale fluorescence correlation spectroscopy

Short-time heat diffusion in compact domains with discontinuous transmission boundary conditions

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