Johannes M. Nitsche

Different ionic selectivities for connexins 26 and 32 produce rectifying gap junction channels.

The functional diversity of gap junction intercellular channels arising from the large number of connexin isoforms is significantly increased by heterotypic interactions between members of this family. This is particularly evident in the rectifying behavior of Cx26/Cx32 heterotypic channels (. Proc. Natl. Acad. Sci. USA. 88:8410-8414). The channel properties responsible for producing the rectifying current observed for Cx26/Cx32 heterotypic gap junction channels were determined in transfected mouse neuroblastoma 2A (N2A) cells. Transfectants revealed maximum unitary conductances (gamma(j)) of 135 pS for Cx26 and 53 pS for Cx32 homotypic channels in 120 mM KCl. Anionic substitution of glutamate for Cl indicated that Cx26 channels favored cations by 2.6:1, whereas Cx32 channels were relatively nonselective with respect to charge. In Cx26/Cx32 heterotypic cell pairs, the macroscopic fast rectification of the current-voltage relationship was fully explained at the single-channel level by a rectifying gamma(j) that increased by a factor of 2.9 as the transjunctional voltage (V(j)) changed from -100 to +100 mV with the Cx26 cell as the positive pole. A model of electrodiffusion of ions through the gap junction pore based on Nernst-Planck equations for ion concentrations and the Poisson equation for the electrical potential within the junction is developed. Selectivity characteristics are ascribed to each hemichannel based on either pore features (treated as uniform along the length of the hemichannel) or entrance effects unique to each connexin. Both analytical GHK approximations and full numerical solutions predict rectifying characteristics for Cx32/Cx26 heterotypic channels, although not to the full extent seen empirically. The model predicts that asymmetries in the conductance/permeability properties of the hemichannels (also cast as Donnan potentials) will produce either an accumulation or a depletion of ions within the channel, depending on voltage polarity, that will result in rectification.

Break-up of a falling drop containing dispersed particles

The general purpose of this paper is to investigate some consequences of the randomness of the velocities of interacting rigid particles falling under gravity through viscous fluid at small Reynolds number. Random velocities often imply diffusive transport of the particles, but particle diffusion of the conventional kind exists only when the length characteristic of the diffusion process is small compared with the distance over which the particle concentration is effectively uniform. When this condition is not satisfied, some alternative analytical description of the dispersion process is needed. Here we suppose that a dilute dispersion of sedimenting particles is bounded externally by pure fluid and enquire about the rate at which particles make outward random crossings of the (imaginary) boundary. If the particles are initially distributed with uniform concentration within a spherical boundary, we gain the convenience of approximately steady conditions with a velocity distribution like that in a falling spherical drop of pure liquid. However, randomness of the particle velocities causes some particles to make an outward crossing of the spherical boundary and to be carried round the boundary and thence downstream in a vertical ‘tail’. This is the nature of break-up of a falling cloud of particles. A numerical simulation of the motion of a number of interacting particles (maximum 320) assumed to act as Stokeslets confirms the validity of the above picture of the way in which particles leak away from a spherical cluster of particles. A dimensionally correct empirical relation for the rate at which particles are lost from the cluster involves a constant which is indeed found to depend only weakly on the various parameters occurring in the numerical simulation. According to this relation the rate at which particles are lost from the blob is proportional to the fall speed of an isolated particle and to the area of the blob boundary. Some photographs of a leaking tail of particles in figure 5 also provide support for the qualitative picture.

INSTABILITY OF STATIONARY UNBOUNDED STRATIFIED FLUID

Suppose that the density of stationary unbounded viscous fluid is a sinusoidal function of the vertical position coordinate z. Is this body of fluid gravitationally unstable to small disturbances, and, if so, under what conditions, and to what type of disturbance? These questions are considered herein, and the answers are that the fluid is indeed unstable, for any non-zero value of the amplitude of the sine wave, to disturbances with large horizontal wavelength. These disturbances have approximately vertical velocity everywhere and tilt the alternate layers of heavier and of lighter fluid, causing the fluid in the former to slide down and that in the latter to slide up, leading to a sinusoidal variation of the vertically averaged density and thereby to reinforcement of the vertical motion. The identification of this novel and efficient global instability mechanism prompts a consideration of the stability of other cases of unbounded fluid stratified in layers. Two other types of undisturbed density distribution, the first an isolated central layer of heavier or lighter fluid, with density varying say as a Gaussian function, and the second an isolated layer of fluid in which the density varies as the derivative of a Gaussian function, are found to be unstable, at all values of the magnitude of the density variation, to disturbances having the same global character. For the first of these two types of density distribution, the behaviour of a disturbance with long horizontal wavelength depends only on the net excess mass of unit area of the central layer, and for the second it depends only on the first moment of the density in the central layer. For the second type there arises another global instability mechanism in which light fluid is stripped away from one side of the layer and heavy fluid from the other without any tilting. In all cases the properties of a neutral disturbance are determined numerically, and the growth rate is found as a function of the Rayleigh number, the Prandtl number, and the horizontal wavenumber of the disturbance. An energy argument gives results easily for the inviscid non-diffusive limit, when all disturbances grow, and reveals the tilting-sliding mechanism of the instability of a disturbance with large horizontal wavelength in its simplest form.

Dermal clearance model for epidermal bioavailability calculations.

A computational model for estimating dermal clearance in humans of arbitrary, nonmetabolized solutes is presented. The blood capillary component employs slit theory with contributions from both small (10 nm) and large (50 nm) slits. The lymphatic component is derived from previously reported clearance measurements of dermal and subcutaneous injections of (131)I-albumin in humans. Model parameters were fitted to both blood capillary permeability data and lymphatic clearance data. Small molecules are cleared largely by the blood and large molecules by the lymph. The combined model shows a crossover behavior at approximately 29 kDa, in acceptable agreement with the reported value of 16 kDa. When combined with existing models for stratum corneum permeability and appropriate measures of tissue binding, the developed model has the potential to significantly improve tissue concentration estimates for large or highly protein-bound permeants following dermal exposure.

Tissue Binding Affects the Kinetics of Theophylline Diffusion Through the Stratum Corneum Barrier Layer of Skin

New data sets on both (i) equilibrium theophylline (TH) partitioning/binding in stratum corneum and (ii) transient TH diffusion through human epidermis are explained by an extended partition-diffusion model with reversible binding. Data conform to a linear binding isotherm within the tested concentration range (0-2000 μg/mL) with an equilibrium ratio of bound-to-free solute of approximately 1.4. The permeability coefficient for TH is 4.86 × 10(-5) cm/h, and the lag time is 20.1 h. Binding occurs as a slow process, significantly affecting the kinetics of dermal penetration.

Transport and kinetic processes underlying biomolecular interactions in the BIACORE optical biosensor.

The transport and kinetic processes describing biomolecular interactions in the BIACORE optical biosensor have been studied with the help of a mathematical model. In comparison to previous models, the model presented here couples, for the first time, transport phenomena in the flow channel with hindered diffusive transport and reactions inside the hydrogel. Simulated experiments based on this model, and two simpler models extant in the literature, are used to identify cases under which the detailed model is essential for accurate prediction of kinetic parameters. It is shown that this model can substantially improve the accuracy of kinetic parameter estimation when transport limitations in the flow channel and/or the hydrogel significantly influence the observed instrument response curves. The model can extend the range of the instruments applicability to higher concentrations of immobilized species within the hydrogel. It can also be used for accurate design of experiments with the purpose of minimizing errors in the estimation of the kinetic parameters.

Transport effects on the kinetics of protein-surface binding.

A detailed model is presented for protein binding to active surfaces, with application to the binding of avidin molecules to a biotin-functionalized fiber optic sensor in experiments reported by S. Zhao and W. M. Reichert (American Chemical Society Symposium Series 493, 1992). Kinetic data for binding in solution are used to assign an intrinsic catalytic rate coefficient k to the biotin-avidin pair, deconvoluted from transport and electrostatic factors via application of coagulation theory. This intrinsic chemical constant is built into a reaction-diffusion analysis of surface binding where activity is restricted to localized sites (representing immobilized biotin molecules). The analysis leads to an effective catalytic rate coefficient keff characterizing the active surface. Thereafter, solution of the transport problem describing absorption of avidin molecules by the macroscopic sensor surface leads to predictions of the avidin flux, which are found to be in good agreement with the experimental data. The analysis suggests the following conclusions. 1) Translational diffusion limitations are negligible for avidin-biotin binding in solution owing to the small (kinetically limiting) value k = 0.00045 m/s. 2) The sparse distribution of biotin molecules and the presence of a repulsive hydration force produce an effective surface-average catalytic rate coefficient keff of order 10(-7) m/s, much smaller than k. 3) Avidin binding to the fiber optic sensor occurs in an intermediate regime where the rate is influenced by both kinetics and diffusion.

Expulsion of particles from a buoyant blob in a fluidized bed

It is a significant feature of most gas-fluidized beds that they contain rising ‘bubbles’ of almost clear gas. The purpose of this paper is to account plausibly for this remarkable property first by supposing that primary and secondary instabilities of the fluidized bed generate compact regions of above-average or below-average particle concentration, and second by invoking a mechanism for the expulsion of particles from a buoyant compact blob of smaller particle concentration. We postulate that the rising of such an incipient bubble generates a toroidal circulation of the gas in the bubble, roughly like that in a drop of liquid rising through a second liquid of larger density, and that particles in the blob carried round by the fluid move on trajectories which ultimately cross the bubble boundary. Numerical calculations of particle trajectories for practical values of the relevant parameters show that a large percentage of particles, of such small concentration that they move independently, are expelled from a bubble in the time taken by it to rise through a distance of several bubble diameters. Similar calculations for a liquid-fluidized bed show that the expulsion mechanism is much weaker, as a consequence of the larger density and viscosity of a liquid, which is consistent with the absence of observations of relatively empty bubbles in liquid-fluidized beds. It is found to be possible, with the help of the Richardson-Zaki correlation, to adjust the results of these calculations so as to allow approximately for the effect of interaction of particles in a bubble in either a gas- or a liquid-fluidized bed. The interaction of particles at volume fractions of 20 or 30 % lengthens the expulsion times, although without changing the qualitative conclusions.

A Microscopic Multiphase Diffusion Model of Viable Epidermis Permeability

A microscopic model of passive transverse mass transport of small solutes in the viable epidermal layer of human skin is formulated on the basis of a hexagonal array of cells (i.e., keratinocytes) bounded by 4-nm-thick, anisotropic lipid bilayers and separated by 1-μm layers of extracellular fluid. Gap junctions and tight junctions with adjustable permeabilities are included to modulate the transport of solutes with low membrane permeabilities. Two keratinocyte aspect ratios are considered to represent basal and spinous cells (longer) and granular cells (more flattened). The diffusion problem is solved in a unit cell using a coordinate system conforming to the hexagonal cross section, and an efficient two-dimensional treatment is applied to describe transport in both the cell membranes and intercellular spaces, given their thinness. Results are presented in terms of an effective diffusion coefficient, D¯(epi), and partition coefficient, K¯(epi/w), for a homogenized representation of the microtransport problem. Representative calculations are carried out for three small solutes-water, L-glucose, and hydrocortisone-covering a wide range of membrane permeability. The effective transport parameters and their microscopic interpretation can be employed within the context of existing three-layer models of skin transport to provide more realistic estimates of the epidermal concentrations of topically applied solutes.

Permeability of Fluid-Phase Phospholipid Bilayers: Assessment and Useful Correlations for Permeability Screening and Other Applications

Permeability data (P(lip/w) ) for liquid crystalline phospholipid bilayers composed of egg lecithin and dimyristoylphosphatidylcholine (DMPC) are analyzed in terms of a mathematical model that accounts for free surface area and chain-ordering effects in the bilayer as well as size and lipophilicity of the permeating species. Free surface area and chain ordering are largely determined by temperature and cholesterol content of the membrane, molecular size is represented by molecular weight, and lipophilicity of the barrier region is represented by the 1,9-decadiene/water partition coefficient, following earlier work by Xiang, Anderson, and coworkers. A correlating variable χ = MW(n) σ/(1 -σ) is used to link the results from different membrane systems, where different values of n are tried, and σ denotes a reduced phospholipid density. The group (1 -σ)/σ is a measure of free surface area, but can also be interpreted in terms of free volume. A single exponential function of χ is developed that is able to correlate 39 observations of P(lip/w) for different compounds in egg lecithin at low density, and 22 observations for acetic acid in DMPC at higher densities, spanning nine orders of magnitude to within an rms error for log 10 P(lip/w) of 0.20. The best fit found for n = 0.87 ultimately makes χ much closer to the ratio of molecular to free volumes than surface areas. The results serve as a starting point for estimating passive permeability of cell membranes to nonionized solutes as a function of temperature and cholesterol content of the membrane.