Liposome/saline partition coefficients of low-molecular-weight solutes by gel chromatography

A chromatographic method for the determination of association constants of rapidly dissociable complexes is described and applied to quantification of liposome/saline partition coefficients using gel chromatography. The approach allows for estimation of the free solute concentration in the sample by simple manual processing of the intact right-hand part of the solute peak deformed due to gradual diffusion of the accumulated solute from the liposomes along the separation column. Validity of the procedure was confirmed by both reasonable agreement with equilibrium dialysis data and model-based deconvolution of the distorted peak into its two components corresponding to initially unbound compound and to that escaped from the liposomes during the separation process.     

Transient solute diffusion in articular cartilage

The one-dimensional transient diffusion of glucose, inulin and dextran into adult bovine knee articular cartilage was determined for transport times of 1, 5, 15 and 60 min, and 4, 12, 24 and 48 h. The apparent diffusion coefficient and apparent interface partition coefficient were calculated from the concentration-depth profiles within the tissue using a theoretical model for non-steady state solute diffusion. The diffusion coefficient was found to decrease with both solute size and transport time. The partition coefficient also decreased with solute size but increased with transport time. Neither coefficient was dependent on normal tissue fluid or proteoglycan content variations.     

Diffusion in immobilized-cell gels

Summary The relationship between the diffusion coefficient, the effective diffusion coefficient and the partition coefficient for a solute in a cell-containing gel is discussed. The use of correlation equations that are based on some kind of physical model is recommended when the effect of cell concentration on diffusion is interpreted.     

Role of Hydrogen-Bonding in Nonelectrolyte Diffusion through Dense Artificial Membranes

The diffusion of two series of alcohols and amides through complex cellulose acetate membranes was studied. The thin dense part of these membranes behaves as a nonporous layer of low water content. In this layer, called the skin, the solute diffusion coefficients, ω, depend upon size, steric configuration, and the partition coefficient, K₈, between membrane and bathing solution. From the experimental values of ω and K₈, the over-all friction, f, experienced by the solutes in the membrane was computed. It was found that f depends upon the chemical nature of the solute and is related to hydrogen-bonding ability. In the coarse, porous layer of the cellulose acetate membrane, diffusion occurs mainly through aqueous channels. In this instance also the hydrogen-bonding ability of the solute seems to exercise a smaller but significant influence.     

Enzyme reactions at the surface of living cells. I. Electric repulsion of charged ligands and recognition of signals from the external milieu

The dynamic behaviour of a polyelectrolyte-bound enzyme is studied when diffusion of substrate or diffusion of product is coupled to electric repulsion and to Michaelis-Menten enzyme reaction. The definition of the classical concepts of electric partition coefficients and Donnan potential of a polyelectrolyte membrane has been extended under global non-equilibrium conditions. This extension is permissible when a strong repulsion exists of substrate and product by the fixed negative charges of the membrane. Coupling between product diffusion, electric repulsion and enzyme reaction at constant advancement may result in a hysteresis loop of the partition coefficient as the product concentration is increased in the reservoir. This hysteresis loop vanishes as the rate of product diffusion increases. No hysteresis loop may occur when electric repulsion effects are coupled to substrate diffusion and reaction. The existence of multiple values of the partition coefficient for a fixed concentration of product implies that the membrane may store short-term memory of the former product concentration present in the external milieu. The occurrence of hysteresis generated by coupling enzyme reaction, product diffusion, electric partition effects at constant advancement of the reaction may be viewed as a sensing device of product concentration in the external milieu. Surprisingly, non-linearities required to generate this sensing device come from electrostatic effects and not from enzyme kinetics.     

Relative Cosolute Size Influences the Kinetics of Protein-Protein Interactions

Protein signaling occurs in crowded intracellular environments, and while high concentrations of macromolecules are postulated to modulate protein-protein interactions, analysis of their impact at each step of the reaction pathway has not been systematically addressed. Potential cosolute-induced alterations in target association are particularly important for a signaling molecule like calmodulin (CaM), where competition among >300 targets governs which pathways are selectively activated. To explore how high concentrations of cosolutes influence CaM-target affinity and kinetics, we methodically investigated each step of the CaM-target binding mechanism under crowded or osmolyte-rich environments mimicked by ficoll-70, dextran-10, and sucrose. All cosolutes stabilized compact conformers of CaM and modulated association kinetics by affecting diffusion and rates of conformational change; however, the results showed that differently sized molecules had variable effects to enhance or impede unique steps of the association pathway. On- and off-rates were modulated by all cosolutes in a compensatory fashion, producing little change in steady-state affinity. From this work insights were gained on how high concentrations of inert crowding agents and osmolytes fit into a kinetic framework to describe protein-protein interactions relevant for cellular signaling.     

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.     

Natural and engineered hydroxyectoine production based on the Pseudomonas stutzeri ectABCD-ask gene cluster

We report on the presence of a functional hydroxyectoine biosynthesis gene cluster, ectABCD-ask, in Pseudomonas stutzeri DSM5190(T) and evaluate the suitability of P. stutzeri DSM5190(T) for hydroxyectoine production. Furthermore, we present information on heterologous de novo production of the compatible solute hydroxyectoine in Escherichia coli. In this host, the P. stutzeri gene cluster remained under the control of its salt-induced native promoters. We also noted the absence of trehalose when hydroxyectoine genes were expressed, as well as a remarkable inhibitory effect of externally applied betaine on hydroxyectoine synthesis. The specific heterologous production rate in E. coli under the conditions employed exceeded that of the natural producer Pseudomonas stutzeri and, for the first time, enabled effective hydroxyectoine production at low salinity (2%), with the added advantage of simple product processing due to the absence of other cosolutes.     

Cosolute modulation of protein oligomerization reactions in the homeostatic timescale

Protein oligomerization processes are widespread and of crucial importance to understand degenerative diseases and healthy regulatory pathways. One particular case is the homo-oligomerization of folded domains involving domain swapping, often found as a part of the protein homeostasis in the crowded cytosol, composed of a complex mixture of cosolutes. Here, we have investigated the effect of a plethora of cosolutes of very diverse nature on the kinetics of a protein dimerization by domain swapping. In the absence of cosolutes, our system exhibits slow interconversion rates, with the reaction reaching the equilibrium within the average protein homeostasis timescale (24–48 h). In the presence of crowders, though, the oligomerization reaction in the same time frame will, depending on the protein's initial oligomeric state, either reach a pure equilibrium state or get kinetically trapped into an apparent equilibrium. Specifically, when the reaction is initiated from a large excess of dimer, it becomes unsensitive to the effect of cosolutes and reaches the same equilibrium populations as in the absence of cosolute. Conversely, when the reaction starts from a large excess of monomer, the reaction during the homeostatic timescale occurs under kinetic control, and it is exquisitely sensitive to the presence and nature of the cosolute. In this scenario (the most habitual case in intracellular oligomerization processes), the effect of cosolutes on the intermediate conformation and diffusion-mediated encounters will dictate how the cellular milieu affects the domain-swapping reaction.     

Scanning gel chromatography: determination of transport parameters from dynamic profiles measured at low solute concentration

Direct optical scanning of solute boundaries in large zone gel Chromatography experiments provides an accurate means of determining boundary profile shapes and rates of motion. A method has been developed for correcting such boundaries to a constant time frame, eliminating the distortion which arises from finite column scanning rate Centroids or the corrected profiles can be used to determine the partition cross section for the solute of interest The partition cross section and flow rate determine translational motion within the column. The axial dispersion coefficient, L, which characterizes rate of boundary spreading may also be calculated from the profiles. In order to explore these procedures a study of four noninteracting solutes was conducted. Partition cross sections determined from rates of motion of boundary centroids were found to be in good agreement with those determined by the equilibrium saturation method on the same column.In order to explore the lowest concentration limits of the technique and to illustrate the boundary characteristics for a selfassociating solute, a study of carboxyhemoglobin was conducted over a wide concentration range. From measurements at 220 nm the lowest concentration where useful data could be obtained was 2 micrograms per ml (0.12 πM heme) These results establish validity of the procedures used in analyzing the rates of boundary transport and in studying solute transport over a wide range of conditions.     

The nonelectrolyte permeability of planar lipid bilayer membranes

The permeability of lecithin bilayer membranes to nonelectrolytes is in reasonable agreement with Overton's rule. The is, Pd alpha DKhc, where/Pd is the permeability coefficient of a solute through the bilayer, Khc is its hydrocarbon:water partition coefficient, and D is its diffusion coefficient in bulk hydrocarbon. The partition coefficients are by far the major determinants of the relative magnitudes of the permeability coefficients; the diffusion coefficients make only a minor contribution. We note that the recent emphasis on theoretically calculated intramembranous diffusion coefficients (Dm'S) has diverted attention from the experimentally measurable and physiologically relevant permeability coefficients (Pd'S) and has obscured the simplicity and usefulness of Overton's rule.     

Diffusion of (de)acylated antibiotic A40926 in alginate and carrageenan beads with or without cells and/or soybean meal

Effective diffusion coefficients (D(e)) of antibiotic A40926 and its deacylated derivative were determined in Ca-alginate (2% wt/wt) and kappa-carrageenan (2.6% wt/wt) gel beads with or without immobilized Actinoplanes teichomyceticus cells and/or soybean meal (SBM). The method used was based on transient concentration changes in a well-stirred antibiotic solution in which gel beads, initially free of solute, were suspended. Unsteady-state diffusion in a sphere was applied and D(e) determined from the best fit of experimental data. A40926 showed markedly different diffusion characteristics than its deacylated derivative. Diffusivity of deacyl-A40926 in alginate or carrageenan gel beads was six to seven times that of A40926. Large differences in partition coefficients (Kp) were also found. In case of beads without additions, A40926, in contrast to deacyl-A40926, strongly partitioned to the liquid phase. Introduction of SBM and/or mycelium in the gel beads decreased the effective diffusivity of deacyl-A40926, but increased its partitioning to the solid phase. Our findings indicate that a relatively moderate structural change of a lipoglycopeptide molecule could lead to a major change in its diffusion/partition characteristics.     

Exposure to buffer solution alters tendon hydration and mechanics

A buffer solution is often used to maintain tissue hydration during mechanical testing. The most commonly used buffer solution is a physiological concentration of phosphate buffered saline (PBS); however, PBS increases the tissue’s water content and decreases its tensile stiffness. In addition, solutes from the buffer can diffuse into the tissue and interact with its structure and mechanics. These bathing solution effects can confound the outcome and interpretation of mechanical tests. Potential bathing solution artifacts, including solute diffusion, and their effect on mechanical properties, are not well understood. The objective of this study was to measure the effects of long-term exposure of rat tail tendon fascicles to several concentrations (0.9–25%) of NaCl, sucrose, polyethylene glycol (PEG), and SPEG (NaCl + PEG) solutions on water content, solute diffusion, and mechanical properties. We found that with an increase in solute concentration the apparent water content decreased for all solution types. Solutes diffused into the tissue for NaCl and sucrose, however, no solute diffusion was observed for PEG or SPEG. The mechanical properties changed for both NaCl solutions, in particular after long-term (8 h) incubation the modulus and equilibrium stress decreased compared to short-term (15 min) for 25% NaCl, and the cross sectional area increased for 0.9% NaCl. However, the mechanical properties were unchanged for both PEG and SPEG except for minor alterations in stress relaxation parameters. This study shows that NaCl and sucrose buffer solutions are not suitable for long-term mechanical tests. We therefore propose using PEG or SPEG as alternative buffer solutions that after long-term incubation can maintain tissue hydration without solute diffusion and produce a consistent mechanical response.     

Fluctuations and the Hofmeister effect

The Hofmeister effect consists in changes of protein solubility triggered by neutral electrolyte cosolutes. Based on the assumption that salts cause stochastic fluctuations of the free energy barrier profiles, a kinetic theory of this phenomenon is proposed. An exponentially correlated noise, of amplitude proportional to the salt concentration, is added to each energy level, and the time-dependence of the mean protein concentration is calculated. It is found that the theory yields the well-known Setschenow equation if the noise correlation time is low in comparison to the aggregation time constant. Experimental data on salting-in agents are well fitted, whereas, in the case of salting-out cosolutes, two independent dichotomic fluctuations are needed to fit the data. This may result from the fact that, in both cases, the low-concentration regime is dominated by salting-in electrostatic contributions, whereas, at high salt concentrations, electron donor/acceptor interactions become important; these have opposite effects. The theory offers a novel way to metricate Hofmeister effects and also leads to thermodynamic quantities, which account for the influence of salts. The formalism may also be applied to describe kinetic phenomena in the presence of cosolutes.     

Crowding alone cannot account for cosolute effect on amyloid aggregation

Amyloid fiber formation is a specific form of protein aggregation, often resulting from the misfolding of native proteins. Aimed at modeling the crowded environment of the cell, recent experiments showed a reduction in fibrillation halftimes for amyloid-forming peptides in the presence of cosolutes that are preferentially excluded from proteins and peptides. The effect of excluded cosolutes has previously been attributed to the large volume excluded by such inert cellular solutes, sometimes termed "macromolecular crowding". Here, we studied a model peptide that can fold to a stable monomeric β-hairpin conformation, but under certain solution conditions aggregates in the form of amyloid fibrils. Using Circular Dichroism spectroscopy (CD), we found that, in the presence of polyols and polyethylene glycols acting as excluded cosolutes, the monomeric β-hairpin conformation was stabilized with respect to the unfolded state. Stabilization free energy was linear with cosolute concentration, and grew with molecular volume, as would also be predicted by crowding models. After initiating the aggregation process with a pH jump, fibrillation in the presence and absence of cosolutes was followed by ThT fluorescence, transmission electron microscopy, and CD spectroscopy. Polyols (glycerol and sorbitol) increased the lag time for fibril formation and elevated the amount of aggregated peptide at equilibrium, in a cosolute size and concentration dependent manner. However, fibrillation rates remained almost unaffected by a wide range of molecular weights of soluble polyethylene glycols. Our results highlight the importance of other forces beyond the excluded volume interactions responsible for crowding that may contribute to the cosolute effects acting on amyloid formation.     

Static compression is associated with decreased diffusivity of dextrans in cartilage explants

The chondrocytes of adult articular cartilage rely upon transport phenomena within their avascular extracellular matrix for many biological activities. Therefore, changes in matrix structure which influence cytokine transport parameters may be an important mechanism involved in the chondrocyte response to tissue compression. With this hypothesis in mind, partitioning and diffusion of 3-, 10-, and 40-kDa dextrans conjugated to tetramethylrhodamine, and 430-Da tetramethylrhodamine itself, were measured within statically compressed bovine articular cartilage explants using a novel experimental apparatus and desorption fluorescence method. Partitioning and diffusion were examined as functions of solute molecular weight and matrix proteoglycan density, and diffusion was measured versus static compression up to 35% volumetric strain. In general, partition coefficients and diffusivities were found to decrease with increasing solute molecular weight. In addition, for a given solute, diffusivities decreased significantly with increasing static compression. Results therefore suggest a possible role for transport limitations of relatively large molecular weight solutes within the extracellular matrix in mediating the biological response of chondrocytes to cartilage compression.     

Diffusion coefficients of metabolites in active biofilms

Diffusion coefficients of actual metabolites in completely active biofilms can be determined by applying a new concept that is based on a constant local activity in the entire biofilm. In that case, a concentration step will be transmitted unattenuated. Subsequently, the diffusion coefficient can be calculated from the response monitored with a microelectrode positioned in the biofilm without quantitative knowledge of the local microbial kinetics. The conditions required for such a constant microbial biofilm activity were formulated in terms of the Thiele modulus and the substrate concentration in the bulk liquid. This proposed method was successfully applied to determine diffusion coefficients of oxygen and glucose in agar gels containing various fractions of active immobilized microorganisms. The values obtained were compared to experimental results from well-defined inert systems. The transient response of oxygen was far more affected by the presence of the immobilized cells than glucose. This can be explained by partition of the diffusing solute between the microbial cells and the aqueous phase.     

Diffusion through a membrane: Approach to equilibrium

The transfer of solute through a membrane separating two aqueous solutions is studied with the time-dependent diffusion equation for composite media. By introducing new independent and dependent variables it is shown that the differential equations and boundary conditions can be transformed into a dimensionless form which does not explicitly depend on the diffusivities of the media. Laplace transforms are used to derive explicit solutions for the solute concentration as a function of position and time. It is shown that at large time the concentration approaches the equilibrium distribution exponentially. Explicit results are given for the decay time as a function of the parameters of the system. In addition, an accurate and simplified expression is derived for the decay time for the case of small membrane permeability. The accuracy of the analytic solutions for the concentration profiles is tested by comparing them with numerical results obtained by solving the diffusion equations by the method of finite differences. Excellent agreement is found. Research supported in part by a grant from the National Science Foundation.