Nuclear magnetic resonance study of the rate of electron transfer between cytochrome c and iron hexacyanides

The rates of electron exchange between ferricytochrome c (C^III)3 and ferrocytochrome c (C^II) were observed as a function of the concentrations of ferrihexacyanide (Fe^III) and ferrohexacyanide (Fe^II) by monitoring the line widths of several proton resonances of the protein. Addition of Fe^II to C^III homogeneously increased the line widths of the two downfield paramagnetically shifted heme methyl proton resonances to a maximal value. This was interpreted as indicating the formation of a stoichiometric complex, C^III·Fe^II, in the over-all reaction:

$\text{C}{}^{\mathrm{III}}\text{+}\text{Fe}{}^{\mathrm{II}}\text{?}\text{k}{}_{\mathrm{?1}}\text{k}{}_1\text{C}{}^{\mathrm{III}}\text{·}\text{Fe}{}^{\mathrm{II}}\text{?}\text{k}{}_{\mathrm{?2}}\text{k}{}_2\text{C}{}^{\mathrm{II}}\text{·}\text{Fe}{}^{\mathrm{III}}\text{?}\text{k}{}_{\mathrm{?3}}\text{k}{}_3\text{C}{}^{\mathrm{III}}\text{+}\text{Fe}{}^{\mathrm{II}}$

Values for $\text{k}{}_1\text{k}{}_{\mathrm{?1}}\text{= 0.4 × 10}{}^3\text{m}{}^{\mathrm{?1}}\text{and}\text{k}{}_2\text{= 208}\text{s}{}^{\mathrm{?1}}$, respectively, were calculated from the maximal change in line width observed at pH 7.0 and 25 °C. Changes in the line width of C^III in the presence of Fe^II and either KCl or Fe^III suggest that complexation is principally ionic, that Fe^III and Fe^II compete for a common site. Addition of saturating concentrations of Fe^III to C^III produced only minor changes in the nuclear magnetic resonance spectrum of C^III suggesting that complexation occurs on the protein surface.Addition of Fe^III to C^II in the presence of excess Fe^II (to retain most of the protein as C^II) increased the line width of the methyl protons of ligated methionine 80. A value for k_?2 ≈ 2.08 × 10⁴ s^?1 was calculated from the dependence of linewidth on the concentration of Fe^II at 24 °C. These rates are shown to be consistent with the over-all rates of reduction and oxidation previously determined by stopped flow measurements, indicating that k₂ and k_?2 were rate limiting. From the temperature dependence the enthalpies of activation are 7.9 and 15.2 kcal/mol for k₂ and k_?2, respectively.     

Evidence for general catalysis and formation of nitrobenzene in the oxidation of phenylhydroxylamine in aqueous phosphate buffer

N-Phenylhydroxylamine is oxidized in aqueous phosphate buffer to nitrosobenzene, nitrobenzene, and azoxybenzene. Degradation is O₂ dependent and shows general catalysis by $\text{H}{}_2\text{PO}{}_4{}^{\mathrm{?}}$ (k₁ = 2.3 M^?2 sec^?1) and $\text{PO}{}_4{}^{\mathrm{?3}}$ (k₂ = 2.3 × 10⁵M^?2 sec^?1) or kinetically equivalent terms. Evidence is presented suggesting the intermediacy of a highly reactive species leading to these products.     

Kinetic studies on the reaction of ethylenediaminetetraacetatochromium(III) complex with hydrogen peroxide

The rate of reaction of [Cr(III)Y]_aq (Y is EDTA anion) with hydrogen peroxide was studied in aqueous nitrate media [μ = 0.10 M (KNO₃)] at various temperatures. The general rate equation, Rate = $\text{k}{}_1\text{+}\text{k}{}_2\text{K}{}_1\text{[H}{}^{\mathrm{+}}\text{]}{}^{\mathrm{?1}}\text{1 +}\text{K}{}_1\text{[H}{}^{\mathrm{+}}\text{]}{}^{\mathrm{?1}}$ [Cr(III)Y]_aq[H₂O₂] holds over the pH range 5–9. The decomposition reaction of H₂O₂ is believed to proceed via two pathways where both the aquo and hydroxo-quinquedentate EDTA complexes are acting as the catalyst centres. Substitution-controlled mechanisms are suggested and the values of the second-order rate constants k₁ and k₂ were found to be 1.75 × 10^?2 M^?1 s^?1 and 0.174 M^?1 s^?1 at 303 K respectively, where k₂ is the rate constant for the aquo species and k₂ is that for the hydroxo complex. The respective activation enthalpies (ΔH^*₁ = 58.9 and ΔH^*₂ = 66.5 KJ mol^?1) and activation entropies (ΔS^*₁ = ?85 and ΔS^*₂ = ?40 J mol^?1 deg^?1) were calculated from a least-squares fit to the Eyring plot. The ionisation constant pK₁, was inferred from the kinetic data at 303 K to be 7.22. Beyond pH 9, the reaction is markedly retarded and ceases completely at pH ? 11. This inhibition was attributed in part to the continuous loss of the catalyst as a result of the simultaneous oxidation of Cr(III) to Cr(VI).     

Equilibrium constants for association of guanidinium and ammonium ions with oxyanions: The effect of changing basicity of the oxyanion

Using guanidinium and n-butylammonium cations (C⁺) as models for the positively charged side chains in arginine and lysine, we have determined the association constants with various oxyanions by potentiometric titration. For a dibasic acid, H₂A, three association complexes may exist: $\text{K}{}_{\mathrm{<mtext>1M</mtext>}}\text{=}\text{[CHA]}\text{[C}{}^{\mathrm{+}}\text{]}\text{[HA}{}^{\mathrm{?}}\text{]}$; $\text{K}{}_{\mathrm{<mtext>1D</mtext>}}\text{=}\text{[CA}{}^{\mathrm{?}}\text{]}\text{[C}{}^{\mathrm{+}}\text{]}\text{[A}{}^{\mathrm{2?}}\text{]}$; $\text{K}{}_{\mathrm{<mtext>2D</mtext>}}\text{=}\text{[C}{}_2\text{A]}\text{[C}{}^{\mathrm{+}}\text{]}\text{[CA}{}^{\mathrm{?}}\text{]}$. For guanidinium ion and phosphate, K_1M = 1.4, K_1D = 2.6, and K_2D = 5.1. The data for carboxylates indicate that the basicity of the oxyanion does not affect the association constant: acetate, pK_a = 4.8, K_1M = 0.37; formate, pK_a = 3.8, K_1M = 0.32; and chloroacetate, pK_a = 2.9, K_1M = 0.43, all with guanidinium ion. Association constants are also reported for carbonate, dimethylphosphinate, benzylphosphonate, and adenylate anions.     

Model of singlet oxygen scavenging by α-tocopherol in biomembranes

Quenching of singlet molecular oxygen (${}^1\text{Δ}{}_{\mathrm{g}}\text{O}{}_2$) by α-tocopherol (I) involves the hydroxy function of the chromanol ring of I. In phosphatidylcholine (PC) uni- and multilamellar vesicles this structural element of I is localized at the interface polar headgroup/hydrophobic core. A dielectric constant of ? ～ 25 was determined for this special region of the PC bilayer. The ratio k_Q/k_R of rate constants of quenching processes (k_Q) and irreversible reactions (k_R) of I with ${}^1\text{Δ}{}_{\mathrm{g}}\text{O}{}_2$ increases with decreasing polarity of the solvent. In ethanolic solutions where ? = 25.5, k_Q/k_R is about 40. Extrapolation of these results to phospholipid bilayers suggests that at the nearness of the ester carbonyl oxygen of the PC fatty acid moieties, α-tocopherol can deactivate approximately 40 ${}^1\text{Δ}{}_{\mathrm{g}}\text{O}{}_2$ molecules before being destroyed. It is concluded that in vivo, one may expect to find a higher k_Q/k_R ratio if the chromanol ring of I hides within the more hydrophobic interiors of the membrane surface peptides.     

Influence of ionic strength upon the proton inventory for the water-catalyzed hydrolysis of N-acetylbenzotriazole

Proton inventory investigations of the hydrolysis N-acetylbenzotriazole at pH 3.0 (or the equivalent point on the pD rate profile) have been conducted at two different temperatures and at ionic strengths ranging from 0 to 3.0 M. The solvent deuterium isotope effects and proton inventories are remarkably similar over this wide range of conditions. The proton inventories suggest a cyclic transition state involving four protons contributing to the solvent deuterium isotope effect for the water-catalyzed hydrolysis. The hydrolysis data are described by the equation $\text{k}{}_{\mathrm{n}}\text{= k}{}_{\mathrm{<mtext>o</mtext>}}\text{(1 ? n + nπ}{}_{\mathrm{<mtext>a</mtext>}}{}^1\text{)}{}^4$ with $\text{π}{}_{\mathrm{<mtext>a</mtext>}}{}^1\text{～ 0.74}$, where k_o is the observed first-order rate constant in protium oxide, n is the atom fraction of deuterium in the solvent, k_n is the rate constant in a protium oxide-deuterium oxide mixture, and $\text{π}{}_{\mathrm{<mtext>a</mtext>}}{}^1$ is the isotopic fractionation factor.     

Interaction of lymphocytes and macrophage cell line cells (M1 cells). I. Functional maturation and appearance of Fc receptors im M1 cells

M₁ cells, which are cell line cells established from myeloid leukemia cells of the SL strain mouse, can differentiate from blast cells ($\text{M}{}_1{}^{\mathrm{?}}$) to mature macrophages ($\text{M}{}_1{}^{\mathrm{+}}$) within 48 hr, when they are cultured with conditioned medium (CM) obtained from murine embryonic fibroblasts. While $\text{M}{}_1{}^{\mathrm{?}}$ cells have no phagocytic activity nor Fc receptor (FcR), $\text{M}{}_1{}^{\mathrm{+}}$ cells possess both characteristics. The appearance of FcR is temperature-dependent and inhibited by a metabolic inhibitor, cycloheximide. FcR on $\text{M}{}_1{}^{\mathrm{+}}$ cells is resistant to trypsin and pronase. $\text{M}{}_1{}^{\mathrm{+}}$ cells improve the viability of macrophage-depleted SL splenic lymphocytes and restore the in vitro secondary plaque forming cell response of macrophage-depleted spleen cells to particulate and soluble antigens. $\text{M}{}_1{}^{\mathrm{?}}$ cells lack this macrophage-substituting capacity. Mm₁ cells, mutant cells from M₁ cells, having FcR and higher phagocytic activity than $\text{M}{}_1{}^{\mathrm{+}}$ cells, are also devoid of this capacity.     

A convective mass transfer model for determining intestinal wall permeabilities: laminar flow in a circular tube

A convective mass transfer model as analyzed and developed for use in determining intestinal wall permeabilities from external perfusion experiments. Analysis of the model indicates that the ratio of the exit to inlet concentration $\text{C}{}_{\mathrm{m}}\text{C}{}_0$ is a function of only two dimensionless independent variables, the wall permeability, $\text{P}{}_{\mathrm{w}}{}^1$ and Graetz number, Gz = πDL/2Q. The Graetz number contains the independent variables of interest, length, diflusivity, and flow rate. The radius of the intestine is included implicitly in the flow rate. Since $\text{C}{}_{\mathrm{m}}\text{C}{}_0$ and Gz are the experimental quantities, and the solution to the model system contains P_ω¹ implicitly, a convenient approximate method is developed which allows a direct calculation of P_ω¹. This method is in error by 10–20% in the worst cases. The approach is illustrated by application to the determination of the wall permeabilities for two non polar compounds.     

Structure and action of heteronemertine polypeptide toxins Binding of cerebratulus lacteus toxin B-IV to axon membrane vesicles

The binding of the crustacean selective protein neurotoxin, toxin B-IV, from the nemertine Cerebratulus lacteus to lobster axonal vesicles has been studied. A highly radioactive, pharmacologically active derivative of toxin B-IV has been prepared by reaction with Bolton-Hunter reagent. Saturation binding and competition of ¹²⁵I-labeled toxin B-IV by native toxin B-IV have shown specific binding of ¹²⁵I-labeled toxin B-IV to a single class of binding sites with a dissociation constant of 5–20 nM and a binding site capacity, corrected for vesicle sidedness, of 6–9 pmol per mg membrane protein. This compares to a value of 3.8 pmol [³H]saxitoxin bound per mg in the same tissue. Analysis of the kinetics of toxin B-IV association ($\text{k}{}_{\mathrm{+1}}\text{=7.3·10}{}^5\text{M}{}^{\mathrm{?1}}\text{·s}{}^{\mathrm{?1}}$) and dissociation ($\text{k}{}_{\mathrm{?\; 1}}\text{=2·10}{}^{\mathrm{?3}}\text{s}{}^{\mathrm{?1}}$) shows a nearly identical $\text{K}{}_{\mathrm{<mtext>d</mtext>}}$ of about 3 nM. There is no competition of toxin B-IV binding by purified toxin from Leiurus quinquestriatus venom while Centruroides sculpturatus Ewing toxin I appears to cause a small enhancement of toxin B-IV binding.     

Inhibition of chymotrypsin by alkyl phosphonates: a quantitative structure-activity analysis.

A quantitative structure-activity relationship has been formulated for 53 alkyl phosphonates [R₂OPO(CH₃)SR₃] inhibiting chymotrypsin: . In this so-called bilinear model, k_i is the bimolecular rate constant (m^?1 s^?1), β is a disposable parameter evaluated by a computerized iterative procedure, MR is the molar refractivity of a substituent, $\text{σ}{}_3{}^1$ is Taft's polar parameter, and I is an indicator variable for substituents containing a sulfonium group. The correlation coefficient for this equation is 0.985. This quantitative structure-activity relationship is compared with those previously formulated for the action of chymotrypsin on acylamino acid ester substrates.     

A stable traveling-wave solution of a model of cellular control processes with positive feedback

Edelstein's model

$\text{?E}\text{?τ}\text{=F(M, E)}$

,

$\text{?M}\text{?τ}\text{=G(M, E)+D}\text{?}{}^2\text{M}\text{?s}{}^2$

,

$\text{M(s,0)=?(s)}$

,

$\text{E(s,0)=ψ(s)}$

, where τ ? 0 and ?∞<s<∞, $\text{F(M, E>) = (K}{}_1\text{+M}{}^{\mathrm{m}}\text{)}\text{(K}{}_2\text{+M}{}^{\mathrm{m}}\text{)?k}{}_1\text{E, G(M, E)}\text{= k}{}_1\text{E ? k}{}_2\text{M,}$ m ? 2, describes the behavior of two basic chemical species during the cellular differentiation in a linear ensemble of the same cell type. We prove the existence and uniqueness of a travelling-wavefront solution. We also demonstrate one kind of stability for this solution.     

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.     

Kinetics of phospholipid exchange between bilayer membranes

In an accompanying publication by Duckwitz-Peterlein, Eilenberger and Overath ((1977) Biochim. Biophys. Acta 469, 311–325) it is shown that the exchange of lipid molecules between negatively charged vesicles consisting of total phospholipid extracts from Escherichia coli occurs by the transfer of single lipid monomers or small micelles through the water. Here a kinetic interpretation is presented in terms of a rate constant, $\text{k}{}_{\mathrm{?}}$, for the escape of lipid molecules from the vesicle bilayer into the water. The evaluated rate constants are $\text{k}{}_{\mathrm{?}}{}^{\mathrm{<mtext>P</mtext>}}\text{= (0.86 ± 0.05) · 10}{}^{\mathrm{?5}}\text{s}{}^{\mathrm{?1}}$ and $\text{k}{}_{\mathrm{?}}{}^{\mathrm{<mtext>E</mtext>}}\text{= (1.09 ± 0.13) · 10}{}^{\mathrm{?6}}\text{s}{}^{\mathrm{?1}}$ for phospholipid molecules with $\text{trans-}\text{Δ}{}^9\text{-hexadecenoate}$ and $\text{trans-}\text{Δ}{}^9\text{-octadecenoate}$, respectively, as the predominant acyl chain component. The rate constants are discussed in terms of the acyl chain and polar head group composition of the lipids.     

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.     

Effect of N-alkyl-N,N,N-trimethylammonium ions on phosphatidylcholine model membrane structure as studied by 31P-NMR

The interaction of |C_nH_2n+1N⁺(CH₃)₃| · I^? (n = 3, 6, 9, 12, 14, 16 or 18) with egg-yolk phosphatidylcholine-water dispersions has been studied by ³¹P-NMR spectroscopy. It is shown that the effective anisotropy of ³¹P chemical shift (?Δσ_eff) of the lamellar phospholipid liquid-crystalline phase L_α increases with increasing concentration and alkyl chain length of the drug. Addition of $\text{|}\text{C}{}_6\text{H}{}_{13}\text{N}{}^{\mathrm{+}}\text{(CH}{}_3\text{)}{}_3\text{| ·I}{}^{\mathrm{?}}$ or |C₉H₁₉N⁺(CH₃)₃|·I^? to the phospholipid-water dispersion at a molar ratio ammonium salt:phospholipid > 0.8 induces in the dispersion a structure with an effective isotropic phospholipid motion. This structure is unstable and slowly transforms into the hexagonal phase. These effects have not been observed in phospholipid-water dispersions mixed with the ammonium derivatives with the longer alkyl chains n  12, 14, 16 or 18. It is proposed that these results might explain the effects of the investigated drugs on the nerve, muscle and bacterial cells.     

The explicit analysis of consecutive pseudo-first-order reactions: Application to kinetics of thiolysis of dithiasuccinoyl (Dts) amino acids

An explicit set of general methods for the experimental determination of the rates k₁ and k₂ of consecutive pseudo-first-order reactions is described and discussed. These rely on the direct simultaneous analytical quantitation of the starting material, intermediate, and product of the reaction, and thus differ from present techniques based on measurement of coreactant consumption or coproduct appearance. The quantity $\text{k}{}^{\mathrm{<mtext>env</mtext>}}\text{=}\text{k}{}_1\text{k}{}_2\text{(k}{}_1\text{+ k}{}_2\text{)}$ is shown to define a good “envelope” approximation to product formation according to the simple law 100% [1 ? exp(?k^envt)]. The theory of envelopes is useful for comparing overall rates of reactions with widely differing values of $\text{κ =}\text{k}{}_2\text{k}{}_1$. The kinetic pattern of thiolysis of dithiasuccinoyl amino acids to carbamoyl disulfide intermediates to product free amino acids is analyzed and shown to agree quantitatively with theory.     

Preferential solvation of methylmercurated calf thymus deoxyribonucleic acid.

The changes in polymer-solvent interactions that occur when native calf thymus DNA is dialyzed against Na₂SO₄ solutions of a given ionic strength and buffer concentration but of varying concentrations in methylmercuric hydroxide have been investigated with the help of solution density measurements at 25 °C and pH 6.8–7.0. From measurements executed under equilibrium dialysis conditions at the three salt levels 5 mm, 0.05 m, and 0.5 m Na₂SO₄ (m refers to molality) and in the presence of 5 mm cacodylic acid buffer, the density increments $\text{(}\text{??}\text{?c}{}_2\text{)}{}_{\mathrm{\mu }}{}^0$ for native calf thymus DNA were determined as a function of CH₃HgOH concentration. $\text{(}\text{??}\text{?c}{}_2\text{)}{}_{\mathrm{\mu }}{}^0$ was found not to vary with organomercurial concentration, irrespective of the concentration of supporting electrolyte, until a certain CH₃HgOH concentration level has been reached, viz., , beyond which $\text{(}\text{??}\text{?c}{}_2\text{)}{}_{\mathrm{\mu }}{}^0$ increases strongly with increasing concentration of CH₃HgOH. As is shown by optical melting, $\text{(}\text{??}\text{?c}{}_2\text{)}{}_{\mathrm{\mu }}{}^0$ becomes a function of organomercurial concentration the moment DNA undergoes denaturation brought about by the complexing of CH₃HgOH with the various N-binding sites of the base residues in the DNA double helix.Polymer-solvent interactions, expressed in terms of preferential water interactions (“net hydration”) and preferential salt interactions (“salt solvation”), were derived from the $\text{(}\text{??}\text{?c}{}_2\text{)}{}_{\mathrm{\mu }}{}^0$ data in combination with data obtained on the preferential interaction of CH₃HgOH with denatured DNA and data on the partial specific volumes of all major solution components, gathered from density measurements on solutions with fixed concentrations of diffusible components. Evidence is presented which shows that denaturation in general decreases the net hydration while salt becomes preferentially associated with the polyelectrolyte. This process is further amplified by the interaction of CH₃HgOH with denatured DNA: Methylmercurated DNA alters the redistribution of diffusible components at dialysis equilibrium to such an extent that in a formal sense large amounts of water are rejected from the immediate vicinity of the polymer. The molecular implications of these findings are explored. The results are further discussed in the light of previous findings where the methylmercury-induced denaturation of DNA had been studied with the help of buoyant density measurements in a Cs₂SO₄ density gradient and by velocity-sedimentation in a variety of sulfate media.     

Construction and analytical applications of liquid membrane electrode for trinitrobenzenesulfonic acid (TNBS)

A new liquid membrane electrode which responds to trinitrobenzenesulfonate (TNBS^?) ion is described. The electrode exhibits very good experimental characteristics: (i) The working pH range is 2.0–12.5; (ii) its response is consistent with the Nernst equation in the range 1.10^?1–5.10^?5m; (iii) its response time is 5 s; and (iv) its selectivity for TNBS^? against 14 tested ions is very high. Ions such as $\text{ClO}{}_4{}^{\mathrm{?}}$, $\text{IO}{}_4{}^{\mathrm{?}}$, I^?, and biphthalates interfere with potentiometric selectivity coefficients in the range 1.0 × 10^?2–9.0 × 10^?2. The electrode is suitable for direct potentiometry, potentiometric titrations, and kinetic potentiometric methods. Instructions for the application of the electrode for the potentiometric assay of aminoacids are given. The application of the electrode in the potentiometric precipitation titration of methylene blue with TNBS, and its use in the kinetic potentiometric determination of aminoacids is also described. The electrode has very good slope stability (60 mV/decade change of activity) for a period ofat least 2 months.     

New experimental approach to the estimation of rate of electron transfer from the primary to secondary acceptors in the photosynthetic electron transport chain of purple bacteria

A method for calculating the rate constant ($\text{K}{}_{\mathrm{<mtext>A</mtext><mtext>1</mtext><mtext>A</mtext><mtext>2</mtext>}}$) for the oxidation of the primary electron acceptor (A₁) by the secondary one (A₂) in the photosynthetic electron transport chain of purple bacteria is proposed.The method is based on the analysis of the dark recovery kinetics of reaction centre bacteriochlorophyll (P) following its oxidation by a short single laser pulse at a high oxidation-reduction potential of the medium. It is shown that in Ectothiorhodospira shaposhnikovii there is little difference in the value of $\text{K}{}_{\mathrm{<mtext>A</mtext><mtext>1</mtext><mtext>A</mtext><mtext>2</mtext>}}$ obtained by this method from that measured by the method of Parson ((1969) Biochim. Biophys. Acta 189, 384–396), namely: $\text{(4.5±1.4) · 10}{}^3\text{s}{}^{\mathrm{?1}}$ and $\text{(6.9±1.2) · 10}{}^3\text{s}{}^{\mathrm{?1}}$, respectively.The proposed method has also been used for the estimation of the $\text{K}{}_{\mathrm{<mtext>A</mtext><mtext>1</mtext><mtext>A</mtext><mtext>2</mtext>}}$ value in chromatophores of Rhodospirillum rubrum deprived of constitutive electron donors which are capable of reducing P⁺ at a rate exceeding this for the transfer of electron from A₁ to A₂. The method of Parson cannot be used in this case. The value of $\text{K}{}_{\mathrm{<mtext>A</mtext><mtext>1</mtext><mtext>A</mtext><mtext>2</mtext>}}$ has been found to be $\text{(2.7±0.8) · 10}{}^3\text{s}{}^{\mathrm{?1}}$.The activation energies for the A₁ to A₂ electron transfer have also been determined. They are 12.4 kcal/mol and 9.9 kcal/mol for E. shaposhnikovii and R. rubrum, respectively.     

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.