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.     

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.     

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.     

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.     

Cyclic AMP transport in human erythrocyte ghosts

10^?5 M cyclic AMP has high permeability in human erythrocyte ghosts ($\text{p = 0.061 · 10}{}^{\mathrm{?6}}\text{cm}\text{·}\text{s}{}^{\mathrm{?1}}$). Saturation of influx and efflux occurs. $\text{K}{}_{\mathrm{<mtext>z</mtext><mtext>t</mtext>}}{}^{\mathrm{<mtext>oi</mtext>}}\text{= 4.43}\text{mM}$. $\text{V}{}_{\mathrm{zt}}{}^{\mathrm{oi}}\text{= 259.6 μ}\text{M · min}{}^{\mathrm{?1}}$. $\text{K}{}_{\mathrm{<mtext>z</mtext><mtext>t</mtext>}}{}^{\mathrm{<mtext>io</mtext>}}\text{= 0.475 μ}\text{M}$. $\text{V}{}_{\mathrm{<mtext>z</mtext><mtext>t</mtext>}}{}^{\mathrm{<mtext>io</mtext>}}\text{= 28.3 μ}\text{M · min}{}^{\mathrm{?1}}$ at 30°C. Equilibrium exchange entry of cyclic AMP has similar kinetics to zero trans influx, though the system does show counterflow. Cythochalasin B is an apparent competitive inhibitor of cyclic AMP exit. ($\text{K}{}_{\mathrm{<mtext>i</mtext>}}\text{= 3.9 · 10}{}^{\mathrm{?7}}\text{M}$).Control experiments indicated that cyclic AMP remains intact during incubation with red blood cell ghosts and is contained within the intravesicular space during the transport experiments.     

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.     

Electrokinetic properties of (Na+, K+)-ATPase vesicles as studied by laser doppler spectroscopy

The technique of laser Doppler electrophoresis was applied for the study of the surface charge properties of (Na⁺,⁺)-ATPase containing microsomal vesicles derived from guinea-pig kidney. The influence of pH, the screening and binding of uni- and divalent cations and the binding of ATP show: (1) one net negative charge per protein unit with a $\text{p}\text{K = 3.9}$; (2) deviation from the Debye relation between surface potential and ionic strength for univalent cations, with no difference in the effect of Na⁺ and K⁺; (3) Mg²⁺ binds with an association constant of $\text{K}{}_{\mathrm{<mtext>a</mtext>}}\text{= 1.1 · 10}{}^2\text{M}{}^{\mathrm{?1}}$ while ATP binds with an apparent $\text{K}{}_{\mathrm{<mtext>a</mtext>}}\text{= 1.1 · 10}{}^4\text{M}{}^{\mathrm{?2}}$ for 1 mM Nacl, 0.2 mM KCI, 0.1 mM MgCl₂, 0.1 mM Tris-HCI (pH 7.3). The binding is weaker at higher Mg²⁺ concentrations. There is no ATP binding in the absence of Mg²⁺. In addition, the average vesicle size derived from the linewidth of the quasi-elastic light scattering spectrum is $\text{203.7 ± 15.2}\text{nm}$. In the presence of ATP a reduction in size is observed.     

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.     

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.     

Time lag in a model of a biochemical reaction sequence with end product inhibition

The model studied is that of Goodwin, in which all but one of the reactions obey linear kinetics, while the end-product inhibits the first reaction in a term of Michaelis-Menten form, with Hill coefficient ?:

$\text{z=}\text{∫}\text{?∞}\text{t}\text{x}{}_{\mathrm{n}}\text{(T)G(t?T)dt}$

The results obtained relate to time lag in the off diagonal terms in these equations. The time lag is taken in distributed form, for example replacing x_n in the first equation by

$\text{dx}{}_{\mathrm{t}}\text{dt}\text{=k}{}_1\text{x}{}_{\mathrm{t??}}\text{1?b}{}_1\text{x}{}_{\mathrm{t}}\text{, i=2, …n.}$

For any non-negative G, time lag in these terms can not destabilize the equilibrium point in the case ? = 1. For a particular class of functions G one can obtain some insight into the consequences of time lag by relating the model to that with a longer loop of reactions. Then known results can be used for general ? and n.     

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.     

Ammonium (methylammonium) transport by Klebsiella pneumoniae

Klebsiella pneumoniae can accumulate methylammonium up to 80-fold by means of a transport system as indicated by the energy requirement, saturation kinetics and a narrow pH profile around pH 6.8. Methylammonium transport (apparent $\text{K}{}_{\mathrm{<mtext>m</mtext>}}\text{= 100 μ}\text{M}$, $\text{V = 40 μ}\text{mol/min}$ per g dry weight at 15°C) is competitively inhibited by ammonium (apparent $\text{K}{}_{\mathrm{<mtext>i</mtext>}}\text{= 7 μ}\text{M}$). The low $\text{K}{}_{\mathrm{<mtext>i</mtext>}}$ value and the finding that methylammonium cannot serve as a nitrogen source indicate that ammonium rather than methylammonium is the natural substrate. Uphill transport is driven by a component of the protonmotive force, probably the membrane potential. The transport system is under genetic control; it is partially repressed by amino acids and completely by ammonium. Analysis of mutants suggest that the synthesis of the ammonium transport system is subject to the same ‘nitrogen control’ as nitrogenase and glutamine synthetase.     

Adenosine 3′, 5′-cyclic monophosphate in Schistosoma mansoni

Homogenates of adult $\text{Schistosoma mansoni}$ (blood flukes), isolated from the porto-mesenteric veins of infected mice, contain substantial activities of adenylyl cyclase, cyclic AMP phosphodiesterase, and a cyclic AMP stimulated protein kinase. The adenylyl cyclase, which is largely sedimentable at 10,000xg, is stimulated 20-fold by 10mM sodium fluoride and 1.4 to 2-fold by serotonin, glucagon, prostaglandins E₁, E₂ or B₁. The phosphodiesterase, which is largely sedimentable at 10,000xg, is inhibited by both aminophylline and papaverine but is not influenced by 10mM sodium fluoride. The protein kinase, which is present in the 10,000xg supernatant is stimulated 4 to 8-fold by either cyclic AMP or cyclic GMP. There is a preference for cyclic AMP ($\text{K}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 1.1×10}{}^{\mathrm{?7}}\text{M}$) over cyclic GMP ($\text{K}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{= 4.5×10}{}^{\mathrm{?6}}\text{M}$). If intact worms are incubated in a glucose free medium there is a mobilization of glycogen stores which is preceded by a rise in cyclic AMP concentration. In a medium with 5mM glucose there is neither a rise in cyclic AMP nor mobilization of glycogen.     

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.     

Isolation and characterization of isocitrate lyase of castor endosperm

Isocitrate lyase (threo-D_S-isocitrate glyoxylate-lyase, EC 4.1.3.1) has been purified to homogeneity from castor endosperm. The enzyme is a tetrameric protein (molecular weight about 140,000; gel filtration) made up of apparently identical monomers (subunit molecular weight about 35,000; gel electrophoresis in the presence of sodium dodecyl sulfate). Thermal inactivation of purified enzyme at 40 and 45 °C shows a fast and a slow phase, each accounting for half of the intitial activity, consistent with the equation: , where A₀ and A_t are activities at time zero at t, and k₁ and k₂ are first-order rate constants for the fast and slow phases, respectively. The enzyme shows optimum activity at pH 7.2–7.3. Effect of [S]on enzyme activity at different pH values (6.0–7.5) suggests that the proton behaves formally as an “uncompetitive inhibitor.” A basic group of the enzyme (site) is protonated in this pH range in the presence of substrate only, with a pK_a equal to 6.9. Successive dialysis against EDTA and phosphate buffer, pH 7.0, at 0 °C gives an enzymatically inactive protein. This protein shows kinetics of thermal inactivation identical to the untreated (native) enzyme. Full activity is restored on adding Mg²⁺ (5.0 mm) to a solution of this protein. Addition of Ba²⁺ or Mn²⁺ brings about partial recovery. Other metal ions are not effective.     

Hydrodynamic properties of rat hepatic prolactin receptors

The hydrodynamic properties of rat hepatic prolactin receptors have been determined by a combination of gel chromatography and ultracentrifugation. Prolactin receptors were detergent extracted from partially purified plasma membranes prepared from female rat livers. Fifteen different nonionic detergents were tested for solubilizing prolactin receptors, including Triton X-100, Polyoxyethylene W-1, Lubrol WX, detergents of the Tween and Brij series, and digitonin. When the receptors were detergent solubilized after ligand was bound to the receptor, 1% Triton X-100 had the highest efficacy of solubilization. However, if the receptors were solubilized prior to exposure to ligand, maximum binding was to receptors solubilized with 0.25% Triton X-100. The K_d of 43.2–74.5 pM for binding to the soluble receptor was three to fivefold lower than the K_d for the membrane receptor. Gel chromatography (Bio-Gel A-1.5m, 2.5 × 50 cm) of the soluble receptor indicated a Stokes radius (R_s) of 5.0 nm for the hormonereceptor-detergent complex. The hydrodynamic properties of the receptor-detergentligand complex were determined by centrifugation in 5–20% sucrose gradients in H₂O and in D₂O. They are $\text{v}\text{?}\text{= 0.7; s}{}_{\mathrm{<mtext>20,</mtext><mtext>w</mtext>}}\text{= 4.7;}\text{f}\text{f}{}_0\text{= 1.49; M}{}_{\mathrm{<mtext>r</mtext>}}\text{= 118,000}$ for the complex, 73,000 for the receptor alone. Approximately 0.22 mg of Triton X-100 is estimated bound per milligram of protein. This represents about 25 mol detergent/mol receptor.     

The insect brain (Na+ + K+)-ATPase Binding of ouabain in the hawk moth, Manduca sexta

(1) A quantitative study has been made of the binding of ouabain to the ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$ in homogenates prepared from brain tissue of the hawk moth, Manduca sexta. The results have been compared to those obtained in bovine brain microsomes. (2) The insect brain ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$ will bind ouabain either in the presence of Mg²⁺ and P_i, (‘Mg²⁺, P_i’ conditions) or in the presence of Na⁺, Mg²⁺, and an adenine nucleotide (‘nucleotide’ conditions) as is the case for the bovine brain ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$. The binding conditions did not alter the total number of receptor sites measured at high ouabain concentrations in either tissue. (3) Potassium ion decreases the affinity (increases the $\text{K}{}_{\mathrm{<mtext>D</mtext>}}$) of ouabain to the M. sexta brain ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$ under both binding conditions. However, ouabain binding is more sensitive to K⁺ inhibition under the nucleotide conditions. In bovine brain ouabain binding is equally sensitive to K⁺ inhibition under the both conditions. (4) The enzyme-ouabain complex has a rate of dissociation that is 10-fold faster in the M. sexta preparation than in the bovine brain preparation. Because of this, the M. sexta ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$ has a higher $\text{K}{}_{\mathrm{<mtext>D</mtext>}}$ for ouabain binding and is less sensitive to inhibition by ouabain than the bovine brain enzyme. (5) This data supports the hypothesis that two different conformational states of the M. sexta ($\text{Na}{}^{\mathrm{+}}\text{+}\text{K}{}^{\mathrm{+}}\text{)-}\text{ATPase}$ can bind ouabain.     

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.