A Further Problem of Interval Estimation of an Unknown Regressor in Model I of Linear Regression

For the model y = α + βx + ? (model I) of linear regression we dealt with in KUHNERT and HORN (1980) the determination of a confidence interval for that x₀ where the expectation Ey reaches a given value y₀. Here we start with realizations of random variables y (i = 1,…, m) being independent of x which are given in addition to the realizations of-y. Now y₀ denotes the unknown value of \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^m $\end{document} ciEy and x₀ the x-value where the expectation Ey reaches that value y₀. For this x₀ we give a confidence interval. Applications stem from dose response assays.     

Dependency as a measure to estimate the order and the values of Markov processes

To evaluate the order and the values of Markov properties of the time series of events, we have proposed a statistical measure dependency:D _m = (H ₀ –H _m )/H ₀ , whereH ₀ andH _m are Shannon's entropy and them-th order conditional entropy, respectively. It is indicated that is a better point estimator ofD _m, giving a total value of them-th order Markov process. Here and are the estimate ofD _m and the arithmetic mean of when them-th order shuffling is made many times for a given observed series, respectively. The value represents Markov value of the orderm. Under the assumption that the series has continuous variables and the normal distribution, simplified dependency is defined by, where |S _m | is the determinant of serial correlation coefficients. It is shown that is practically useful for the estimation of the order and the values of Markov processes with small sample size. It is also indicated that analysis is basically equivalent to the least mean-square analysis of autoregressive models.     

Contribution to the genetics of serum β-lipoproteins in man

Summary The genetic behaviour of a human serum -lipoprotein factor, called Ag(a₁), was studied by agar micro-diffusion technique, utilizing an antibody detected in the serum from a transfused thalassemia patient. It behaves as an inherited, dominant, autosomal character, with complete penetrance at birth. It is controlled by a gene and is closely linked to the Ag ^x and Ag ^y genes.The existence of a gene Ag ^b , allelic to , is postulated but the Ag(b) antigen has not so far been detected by specific antisera.The frequency of the gene in a Milan population was found to be 0,43, and in a Berne population was 0,46. The frequencies of the four possible gene combinations in the sample group from Milan were: Ag ^yb =0,53; =0,22; =0,21; Ag ^xb =0,04.The observed frequencies of the factor Ag(a₁) were 0,676 and 0,713, respectively among the Milan and Berne populations.     

A function for describing nitrogen uptake and dry matter production by winter barley crops

The quantityY, of dry matter produced,Y _d , and nitrogen taken up,Y _n , during the growth of winter barley, was shown to be a function of thermal time,x,

Foam behavior of biological media

Summary The influence of the alcohol concentration on the foaminess, , of-BSA-solutions is considered. This effect is calculated by means of the function (C_BSA . f), where f=1 for pure protein solutions and f>1 for alcohol solutions. f is calculated by f = 2^TT_eff. Here, where T_T is the turbidity temperature change due to solvent structure effects and T_D, the temperature correction due to alcohol-protein interaction. The constants necessary to calculate T_T and T_D are tabulated. The agreement between the calculated and measured foaminess , as a function of the n-propanol concentration is satisfactory and for methanol or ethanol excellent.     

A trophic diversity index for presence-absence food data

Summary An index to assess trophic diversity from presence-absence food data is proposed. The index is computed according to the expression , where the 's are the frequencies of occurrence of the various prey categories. The upper and lower limits of D are derived. A test of the reliability of D was carried out by comparing D and H (Shannon's information function) values obtained from a set of twenty-three food analyses from vertebrate animals. Results show that, although a significant correlation exists between D and H, only a small fraction of H-variation is explained by D-variation. D contains two kinds of information, one referred to species richness and another relative to the degree of between-samples heterogeneity. The former is shared in common with H and this presumably explains the fairly weak correlation found between both measures.     

Suitability of the shaking flask for oxygen supply to microbiological cultures

Due of its simplicity the shaking flask is used in serial studies, e.g. in the screening for secondary metabolites or in the optimization of fermentation processes. Experimental investigations in these small bioreactors are often the first step in developing a large-scale fermentation process.Movement of the flask should produce sufficient mixing, supply of oxygen, and removal of carbon dioxide. In the case of fluids with low or moderate viscosity, gas transport is the most important aspect. This publication summarizes data necessary to calculate the gas transport. These data are derived from the consideration of the gas diffusions through the cotton plug as well as from the substance transport between the gas and liquid phases. As a result suitable fermentation conditions can be selected. Finally, the performance limits of the shaking flask are illustrated using the example of the oxygen supply in a Streptomyces tendae fermentation.List of Symbols A _s Cross section of plug - A Surface area of liquid in flask - a A/V _F specific phase interface area - c Concentration - c ^* Saturation concentration - c Plug diffusion term - D Widest diameter of flask - Diffusion coefficients in multicomponent gas mix tures - Diffusion coefficients in binary gas mixtures - Diffusion coefficient of oxygen in the liquid - d Diameter of neck of flask - e Eccentricity - G Volume-based mass flow - G _m Maximum volume-based mass flow - g Acceleration due to gravity - h Height coordinate - ¯H Mean height of plug - Hy p _i/c ^*, Henry constant - K Consistency index - k D _xy/D _xz, Ratio of diffusion coefficients in binary gas mixtures - k _M Monod constant - k _L a Mass transport coefficient: gas/liquid - M Molecular weight - m Flow exponent - n Speed of shaking - p Pressure - p _i Partial pressure of gas component i - q Area-based flow of volume - R , respiration ratio - Sc , Schmidt number - T Absolute temperature - V Flask volume - V _F Volume of liquid in flask - w Velocity of the Stefan flow - x, y, z Ratios of the partial pressures of the gases O₂, CO₂, N₂ - Rate of shear - Dynamic viscosity of the liquid - Kinematic viscosity of the liquid - Density of the liquid - _x, Density of O₂ gas - Surface tension Indices 0 State in gas volume of shaking flask - 1 State in outside air - G Gas volume - x, y, z O₂, CO₂, N₂     

Reversed bohr and root shifts in hemocyanin of the marine prosobranch,Buccinum undatum: Adaptations to a periodically hypoxic habitat

Summary Oxygen binding properties of the hemocyanin-containing blood ofBuccinum undatum were examined in vitro and in vivo under normoxic ( 150 mmHg) and hypoxic ( 50 mmHg) conditions at 10°C. Blood pH and showed a decrease in vivo under hypoxic conditions. Oxygen uptake at high water , was about 18 ml O₂/kg·h (wet weight) and the critical oxygen tension between 25 and 50 mm Hg. In vitro the O₂ binding to hemocyanin showedn-values independent of pH, while both O₂ affinity and oxygen carrying capacity were strongly pH dependent. Oxygen affinity increased below pH=8.1 and thus showed a pronounced reversed Bohr shift in the physiological pH range (7.5<pH<8.1). The oxygen carrying capacity similarly increased markedly with falling pH in the physiological pH range (reversed Root shift). Astrup titration curves showed a metabolic and respiratory acidosis under hypoxic conditions ( 50 mm Hg). The role of hemocyanin in the transport of oxygen in relation to ambient O₂ availability is discussed.     

Root biomass fraction as a function of growth degree days in wheat

Root, underground and above-ground biomass were measured on various wheat cultivars from 1986 to 1988 in the south-east of France. The results are expressed as root: total (f _r) or underground: total (f _u) biomass fractions. Observed f _r and f _u values are in good agreement with previous results. f _r and f _u decrease steadily from emergence to maturity, with an exponential tendency. When using cumulative growth degree days since emergence relative to cumulative growth degree days until ear emergence () as time scale, f _r and f _u can be expressed as simple functions of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGceaqabeaacaWGMb% addaWgaaqaaiaadkhaaeqaamaabmaabaGccqaH4oqCdaahaaWcbeqa% aiaacQcaaaaamiaawIcacaGLPaaakiabg2da9iaaicdacaGGUaGaaG% imaiaaiwdacqGHRaWkcaaIWaGaaiOlaiaaiwdacaaI4aGaamyzamaa% CaaaleqabaGaeyOeI0IaaGymaiaac6cacaaI0aGaaGioaiabeI7aXn% aaCaaameqabaGaaiOkaaaaaaaakeaacaWGMbaddaWgaaqaaiaadwha% aeqaamaabmaabaGccqaH4oqCdaahaaWcbeqaaiaacQcaaaaamiaawI% cacaGLPaaakiabg2da9iaaicdacaGGUaGaaGymaiaaikdacqGHRaWk% caaIWaGaaiOlaiaaiIdacaaI4aGaamyzamaaCaaaleqabaGaeyOeI0% IaaGOmaiaac6cacaaIYaGaaGioaiabeI7aXnaaCaaameqabaGaaiOk% aaaaaaaaaaa!610D!\[\begin{gathered} f_r \left( {\theta ^* } \right) = 0.05 + 0.58e^{ - 1.48\theta ^* } \hfill \\ f_u \left( {\theta ^* } \right) = 0.12 + 0.88e^{ - 2.28\theta ^* } \hfill \\ \end{gathered} \]The incremental root biomass partitioning coefficient, % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySde2aaS% baaSqaaiaadkhaaeqaaOGaeyypa0JaaiikaiaadsgacaWGxbWaaSba% aSqaaiaadkhaaeqaaOGaai4laiaadsgacaWG0bGaaiykaiaac+caca% GGOaGaamizaiaadEfadaWgaaWcbaGaamiDaaqabaGccaGGVaGaamiz% aiaadshacaGGPaaaaa!4834!\[\alpha _r = (dW_r /dt)/(dW_t /dt)\], which describes the net increase in root biomass dW _r over time dt relative to the increase in total biomass (dW _r) over the same time period, has been derived from f and the relative growth rate. Its time course is accurately represented by% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeqySdegdda% WgaaqaaiaadkhaaeqaamaabmaabaGccqaH4oqCdaahaaWcbeqaaiaa% cQcaaaaamiaawIcacaGLPaaakiabg2da9iabgkHiTiaaicdacaGGUa% GaaGymaiaaiwdacqGHRaWkcaaIWaGaaiOlaiaaiAdacaaIZaGaamyz% amaaCaaaleqabaGaeyOeI0IaaGimaiaac6cacaaI5aGaaGioaiabeI% 7aXnaaCaaameqabaGaaiOkaaaaaaaaaa!4D15!\[\alpha _r \left( {\theta ^* } \right) = - 0.15 + 0.63e^{ - 0.98\theta ^* } \]Under our experimental conditions, with no severe water stresses or nutrient deficiencies, and for our sampling frequency, around 2 weeks, the development scale , is the main factor governing the time courses of f _r, f _u and _r.     

Interaction between catabolism and anabolism in the oxidative assimilation of dissolved organic carbon

Catabolism is tightly coupled to anabolism in substrate-limited cultures. However, the dissolved organic carbon (DOC) distribution between catabolism and anabolism has been hardly studied. Based on a balanced DOC reaction, the DOC distribution between catabolism and anabolism was defined using a ratio of the DOC channeled into CO₂ ( ) to that DOC converted to biomass (S _g). A /S _g-dependent growth yield model was proposed for substrate-limited cultures and was verified using the literature data obtained in the oxidative assimilation processes of different types of organic substrates. The model showed that the growth yield (Y _s) was proportional to anabolic activity, but was inversely related to catabolic activity. Results indicated that both Y _s and /S _g varied markedly with the free energy of oxidation of the organic substrate. Further, the observed phenomena were closely associated with maintenance metabolism under substrate-limited conditions.     

An evolutionary analytical model of a complementary circular code simulating the protein coding genes, the 5′ and 3′ regions

The self-complementary subset ∪{AAA,TTT} with = {AAC, AAT, ACC, ATC, ATT, CAG, CTC, CTG, GAA, GAC, GAG, GAT, GCC, GGC, GGT, GTA, GTC, GTT, TAC, TTC} of 22 trinucleotides has a preferential occurrence in the frame 0 (reading frame established by the ATG start trinucleotide) of protein (coding) genes of both prokaryotes and eukaryotes. The subsets ∪{CCC} and ∪{GGG} of 21 trinucleotides have a preferential occurrence in the shifted frames 1 and 2 respectively (frame 0 shifted by one and two nucleotides respectively in the 5′-3′ direction). and are complementary to each other. The subset contains the subset which has the rarity property (6 × 10⁻⁸) to be a complementary maximal circular code with two permutated maximal circular codes and in the frames 1 and 2 respectively. is called a C³ code. A quantitative study of these three subsets in the three frames 0, 1, 2 of protein genes, and the 5′ and 3′ regions of eukaryotes, shows that their occurrence frequencies are constant functions of the trinucleotide positions in the sequences. The frequencies of in the frame 0 of protein genes are 49, 28.5 and 22.5% respectively. In contrast, the frequencies of in the 5′ and 3′ regions of eukaryotes, are independent of the frame. Indeed, the frequency of in the three frames of 5′ (respectively 3′) regions is equal to 35.5% (respectively 38%) and is greater than the frequencies and , both equal to 32.25% (respectively 31%) in the three frames. Several frequency asymmetries unexpectedly observed (e.g. the frequency difference between and in the frame 0), are related to a new property of the subset involving substitutions. An evolutionary analytical model at three parameters (p, q, t) based on an independent mixing of the 22 codons (trinucleotides in frame 0) of with equiprobability (1/22) followed by t ≈ 4 substitutions per codon according to the proportions p ≈ 0.1; q ≈ 0.1 and r = 1 − p − q ≈ 0.8 in the three codon sites respectively, retrieves the frequencies of observed in the three frames of protein genes and explains these asymmetries. Furthermore, the same model (0.1, 0.1, t) after t ≈ 22 substitutions per codon, retrieves the statistical properties observed in the three frames of the 5′ and 3′ regions. The complex behaviour of these analytical curves is totally unexpected and a priori difficult to imagine.     

Contribution to the genetics of serum β-lipoprotein in man

Summary The study of some families of the double black cross type confirmed complete linkage of theAg ^x/y , andAg ^c/g loci.

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Zusammenfassung An Hand einer Untersuchung einiger Familien vom double back cross-Typ konnte das komplette linkage der Gen-LociAg ^x/y , undAg ^c/g bestätigt werden.

     

Energetics of the growth of Methanobacterium thermoautotrophicum and Methanococcus thermolithotrophicus on ammonium chloride and dinitrogen

Methanobacterium thermoautotrophicum was grown in continuous culture in a fermenter gassed with H₂ and CO₂ as sole carbon and energy sources, and in a medium which contained either NH₄Cl or gaseous N₂ as nitrogen source. Growth was possible with N₂. Steady states were obtained at various gas flow rates with NH₄Cl and with and the maintenance coefficient varied with the gas input and with the nitrogen source. Growth of Methanococcus thermolithotrophicus in continuous culture in a fermenter gassed with H₂, CO₂ as nitrogen, carbon and energy sources was also examined.Abbreviations molecular growth yield (g dry weight of cells per mol of CH₄ evolved) - growth rate (h^-1) - D dilution rate (h^-1) - rate (h_-1); relation of Neijssel and Tempest and of Stouthamer and Bettenhaussen - energy     

Bounds on the total population for species governed by reaction-diffusion equations in arbitrary two-dimensional regions

Analysis based on the integration of differential inequalities is employed to derive upper and lower bounds on the total populationN(t) = ∫ _R θ(x ₁,x ₂,t) dx ₁ dx ₂ of a biological species with an area-density distribution function θ=θ(x ₁,x ₂,t) (≥0) governed by a reaction-diffusion equation of the form ∂θ/∂t =D∇²θ +fθ −gθ ⁿ⁺¹ whereD (>0),n (>0),f andg are constant parameters, θ=0 at all points on the boundary ∂R of an (arbitrary) two-dimensional regionR, and the initial distribution (θ(_{x 1},x ₂, 0) is such thatN(0) is finite. Forg≥0 withR the entire two-dimensional Euclidean space, a lower bound onN(t) is obtained, showing in particular thatN(∞) is bounded below by a finite positive quantity forf≥0 andn>1. An upper bound onN(t) is obtained for arbitrary bounded or unbounded)R withn=1,f andg negative, and ∫ _R θ(x ₁,x ₂, 0)² dx ₁ dx ₂ sufficiently small in magnitude, implying that the population goes to extinction with increasing values of the time,N(∞)=0. Forg≥0 andR of finite area, the analysis yields upper bounds onN(t), predicting eventual extinction of the population if eitherf≤0 or if the area ofR is less than a certain grouping of the parameters in cases for whichf is positive. These results are directly applicable to biological species with distributions satisfying the Fisher equation in two spatial dimensions and to species governed by certain specialized population models.     

Holling's “hungry mantid” model for the invertebrate functional response considered as a Markov process. Part I: The full model and some of its limits

In this paper we give an analytical reformulation of Holling's (1966) simulation model for invertebrate predatory behaviour. To this end we represent a population of predators as a frequency distribution over a space of (physiological) states. The functional response of a predator is calculated from the (stable) equilibrium distribution of its state as a function of prey density.Starting from the general model various other models are obtained by limit processes, some of them new and some of them old. The more interesting of which will be studied in further papers in this series.List of Notation a rate constant of digestion - b maximum of rate constant of prey encounter in the mantid - b maximum pursuit duration in the mantid (_p(0)) - c satiation threshold for search - c satiation threshold for pursuit in the mantid: c=c(b-D_s/v)/b - D _m maximum sighting distance - D _p pursuit distance - D _s strike distance - expectation operator - f, f ₀ rate of change of satiation during search - f ₁ rate of change of satiation during prey handling - F functional response: number of prey eaten per unit of time by one predator - g rate constant of effective prey encounter in the gobbler and sucker - g₀ rate constant of prey encounter - g₁ probability of no prey loss from pursuit - g₂ probability of no prey escaping during pursuit - H Holling secretary correction factor in the sucker: fraction of the time spent searching - k _R density of R - k_T probability density of maximum prey handling time - K probability that maximum prey handling time is _e, i.e. pursuit duration is zero - K _R distribution function of R - N number of prey caught - p (marginal) density of S - p₀ density of S in search - p₁ simultaneous density of S and T - P probability - p ₁ marginal density of S in handling prey - q probability of strike success - R ratio of realized to maximum sighting distance - s, S satiation - satiation axis - t time - handling time axis - u eating speed - U homogeneous(0,1) random variable - v pursuit speed - V exponential(1) random variable - w prey weight - W exponential(_m) random variable - x prey density - ratio of maximum successful pursuit duration to meal duration (_pm/_e) - _pm - relative duration of successful pursuit (_p/_pm) - ratio of shortest to largest sighting distance - x_e - time already spent handling a prey item - rate of prey loss during prey handling - prey escape rate during pursuit - prey biomass density (xw) - , T maximum time still to be spent handling a prey item - _e meal duration - _m maximum handling time ( _e+ _p) - _p duration of successful pursuit - _pm maximum duration of successful pursuit (_p(0)) - hazard rate - _m maximum of hazard rate - scaled functional response (wF) - minimal i-state space     

Energy requirements of Adélie penguin (Pygoscelis adeliae) chicks

Summary The energy requirements of Adélie penguin (Pygoscelis adeliae) chicks were analysed with respect to body mass (W, 0.145–3.35 kg, n=36) and various forms of activity (lying, standing, minor activity, locomotion, walking on a treadmill). Direct respirometry was used to measure O₂ consumption ( ) and CO₂ production. Heart rate (HR, bpm) was recorded from the ECG obtained by both externally attached electrodes and implantable HR-transmitters. The parameters measured were not affected by hand-rearing of the chicks or by implanting transmitters. HR measured in the laboratory and in the field were comparable. Oxygen uptake ranged from in lying chicks to at maximal activity, RQ=0.76. Metabolic rate in small wild chicks (0.14–0.38 kg) was not affected by time of day, nor was their feeding frequency in the colony (Dec 20–21). Regressions of HR on were highly significant (p< 0.0001) in transmitter implanted chicks (n=4), and two relationships are proposed for the pooled data, one for minor activities ( ), and one for walking ( ). Oxygen consumption, mass of the chick (2–3 kg), and duration of walking (T, s) were related as , whereas mass-specific O₂ consumption was related to walking speed (S, m·s^-1) as .Abbreviations bpm beats per minute - D distance walked (m) - ECG electrocardiogram - HR heart rate (bpm) - ns number of steps - RQ respiratory quotient - S walking speed (m·s^-1) - T time walked (s) - W body mass (kg)     

Optimal control of continuous fermentation processes

Three layer control structure is proposed for optimal control of continuous fermentation processes. The start-up optimization problems are solved as a first step for optimization layer building. A steady state optimization problem is solved by a decomposition method using prediction principle. A discrete minimum time optimal control problem with state delay is formulated and a decomposition method, based on an augmented Lagrange's function is proposed to solve it. The problem is decomposed in time domain by a new coordinating vector. The obtained algorithms are used for minimum time optimal control calculation of Baker's Yeast fermentation process.List of Symbols x(t) g/l biomass concentration - s(t) g/l limiting substrate concentration - x ⁰ g/l inlet biomass concentration - s ⁰(t) g/l inlet substrate concentration - D(t) h^–1 dilution rate - (t) h^–1 specific growth rate - Y g/g yield coefficient - (t) h^–1 specific limiting substrate consumption rate - k _D h^–1 disappearing constant - w ₁, w ₂ known constant or piece-wise disturbances - _m h^–1 maximum specific growth rate - k _s g/l Michaelis-Menten's parameter - h time delay - x ₀, s ₀ g/l initial concentrations - ¯x, ¯s, ¯D optimal steady state value - V _min , V _max , v=x,s,d,t bounds of variables - t h sampling period - K number of steps in the optimization horison - Js, J _d performance indexes - L _s Lagrange's function - L _d Lagrange's functional - ₀ weighting coefficient for the amount of the limiting substrate throwing out of the fermentor - ₁, ₂ dual variables of Lagrange's function - steps in steady state coordination procedure - errors values for steady state coordination process - _v , v=x, s conjugate variables of Lagrange's functional - _v , v=x,s penalty coefficients of augmented Lagrange's functional - _v , v=x, s interconnections of the time - e _v , v=x,s, D, _x , _s gradients of Lagrange's functional - j, l indexes of calculation procedures - values of errors in calculations The researches was supported by National Scientific Research Foundation under grants No NITN428/94 and No NITN440/94     

A mathematical model of biological evolution

In order to understand generally how the biological evolution rate depends on relevant parameters such as mutation rate, intensity of selection pressure and its persistence time, the following mathematical model is proposed: dN _n (t)/dt=(m _n (t-)N _n (t)+N _n-1(t) (n=0,1,2,3...), where N _n (t) and m _n (t) are respectively the number and Malthusian parameter of replicons with step number n in a population at time t and is the mutation rate, assumed to be a positive constant. The step number of each replicon is defined as either equal to or larger by one than that of its parent, the latter case occurring when and only when mutation has taken place. The average evolution rate defined by is rigorously obtained for the case (i) m _n (t)=m _n is independent of t (constant fitness model), where m _n is essentially periodic with respect to n, and for the case (ii) (periodic fitness model), together with the long time average m of the average Malthusian parameter . The biological meaning of the results is discussed, comparing them with the features of actual molecular evolution and with some results of computer simulation of the model for finite populations.An early version of this study was read at the International Symposium on Mathematical Topics in Biological held in kyoto, Japan, on September 11–12, 1978, and was published in its Procedings.     

Redox control of proton transfers in membrane b-type cytochromes: an absorption and resonance Raman study on bis(imidazole) and bis(imidazolate) model complexes of iron-protoporphyrin

Optical absorption spectra and resonance Raman (RR) spectra, obtained with Soret excitation, are reported for bis(imidazole) and bis(imidazolate) complexes of iron(II)- and iron(III)-protoporphyrin IX, prepared in aqueous conditions. Perdeuteration experiments on the axial ligands permitted the assignment of the symmetric Fe-(ligand)₂ stretching mode of Fe[x]PP(L)₂ to RR bands at 203 (x = II; L = ImH), 212 (x = II; L = Im^–), 201 (x = III; L = ImH) and 226 cm^–1 (x = III; L = Im^–). These frequency differences indicate a strengthening of the axial bonds when the imidazole deprotonations occur. The larger difference observed for the ferric derivatives reflects the stronger -donor capability of the Im^– anion for iron(III) over iron(II). For the ferrous derivatives, the frequencies of several skeletal porphyrin modes (₄, ₁₀, ₁₁ and ₃₈) are downshifted by 2–10 cm^–1 upon deprotonation of the ligands. This effect corresponds to an increased back-bonding from the metal atom to the porphyrin ring when the axial ligand decreases its -acid strength. Bringing further support to this interpretation, an inverse linear relationship is established between the frequencies of (Fe(Il)-L₂) and ₁₁. This correlation is expected to monitor the overall H-bonding state of histidine ligands of reduced cytochromes b. On the other hand, absorption measurements have characterized large pK_a differences for the sequential imidazole ionizations of Fe[x]PP(ImH)₂ in aqueous cetyltrimethylammonium bromide (9.0 and 10.8 for x = 111; 13.0 and 14.1 for x = II). These titrations show that Fe(II)PP(Im^–)₂ and Fe(III)PP(ImH)₂ are good proton-acceptor and proton-donor, respectively, and suggest a model by which heme, located in a favorable environment inside a cytochrome, could couple a cycle of electron transfer with a proton transfer. Based on sequence data and structural models, it is further proposed that, in several membrane cytochromes b (b, b ₆, b ₅₅₉), a positively charged amino acid residue and an imidazolate ligand of the ferriheme could form an ion pair involved in a redox control of proton transfer.Abbreviations RR resonance Raman - EPR electron paramagnetic resonance - PP protoporphyrin IX - ImH imidazole - Im^– imidazolate - Im* imidazole or imidazolate - 1MeIm 1-methylimidazole - HisH histidine - His^– histidinate - CTABr cetyltrimethylammonium bromide - NaDS sodium dodecylsulphate - VLP very low potential - LP low potential - HP high potential     

Activity and oxygen consumption during hypoxic exposure in high altitude and lowland sceloporine lizards

Summary Resting rates of O₂ consumption against , exercise endurance times and during recovery from vigorous exercise were measured inSceloporus occidentalis captured near sea level and inS. graciosus captured above 2850 m. Oxygen consumption against was also measured inS. occidentalis captured above 2850 m. When was recorded continuously, as ambient was slowly reduced from 155 Torr, it became directly dependent upon ambient between 110 and 120 Torr. The critical for the high altitude lizards was lower than that for the lowland lizards, which enabled the former to maintain relatively higher 's when ambient was reduced below 120 Torr. The high altitude lizards also had significantly greater endurance when stimulated to exercise at 1600 m ( 130 Torr). Both the higher under hypoxia and the greater endurance roughly parallel a significantly greater maximum in the high altitude lizards. At a simulated altitude of 3600 m ( 100 Torr), maximum and rate of recovery of the O₂ debt calculated from post active were significantly reduced in the lowland but not the high altitude lizards. The effects of simulated altitude conditions on the lowland but not the mountaine animals indicate adaptations to altitude in these sceloporine lizards. We did not find any consistent relationship between organ/body weight ratios or hematocrit and our measures of endurance or the altitude at which the lizards were captured.