The effect of multiple inseminations on the evolution of social behaviors in diploid and haplo-diploid organisms

Using a classical population genetic model, the necessary conditions for the spread of genes that determine social behaviors and the rate of spread of these genes are derived. The influence of 1, 2, 3, or k inseminations per female on these conditions is investigated for both diploid and haplodiploid organisms. These results are then extended to a population in which there are arbitrary variations among females in their numbers of mates. These results do not depend upon assuming equal paternity by all inseminating males; the effects of sperm competition and unequal paternity are also derived. The rates and conditions for social evolution in these groups of complex composition are discussed in relation to Hamilton's rule.For all models, the total change in gene frequency, Δq, is partitioned into two components: (1) $\text{Δq}{}_{\mathrm{I}}$, the change in gene frequency caused by selection within groups; this component is always negative, illustrating that individual selection always operates against the evolution of social behaviors; and (2) Δq_G, the change in gene frequency caused by selection between groups; this component is generally positive. Hamilton's rule is shown to specify the necessary and sufficient conditions for $\text{Δq}{}_{\mathrm{G}}\text{> |}\text{Δq}{}_{\mathrm{I}}\text{|}$, that is, for selection among kin groups to over-ride individual selection within kin groups.     

Proton nuclear magnetic resonance studies of the manganese (II) binding site of concanavalin A. Effect of saccharides on the solvent relaxation rates

The longitudinal relaxation rate ($\text{1}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>p</mtext>}}$) of water protons was studied in solutions of Mn(II)-concanavalin A at a number of frequencies. These relaxation rates were lowered in the presence of a variety of saccharides which have affinities for concanavalin A which range over two orders of magnitude. A good correlation was found in which saccharides which bind tightly have the greatest effect and saccharides which bind weakly or not at all have little effect on the $\text{1}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>p</mtext>}}$ values. The temperature dependence of the proton relaxation rates showed that the lowering of these rates in the presence of saccharides was most likely due to a change in the exchange rate of solvent interacting with protein-bound Mn(II), $\text{1}\text{T}{}_{\mathrm{<mtext>m</mtext>}}$.An analysis of the temperature and frequency dependence of the $\text{1}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>p</mtext>}}$ and $\text{1}\text{T}{}_{\mathrm{<mtext>2</mtext><mtext>p</mtext>}}$ (transverse) solvent proton relaxation rates resulted in evaluation of a number of parameters for solvent water molecules interacting in the first coordination sphere of Mn(II) bound to concanavalin A. The ratio of the number of water molecules (q) to the Mn(II)-proton distance (r) obtained from a computer fit of the data over a limited temperature range is in accord with the findings of Koenig et al. ((1973) Proc. Nat. Acad. Sci.70, 475) and Meirovitch and Kalb ((1973) Biochim. Biophys. Acta303, 258). However, our studies of $\text{1}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>p</mtext>}}$ and $\text{1}\text{T}{}_{\mathrm{<mtext>2</mtext><mtext>p</mtext>}}$ of water over a more extensive temperature range are best fit with the following conclusions: at low temperatures (<20 °C), the data are consistent with an outer-sphere relaxation process. At higher temperatures (> 30 °C), the water molecule in the inner coordination sphere of the bound Mn(II) begins exchanging more rapidly and contributes to the relaxation processes ($\text{1}\text{T}{}_{\mathrm{<mtext>1</mtext><mtext>p</mtext>}}$ and $\text{1}\text{T}{}_{\mathrm{<mtext>2</mtext><mtext>p</mtext>}}$). The relaxation time of protons in the inner coordination shell, T_1M, contributes over the entire temperature range and produces a frequency dependence in the relaxivity data from 6 to 100 MH_z since the contributions to the correlation times are in the range 10^?9-10^?8 sec.     

The polymorphic phase behaviour and miscibility properties of synthetic phosphatidylethanolamines

(1) The polymorphic phase behaviour of aqueous dispersions of various synthetic phosphatidylethanolamines, both singly and in mixtures, has been investigated by ³¹P-NMR. (2) $\text{14:0}\text{14:0}$ PE remains in the lamellar phase up to 90°C. $\text{18:1}{}_{\mathrm{<mtext>t</mtext>}}\text{18:1}{}_{\mathrm{<mtext>t</mtext>}}$ PE exhibits a lamellar to hexagonal (H_II) transition between 60°C and 63°C. For $\text{18:1}{}_{\mathrm{<mtext>c</mtext>}}\text{18:1}{}_{\mathrm{<mtext>c</mtext>}}$ PE, the lamellar to hexagonal (H_II) transition occurs between 7 and 12°C, whereas for $\text{18:2}{}_{\mathrm{<mtext>c</mtext>}}\text{18:2}{}_{\mathrm{<mtext>c</mtext>}}$ PE, the hexagonal (H_II) phase is the preferred structure above ?15°C. (3) Mixtures of $\text{18:1}{}_{\mathrm{<mtext>c</mtext>}}\text{18:1}{}_{\mathrm{<mtext>c</mtext>}}$ PE and $\text{18:1}{}_{\mathrm{<mtext>t</mtext>}}\text{18:1}{}_{\mathrm{<mtext>t</mtext>}}$ PE exhibit near-ideal miscibility behaviour. For mixtures of $\text{18:1}{}_{\mathrm{<mtext>c</mtext>}}\text{18:1}{}_{\mathrm{<mtext>c</mtext>}}$ PE and $\text{14:0}\text{14:0}$ PE there is evidence of fluid-solid immiscibility at temperatures below the gel-liquid crystalline transition temperature of the $\text{14:0}\text{14:0}$ PE component. Mixtures of $\text{18:2}{}_{\mathrm{<mtext>c</mtext>}}\text{18:2}{}_{\mathrm{<mtext>c</mtext>}}$ PE and $\text{18:1}{}_{\mathrm{<mtext>t</mtext>}}\text{18:1}{}_{\mathrm{<mtext>t</mtext>}}$ PE exhibit complex phase behaviour involving limited fluid-solid immiscibility at low temperatures and formation of a phase allowing isotropic motional averaging at higher temperatures. (4) ³¹P-NMR provides a graphic method for investigating the miscibility properties of mixed PE systems.     

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.     

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.     

A comparison of the effects of ouabain and 2-deoxy-d-glucose on the thermodynamic variables of the frog skin

Previous studies support the validity of a linear thermodynamic formalism relating the rates of active Na⁺ transport and oxygen consumption J_r to the electrical potential difference ΔΨ an the affinity α (negative free energy) of the metabolic driving reaction. The formulation was further tested in paired control and experimental hemiskins by the use of two inhibitors of Na⁺ transport. Ouabain, a specific inhibitor of the Na⁺ pump, might be expected to diminish the dependence of J_r on ΔΨ without affecting α, whereas 2-deoxy-d-glucose, a competitive inhibitor of glucose metabolism, should be expected to diminish α. Both inhibitors were used at concentrations adequate to depress Na⁺ transport (i.e. short-circuit current J_o) to some 50°_o of control level. Measurements were made of I_o and $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(ΔΨ)}$, and the apparent value of the affinity α_app was calculated according to the thermodynamic formulation. Ouabain depressed $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(ΔΨ)}$ without affecting α_app whereas 2-deoxy-d-glucose depressed α_app without affecting $\text{d}\text{J}{}_{\mathrm{<mtext>r</mtext>}}\text{d}\text{(αΨ)}$. The demonstration of these effects indicates the utility of the formalism.     

Lipid structural order parameters (reciprocal of fluidity) in biomembranes derived from steady-state fluorescence polarization measurements

This paper presents an interpretation of fluorescence polarization measurements in lipid membranes which are labelled with the apolar probe 1,6-diphenyl-1,3,5-hexatriene. The steady-state fluorescence anisotropy, $\text{r}{}_{\mathrm{<mtext>S</mtext>}}$, is resolved into a fast decaying or kinetic component, $\text{r}{}_{\mathrm{<mtext>f</mtext>}}$, and an infinitely slow decaying or static component, $\text{r}{}_{\mathrm{\infty }}$. The latter contribution, which predominates in biological membranes, is exclusively determined by the degree of molecular packing (order) in the apolar regions of the membrane; $\text{r}{}_{\mathrm{\infty }}$ is proportional to the square of the lipid order parameter. An empirical relation between $\text{r}{}_{\mathrm{<mtext>S</mtext>}}$ and $\text{r}{}_{\mathrm{\infty }}$ is presented, which is in agreement with a prediction based on a theory of rotational dynamics in liquid crystals. This relation enabled us to estimate a lipid structural order parameter directly from simple steady-state fluorescence polarization measurements in a variety of isolated biological membranes. It is shown that major factors determining the order parameter in biomembranes are the temperature, the cholesterol and sphingomyelin content and (in a few systems) the membrane intrinsic proteins.     

Bovine fibrinogens: Reversible polymer formation

Reversible flbrinogen polymer formation was examined at pH 6.6 and Γ/2 0.3. The equilibrium fraction of fibrinogen present as polymer, (P_mf)_e, was determined by gel filtration for fibrinogen concentrations, F_O, from 48 to 166 μm. Using F_O in molarity, the experimental relation is ln [F_O(P_mf)_e] = 3.53 ln[F_O(1 ? (P_mf)_e)] + 23.73. This relation and attendant confidence limits are examined assuming, during filtration, that the original polymer population is either stable or selected polymer species dissociate to monomer. The possibility that all polymers are open is excluded since the calculated microscopic association constant would then increase with F_O. Acceptable models are based on the assumptions that polymers are open, with association constant K_a, until restricted by closure, with association constant K_r, at an integral degree of polymerization, n. Values are selected on the basis that interaction parameters are independent of F_O and that the required molar decrease in free energy is a minimum. Assuming polymer stability, the experimental relation at 273 °K gives $\text{n = 4,}\text{K}{}_{\mathrm{r}}\text{K}{}_{\mathrm{a}}\text{= 1.2 m,}\text{and}\text{K}{}_{\mathrm{a}}$ = 736 m^?1. Temperature dependence gives $\text{ΔH= ?16.9 kcal/mol}\text{and}\text{ΔS}{}^{\mathrm{O}}{}_{\mathrm{a}}$ = ?48.8 e.u. $\text{K}{}_{\mathrm{r}}\text{K}{}_{\mathrm{a}}$ indicates a relation between changes in entropy. The probability is >0.90 that $\text{K}{}_{\mathrm{r}}\text{K}{}_{\mathrm{a}}\text{? 56 m}$, which indicates a greater loss of degrees of freedom on closure than on association. Conclusions are not altered by the assumption that only the closed polymer species is stable. As ionic strength is decreased at pH 6.6, K_a increases. The clotting time of an otherwise constant system decreases as system P_mf is increased.     

Hydration of Escherichia coli lipids: Deuterium T1 relaxation time studies of phosphatidylglycerol,phosphatidylethanolamine and phosphatidylcholine

The hydration properties of Escherichia coli lipids (phosphatidylglycerol, phosphatidylethanolamine) and synthetic $\text{1,2-}\text{dioleoyl}\text{-sn-}\text{glycero-3-phosphocholine}$ in H₂O/²H₂O mixtures (9:1, v/v) were investigated with ²H-NMR. Comparison of the ²H₂O spin lattice relaxation time ($\text{T}{}_1$) as a function of the water content revealed a remarkable quantitative similarity of all three lipid-H₂O systems. Two distinct hydration regions could be discerned in the $\text{T}{}_1$ relaxation time profile. (1) A minimum of 11–16 water molecules was needed to form a primary hydration shell, characterized by an average relaxation time of $\text{T}{}_1\text{≈ 90}\text{ms}$. (2) Additional water was found to be in exchange with the primary hydration shell. The exchange process could be described in terms of a two-site exchange model, assuming rapid exchange between bulk water with $\text{T}{}_1\text{= 500}\text{ms}$ and hydration water with $\text{T}{}_1\text{= 80–120}\text{ms}$. Analysis of the linewidth and the residual quadrupole splitting (at low water content) confirmed the size of the primary hydration layer. However, each lipid-water system exhibited a somewhat different linewidth behavior, and a detailed molecular interpretation appeared to be preposterous.     

The consequences of contact pressure in phyllotaxis

To determine the consequences of contact pressure in phyllotaxis, a mathematical model is constructed in which a leaf distribution is represented by a point lattice of n + 1 lattice points at equal intervals on a helix wound around a cylinder. The model is normalized by taking the girth of the cylinder as 1 and by measuring time T in plastochrones, so that n = [T]. r stands for the normalized internode distance (component of the distance between two consecutive lattice points that is parallel to the axis of the cylinder). d stands for the divergence (fraction of a turn between consecutive lattice points). It is assumed that r is a monotonic decreasing function of T such that r(T) → 0 as T → ∞. Contact pressure is represented by the assumption that the minimum geodesic distance between lattice points is maximized. It is shown that if (p, q), with p < q, is the contact phyllotaxis determined when contact pressure first becomes effective, then the continuation of contact pressure requires that the advance to higher phyllotaxis as r decreases must proceed via successive pairs of consecutive terms of the Fibonacci sequence generated by the numbers p and q, namely, p, q, p + q, p + 2q, 2p + 3q, …. The divergence, starting from some value $\text{d =}\text{1}\text{t}\text{+}\text{1}\text{a}{}_2\text{+ … +}\text{1}\text{(a}{}_{\mathrm{n}}\text{+ x)}$ determined by p and q converges to an ideal angle $\text{1}\text{t}\text{+}\text{1}\text{a}{}_2\text{+ … +}\text{1}\text{a}{}_{\mathrm{n}}\text{+}\text{1}\text{τ}$, where τ is the golden section. A necessary and sufficient condition for the ideal angle to be $\text{1}\text{2}\text{+}\text{1}\text{τ}\text{= τ}{}^{\mathrm{?2}}$ is that the p and q of the initial contact phyllotaxis be consecutive Fibonacci numbers of the sequence 1, 2, 3, 5, 8, …. It is proved that a sufficient condition for convergence to the ideal angle τ^?2 of normal phyllotaxis is that contact pressure begin before T = 5 or before $\text{r <}\text{3}\text{38}\text{1}\text{2}$ with d initially between $\text{1}\text{3}$ and $\text{1}\text{2}$.     

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.     

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.     

Lipid-protein interactions in membrane models fluorescence polarization study of cytochrome b5-phospholipids complexes

According to previous authors, cytochrome $\text{b}{}_5$, when extracted from bovine liver by a detergent method, is called cytochrome $\text{d-b}{}_5$. On the other hand, the protein obtained after trypsin action, which eliminates an hydrophobic peptide of about 54 residues, is called cytochrome $\text{t-b}{}_5$.Fluorescence polarization of the dansyl phosphatidylethanolamine probe inserted into phospholipid vesicles is very senstive to the binding of proteins, and so is a useful method to study lipid-protein interactions.The chromophore mobility, $\text{R}$, decreases markedly when dipalmitoyl phosphatidylcholine vesicles are incubated with cytochrome $\text{d-b}{}_5$, whereas $\text{R}$ does not change for cytochrome $\text{c}$ and cytochrome $\text{t-b}{}_5$. This can be interpreted as a strengthening of the bilayer, only due to the interaction of the hydrophobic peptide tail.Interaction of dipalmitoyl phosphatidylcholine vesicles with cytochrome $\text{d-b}{}_5$ occurs either below or above the melting temperature of the aliphatic chains (41 °C). Even for a high protein to lipid molar ratio (1 molecule of protein for 40 phospholipid molecules), the melting temperature is apparently unaffected.Phosphatidylserine and phosphatidylinositol do not interact at pH 7.7 with cytochrome $\text{d-b}{}_5$, because electrostatic forces prevent formation of complexes. At low pH, the interaction with the protein occurs, but the binding is mainly of electrostatic nature.     

A general method for the direct isolation of the 3'-terminal fragments derived from transfer RNA molecules

A general procedure for the isolation of 3′-linked fragments derived from tRNA molecules is described. Purified N-2-naphthoxyacetylglycyl derivatives of the $\text{tRNA}{}_1{}^{\mathrm{Gly}}$ and $\text{tRNA}{}_2{}^{\mathrm{Gly}}$ of yeast were exhaustively digested with RNase T₁ and the 3′-linked fragments (bearing the derivative) were separated from other degradation products (lacking the derivative) by stepwise chromatography on BD-cellulose. Subsequent chromatographic resolution and base-composition analysis allowed tentative identification of the 3′-terminals of $\text{tRNA}{}_1{}^{\mathrm{Gly}}$ and $\text{tRNA}{}_2{}^{\mathrm{Gly}}$ as Gp(Cp,Ap)CpCpA and Gp(Cp,Cp,Up,Ap)CpCpA, respectively. The potential utility of this procedure for development of a novel approach to nucleic acid sequence analysis is discussed.     

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.     

Biochemical adaptation of mitochondria,muscle, and whole-animal respiration to endurance training

The experimental intervention of exercise training has been used to study mitochondrial biosynthesis, and the physiologic integration of subcellular, cellular, and whole-animal energetics. Gross mitochondrial composition was unchanged in rat muscle by a 10-week program of endurance treadmill running. The mitochondrial concentration of iron-sulfur clusters, cytochromes, flavoprotein, dehydrogenases, oxidases, and membrane protein and lipid, as well as the ratios of each component to the others, maintained constant proportions. The mitochondrial content of muscle, however, increased by approximately 100% as did absolute tissue oxidative capacity. The soluble portions of mitochondria maintained a constant total protein content and mass, relative to the membrane fraction, despite adaptive changes in the specific activities of some citric acid-cycle enzymes. Mitochondria from endurance-trained muscles generated normal transmembrane potentials, ADP/O ratios, and respiratory control ratios. Muscle oxidase activity was highly correlated (r = 0.92) with endurance capacity, which increased 403%. Whole-animal maximal O₂ consumption (), however, increased only 14% and was a relatively poor predictor of endurance. Thus, mitochondrial factors, rather than , must play an important role in dictating the limits of endurance activity. Conversely, was strongly related to the maximal intensity of work which could be attained aerobically (r = 0.82). Comparison of O₂ consumption at the mitochondrial, muscle, and whole-animal levels revealed that maximal muscle oxidase activity was not an absolute limitation to : It is concluded that other factors intervene to control the percentage of muscle O₂ consumption capacity which may be utilized during exercise.     

Some dilute-solution parameters of the levan of streptococcus salivarius in various solvents

The intrinsic viscosities, weight-average molecular weights (M?_w), and radii of gyration [($\text{R}{}^2{}_{\mathrm{g}}$)^{$\text{1}\text{2}$}≈] of Streptococcus salivarius levan in various solvents were respectively obtained from viscosity and light-scattering measurements. The data showed that the levan in water is not aggregated by hydrogen bonds, and that the values of both the refractive index and ($\text{R}{}^2{}_{\mathrm{g}}$)^{$\text{1}\text{2}$} are lower in water than in aqueous solutions of urea. Urea may break intramolecular hydrogen-bonds, e.g., between branches, allowing the molecule to expand.     

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.