Topological biology: A note on Rashevsky's transformation T.

In the bio-topological transformation between graphs denoted by (T ⁽¹⁾ X) N. Rashevsky (Bull. Math. Biophysics,18, 173–88, 1956) considers the number of fundamental sets which (a) have only one specialized point as source (and no other sources), (b) have no points in common (are “disjoined”); he proves that this number is an invariant of the transformation. In this note we show that Rashevsky's Theorem can be extended as follows:The number of fundamental sets of the first category is an invariant of the transformation. We must, however, count the subsidiary points of the transformed graph as specialized points. We recall that fundamental sets of the first category are those whose sources consist of specialized points only (Trucco,Bull. Math. Biophysics,18, 65–85, 1956). But in this modified version of the Theorem the fundamental sets may have more than one source and need not be disjoined.     

The Point Evaluation Method for Approximating Function Means,Variances and Covariances

A perennial problem in statistics is the determination of biases, variances and covariances for functions of random variables X₁, X₂, …, X_n which themselves have a known distribution. A common approach is through equations based upon Taylor series approximations but a “point evaluation” method may sometimes be a useful alternative. This involves approximating the multivariate distribution of the X variables by the 2ⁿ points given by X₁=μ₁±₁, X₂ = μ₂ ±₂, …, X_n = = μ_n μ_n, where μ_i is the mean and σ_i the standard deviation of Xi, with appropriate point weights. An advantage over the Taylor series approach is that function derivatives do not have to be explicitely calculated. The point evaluation method is particularly useful in cases where the X variables are uncorrelated. Then the evaluation of the 2ⁿ points can be replaced by the evaluation of 2n points. The point evaluation method is illustrated with powers of a normally distributed variable, and with estimation of gene frequencies from ABO blood group frequencies.     

降雨和非降雨日兴安落叶松天然林蒸腾及蒸散发特征

综合利用树干液流法和涡动相关技术,对大兴安岭北部寒温带兴安落叶松(Larix gmelinii)天然林的林木蒸腾(T)和生态系统蒸散发(ET)进行连续监测;采用边材面积对单木蒸腾耗水进行尺度扩展,分析降雨和非降雨日林木总蒸腾(T_(tot))及其蒸腾组分(优势木蒸腾T_d、中等木蒸腾T_i和劣势木蒸腾T_s)与生态系统ET的变化特征,探讨T_(tot)与ET对水汽压亏缺(VPD)和净辐射(R_n)变化的响应。结果表明:降雨和非降雨日各分化等级林木液流速率的日变化均呈典型单峰格局,且降雨日的T_(tot)(9.7mm)低于非降雨日(31.4 mm),同时T_d在降雨和非降雨日均明显高于T_i和T_s。降雨日的ET(24.7 mm)同样低于非降雨日(50.6mm),而潜热通量与同期R_n之比(31%)则高于非降雨日(25.1%),表明非降雨日的环境条件较有利于植物-大气界面的水汽通量交换。降雨日T_(tot)/ET、T_d/ET、T_i/ET和T_s/ET(分别为38.1%、27.2%、8.5%和2.4%)均低于非降雨日(分别为65.0%、45.5%、15.3%和4.2%),说明降雨日的ET以自由水蒸发为主,而非降雨日时则以T_d占优;同时,仅以优势木蒸腾耗水作为平均水平进行尺度上推易高估林分的蒸腾能力。总体上,T_(tot)与VPD、R_n的相关性均较ET的高,即T_(tot)对环境因子的响应略敏感;同时R_n与T_(tot)、ET的相关性均较VPD高,说明R_n是驱动生态系统水汽通量的首要条件。     

A weighting method for the korean ECO-indicator

A weighting factor proposed in this paper is a product of a reduction factor (N_i/T_i) and a relative significance factor (f_i). A politically determined critical impact (T_i/f_i) is assumed to cause a critical damage defined as a level of damage acceptable to a society. A graph showing the relationship between relative damage and normalized impact indicates that the weighting factor ((N_i/T_i) f_i) is the slope of this graph. It shows further that the relative damage is the same as the weighted impact.     

Dynamic response of a cricadian pacemaker

The term cell assembly, first introduced by D. O. Hebb, is defined in the framework of graph theory. This definition leads to some beautiful problems concerning the number and size of cell assemblies in large graphs. Some approaches to solve these problems are presented. In particular, the graphs K _n xK _m are constructed that have n·m points, n+m-2 connections per point, and at least 2ⁿ+2^m-4 assemblies. Several new notions of connectivity in directed graphs are introduced and their relationships are investigated. The insight into these notions and their relationships will be helpful for further construction of graphs with many assemblies and/or high connectivity. The resulting graphs are not only important for the idea of cell assemblies in the context of neurodynamics, they may also find applications in the construction of communication networks and associative memories.     

Photosynthetic temperature response of the Antarctic vascular plants Colobanthus quitensis and Deschampsia antarctica

The photosynthetic temperature response of the Antarctic vascular plants Colobanthus quitensis and Deschampsia antarctica was examined by measuring whole-canopy CO₂ gas exchange and chlorophyll (Chl) a fluorescence of plants growing near Palmer Station along the Antarctic Peninsula. Both species had negligible midday net photosynthetic rates (P_n) on warm, usually sunny, days (canopy air temperature [T_c]> 20°C), but had relatively high P_n on cool days (T_c<10°C). Laboratory measurements of light and temperature responses of P_n showed that high temperature, not visible irradiance, was responsible for depressions in P_n on warm sunny days. The optimal leaf temperatures (T_l) for P_n in C. quitensis and D. antarctica were 14 and 10°C, respectively. Both species had substantial positive P_n at 0°C T_l, which were 28 (C. quitensis) and 32% (D. antarctica) of their maximal P_n, and we estimate that their low-temperature compensation points occurred at ?2°C T_l (C. quitensis) and ?3°C (D. antarctica). Because of the strong warming trend along the peninsula over recent decades and predictions that this will continue, we were particularly interested in the mechanisms responsible for their negligible rates of P_n on warm days and their unusually low high-temperature compensation points (i.e., 26°C in C. quitensis and 22°C in D. antarctica). Low P_n at supraoptimal temperature (25°C) appeared to be largely due to high rates of temperature-enhanced respiration. However, there was also evidence for direct impairment of the photosynthetic apparatus at supraoptimal temperature, based on Chl fluorescence and P_n/intercellular CO₂ concentration (c_i) response curve analyses. The breakpoint or critical temperature (T_cr) of minimal fluorescence (F_o) was ≈42°C in both species, which was well above the temperatures where reductions in P_n were evident, indicating that thylakoid membranes were structurally intact at supraoptimal temperatures for P_n. The optimal T_l for photochemical quenching (q_p) and the quantum yield of photosystem II (PSII) electron transfer (φ_PSII) were 9 and 7°C in C. quitensis and D. antarctica, respectively. Supraoptimal temperatures resulted in lower q_p and greater non-photochemical quenching (q_NP), but had little effect on F_o, maximal fluorescence (F_m) or the ratio of variable to maximal fluorescence (F_v/F_m) in both species. In addition, carboxylation efficiencies or initial slopes of their P_n/c_i response were lower at supraoptimal temperatures, suggesting reduced activity of ribulose-1,5-bisphosphate carboxylase/oxygenase (Rubisco). Although continued warming along the peninsula will increase the frequency of supraoptimal temperatures, T_c at our field site averaged 4.3°C and was below the temperature optima for P_n in these species for the majority of diurnal periods (86%) during the growing season, suggesting that continued warming will usually improve their rates of P_n.     

桂西南岩溶区八种适生植物光合性状的变异与关联

为探究岩溶植物的光合生理适应机制，采用Li-6400XT便携式光合作用测量系统，对广西平果市岩溶区8种适生植物的叶片净光合速率(P_n)、气孔导度(G_s)、胞间CO₂浓度(C_i)、蒸腾速率(T_r)、水分利用效率(WUE)和气孔限制值(L_s)等光合特征参数进行了测定分析。结果表明：(1)6个光合特征参数在种内和种间均存在不同程度的变异，并且种内变异均大于种间变异。(2)G_s和T_r的变化主要来源于种间变异(46.72%～49.76%),而P_n、C_i、WUE和L_s变化主要来源于种内变异(48.66%～64.50%)。在生活型水平上，P_n、G_s和T_r的种内变异表现为常绿植物小于落叶植物，而C_i、WUE和L_s则相反。(3)各参数的种间变异均表现为落叶植...     

Thermodynamics of DNA Containing Very Stable Chemically Modified Base Pairs

Abstract

DNA chemical modifications caused by the binding of some antitumor drugs give rise to a very strong local stabilization of the double helix. These sites melt at a temperature that is well above the melting temperatures of ordinary AT and GC base pairs. In this work we have examined the melting behavior of DNA containing very stable sites. Analytical expressions were derived and used to evaluate the thermodynamic properties of homopolymers DNA with several different distributions of stable sites. The results were extended to DNA with a heterogeneous sequence of AT and GC base pairs. The results were compared to the melting properties of DNA with ordinary covalent interstrand cross-links. It was found that, as with an ordinary interstrand cross-link, a single strongly stabilized site makes a DNA's melting temperature (T_m ) independent of strand concentration. However in contrast to a DNA with an interstrand cross-link, a strongly stabilized site makes the DNA's T_m independent of DNA length and equal to T _∞, the melting temperature of an infinite length DNA with the same GC-content and without a stabilized site. Moreover, at a temperature where more than 80% of base pairs are melted, the number of ordinary (non-modified) helical base pairs (n) is independent of both the DNA length and the location of the stabilized sites. For this condition, n(T) = (2ω-a) S (1- S ) and S = exp[ΔS(T∞-T)/(RT)] where ω is the number of strongly stabilized sites in the DNA chain, a is the number of DNA ends that contain a stabilized site, and ΔS, T, and R are the base pair entropy change, the temperature, and the universal gas constant per mole. The above expression is valid for a temperature interval that corresponds to n<0.2N for ω=1, and n<0.1N for ω>1, where N is the number of ordinary base pairs in the DNA chain.     

Fluctuations of an alpha-helix.

Fluctuations in backbone dihedral angles in the α-helical conformation of homopolypeptides are studied based on an assumption that the conformational energy function of a polypeptide consisting of n amino-acid residues can be approximated by a 2n-dimensional parabola around the minimum point in the range of fluctuations. A formula is derived that relates 〈Δθ_iΔθ_j〉, the mean value of the product of deviations of dihedral angles ?_i and ψ_i (collectively designated by θ_i) from their energy minimum values, with a matrix inverse to the second derivative matrix F ,_n of the conformational energy function at the minimum point. A method of calculating the inverse matrix F _n^?1 explicitly is given. The method is applied to calculating 〈Δθ_iΔθ_j〉 for the α-helices of poly(L -alanine) and polyglycine. The autocorrelations 〈(Δ?_i)²〉 and 〈(Δψ_i)²〉 at 300°K are found to be about 66 deg² and 49 deg², respectively, for poly(L -alanine), and 84 deg² and 116 deg², respectively, for polyglycine. The length of correlations of fluctuations along the chain is found for both polypeptides to be about eight residues long.     

A method for numbering binary rooted and unrooted phylogenies and their hypothetical taxonomic units

A set of 2n−2 relations (edges) and a set ofn−1 hypothetical taxonomic units (HTUs) derive from the estimation of a binary phylogeny of a set ofn operational taxonomic units (OTUs). We propose an easy way for numbering thesen−1 hypothetical taxonomic units, as well as for then−2 interior points of an unrooted binary phylogeny. We also present an alternative method to the one proposed by Rohlf (Bull. math. Biol. 45, 33–40, 1983) for numbering the π _i=1 ⁿ (2i−3) possible rooted binary phylogenies and the π _i=1 ⁿ⁻¹ (2i−3) possible unrooted binary phylogenies conerning a set ofn operational taxonomic units. An illustrative example of the method is presented. It is hoped that some studies in phylogenetics will become more accessible, from the viewpoint of computational economy, by the use of this method.     

A contribution to Rashevsky’s mathematical theory of development

The application of Rashevsky’s transformationT to a primordial graph yields a set of graphs corresponding to different stages in the development of the organism. However, sinceT is multiple-valued the graphs obtained are not ordered. To obtain an ordering, it is first shown that the set of graphs under consideration is equivalent to a well defined setO (for “organism”) ofn-tuples. A metric is then introduced which is based on a biological consideration discussed by Rashevsky (Bull. Math. Biophysics,16, 317–348, 1954). Since a metric implies an ordering of the setO, with a knowledge of the structure of the primordial, one can obtain the developmental sequence. Unfortunately, at present, the structure of the primordial graph is unknown which makes the direct application of the above principle impossible. Consequently, an indirect approach which makes use of more accessible biological phenomena is discussed as well. The hypothesis thatrate of development decreases exponentially and the implications this has with regard to the metric onO are discussed. It is shown that if the hypothesis is accepted the search for the developmental sequence is narrowed.     

Some remarks on topological biology

With reference to several recent papers by the author, it is pointed out that within the principle of biotopological mapping a choice of a primordial graph and of a particular transformation defines a system of abstract biology, similar to systems of abstract geometries. The study of such abstract systems is necessary before one can be found which is isomorphic to the actual biological world. A brief survey of the structure and properties of the system based on the choice of the primordial graph and of the transformationT defined in a previous paper (Bull. Math. Biophysics,16, 317–48, 1954) is made. Two more topological theorems are demonstrated, which, interpreted biologically, lead to the conclusion that the higher an organism, the more adaptable it is. Finally a criticism of that particular system of abstract biology is made, and its inadequacy for the representation of the actual biological phenomena pointed out, and a suggestion is made for a possible point set topological approach to biology.     

The number of species occurring in a sample of a biotic community and its connections with species-abundance relationship and spatial distribution

Connections among species-abundance (i-m _i ), species-frequency (i-F _i ), and species-sample size (S _n -n) relationships were examined on the basis of the mapping data of a natural forest in Thailand. The spatial distribution of individual trees without any discrimination of species was nearly random. Provided that the spatial distribution of each species was random, thei-m _i and thei-F _i relationship was reconstructed from each other in terms of the total number of species (S) and the total number of individuals (N) in the data. The number of species (S _n ) in a subsample consisting ofn individuals was then obtained from thei-F _i relationship. Logarithm ofS _n increased with logn and showed a convex curve through the origin. The values of diversity indices based onN andS(orn andS _n ) were affected by sample size. These trends were further examined on the basis of 944 data sets of biotic communities and three mathematical models of anS-N relationship. The properties of species-area relation were discussed in the light of these results.     

遮光对香果树幼苗光合特性及叶片解剖结构的影响

设置了全光照(L0)、透光率60%(L1)、透光率25%(L2)、透光率10%(L3)4种光环境,研究了不同遮光处理对香果树幼苗光合作用及叶片解剖结构的影响。结果表明:(1)遮光对香果树幼苗净光合速率(P_n)、蒸腾速率(T_r)、气孔导度(G_s)、气孔限制值(L_s)、胞间CO_2浓度(C_i)、蒸汽压亏缺(V_(pdl))均产生了显著影响。全光和L1处理下Pn和Tr日变化呈明显的双峰曲线,中午出现了明显的"午休",其余处理的变化相对缓和,双峰和"午休"现象不明显;G_s的日变化规律与Pn基本一致;C_i的日变化整体呈先期缓慢降低后期抬升的趋势,与对照相比遮光显著提高了叶片胞间CO_2浓度;Ls和V_(pdl)呈现出先升后降的弧形变化,并且遮光下L_s和V_(pdl)日均值显著低于全光照。一天中P_n和T_r的日均值大小排序为L1L0L2L3。(2)不同光环境下香果树幼苗的光合响应特征明显不同。全光下,香果树幼苗能够维持较高的净光合作用速率而未呈现明显的光抑制,表现出一定的光忍耐和喜光性。L1处理下的最大净光合速率(P_(max))、暗呼吸速率(R_d)和表观量子效率(AQY)显著增加,说明香果树对光强具有一定的可塑性,轻度遮光有利于光合效率提高;强度遮光(L2、L3)导致光补偿点(LCP)和光饱和点(LSP)显著降低,有利于充分利用弱光,但P_(max)、R_d明显下降,光合效率受到抑制。(3)遮光显著影响了香果树叶片的气孔分布。遮光条件下香果树叶片的气孔密度显著减小,气孔器长度、宽度与单个气孔器面积也呈现类似的变化。(4)遮光条件下香果树叶片厚度减小,上表皮增厚,下表/ST增加;维管束内单列导管数目和导管直径均有明显增大,促进了叶片水分传导运输。(5)在育苗生产中,为了适应香果树幼苗生长发育的需求,建议有效辐射强度保持在自然光强的60%以上。     

Dynamical aspects of kinetics

It is shown when and how, and with what advantage, systems of first-order differential equations of the typex _i =X _i (x ₁,...,x _n occurring so frequently in biological and chemical kinetic problems and in other places, may be made to stem from a least-action type of variational principle. Linear systems are treated in some detail, and certain aspects of Volterra's ecological kinetics and of chemical kinetics are discussed. Finally, the general conditions are elaborated under which Gibbs ensemble theory may be used in considering systems with large numbers of degrees of freedom from a statistical point of view.     

甘肃马先蒿寄生对禾草内生真菌共生体光合特性的影响

[目的]甘肃马先蒿与感染内生真菌的禾草(紫花针茅和麦宾草)建立根寄生关系,有关内生真菌对根寄生危害禾草光合作用调控方面的研究较少。[方法]本研究以紫花针茅和麦宾草带菌(E+)、不带菌(E-)植株为研究对象,研究甘肃马先蒿寄生和未寄生处理对紫花针茅和麦宾草E+、E-植株不同生长阶段光合特性影响的动态变化。[结果]甘肃马先蒿寄生显著降低紫花针茅和麦宾草的净光合速率、蒸腾速率和气孔导度,而胞间二氧化碳浓度和水分利用率却显著增加,这与禾草是否感染内生真菌无关。甘肃马先蒿寄生后E+紫花针茅的净光合速率、气孔导度和蒸腾速率高于E-植株,而麦宾草E+植株的净光合速率、气孔导度和蒸腾速率却低于E-植株;同时,根寄生条件下E+紫花针茅的胞间二氧化碳浓度和水分利用率低于E-植株;而E-麦宾草植株的胞间二氧化碳浓度和水分利用率却低于E+植株。[结论]内生真菌侵染影响甘肃马先蒿根寄生危害禾草的光合作用;甘肃马先蒿和内生真菌同时成为禾草营养消耗库时,内生真菌与禾草的共生关系处于一种互惠共生和相互拮抗的动态变化。     

Constructing rooted supertrees using distances

Suppose that a family of rooted phylogenetic trees T _i with different sets X _i of leaves is given. A supertree for the family is a single rooted tree T whose leaf set is the union of all the X _i , such that the branching information in T corresponds to the branching information in all the trees T _i . This paper proposes a polynomial-time method BUILD-WITH-DISTANCES that makes essential use of distance information provided by the trees T _i to construct a rooted tree S ₀. When a supertree also containing the distance information exists, then S ₀ is a supertree. The supertree S ₀ often shows increased resolution over the trees found by methods that utilize only the topology of the input trees. When no supertree exists because the input trees are incompatible, several variants of the method are described which still produce trees with provable properties.     

Tree-based networks: characterisations,metrics, and support trees

Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer. One way to obtain such a network is by starting with a (rooted) phylogenetic tree T, called a base tree, and adding arcs between arcs of T. The class of phylogenetic networks that can be obtained in this way is called tree-based networks and includes the prominent classes of tree-child and reticulation-visible networks. Initially defined for binary phylogenetic networks, tree-based networks naturally extend to arbitrary phylogenetic networks. In this paper, we generalise recent tree-based characterisations and associated proximity measures for binary phylogenetic networks to arbitrary phylogenetic networks. These characterisations are in terms of matchings in bipartite graphs, path partitions, and antichains. Some of the generalisations are straightforward to establish using the original approach, while others require a very different approach. Furthermore, for an arbitrary tree-based network N, we characterise the support trees of N, that is, the tree-based embeddings of N. We use this characterisation to give an explicit formula for the number of support trees of N when N is binary. This formula is written in terms of the components of a bipartite graph.

     

Local consideration of polymorphisms for populations coexisting in stable ecosystems

Summary The stability problem for multiallelic genetic polymorphisms for n populations coexisting in stable ecosystems is considered. Taking into account only density-dependent interactions a generalization of Fisher's theorem is obtained. Specifically, the average fitness of a population must be locally maximized subject to the constraint that the equilibrium population sizes are fixed if the polymorphism is stable. Further, the quasi-equilibrium population sizes N _i ^* corresponding to fixing the genetic structure of all populations in the ecosystem at various values have extrema at the equilibrium point. Such an equilibrium can be a maximum, minimum or saddle point depending upon the type of ecosystem under consideration. A simple test separating these cases on the basis of the so-called ecosystem matrix is suggested. The general equilibrium problem is reformulated as a maximization problem under some restrictions. Conditions under which the maximized function can be expressed as ₌₁ ⁿ N_i are formulated.     

<Emphasis Type="Italic">Agrobacterium</Emphasis>-mediated transformation of oat (<Emphasis Type="Italic">Avena sativa</Emphasis> L.) cultivars via immature embryo and leaf explants

This paper reports on the successful Agrobacterium-mediated transformation of oat, and on some factors influencing this process. In the first step of the experiments, three cultivars, two types of explant, and three combinations of strain/vectors, which were successfully used for transformation of other cereals were tested. Transgenic plants were obtained from the immature embryos of cvs. Bajka, Slawko and Akt and from leaf base explants of cv. Bajka after transformation with A. thumefaciens strain LBA4404(pTOK233). The highest transformation rate (12.3%) was obtained for immature embryos of cv. Bajka. About 79% of the selected plants proved to be transgenic; however, only 14.3% of the T₀ plants and 27.5% of the T₁ showed GUS expression. Cell competence of both types of explant differed in terms of their transformation ability and transgene expression. The next step of the study was to test the suitability for oat transformation of the pGreen binary vector combined with different selection cassettes: nptII or bar under the nos or 35S promoter. Transgenic plants were selected in combinations transformed with nos::nptII, 35S::nptII and nos::bar. The highest transformation efficiency (5.3%) was obtained for cv. Akt transformed with nos::nptII. A detailed analysis of the T₀ plants selected from a given callus line and their progeny revealed that they were the mixture of transgenic, chimeric-transgenic and non-transgenic individuals. Southern blot analysis of T₀ and T₁ showed simple integration pattern with the low copy number of the introduced transgenes.