A stochastic model for the economic management of a renewable animal resource

An optimal economic harvesting policy, which maximizes the present value of an animal population, capable of renewing itself, is discussed. It is assumed that, unhindered, the successive population levels, X_n, form a Markov chain, with transitions

$\text{X}{}_{\mathrm{n+1}}\text{=?(X}{}_{\mathrm{n}}\text{) + ?}{}_{\mathrm{n}}\text{?(X}{}_{\mathrm{n}}\text{)}$

, where f is the recruitment function, and {?_n} is an iid sequence of random shocks. When a positive set-up cost is present an optimal policy is of the (S,s) type. The optimal population level is compared with that of an equivalent deterministic model. Bioeconomic conditions, which imply the optimality of conservation, or extinction are investigated.     

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.     

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.     

A restatement of melittin-induced effects on the thermotropism of zwitterionic phospholipids

Perturbations induced by melittin on the thermotropism of dimyristoyl-, dipalmitoyl-, distearoylphosphatidylcholine and natural sphingomyelin are investigated and rationalized from data obtained by fluorescence polarization, differential scanning calorimetry and Raman spectroscopy. Depending on the technique and / or experimental conditions used, the observed effects differ at the same lipid to protein molar ratio, due to partial binding of melittin. The binding is more efficient for tetrameric than for monomeric melittin, but in both cases its affinity is weaker for phosphatidylcholine dispersions in the gel phase than for sonicated vesicles. For temperatures $\text{T ? T}{}_{\mathrm{<mtext>m</mtext>}}$ efficient binding occurs whatever the initial state of the lipids is. One can summarize the effects induced by melittin on the transition temperature as follows: (i) No upward shift is observed on synthetic phosphatidylcholines when lipid degradation is avoided. This is achieved by using highly purified melittin, phospholipase inhibitors, and / or non-hydrolysable lipids. (ii) Melittin monomer does not change $\text{T}{}_{\mathrm{<mtext>m</mtext>}}$. (iii) When melittin tetramer is stabilized, it decreases $\text{T}{}_{\mathrm{<mtext>m</mtext>}}$ by 10–15 deg. C. The transition broadens, and is finally abolished for $\text{R}{}_{\mathrm{<mtext>i</mtext>}}\text{? 2}$. Very similar results are found for natural sphingomyelin. Fluorescence polarization indicates similar changes in order and dynamics of the acyl chains for all lipid studied. For $\text{T ? T}{}_{\mathrm{<mtext>m</mtext>}}$, fluorescence and Raman show that melittin decreases the amount of CH₂ groups in ‘trans’ conformation and the intermolecular order of the chains. According to fluorescence data, there is an increase of the rigid-body orientational order at $\text{T ? T}{}_{\mathrm{<mtext>m</mtext>}}$, while from Raman the positional intermolecular order decreases without significant change in the CH₂ groups ‘trans’/‘gauche’ ratio.     

Sulphate transport by rat ileum. Effect of molybdate and other anions

Kinetic constants for SO₄^2? transport by upper and lower rat ileum in vitro have been determined by computer fitting of rate vs concentration data obtained using the everted sac technique. MoO₄^2? inhibition of this transport is competitive, and kinetic constants for the inhibition were similarly determined. Transport is also inhibited by the anions WO₄^2?, S₂O₃^2? and SeO₄^2?, in the order $\text{S}{}_2\text{O}{}_3{}^{\mathrm{2?}}\text{> SeO}{}_4{}^{\mathrm{2?}}\text{≧ MoO}{}_4{}^{\mathrm{2?}}\text{> WO}{}_4{}^{\mathrm{2?}}$. These anions have no effect on the transport of l-valine. Low SO₄^2? transport rates were observed in sacs from animals fed a high-molybdenum diet. The significance of the results with respect to the problem of molybdate toxicity in animals is discussed, and related to the known protective effect of SO₄^2?.     

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.     

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.     

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.     

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.     

Inhibition of chymotrypsin by alkyl phosphonates: a quantitative structure-activity analysis.

A quantitative structure-activity relationship has been formulated for 53 alkyl phosphonates [R₂OPO(CH₃)SR₃] inhibiting chymotrypsin: . In this so-called bilinear model, k_i is the bimolecular rate constant (m^?1 s^?1), β is a disposable parameter evaluated by a computerized iterative procedure, MR is the molar refractivity of a substituent, $\text{σ}{}_3{}^1$ is Taft's polar parameter, and I is an indicator variable for substituents containing a sulfonium group. The correlation coefficient for this equation is 0.985. This quantitative structure-activity relationship is compared with those previously formulated for the action of chymotrypsin on acylamino acid ester substrates.     

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.     

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.     

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.     

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 simple procedure for resolution of Escherichia coli RNA polymerase holoenzyme from core polymerase.

The association constant, K_A, for myosin subfragment-1 binding to actin was measured as a function of ionic strength [KCl, LiCl, and tetramethylammonium chloride (TMAC)]and temperature by the method of time-resolved fluorescence depolarization. The following thermodynamic values were obtained from solutions of 0.20 × 10^?6m S-1, 1.00 × 10^?6m actin in 0.15 m KCl, pH 7.0, at 25 °C: ΔG ° = ?39 ± 1 kJ M^?1, ΔH⁰ = 44 ± 2 kJ M^?1 and $\text{ΔS}{}^0\text{= 0.28 ± 0.01 kJ}\text{M}{}^{\mathrm{?1}}{}^0\text{K}{}^{\mathrm{?1}}$. For measurements in KCl (0.05 to 0.60 m), In $\text{K}{}_{\mathrm{a}}\text{= ?8.36 (KCl)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$. Thus, the binding is endothermic and strongly inhibited by high ionic strength. When KCl was replaced by LiCl or TMAC the ionic effects on the binding were cation specific. The nature of actin-(S-1) binding in the rigor state is discussed in terms of these results.     

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.     

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.