Transient state isoelectric focusing: effects of zone load and carrier ampholyte concentration on the kinetics of defocusing and refocusing in sucrose density gradients

The kinetics of focusing, defocusing, and refocusing of l-histidyl-l-tyrosine in a sucrose density gradient have been studied utilizing a special apparatus for repetitive scanning of the isoelectric focusing column, employing uv absorption optics and a digital data acquisition system. Starting from a uniform or triangular concentration profile, the band is “focused” and a nearly linear pH gradient is formed during initial focusing. The electrical field is then abolished and free diffusion occurs. The electrical field is then reapplied (“refocusing”) and the band is allowed to sharpen, presumably reapproaching a steady state. The band width was measured quantitatively as the second moment about the mean (square of the standard deviation, σ²). In theory, measurements of σ² versus time permit the estimation of the apparent diffusion coefficient (D) and the isoelectric focusing parameter (pE). If the electrical field strength E and the pH gradient, $\text{d(}\text{pH}\text{)}\text{dx}$, were also measured, then one could calculate the slope of the pH mobility curve of the protein $\text{dM}\text{d(}\text{pH}\text{)}$ evaluated at the isoelectric point. D can be measured during the defocusing stage, and $\text{pE,}\text{D}\text{pE}\text{,}\text{or}\text{D}$ can be measured during focusing or refocusing. Several limitations and difficulties in the verification of this theory have been encountered: First, the apparent diffusion coefficient depends on zone load in approximately a linear fashion. Accordingly, it is necessary to measure D at several zone loads, and then extrapolate to zero load by linear regression techniques. Second, the ampholyte concentration has a marked effect on both D and pE. Here we have no a priori reason to extrapolate to zero ampholyte concentration. Also, at present we have no satisfactory method for measurement of E. These preliminary studies should be helpful in indicating further directions for experimental refinement and for generalization of theory.     

Transient state isoelectric focusing: theory

Mathematical theory is developed to describe the transient state of isoelectric focusing (pH-gradient electrophoresis) in a linear pH gradient under highly idealized conditions. This theory makes it possible to predict the concentration profile (distribution) for the protein or other amphoteric species of interest as a function of time, when the sample is applied in a zone of infinitesimal thickness at one end of the column, or in a uniform distribution throughout the column. Further, the position of the centroid, and the second moment around the mean, σ², (square of the standard deviation of peak width) are described as a function of time, irrespective of the initial distribution of the protein in the column. Three arbitrary stages of the “focusing” experiment are considered: (1) Focusing, wherein the sample is applied to a preformed pH gradient; (2) Defocusing, which occurs when the electrical field is abolished after an arbitrary time (usually after the concentration profile has begun to approach its steady state) and diffusion is allowed to occur. (3) Refocusing, which occurs after the electrical field is reapplied. Although stages 1 and 3 are conceptually identical aside from the difference in initial conditions, they may differ in several important respects in practice, both with regard to technical problems of measurement, and with regard to the closeness of conditions to the stated assumptions.This theory should make it possible to predict the time necessary to achieve any desired degree of focusing, i.e., approach to the steady-state distribution. Further, this theory and the techniques of analytical scanning isoelectric focusing provide the basis for measurement of the apparent diffusion coefficient (D), the derivative of velocity with respect to position, and if the field strength is known, the slope of the mobility-pH curve at the isoelectric point, {$\text{dM}\text{d(}\text{pH}\text{)}$}.     

Transient state isoelectric focusing. Digital measurement of zone position, zone area, segmental pH gradient, and isoelectric point as a function of time

Transient state isoelectric focusing (TRANSIF) is a kinetic method which offers quantitative information about relevant parameters pertaining both to methodological aspects and to the physical characterization of amphoteric molecules. TRANSIF data are obtained with an improved scanning isoelectric focusing assembly coupled to an on-line digital data acquisition and processing system which is used to continuously record changes in peak position ($\text{x}$), peak area, segmental pH gradient ($\text{Δ(pH)}\text{Δx}$), and isoelectric point (pI) of proteins during focusing. This improved apparatus has made it feasible to follow the temporal stability of an isoelectric focusing system in a quantitative fashion.     

Deamination of 2-amino-2-deoxyhexitols and of their per-O-methylated derivatives with nitrous acid

The products of nitrous acid deamination of per-O-methylated 2-amino-2-deoxy-d-glucitol and $\text{2-}\text{amino}\text{-2-}\text{deoxy}\text{-3-O-β-}\text{d}\text{-galactopyranosyl-}\text{d}\text{-glucitol}$ and its per-O-methylated derivative have been characterized by g.l.c.—mass spectrometry after treatment with sodium borodeuteride and further substitution by acetylation, methylation, or (trideuteriomethyl)ation. The results confirm that the most important reaction pathway (1) involves a 1 → 2-hydride shift to give $\text{2-}\text{deoxy-}\text{d}\text{-arabino-}\text{hexoses}$, but that significant side-reactions include (2) solvolytic displacement at C-2, (3) a 3 → 2-hydride shift, to give $\text{2-}\text{deoxy-}\text{d}\text{-erythro-3-}\text{hexuloses}$, and (4) a C-4→C-2 migration to give $\text{2-}\text{deoxy}\text{-2-C-}\text{(hydroxymethyl)-}\text{d}\text{-ribose}$ and -d-arabinose. Reactions (3) and (4) result in elimination of the original 3-O-substituents, with the exposure of new reducing groups, from oligosaccharides terminated by 3-O-substituted 2-amino-2-deoxyhexitols.     

Thermotropic gelation of ovalbumin: 2. Boundary conditions on the formation and the concentration dependence of equilibrium elastic modulus for thermotropic ovalbumin gels

Studies were made on the boundary conditions for thermotropic ovalbumin gelation at pH within the range 2.5 to 10.0. The pH dependence of the gelation threshold, C₀, and denaturation temperature, T_d, were obtained. The dependence C₀(pH) has a sharp minimum close to the isoelectric point (pl). Over pH range 2.5 to 4.0 the dependence T_d(pH) is linear; although above pI it shows unusual behaviour. T_d increases smoothly, becoming a constant value (T_d=80°C) at pH 7. Analysis of the temperature dependence of Leu's line integral intensity in the p.m.r. spectrum of ovalbumin shows that the temperature threshold of thermotropic gelation closely approximates to T_d. A diagram for the state of an ovalbumin -water system was constructed in temperature-concentration-pH coordinates. The dependences of the initial shear modulus for thermotropic ovalbumin gels on the concentration (0.06≤C≤0.25g/cm³ were obtained at pH 4.0, 7.0, 8.5, 10.0. They are equivalent to the concentration dependence of the equilibrium elastic modulus E_e(C). The dependences obtained may be reduced to the theoretical master dependence of Hermans, $\text{E}{}_{\mathrm{e}}\text{(rm}\text{C}\text{?}\text{)}$, where $\text{C}\text{?}\text{=}\text{C}\text{/}\text{C}{}_0$ is the reduced concentration. Hermans' theory, based o the model for random cross-linking of linear identical macromolecules without cyclization, adequately describes the equilibrium elastic properties of thermotropic ovalbumin gels.     

The synthesis of methyl 4-O-(4-O-α-d-galactopyranosyl-β-d-galactopyranosyl)-β-d-glucopyranoside: The methyl β-glycoside of the trisaccharide related to Fabry's disease

As part of a program to synthesize the ceramide trisaccharide (1) related to Fabry's disease, methyl 4-O-(4-O-α-$\text{d}$-galactopyranosyl-β-$\text{d}$-galactopyranosyl)-β-$\text{d}$-glucopyranoside (12) was prepared. Methyl β-lactoside (2) was converted into methyl 4-O-(4,6-O-benzylidene-β-$\text{d}$-galactopyranosyl)-β-$\text{d}$-glucopyranoside (4). Methyl 2,3,6-tri-O-benzoyl-4-O-(2,3,6-tri-O-benzoyl-β-$\text{d}$-galactopyranosyl)-β-$\text{d}$-glucopyranoside (7) was synthesized from 4 through the intermediates methyl 2,3,6-tri-O-benzoyl-4-O-(4,6-O-benzylidene-2,3-di-O-benzoyl-β-$\text{d}$-galactopyranosyl)-β-$\text{d}$-glucopyranoside (5) and methyl 2,3,6-tri-O-benzoyl-4-O-(2,3-di-O-benzoyl-β-$\text{d}$-galactopyranosyl)-β-$\text{d}$-glucopyranoside (6). The halide-catalyzed condensation of 7 with 2,3,4,6-tetra-O-benzyl-$\text{d}$-galactopyranosyl bromide (8) gave methyl 2,3,6-tri-O-benzoyl-4-O-[2,3,6-tri-O-benzoyl-4-O-(2,3,4,6-tetra-O-benzyl-α-$\text{d}$-galactopyranosyl)- β-$\text{d}$-galactopyranosyl]-β-$\text{d}$-glucopyranoside (10). Stepwise deprotection of 10 led to 12, the methyl β-glycoside of the trisaccharide related to Fabry's disease.     

Solubilization,stabilization and isoelectric focusing of human liver neuraminidase activity

Homogenate preparations of human liver have been prepared and over 75% of the particulate neuraminidase activity (which comprises approx. 90% of the total activity) has been solubilized using 0.85% (w/v) Triton X-100 in 25 mM phosphate buffer (pH 6.8). The solubilized neuraminidase activity is extremely labile, but can be stabilized for at least 4 weeks at 2–4°C, using 10 mM N-acetylneuraminic acid. Kinetic characterization of homogenate and solubilized supernatant fluid neuraminidase activities indicated comparable pH optimum curves (maximum activity at pH 4.5–4.7) and apparent K_m values (0.2–0.4 mM) for the synthetic fluorometric substrate $\text{4-}\text{methylbelliferyl}\text{-α-}\text{D}\text{-N-}\text{acetylneuraminic}$ acid. Isoelectric focusing has been performed on human liver homogenates and Triton X-100-solubilized neuraminidase activities, and the presence of several forms (4–6) with isoelectric points (pI values) between 4.4 and 5.2 has been demonstrated in both preparations. The similar kinetic and isoelectric focusing properties of the two preparations suggest that the solubilized enzyme activity is representative of the homogenate activity and that the solubilized enzyme is suitable for purification purposes.     

Analysis of the primary structure of collagen for the origins of molecular packing

The amino acid sequence in the triplet region of the α1 chain of collagen was analyzed for complementary relationships that would explain the stagger of multiples of 670 Å between the rod-like molecules in the fibril. The analysis was done by moving the sequence of 1011 amino acids past itself and scoring for complementarity between opposing amino acids allowing a range of ±2 to 3 residues. It was found that interactions between amino acids of opposite charge and between large hydrophobic amino acids in the overlapping region between two chains are maximal when the chains are staggered by 0D, 1D, 2D, 3D and 4D, where D = 234 ± 1 residues. The residue repeat derived from this value is 2.86 ± 0.02 Å. The existence of a D separation between interacting residues was shown to be reflected in the actual distribution of large hydrophobic amino acids. Surprisingly, the distribution approximates the pattern ($\text{2D}\text{11}$)₅($\text{D}\text{11}$) repeated over 4.4D intervals. The regularity may arise from structural constraints imposed by super-coiling. The distribution of charged residues is less regular and does not show a well-defined periodicity. However, positively-charged residues tend to be near negatively-charged residues, allowing intramolecular charge neutralization as well as strong intermolecular charge interactions at 0D.     

A comparison of the effects of ouabain and 2-deoxy-d-glucose on the thermodynamic variables of the frog skin

Previous studies support the validity of a linear thermodynamic formalism relating the rates of active Na⁺ transport and oxygen consumption J_r to the electrical potential difference ΔΨ an the affinity α (negative free energy) of the metabolic driving reaction. The formulation was further tested in paired control and experimental hemiskins by the use of two inhibitors of Na⁺ transport. Ouabain, a specific inhibitor of the Na⁺ pump, might be expected to diminish the dependence of J_r on ΔΨ without affecting α, whereas 2-deoxy-d-glucose, a competitive inhibitor of glucose metabolism, should be expected to diminish α. Both inhibitors were used at concentrations adequate to depress Na⁺ transport (i.e. short-circuit current J_o) to some 50°_o of control level. Measurements were made of I_o and $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(ΔΨ)}$, and the apparent value of the affinity α_app was calculated according to the thermodynamic formulation. Ouabain depressed $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(ΔΨ)}$ without affecting α_app whereas 2-deoxy-d-glucose depressed α_app without affecting $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(αΨ)}$. The demonstration of these effects indicates the utility of the formalism.     

A rapid four column purification of 2-deoxy-D-glucoside-2-sulphamate sulphohydrolase from human liver

2-Deoxy-D-glucoside-2-sulphamate sulphohydrolase was extracted from human liver and purified 40 000-fold by a simple four column procedure. The purification was followed using a specific substrate isolated from an acid hydrolysate of heparin, $\text{O-(α-2-}\text{sulphamino}\text{-2-}\text{deoxy-}\text{D}\text{-glucopyranosyl}\text{)-(1→3)-}\text{L}\text{-[6,}{}^3\text{H]}\text{idonic}$ acid. Only one form of the enzyme was seen on either ion exchange chromatography or isoelectric focussing, with a pI of 6.8. The apparent M_r of the haloenzyme as determined by gel filtration was 190 000 ± 20 000. Two other larger M_r protein peaks observed on gel filtration appear to be an inactive dimer of the 190 000 dalton peak and a larger aggregate near the exclusion limit of the column. On polyacrylamide disc gel electrophoresis in sodium dodecyl sulphate, with or without prior reduction, each protein peak from the gel filtration column electrophoreced as a single major band with an apparent M_r corresponding to 55 000 ± 6000.     

DNA synthesis during the division cycle of three substrains of Escherichia coliBr

The relationship between chromosome replication and the bacterial division cycle has been examined in three substrains of Escherichia coli$\text{B}\text{r}$ obtained from different sources and designated $\text{B}\text{r}$ A, $\text{B}\text{r}$ F and $\text{B}\text{r}$ K. At growth rates greater than 1.0 doubling per hour (μ > 1.0), the time for a round of chromosome replication (C) was 42 minutes in all three substrains, but the time between the end of a round and cell division (D) was 22 minutes in $\text{B}\text{r}$ A, 16 minutes in $\text{B}\text{r}$ F and 14 minutes in $\text{B}\text{r}$ K. At slower growth rates C and D increased, but to significantly different extents in the three substrains. When μ = 0.5, C and D were approximately 80 and 40 minutes in $\text{B}\text{r}$ A, 60 and 20 minutes in $\text{B}\text{r}$ F, and 70 and 20 minutes in $\text{B}\text{r}$ K.As a consequence of the lengths of the C and D periods in the three stocks of E. coli$\text{B}\text{r}$, the patterns of chromosome replication during the division cycle differed. The most obvious difference was that E. coli$\text{B}\text{r}$ F and E. coli$\text{B}\text{r}$ K possessed periods devoid of DNA synthesis at both the beginning and the end of the division cycle during slow growth, whereas E. coli$\text{B}\text{r}$ A contained only one period devoid of DNA synthesis at the end of the cycle.     

Sequence regularities and packing of collagen molecules

Fourier analysis of sequences along edges of the type I collagen molecule constructed from two α1(I) and one α2 chains shows that the molecule is two-sided if the supercoil pitch of the α chains along the molecular axis, P, is 39 residues ($\text{D}\text{6}$, where D = 234 residues or 67 nm). One side has alternating charged and hydrophobic regions with spacings of $\text{D}\text{6}$, while the other side has an excess of hydrophobic residues with a spacing of $\text{D}\text{11}$. These characteristics arise from sequence regularities in the α chains and the geometric relationship between the chains. The pattern is marginally strongest with α2 as chain 1. The $\text{D}\text{6}$ sides could form the inside of a helical microfibril where contacts between molecules would fall P apart along the α chains. The $\text{D}\text{11}$ sides could form the outside of the microfibril where contacts between microfibrils would be spaced apart by the α chain supercoil along the microfibril axis, P′. If the microfibril is a 5₄ helix of D-staggered collagen molecules with a left-handed supercoil of pitch $\text{20D}\text{11}$, P′ is close to $\text{2D}\text{11}$ (43 residues). $\text{2D}\text{11}$ subsets in the α chains give rise to the $\text{D}\text{11}$ spacing along the molecule. The microfibril has 4₁ screw symmetry satisfying X-ray diffraction evidence that microfibrils pack in a tetragonal unit cell.This model is the same as proposed previously by us (Trus & Piez, 1976: Piez & Trus, 1977) except that P = 39 rather than 30 residues. Contrary to our earlier assumption, P = 39 residues is within the range allowed by X-ray diffraction measurements. The present results favor P = 39 since it relates regularities in the α chain sequences to helical parameters in a direct way. Furthermore, model studies show that geometric arguments which support P = 30 are equally strong at P = 39 residues.     

Erythropoiesis in normal and mutant chick embryos

Hemoglobin D_Davis (Hb D_D), an autosomal codominant in chickens, the α^D-globin chain of Hb M of primitive cells and Hb D of definitive erythrocytes. Erythropoiesis and Hb synthesis was investigated in normal, heterozygous, and homozygous Hb D_D mutant embryos (stages 15–44) and adults. The time of appearance, morphology, relationships to developmental changes, and number of primitive and definitive cells were determined. Primitive hemoglobins between stages 17 and 44 showed four components, P1, P2, E, and M (or M_D), on high-resolution isoelectric focusing gels. Comparison of $\text{P1}\text{P2}$ ratios in the four phenotypes indicated that homozygous Hb D_D embryos had an increased proportion of Hb P2 relative to Hb P1 between stages 17 and 35. This difference coincided with an increase in the number of large primitive cells. In all phenotypes the proportions of primitive hemoglobins decreased after stage 25 and they were not detected after stage 40. Basophilic definitive erythroblasts were present in cell suspensions from all phenotypes between stages 24 and 25. Hb A, the major Hb and Hb D, the minor Hb, of definitive cells of embryos and adults were detected by isoelectric focusing of lysates by stage 29. Definitive cells from late embryos of all phenotypes had higher proportions of Hb D (or Hb D_D) than did red cells from corresponding adult birds. Heterozygous Hb D_D embroys and adults had both Hb D and Hb D_D. Hb D_D comprises about 30% of the total minor Hb rather than 50% expected for heterozygosity at a single locus. In this respect heterozygous Hb D_D chick embryos and adult birds are similar to certain heterozygous α-chain variants in humans. A minor Hb, H, found in lysates of later embryos disappears in lysates of normal chicks 65 days after hatching, but was present in the circulation of homozygous Hb D_D chicks until at least 195 days after hatching. Additionally, several minor Hb components which may be asymmetrical hybrids or derived precursors of Hb A and Hb D (or Hb D_D) were observed. This study provides the precise developmental stages when the switchover of erythroid cell populations and hemoglobins in the chick embryo occurs. This is the first investigation of an α-globin chain mutant which is synthesized during all stages of red cell development and may be a useful animal model for the study of hemoglobinopathies in vertebrates.     

4-ethenylidene steroids as mechanism-based inactivators of 3β-hydroxysteroid dehydrogenases

The synthesis of 4-ethenylidene-5α-androstane-3β, 17β-diol ($\text{5}$) and of 4-ethenylidene-5α-androstane-3,17-dione ($\text{4}$) is described. Compound $\text{5}$ is a competitive inhibitor of solubilized bovine microsomal adrenal Δ⁵-3β-hydroxysteroid dehydrogenase, with Ki =2.7μM, and is converted by the enzyme to the corresponding 3-ketone. Compound $\text{4}$ shown to irreversibly inactivate the enzyme in a time-dependent manner ($\text{t}\text{1}\text{2}\text{=31}\text{min}\text{; 55μ}\text{M}\text{;}\text{pH}\text{=7.0}$). The substrate, dehydroepiandrosterone, protects against inactivation by compound $\text{4}$. In contrast, compound $\text{5}$ is not oxidized at the 3-position by the 3β-(and 17β)-hydroxysteroid dehydrogenase from $\text{P. testosteroni}$, but is oxidized at the 17-position. Nevertheless, the 4-ethenylidene-3,17-diketone ($\text{4}$) causes irreversible time-dependent inactivation ($\text{t}\text{1}\text{2}\text{=28}\text{min}\text{; 64μ}\text{M}\text{;}\text{pH}\text{=7.0}$) when incubated directly with this bacterial enzyme, acting as an affinity label.     

Computer-determined rate constants of hemolysis induced by Prymnesium parvum toxin

Rates of hemolysis of rabbit erythrocyte suspensions induced by P. parvum (prymnesin) have been measured colorimetrically at 25.5°C and pH 5.5. The data have been treated previously as consecutive first-order rate processes associated with the prolytic and lytic periods from which two specific rate constants have been obtained, k′ and kψ, respectively. These constants have been related to those obtained by a computer-generated fit of the rate data (absorbance A_t, as a function of time t) with the rate equation $\text{Y =}\text{D}\text{[1 +}\text{exp}\text{((X ? B)}\text{C)}\text{]}\text{+ E}$. Here Y equals A_t, X = time, t; D is equal to a spread factor, A_i ? A_∞; C is the slope of the curve at the inflection point; B is the midpoint time value, i.e., the time at which $\text{A}{}_{\mathrm{t}}\text{=}\text{D}\text{2}$; E is termed the off-set constant and is equal to A_∞. Of these constants, B is directly related to the length of the prolytic period, and C^?1 is directly related to the specific first-order rate constant for hemolysis, k_ψ.     

A study of the diffusion of compact particles in polymer solutions using quasi-elastic light scattering

This paper describes an investigation, using quasi-elastic light scattering, of the diffusion of polystyrene spheres through solutions of dextran. The diffusion coefficient, D, of the spheres is shown to vary inversely with the volume fraction, φ, of dextran according to $\text{D =}\text{D}{}_0\text{(1 + νφ + κφ}{}^2\text{)}$. Changes in the molecular weight of dextran are shown to reflect changes in the macromolecular shape parameter, ν, and the interaction parameter, κ. This result differs from previous studies which suggested an $\text{exp}\text{(?}\text{B}\text{φ}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ dependence and no molecular weight dependence [8].     

Structural studies on the extracellular polysaccharide of the red alga, Porphyridium cruentum

Partial acid hydrolyzates of the extracellular polysaccharide from Porphyridiunm cruentum yield three disaccharides and two uronic acids. These constitute all of the uronic acid in the polymer. The novel disaccharides are 3-O-(α-$\text{D}$-glucopyranosyl- uronic acid)-$\text{L}$-galactose, 3-O-(2-O-methyl-ca-glucopyranosyluronic acid)-$\text{D}$- galactose, and 3-0-(2-0-methyl-a-$\text{D}$-glucopyranosyluronic acid)-$\text{D}$-glucose. The polyanion of high molecular weight contains $\text{D}$- and $\text{L}$-galactose, xylose, $\text{D}$-glucose, $\text{D}$-glucuronic acid and 2-O-methyl-D-glucuronic acid, and sulfate in molar ratio (relative to $\text{D}$-glucose) of 2.12:2.42:1.00:1.22:2.61. Preliminary periodate-oxidation studies suggest that the hexose and uronic acids are joined to other residues by ( 1→3) glycosidic linkages. About one-half of the xylose residues are (1→3)-linked.     

Studies of lectins XXXVI. Properties of some lectins prepared by affinity chromatography on O-glycosyl polyacrylamide gels

A number of lectins has been purified by affinity chromatography on O-glycosyl polyacrylamide gels. The lectins isolated (and the particular sugar ligands used in the affinity carriers) are as follows: Anguilla anguilla, serum (α-L-fucosyl-), Vicia cracca, seeds; Phaseolus lunatus, seeds; Glycine soja, seeds; Dolichos biflorus, seeds; Maclura pomifera, seeds; Sarothamnus scoparius, seeds; Helix pomatia, ablumin glands; Clitocybe nebularis, fruiting bodies (all $\text{N-}\text{acetyl}\text{-α-}\text{d}\text{-galactosaminyl-}$); Ricinus communis, seeds (β-lactosyl-); Onomis spinosa, root; Fomes fomentarius, fruiting bodies; Marasmius oreades, fruiting bodies (all $\text{α-}\text{d}\text{-galactosyl-}$), Canavalia ensiformis, seeds, (i.e., concanavalin A) ($\text{α-}\text{d}\text{-glucosyl-}$).Physicochemical properties of Glycine soja, Dolichos bifloras, Phaseolus lunatus, Helix pomatia and Ricinus communis lectins correponded well to properties of the preparations studied earlier by other workers. For the other purified lectins the essential physicochemical data (sedimentation coefficient, molecular weight, subunit composition, electrophoretic patterns, amino acid composition, carbohydrate content, isoelectric point) were established and their precipitating, hemagglutinating and mitogenic activities determined.     

Derivation of the equations that describe the effects of unstirred water layers on the kinetic parameters of active transport processes in the intestine

Unidirectional flux of solutes into the intestinal mucosal cells is determined by the rate of movement of these molecules across both an unstirred water layer and the microvillus membrane of the epithelial cell. Therefore, an equation is derived in this paper that describes the velocity of active transport as a function of the characteristics of both the transport carrier in the membrane and the resistance of the overlying unstirred water layer. Using this equation a series of curves are presented that depict the effect on the kinetics of active transport of varying the thickness (d) or surface area (S_w) of the unstirred water layer, the free diffusion coefficient (D) of the solute, the distribution of active transport sites along the villus ($\text{?}{}_{\mathrm{<mtext>n</mtext>}}$), the maximal transport velocity (J^m_d) and the true Michaelis constant (K_m). These theoretical curves illustrate the serious limitations inherent in interpretation of previously published data dealing with active transport processes in the intestine.