Study on models of single populations: an expansion of the logistic and exponential equations

Using the adsorption theory of chemical kinetics, a new equation concerning the growth of single populations is presented:

$\text{d}\text{X}\text{d}\text{t}\text{=}\text{μ}{}_{\mathrm{c}}\text{X(1 ?)}\text{X}\text{X}{}_{\mathrm{m}}\text{1?}\text{X}\text{X}{}_{\mathrm{m}}{}^{\mathrm{\prime }}$

or in its integral form:

$\text{ln}\text{X}\text{X}{}_{\mathrm{o}}\text{?}\text{ln}\text{X}{}_{\mathrm{m}}\text{?X}\text{X}{}_{\mathrm{m}}\text{?X}{}_{\mathrm{o}}\text{+}\text{X}{}_{\mathrm{m}}\text{X}{}^{\mathrm{\prime }}{}_{\mathrm{m}}\text{X}{}_{\mathrm{m}}\text{?X}\text{X}{}_{\mathrm{m}}\text{?X}{}_{\mathrm{o}}\text{=μ}{}_{\mathrm{c}}\text{(t?t}{}_{\mathrm{o}}\text{)}$

This equation attempts to explain the relationship between population increment and limiting resources. It can be reduced to either the logistic or exponential equation under two extreme conditions. The new equation has three parameters, X_m, X′_m and μ_c, each of which has ecological significance. $\text{X}{}_{\mathrm{m}}\text{X′}{}_{\mathrm{m}}$ concerns the efficiency of nutrient utilization by an organism. Its value is between zero and one. With ratios approaching unity, the efficiency is high; lower ratios indicate that population increment is quickly restricted by limiting resources. μ_c, is a velocity parameter lying between μ_e, (exponential growth) and μ_L (logistic growth), and is dependent on the value of $\text{solX}{}_{\mathrm{m}}\text{X′}{}_{\mathrm{m}}$. From μ_c we can predict the time course of population incremental velocity ($\text{d}\text{X}\text{d}\text{t}$), and can observe that it is not symmetrical, unlike that derived from the logistic equation. At $\text{X}{}_{\mathrm{m}}\text{X′}{}_{\mathrm{m}}\text{= 1}$ the maximum velocity of the population increment predicted from the new equation is twice that of the logistic equation.Population growth in nature seems to support the new equation rather than the logistic equation, and it can be successfully fitted by means of a least square method.     

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.     

Bacillus subtilis aminopeptidase: specificity toward amino acyl-beta-naphthylamides.

The kinetic parameters for the hydrolyses of different l-α-amino acid-β-naphthylamides by Bacillus subtilis aminopeptidase have been measured for the native enzyme and for the enzyme activated in 5 mm Co(NO₃)₂. In most cases Co²⁺ activation decreased K_m(app) values and increased k_cat values, in other cases k_m(app) and k_cat values were increased; for the remainder of the substrates tested k_m(app) values and k_cat values were decreased. In all cases tested the ratios of $\text{(}\text{k}\text{cat}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)</mtext>}}\text{)}\text{CO}{}^{\mathrm{2+}}\text{/(}\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{<mtext>m(</mtext><mtext>app</mtext><mtext>)nativ</mtext>}}\text{)}$ were increased (2- to 108-fold). For the native enzyme the order of specificity toward the l-amino acid-β-naphthylamides was Arg > Met > Trp > Lys > Leu and for the Co²⁺ activated enzyme the order of specificity was Lys > Arg > Met > Trp > Leu. The native enzyme hydrolyzed Pro-β-naphthylamide, but not α-Glu-β-naphthylamide; Co²⁺ activation of the enzyme affected an appreciable rate of hydrolysis of the latter substrate.     

Base-group specificity at the primary recognition site of ribonuclease T1 for minimal RNA substrates

Kinetic studies on the RNase T₁-catalyzed transesterification of 12 dinucleoside monophosphates, N_p¹N² (N¹ = A, C, and U; N² = A, C, G, and U) at pH 5, 25 °C, and 0.2 m ionic strength, revealed that the catalytic efficiency ($\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$) for GpN substrates (H. L. Osterman, and F. G. Walz, Jr., 1978, Biochemistry, 17, 4142) was ~10⁶-fold greater than corresponding ApNs and at least 10⁸-fold greater than corresponding CpNs and UpNs. The catalytic activity with ApN substrates survives phenol extraction which indicates (along with other criteria) that it is intrinsic to RNase T₁ and is not due to trace contamination by other nucleases. Circumstantial evidence is presented which suggests that homologous GpN and ApN substrates bind productively at different sites on the enzyme. The results of steady-state kinetic studies of RNase T₁ with IpNs (N = C and U) were compared with those for GpNs and indicated that the primary effect of the guanine 2-NH₂ group is to enhance substrate binding at the primary recognition site by ~2.6 kcal/mol. Values of ($\text{k}{}_{\mathrm{<mtext>cat</mtext>}}\text{K}{}_{\mathrm{m}}$) showed the order NpC > NpU (N = A, G, and I) which evidences the existence of a subsite for the leaving nucleoside group that prefers cytidine: interactions at this subsite are reflected in k_cat rather than K_m.     

A mathematical model describing the effect of temperature and substrate concentration on the activities of M4 and H4 lactate dehydrogenase from the big brown bat (Eptesicus fuscus)

The effect of temperature on the activities of M₄ and H₄ lactate dehydrogenases (LDH, EC 1.1.1.27) isolated from the big brown bat (Eptesicus fuscus) was examined. Temperature effects were dependent on the concentrations of all four LDH substrates, pyruvate, lactate, NADH, and NAD. Arrhenius plots of In v_i vs reciprocal of absolute temperature were linear for all but the lowest substrate concentrations. The slopes of these Arrhenius plots were used to calculate the temperature effect parameter (μ). Substrate-dependent temperature effects for M₄ and H₄ LDH were described by an equation for a rectangular hyperbola, $\text{μ =}\text{[E}{}_{\mathrm{\beta }}\text{S + E}{}_{\mathrm{\alpha }}\text{K}{}_{\mathrm{t}}\text{]}\text{[K}{}_{\mathrm{t}}\text{+ S]}$ proposed by G. R. Harbison and J. R. Fisher (1974, Comp. Biochem. Physiol.47B, 27–32) for adenosine deaminase. The parameters E_α (μ at infinitely low substrate concentration), E_β (μ at infinitely high substrate concentration), and K_t (the concentration of substrate when $\text{μ =}\text{[E}{}_{\mathrm{\alpha }}\text{+ E}{}_{\mathrm{\beta }}\text{]}\text{2}$) can be used to describe the temperature dependence of LDH activity at any substrate concentration and to compare the substrate-dependent temperature effects on the two isoenzymes. Significantly different E_β and K_t values for pyruvate-dependent temperature effects and different E_β, E_α, K_t, and E_β ? E_α (the range of possible μ values) for lactate-dependent temperature effects were found between M₄ and H₄ LDH isoenzymes. High lactate concentrations inhibited bat H₄ LDH activity to a greater degree at low temperatures than at high temperatures. Thus substrate inhibition plays an important role in the effect of temperature on the activity of H-type LDH at high lactate concentrations. Substrate-dependent temperature effects on bat LDH activity were the result of temperature effects on the apparent K_m value of the respective substrate. Since both the apparent K_m for pyruvate and the K_i for the competitive inhibitor oxamate decreased with decreasing temperature, the substrate-dependent temperature effects observed for pyruvate probably resulted from an increased affinity between pyruvate and the LDH-NADH complex with decreasing temperature.     

A thermodynamic description of the self-association of flavin mononucleotide.

Systematic heat of dilution studies of the self-association of flavin mononucleotide (FMN) have been conducted as a function of ionic strength (0.05 – 2.0 m) and pH (5–9) in aqueous solution. The data are adequately described by the expression $\text{Q}{}_{\mathrm{T}}\text{= ΔH ? (}\text{ΔH}\text{K}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(}\text{Q}{}_{\mathrm{T}}\text{c}{}_{\mathrm{T}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ for an isodesmic self-association. Q_T is the molar heat of dilution, ΔH and K are the derived enthalpy and equilibrium constants for the process FMN + (FMN)_i?1 ? (FMN)_i, and c_T is the concentration of FMN expressed in monomer units. Typical values derived for the various thermodynamic parameters at 25 °C are ΔG = ?3.56 kcal mol^?1, ΔH = ?3.72 kcal mol^?1, and ΔS = ?0.54 cal (mol · deg)^?1. These data, plus nuclear magnetic resonance evidence (Yagi, K., Ohishi, N., Takai, A., Kawano, K., and Kyogoku, Y., 1976, Biochemistry15, 2877–2880) argue in favor of an open-ended association of flavin molecules. The signs of the various thermodynamic parameters suggest that both hydrophobic and surface energy forces contribute significantly to the association, while the lack of any significant ionic strength dependence indicates the lack of any ionic centers in the association.     

Ouabain receptor interactions in (Na+ + K+)-ATPase preparations. II. Effect of cations and nucleotides on rate constants and dissociation constants

The action of ATP and its analogs as well as the effects of alkali ions were studied in their action on the ouabain receptor. One single ouabain receptor with a dissociation constant ($\text{K}{}_{\mathrm{<mtext>D</mtext>}}$) of 13 nM was found in the presence of ($\text{Mg}{}^{\mathrm{2+}}\text{+ P}{}_{\mathrm{i}}$) and ($\text{Na}{}^{\mathrm{+}}\text{+ Mg}{}^{\mathrm{2+}}\text{+ ATP}$). pH changes below pH 7.4 did not affect the ouabain receptor. Ouabain binding required Mg²⁺, where a curved line in the Scatchard plot appeared. The affinity of the receptor for ouabain was decreased by K⁺ and its congeners, by Na⁺ in the presence of ($\text{Mg}{}^{\mathrm{2+}}\text{+ P}{}_{\mathrm{i}}$), and by ATP analogs (ADP-C-P, ATP-OCH₃). Ca²⁺ antagonized the action of K⁺ on ouabain binding. It was concluded that the ouabain receptor exists in a low affinity (R_α) and a high affinity conformational state (R_β). The equilibrium between both states is influenced by ligands of $\text{(Na}{}^{\mathrm{+}}\text{+ K}{}^{\mathrm{+}}\text{)-ATPase}$. With 3 mM Mg²⁺ a mixture between both conformational states is assumed to exist (curved line in the Scatchard plot).     

Optimizing enzyme assays with one or two coupling enzymes

The cost of assays using one or two coupling enzymes is optimized by using equations to calculate the minimum amount(s) of enzyme(s) which should be used to obtain a given time (t₉₉) in which 99% of the rate V₀ of the first reaction is obtained. Using two coupling enzymes and given a value of t₉₉, the induction period L = L₁ + L₂ fulfills the requirement $\text{t}{}_{99}\text{2}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{4.6}\text{≥ L ≥}\text{t}{}_{99}\text{4.6}$, allowing one to choose a cost lower than that derived from the until-now generally applied assumption of t₉₉ = 4.6L. Being $\text{α =}\text{L}{}_1\text{L}{}_2$, in optimized assays the values α, t₉₉, and L are related by $\text{T}{}_{99}\text{=4.6}\text{(1+α)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{1+α}\text{L}$, thus allowing (graphical) calculation of the amounts of coupling enzymes which will minimize the cost for every chosen t₉₉ or L. Maximum practical rates, allowed in some supposed interesting cases, have been calculated.     

Laser-light scattering investigation of the micellar properties of gangliosides

The micellar properties of gangliosides in water solutions were investigated by quasielastic light scattering measurements. G_M1 and G_D1a gangliosides were isolated from calf brain, purified to more than 99% and dissolved in 0.025 M Tris—HCI buffer (pH 6.8) at 37°C. The average intensity of scattered light and the intensity correlation function were measured by an apparatus including a 5145 Å argon laser and a real-time digital correlator. The scattered intensity data allowed the derivation of an upper limit to the critical micelle concentration (c₀) and the evaluation of the molecular weight (M) of the micelle. The intensity correlation function gave the diffusion coefficient D, and hence the hydrodynamic radius R_H, and also contained information on the polydispersity of the sample. We find c_o < 1 × 10^?6 M for both G_M1 and G_D1a, M = 532 000 ± 50 000 and $\text{R}{}_{\mathrm{<mtext>H</mtext>}}\text{= 63.9 ± 2}\text{A}\text{?}$ for G_M1, and M = 417 000 ± 40 000 and $\text{R}{}_{\mathrm{<mtext>H</mtext>}}\text{= 59.5 ± 2}\text{A}\text{?}$ for G_D1a. The mixture 3:1 of the two gangliosides gave intermediate values for all examined parameters. The presence of cations, within the physiological concentration range. and, in particular of Ca²⁺, did not influence significantly the values of c_o and the main features of the micelle.     

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.     

In vitro reaction of radioactive 7beta, 8alpha, --dihydroxy--9alpha, 10alpha-epoxy--7,8,9,10--tetrahydrobenzo (A) pyrene and 7beta,8alpha--dihydroxy--9beta, 10beta--epoxy--7,8,9,10--tetrahydrobenzo (A) pyrene with DNA.

The $\text{in vitro}$ reaction of bacteriophage T7-DNA with the radioactive diastereomeric benzo(a)pyrene-diol-epoxides, (±) [${}^3\text{H}{}_9$, ${}^3\text{H}{}_{10}$]-7β,8α-dihydroxy-9α,10β-epoxy-7,8,9,10-tetrahydrobenzo(a)pyrene, and (±) [${}^3\text{H}{}_9$, ${}^3\text{H}{}_{10}$]-7β,8α-dihydroxy-9β,19β-epoxy-7,8,9,10-tetrahydrobenzo(1)pyrene, was investigated. Chromatographic analysis of digests of the DNA allowed the distinction of characteristic deoxynucleoside adduct peaks for the two benzo(a)pyrene-diol-epoxides. Our results, together with data from the literature, allow the identification of these adducts as mostly N₂-(10-7β,8α,9α-trihydroxy-7,8,9,10-tetrahydrobenzo(a)pyreney1)deoxyguanosine and N₂-(10-7β,8α,9β-trihydroxy-7,8,9,10-tetrahydrobenzo(a)pyreney1)deoxyguanosine, respectively. DNA-benzo(a)pyrene adducts with the same chromatographic properties were formed in mouse embryo fibroblasts upon treatment with benzo(a)pyrene.     

Protein affinities for small molecules: conceptions and misconceptions.

There is much confusion and error in published treatments of data for multiple binding of ligands (e.g., substrates) by proteins (e.g., enzymes). There is a widespread impression that if the equilibrium binding, r, of ligand, A, by a protein with n sites can be fitted to an equation with two hyperbolic terms, i.e., $\text{r=}\text{n}{}_{\mathrm{\alpha }}\text{k}{}_{\mathrm{\alpha }}\text{(A)}\text{1+k}{}_{\mathrm{\alpha }}\text{(A)}\text{+}\text{n}{}_{\mathrm{\beta }}\text{k}{}_{\mathrm{\beta }}\text{(A)}\text{1+k}{}_{\mathrm{\beta }}\text{(A)}\text{(n}{}_{\mathrm{\alpha }}\text{+n}{}_{\mathrm{\beta }}\text{=n)}$ then k_β and k_β are always the intrinsic binding constants for two sets of sites. Such a conclusion is often incorrect. For example, in many cases, the protein is constituted of identical protomers with initially identical sites for binding ligands, and yet graphical representations of the binding data appear to behave as if the sites are partitioned between two classes. Although the use of a linear combination of hyperbolic terms to represent binding of ligands by macromolecules always yields empirical parameters k_α, k_β … k_λ, they cannot correspond to site binding constants when there are interactions between sites. In some circumstances their values may even be imaginary, complex numbers. On the other hand, stoichiometric binding constants can be assigned unambiguously without making any assumption regarding the nature of the interactions among binding sites. These principles are illustrated concretely by analyses of binding measurements for several different proteins containing two to six sites.     

Hymenolepis diminuta: The non-saturable component of methionine uptake

Lussier P. E., Podesta R. B. and Mettrick D. F. 1982. Hymenolepis diminuta: the non-saturable component of methionine uptake. International Journal for Parasitoiogy12: 265–270. The concentration dependence of in vitro unidirectional methionine influx by Hymenolepis diminuta was analysed by the relation: $\text{J =}\text{(J}{}_{\mathrm{<mtext>m</mtext>}}\text{C}{}_{\mathrm{<mtext>b</mtext>}}\text{)}\text{(K}{}_{\mathrm{t}}\text{+ C}{}_{\mathrm{<mtext>b</mtext>}}\text{)}\text{+ K}{}_{\mathrm{d}}\text{(C}{}_{\mathrm{<mtext>b</mtext>}}\text{)}$, where J_m is the maximum uptake rate, K_t is the the apparent affinity constant and C_b is the medium substrate concentration. The linear component was separated using an asymptotic least squares curve fitting procedure and the resulting constant, K_d, is thought to be an apparent permeability coefficient. K_d may be a reflection of a simple diffusive component, a second mediated component or a combination of a passive and mediated influx. The low Q₁₀ value of the K_d's for methionine uptake (Q₁₀ = 1.31) indicated that this component is probably a reflection of diffusion within the membrane. However, the decrease in the K_d component in the presence of leucine and glycine, implies that there is also a small, second, mediated component in addition to the diffusive component. K_d derived from the asymptotic portion of the concentration-flux relation was compared with the residual flux of methionine after near complete inhibition of the mediated component with leucine and glycine. The K_d component was found to be pH-sensitive, increasing as the pH decreased and was not affected by external sodium. Results indicate that the mediated component of methionine influx was accelerated by increasing external Na⁺ and H⁺ concentrations.     

Cooperativity in ligand binding: a new graphic analysis.

When analyzing binding of ligands to macromolecules, the existence of site-site interactions complicates a straightforward interpretation of the binding parameters obtained through classical analytical methods, such as the Scatchard plot. For describing site-site interactions, we propose a new parameter, the $\text{average affinity}$ of the receptor sites, $\text{K}$, calculated as $\text{(}\text{B}\text{F}\text{)/(R}{}_{\mathrm{o}}\text{?B)}$. Plotting $\text{K}$ as a function of fractional occupancy ($\text{B}\text{R}{}_{\mathrm{o}}$), reveals that: (1) at very low occupancy a limiting high $\text{K}$ is obtained ($\text{K}$_e) (“empty sites” conformation); (2) when the fraction of sites filled increases above a certain threshold, $\text{K}$ begins to fall due to increasing site-site interactions until (3) a limiting low $\text{K}$ ($\text{K}$_f) is obtained (“filled sites” conformation). This method has been successfully applied to the negative cooperativity of insulin receptors.     

Bathymetric adaptations of reef-building corals at davies reef,great barrier reef,Australia. II. Light saturation curves for photosynthesis and respiration

Light saturation (P-I) curves for oxygen production and consumption were constructed in the laboratory for corals collected from depths of 1 to 45 m on the southeastern (seaward) side of Davies Reef, Great Barrier Reef, Australia. This depth range represents a gradient of from 82.6 to 2.9% of surface light, which was measured as photosynthetic photon flux density (PPFD) between 400 and 700 nm. Adaptative changes in photokinetic parameters were observed over the entire range of light intensities. The compensation intensity (I_c), I_k, the intensity at which photosynthesis was 95% light saturated (I_0.95), and the respiration rate (?R), all decreased with decreasing light intensity. The maximal rate of photosynthesis when normalized on the basis of coral chlorophyll-a content (P_ma^g) tended to decrease with decreasing irradiance but the change was not statistically significant. The $\text{P}\text{R}$ ratio ($\text{P}{}_{\mathrm{m}}{}^{\mathrm{g}}\text{?R}$), the initial slope of a light saturation curve (α), and the maximum rate of photosynthesis when normalized by coral protein content (P_mp^g), all increased with decreasing light intensity. The logarithms of the values for each variable parameter were proportional to the logarithms of the fraction of the surface PPFD (T) transmitted to the depth at which the corals grew. This enabled changes in these parameters to be accurately estimated for corals growing at any depth on the reef. Comparison of experimental data with published values for “saturating” irradiance and P_ma^g, suggests that the endosymbiotic algae within reef-building corals are photosynthetically intermediate between classical “sun” and “shade” plants.     

Respiration-driven proton translocation with nitrite and nitrous oxide in Paracoccus denitrificans

(1) $\text{H}$⁺/electron acceptor ratios have been determined with the oxidant pulse method for cells of denitrifying Paracoccus denitrificans oxidizing endogenous substrates during reduction of O₂, NO^?₂ or N₂O. Under optimal H⁺-translocation conditions, the ratios $\text{H}{}^{\mathrm{+}}\text{O}$, $\text{H}{}^{\mathrm{+}}\text{N}{}_2\text{O}$, $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂ and $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂O were 6.0–6.3, 4.02, 5.79 and 3.37, respectively. (2) With ascorbate/N,N,N′,N′-tetramethyl-p-phenylenediamine as exogenous substrate, addition of NO^?₂ or N₂O to an anaerobic cell suspension resulted in rapid alkalinization of the outer bulk medium. $\text{H}{}^{\mathrm{+}}\text{N}{}_2\text{O}$, $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂ and $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂O were ?0.84, ?2.33 and ?1.90, respectively. (3) The $\text{H}{}^{\mathrm{+}}\text{oxidant}$ ratios, mentioned in item 2, were not altered in the presence of $\text{valinomycin}\text{K}{}^{\mathrm{+}}$ and the triphenylmethylphosphonium cation. (4) A simplified scheme of electron transport to O₂, NO^?₂ and N₂O is presented which shows a periplasmic orientation of the nitrite reductase as well as the nitrous oxide reductase. Electrons destined for NO^?₂, N₂O or O₂ pass two H⁺-translocating sites. The $\text{H}{}^{\mathrm{+}}\text{electron}$ acceptor ratios predicted by this scheme are in good agreement with the experimental values.     

Intracellular ionic compartmentation, electrical membrane properties, and cell membrane permeability before and during first cleavage in the Ambystoma egg.

The intracellular ionic distribution in uncleaved and cleaving Ambystoma eggs was investigated by analysing the influx of ³H₂O, by determining the total content of Na⁺, K⁺ and Cl^? in extracts of eggs at different stages by both flame spectrophotometry and ion-selective microelectrodes, and by the continuous measurement of the Na⁺, K⁺ and Cl^? activities (a_Naⁱ, a_Kⁱ and a_Clⁱ) using intracellular ion-selective microelectrodes. The electrical membrane potential (E_m) and membrane resistance (R_m) were measured continuously in uncleaved and normally cleaving eggs as well as in eggs cleaving after removal of the vitelline membrane. The latter eggs expose their newly formed cleavage membrane to the external medium. Ionic permeability of the cell membrane before and during cleavage was analysed by a statistical comparison of the experimentally determined relationship between E_m and the ionic gradients across the cell membrane with those predicted theoretically from a constant field equation in dependence on the relative permeability, through insertion of the measured intracellular ion activities.³H₂O influx revealed the existence of a single intracellular water compartment (3.06 μl/egg) and a low water permeability (5.35 × 10^?5 cm sec^?1). Na⁺, K⁺ and Cl^? concentrations were constant at 54.1, 72.1 and 73.1 mM respectively, while a_Naⁱ, a_Kⁱ and a_Clⁱ were constant at 5.8, 51.8 and 59.7 mM respectively. It was concluded that all Cl^? ions are in solution, while 12.5% of all K⁺ and 86% of all Na⁺ is bound. The uncleaved egg showed a positive E_m of ca 40 mV and a specific membrane resistance of 39 kOhm cm². E_m could be described by a constant field equation with a permeability ratio $\text{P}{}_{\mathrm{<mtext>K</mtext>}}\text{P}{}_{\mathrm{<mtext>Na</mtext>}}\text{= 0.073}$. Shortly after the onset of first cleavage, E_m rapidly decreased concomitant with a rise in R_m (68.5 kOhm cm²). This was interpreted as a drop in Na⁺ permeability. During the cleavage process E_m progressively hyperpolarized and R_m decreased due to the insertion of a small fraction (3.3%) of the newly formed intercellular membrane into the cleavage furrow. This new membrane had a low specific resistance (0.69 kOhm cm²). Both in normally cleaving eggs and in eggs cleaving in the absence of the vitelline membrane E_m behaved according to the constant field equation, $\text{P}{}_{\mathrm{<mtext>Na</mtext>}}\text{P}{}_{\mathrm{<mtext>K</mtext>}}$ being 0.69 and 0.39, respectively. The differences with other amphibian eggs were discussed.     

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.     

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.