Malate dehydrogenase. Kinetic studies with meso-tartrate and 2-keto-3-hydroxysuccinate, comparison of the mitochondrial and supernatant pig heart enzymes.

Initial rate, product inhibition, and isotope rate kinetic studies of pig heart mitochondrial and supernatant malate dehydrogenases, acting upon the nonphysiological substrates, meso-tartrate and 2-keto-3-hydroxysuccinate, are reported. The measured spontaneous keto-enol equilibrium for 2-keto-3-hydroxysuccinate in 0.05 m Tris-acetate (pH 8.0) at 25 °C favors the enol form, dihydroxyfumarate, with an apparent equilibrium constant of 0.036. The enzyme-catalyzed reaction favors meso-tartrate with an apparent equilibrium constant of 1.25 × 10^?6, M^?1 at pH 8.0. The mechanism apparently remains ordered bi bi for both enzymes when these nonphysiological substrates are used, and the chemical-converting hydride transfer step becomes more rate limiting for both enzymes. This conclusion is supported by $\text{V}{}_{\mathrm{<mtext>H</mtext>}}\text{V}{}_{\mathrm{<mtext>D</mtext>}}$ and $\text{(}\text{V}{}_{\mathrm{<mtext>H</mtext>}}\text{K}{}_{\mathrm{<mtext>H</mtext>}}\text{)}\text{V}{}_{\mathrm{<mtext>D</mtext>}}\text{K}{}_{\mathrm{<mtext>D</mtext>}}$ values of 2.6 and 3.1, respectively, for the mitochondrial enzyme and 1.9 and 2.9, respectively, for the supernatant enzyme.     

Steady-state kinetics of ADP-arsenate and ATP-synthesis in Rhodospirillum rubrum chromatophores

(1) Rates of ATP synthesis and ADP-arsenate synthesis catalyzed by Rhodospirillum rubrum chromatophores were determined with the firefly luciferase method and by a coupled enzyme assay involving hexokinase and glucose-6-phosphate dehydrogenase. (2) V_m for ADP-arsenate synthesis was about 2-times lower than V_m for ATP-synthesis. With saturating [ADP], K(As_i) was about 20% higher than K(P_i). With saturating [anion], K(ADP) was during arsenylation about 20% lower than during phosphorylation. (3) Plots of $\text{1}\text{v}$ vs. $\text{1}\text{[}\text{substrate}\text{]}$ were non-linear at low concentrations of the fixed substrate. The non-linearity was such as to suggest a positive cooperativity between sites binding the variable substrate, resulting in an increased $\text{V}{}_{\mathrm{<mtext>m</mtext>}}\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ ratio. High concentrations of the fixed substrate cause a similar increase in $\text{V}{}_{\mathrm{<mtext>m</mtext>}}\text{K}{}_{\mathrm{<mtext>m</mtext>}}$, but abolish the cooperativity of the sites binding the variable substrate. (4) Low concentrations of inorganic arsenate (As_i) stimulate ATP synthesis supported by low concentrations of P_i and ADP about 2-fold. (5) At high ADP concentrations, the apparent K_i of As_i for inhibition of ATP-synthesis was 2–3-times higher than the apparent K_m of As_i for arsenylation; the apparent K_i of P_i for inhibition of ADP-arsenate synthesis was about 40% lower than the apparent K_m of P_i for ATP synthesis. (6) The results are discussed in terms of a model in which P_i and As_i compete for binding to a catalytic as well as an allosteric site. The interaction between these sites is modulated by the ADP concentration. At high ADP concentrations, interaction between these sites occurs only when they are occupied with different species of anion.     

pH kinetic studies of the N-demethylation of N,N-dimethylaniline catalyzed by chloroperoxidase

The effect of pH on the kinetic parameters for the chloroperoxidase-catalyzed N-demethylation of N,N-dimethylaniline supported by ethyl hydroperoxide was investigated from pH 3.0 to 7.0. Chloroperoxidase was found to be stable throughout the pH range studied. Initial rate conditions were determined throughout the pH range. The V_max for the demethylation reaction exhibited a pH optimum at approximately 4.5. The K_m for N,N-dimethylaniline increased with decreasing pH, while the K_m for ethyl hydroperoxide varied in a manner paralleling V_max. Comparison of the $\text{V}{}_{\mathrm{<mtext>max</mtext>}}\text{K}{}_{\mathrm{m}}$ values for N,N-dimethylaniline and ethyl hydroperoxide indicated that the interaction of N,N-dimethylaniline with chloroperoxidase compound I was rate-limiting below pH 4.5, while compound I formation was rate-limiting above pH 4.5. The log of the $\text{V}{}_{\mathrm{<mtext>max</mtext>}}\text{K}{}_{\mathrm{m}}$ for ethyl hydroperoxide was independent of pH, indicating that chloroperoxidase compound I formation is not affected by ionizations in this pH range. The plot of the log of the $\text{V}{}_{\mathrm{<mtext>max</mtext>}}\text{K}{}_{\mathrm{m}}$ for N,N-dimethylaniline versus pH indicated an ionization on compound I with a pK of approximately 6.8. The plot of the log of the V_max versus pH indicated an ionization on the compound I-N,N-dimethylaniline complex, with a pK of approximately 3.1. The results show that chloroperoxidase can demethylate both the protonated and neutral forms of N,N-dimethylaniline (pK approximately 5.0), suggesting that hydrophobic binding of the arylamine substrate is more important in catalysis than ionic bonding of the amine moiety. For optimal catalysis, a residue in the chloroperoxidase compound I-N,N-dimethylaniline complex with a pK of approximately 3.1 must be deprotonated, while a residue in compound I with a pK of approximately 6.8 must be protonated.     

Mechanistic studies of epoxide hydrolase utilizing a continuous spectophotometric assay

A precise continuous photometric assay has been devised and utilized for mechanistic studies of chicken and rat liver microsomal epoxide hydrolase (EH). The assay is based on monitoring the hydration of p-nitrostyrene oxide (PNSO) at 310 nm. Rat liver EH hydrates S-(+)- and R-(?)-PNSO differentially, the K_m and V values for the former being ca. four times those for the latter; in contrast, enantiomeric differences are negligible with chicken liver EH. With rat EH V increases slightly from pH 7 to 8 and then falls rapidly from pH 8 to 9.5; K_m remains constant from pH 7 to 8 and then increases steadily from pH 8 to 9.5. In 86 mol% D₂O the solvent isotope effect on V ($\text{H}{}_2\text{O}\text{D}{}_2\text{O}$) is 1.103 ± 0.015. Both rat and chicken EH show a 3% inverse isotope effect for the hydration of [7-²H]PNSO and a 4% normal isotope effect for the hydration of [8-²H₂]PNSO. These observations are discussed in terms of the possible participation of acid as well as base catalysis in the enzymatic mechanism.     

Kinetics and mechanism of the F1 isozyme of horse liver aldehyde dehydrogenase.

The reaction mechanism of the F1 isozyme of horse liver aldehyde dehydrogenase (EC 1.2.1.3) was investigated using both steady-state and rapid kinetic techniques. Using the steady-state substrate velocity patterns, the NADH inhibition patterns at several aldehyde concentrations, and the substrate analog (adenosine diphosphoribose and chloral hydrate) inhibition patterns, the enzymic catalysis was shown to involve ordered addition of NAD followed by aldehyde. This mechanism was confirmed using the kinetics of the hydrolysis of p-nitrophenyl acetate as an indicator of the dehydrogenase substrate binding. Steady-state experiments with deuteroacetaldehyde showed the V to be unchanged, but the K_m increased (). Stopped flow experiments where E-NAD was rapidly mixed with aldehyde showed a burst of NADH formation followed by slower steady-state turnover. This result clearly indicates that the rate limiting step lies after NAD reduction. The NADH off rate (0.7 s^?1) as estimated by displacement of NADH from the E-NADH complex upon rapid addition of NAD was found to be very close to the steady-state site turnover number (0.3 s^?1). This fact and the relatively small effect of aldehyde R-group on maximal velocity suggest that the slow rate of NADH release contributes significantly to limitation of the enzyme catalytic velocity.     

Nitro analogs of substrates for adenylosuccinate synthetase and adenylosuccinate lyase

The reactivities of the nitro analogs of the substrates of adenylosuccinate synthetase and adenylosuccinate lyase, the enzymes which catalyze the penultimate and last step, respectively, in the pathway for AMP biosynthesis have been examined. Alanine-3-nitronate, an aspartate analog, was a substrate for the synthetase from Azotobacter vinelandii, having a $\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$ which was ~30% that for aspartate. The product of this reaction was N⁶-(l-1-carboxy-2-nitroethyl)-AMP. Of nine other substrate analogs tested, only cysteine sulfinate (having 5.5% of the activity of aspartate) was reactive. These results demonstrate the strict requirement of the synthetase for a negatively charged substituent, with a carboxylate-like geometry, at the β-carbon of the α-amino acid substrate. The lyase, purified to homogeneity from brewer's yeast by a new procedure, did not utilize N⁶-(l-1-carboxy-2-nitroethyl)-AMP as a substrate. However, the nitronate form of this analog was a good inhibitor of the lyase ($\text{K}{}_{\mathrm{m}}\text{K}{}_{\mathrm{i}}\text{= 28}$ when compared to adenylosuccinate), suggesting that it mimics a carbanionic intermediate in the reaction pathway. The avid binding of bromphenol blue by the lyase (_i = 0.95 μM) was used for active site titrations and for displacement of the enzyme, in the purification protocol, from blue Sepharose.     

An improved spectrophotometric assay for human plasma carboxypeptidase N

A continuous spectrophotometric assay for human plasma carboxypeptidase N utilizing furylacryloyl-alanyl-lysine is described. Synthesis was made by use of 9-(2-sulfo)fluorenylmethyloxycarbonyl (Sulfmoc) chloride as the N-?-amino-blocking group for lysine. The substrate has the advantage of containing a chromophore which allows difference measurements above 324 nm. The kinetic parameters K_m and $\text{K}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$ have been determined for furylacryloyl-alanyl-lysine and -arginine. Difference measurements were related to micromoles of lysine or arginine released and were expressed as units.     

Kinetic considerations for the regulation of adenosine and deoxyadenosine metabolism in mouse and human tissues based on a thymocyte model

Metabolic regulation at a branch point may be determined primarily by relative enzyme activities and affinity for common substrate. Adenosine and deoxyadenosine are both phosphorylated and deaminated and their metabolism was studied in intact mouse thymocytes. From kinetic considerations of two activities competing for a common substrate, the deamination:phosphorylation ratio, $\text{v}{}^{\mathrm{<mtext>d</mtext>}}\text{v}{}^{\mathrm{<mtext>k</mtext>}}$, at high nucleoside concentration, $\text{[}\text{S}\text{]?∞}$, is equal to $\text{V}{}^{\mathrm{<mtext>d</mtext>}}\text{V}{}^{\mathrm{<mtext>k</mtext>}}$, or 34 and 1090 for adenosine and deoxyadenosine, respectively. At low substrate concentrations, $\text{[}\text{S}\text{]?0}$, $\text{v}{}^{\mathrm{<mtext>d</mtext>}}\text{v}{}^{\mathrm{<mtext>k</mtext>}}$ is equal to $\text{V}{}^{\mathrm{<mtext>d</mtext>}}\text{K}{}^{\mathrm{<mtext>k</mtext>}}{}_{\mathrm{<mtext>m</mtext>}}\text{V}{}^{\mathrm{<mtext>k</mtext>}}\text{K}{}^{\mathrm{<mtext>d</mtext>}}{}_{\mathrm{<mtext>m</mtext>}}$, or 0.7 and 285 for adenosine and deoxyadenosine, respectively. The analysis was extended to other mouse and human tissues by measurement of adenosine kinase, deoxyadenosine kinase and adenosine deaminase activities. All tissues were found to preferentially deaminate deoxyadenosine. Three tissue types were apparent with respect to adenosine metabolism: those which preferentially phosphorylate adenosine at all concentrations, those which switch from phosphorylation to deamination between low and high adenosine concentration and those for which deamination is quantitatively important at all concentrations. Lymphoid tissues are representative of the latter category. The kinetic approach we describe offers a means of predicting nucleoside metabolism over a range of concentration which may be technically difficult to otherwise measure. The phosphorylation of adenosine and deoxyadenosine was also studied in intact thymocytes in the presence of adenosine deaminase inhibitors. The rate of deoxyadenosine phosphorylation was unaffected by coformycin or EHNA, whereas adenosine phosphorylation decreased with increasing substrate concentrations to 18% the rate in the absence of adenosine deaminase inhibitors.     

Presteady-state kinetic study of the elementary processes in the chymotrypsin-catalyzed hydrolysis of specific ester substrate. Rate-limiting association process due to the secondary binding.

Presteady-state kinetic studies of α-chymotrypsin-catalyzed hydrolysis of a specific chromophoric substrate, N-(2-furyl)acryloyl-l-tryptophan methyl ester, were performed by using a stopped-flow apparatus both under [E]₀ ? [S]₀ and [S]₀ ? [E]₀ conditions in the pH range of 5–9, at 25 °C. The results were accounted for in terms of the three-step mechanism involving enzyme-substrate complex (E · S) and acylated enzyme (ES′); no other intermediate was observed. This substrate was shown to react very efficiently, i.e., the maximum of the second-order acylation rate constant ($\text{k}{}_2\text{K}{}_{\mathrm{s}}\text{′}\text{)}{}_{\mathrm{<mtext>max</mtext>}}\text{= 4.2 × 10}{}^7\text{M}{}^{\mathrm{?1}}\text{s}{}^{\mathrm{?1}}$. The limiting values of K_s′ (dissociation constant of E · S), K₂ (acylation rate) and k₃ (deacylation rate) were obtained from the pH profiles of these parameters to be 0.6 ± 0.2 × 10^?5 m, 360 ± 15 s^?1 and 29.3 ± 0.8 s^?1, respectively. Likewise small values were observed for K_i of N-(2-furyl)-acryloyl-l-tryptophan and N-(2-furyl)acryloyl-d-tryptophan methyl ester and K_m of N-(2-furyl)acryloyl-l-tryptophan amide. The strong affinities observed may be due to intense interaction of β-(2-furyl)acryloyl group with a secondary binding site of the enzyme. This interaction led to a $\text{k}{}_{\mathrm{?1}}\text{k}{}_2$ value lower than unity, i.e., the rate-limiting process of the acylation was the association, even with the relatively low k₂ value of this methyl ester substrate, compared to those proposed for labile p-nitrophenyl esters.     

An allosteric pore model for sugar transport in human erythrocytes

Glucose transport in human erythrocytes is characterized by a marked asymmetry in the $\text{V}$ and $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values for entry and for exit. In addition, they show a high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ and a high $\text{V}$ for equilibrium exchange but low $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ values for infinite cis and for infinite trans exit and entry. An allosteric pore model has been proposed to account for these characteristics. In this model, substrate-induced conformational changes destabilize the interfaces between protein subunits (the pore gates).Pores doubly occupied from inside destabilize the transport gates and result in high $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ and high $\text{V}$ transport parameters. This effect is less marked when pores are doubly occupied from outside and therefore transport asymmetry results.     

Quantitative structure-activity relationships of chymotrypsin-ligand interactions: An analysis of interactions in p3 space.

Fourteen derivatives of l-alanine of the type CH₃CH(NHCO-3-C₅H₄N)COOR₃ have been synthesized and their hydrolysis by chymotrypsin was studied with the object of characterizing enzymic space (?₃) to which R₃ binds. The binding of R₃ ($\text{log}\text{1}\text{K}{}_{\mathrm{m}}$) was shown via correlation analysis to correlate with molar refractivity (MR) of R₃ rather than hydrophobicity (π). The results confirmed our earlier predictions. A correlation equation for the hydrolysis of 77 acyl-amino acid esters of the general formula R₂CH(NHCOR₁)COOR₃ relating $\text{log}\text{(k}{}_{\mathrm{<mtext>cat</mtext>}}\text{k}{}_{\mathrm{m}}\text{)}$ to molar refractivity of R₁, R₂, and R₃ and to $\text{σ}{}^1$ (Taft's polar parameter) of R₃ was formulated. The general picture of ligand interactions with chymotrypsin as seen with correlation analysis is discussed.     

Determination of enzyme kinetic parameters by continuous addition of substrate to a single reaction mixture and analysis by a tangent-slope procedure: I. Analysis of the method using computed progress curves

A new method has been developed which provides reliable estimates of enzyme kinetic constants from single reaction progress curves recorded under conditions of continuously increasing substrate concentration. Equally spaced data points simulating such progress curves and containing known amounts of superimposed random noise were fit to the Hill equation by (i) direct nonlinear curve-fitting of raw data, and (ii) a tangent-slope technique in which the raw data are numerically differentiated, transformed into substrate versus velocity data, and then analyzed as linear plots. Both integral and differential procedures provided accurate and precise estimates of the Hill parameters (S_0.5, V, and n) from single reaction mixtures. However, the tangent-slope method was at least 10-fold faster to compute and was not dependent on accurate initial guesses of the Hill parameters or integration of the rate equation. With the tangent-slope method, the optimal number of data points used in calculating tangent slopes was found to be 9 or 11. The reliability of the Hill parameters determined with the tangent-slope method was relatively insensitive to the maximum substrate concentration over a range of $\text{S}{}_{\mathrm{<mtext>max</mtext>}}\text{S}{}_{0.5}$ of 1.5 to 10; the optimal value was 3. Through further analysis of simulated data, it was found that slow enzyme inactivation (<4% loss during the assay), or product competitive inhibition (maximum product concentration < 30% of the inhibitor dissociation constant) does not produce serious errors in the Hill parameters. Methods are presented to detect and distinguish enzyme inactivation and product competitive inhibition. It is suggested that continuous addition methodology combined with tangent-slope analysis provides the basis for a flexible system for kinetic characterization of enzymes which has wider applicability and other advantages over multicuvette or conventional progress curve methodology. A major advantage in contrast to the progress curve approach is that product accumulation and associated product effects are lowest at lower substrate concentrations.     

Lactose transport in Escherichia coli cells Dependence of kinetic parameters on the transmembrane electrical potential difference

We determine the kinetic parameters $\text{V}$ and $\text{K}{}_{\mathrm{<mtext>T</mtext>}}$ of lactose transport in Escherichia coli cells as a function of the electrical potential difference (Δψ) at pH 7.3 and $\text{Δ}\text{pH}\text{= 0}$. We report that transport occurs simultaneously via two components: a component which exhibits a high $\text{K}{}_{\mathrm{<mtext>T</mtext>}}$ (larger than 10 mM) and whose contribution is independent of Δψ, a component which exhibits a low $\text{K}{}_{\mathrm{<mtext>T</mtext>}}$ independent of Δψ (0.5 mM) but whose $\text{V}$ increases drastically with increasing Δψ. We associate these components of lactose transport with facilitated diffusion and active transport, respectively. We analyze the dependence upon Δψ of $\text{K}{}_{\mathrm{<mtext>T</mtext>}}$ and $\text{V}$ of the active transport component in terms of a mathematical kinetic model developed by Geck and Heinz (Geck, P. and Heinz, E. (1976) Biochim. Biophys. Acta 443, 49–63). We show that within the framework of this model, the analysis of our data indicates that active transport of lactose takes place with a H⁺/lactose stoichiometry greater than 1, and that the lac carrier in the absence of bound solutes (lactose and proton(s)) is electrically neutral. On the other hand, our data relative to facilitated diffusion tend to indicate that lactose transport via this mechanism is accompanied by a H⁺/lactose stoichiometry smaller than that of active transport. We discuss various implications which result from the existence of H⁺/lactose stoichiometry different for active transport and facilitated diffusion.     

Cockroaches on a treadmill: Aerobic running

Five species of cockroach were tested on a miniature treadmill at three velocities as O₂ consumption () was measured: Gromphadorhina chopardi, Blaberus discoidalis, Eublaberus posticus, Byrsotria fumagata and Periplaneta americana. All cockroaches showed a classical aerobic response to running: increased rapidly from a resting rate to a steady-state on-response varied from under 30 s to 3 min. Recovery after exercise was rapid as well; $\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ off-response varied from under 30 s to 6 min. These times are faster or similar to mammalian values. varied directly with velocity as in running mammals, birds and reptiles. during steady-state running was only 4–12 times higher than at rest. Running is energetically much less costly per unit time than flying, but the cost of transport per unit distance is much more expensive for pedestrians. The minimal cost of transport (M_run), the lowest necessary to transport a given mass a specific distance, is high in cockroaches due to their small size. The new data suggest that insects may be less economical than comparable sized vertebrates.     

Effects of oligomycin and quercetin on the hydrolytic activities of the (Na+ + K+)-dependent ATPase

Quercetin inhibited a dog kidney ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$ preparation without affecting $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ for ATP or $\text{K}{}_{0.5}$ for cation activators, attributable to the slowly-reversible nature of its inhibition. Dimethyl sulfoxide, a selector of E₂ enzyme conformations, blocked this inhibition, while the K⁺-phosphatase activity was at least as sensitive to quercetin as the ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$ activity, all consistent with quercetin favoring E₁ conformations of the enzyme. Oligomycin, a rapidly-reversible inhibitor, decreased the $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ for ATP and the $\text{K}{}_{0.5}$ for cation activators, and its inhibition was also diminished by dimethyl sulfoxide. Although oligomycin did not inhibit the K⁺-phosphatase activity under standard assay conditions, a reaction presumably catalyzed by E₂ conformations, its effects are nevertheless accommodated by a quantitative model for that reaction depicting oligomycin as favoring E₁ conformations. The model also accounts quantitatively for effects of both dimethyl sulfoxide and oligomycin on $\text{V}{}_{\mathrm{<mtext>max</mtext>}}$, $\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ for substrate, and $\text{K}{}_{0.5}$ for K⁺, as well as for stimulation of phosphatase activity by both these reagents at low K⁺ but high Na⁺ concentrations.     

On advection in phytoplankton models

Scale analysis is used to deduce a new non-dimensional number, $\text{S =}\text{C}\text{[(A}{}_{\mathrm{H}}\text{τ)}\text{1}\text{2}\text{V}{}_{\mathrm{<mtext>m</mtext>}}\text{]}$ which defines the importance of advection of phytoplankton by organized fluid motion in spatial models of marine food chains. When S ? 1, advection greatly affects biological productivity; when S ? I, advection may be neglected. When S is order one, advection and biological productivity play competing roles in determining the spatial configuration of the plankton biomass.     

Graphic method for determination of allosteric constants

The maximum slope of the plot, appearing in the paper of Watari & Isogai (1976), was derived algebraically as a function of allosteric constants c and α_mor β_m (= cα_m), and the relation between L, c, and α_mor β_m, was also obtained, where $\text{L =}\text{T}{}_{\mathrm{o}}\text{R}{}_{\mathrm{o}}\text{, c =}\text{K}{}_{\mathrm{R}}\text{K}{}_{\mathrm{T}}\text{, α}{}_{\mathrm{m}}\text{=}\text{F}{}_{\mathrm{m}}\text{K}{}_{\mathrm{R}}\text{, β}{}_{\mathrm{m}}\text{=}\text{F}{}_{\mathrm{m}}\text{K}{}_{\mathrm{T}}\text{, R}{}_{\mathrm{o}}\text{and}\text{T}{}_{\mathrm{o}}$ are concentrations of unligated R and T states respectively, K_Rand K_T are microscopic dissociation constants, and F_m is the ligand concentration at the maximum slope of the plot. When the maximum slope is increased by one, the value becomes Hill constant, n. Nomographs which enable easier estimation of allosteric constants, L and c, were constructed from the two given values, the maximum slope of the plot, n ? 1, and α_mor β_m, in the cases where the maximum number of ligands, N, was 2 and 4. In the nomograph, log c is plotted against log L²c^N keeping the value of the maximum slope of the plot and that of α_mor β_m constant. These nomographs show that the representation is symmetrical in the cases of L²c^N > 1 and L²c^N < 1.     

Anaerobic stimulation of sugar transport in avian erythrocytes

The kinetic parameters of the sugar transport in avian erythrocytes were evaluated under aerobic and anaerobic conditions. In anaerobic cells, transport measurements with $\text{3-O-[}{}^{14}\text{C}\text{]}$ methylglucose resulted in a set of similar dissociation-like constants. Thus the Michaelis constants of $\text{3-O-[}{}^{14}\text{C}\text{]}$ methylglucose entry and exit, $\text{K}{}_{\mathrm{<mtext>so</mtext>}}$ and $\text{K}{}_{\mathrm{<mtext>si</mtext>}}$, were 8 and 7 mM, respectively. The equilibrium exchange constant, $\text{B}{}_{\mathrm{<mtext>s</mtext>}}$, and the counterflow constant, $\text{R}{}_{\mathrm{<mtext>s</mtext>}}$, were 9 and 11 mM, respectively. The activity constant for $\text{3-O-}\text{methylglucose}$ transport, $\text{F}{}_{\mathrm{<mtext>s</mtext>}}$, defined as $\text{V/K}{}_{\mathrm{<mtext>m</mtext>}}$, was 4 ml/h per g. This set of kinetic constants was compatible with a symmetrical mobile-carrier model. In contrast, the Michaelis constant for glucose entry, $\text{K}{}_{\mathrm{<mtext>go</mtext>}}$, was 2 mM and less than the counterflow constant, $\text{R}{}_{\mathrm{<mtext>g</mtext>}}$ (8 mM). This result could be accounted for by slower movement of the glucose-carrier complex than the free carrier. The activity constant for glucose transport, $\text{F}{}_{\mathrm{<mtext>g</mtext>}}$, was 5 ml/h perg.Under aerobic conditions, two of the dissociation-like constants ($\text{K}{}_{\mathrm{<mtext>si</mtext>}}$ and $\text{B}{}_{\mathrm{<mtext>s</mtext>}}$) for $\text{3-O-}\text{methylglucose}$ transport were significantly larger than those obtained in anaerobic cells, but the remaining two ($\text{K}{}_{\mathrm{<mtext>so</mtext>}}$ and $\text{R}{}_{\mathrm{<mtext>s</mtext>}}$) remained unchanged. The values, for $\text{K}{}_{\mathrm{<mtext>so</mtext>}}\text{, K}{}_{\mathrm{<mtext>si</mtext>}}\text{, B}{}_{\mathrm{<mtext>s</mtext><mtext>\; and</mtext>}}\text{R}{}_{\mathrm{<mtext>s</mtext>}}$ were 8, 26, 20 and 8 mM, respectively. The activity constant, $\text{F}{}_{\mathrm{<mtext>s</mtext>}}$, decreased to 2 ml/h per g. These changes in kinetic constants were consistent with the hypothesis that anoxia accelerated sugar transport by releasing free carrier that was previously sequestered on the inside of the cell membrane.     

Coevolution in resource-limited competition communities

A coevolutionary model of species packing is developed which allows evolutionary adjustment in both niche position and within-phenotype niche width of from one of three competing species. The environment is specified as a single resource dimension x and availability of resources along x is given by a Gaussian curve with parameters ($\text{x}\text{?}{}_{\mathrm{R}}\text{and}\text{σ}{}_{\mathrm{R}}$). The model predicts that for S species the ratio of optimal niche width (?) to σ_R is roughly independent of σ_R and can be approximated by $\text{1}\text{S}$ when the competitors are completely resource limited. Niche separation ($\text{d}\text{?}\text{w}\text{?}$) increases only moderately with increases in resource diversity σ_R and is greater for two than for three competing species. To the extent that the competitors do not utilize all resources, both optimal niche separation and niche width decrease. Many of the general trends in niche width and niche separation predicted by this coevolutionary model parallel those from optimal foraging theory and limiting similarity models of community structure. The coevolutionary model stands out, however, in the singularly high values predicted for niche separation, making coevolved communities highly invadeable. Hence, the theory suggests, as some empirical evidence indicates, that coevolved competition communities can only exist as such on remote islands or in other habitats which might be free from invasion by outside species. For such communities, resource diversity (σ_R) should have much less effect on species packing than either species number itself or the extent that these competitors are resource limited.     

Some dilute-solution parameters of the levan of streptococcus salivarius in various solvents

The intrinsic viscosities, weight-average molecular weights (M?_w), and radii of gyration [($\text{R}{}^2{}_{\mathrm{g}}$)^{$\text{1}\text{2}$}≈] of Streptococcus salivarius levan in various solvents were respectively obtained from viscosity and light-scattering measurements. The data showed that the levan in water is not aggregated by hydrogen bonds, and that the values of both the refractive index and ($\text{R}{}^2{}_{\mathrm{g}}$)^{$\text{1}\text{2}$} are lower in water than in aqueous solutions of urea. Urea may break intramolecular hydrogen-bonds, e.g., between branches, allowing the molecule to expand.