A unified approach to ion transport through membranes. I. Membrane-soluble ions.

Theoretical membrane potential transient produced by applying a current step to nerve cells has been derived based on the compartment neuron model and also on the equivalent cylinder model developed by W. Rall. It is expressed as a sum of exponential functions as

$\text{∑}\text{i=0}\text{n?1}\text{E}{}_{\mathrm{i}}\text{[1?}\text{exp}\text{(}\text{t}\text{τ}{}_{\mathrm{i}}\text{)]}$

where n is the number of compartments. The ratio of the amplitudes of the first and the second largest exponential functions, ($\text{E}{}_1\text{E}{}_0$), was found to be proportional to that of their respective time constants, ($\text{τ}{}_1\text{τ}{}_0$), in these neuron models. The constant of proportionality is given in a form that depends on the number of compartments as $\text{E}{}_1\text{E}{}_0\text{= (1 +}\text{cos}\text{π}\text{n}\text{)}\text{τ}{}_1\text{τ}{}_0$. This theoretical result is discussed in the light of recent experimental results in cat red nucleus neurons.     

Magnetic field affects the fluorescence yield in reaction center preparations from Rhodopseudomonas sphaeroides R-26

Purified photochemical reaction centers from Rhodopseudomonas sphaeroides R-26 were reduced with Na₂S₂O₄ so as to block their photochemical electron-transfer reactions. The magnetic field induced an increase in the emission yield. Our results support the hypothesis that under these conditions, charge recombination in the singlet radical pair composed of the oxidized primary donor and reduced primary acceptor predominantly generates the excited singlet state of the reaction center bacteriochlorophyll.The maximum relative fluorescence change and the value of the magnetic field at which half-saturation of the effect is achieved ($\text{B}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$) at room temperature are 5.5% and 75 G, respectively. For the whole cells of Rps. sphaeroides R-26 these parameters are 1.2% and 120 G.The relative fluorescence change at 600 G, $\text{ΔF}\text{F(600)}$, and $\text{B}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ are studied as functions of temperature. The temperature dependencies of $\text{ΔF}\text{F(600)}$ for reaction centers and whole cells of Rps. sphaeroides R-26 are qualitatively the same, with the maximum effect (8% for reaction centers) occurring at 230 K. However, the $\text{B}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ curves for the two preparations are different.     

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.     

Saturation transfer electron paramagnetic resonance on membrane bound proteins. II-Absence of rotational diffusion of the cholinergic receptor protein in Torpedo marmorata membrane fragments.

We have applied the technique of saturation transfer electron paramagnetic resonance to study the rotational diffusion of spin labeled membrane bound cholinergic receptors from Torpedo marmorata. Two different spin labels were used: a spin labeled maleimide derivative which binds covalently to proteins and a long chain spin labeled acylcholine which binds reversibly with a high affinity to the receptor protein. The maleimide spin label has a motion whose rotational correlation time is τ₂ > 10^?3 sec. The long chain spin labeled acylcholine indicates slightly more motion ($\text{τ}{}_2\text{? 10}{}^{\mathrm{?4}}\text{sec}$), but the nitroxide in this latter case is probably more loosely bound.     

The study of the primary photoprocesses in Photosystem I of chloroplasts Recombination luminescence,chlorophyll triplet state and triplet-triplet annihilation

The dependence of the delayed luminescence of Photosystem I on the state of the reaction centers has been studied. Light flash induces a charge separation in the centers: $\text{P-700 · P-430}\textcolor{red}{}\text{P-700}{}^{\mathrm{+}}\text{· P-430}{}^{\mathrm{?}}$. Dark recombination of charges is accompanied by the recombination luminescence with $\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 20}\text{ms}$.If the centers are in the P-700 · P-430^? state or if P-430 is inactivated by heat, then flashing of Photosystem I generates the triplet state chlorophyll with $\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{? 0.5}\text{ms}$. The triplet state has been measured by the delayed fluorescence of chlorophyll at 20 °C and 77 °K and by the chlorophyll phosphorescence at 77 °K. The delayed fluorescence at 20 °C arises from the thermal activation of the triplet state up to the excited singlet level of chlorophyll and at 77 °K it is due to triplet-triplet annihilation. The quantum yield of the triplet formation, estimated by a comparison of the light saturation curves of delayed fluorescence at 20 °C and of P-700 photooxidation under the same experimental (optical) conditions, is ≈ 0.9 of the P-700⁺ yield. Only one triplet of chlorophyll can be generated per P-700. Under heat inactivation of P-430 the triplet formation is not observed when P-700 is oxidized.It is assumed that the triplet-triplet annihilation at 77 °K is related with the strong interaction between the chlorophyll molecules in the pigment complex of Photosystem I. The possibility of a triplet participation in the primary processes of photosynthesis is discussed.     

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.     

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.     

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.     

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

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

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.     

Two photocycles in halobacterium halobium that lacks bacteriorhodopsin

The photochemical reactions in bacteriorhodopsin-free mutant (bR^?) of Halobacterium halobium (JW-1) membranes have been studied using flash photolysis. Two photocycles were found in envelope vesicles as well as in a membrane fragment from (JW-1). A pigment absorbing at ca. 590 nm undergoes a faster photocycle, with a phototransient at ca. 500 nm ($\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{～- 10 ms}$). A second pigment absorbing at ca. 580 nm undergoes a slower photocycle, accompanying a phototransient absorbing below 410 nm ($\text{τ}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{～- 0.8 s}$).     

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

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

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.     

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

Edelstein's model

$\text{?E}\text{?τ}\text{=F(M, E)}$

,

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

,

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

,

$\text{E(s,0)=ψ(s)}$

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

Respiration-driven proton translocation with nitrite and nitrous oxide in Paracoccus denitrificans

(1) $\text{H}$⁺/electron acceptor ratios have been determined with the oxidant pulse method for cells of denitrifying Paracoccus denitrificans oxidizing endogenous substrates during reduction of O₂, NO^?₂ or N₂O. Under optimal H⁺-translocation conditions, the ratios $\text{H}{}^{\mathrm{+}}\text{O}$, $\text{H}{}^{\mathrm{+}}\text{N}{}_2\text{O}$, $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂ and $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂O were 6.0–6.3, 4.02, 5.79 and 3.37, respectively. (2) With ascorbate/N,N,N′,N′-tetramethyl-p-phenylenediamine as exogenous substrate, addition of NO^?₂ or N₂O to an anaerobic cell suspension resulted in rapid alkalinization of the outer bulk medium. $\text{H}{}^{\mathrm{+}}\text{N}{}_2\text{O}$, $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂ and $\text{H}{}^{\mathrm{+}}\text{NO}{}^{\mathrm{?}}{}_2$ for reduction to N₂O were ?0.84, ?2.33 and ?1.90, respectively. (3) The $\text{H}{}^{\mathrm{+}}\text{oxidant}$ ratios, mentioned in item 2, were not altered in the presence of $\text{valinomycin}\text{K}{}^{\mathrm{+}}$ and the triphenylmethylphosphonium cation. (4) A simplified scheme of electron transport to O₂, NO^?₂ and N₂O is presented which shows a periplasmic orientation of the nitrite reductase as well as the nitrous oxide reductase. Electrons destined for NO^?₂, N₂O or O₂ pass two H⁺-translocating sites. The $\text{H}{}^{\mathrm{+}}\text{electron}$ acceptor ratios predicted by this scheme are in good agreement with the experimental values.