'Steady/equilibrium approximation' in relaxation and fluctuation. II. Mathematical theory of approximations in first-order reaction

A mathematical theory of the steady/equilibrium approximation for first-order reactions is presented. This gives the theoretical basis for the methods of simplifying the complex first-order reactions described in the preceding work The steady/equilibrium relation holds on every fast component after a proper inducation period T degrees T degrees is either of O(1) or less, or nearly of O(1/epsilon) depending on the reaction scheme and on the initial condition but is always less than O(1/epsilon) (as in the preceding paper [1], we use the symbol O(1) to denote a positive number of the order of unity). In the open group, the determinant of the submatrix M(p), representing the interconversion between the fast components in the group and their dissipation, is of O(1). The concentration of the fast components in the open group can thus be expressed as a linear combination of those components neighboring the group after the establishment of a steady/equilibrium relation, and can be eliminated from the reaction scheme leaving the pathway through them. On the other hand, in the closed group the determinant of Mp is of O(epsilon) or less and the components in the group are in quasi equilibrium with each other after T degrees . They are eliminated from the reaction scheme leaving the sum of the components in the closed group as a slow component.     

‘Steady/equilibrium approximation’ in relaxation and fluctuation: I. Procedure to simplify first-order reaction

A general procedure to simplify a complex first-order reaction by two approximations, the principle of fast equilibration and the steady-state approximation, is presented. Rate constants are classified into two groups: those of the order of unity and those of the order of ?(? 1) or less, and are represented in the schemes by thick and thin arrows, respectively. The fast and the slow components are defined: from the fast component at least one thick arrow originates and from the slow component no thick arrow originates. Fast components are divided into several groups. In a group, the fast components are connected by thick arrows in both directions in each reaction step. When at least one thick arrow originates from the components in a group G and terminates on a component not belonging to group G (group G is open), then the steady-state approximation or principle of fast equilibration holds on each component in group G after an induction period T°. When no thick arrow originating from group G is directed to components not belonging to group G (group G is closed), the principle of fast equilibration holds on the fast components in group G after T°. The induction period T° is less than the order of I/?.     

Molecular Dynamics as a Mathematical Mapping. II. Partial Derivatives in the Microcanonical Ensemble

Abstract

Performing molecular dynamics in a fully continuous and differentiable framework can be viewed as a deterministic mathematical mapping between, on one side, the force field parameters that describe the potential energy interactions and input macroscopic conditions, and, on the other, the calculated corresponding macroscopic properties of the bulk molecular system.

Within this framework, it is possible to apply standard methods of variational calculus for the computation of the partial derivatives of the molecular dynamics mapping based on the integration of either the adjoint equations or the sensitivity equations of the classical Newtonian equations of motion. We present procedures for these computations in the standard microcanonical (N, V, E) ensemble, and compare the computational efficiency of the two approaches. The general formulations developed are applied to the specific example of bulk ethane fluid.

With these procedures in place, it is now possible to compute the partial derivatives of any property determined by molecular dynamics with respect to any input property and any potential parameter. Moreover, these derivatives are computed to essentially the same level of numerical accuracy as the output properties themselves.     

The Potential of Photochemical Transition Metal Reactions in Prebiotic Organic Synthesis. I. Observed Conversion of Methanol into Ethylene Glycol as Possible Prototype for Sugar Alcohol Formation

Photochemical processes involving redox reactions between metal ions and organic substrates possess the versatile potential for having harnessed solar energy for prebiotic organic synthesis. The present study in our Laboratory has shown that ultraviolet irradiation of transition metal ions such as of Ni, Co, Fe, Cu and Ti dissolved in primary or secondary alcohols causes photoreduction of the metal ions with the concomitant oxidation of the alcohol to aldehyde or ketone. An observed accompaniment of this novel 'light' reaction has been the known 'dark' pinacol reaction, whereby the carbonyl derivative underwent bimolecular coupling to the diol by the photogenerated reduced transition metal reagent. These tandem 'light-dark' processes possess the potential for the stepwise synthesis of dimeric 1,2-diols from simpler alcohols under conditions that might have prevailed on the prebiotic earth. Experiments reported here have demonstrated that such a tandem 'light-dark' conversion of methanol into ethylene glycol, via formaldehyde, does in fact occur, when nickel(II) acetylacetonate solutions in methanol undergo prolonged irradiation at 185-254 nm. Since ethylene glycol can be considered as the simplest sugar alcohol, these findings may provide novel insight into the prebiotic oligomerization of formaldehyde into higher sugar alcohols or even sugars.     

The use of potassium iodide equilibrium density gradient centrifugation in the purification of RNA for hybridization with nonreiterated DNA sequences.

A new instrument has been developed that is able to monitor enzyme activities in chromatography column eluents automatically. The instrument consists of a simple stopped-flow instrument, equipped with a multishutoff valve to direct reagents and eluent flow. Assays of the eluate may be done at present intervals. The instrument may also be used for monitoring enzyme activities in perfasates as well as for monitoring the elution of metabolites.     

环境科学国际合作的理论机制研究

迄今科学界尚无形成系统的国际科学合作理论,也鲜有就环境科学国际合作进行理论研究。首次从全球资源配置的角度来看待环境科学国际合作。通过国际合作,环境科学在内在科学动力和外在社会动力的驱动下,促使全球科学资源和社会资源向有利于环境学科自身发展的方向流动和积聚。其中,配置科学资源遵循"最优要素选择原则",配置社会资源遵循"最小省力原则",两种内在动力和两个调节手段共同构成了环境科学国际合作的理论机制。     

The copper-molybdenum antagonism in ruminants. I. The formation of thiomolybdates in animal rumen

The formation of thiomolybdates, MoO_xS_4?x^2?(x = 0, 1, 2, or 3), from molybdate and sulphide salts in aqueous media has been studied under conditions which simulate the fluid phase in the rumen. The influences of the sulphide:molybdenum ratio, pH and phosphate levels on the nature of the species formed were investigated. The thiomolybdates, in particular the MoS_4^2? ion, have been implicated as the active intermediates in the widespread molybdenum induced copper deficiency that affects ruminants. The results presented here show that, under physiological conditions, di- and trithiomolybdates will form more readily than tetrathiomolybdate.     

城市化对合肥蝶类多样性的影响

2010年3—10月,沿城市发展梯度选取了合肥市3个区域(城市、城郊和农村),进行蝴蝶调查。共采集蝴蝶1484只,隶属7科28属34种。结果表明:研究区域优势种蝶类为菜粉蝶(Pieris rapae)、酢浆灰蝶(Pseudozizeeria maha)、黄钩蛱蝶(Polygonia c-aureum);合肥不同城市化区域蝶类多样性存在差异,其多样性指数变化趋势为农村城郊城市;农村和城郊的多样性指数和丰富度指数在7月最高,城市8月最高;城市和城郊的优势度指数在8月最高,农村7月最高;3种不同城市化区域的均匀度指数均是8月最高。在快速城市化过程中,应根据不同城市化水平、不同生境类型采取不同的措施,保护和促进城市生物多样性。     

The evolution of body size in birds. I. Evidence for non-random diversification

The hypothesis that evolution of body size in birds was a random process coupled with an absolute lower boundary on body mass was tested using data on 6217 species of extant birds. The test was based on the fact that subclades within birds that have body masses much larger than this minimum should not have skewed log body mass distributions, while clades close to this boundary should. Bird species were classified into 23 orders suggested by Sibley and Monroe (1988). Thirteen orders that had average log body masses greater than the average for all birds had significantly skewed log body mass distributions. This is inconsistent with the hypothesis that evolution of body size in birds is random, but is constrained only at the smallest body masses. Most orders of birds cannot be considered random samples from the parental distribution of all birds. When the pattern of body mass evolution in birds is reconstructed using an estimate of the phylogenetic relationships among orders, there are many more instances where a large taxon putatively originated from a smaller one than vice versa. The non-random nature of body mass evolution in birds is consistent with models that postulate that evolution is constrained by the ability of individuals to turn resources into offspring.     

The binding of divalent metal ions to polyelectrolytes in mixed counterion systems. I. The dye spectrophotometric method

The dye spectrophotometric method for the measurement of the activity of divalent metal ions in polyelectrolyte solutions containing added electrolytes is discussed.The method is applied to mixtures containing the dextransulfate polyanion, NaCl, and MgCl2 or Ca2. A two wavelength ratio method as applied to polyelectrolyte solutions is compared to the standard method which makes use of the previous determination of the dye-metal ion formation constant. The ratio method is found to be a convenient and reliable method which is not influenced by decomposition of the dye or by statistical errors in the extrapolation procedure. The activity coefficients as determined by the two wavelength dye spectrophotometric method are compared to results of Donnan exclusion measurements, and of EMF measurements using a calcium ion selective electrode. The results of the spectrophotometric method are equal to those of the two other methods within the limits of error in the latter. The spectrophotometric measurements can extend to much lower ion activaties than the other two methods, and can be done in the presence of a large excess of added electrolyte, yielding results of considerably improved precision when compared to Donnan and EMF methods.     

Signal Analysis of Irradiation,Temperature and Primary Production in a Small Artificial Pond: I. The Annual Signals

This paper provides an example of some initial steps in signal analysis applied to a simple aquatic ecosystem in the form of a small artificial pond. Irradation, water temperature and dissolved oxygen concentration were continuously recorded over a two year period. Following the definition and discussion of several related parameters, an analysis procedure for trends and forced annual patterns was proposed and carried out. The annual pattern of photosynthetic fixation of solar energy is characterized by the annual level transfer efficiency, and for the periodic part of the process, by the transfer gain and phase shift. The possible role of temperature is briefly discussed.     

Gonadal receptors I. Evidence for irreversibility in the binding of human chorionic gonadotropin and human luteinizing hormone

The binding of human chorionic gonadotropin and human luteinizing hormone to particulate receptors of rat testes has generally been assumed to follow an equilibrium model similar to that proposed for many enzyme systems. Our work shows that equilibrium dissociation constant (K_d) and number of hormone binding sites (B_max) are highly sensitive to changes in hormone and/ or receptor concentration and to treatment received by tissue or receptor preparation prior to the assay. The results of binding assays obtained using receptor preparation pretreated with hormone (labeled as well as unlabeled) indicated that the binding reaction between hormone and receptor was irreversible and that pretreatment of the tissue with hormone greatly alters the number of high affinity gonadotropin binding sites in the testicular homogenate. Data from studies involving increasing receptor concentrations revealed that increasing the mass of particulate receptors in the binding assays leads to higher K_d as well as B_max values. These findings are incompatible with a binding model based upon occupancy of receptor sites and the state of equilibrium implied. The incompatibilities are analyzed and an alternate model advanced (Bhalla, V.K., Trowbridge, C.G., Chen, C.J.H., Lindeman, J.G. and Rojas, F.J. (1979) Biochim. Biophys. Acta 584, 436–453).     

The Role of Elytra in Beetle Flight: I. Generation of Quasi-Static Aerodynamic Forces

We conducted a comprehensive study to investigate the aerodynamic characteristics and force generation of the elytra of abeetle,Allomyrina dichotoma.Our analysis included wind tunnel experiments and three-dimensional computational fluiddynamics simulations using ANSYS-CFX software.Our first approach was a quasi-static study that considered the effect ofinduced flapping flow due to the flapping motion of the fore-wings (elytra) at a frequency of around 30 Hz to 40 Hz.The dihedralangle was varied to represent flapping motion during the upstroke and downstroke.We found that an elytron producespositive lift at 0° geometric angle of attack,negative lift during the upstroke,and always produces drag during both the upstrokeand downstroke.We also found that the lift coefficient of an elytron does not drop even at a very high geometric angle of attack.For a beetle with a body weight of 5 g,based on the quasi-static method,the fore-wings (elytra) can produce lift of less than 1%of its body weight.     

Antigen-specific helper activity in serum of mice primed with sheep red cells. I. Definition of the test system and comparison with other systems

An adoptive transfer system is described to measure serum helper activity in the primary antibody response to sheep red blood cells (SRBC). Mice injected with a high dose of cyclophosphamide and reconstituted with rabbit anti-thymocyte serum-treated spleen cells were used as recipients. Serum obtained 9 hr after ip injection of normal mice with 2 × 10⁸ SRBC (S(SRBC)) injected i.v. in the recipients caused a significant enhancement of the antibody response to 2 × 10⁷ SRBC. The serum helper activity was not generated in thymectomized animals and could be absorbed from S(SRBC) by normal and formalinized SRBC. The SRBC-specific serum helper activity (SSHA) is heat labile (30 min 56 °C) and shows allogeneic restriction. Another test system described in literature for measuring T-cell help in vivo was less suited to measure SSHA in the response to 2 × 10⁷ SRBC. A system using normal mice injected with 10⁵ SRBC for determining specific immune response-enhancing factor (SIREF), demonstrated SIREF activity in S(SRBC). It did, however, not measure SSHA, as absorption of S(SRBC) with formalinized SRBC did not abolish the activity in that system.     

Internode length in Pisum. I. The effect of the Le/le gene difference on endogenous gibberellin-like substances

The allelopathic potential of the dry fruits of Washingtonia filifera (L. Linden) H. Wendl. was investigated. Leachates from fruits inhibited the germination of lettuce, wheat, red cabbage and cucumber seeds. The inhibitory effect was partly neutralized by kinetin (20 mg 1⁻¹) and gibberellic acid (50 mg 1⁻¹). The effect of kinetin was more pronounced at 25°C than at 20°C. Substances inhibiting germination were localized in the pericarp of the fruit and were resistant to high temperature.     

Countercurrent distribution of lymphocytes from human peripheral blood in an aqueous two-phase system. I. Separation into subsets of lymphocytes bearing distinctive markers

Lymphocytes from human peripheral blood have been separated by countercurrent distribution in a charged aqueous two-phase system composed of Dextran T 500 and polyethylene glycol 6000 with a cell yield of 59–88% and viability above 90%. A highly reproducible partition pattern was seen with four distinct peaks. Lymphocytes with surface membrane immunoglobulin (SmIg) were located in the first part of the distribution corresponding mainly to peak I. T lymphocytes as detected by E rosetting and α-naphthyl acetate esterase (ANAE) staining showed a broad distribution with a maximum in peaks II and III. ANAE-negative lymphocytes were seen in both extremes of the distribution, corresponding to B cells in the first part and to a population of E^? and SmIg^? lymphocytes in the last part. Monocytes were present in all fractions with some enrichment in peaks II–IV. Lymphocytes with low-affinity Fc receptors were found in B-cell-containing fractions in the first part of the distribution, but also in the last part. Lymphocytes with high-affinity Fc receptors were detected mainly in peak IV. It is thus demonstrated that peripheral blood lymphocytes can be fractionated into subpopulations enriched in cells with characteristic markers.