Scanning molecular sieve chromatography of interacting protein systems. Simulation of large zone behavior for self-associating solutes undergoing rapid chemical equilibration under kinetic control

Theoretical large zone reaction boundaries for molecular sieve chromatography have been simulated by computer for a self-associating solute undergoing rapid chemical equilibration under kinetic control. These patterns show that the kinetically-controlled reaction rate between the mobile and stationary phases is the principal determinant of the elution boundary profile in molecular sieve chromatography. The overall chemical reaction rate in the mobile phase was found to have a much greater role in a rapidly equilibrating system than did the effect of axial dispersion within the gel matrix.     

Identification and interpretation of complexity in sedimentation velocity boundaries.

Synthetic sedimentation velocity boundaries were generated using finite-element solutions to the original and modified forms of the Lamm equation. Situations modeled included ideal single- and multicomponent samples, concentration-dependent samples, noninteracting multicomponent samples, and reversibly self-associating samples. Synthetic boundaries subsequently were analyzed using the method of van Holde and Weischet, and results were compared against known input parameters. Results indicate that this analytical method provides rigorous diagnostics for virtually every type of sample complexity encountered experimentally. Accordingly, both the power and utility of sedimentation velocity experiments have been significantly expanded.     

Sedimentation analysis of noninteracting and self-associating solutes using numerical solutions to the Lamm equation.

The potential of using the Lamm equation in the analysis of hydrodynamic shape and gross conformation of proteins and reversibly formed protein complexes from analytical ultracentrifugation data was investigated. An efficient numerical solution of the Lamm equation for noninteracting and rapidly self-associating proteins by using combined finite-element and moving grid techniques is described. It has been implemented for noninteracting solutes and monomer-dimer and monomer-trimer equilibria. To predict its utility, the error surface of a nonlinear regression of simulated sedimentation profiles was explored. Error contour maps were calculated for conventional independent and global analyses of experiments with noninteracting solutes and with monomer-dimer systems at different solution column heights, loading concentrations, and centrifugal fields. It was found that the rotor speed is the major determinant for the shape of the error surface, and that global analysis of different experiments can allow substantially improved characterization of the solutes. We suggest that the global analysis of the approach to equilibrium in a short-column sedimentation equilibrium experiment followed by a high-speed short-column sedimentation velocity experiment can result in sedimentation and diffusion coefficients of very high statistical accuracy. In addition, in the case of a protein in rapid monomer-dimer equilibrium, this configuration was found to reveal the most precise estimate of the association constant.     

Graphical analysis of nonideal monomer N-mer, isodesmic, and type II indefinite self-associating systems by equilibrium ultracentrifugation.

A graphical procedure is described by which one can obtain in principle the monomer molecular weight, stoichiometry, equilibrium constant, and second virial coefficient of nonideal monomer N-mer, isodesmic, and type II indefinite self-associating systems. In addition, a method is presented for obtaining both the equilibrium constant and the second virial coefficient from the maximum in a plot of apparent molecular weight vs. concentration if the monomer molecular weight and stoichiometry are known. The usefulness and limitations of the methods are discussed, as well as the quality and range of data required for determination of the relevant parameters. The techniques described are applicable to analysis of self-associating systems by osmotic pressure and light scattering, as well as equilibrium ultracentrifugation measurements.     

Specificity of Prodan for the Self-associating Domain of Spectrin: A Molecular Docking Study

Abstract

The hydrophobic fluorescent probe Prodan binds to the self-associating domain of spectrin with 1:1 stoichiometry. A model of the self-associating domain was generated based on its homology with other domains of spectrin. Prodan was then docked onto the model, and several sites with low interaction energy were identified. To verify whether the binding of Prodan is specific towards the self-associating domain of spectrin, it was docked on to several other domains of spectrin, having a known three-dimensional structure. Analysis of the docking results suggests that the binding of Prodan to the self-associating domain of spectrin will involve hydrophobic and hydrophilic groups of Prodan. The results clearly indicate the preference of Prodan for a particular binding site of the self-associating domain.     

Specificity of Prodan for the self-associating domain of spectrin: a molecular docking study

The hydrophobic fluorescent probe Prodan binds to the self-associating domain of spectrin with 1:1 stoichiometry. A model of the self-associating domain was generated based on its homology with other domains of spectrin. Prodan was then docked onto the model, and several sites with low interaction energy were identified. To verify whether the binding of Prodan is specific towards the self-associating domain of spectrin, it was docked on to several other domains of spectrin, having a known three-dimensional structure. Analysis of the docking results suggests that the binding of Prodan to the self-associating domain of spectrin will involve hydrophobic and hydrophilic groups of Prodan. The results clearly indicate the preference of Prodan for a particular binding site of the self-associating domain.     

Mathematical modelling of the transport of low molecular weight solutes across biological membranes. The transport of Leu, His and Glu into human blood platelets

A model describing the transport of low molecular weight solutes across cell membranes is presented. The model accounts for many different systems which may mediate the fluxes of various solutes, for the effect of Na+ ions, and for time dependence of the processes. It generalizes the classical three-parameter equation for transport. Solutions to the model were employed to interprete experimental data obtained for the uptake of DL-leu, L-his and L-glu by human blood platelets.     

Studies on human serum high density lipoproteins. Self-association of apolipoprotein A-I in aqueous solutions.

Human serum apolipoprotein A-I (apo-A-I), the major protein component of the human serum high density lipoproteins, was studied in aqueous solutions of differing ionic strength and pH by the techniques of sedimentation equilibrium ultracentrifugation and frontal analysis gel chromatography. The ultracentrifugal studies indicate the apo-A-I is a self-associating system that is dependent upon protein concentration, but relatively independent of the nature of the medium. The apparent weight average molecular weights obtained from solutions of initial apo-A-I concentration between 0.2 and 0.9 mg/ml were in the range of 3.0 to 16.7 x 10(4) (monomer molecular weight = 28,014). Of the several models of self-associated examined, that which gave the best theoretical fit was for the monomer-dimertetramer-octamer model. The self-association of apo-A-I in aqueous solutions was further documented by frontal analysis gel chromatography, which not only corroborated the ultracentrifugal results, but also indicated that the multiple species of apo-A-I in solution attain equilibrium rather rapidly. Besides having intrinsic importance, these results indicate that the solution properties of apo-A-I must be established before ligand binding studies are conducted and interpreted.     

Osmotic pressure measurements on insulin: anomalous results indicate that the monomer is preferentially adsorbed

The concentration dependence of the number average molecular weight of insulin at pH 2, ionic strength 0.05, and 20 degrees C as determined by osmotic pressure measurements indicates that the hormone is a homogeneous protein of molecular weight close to that of the dimer. Since sedimentation equilibrium experiments confirm what is well known, namely that insulin is a self-associating protein dissociating to monomer under these conditions, an explanation for the anomaly was sought in the possible loss of protein from solution by adsorption. Analysis of the results strongly supports this conclusion and consideration of the adsorption properties of insulin in terms of hydrophobic interactions shows them to be consistent with the behaviour of insulin as a self-associating protein. The monomer appears to be the primary molecular species responsible for insulin adsorption.     

Effects of inert volume-excluding macromolecules on protein fiber formation. I. Equilibrium models

The equilibrium Oosawa-Asakura model for nucleated assembly of rod-like protein fibers is recast in terms of dimensionless (scaled) quantities. The model is then generalized to treat arbitrarily large deviations from thermodynamic ideality arising from high fractional volume occupancy by an inert protein or polymer. Each state of association of the self-associating protein is modeled as an equivalent rigid convex particle (sphere or spherocylinder) and the crowding species is modeled either as an equivalent sphere or cylindrical rod. The resulting conservation of mass relation is readily solved to yield the fractional abundance of monomer, from which the entire equilibrium distribution of oligomeric species can be calculated, either directly or through the use of an additional scaling relationship. Results indicating the potential effect of volume occupancy on the equilibrium solubility of the self-associating protein and upon the equilibrium distribution of polymer size are presented. It is found that the fractional (logarithmic) change in both solubility and in the breadth of the polymer size distribution scale almost linearly with the fractional (logarithmic) change in the thermodynamic activity of monomer.     

Interaction between heparan sulphate chains. I. A gel chromatographic, light-scattering and structural study of aggregating and non-aggregating chains

1. Heparan sulphate from bovine lung was fractionated with cetylpyridinium chloride. Solubilisation of complexes was accomplished by increasing concentrations of NaCl in a step-wise manner. Fractions I-IV, which were low-sulphated, contained more D-glucuronic acid than L-iduronic acid, fraction V contained equal proportions while fraction VI was L-iduronic acid-rich. 2. Gel chromatography of heparan sulphates II-IV in 0.5 M sodium acetate yielded extremely asymmetric profiles, while fractions V, VI and heparin did not. 3. Heparan sulphate IV was separated into aggregatable and non-aggregatable species by gel chromatography in 0.5 M sodium acetate. The particle/molecular weights of the two species were determined by light scattering. In 0.15 M NaCl or KCl the aggregatable chains yielded particle weights of 60 000-100 000 while the molecular weight was 20 000 (in 4.0 M guanidine HCl). Non-aggregatable chains afforded 'monomeric' values in 0.15 M NaCl or KCl. 4. Periodate oxidation of D-glucuronic acid residues in N-acetylated block regions followed by scission in alkali was used to fragment aggregating and non-aggregating heparan sulphate IV. The former chains yielded, on average, shorter oligosaccharides than did the latter. Reoxidation of the remaining D-glucuronic acid residues (adjacent to N-sulphated amino sugars) in the oligosaccharides followed by alkaline cleavage resulted in distinctly different fragmentation patterns in the two cases. The iduronate-containing oligosaccharides derived from aggregatable chains were markedly degraded into fragments ranging from glucosamine-L-iduronic acid-glucosamine-(C-3 fragment) to higher saccharides. Only higher saccharides were obtained from fragments of non-aggregatable chains. 5. It is concluded that self-associating heparan sulphates comprise both D-glucuronic acid- and L-iduronic acid-containing repeating units and that these units are arranged in an alternating or mixed fashion. These characteristics are analogous to those observed with self-associating dermatan sulphate species (Fransson, L.-A. and C?ster, L. (1979) Biochim. Biophys. Acta 582, 132-144).     

An improved function for fitting sedimentation velocity data for low-molecular-weight solutes.

Many traditional approaches to the analysis of sedimentation velocity data work poorly with data for low-molecular-weight solutes, which have sedimentation boundaries that are severely broadened by diffusion. An approach that has previously had some success is to directly fit these broad boundaries to approximate solutions of the Lamm equation that directly account for the high diffusion. However, none of the available approximate solutions work well at times both early and late in the run, or give boundary shapes that are highly accurate, especially for species of molecular weight < 10,000. An improved fitting function has been developed to overcome some of these limitations. The new function adds two correction terms to the Fujita-MacCosham solution. The optimum coefficients for these new correction terms were determined by a least-squares approach. The accuracy and limitations of fitting with this new function were tested against synthetic data sets obtained by finite-element methods, for analysis of samples containing either single species or several noninteracting species. We also compare the strengths and weaknesses of this method of analysis, and its ability to work with noisy data, relative to recently developed time-derivative methodologies.     

Solutes modify a conformational transition in a membrane transport protein

The bacterial outer-membrane vitamin B₁₂ transporter, BtuB, undergoes a dramatic order-to-disorder transition in its N-terminal energy-coupling motif (Ton box) upon substrate binding. Here, site-directed spin labeling (SDSL) is used to show that a range of solutes prevents this conformational change when ligand is bound to BtuB, resulting in a more ordered Ton box structure. For each solute examined, the data indicate that solutes effectively block this conformational transition through an osmotic mechanism. The molecular weight dependence of this solute effect has been examined for a series of polyethylene glycols, and a sharp molecular weight cutoff is observed. This cutoff indicates that solutes are preferentially excluded from a cavity within the protein as well as the protein surface. Furthermore, the sensitivity of the conformational change to solution osmolality is consistent with a structural model predicted by SDSL. When the Ton box is unfolded by detergents or mutations (rather than by ligand binding), solutes, such as polyethylene glycols and salts, also induce a more structured compacted conformation. These results suggest that conformational changes in this class of outer membrane transporters, which involve modest energy differences and changes in hydration, may be modulated by a range of solutes, including solutes typically used in protein crystallization.     

Gel electrophoresis of reacting macromolecules. Rate-limited self-association

Prompted by experimental sodium dodecyl sulfate-gradient polyacrylamide gel electrophoresis (PAGE) patterns of an oligomerizing 73-residue peptide, PAGE and gradient PAGE patterns were simulated numerically for two rate-limited, reversible self-associating systems, viz., monomer-dimer and monomer-dimer-tetramer interactions. A wide range of values for rate constants and other relevant parameters was examined. The cardinal result for interactions with half-times comparable to the time of electrophoresis is that the number of peaks in the pattern can exceed the number of interacting species. Since peaks of intermediate migration velocities are composed of interconverting monomer and oligomers, molecular weights corresponding to individual species cannot be assigned to them.     

Sedimentation equilibrium in macromolecular solutions of arbitrary concentration. I. Self-associating proteins

Relations describing sedimentation equilibrium in solutions of self-associating macromolecules at arbitrary concentration are presented. These relations are obtained by using scaled-particle theory to calculate the thermodynamic activity of each species present at a given radial distance. The results are expected to be valid for solutions of globular proteins under conditions such that interactions between individual solute molecules may be approximated by a hard-particle potential. Sedimentation equilibria in solutions containing either a nonassociating solute or a solute that self-associates according to several different schemes are simulated using the derived relations. The results of these simulations are presented in terms of the dependence of apparent weight-average molecular weight upon solute concentration. Simple empirical relations are presented for estimating the true weight-average molecular weight from the apparent weight-average molecular weight, without reference to any particular self-association scheme. The weight-average molecular weight estimated in this fashion is within a few percent of the true weight-average molecular weight at all experimentally realizable solute concentrations ( < 400 g/L).     

Species range size distributions for some marine taxa in the Atlantic Ocean. Effect of latitude and depth

The range size distributions of 6643 species in ten different fish and invertebrate taxa dwelling in pelagic (latitudinal range sizes) and benthic (latitudinal and depth range sizes) habitats on both sides of the Atlantic Ocean (80°N−70°S) were studied. The objectives were to analyse: (1) the range size distribution patterns for the various taxa and whether they have right/left skewed or lognormal distributions; (2) the geographical species distributions, to ascertain whether the distribution ranges change with latitude (Rapoport's rule); and (3) the relationship between the depth ranges of benthic species and their maximum depth of occurrence and how depth range size distributions change with latitude. The pelagic taxa exhibited larger range sizes than did the benthic taxa, continental slope/rise species excepted. On the other hand, the boundaries between geographical provinces for both benthic taxa and pelagic taxa tended to occur in association with major oceanographic processes. The shape of the latitudinal range frequency distributions (LRFDs) of the pelagic organisms were distinctly left‐skewed, and the LRFDs for most taxa were significantly different from lognormal. There was no common pattern for the distributions of the benthic organisms, which were lognormal in Cephalopoda, Stomatopoda, and Crustacea Decapoda and tended to be left‐skewed and significantly different from lognormal in Pisces. The applicability of Rapoport's rule was not clearly inferable from the results, and the rule appears to be conditioned by the location of biogeographical boundaries and the endemism rate in the different biogeographical provinces. A clear increase in depth range size with maximum depth range was observable for benthic species, confirming previous studies. Species’ depth range distributions displayed a discernible latitudinal pattern, right‐skewed at high latitudes and left‐skewed at low latitudes. The location of biogeographical boundaries, and endemism rate by biogeographical province were considered to be the factors most useful in explaining species’ distribution patterns and their conformity or nonconformity to Rapoport's rule. © 2003 The Linnean Society of London, Biological Journal of the Linnean Society, 2003, 80 , 437–455.     

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.     

Use of retinoids to analyze the cellular basis of positional memory in regenerating amphibian limbs

Cells of the amphibian limb regeneration blastema inherit memories of their level of origin (positional memory) along the limb axes. These memories serve as boundaries of what is to be regenerated, thus preventing regeneration of any but the missing structures. Because of its importance in determining the boundaries of regenerate pattern, it is essential to understand the cellular and molecular basis of positional memory. One approach to this problem is to look for position-related differences in a cell or molecular property along a limb axis and then show, using an agent that modifies regenerate pattern, that the cell or molecular property and the pattern are coordinately modified. We have done this using retinoic acid (RA) as a pattern-modifying agent and an in vivo assay that detects position-related differences in a cell recognition-affinity property along the proximodistal (PD) axis of the regenerating axolotl limb. RA proximalizes positional memory in the PD axis, posteriorizes it in the anteroposterior axis, and ventralizes it in the dorsoventral axis. The level-specific PD cell recognition-affinity property is proximalized by RA, indicating that this property and positional memory are causally related. The effects of RA on positional memory may be mediated through a cellular RA-binding protein (CRABP), since the concentration of unbound (apo) CRABP molecules is highest during early stages of regeneration when the proximalizing effects of RA are greatest.     

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.     

MSTARA and MSTARI: interactive PC algorithms for simple, model independent evaluation of sedimentation equilibrium data

This paper describes a program available for PC's for the evaluation of molecular weights from sedimentation equilibrium. This program, in its two forms – MSTARA for absorption optical records and MSTARI for interference optical records – requires no prior assumption of the nature of the system (ideal, non-ideal, monodisperse, polydisperse, self-associating etc.) and takes into consideration the whole solute distribution (i.e. from solution meniscus to cell base) in the ultracentrifuge cell rather than just a selected data-set. MSTARA or MSTARI are therefore recommended as a first analysis programme of sedimentation equilibrium data coming off an absorption or interference based analytical ultracentrifuge. These programmes are therefore particularly well suited if heterogeneity (polydispersity or interaction phenomena) or non-ideality is suspected. Their use is demonstrated for a series of data-set types (ideal, non-ideal, polydisperse and self-associating). Although MSTARA and MSTARI are model independent, they provide the basis for more detailed analysis of interactions, polydisperse distributions or non-ideality via easy export of ASCII datafiles to model dependent routines. Received: 4 November 1996 / Accepted: 15 November 1996