Equilibrium,kinetic and structural properties of hemoglobin Cranston,an elongated β chain variant

Hemoglobin Cranston has an elongated β subunit owing to a frame shift mutation. Oxygen equilibrium measurements of stripped Hb Cranston³ at 20 °C in the absence of phosphate revealed a high affinity (P₅₀ = 0·2 mm Hg at pH 7), non-co-operative hemoglobin variant with markedly reduced Böhr effect ($\text{?Δ}\text{log}\text{P}{}_{50}\text{Δ}\text{pH}{}_{\mathrm{7–8}}\text{= 0·2}$). The addition of inositol hexaphosphate resulted in an overall decrease in oxygen affinity (P₅₀ = 0·7 mm Hg at pH 7), as well as an increase in co-operativity and Böhr effect ($\text{?Δ}\text{log}\text{P}{}_{50}\text{Δ}\text{pH}{}_{\mathrm{7–8}}\text{= 0·2}$). Rapid mixing and flash photolysis experiments reflected the equilibrium results. Over a pH range from 6 to 9 in the absence of phosphate, the rate of combination of carbon monoxide with Hb Cranston measured by a stopped-flow technique and following full or partial flash photolysis was extremely rapid (l′, l′₄, of ～ 6 × 10⁶m^?1s^?1). In rapid kinetic experiments the addition of inositol hexaphosphate lowered the value of l′ to ～ 0·5 × 10⁶m^?1s^?1 only after prior incubation with the deoxygenated protein. Inositol hexaphosphate had no effect on the rate of recombination of carbon monoxide following either full or partial flash photolysis. Overall oxygen dissociation and oxygen dissociation with carbon monoxide replacement, were measured and found to be slow (k, k₄～ 11 s^?1), consistent with a high affinity hemoglobin. Sedimentation equilibrium experiments revealed that Hb Cranston, at concentrations used in the functional studies, is somewhat less tetrameric than Hb A but nonetheless does not exist solely as a non-co-operative dimer. These kinetic and centrifugational findings in conjunction with X-ray diffraction evidence suggested that a high affinity tetramer of Hb Cranston exists which may equilibrate slowly with inositol hexaphosphate. Oxygen equilibrium measurements, ligand binding kinetics and X-ray diffraction studies on equivalent mixtures of Hb Cranston and Hb A revealed an interaction between these two hemoglobins in vitro that most probably exists in vivo. The presence of asymmetric hybrid molecules, α₂β^Aβ^Cranston, in the difference Fourier maps indicated that the hydrophobic tail of Hb Cranston is accommodated in the central cavity of the hybrid molecule between the two β chains and is relatively protected from the water environment, thus aiding in the stability of Hb Cranston in the red cell.     

Structural and functional studies of Hemoglobin Wayne: An elongated α-chain variant

Hemoglobin Wayne (Hb Wayne) is a frame-shift, elongated α-chain variant that exists in two forms, with either asparagine or aspartic acid as residue 139. Oxygen equilibrium studies showed that stripped Hb Wayne Asn and Hb Wayne Asp possessed high oxygen affinity ($\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 0.60}$ and 0.23 mmHg at pH 7, respectively), were non-co-operative and have a markedly reduced Bohr effect ($\text{?Δ}\text{log}\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{/}\text{pH}\text{(7}\text{to}\text{8) = 0.34}$ and 0.10, respectively). Adding organic phosphate results in a decreased oxygen affinity and increased Bohr effect for both Hbs Wayne. The overall rate of carbon monoxide binding at pH 7 (l′ = 5.6 × 10⁶m^?1s^?1) was similar for both stripped Hbs Wayne and was 25-fold more rapid than that of stripped Hb A. When organic phosphate was added, Hb Wayne Asn exhibited a homogeneous slower rate of carbon monoxide binding (l′ = 2.6 × 10⁶m^?1s^?1), whereas Hb Wayne Asp showed heterogeneous binding (l′ = 6.1 × 10⁶ and 2.6 × 10⁶m^?1s^?1 for fast and slow phases, respectively). The rates of overall oxygen dissociation and oxygen dissociation with carbon monoxide replacement for both Hbs Wayne were found to be slow compared to Hb A and uniquely different from each other. Similarly, sedimentation velocity experiments indicated that, although Hb Wayne Asn and Hb Wayne Asp were both less tetrameric than Hb A, each hemoglobin exhibited a distinct degree of oxygen-linked subunit dissociation. These observed differences in the allosteric properties of Hb Wayne Asn and Hb Wayne Asp appeared to be directly attributable to residue 139. The equilibrium and kinetic data are consistent with the X-ray diffraction analysis of Hb Wayne Asp, which shows that the C terminus of the deoxytetramers are severely disordered, a condition that results in major destabilization of the T conformation and disruption of normal hemoglobin function.     

Enthalpy changes for hemoglobin-ligand interactions: revised calorimetric data

Recently we reported values for the succesive enthalpy changes for the four steps of oxygen binding by diphosphoglycerate-free adult human hemoglobin [Biochem. Biophys. Res. Comm., $\text{56}$, 555 (1974)]. Systematic errors in the data render these results invalid. New data shows that cooperativity prevents resolution of successive heats of reaction and only average heats are currently accessible. At pH 7.4 and 6^o we obtain: $\text{Δ}\text{H[}\text{1}\text{4}\text{Hb+O}{}_2\text{→}\text{1}\text{4}\text{Hb (O}{}_2\text{)}{}_4\text{]=?13.2±0.4}$, $\text{Δ}\text{H[}\text{1}\text{4}\text{Hb(O}{}_2\text{)}{}_4\text{+CO→}\text{1}\text{4}\text{Hb(CO)}{}_4\text{+O}{}_2\text{]=?4.0±0.1}$, $\text{Δ}\text{H[}\text{1}\text{4}\text{Hb+CO→}\text{1}\text{4}\text{Hb(CO)}{}_4\text{] =?17.7±0.4 kcal/mole}$ ligand. These data form a consistent thermodynamic cycle.     

Carp hemoglobin: Functional analysis and thermodynamics of precise oxygen equilibria according to the simple sequential model of Koshland,Némethy and Filmer

Precise oxygen equilibrium curves for carp hemoglobin were determined at 15 °C in bis-Tris buffer, and in phosphate buffer in the presence and absence of P₆-inositol, and at various temperatures in phosphate buffer. Parameters of the Koshland, Némethy and Filmer (1966) (KNF) simple, sequential models (square and tetrahedral) were estimated by non-linear least-square fit of the experimental data to Hill plots. Non-, negative and positive co-operativity can be fitted by the KNF models. Considering equilibrium arguments, $\text{K}{}^2{}_{\mathrm{<mtext>AB</mtext>}}\text{K}{}_{\mathrm{<mtext>BB</mtext>}}$, the KNF parameter governing the co-operativity of the system, predicts a symmetry conserved mode of action in regions of high, positive co-operativity, and a symmetry non-conserved mode of action in regions of low, non- or negative co-operativity. The simple, sequential, square KNF model fits better the Hill plots than does the simple, sequential, tetrahedral KNF model. From the effect of temperature on carp hemoglobin in phosphate buffer, the heats and entropies of the subunit interaction parameter, $\text{K}{}^2{}_{\mathrm{<mtext>AB</mtext>}}\text{K}{}_{\mathrm{<mtext>BB</mtext>}}$, and of the oxygenation parameters, K_BBK_xBK_tAB and $\text{K}{}^{\mathrm{<mtext>3</mtext><mtext>2</mtext>}}{}_{\mathrm{<mtext>BB</mtext>}}\text{K}{}_{\mathrm{<mtext>xB</mtext>}}\text{K}{}_{\mathrm{<mtext>tAB</mtext>}}$, for the square and tetrahedral models, respectively, were calculated and show the square model to account well for previously published data on the carp hemoglobin molecule. This study indicates that the KNF model, in its simplest form, is capable of explaining many of the functional properties of cooperative systems, as opposed to the Monod, Wyman and Changeux (1965) model which seems only to be a special case of the KNF model in regions of high, positive co-operativity.     

Equilibrium and kinetic measurements of carbon monoxide binding to hemoglobin kansas in the presence of inositol hexaphosphate

Previous proton nuclear magnetic resonance (nmr) studies have indicated that inositol hexaphosphate (IHP) can stabilize hemoglobin (Hb) Kansas in a deoxy-like quaternary structure even when fully liganded with carbon monoxide (CO) (S. Ogawa, A. Mayer, and R. G. Shulman, 1972, Biochem. Biophys. Res. Commun., 49, 1485–1491). In the present report we have investigated both CO binding at equilibrium and the CO binding and release kinetics to determine if Hb Kansas + IHP is devoid of cooperativity, as would be suggested by the nmr studies just quoted. The equilibrium measurements show that Hb Kansas + IHP has a very low affinity for CO ($\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 1.2}\text{mm}$ Hg and K_eq = 5.4 × 10⁵M^?1) and almost no cooperativity (n = 1.1) at pH 7, 25 °C. The CO “on” and “off” kinetics also show no evidence for cooperativity. In addition, the equilibrium constant estimated from the kinetic rate constants (K_eq = 5.2 × 10⁵M^?1 with k_on = 1.03 × 10⁵M^?1 · S^? and k_off = 0.198 S^?1) is in excellent agreement with the equilibrium constant determined directly. Thus, both kinetic and equilibrium measurements allow us to conclude that CO binding to Hb Kansas + IHP occurs without significant cooperativity.     

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.     

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.     

Studies of the nucleotide-binding sites on the mitochondrial F1-ATPase through the use of a photoactivable derivative of adenylyl imidodiphosphate

(1) $\text{N-4-}\text{Azido}\text{-2-}\text{nitrophenyl}\text{-γ-[}{}^3\text{H]aminobutyryl-Ado}\text{PP[}\text{NH}\text{]P(}\text{NAP}{}_4\text{-}\text{Ado}\text{PP[}\text{NH}\text{]P)}$ a photoactivable derivative of 5-adenylyl imidodiphosphate (AdoPP[NH]P), was synthesized. (2) Binding of ³H]NAP₄-AdoPP[NH]P to soluble ATPase from beef heart mitochrondria (F₁) was studied in the absence of photoirradiation, and compared to that of $\text{[}{}^3\text{H]Ado}\text{PP[}\text{NH}\text{]P}$. The photoactivable derivative of AdoPP[NH]P was found to bind to F₁ with high affinity, like AdoPP[NH]P. Once $\text{[}{}^3\text{H]NAP}{}_4\text{-}\text{Ado}\text{PP[}\text{NH}\text{]P}$ had bound to F₁ in the dark, it could be released by AdoPP[NH]P, ADP and ATP, but not at all by NAP₄ or AMP. Furthermore, preincubation of F₁ with unlabeled AdoPP[NH]P, ADP, or ATP prevented the covalent labeling of the enzyme by $\text{[}{}^3\text{H]NAP}{}_4\text{-}\text{Ado}\text{PP[}\text{NH}\text{]P}$ upon photoirradiation. (3) Photoirradiation of F₁ by $\text{[}{}^3\text{H]NAP}{}_4\text{-}\text{Ado}\text{PP[}\text{NH}\text{]P}$ resulted in covalent photolabeling and concomitant inactivation of the enzyme. Full inactivation corresponded to the binding of about 2 mol $\text{[}{}^3\text{H]NAP}{}_4\text{-}\text{Ado}\text{PP[}\text{NH}\text{]P}\text{mol F}{}_1$. Photolabeling by NAP₄-AdoPP[NH]P was much more efficient in the presence than in the absence of MgCl₂. (4) Bound $\text{[}{}^3\text{H]NAP}{}_4\text{-}\text{Ado}\text{PP[}\text{NH}\text{]P}$ was localized on the α- and β-subunits of F₁. At low concentrations (less than 10 μM), bound $\text{[}{}^3\text{H]NAP}{}_4\text{-}\text{Ado}\text{PP[}\text{NH}\text{]P}$ was predominantly localized on the α-subunit; at concentrations equal to, or greater than 75 μM, both α- and β-subunits were equally labeled. (5) The extent of inactivation was independent of the nature of the photolabeled subunit (α or β), suggesting that each of the two subunits, α and β, is required for the activity of F₁. (6) The covalently photolabeled F₁ was able to form a complex with aurovertin, as does native F₁. The ADP-induced fluorescence enhancement was more severely inhibited than the fluorescence quenching caused by ATP. The percentage of inactivation of F₁ was virtually the same as the percentage of inhibition of the ATP-induced fluorescence quenching, suggesting that fluorescence quenching is related to the binding of ATP to the catalytic site of F₁.     

Heterozygote frequencies in small subpopulations.

The mean fixation index within subpopulations (F_IS) has been defined as $\text{F}\text{̄}{}_{\mathrm{IS}}\text{= ∑w}{}_{\mathrm{i}}\text{F}{}_{\mathrm{ISi}}\text{or as}\text{F}\text{̂}{}_{\mathrm{IS}}\text{=}\text{∑w}{}_{\mathrm{i}}\text{p}{}_{\mathrm{i}}\text{q}{}_{\mathrm{i}}\text{F}{}_{\mathrm{ISi}}\text{∑w}{}_{\mathrm{i}}\text{p}{}_{\mathrm{i}}\text{q}{}_{\mathrm{i}}$. The latter definition is preferred because it can be obtained from the two other fixation indices, F_ST and F_IT and because it is unaffected by the mean gene frequency. The expected frequency of heterozygotes in small subpopulations of dioecious organisms will exceed Hardy-Weinberg expectations and this can be measured by $\text{F}\text{̂}{}_{\mathrm{IS}}$. In an isolated subpopulation of constant variance effective size $\text{N,}\text{F}\text{̂}{}_{\mathrm{IS}}$ rapidly tends to $\text{1 − 4N}{}^2\text{(N − 1 + [N}{}^2\text{+ 1]}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}{}^2$. In the Island model of population structure, $\text{F}\text{̂}{}_{\mathrm{IS}}$ is approximately $\text{−(1 − m)}\text{N}\text{where}\text{m}$ is the immigration rate.When a sample is drawn from a natural population, the observed F_IS will depend upon the genetic structure of the population. The values of F_IS expected in three different types of population structure are discussed.     

Developmental biochemistry of cotton seed embryogenesis and germination. VII. Characterization of the cotton genome.

The DNA of cotton, Gossypium hirsutum, has been characterized as to spectral characteristics, buoyant density in CsCl, base composition, and genetic complexity. The haploid genome size is found to bo 0.795 pg DNA/cell. However, the amount of DNA per cell in the cotyledons increases during embryogenesis to an average ploidy level of 12N in the mature seed cotyledons. Reassociation kinetics indicate that this increase is due to endoreduplication of the entire genome.Non-repetitive deoxynucleotide sequences account for approximately 60.5% of the cotton genome ($\text{C}{}_0\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$pure⁵ = 437); highly repetitive sequences (> 10,000 repetition frequency) constitute about 7.7% of the genome. ($\text{C}{}_0\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{pure}\text{= 4.6 × 10}{}^{\mathrm{?4}}$) and intermediately repetitive sequences constitute the remaining 27% of the genome ($\text{C}{}_0\text{t}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{pure}\text{= 1.46}$). Hybridization of ¹²⁵I-labeled cytoplasmic ribosomal RNA to whole-cell DNA on filters and in solution indicate approximately 300 to 350 copies of the rRNA cistrons per haploid genome.The interspersion of repetitive sequences that reassociate between C₀t values of 0.1 and 50 with non-repetitive sequences of the cotton genome has been examined by determining the reassociation kinetics of DNA of varying fragment lengths and by the electron microscopy of reassociated molecules. About 60% of the genome consists of non-repetitive regions that average 1800 base-pairs interpersed with repetitive sequences that average 1250 base-pairs. Approximately 20% of the genome may be involved in a longer period interspersion pattern containing non-repetitive sequences of approximately 4000 base-pairs between repetitive sequences. Most of the individual sequences of the interspersed repetitive component are much smaller than the mass average size, containing between 200 and 800 base-pairs. Sequence divergence is evident among the members of this component.Highly repetitive sequence elements that are reassociated by a C₀t value of 0.1 average 2500 base-pairs in length, appear to have highly divergent regions and do not appear to be highly clustered. A portion of this highly repetitive component reassociates by C₀t = 10^?4, zero-time binding DNA, and accounts for less than 3% of the genome. At least a third of these sequences appear by electron microscopy to be intramolecular duplexes (palindromes) of 150 to 200 base-pairs and to occur in clusters.     

Studies on the mechanism of electron transport in the bc1-segment of the respiratory chain in yeast. II. The binding of antimycin to mitochondrial particles and the function of two different binding sites

1. In mitochondrial particles antimycin binds to two separate specific sites with dissociation constants $\text{K}{}_{\mathrm{<mtext>d</mtext><mtext>1</mtext>}}\text{≦ 4 · 10}{}^{\mathrm{?13}}\text{M}$ and $\text{K}{}_{\mathrm{<mtext>d</mtext><mtext>2</mtext>}}\text{= 3 · 10}{}^{\mathrm{?9}}\text{M}$, respectively.2. The concentrations of the two antimycin binding sites are about equal. The absolute concentration for each binding site is about 100 – 150 pmol per mg of mitochondrial protein.3. Antimycin bound to the stronger site mainly inhibits NADH- and succinate oxidase. Binding of antimycin to the weaker binding site inhibits the electron flux to exogenously added cytochrome c after blocking cytochrome oxidase by KCN.4. Under certain conditions cytochrome b and c₁ are dispensible components for antimycin-sensitive electron transport.5. A model of the respiratory chain in yeast is proposed which accounts for the results reported here and previously. (Lang, B., Burger, G. and Bandlow, W. (1974) Biochim. Biophys. Acta 368, 71–85).     

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.     

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.     

Effects of 5-hydroxylysine on acetylene reduction and NH4+-assimilation in the cyanobacterium Anabaena cylindrica.

5-hydroxylysine, an analogue of glutamate and lysine, causes $\text{NH}{}_4{}^{\mathrm{+}}$ production by N₂-fixing A. cylindrica; it also reversibly inhibits GS activity in vitro but has no effect on alanine dehydrogenase or GOGAT. On adding 5-hydroxylysine intracellular pools of glutamine, glutamate and aspartate decrease; those of alanine and serine increase. 5-hydroxylysine alleviates the inhibitory effect of $\text{NH}{}_4{}^{\mathrm{+}}$ on heterocyst production and C₂H₂ reduction and in $\text{NH}{}_4{}^{\mathrm{+}}\text{-grown}$ cultures results in heterocyst synthesis and in C₂H₂ reduction. The data suggest that the GS-GOGAT pathway is the sole route of importance in primary $\text{NH}{}_4{}^{\mathrm{+}}$ assimilation in A. cylindrica, that $\text{NH}{}_4{}^{\mathrm{+}}$ alone does not inhibit nitrogenase and heterocyst production, and that GS and/or a product is involved in regulating the production of both.     

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.     

Ruthenium(II) complexes derived from 2-(methylamino)pyridine

2-(Methylamino)pyridine reacts with RuCl₂(CO)₃ to give a carbamoyl complex, [$\text{Ru(C(O)N(CH}{}_3\text{)(C}{}_5\text{H}{}_4\text{N}$)Cl(CO)₂], which yields with pyridine (py) and acetylacetone (Hacac), respectively, [$\text{Ru(C(O)N(CH}{}_3\text{)C}{}_5\text{H}{}_4\text{N}$)Cl(CO)₂(py)] and [$\text{Ru(C(O)N(CH}{}_3\text{)C}{}_5\text{H}{}_4\text{N}$)(CO)₂(acac)]. These complexes are characterized spectroscopically. The amino group of the ligand is carbonylated and the resulted carbamoyl ligand is chelating through a pyridine ring-N and a carbamoyl-C atom. 2-Aminopyridine and 2-aminopyrimidine react similarly with RuCl₂(CO)₃ to give the corresponding carbamoyl complexes.