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.     

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.     

Flow analysis in a biological system adopting the buffer capacitor concept.

The flow measurement of each component in each compartment is important in works on transport phenomena in a biological system. The method of flow measurement was studied adopting the capacitor concept derived from network thermodynamics.A biologically active component i in a compartment is defined as follows,

$\text{n}{}_{\mathrm{i}}\text{=n}{}_1\text{+n}{}_2\text{=c}{}_1\text{V+c}{}_2\text{V}$

where the total quantity ni consists of a measurable form n_i (free form, conc. c₁) and concealed form n₂ (conc, c₂). Capacitor for the species i of a compartment is defined as follows,

$\text{C=}\text{d}\text{n}{}_{\mathrm{i}}\text{d}\text{μ}{}_{\mathrm{i}}\text{=}\text{1+}\text{c}{}_2\text{c}{}_1\text{c}{}_1\text{dV}\text{dμ}{}_{\mathrm{i}}\text{+}\text{1+}\text{dc}{}_2\text{dc}{}_1\text{v}\text{dc}{}_1\text{dμ}{}_{\mathrm{i}}$

,

$\text{=Ac}{}_1\text{dV}\text{dμ}{}_{\mathrm{i}}\text{+BV}\text{d}\text{c}{}_1\text{d}\text{t}$

Thus flow of each component is expressed as,

$\text{J}{}_{\mathrm{i}}\text{=}\text{d}\text{n}{}_{\mathrm{i}}\text{d}{}_{\mathrm{i}}\text{=}\text{d}\text{n}{}_{\mathrm{i}}\text{dμ}{}_{\mathrm{i}}\text{dμ}\text{n}{}_{\mathrm{i}}\text{dt}\text{=C}\text{d}\text{μ}{}_{\mathrm{i}}\text{dt}$

,

$\text{=Ac}{}_1\text{d}\text{V}\text{dt}\text{+BV}\text{d}\text{c}{}_1\text{dt}$

Method of determination of capacitor coefficients A and B by titration experiment was also considered. For an experimental case, the capacitance for H⁺ of blood compartment was determined. The relationship between the capacitor concept and the buffer value of Van Slyke was discussed.     

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.     

On equivalent forms of Whittaker's similarity index

For two N-species assemblages A, B with specific proportionate abundances of the ith species a_i, b_l respectively, we consider the equality

$\text{∑}\text{t=1}\text{N}\text{c}{}_{\mathrm{i}}\text{= 1?}\text{1}\text{2}\text{∑}\text{t=1}\text{N}\text{|a}{}_{\mathrm{i}}\text{?b}{}_{\mathrm{i}}\text{|, c}{}_{\mathrm{i}}\text{=}\text{a}{}_{\mathrm{i}}\text{a}{}_{\mathrm{i}}\text{? b}{}_{\mathrm{i}}\text{b}{}_{\mathrm{i}}\text{a}{}_{\mathrm{i}}\text{> b}{}_{\mathrm{i}}\text{, 0?a,b,c?1}$

. The left-hand term is known as Sanders' minimum faunal abundance value, while the right side is referred to as Whittaker's similarity index. Both measures are commonly used in community studies. Equality between these two measures obtains only when proportionate abundances are utilized. We develop equivalent formulation which is valid for absolute abundance data, reduces to the Sanders-Whittaker equality when proportionate abundance data are employed, and is more sensitive to differences in species abundance distributions. Namely, we show that

$\text{2}\text{α+β}\text{∑}\text{t=1}\text{N}\text{c}{}_{\mathrm{i}}\text{= 1 ?}\text{1}\text{α+β}\text{∑}\text{t=1}\text{N}\text{|a}{}_{\mathrm{i}}\text{?b}{}_{\mathrm{i}}\text{|}$

, where

$\text{α =}\text{∑}\text{t=1}\text{N}\text{a}{}_{\mathrm{i}}\text{, β =}\text{∑}\text{t=1}\text{N}\text{b}{}_{\mathrm{i}}$

, and the a's, b's c's are as defined above.     

Dipole moments of random coil polypeptides

The Rotational Isomeric States model is applied to calculate dipole moments of polypeptides of the twenty natural α-amino acids in the random coil state. Dipole moments of each repeat unit (μ_i), are evaluated using a quantum mechanics procedure. Dipole moment ratios ($\text{D}{}_{\mathrm{x}}\text{=}\text{〈μ}{}^2\text{〉}\text{x}\text{μ}{}_{\mathrm{i}}{}^2\text{,}\text{x = number of repeat units}$) of homopolypeptides are calculated and extrapolated to x →?. With a few exceptions, D_? = 0.36 ± 0.1. Ten actual proteins and three enzymes are also studied; their dipole ratios (D_x′ =〈μ〉/x) range from 7.34 to 10.57 in 10^?59 C² m² (6.6–9.5 D²). Diffferences in the values of D_x′ are due mainly to the different contributions, μ_i, of the amino acid residues contained in each polymer, whereas the sequence of amino acids has a very minor effect.     

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.     

Energetics of coupled Na+ and Cl− entry into epithelial cells of bullfrog small intestine

Na⁺, K⁺ and Cl^? concentrations ($\text{c}{}_{\mathrm{j}}{}^{\mathrm{<mtext>i</mtext>}}$) and activities ($\text{a}{}_{\mathrm{j}}{}^{\mathrm{<mtext>i</mtext>}}$), and mucosal membrane potentials ($\text{E}{}_{\mathrm{<mtext>m</mtext>}}$) were measured in epithelial cells of isolated bullfrog (Rana catesbeiana) small intestine. Segments of intestine were stripped of their external muscle layers, and bathed (at 25°C and pH 7.2) in oxygenated Ringer solutions containing 105 mM Na⁺ and Cl^? and 5.4 mM K⁺. Na⁺ and K⁺ concentrations were determined by atomic absorption spectrometry and Cl^? concentrations by conductometric titration following extraction of the dried tissue with 0.1 M HNO₃. ¹⁴C-labelled inulin was used to determine extracellular volume. $\text{E}{}_{\mathrm{<mtext>m</mtext>}}$ was measured with conventional open tip microelectrodes, $\text{a}{}_{\mathrm{<mtext>Cl</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ with solid-state Cl^?-selective silver microelectrodes and $\text{a}{}_{\mathrm{<mtext>Na</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ and $\text{a}{}_{\mathrm{<mtext>K</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ with Na⁺- and K⁺-selective liquid ion-exchanger microelectrodes. The average $\text{E}{}_{\mathrm{<mtext>m</mtext>}}$ recorded was ?34 mV. $\text{c}{}_{\mathrm{<mtext>Na</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$, $\text{c}{}_{\mathrm{<mtext>K</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ and $\text{c}{}_{\mathrm{<mtext>Cl</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ were 51, 105 and 52 mM. The corresponding values for $\text{a}{}_{\mathrm{<mtext>Na</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$, $\text{a}{}_{\mathrm{<mtext>K</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ and $\text{a}{}_{\mathrm{<mtext>Cl</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ were 18, 80 and 33 mM. These results suggest that a large fraction of the cytoplasmic Na⁺ is ‘bound’ or sequestered in an osmotically inactive form, that all, or virtually all the cytoplasmic K⁺ behaves as if in free solution, and that there is probably some binding of cytoplasmic Cl^?. $\text{a}{}_{\mathrm{<mtext>Cl</mtext>}}{}^{\mathrm{<mtext>i</mtext>}}$ significantly exceeds the level corresponding to electrochemical equilibrium across the mucosal and baso-lateral cell membranes. Earlier studies showed that coupled mucosal entry of Na⁺ and Cl^? is implicated in intracellular Cl^? accumulation in this tissue. This study permitted estimation of the steady-state transapical Na⁺ and Cl^? electrochemical potential differences (Δμ&#x0304;Na and Δμ&#x0304;Cl). Δμ&#x0304;Na (?7000 J · mol^?1; cell minus mucosal medium) was energetically more than sufficient to account for Δμ&#x0304;Cl (1000–2000 J · mol^?1).     

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.     

Characterization of sodium and proton flows in sub-bacterial particles of Halobacterium halobium in terms of nonequilibrium thermodynamics

A thermodynamic characterization of the Na⁺-H⁺ exchange system in Halobacterium halobium was carried out by evaluating the relevant phenomenological parameters derived from potential-jump measurements. The experiments were performed with sub-bacterial particles devoid of the purple membrane, in 1 M NaCl, 2 M KCl, and at pH 6.5–7.0. Jumps in either pH or pNa were brought about in the external medium, at zero electric potential difference across the membrane, and the resulting relaxation kinetics of protons and sodium flows were measured. It was found that the relaxation kinetics of the proton flow caused by a pH-jump follow a single exponential decay, and that the relaxation kinetics of both the proton and the sodium flows caused by a pNa-jump also follow single exponential decay patterns. In addition, it was found that the decay constants for the proton flow caused by a pH-jump and a pNa-jump have the same numerical value. The physical meaning of the decay constants has been elucidated in terms of the phenomenological coefficients (mobilities) and the buffering capacities of the system. The phenomenological coefficients for the Na⁺-H⁺ flows were determined as differential quantities. The value obtained for the total proton permeability through the particle membrane via all available channels, $\text{L}{}_{\mathrm{<mtext>H</mtext>}}\text{= (}\text{?J}{}_{\mathrm{<mtext>H\; +</mtext>}}\text{?Δ}\text{pH}\text{)}{}_{\mathrm{<mtext>\Delta \psi ,\Delta </mtext><mtext>pNa</mtext>}}$, was in the range of 850–1150 nmol H⁺·(mg protein)^?1·h^?1·(pH unit)^?1 for four different preparations; for the total Na⁺ permeability, $\text{L}{}_{\mathrm{<mtext>Na</mtext>}}\text{= (}\text{?J}{}_{\mathrm{<mtext>Na</mtext>}}{}^{\mathrm{+}}\text{?Δ}\text{pNa}\text{)}{}_{\mathrm{<mtext>\Delta \psi ,\Delta </mtext><mtext>pH</mtext>}}$, it was 1620–2500 nmol Na⁺·(mg protein)^?1·h^?1·(pNa unit)^?1; and for the proton ‘cross-permeability’, $\text{L}{}_{\mathrm{<mtext>HNa</mtext>}}\text{= (}\text{?J}{}_{\mathrm{<mtext>H</mtext>}}{}^{\mathrm{+}}\text{?Δ}\text{pNa}\text{)}{}_{\mathrm{<mtext>\Delta \psi ,\Delta </mtext><mtext>pH</mtext>}}$, it was 220–580 nmol H⁺·(mg protein)^?1·h^?1·(pNa unit)^?1, for different preparations. From the above phenomenological parameters, the following quantities have been calculated: the degree of coupling (q), the maximal efficiency of Na⁺-H⁺ exchange (η_max), the flow and force efficacies (?) of the above exchange, and the admissible range for the values of the molecular stoichiometry parameter (r). We found q ? 0.4; η_max ? 5%; 0.36 ? r ? 2; ?_JNa⁺ ? 1.3 · 10⁵μmol · (RT unit)^?1 at J_Na = 1 μmolNa⁺ · (mgprotein)^?1 · h^?1; and ?_ΔpNa ? 5 · 10⁴ ΔpNa · (mg protein) · h · (RT unit)^?1 at ΔpNa = 1 unit, for different preparations.     

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.     

A theory of dynamic and steady responses in chemoreception

A theoretical model which can account for both the dynamic and steady responses is proposed based on the occupation theory. The reaction scheme used is;

Here, S and A are stimulus chemicals and receptor sites unbound, respectively. The binding of S to A leads to an active complex (SA)_active, which is successively transformed into an inactive complex (SA)_active. The response is assumed to be proportional to number of (SA)_active. When a stimulating solution is applied instantaneously at t = 0, the solution to the set of differential equations based on the above scheme is obtained as follows;

where p and C stand for the fraction of (SA)_active to the total number of receptor sites and stimulus concentration, respectively, and α_i, and ω_i (i = 1, 2) are numerical parameters depending on the rate constants and on C. The steady response is expressed as the third term in the above equation, which indicates that the response accords with the Beidler taste equation. Mathematical analysis of the above scheme shows that the dynamic response appears when k₁C > k_?2, and the calculated results for the dynamic response agree approximately with the Hill equation. The Hill coefficient lays within 1·00 and 0·79 and reaches unity with increasing $\text{k}{}_{\mathrm{?1}}\text{k}{}_2$, which implies that the dynamic response under this condition satisfies the Beidler taste equation. For the case of gradual application of stimuli, i.e. the experimental condition, the time course of p is simulated with use of an analogue computer rather than with a numerical solution to the above equation. The results indicate that the dynamic response diminishes with decreasing the application speed of stimulus solution. The present theory accounts consistently for various experimental data observed in the chemoreceptor systems.     

Kinetics of active and passive components of water exchange between the air and a mite, Dermatophagoides farinae

Female North American house dust mites were found to exchange water with the ambient air from two compartments. At humidities above the critical equilibrium activity (CEA), transpiration out of a single large compartment was observed using HTO as a tracer for water. Total sorption into this compartment was also observed by following changes in the specific radioactivity. The sorption data required that an active process or pump be present. The water in this pump is the second compartment above the CEA. Below the CEA the large compartment could be identified as a compartment characterized by a small transpiration rate constant. The pump below the CEA becomes a rapidly transpiring fast compartment. By separating the water pool into two compartments, it was possible to relate a_v to k and $\text{m}\text{?}{}_{\mathrm{<mtext>S</mtext>}}$. The major effect of a_v on k was related to its effect on the permeability of the cuticle. The influence of a_v on $\text{m}\text{?}{}_{\mathrm{<mtext>S</mtext>}}$ was different for active and passive sorption. Above the CEA the pump operated at full capacity and active $\text{m}\text{?}{}_{\mathrm{<mtext>S</mtext>}}$ was directly proportional to a_v. Passive sorption was influenced by a_v in two ways. The driving force for $\text{m}\text{?}{}_{\mathrm{<mtext>S</mtext>}}$ was further reduced below saturation by the effect of a_v on the permeability of the exchange surface.     

The concept of high- and low-affinity reactions in bovine cytochrome c oxidase steady-state kinetics

(1) Analysis of the data from steady-state kinetic studies shows that two reactions between cytochrome c and cytochrome c oxidase sufficed to describe the concave Eadie-Hofstee plots ($\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 1 · 10}{}^{\mathrm{?8}}\text{M}$ and $\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 2 · 10}{}^{\mathrm{?5}}\text{M}$). It is not necessary to postulate a third reaction of $\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{? 10}{}^{\mathrm{?6}}\text{M}$. (2) Change of temperature, type of detergent and type of cytochrome c affected both reactions to the same extent. The presence of only a single catalytic cytochrome c interaction site on the oxidase could explain the kinetic data. (3) Our experiments support the notion that, at least under our conditions (pH 7.8, low-ionic strength), the dissociation of ferricytochrome c from cytochrome c oxidase is the rate-limiting step in the steady-state kinetics. (4) A series of models, proposed to describe the observed steady-state kinetics, is discussed.     

Infinite cis influx of cyclic AMP into human erythrocyte ghosts

Infinite cis uptake of cyclic AMP into red blood cell ghosts has been measured. The $\text{K}{}_{\mathrm{<mtext>i</mtext><mtext>c</mtext>}}{}^{\mathrm{<mtext>oi</mtext>}}$ is calculated from two different integrated rate equations that are applicable when the substrate concentration is unsufficient to cause volume changes. Values of 0.69 mM and 0.66 mM are obtained for the infinite cis$\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ at 30°C using these procedures. These values are only slightly higher than that predicted from zero trans net flux experiments.Lowering the temperature reduces $\text{K}{}_{\mathrm{<mtext>i</mtext><mtext>c</mtext>}}{}^{\mathrm{<mtext>oi</mtext>}}$ from 0.69 mM at 30°C to 0.478 mM at 20°C, 0.108 mM at 10°C and 0.072 mM at 4°C ($\text{Q}{}_{10}\text{= 2.4}$). The $\text{Q}{}_{10}$ for activation of influx permeability of 10^?5 M cyclic AMP is 1.55.     

Soluble and enzymatically stable (Na++K+)-ATPase from mammalian kidney consisting predominantly of protomer αβ-units: Preparation,assay and reconstitution of active Na+, K+transport

Soluble $\text{(Na}{}^{\mathrm{+}}\text{+K}{}^{\mathrm{+}}\text{)-ATPase}$ consisting predominantly of αβ-units with $\text{M}{}_{\mathrm{<mtext>r</mtext>}}$ below 170 000 was prepared by incubating pure membrane-bound $\text{(Na}{}^{\mathrm{+}}\text{+K}{}^{\mathrm{+}}\text{)-ATPase}$ (35–48 μmol P_i/min per mg protein) from the outer renal medulla with the non-ionic detergent dodecyloctaethyleneglycol monoether (C₁₂E₈). $\text{(Na}{}^{\mathrm{+}}\text{+K}{}^{\mathrm{+}}\text{)-ATPase}$ and potassium phosphatase remained fully active in the detergent solution at C₁₂E₈/protein ratios of 2.5–3, at which 50–70% of the membrane protein was solubilized. The soluble protomeric $\text{(Na}{}^{\mathrm{+}}\text{+K}{}^{\mathrm{+}}\text{)-ATPase}$ was reconstituted to Na⁺, K⁺ pumps in phospholipid vesicles by the freeze-thaw sonication procedure. Protein solubilization was complete at C₁₂E₈/protein ratios of 5–6, at the expense of partial inactivation, but $\text{(Na}{}^{\mathrm{+}}\text{+K}{}^{\mathrm{+}}\text{)-ATPase}$ and potassium phosphatase could be reactivated after binding of C₁₂E₈ to Bio-Beads SM2. At C₁₂E₈/protein ratios higher than 6 the activities were irreversibly lost. Inactivation could be explained by delipidation. It was not due to subunit dissociation since only small changes in sedimentation velocities were seen when the C₁₂E₈/protein ratio was increased from 2.9 to 46. As determined immediately after solubilization, $\text{S}{}_{\mathrm{<mtext>20,</mtext><mtext>w</mtext>}}$ was 7.4 S for the fully active $\text{(Na}{}^{\mathrm{+}}\text{+K}{}^{\mathrm{+}}\text{)-ATPase}$, 7.3 S for the partially active particle, and 6.5 S for the inactive particle at high C₁₂E₈/protein ratios. The maximum molecular masses determined by analytical ultracentrifugation were 141 000–170 000 dalton for these protein particles. Secondary aggregation occurred during column chromatography, with formation of enzymatically active $\text{(αβ)}{}_2\text{-}\text{dimers}$ or $\text{(αβ)}{}_3\text{-}\text{trimers}$ with $\text{S}{}_{\mathrm{<mtext>20,</mtext><mtext>w</mtext>}}\text{=10–12}$ S and apparent molecular masses in the range 273 000–386 000 daltons. This may reflect non-specific time-dependent aggregation of the detergent micelles.     

Control of mitochondrial respiration: a quantitative evaluation of the roles of cytochrome c and oxygen.

The dependence of the mitochondrial respiratory rate on the reduction of cytochrome c has been measured as a function of the exogenous $\text{[}\text{ATP}\text{]}\text{[}\text{ADP}\text{][}\text{P}{}_{\mathrm{i}}\text{]}$ ratio and pH. The respiratory rate at $\text{[}\text{ADP}\text{]}\text{[}\text{ADP}\text{][}\text{P}{}_{\mathrm{i}}\text{]}$ values of less than 10^-1m^-1 is proportional to the reduction of cytochrome c and independent of pH from pH 6.5 to pH 8.O. The maximal turnover number (at 100% reduction) for cytochrome c is approximately 70 s^?1. As the $\text{[}\text{ATP}\text{]}\text{[}\text{ADP}\text{][}\text{P}{}_{\mathrm{i}}\text{]}$ ratio is increased from 10^?1m^?1 to 10⁴m^?1, the respiration at any given level of reduction of cytochrome c is progressively inhibited. Greater inhibition is observed at more oxidized levels of cytochorme c with respiratory control values for oxidation of reduced cytochrome c exceeding 10. The behavior of mitochondrial respiratory control is shown to be quantitatively consistent with a proposed mechanism in which the regulation occurs in the reaction of oxygen with cytochrome oxidase. A steady-state rate expression is derived which fits the mitochondrial respiratory rate dependence on (i) the extramitochondrial $\text{[}\text{ATP}\text{]}\text{[}\text{ADP}\text{][}\text{P}{}_{\mathrm{i}}\text{]}$ ratio; (ii) the level of reduction of cytochrome c (or the intramitochondrial $\text{[}\text{NAD}{}^{\mathrm{+}}\text{]}\text{[NADH])}$ at different $\text{[}\text{ATP}\text{]}\text{[}\text{ADP}\text{][}\text{P}{}_{\mathrm{i}}\text{]}$ values; (iii) the pH of the suspending medium. This rate expression appears to correctly predict the relationships of the cytoplasmic $\text{[}\text{ATP}\text{]}\text{[}\text{ADP}\text{][}\text{P}{}_{\mathrm{i}}\text{]}$ ratio, the mitochondrial $\text{[}\text{NAD}{}^{\mathrm{+}}\text{]}\text{[}\text{NADH}\text{]}$ ratio, and the mitochondrial respiratory rate in intact cells as well as suspensions of isolated mitochondria.