Time Course Of Diffusion Research Articles

Membrane mobility of aquaporin‐2 (AQP2) tagged with photoconvertible fluorescence protein in mpkCCD cells

mEos is a photoconvertible fluorescence protein. Its emission can be switched from green to red by an UV pulse. Tagging AQP2 with mEos allows tracking of a subset of AQP2 after photoconversion. Here, we examined whether, 1) AQP2 tagged with mEos to amino‐terminus (Eos‐AQP2) or carboxyl‐terminus (AQP2‐Eos) has similar membrane mobility, and 2) photoconversion alters their membrane mobility. Cells grown on glass‐bottom dishes were transfected with either Eos‐AQP2 or AQP2‐Eos and their membrane mobility were measured by fluorescence recovery after photobleaching (FRAP). A 488 nm laser pulse was used to photobleach a 4 μm spot for FRAP. Fluorescence recovery half‐time (t1/2) was calculated with ImageJ. Eos‐AQP2 was found in cytosolic vesicles and plasma membrane. Apical accumulation of Eos‐AQP2 was stimulated by forskolin. AQP2‐Eos was localized in apical membrane. t1/2 of Eos‐AQP2 and AQP2‐Eos were in the same range (42–50 s). Local photoconversion of green‐Eos to red‐Eos was performed with a 405 nm laser pulse on the apical surface. Photoconversion did not alter the membrane mobility of EOS‐AQP2 or AQP2‐EOS as measured by the diffusion time course of red‐Eos from the photoconversion site. However, forskolin stimulation increased t1/2 of Eos‐AQP2 by 3 folds, and decreased the t1/2 of AQP2‐Eos by 25%. These results indicated that photoconversion did not alter AQP2 membrane mobility.

TRPC3 Channel Underlies Cerebellar Long-Term Depression

Cerebellar long-term depression (LTD) is induced by repetitive pairing of both synaptic inputs provided by climbing fibers (CFs) and parallel fibers (PFs), especially when CF stimulation followed by burst of PFs. Metabotropic glutamate receptor type 1 (mGluR1)-dependent signaling in Purkinje cells is critically involved in the induction of cerebellar LTD. Signaling pathway of mGluR1 has two limbs: one is IP3 receptor-mediated Ca release from intracellular Ca store and the other is activation of transient receptor potential canonical (TRPC) channels. Here, we hypothesized that TRPC3, which is reported to be responsible for mGluR1-evoked slow currents, mediates the induction of the cerebellar LTD. Purkinje cells were loaded with antibodies which act against a cytoplasmic epitope of TRPC3 channels, acting as a specific antagonist of TRPC3. About 30min after achieving a whole-cell configuration, mGluR1-evoked slow currents were significantly reduced; a possible cause of this time delay might be the diffusion time course from patch pipette to the dendrite site of mGluR1 activation. Taking this delay into consideration, we next attempted to induce cerebellar LTD by pairing PFs and CF. It was found that cerebellar LTD was hindered in the presence of TRPC3 antibodies. Taken together, our data suggest that TRPC3 activation may be essential for the induction of LTD in cerebellar Purkinje cells.

Characterisation of the passive permeability barrier of nuclear pore complexes

Nuclear pore complexes (NPCs) restrict uncontrolled nucleocytoplasmic fluxes of inert macromolecules but permit facilitated translocation of nuclear transport receptors and their cargo complexes. We probed the passive barrier of NPCs and observed sieve-like properties with a dominating mesh or channel radius of 2.6 nm, which is narrower than proposed earlier. A small fraction of diffusion channels has a wider opening, explaining the very slow passage of larger molecules. The observed dominant passive diameter approximates the distance of adjacent hydrophobic clusters of FG repeats, supporting the model that the barrier is made of FG repeat domains cross-linked with a spacing of an FG repeat unit length. Wheat germ agglutinin and the dominant-negative importin β45-462 fragment were previously regarded as selective inhibitors of facilitated NPC passage. We now observed that they do not distinguish between the passive and the facilitated mode. Instead, their inhibitory effect correlates with the size of the NPC-passing molecule. They have little effect on small species, inhibit the passage of green fluorescent protein-sized objects >10-fold and virtually block the translocation of larger ones. This suggests that passive and facilitated NPC passage proceed through one and the same permeability barrier.

A theoretical model of the diffusion of glycolytic enzymes and other cytosolic proteins from rabbit skinned muscle fibers

The rate of diffusion of proteins in the cytosol of muscle fibers is known to be considerably less than that of the same proteins in an aqueous solution. We measured the time course of diffusion of seven glycolytic and three other cytosolic proteins from skinned psoas muscle fibers under oil and transferred sequentially through drops of physiological relaxing solution. The rate cytosolic proteins diffused from the fibers into the stirred solution was significantly less than that in bulk water, especially at the onset. Collisions with the myofilament lattice hinder diffusion, and model fits to the data return an effective mesh size of ~12 nm, i.e., comparable to the distance between myofilaments. Binding to fixed structures and other proteins and the initially high concentration of cytosolic protein also reduce the rate of diffusion, but the initial lag in diffusion cannot be entirely accounted for by current models incorporating these features. A model fit to the diffusion time course of phosphoglucose isomerase (an exemplar protein) shows that, at the onset, steric hindrance and binding reduces the diffusion coefficient to 0.126 that in bulk water, 3.22e‐7 cm2/s, with a further reduction to 7.02e‐11 cm2/s due to protein crowding, which dissipates with time. We conclude that a complex mathematical description of the effect of protein crowding is required to represent the diffusion of proteins from skinned muscle fibers.

Diffusion in a dendritic spine: The role of geometry

Dendritic spines, the sites where excitatory synapses are made in most neurons, can dynamically regulate diffusing molecules by changing their shape. We present here a combination of theory, simulations, and experiments to quantify the diffusion time course in dendritic spines. We derive analytical formulas and compared them to Brownian simulations for the mean sojourn time a diffusing molecule stays inside a dendritic spine when either the molecule can reenter the spine head or not, once it is located in the spine neck. We show that the spine length is the fundamental regulatory geometrical parameter for the diffusion decay rate in the neck only. By changing the spine length, dendritic spines can be dynamically coupled or uncoupled to their parent dendrites, which regulates diffusion, and this property makes them unique structures, different from static dendrites.

The effect of auxiliary conditions on intestinal unstirred layer diffusion modelled by numerical simulation

Estimation of intestinal unstirred layer thickness usually involves inducing transmural potential difference changes by altering the content of the solution used to perfuse the small intestine. Osmotically active solutes, such as mannitol, when added to the luminal solution diffuse across the unstirred water layer (UWL) and induce osmotically dependent changes in potential difference. As an alternative procedure, the sodium ion in the luminal fluid can be replaced by another ion. As the sodium ion diffuses out of the UWL, the change in concentration next to the intestinal membrane alters the transmural potential difference. In both cases, UWL thickness is calculated from the time course of the potential difference changes, using a solution to the diffusion equation. The diffusion equation solution which allows the calculation of intestinal unstirred layer thickness was examined by simulation, using the method of numerical solutions. This process readily allows examination of the time course of diffusion under various imposed circumstances. The existing model for diffusion across the unstirred layer is based on auxiliary conditions which are unlikely to be fulfilled in the same intestine. The present simulation additionally incorporated the effects of membrane permeability, fluid absorption and less than instantaneous bulk phase concentration change. Simulation indicated that changes within the physiologically relevant range in the chosen auxiliary conditions (with the real unstirred layer length kept constant) can alter estimates of the apparent half-time. Consequently, changes in parameters unassociated with the unstirred layer would be misconstrued as alterations in unstirred layer thickness.

Kinetics of diffusion in a spherical cell. II. Solute buffering included

This paper on diffusion kinetics in neurons presents an analysis of diffusion in the presence of solute buffering. Computational rather than theoretical methods are usually necessary since buffering generally precludes an analytical solution to the diffusion equations. As in the companion paper, our methods are illustrated in the context of calcium diffusion in a spherical cell. However, the same methods can be applied to the spread of any second messenger and other geometries. Analytical or computational predictions of the time course of diffusion and buffering may help guide further experiments and simulations. For example, simulations of calcium diffusion in a model of the bullfrog sympathetic ganglion cell show that buffering at depths greater than 5–6 μm is almost instantaneous compared to diffusion from sources at the cell membrane. Since buffering complicates the design of multicompartmental models, we demonstrate that a few compartments designed on the basis of diffusion alone (Carnevale and Rosenthal, 1992) may be a satisfactory framework for a model that includes bimolecular buffering. An analytical solution may be possible if the buffering reaction can be linearized. We describe a method for linearizing bimolecular saturating buffering, i.e., approximating it by a unimolecular non-saturating process that immobilizes solute. The analytical solution for the linearized reactive diffusion problem fits a non-linear model of calcium movement in the bullfrog sympathetic ganglion cell quite well after a few milliseconds.

ATP dependence of KATP channel kinetics in isolated membrane patches from rat ventricle

The dependence of KATP channel activity on [ATP] has been examined in isolated membrane patches from rat ventricular myocytes. The steady-state [ATP] dependence of channel open probability could be described by a sigmoidal relationship with the ki ([ATP] causing half-maximal inhibition of open probability) = 25 microM and Hill coefficient of 2. Description of channel open- and closed-time distributions required at least 2, and 3, time constants, respectively. Long open-channel lifetimes decreased with [ATP]; unconditional mean channel closed-times increased with [ATP]. Step decrease (jump) in bathing [ATP] resulted in a delay (of up to hundreds of milliseconds) followed by a pseudo-exponential rise of current (with a time constant of up to hundreds of milliseconds). The time course of channel current after changes of [ATP] (or the ATP-analogue AMP-PNP) was shown to be predominantly determined by the time course of diffusion into the tip of the electrode and to the membrane. This time course of diffusion of ATP into the pipette tip had to be taken into account when analyzing the current response to [ATP] steps. Several possible kinetic models of the ATP-dependent regulation of channel activity were considered. Adequate explanation of the data required a model with sequential ATP-binding sites. The model can account for the time course of channel opening after steps of [ATP], as well as for the steady-state dependence of P0 on [ATP]. The model predicts [ATP]-dependent closed and open lifetimes as were observed experimentally.

Ion diffusion modified by tortuosity and volume fraction in the extracellular microenvironment of the rat cerebellum.

1. The validity of the macroscopic laws of ion diffusion was critically examined within the microenvironment of the extracellular space in the rat cerebellum using ion-selective micropipettes and ionophoretic point sources. 2. The concepts of volume averaging, volume fraction (alpha) and tortuosity (lambda) were defined and shown to be theoretically appropriate for quantifying diffusion in a complex medium such as the brain. 3. Diffusion studies were made with the cations tetramethylammonium and tetraethylammonium and the anions alpha-naphthalene sulphonate and hexafluoro-arsenate, all of which remained essentially extracellular during the measurements. Diffusion parameters were measured for a period of 50s and over distances of the order of 0.1 mm. 4. Measurements of the diffusion coefficients of the ions in agar gel gave values that were very close to those derivable from the literature, thus confirming the validity of the method. 5. Measurements in the cerebellum did not reveal any systematic influences of ionophoretic current strength, electrode separation, anisotropy, inhomogeneity, charge discrimination or uptake, within the limits tested. 6. The pooled data from measurements with all the ions gave alpha = 0.21 +/- 0.02 (mean +/- S.E. of mean) and lambda = 1.55 +/- 0.05 (mean +/- S.E. of mean). 7. These results show that the extracellular space occupies about 20% of the rat cerebellum and that the diffusion coefficient for small monovalent extracellular ions is reduced by a factor of 2.4 (i.e. lambda 2) without regard to charge sign. The over-all effect of this is to increase the apparent strength of any ionic source in the cerebellum by a factor of lambda 2/alpha, about 12-fold in the present case, and to modify the time course of diffusion. 8. These conclusions confirm that the laws of macroscopic diffusion are closely obeyed in the cerebellum for small ions in the extracellular space, provided that volume fraction and tortuosity are explicitly taken into account. It is likely that these conclusions are generally applicable to other brain regions and other diffusing substances.

Effects of long range interactions in harmonically coupled systems. I. Equilibrium fluctuations and diffusion

Systems of harmonically coupled identical particles at thermal equilibrium provide dynamical models for studies of diffusion due to equilibrium fluctuations. The velocity autocorrelation function and mean square displacement of a particle selected from a given system are investigated for various models which have the common feature that the particle is directly coupled to L > 1 neighbors, reflecting the influence of long range interactions. Theorems are developed which indicate how the time course of diffusion is dictated by analytic properties of the vibrational frequency distribution as well as by quantum fluctuations whose presence is betrayed by the increasingly important role at progressively lower temperatures of τq = ℏ/πk T, the quantum transient time. The formalism is first applied to a system for which the long range couplings are so parametrized by a range parameter z that when z=0 the frequency distribution is identical to that for nearest neighbor coupling only (L=1), while as z approaches unity (L→∞) the frequency distribution becomes identifiable with that of Ford, Kac, and Mazur which served as the starting point for their dynamical theory of Brownian motion. Consequences of this model are: (1) when z <0.5, the classical velocity autocorrelation functions exhibit similar qualitative features to those computed for molecular diffusion in simple liquids; (2) as z approaches unity, the classical velocity autocorrelation function approaches the e-λτ Gaussian Markoffian form, and the mean square displacement in the same limit is identical to that predicted by the Langevin equation; (3) at low temperatures such that λτq>1, quantum fluctuations tend to dominate thermal fluctuations, resulting in severe departures from Gaussian Markoffian behavior. The low temperature effects are analyzed in some detail, and it is suggested that the predicted departure of the mean square displacement from its classical behavior might be displayed by a particle of macroscopic size suspended in a superfluid. Other models are developed which yield mean square displacements which depart even at high temperature from the linear dependence upon time characteristic of classical diffusion. The reasons and possible physical implications of these behaviors are discussed, together with a brief consideration of Poincaré cycles, whose neglect is implicit in any dynamical theory of irreversible processes.

Diffusion equilibrium in the lungs examined by nodal analysis

The time course of gaseous diffusion in a model of the human lung has been investigated using the relaxation method of nodal analysis. The model of the lung used takes account of known information about alveolar geometry and airways branching, but the asymmetrical characteristics of bronchial branching have not been considered. Analysis has been done using different sets of boundary conditions — in the first an interface between inspired and residual gas has been instituted at two appropriate volumes within the lung, and in the second the interface has been moved into and out of the lung model whilst diffusion continued. The two boundary conditions give entirely different results in respect of the gradient of concentration within the alveolar gas. The analysis permits a precise definition in mathematical terms of dead space and this suggests a clinical application. The conclusion drawn from the analysis is that the computed time course of diffusive mixing in a given lung model, and its effects on the concentration gradients in the alveolar gas, are crucially dependent upon the boundary conditions employed. It is possible to obtain a horizontal or sloping concentration gradient at will by inserting appropriate boundary conditions. Both the anatomy of the terminal airways and the boundary conditions obtaining within the lungs must be accurately defined before a realistic mathematical analysis is possible. It is likely that no analysis yet published has satisfactorily defined these parameters.