Unstirred layers

The lower rates of nutrient absorption associated with diets high in nonstarch polysaccharides are probably due to the increased viscosity of digesta (Vaugelade et al., 2000), which increases the thickness of the unstirred layer overlying the enterocytes and causes anon-specific decline in solute absorption. This explains why diets high in 3-glucans, which are structural carbohydrates and which increase viscosity of digesta, reduce absorption of nutrients and... 

Gutknecht, J. Tosteson, D. C., Diffusion of weak acids across lipid membranes Effects of chemical reactions in the unstirred layers, Science 182, 1258-1261 (1973). 

Gutknecht, J. Bisson, M. A. Tosteson, F. C., Diffusion of carbon dioxide through lipid bilayer membranes. Effects of carbonic anhydrase, bicarbonate, and unstirred layers, J. Gen. Physiol. 69, 779-794 (1977). 

Cotton, C. U. Reuss, L., Measurement of the effective thickness of the mucosal unstirred layer in Necturus gallbladder epithelium, J. Gen. Physiol. 93, 631-647 (1989). 

It may be appropriate here to introduce film theory. As mentioned in reference to the steady diffusion across a thin film, we often hypothesize a film called an unstirred layer to account for the aqueous diffusion resistance to mass transfer. Film theory is valuable not only because of its simplicity but also because of its practical utility. However, the thickness of the film is often difficult to determine. In the following, we try to answer the question, What does the thickness of the film represent ... 

A Strocchi, MD Levitt. A reappraisal of the magnitude and implications of the intestinal unstirred layer. Gastroenterology 101 843-847, 1991. 

The majority of evidence supporting the pH-partition hypothesis is from studies of gastrointestinal absorption, renal excretion, and gastric secretion of drugs [11]. While correlation between absorption rate and pKa was found to be consistent with the pH-partition hypothesis, deviations from this hypothesis were often reported [12]. Such deviations were explained by the existence of a mucosal unstirred layer [13,14] and/or a microclimate pH [15]. 

Such layers are frequently denoted as unstirred layers. The term unstirred however, is... 

An idealised eukaryotic epithelium is represented in Figure 1. This might, for example, be the gut mucosa, the reabsorbing portion of a renal tubule system, or a gill epithelium. The solute must move from the bulk solution (e.g. the external environment, or a body fluid such as urine) into an unstirred layer... 

Figure 1. Solute transfer across an idealised eukaryote epithelium. The solute must move from the bulk solution (e.g. the external environment, or a body fluid) into an unstirred layer comprising water/mucus secretions, prior to binding to membrane-spanning carrier proteins (and the glycocalyx) which enable solute import. Solutes may then move across the cell by diffusion, or via specific cytosolic carriers, prior to export from the cell. Thus the overall process involves 1. Adsorption 2. Import 3. Solute transfer 4. Export. Some electrolytes may move between the cells (paracellular) by diffusion. The driving force for transport is often an energy-requiring pump (primary transport) located on the basolateral or serosal membrane (blood side), such as an ATPase. Outward electrochemical gradients for other solutes (X+) may drive import of the required solute (M+, metal ion) at the mucosal membrane by an antiporter (AP). Alternatively, the movement of X+ down its electrochemical gradient could enable M+ transport in the same direction across the membrane on a symporter (SP). A, diffusive anion such as chloride. Kl-6 refers to the equilibrium constants for each step in the metal transfer process, Kn indicates that there may be more than one intracellular compartment involved in storage. See the text for details...

Figure 2. Sodium and chloride uptake across an idealised freshwater-adapted gill epithelium (chloride cell), which has the typical characteristics of ion-transporting epithelia in eukaryotes. In the example, the abundance of fixed negative charges (muco-proteins) in the unstirred layer may generate a Donnan potential (mucus positive with respect to the water) which is a major part of the net transepithelial potential (serosal positive with respect to water). Mucus also contains carbonic anhydrase (CA) which facilitates dissipation of the [H+] and [HCO(] to CO2, thus maintaining the concentration gradients for these counter ions which partly contribute to Na+ import (secondary transport), whilst the main driving force is derived from the electrogenic sodium pump (see the text for details). Large arrow indicates water flow...

However, some effects are less intuitively obvious, and have been neglected. Unstirred layer formation can have large effects on solute transport, and, on a minute-by-minute basis, animals are constantly readjusting physiological systems (e.g. gill ventilation rate, blood flow) which will affect unstirred layer formation. Ventilation and blood flow are influenced by many environmental factors, but the interrelationship between environmentally induced cardiovascular adjustment, unstirred layer formation, and the cost of solute transport remain to be explored. 

Transepithelialpotential the voltage measured across an epithelium. Unstirred layer, a relatively nonmobile layer of water and/or mucus secretions adjacent to a biological membrane. 

Pedley, T. J. (1983). Calculations of unstirred layer thickness in membrane transport experiments a survey, Q. Rev. Biophys., 16, 115-150. 

Barry, P. H. (1998). Derivation of unstirred-layer transport number equations from the Nernst-Planck flux equations, Biophys. J., 74, 2903-2905. 

Winne, D. (1973). Unstirred layer, source of biased Michaelis constant in membrane transport, Biochim. Biophys. Acta, 298, 27-31. 

Wilson, F.A. and Dietschy, J.M. (1974). The intestinal unstirred layer—its surface area and effect on active transport kinetics. Biochem. Biophys. Acta. 363 112-126. 

Winne, D. (1978). Dependence of intestinal absorption in vivo in the unstirred layer. Nauyn-Schmiedelberg s Arch. Pharmacol. 304 175-181. 

Phase-separation immunoassays have been reported, in which the solid phase particles are formed after the immunoreaction is completed.(42) Phase-separation immunoassays are advantageous since the unstirred layer of solution near a solid surface alters diffusion and binding kinetics at the surface in comparison with the properties of the bulk solution. In phase-separation assays for IgG and IgM, capture antibodies are bound with monomers suitable for styrene or acrylamide polymerization.(42) Monomer-labeled capture antibodies are reacted with analyte and with fluorescein- and/or phycoerythrin-labeled antibodies in a sandwich assay, followed by polymerization of the monomers. Fluorescence of the resulting particles is quantitated in a FACS IV flow microfluorometer, and is directly proportional to analyte concentration. 

Interaction with local tissues. Sucralfate appears to augment the protective function of the mucous-bicarbonate barrier, partly due to increased bicarbonate and mucous secretion, and partly to an interaction with the unstirred layer overlying gastric epithelium, as well as by making the mucous gel more hydrophobic. It binds bile acids and pepsin and adheres to both ulcerated and nonulcerated mucosa. 

I can easily understand a thickness of the order of 50 to 100 ptm for the unstirred diffusion layers of the flat and thin macromembranes you discussed. In microsystems such as mitochondria with diameters around a few p.m these unstirred layers must, however, be considerably smaller. Would you please comment on this substantial difference between the model membranes you studied and actual biological membrane systems ... 

The size of the unstirred layer does not depend on the thickness of the membrane. The water does not know what is the thickness of the membrane. 

On the matter of the unstirred layer, it must be remembered that model membranes are static structures, whereas natural membranes are highly dynamic that is, they continuously move in their normal environment. This is certainly going to disturb the formation and the maintenance of unstirred layers more than a few molecules thick. 

In a hydrodynamically free system the flow of solution may be induced by the boundary conditions, as for example when a solution is fed forcibly into an electrodialysis (ED) cell. This type of flow is known as forced convection. The flow may also result from the action of the volume force entering the right-hand side of (1.6a). This is the so-called natural convection, either gravitational, if it results from the component defined by (1.6c), or electroconvection, if it results from the action of the electric force defined by (1.6d). In most practical situations the dimensionless Peclet number Pe, defined by (1.11b), is large. Accordingly, we distinguish between the bulk of the fluid where the solute transport is entirely dominated by convection, and the boundary diffusion layer, where the transport is electro-diffusion-dominated. Sometimes, as a crude qualitative model, the diffusion layer is replaced by a motionless unstirred layer (the Nemst film) with electrodiffusion assumed to be the only transport mechanism in it. The thickness of the unstirred layer is evaluated as the Peclet number-dependent thickness of the diffusion boundary layer. 

Locally electro-neutral concentration polarization of a binary electrolyte at an ideally cation-permselective homogeneous interface. Consider a unity thick unstirred layer of a univalent electrolyte adjacent to an ideally cation-permselective homogeneous flat interface. Let us direct the x-axis normally to this interface with the origin x = 0 coinciding with the outer (bulk) edge of the unstirred layer. Let a unity electrolyte concentration be maintained in the bulk. 

The stationary ionic transport across the unstirred layer is described by the following b.v.p. 

According to (4.4.4) this corresponds to the greatest achievable constant concentration gradient within the unstirred layer. 

Consider again an unstirred layer (or thickness 6) of a symmetric z-valent electrolyte (of bulk concentration Co), adjacent to the membrane. Let us introduce a rectangular system of coordinates ylt y2, x, with the axis x directed normally to the membrane, through the center of the conductive spot, with the origin x = 0 coinciding with the outer edge of the unstirred layer. 

Due to symmetry, the description of the ionic transfer across the unstirred layer is equivalent to that in the rectangular cell... 

A stationary electro-diffusion in the unstirred layer is then described by the following b.v.p. (compare with (4.4.1)) ... 

Furthermore, Figs. 4.4.6 and 4.4.7 depict the i dependence on V for different values of R and 8 = 200,20, respectively. When the thickness of the unstirred layer is much larger than the typical distance between the conductive inhomogeneities of the membrane surface (8 1), the deviation in the limiting current density at a nonhomogeneous membrane from the appropriate value at a homogeneous surface is hardly noticeable, unless the proportion of the conductive membrane surface area is very small (R 1). 

On the other hand, for thin unstirred layers (8 = 0(1)), the deviation... 

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