A note on the nonautonomous delay Beverton-Holt model

It is well known that the periodic cycle {x(n)} of a periodically forced nonlinear difference equation is attenuant (resonant) if av(x(n)) < av(K(n))(av(x(n)) > av(K(n))),where {K ( n )} is the carrying capacity of the environment and av(t(n)) = (1/p)∑(p?1) (i=0) ti (arithmetic mean of the p-periodic cycle {t ( n )}). In this article, we extend the concept of attenuance and resonance of periodic cycles using the geometric mean for the average of a periodic cycle. We study the properties of the periodically forced nonautonomous delay Beverton-Holt model x(n+1) = r(n)x(n)/1 + (r(n?l) ? 1)x(n?k)/K(n?k), n= 0, 1, . . . , where {K ( n )} and {r ( n )} are positive p-periodic sequences; (K ( n )>0, r ( n )>1) as well as k and l are nonnegative integers. We will show that for all positive solutions {x ( n )} of the previous equation lim sup (n→∞) (∏(n?1)(i=0)xi)(1/n) ≤ ((∏(p?1)(i=0)ri)(1/p) ? 1)(∏(p?1)(i=0)(ri ? 1))(?1/p)(∏(p?1)(i=0)Ki)(1/p). In particular, in the case where {x(n)} is a p-periodic solution of the above equation (assuming that such solution exists) and r ( n )=r>1, the periodic cycle is g-attenuant, that is (∏(p?1)(i=0)x(i))(1/p)<(∏(p?1)(i=0)K(i))(p?1) Surprisingly, the obtained results show that the delays k and l do not play any role.     

The discrete dynamics of symmetric competition in the plane

We consider the generalized Lotka-Volterra two-species system xn + 1 = xn exp(r1(1 - xn) - s1yn) yn + 1 = yn exp(r2(1 - yn) - s2xn) originally proposed by R. M. May as a model for competitive interaction. In the symmetric case that r1 = r2 and s1 = s2, a region of ultimate confinement is found and the dynamics therein are described in some detail. The bifurcations of periodic points of low period are studied, and a cascade of period-doubling bifurcations is indicated. Within the confinement region, a parameter region is determined for the stable Hopf bifurcation of a pair of symmetrically placed period-two points, which imposes a second component of oscillation near the stable cycles. It is suggested that the symmetric competitive model contains much of the dynamical complexity to be expected in any discrete two-dimensional competitive model.     

Parameter dependence of myoglobin-facilitated transport of oxygen in the presence of membranes

Some physicochemical entities involved in the facilitated transport of oxygen along a transport path z1 less than or equal to z less than or equal to zn with membranes impermeable to myoglobin at zi, i = 1,...,n, were identified in an earlier paper [Math. Biosci. 95:209 (1989)]. These entities are the partition between the oxygen and oxymyoglobin flows, the flow transfers taking place near a membrane, and the membrane resistance. Expressions for these entities were obtained that explicitly involve the parameters of the system. In this paper, for the case of prescribed boundary oxygen concentrations x1 and xn, these expressions are incorporated into (i) an explicit representation for the facilitated transport value in terms of the difference, E(x1)-E(xn), between the boundary oxymyoglobin equilibrium values and the sum, gamma, of the membrane resistances, and (ii) a representation for the distribution of the membrane oxygen concentrations xi at zi, i = 2,...,n-1. This makes it possible to analyze the manner in which the facilitated transport depends on the parameters. For a physiological range of parameter values, the facilitated transport was found to increase as either the oxygen-myoglobin association rate constant k', the dissociation rate constant k, the oxygen diffusion coefficient, or the oxymyoglobin diffusion coefficient increases. Thus, the facilitated transport does not depend directly on ratios of chemical and diffusion coefficients. Although the increase in the oxygen diffusion coefficient does not per se affect the chemical conductance, it diminishes the membrane resistance through an interface feature, with a resulting increase in the facilitated transport. For a larger range of values of k' and k, the dependences of the facilitated transport on k' and on k are both biphasic and are similar in shape. However, the mechanisms involved are different: The associated changes in E(x1)-E(xn) and in gamma that result from the increase in k' are opposite to those that result from an increase in k. The use of (i) and (ii) permits, also, discrimination between the different roles of the physicochemical entities involved in a given facilitated transport change. In some cases (e.g., the decreasing phase of the facilitated transport as k' increases), this change depends in an essential manner on a secondary modification of the profile xi, i = 1,...,n, along the transport path.     

具状态依赖时滞单种群模型周期正解的存在性

用重合度论的连续性定理,本文获得如下具状态依赖时滞的单种群增长模型周期正解的存在性x(t)=x(t)[a(t)+b(t)xp(t-τ(t,x(t)))-c(t)xq(t-τ(t,x(t)))]这里a,b,c∈C((0,∞),R)是周期为ω(ω>0)的连续函数,且a>0,c>0.m,p,q为正整数且q>p.     

Differential sequence dynamics of homopolymeric and alternating AT tracts in a small plasmid DNA

The location of OsO4 bispyridine hyper- and hyporeactivity in a small deletion derivative of plasmid ColE1 (PTC12, 1727 bp) has been determined for approximately 70% of the molecule. Thymine bases in homopolymeric (dA)n.(dT)n tracts (n greater than or equal to 4) were always found to be resistant toward OsO4 modification. DNA supercoiling did not destabilize these tracts. The extent of OsO4 bispyridine reactivity of homopolymeric (dA)n.(dT)n tracts, where n = 3, was found to be dependent on the rate of base unpairing of the sequence immediately 5' and 3' to the tract. Repressed OsO4 reactivity of thymine bases in (dA)3.(dT)3 tracts was observed if immediately both 5' and 3' to the tract were stable DNA sequences composed of GC base pairs and/or a homopolymeric (dA)n.(dT)n tract (n greater than or equal to 4). Homopolymeric tracts of n = 3 not having adjacent sequences with repressed unpairing rates did not show reduced levels of OsO4 bispyridine reactivity. Alternating d(TA)n tracts (n greater than or equal to 2) were found to exhibit hyperreactivity with OsO4. The extent of this hyperreactivity was dependent on the length of the tract and superhelical torsional stress. The distribution and frequency of homopolymeric (dA)n.(dT)n (n greater than or equal to 4) tracts in Escherichia coli promoter sequences were examined, and the possible implications of these tracts on promoter function are discussed.     

Increase of hybrids in yeast electrofusion by mitochondrial mutations

Yeast mitochondria were found to affect the zeta-potential of protoplasts, resulting in electrofusion of membrane behavior. For modeling purposes, two fusion systems were investigated: (1) parent yeasts of Saccharomyces cerevisiae G706 (rho(+)) x O708-11-16A (rho(+)), with zeta-potentials of -10 to -27 mV and -28 to -45 mV, depending on MgCl(2) concentration in the medium, respectively; and (2) parent yeasts of S. cerevisiae G706-1 (rho(-)) x O708-11-16A (rho(+)), with zeta-potentials of -30 to -60 mV, depending on MgCl(2). Yields of the hybrids in system (2) were over 100-fold higher than those in system (1). Thus, regulation of yeast electrofusion was found to be possible by mitochondrial mutations.     

Some redox properties of myohemerythrin from retractor muscle of Themiste zostericola

Distinct semimetmyohemerythrin species are produced by one-electron oxidation of deoxymyohemerythrin and one-electron reduction of metmyohemerythrin. The former, (semimetmyo)o, changes (greater than or equal to 90%) to the latter, (semimetmyo)R, with k = 1.0 x 10(-2) s-1, delta H = 15.1 kcal mol-1 and delta S = -17 eu. Oxidation of (semimetmyo)o by Fe(CN)6(3)- rapidly produces an unstable metmyohemerythrin form which converts to the final metmyohemerythrin with k = 4.6 x 10(-3) s-1, delta H = 16.8 kcal mol-1, and delta S = -13 eu. The two met forms react at the same rate with N3-, but the unstable form reacts very rapidly with S2O4(2-) in contrast to stable metmyohemerythrin. (Semimetmyo)R or a mixture of metmyohemerythrin and deoxymyohemerythrin equilibrate very slowly to a mixture containing all three species. The rate constants for disproportionation and comproportionation are 0.89 M-1 s-1 and 9.4 M-1 s-1, respectively. EPR spectra near liquid He temperatures and optical absorption spectra have been used to characterize and measure the rates at 25 degrees C, pH 8.2, and I = 0.15 M. The comparative behavior of octameric and monomeric protein is discussed.     

Analysis of biochemical phase shift oscillators by a harmonic balancing technique

The use of harmonic balancing techniques for theoretically investigating a large class of biochemical phase shift oscillators is outlined and the accuracy of this approximate technique for large dimension nonlinear chemical systems is considered. It is concluded that for the equations under study these techniques can be successfully employed to both find periodic solutions and to indicate those cases which can not oscillate. The technique is a general one and it is possible to state a step by step procedure for its application. It has a substantial advantage in producing results which are immediately valid for arbitrary dimension. As the accuracy of the method increases with dimension, it complements classical small dimension methods. The results obtained by harmonic balancing analysis are compared with those obtained by studying the local stability properties of the singular points of the differential equation. A general theorem is derived which identifies those special cases where the results of first order harmonic balancing are identical to those of local stability analysis, and a necessary condition for this equivalence is derived. As a concrete example, the n-dimensional Goodwin oscillator is considered where p, the Hill coefficient of the feedback metabolite, is equal to three and four. It is shown that for p = 3 or 4 and n less than or equal to 4 the approximation indicates that it is impossible to construct a set of physically permissible reaction constants such that the system possesses a periodic solution. However for n greater than or equal to 5 it is always possible to find a large domain in the reaction constant space giving stable oscillations. A means of constructing such a parameter set is given. The results obtained here are compared with previously derived results for p = 1 and p = 2.     

A first mathematical approximation of cerebral cortical responses to cerebello-thalamic signals using a thermodynamic analogue.

A mathematical approximation is developed to predict cerebral cortical responses CTX(t, x, R) at a distance R (R greater than or equal to 0) from a focal point in the cerebral cortex, at a depth x (0 less than or equal to x less than or equal to 500 mu) from the cortical surface and at any time t, to thalamic signals THAL(t) whose amplitudes also vary with time t. The equation is derived from a thermodynamic analogue, which is the time dependent heating of a focus at the surface of a semi-infinite solid.     

具有周期传染率的SIR传染病模型的周期解

考虑了具有周期传染率的SIR流行病模型,定义了基本再生数^-R0=β／（μ＋γ）,分析了该模型的动力学性态,证明了当^-R0〈1时无病平衡点是全局稳定的;^-R0〉1时,无病平衡点是不稳定的,模型至少存在一个周期解。对小振幅的周期传染率模型,给出了模型周期解的近似表达式,证明了该周期解的稳定性,最后做了数值模拟,结果显示周期解可能是全局稳定的。     

Variance-component estimation from human sibship data

The large-sample relative efficiencies of the analysis-of-variance (ANOVA) estimators of variance components and the intraclass correlation coefficient rho are investigated for the unbalanced single classification in the context of family studies. The efficiency of an analysis based on the method of unweighted group means is also investigated. From a Monte Carlo study which generates the group sizes from typical family-size distributions it is found that the relative efficiency of the ANOVA estimators of the between-group variance component exceeds 95% for values of .2 less than or equal to rho less than or equal to .4, but can fall below 60% for values of rho that are very close to zero. For the estimation of the between-group variance component the method of unweighted means tends to be preferable to the ANOVA method only if rho greater than .5.     

Mapping meristem respiration of Prunus persica (L.) Batsch seedlings: potential respiration of the meristems, O2 diffusional constraints and combined effects on root growth

Root system architecture partially results from meristem activities, which themselves depend on endogenous and environmental factors, such as O2 depletion. In this study, meristem respiration and growth was measured in the root systems of three Prunus persica (L.) Batsch seedlings. The spatial distribution of meristem respiration within the root system was described, and the relationship between the respiration rates and meristem radii was analysed, using a model of radial O2 diffusion and consumption within the root. Histological observations were also used to help interpret the results. Respiration rates were linearly correlated to the root growth rates (rho 2 = 0.9). Respiration reached values greater than 3.5 x 10(-13) mol O2 s-1 for active meristems. The taproot meristem consumed more O2 than the rest of the entire root system meristems. Similarly, the first order lateral meristems used more O2 than the second order ones. A near hyperbolic relationship between respiration rates and meristem radii was observed. This can be explained by a model of radial O2 diffusion and consumption within the root. Therefore, only one maximum potential respiration rate and one O2 diffusion coefficient was estimated for all the meristems.     

Reproduction numbers and thresholds in stochastic epidemic models. I. Homogeneous populations.

We compare threshold results for the deterministic and stochastic versions of the homogeneous SI model with recruitment, death due to the disease, a background death rate, and transmission rate beta cXY/N. If an infective is introduced into a population of susceptibles, the basic reproduction number, R0, plays a fundamental role for both, though the threshold results differ somewhat. For the deterministic model, no epidemic can occur if R0 less than or equal to 1 and an epidemic occurs if R0 greater than 1. For the stochastic model we find that on average, no epidemic will occur if R0 less than or equal to 1. If R0 greater than 1, there is a finite probability, but less than 1, that an epidemic will develop and eventuate in an endemic quasi-equilibrium. However, there is also a finite probability of extinction of the infection, and the probability of extinction decreases as R0 increases above 1.     

Hierarchical selection theory and sex ratios I. General solutions for structured populations

Models of sex-ratio evolution in structured populations are derived with G.R. Price's covariance form for the hierarchical analysis of natural selection (1970, Nature 227, 520-521). Previous work on competition among related males for mates (local mate competition), competition among related females for a limiting resource (local resource competition), inbreeding, group selection, and asymmetry of genetic inheritance between males and females, are subsumed under a general formulation for sex-ratio biases in structured populations. I found that the evolutionarily stable strategy sex ratio (males:females) for diploids is 1 - rho m:1 - rho f, where rho m is the regression coefficient of relatedness of the controlling genotypes on males competing for mates, rho f is the regression of controlling genotypes on females that compete for a fixed, limiting resource, and there is no inbreeding. For inbreeding and no competition among females, the evolutionarily stable strategy is 1 - rho m:1 + rho mf, where rho mf is the regression of controlling genotypes on females' mates.     

State-dependent impulsive models of integrated pest management (IPM) strategies and their dynamic consequences

A state-dependent impulsive model is proposed for integrated pest management (IPM). IPM involves combining biological, mechanical, and chemical tactics to reduce pest numbers to tolerable levels after a pest population has reached its economic threshold (ET). The complete expression of an orbitally asymptotically stable periodic solution to the model with a maximum value no larger than the given ET is presented, the existence of which implies that pests can be controlled at or below their ET levels. We also prove that there is no periodic solution with order larger than or equal to three, except for one special case, by using the properties of the LambertW function and Poincare map. Moreover, we show that the existence of an order two periodic solution implies the existence of an order one periodic solution. Various positive invariant sets and attractors of this impulsive semi-dynamical system are described and discussed. In particular, several horseshoe-like attractors, whose interiors can simultaneously contain stable order 1 periodic solutions and order 2 periodic solutions, are found and the interior structure of the horseshoe-like attractors is discussed. Finally, the largest invariant set and the sufficient conditions which guarantee the global orbital and asymptotic stability of the order 1 periodic solution in the meaningful domain for the system are given using the Lyapunov function. Our results show that, in theory, a pest can be controlled such that its population size is no larger than its ET by applying effects impulsively once, twice, or at most, a finite number of times, or according to a periodic regime. Moreover, our theoretical work suggests how IPM strategies could be used to alter the levels of the ET in the farmers' favour.     

Cooperative ligand-lattice binding. Approximate Gaussian binding distribution

Nearest-neighbor cooperative binding of a ligand covering n sites and binding with equilibrium constant K and cooperativity factor omega to a large molecule with m binding sites (m much greater than n omega, n/omega) can be approximately described by a Gaussian distribution P(q-qmax), where q is the number of ligands bound and qmax the most probable value of q. The variance of the Gaussian is equal to the derivative dqmax/d ln(L), where L is the free ligand concentration. This variance, sigma 2, is a complicated function of qmax. However, in the limits of very large cooperativity, omega much greater than 1, very large anticooperativity, omega much less than 1, or noncooperativity, omega = 1, simpler expressions for sigma 2 can be given. For qmax = m/(n + 1), where the most probable number of bound ligands equals the number of free binding sites, sigma 2 has a particularly simple form: sigma 2 = 2m omega 1/2/(n + 1)3. The Gaussian and the infinite lattice approximations for the average number of ligands bound are good approximations only if sigma is much smaller than the number of binding sites. The variance may therefore provide an easy check on the validity of the infinite lattice approximation, which is commonly used to analyze experimental binding data.     

An impulsive delayed SEIRS epidemic model with saturation incidence

A delayed SEIRS epidemic model with pulse vaccination and saturation incidence rate is investigated. Using Krasnoselskii's fixed-point theorem, we obtain the existence of infection-free periodic solution of the impulsive delayed epidemic system. We define some new threshold values R(1), R(2) and R(3). Further, using the comparison theorem, we obtain the explicit formulae of R(1) and R(2). Under the condition R(1) < 1, the infection-free periodic solution is globally attractive, and that R(2) > 1 implies that the disease is permanent. Theoretical results show that the disease will be extinct if the vaccination rate is larger than θ* and the disease is uniformly persistent if the vaccination rate is less than θ(*). Our results indicate that a long latent period of the disease or a large pulse vaccination rate will lead to eradication of the disease. Moreover, we prove that the disease will be permanent as R(3) > 1.     

Fluorescence quenching of a series of membrane probes measured in living cells by flow cytometry

The transverse location normal to the bilayer surface of a series of n-(9-anthroyloxy) fatty acid probes, where n = 2, 3, 6, 7, 9, 12, and 16, was determined by fluorescence quenching measurements with a flow cytometer. We show that the anthroyloxy moieties of the probes locate at a graded series of depths in the outer leaflet of the plasma membrane of living HeLa cells, in a manner similar to that previously observed for model membrane systems, and mitochondria. For different n, the efficiency of quenching with an aqueous phase quencher, Cu+2, was 2 greater than or equal to 3 greater than 6 greater than or equal to 7 greater than 9 greater than 12 greater than 16. Therefore, flow cytometry permits use of these probes for measurements of dynamic parameters related to membrane fluidity at different depths in the plasma membranes of living cells.     

Meiotic Gene Conversion Tract Length Distribution within the Rosy Locus of Drosophila Melanogaster

Employing extensive co-conversion data for selected and unselected sites of known molecular location in the rosy locus of Drosophila melanogaster, we determine the parameters of meiotic gene conversion tract length distribution. The tract length distribution for gene conversion events can be approximated by the equation P(L >/= n) = (n) where P is the probability that tract length (L) is greater than or equal to a specified number of nucleotides (n). From the co-conversion data, a maximum likelihood estimate with standard error for is 0.99717 +/- 0.00026, corresponding to a mean conversion tract length of 352 base pairs. (Thus, gene conversion tract lengths are sufficiently small to allow for extensive shuffling of DNA sequence polymorphisms within a gene.) For selected site conversions there is a bias towards recovery of longer tracts. The distribution of conversion tract lengths associated with selected sites can be approximated by the equation P(L >/= n| selected = (n)(1 - n + n/), where P is now the probability that a selected site tract length (L) is greater than or equal to a specified number of nucleotides (n). For the optimal value of determined from the co-conversion analysis, the mean conversion tract length for selected sites is 706 base pairs. We discuss, in the light of this and other studies, the relationship between meiotic gene conversion and P element excision induced gap repair and determine that they are distinct processes defined by different parameters and, possibly, mechanisms.     

Differential interactions of estrogens and antiestrogens at the 17 beta-hydroxy or counterpart function with the estrogen receptor

The action of diethylpyrocarbonate on lamb uterine estrogen receptor produced an homogeneous population of the receptor (approximately 55%) which still bound triarylethylene antiestrogens such as 4-hydroxytamoxifen with a high affinity but bound classical potent estrogens such as estradiol or diethylstilbestrol with a very low affinity. To specify the structural features of the ligands involved in the decrease of ligand affinity upon modification of the estrogen receptor, we determined the relative affinity constants of 17 steroidal estrogens or antiestrogens (deriving from estradiol by a 7 alpha- or 11 beta-substitution) and 14 nonsteroidal estrogens or antiestrogens (all including the 1,2-trans-diphenylethylene structure of diethylstilbestrol) for native and diethylpyrocarbonate-modified estrogen receptors. Then the ratio of the relative affinity constant for the native receptor to that for the modified receptor (rho) was calculated for each ligand, to compare the variation in the affinity of the ligand upon modification of the receptor to that of 4-hydroxytamoxifen (rho = 1). The results showed that the strong decrease of ligand affinity upon modification of the receptor displayed by classical estrogens (rho greater than or equal to 200) is strictly dependent on the presence of the 17 beta-hydroxyl group in steroidal compounds or its alpha-4- and beta-4-counterparts in diethylstilbestrol-related compounds. However, for the 7 alpha- or 11 beta-derivatives of estradiol displaying potent antiestrogenic properties, the relative decrease in affinity was much more limited (rho less than or equal to 19). For 11 beta-derivatives displaying a relative estrogenic activity weaker than that of estradiol itself, an average decrease in affinity was observed (23 less than or equal to rho less than or equal to 62). With the diethylstilbestrol-related compounds, bearing or not the alpha-4-hydroxyl and/or the beta-4-hydroxy functions and showing either weak relative estrogenic or antiestrogenic properties, the relative variation in affinity was weak (0.6 less than or equal to rho less than or equal to 24). These results indicate that the interaction of 7 alpha- or 11 beta-substituted steroidal antiestrogens and of 1,2-trans-diphenylethylene or triphenylethylene derivatives, displaying either weak relative estrogenic or antiestrogenic properties with the receptor, differs at the 17 beta-hydroxy or at the alpha-4-/beta-4-hydroxy functions from that of potent estrogens. They suggest that the strong decrease in the relative affinity of ligands upon receptor modification may reflect the high efficiency of the ligands to activate the receptor properly.(ABSTRACT TRUNCATED AT 400 WORDS)