A review of experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms

Experimental measurements of effective diffusive permeabilities and effective diffusion coefficients in biofilms are reviewed. Effective diffusive permeabilities, the parameter appropriate to the analysis of reaction-diffusion interactions, depend on solute type and biofilm density. Three categories of solute physical chemistry with distinct diffusive properties were distinguished by the present analysis. In order of descending mean relative effective diffusive permeability (De/Daq) these were inorganic anions or cations (0.56), nonpolar solutes with molecular weights of 44 or less (0.43), and organic solutes of molecular weight greater than 44 (0.29). Effective diffusive permeabilities decrease sharply with increasing biomass volume fraction suggesting a serial resistance model of diffusion in biofilms as proposed by Hinson and Kocher (1996). A conceptual model of biofilm structure is proposed in which each cell is surrounded by a restricted permeability envelope. Effective diffusion coefficients, which are appropriate to the analysis of transient penetration of nonreactive solutes, are generally similar to effective diffusive permeabilities in biofilms of similar composition. In three studies that examine diffusion of very large molecular weight solutes (>5000) in biofilms, the average ratio of the relative effective diffusion coefficient of the large solute to the relative effective diffusion coefficient of either sucrose or fluorescein was 0.64, 0.61, and 0.36. It is proposed that large solutes are effectively excluded from microbial cells, that small solutes partition into and diffuse within cells, and that ionic solutes are excluded from cells but exhibit increased diffusive permeability (but decreased effective diffusion coefficients) due to sorption to the biofilm matrix.     

Computer simulation of small molecule permeation across a lipid bilayer: dependence on bilayer properties and solute volume, size, and cross-sectional area

Cell membrane permeation is required for most drugs to reach their biological target, and understanding this process is therefore crucial for rational drug design. Recent molecular dynamics simulations have studied the permeation of eight small molecules through a phospholipid bilayer. Unlike experiments, atomistic simulations allow the direct calculation of diffusion and partition coefficients of solutes at different depths inside a lipid membrane. Further analyses of the simulations suggest that solute diffusion is less size-dependent and solute partitioning more size-dependent than was commonly thought.     

On simultaneous transport of water and solute through plant cell membranes: Evidence for the absence of solvent drag effect and insensitivity of the reflection coefficient

The simultaneous efflux of tritiated water and ¹⁴C labelled ethanol from inner epidermal cells of the bulb scale of Allium cepa was measured with a specially designed efflux chamber. It was found that water and ethanol moved essentially independently. Rates of efflux of tritiated water and ¹⁴C ethanol were essentially the same in the presence or absence of a simultaneous influx of water. Using the same technique the efflux of tritiated water from the epidermal cells was measured during a simultaneous flow of nonlabelled ethanol. When tritiated water and ethanol moved in opposite directions, the water permeability values became slightly reduced depending upon the concentration of ethanol. When ethanol and tritiated water moved in the same direction, however, no effect on water permeability values could be detected. These results are best explained by the molecular theory of diffusion across lipid bilayer membranes, and are consistent with the above findings of lack of interaction between water and ethanol as they are transported across the cell membrane. In another study, the solute permeability coefficients (K_s) for non-electrolytes such as urea and methyl urea were measured by plasmolyzing the epidermal cells and transferring them to equimolal solutions of urea and methyl urea. This method was also used to measure the reflection coefficient (σ) for these nonelectrolytes. The K_s values for methyl urea were 16 times greater than the ones for urea. The values of σ for both of these solutes, however, were very close to 1. Using the K_s data available in the literature for the subepidermal cells of the Pisum sativum stem basis, the σ values were calculated for malonamide, glycerol, methyl urea, ethyl urea, dimethyl urea, and formamide. Again the K_s values for these nonelectrolytes varied by several orders of magnitude, whereas all σ values were found to be close to 1. These findings point out that σ is an insensitive parameter and that K_s, the solute permeability constant, has to be used for characterizing solute transport through the membrane. The present study shows that fast (e.g. ethanol, formamide) as well as slowly permeating molecules do not interact with water as they are transported across the cell membrane. Aqueous pores for the simultaneous transport of water and solutes, therefore, are absent in the plant cell membranes investigated here.     

Red Cell Membrane Permeability Deduced from Bulk Diffusion Coefficients

The permeability coefficients of dog red cell membrane to tritiated water and to a series of[¹⁴C]amides have been deduced from bulk diffusion measurements through a "tissue" composed of packed red cells. Red cells were packed by centrifugation inside polyethylene tubing. The red cell column was pulsed at one end with radiolabeled solute and diffusion was allowed to proceed for several hours. The distribution of radioactivity along the red cell column was measured by sequential slicing and counting, and the diffusion coefficient was determined by a simple plotting technique, assuming a one-dimensional diffusional model. In order to derive the red cell membrane permeability coefficient from the bulk diffusion coefficient, the red cells were assumed to be packed in a regular manner approximating closely spaced parallelopipeds. The local steady-state diffusional flux was idealized as a one-dimensional intracellular pathway in parallel with a one-dimensional extracellular pathway with solute exchange occurring within the series pathway and between the pathways. The diffusion coefficients in the intracellular and extracellular pathways were estimated from bulk diffusion measurements through concentrated hemoglobin solutions and plasma, respectively; while the volume of the extracellular pathway was determined using radiolabeled sucrose. The membrane permeability coefficients were in satisfactory agreement with the data of Sha'afi, R. I., C. M. Gary-Bobo, and A. K. Solomon (1971. J. Gen. Physiol. 58:238) obtained by a rapid-reaction technique. The method is simple and particularly well suited for rapidly permeating solutes.     

Further quantification of the role of internal unstirred layers during the measurement of transport coefficients in giant internodes of Chara by a new stop-flow technique

A new stop-flow technique was employed to quantify the impact of internal unstirred layers on the measurement of the solute permeability coefficient (P(s)) across the plasma membrane of internodes of the giant-celled alga Chara corallina using a cell pressure probe. During permeation experiments with rapidly permeating solutes (acetone, 2-propanol, and dimethylformamide), the solute concentration inside the cell was estimated and the external medium was adjusted to stop solute transport across the membrane, after which responses in turgor were measured. This allowed estimation of the solute concentration right at the membrane. Stop-flow experiments were also simulated with a computer. Both the stop-flow experiments and simulations provided quantitative data about internal concentration gradients and the contribution of unstirred layers to overall measured values of P(meas)(s) for the three solutes. The stop-flow experimental results agreed with stop-flow simulations assuming that solutes diffused into a completely stagnant cell interior. The effects of internal unstirred layers on the underestimation of membrane P(s) declined with decreasing P(s). They were no bigger than 37% in the presence of the most rapidly permeating solute, acetone (P(meas)(s) =4.2 x 10(-6) m s(-1)), and 14% for the less rapidly permeating dimethylformamide (P(meas)(s) =1.6x10(-6) m s(-1)). It is concluded that, even in the case of rapidly permeating solutes such as isotopic water and, even when making pessimistic assumptions about the internal mixing of solutes, an upper limit for the underestimation of P(s) due to internal unstirred layers was 37%. The data are discussed in terms of recent theoretical estimates of the effect of internal unstirred layers and in terms of some recent criticism of cell pressure probe measurements of water and solute transport coefficients. The current stop-flow data are in line with earlier estimations of the role of unstirred layers in the literature on cell water relations.     

Patterns of Nonelectrolyte Permeability in Human Red Blood Cell Membrane

The permeability of human red cell membrane to 90 different molecules has been measured. These solutes cover a wide spectrum of nonelectrolytes with varying chemical structure, chain length, lipid solubility, chemical reactive group, ability to form hydrogen bonds, and other properties. In general, the present study suggests that the permeability of red cell membrane to a large solute is determined by lipid solubility, its molecular size, and its hydrogen-bonding ability. The permeability coefficient increases with increasing lipid solubility and decreasing ability to form hydrogen bonds, whereas it decreases with increasing molecular size. In the case of small solutes, the predominant diffusion factor is steric hindrance augmented by lipid solubility. It is also found that replacement of a hydroxyl group by a carbonyl group or an ether linkage tends to increase permeability. On the other hand, replacement of a hydroxyl group by an amide group tends to decrease the permeability coefficient.     

Permeability of composite chondrocyte-culture-millipore membranes to solutes of varying size and shape.

A model connective-tissue system was developed that is amenable to the determination of permeability coefficients of diffusing solutes. The system involves the culture of 13-day chick-embryo chondrocytes on a Millipore filter (HA:0.45 micron pore size) to form what is, in effect, a confluent, extremely thin cartilage slice of uniform thickness. These cultured chondrocyte membranes were used to measure the steady-state flux of radioactively labelled low-molecular-weight solutes and micro-ions. Similarly, the permeability coefficients of either radioactively labelled or enzymically active proteins across the membranes were determined. The membrane was found to have no marked effects on the diffusional behaviour of low-molecular-weight non-electrolytes (water, proline, ribose, glucose, sorbitol, raffinose). For micro-ions (Na+, SO42-, Cl-, glutamate, glucuronate,), the diffusive behaviour was found to be markedly affected by the ionic strength of the solvent used in a manner which was consistent with a Donnan distribution resulting from the immobilized proteoglycans. Globular proteins permeated the membrane at rates which decreased as the molecular size of the diffusing solute increased. The apparent diffusion rates of fibrinogen and of collagen through the membranes were greater than would be expected on the basis of their diffusion coefficients in free solution. Reasons for this behaviour are discussed.     

Transport parameters in the human red cell membrane: solute-membrane interactions of amides and ureas

We have studied the permeability of a series of hydrophilic amides and ureas through the red cell membrane by determining the three phenomenological coefficients which describe solute-membrane interaction: the hydraulic permeability (Lp), the phenomenological permeability coefficient (omega i) and the reflection coefficient (sigma i). In 55 experiments on nine solutes, we have determined that the reflection coefficient (after a small correction for solute permeation by membrane dissolution) is significantly less than 1.0 (P less than 0.003, t-test), which provides very strong evidence that solute and water fluxes are coupled as they cross the red cell membrane. It is proposed that the aqueous channel is a tripartite assembly, comprising H-bond exchange regions at both faces of the membrane, joined by a narrower sieve-specific region which crosses the lipid. The solutes bind to the H-bond exchange regions to exchange their solvation shell with the H-bonds of the channel; the existence of these regions is confirmed by the finding that the permeation of all the amides and ureas requires binding to well-characterized sites with Km values of 0.1-0.5 M. The sieve-specific regions provide the steric restraints which govern the passage of the solutes according to their size; their existence is shown by the findings that: (1) the reflection coefficient (actually the function [1-corrected sigma i]) is linearly dependent upon the solute molecular diameter; and (2) the permeability coefficient is linearly dependent upon solute molar volume. These several observations, taken together, provide strong arguments which lead to the conclusion that the amides and urea cross the red cell membrane in an aqueous pore.     

Crossover from picosecond collective to single particle dynamics defines the mechanism of lateral lipid diffusion

It has been widely accepted that the thermally excited motions of the molecules in a cell membrane is the prerequisite for a cell to carry its biological functions. On the other hand, the detailed mapping of the ultrafast picosecond single-molecule and the collective lipid dynamics in a cell membrane remains rather elusive. Here, we report all-atom molecular dynamics simulations of a 1,2-dipalmitoyl-sn-glycero-3-phosphocholine bilayer over a wide range of temperature. We elucidate a molecular mechanism underlying the lateral lipid diffusion in a cell membrane across the gel, rippled, and liquid phases using an analysis of the longitudinal and transverse current correlation spectra, the velocity auto-correlation functions, and the molecules mean square displacements. The molecular mechanism is based on the anomalous ultrafast vibrational properties of lipid molecules at the viscous-to-elastic crossover. The macroscopic lipid diffusion coefficients predicted by the proposed diffusion model are in a good agreement with experimentally observed values. Furthermore, we unveil the role of water confined at the water-lipid interface in triggering collective vibrations in a lipid bilayer.     

Aquaporin Nt-TIPa can account for the high permeability of tobacco cell vacuolar membrane to small neutral solutes

Members of the major intrinsic protein (MIP) family, described in plants as water-selective channels (aquaporins), can also transport small neutral solutes in other organisms. In the present work, we characterize the permeability of plant vacuolar membrane (tonoplast; TP) and plasma membrane (PM) to non-electrolytes and evaluate the contribution of MIP homologues to such transport. PM and TP vesicles were purified from tobacco suspension cells by free-flow electrophoresis, and membrane permeabilities for a wide range of neutral solutes including urea, polyols of different molecular size, and amino acids were investigated by stopped-flow spectrofluorimetry. For all solutes tested, TP vesicles were found to be more permeable than their PM counterparts, with for instance urea permeabilities from influx experiments of 74.9 +/- 9.6 x 10(-6) and 1.0 +/- 0.3 x 10(-6) cm sec-1, respectively. Glycerol and urea transport in TP vesicles exhibited features of a facilitated diffusion process. This and the high channel-mediated permeability of the same TP vesicles to water suggested a common role for MIP proteins in water and solute transport. A cDNA encoding a novel tonoplast intrinsic protein (TIP) homologue named Nicotiana tabacum TIPa (Nt-TIPa) was isolated from tobacco cells. Immunodetection of Nt-TIPa in purified membrane fractions confirmed that the protein is localized in the TP. Functional expression of Nt-TIPa in Xenopus oocytes showed this protein to be permeable to water and solutes such as urea and glycerol. These features could account for the transport selectivity profile determined in purified TP vesicles. These results support the idea that plant aquaporins have a dual function in water and solute transport. Because Nt-TIPa diverges in sequence from solute permeable aquaporins characterized in other organisms, its identification also provides a novel tool for investigating the molecular determinants of aquaporin transport selectivity.     

Mycobacterial porins--new channel proteins in unique outer membranes

Mycobacteria protect themselves with an outer lipid bilayer, which is the thickest biological membrane hitherto known and has an exceptionally low permeability rendering mycobacteria intrinsically resistant to many antibiotics. Pore proteins spanning the outer membrane mediate the diffusion of hydrophilic nutrients. Mycobacterium tuberculosis possesses at least two porins in addition to the low activity channel protein OmpATb. OmpATb is essential for adaptation of M. tuberculosis to low pH and survival in macrophages and mice. The channel activity of OmpATb is likely to play a major role in the defence of M. tuberculosis against acidification within the phagosome of macrophages. MspA is the main porin of Mycobacterium smegmatis. It forms a tetrameric complex with a single central pore of 10 nm length and a cone-like structure. This structure differs clearly from that of the trimeric porins of Gram-negative bacteria, which form one 4 nm long pore per monomer. The 45-fold lower number of porins compared to Gram-negative bacteria and the exceptional length of the pores are two major determinants of the low permeability of the outer membrane of M. smegmatis for hydrophilic solutes. The importance of the synergism between slow transport through the porins and drug efflux or inactivation for the development of drugs against M. tuberculosis is discussed.     

Dynamic loading of deformable porous media can induce active solute transport

Active solute transport mediated by molecular motors across porous membranes is a well-recognized mechanism for transport across the cell membrane. In contrast, active transport mediated by mechanical loading of porous media is a non-intuitive mechanism that has only been predicted recently from theory, but not yet observed experimentally. This study uses agarose hydrogel and dextran molecules as a model experimental system to explore this mechanism. Results show that dynamic loading can enhance the uptake of dextran by a factor greater than 15 over passive diffusion, for certain combinations of gel concentration and dextran molecular weight. Upon cessation of loading, the concentration reverts back to that achieved under passive diffusion. Thus, active solute transport in porous media can indeed be mediated by cyclical mechanical loading.     

Coupled water transport in standing gradient models of the lateral intercellular space.

A standing gradient model of the lateral intercellular space is presented which includes a basement membrane of finite solute permeability. The solution to the model equations is estimated analytically using the "isotonic convection approximation" of Segel. In the case of solute pumps uniformly distributed along the length of the channel, the achievement of isotonic transport depends only on the water permeability of the cell membranes. The ability of the model to transport water against an adverse osmotic gradient is the sum of two terms: The first term is simply that for a well-stirred compartment model and reflects basement membrane solute permeability. The second term measures the added strength due to diffusion limitation within the interspace. It is observed, however, that the ability for uphill water transport due to diffusion limitation is diminished by high cell membrane water permeability. For physiologically relevant parameters, it appears that the high water permeability required for isotonic transport renders the contribution of the standing gradient relatively ineffective in transport against an osmotic gradient. Finally, when the model transports both isotonically and against a gradient, it is shown that substantial intraepithelial solute polarization effects are unavoidable. Thus, the measured epithelial water permeability will grossly underestimate the water permeability of the cell membranes. The accuracy of the analytic approximation is demonstrated by numerical solution of the complete model equations.     

Permeability of Lipid Bilayer Membranes to Organic Solutes

A sensitive fluorescence technique was used to measure transport of organic solutes through lipid bilayer membranes and to relate permeability to the functional groups of the solute, lipid composition of the membrane, and pH of the medium. Indole derivatives having ethanol, acetate, or ethylamine in the 3-position, representing neutral, acidic, and basic solutes, respectively, were the primary models. The results show: (a) Neutral solute permeability is not greatly affected by changes in lipid composition but presence or absence of cholesterol in the membranes could greatly alter permeability of the dissociable substrates. (b) Indole acetate permeability was reduced by introduction of phosphatidylserine into membranes to produce a net negative charge on the membranes. (c) Permeability response of dissociable solutes to variation in pH was in the direction predicted but not always of the magnitude expected from changes in the calculated concentrations of the undissociated solute in the bulk aqueous phase. Concentration gradients of amines across the membranes caused substantial diffusion potentials, suggesting that some transport of the cationic form of the amine may occur. It is suggested that factors such as interfacial charge and hydration structure, interfacial polar forces, and lipid organization and viscosity, in addition to the expected solubility-diffusion relations, may influence solute flux.     

Determination of reflection coefficients of liposomes for some non-electrolytes by osmotic pressure measurement

The reflection coefficients of bilayer lipid vesicles (liposomes) of various compositions have been determined for a number of non-electrolytes. The solutes were the same and the method of measurement was essentially the same as those which have been used to estimate an equivalent pore radius for erythrocytes. The method involves matching the osmotic pressure of solutions of a permeant test solute with that of a known inpermeant solute. Reflection coefficients for cholesterol-containing liposomes and those of erythrocytes are, when account is taken of those solutes known to permeate the erythrocyte by specialized pathways, not greatly different. Lipid bilayers can thus account for most of the permeability characteristics of the cell originally interpreted as due to aqueous pores. Reflection coefficients are significantly higher for egg phosphatidylcholine membranes that contain cholesterol than those which do not. There is a strong correlation between relative permeabilities derived from reflection coefficients and oil-water partition coefficients. There is also good agreement between these permeabilities and permeabilities measured by others, which exhibit an inverse dependence on molecular size. It is suggested that this tendency of membranes to pass small molecules more readily than large molecules, other properties being equal, is a consequence of the surface pressure of the constituent monolayers of the membrane.     

A re-examination of the minor role of unstirred layers during the measurement of transport coefficients of Chara corallina internodes with the cell pressure probe

The impact of unstirred layers (USLs) during cell pressure probe experiments with Chara corallina internodes has been quantified. The results show that the hydraulic conductivity (Lp) measured in hydrostatic relaxations was not significantly affected by USLs even in the presence of high water flow intensities ('sweep-away effect'). During pressure clamp, there was a reversible reduction in Lp by 20%, which was explained by the constriction of water to aquaporins (AQPs) in the C. corallina membrane and a rapid diffusional equilibration of solutes in arrays where water protruded across AQPs. In osmotic experiments, Lp, and permeability (Ps) and reflection (sigma s) coefficients increased as external flow rate of medium increased, indicating some effects of external USLs. However, the effect was levelling off at 'usual' flow rates of 0.20-0.30 m s(-1) and in the presence of vigorous stirring by air bubbles, suggesting a maximum thickness of external USLs of around 30 microm including the cell wall. Because the diameters of internodes were around 1 mm, internal USLs could have played a significant or even a dominating role, at least in the presence of the rapidly permeating solutes used [acetone, 2-propanol and dimethylformamide (DMF)]. A comparison of calculated (diffusion kinetics) and of measured permeabilities indicated an upper limit of the contribution of USLs for the rapidly moving solute acetone of 29%, and of 15% for the less rapidly permeating DME The results throw some doubt on recent claims that in C. corallina, USLs rather than the cell membrane dominate solute uptake, at least for the most rapidly moving solute acetone.     

Molecular mechanisms governing aquaporin relocalisation

The aquaporins (AQPs) form a family of integral membrane proteins that facilitate the movement of water across biological membrane by osmosis, as well as facilitating the diffusion of small polar solutes. AQPs have been recognised as drug targets for a variety of disorders associated with disrupted water or solute transport, including brain oedema following stroke or trauma, epilepsy, cancer cell migration and tumour angiogenesis, metabolic disorders, and inflammation. Despite this, drug discovery for AQPs has made little progress due to a lack of reproducible high-throughput assays and difficulties with the druggability of AQP proteins. However, recent studies have suggested that targetting the trafficking of AQP proteins to the plasma membrane is a viable alternative drug target to direct inhibition of the water-conducting pore. Here we review the literature on the trafficking of mammalian AQPs with a view to highlighting potential new drug targets for a variety of conditions associated with disrupted water and solute homeostasis.     

The permeability of the frog choroid plexus to nonelectrolytes

Summary Anin vitro preparation of the frog choroid plexus has been used to measure the permeability of the choroidal epithelium to 50 nonelectrolytes by an osmotic method. The method involves the measurement of nonelectrolyte reflection coefficients () by a rapid electrical procedure. For the majority of compounds tested, there was a good correlation between the rate of solute permeation and the solute's bulk-phase lipid: water partition coefficients; i.e., the higher the partition coefficient the greater the permeability. The membrane lipids of the choroid plexus differ from the membrane lipids of the gall bladder in at least three ways: (1) the lipids of the choroid plexus cannot distinguish between branched chain solutes and their straight chain isomers; (2) small polar solutes such as urea and acetamide permeate via the membrane lipids to a significant extent; and (3) the smaller selectivity ratios suggest that the lipids of the choroid plexus contain more hydrogen bonding sites (i.e., there are stronger solute: lipid intermolecular forces in the choroid plexus). The permeability characteristics of the choroid plexus are qualitatively similar to those of most other cell membranes. In addition, there is evidence for the presence of a special mechanism for the transport of sugar across this epithelium.