植物分枝模型

从生物体总是最有效地利用物质的思想出发,对植物分枝形状建立了一个数学模型,该模型认为,当主干与侧枝的截面积之间存在类似平行四边形法则的关系时,分枝的体积取极小值。该模型揭示植物分枝形态不仅符合力学平衡的原则,在进化上也有显著生物学意义。     

BRC1/TB1基因调控植物分枝的研究进展

植物分枝是决定其形态建成的重要因素,是由叶腋内的腋芽发育成枝条的过程,该过程受光照、营养及内源激素等多种因素的调控。近年来的研究发现,TCP(TEOSINTE BRANCHED1,CYCLOIDEA,PCF)转录因子家族成员BRC1/TB1可响应并整合多种信号来调控植物的分枝。该文总结了BRC1/TB1对光照、营养及不同激素的响应特征,及其在调控植物分枝过程中发挥的核心作用等研究成果,并重点对BRC1/TB1基因上下游调控网络的相关研究进行综述,且对未来的研究方向进行了展望,旨在为后续分枝调控方面的研究提供信息,也为今后创制符合人们期望的优良种质提供参考依据。     

界面发酵红曲霉的图像解析*

利用计算机视觉技术研究了红曲霉界面发酵过程中菌体形态变化与菌体生长的关系。在界面培养中通过检测前期菌落面积,后期隆起部分的表征体积——基于颜色变化的生长点分布,可以有效表示菌体生长状况。基于此建立了含有相应形态参数的动力学模型,该模型与常规动力学模型具有相似的表达形式。     

景深合成技术在植物光学微形态研究上的应用

介绍了利用电脑景深合成技术在光学显微镜上获得植物标本大景深图片的摄影方法。概述了此方法获取植物光学微形态特征清晰图片的基本步骤和优缺点。该方法制片简单,可利用最普通的生物显微镜、电子目镜结合计算机进行摄影,成本低,观察特征明显,获得的图片具有真色彩,并可拍出植物最鲜活的状态。此方法有可能成为未来植物微形态研究的一个重要手段。     

丛藓科（Pottiaceae）植物叶细胞形态特征及其系统学意义

通过光学显微镜（LM）和扫描电镜（SEM）观察了17属国产丛藓科（Pottiaceae）植物叶中上部细胞的形态特征,结果表明：丛藓科植物的叶中上部细胞的形状、大小及表面形态等特征上具较大相似性;据细胞表面特征,叶细胞可分为无疣或具乳突、具圆疣以及具分枝的马蹄形疣3种类型,且该特征在丛藓科不同属、种间有较大的区别。因此,叶细胞形态特征可为丛藓科植物属级和亚科级的划分提供细胞形态学依据。     

支持物倾角对攀援植物栝楼形态和生长的影响

支持物倾角的变化将引起攀援植物“自遮荫”程度的改变 ,从而影响植物的生长和行为。以攀援植物栝楼 ( Trichosantheskirilowii)为材料 ,通过实验生态学的方法 ,研究了 4种支持物倾角下植株的生长和觅食行为的差异。结果表明 :( 1 )不同生长发育期栝楼植株形态对自遮荫差异的可塑性反应程度不一 ,不同角度攀援生长植株在生长前期均比生长后期有较敏感的形态可塑性反应。 ( 2 )自遮荫程度随支持物倾角的增大而增强 ,较强自遮荫环境下植株比较弱自荫环境下的植株有更大的形态可塑性。 ( 3)比主茎长、比叶面积、生物量对叶片和叶柄的配置在 4种攀援生长形式间差异均不显著。不同角度攀援植株主要通过改变分枝数量、分枝形态和分枝生物量配置以适应支持物倾角的变化 ,这说明 ,自遮荫对植株形态和生物量配置仅产生有限的影响。 ( 4 )分枝能力、分枝数量以及分枝生物量配置均在大角度攀援生长中最大 ,且与小角度攀援生长植株间有显著差异。 ( 5 )水平攀援生长植株主要通过增大主茎生物量投资以充分占有生境 ,而大角度攀援生长植株则主要通过分枝茎扩展以占据有利生境 ,不同攀援生长植株有不同的觅食行为。     

水蓼对水淹胁迫的耐受能力和形态学响应

水蓼(Polygonum hydropiper)是一种分布于三峡地区消落带的常见分布种之一,通过模拟4～5月的水淹节律,测定了水蓼对水淹的适应能力和形态学的响应机理.结果表明,在所有的水淹时间胁迫处理下,水蓼均能保持100%的存活率,并能正常开花结果.该植物主要是通过叶片形态的变化和不定根的形成来适应水环境的变化.水淹初期阶段植株叶片的长与宽及叶片的平均面积有显著下降,但随着植株不定根的不断形成与生长,植株叶片的形态可恢复到正常状态.水淹对植株的株高、分枝数、分枝长、节间距都没有显著影响,表明植株形态整体不会受到水淹的影响.而植物根、茎、叶的生物量虽在不同处理之间有所变化,但是都没有达到显著水平,不定根的生物量差异在各处理之间显著.说明水蓼在形态学上对水淹有着适应机制且具有较强耐水淹能力.结合三峡库区消落带未来水位变化的情况,认为水蓼将能适应三峡水库消落带生态环境变化而生存在消落带,并可用于三峡水库退化消落带的生态治理.     

基于功能性状的外来植物入侵预测模型框架构建

预测外来植物的潜在入侵性已成为生物多样性保护研究的重要内容,外来植物与乡土物种间的亲缘关系是预测外来植物能否成功入侵的一个重要途径。然而,达尔文归化难题却预测了两种截然不同的结果(即达尔文归化假说和预适应假说)。该研究解析了达尔文归化难题的内涵,提出了基于功能性状的外来植物与乡土群落间的相似性关系应该是进行外来植物入侵预测的重要切入点,而功能性状的种间分化与种内变异可能是外来植物成功入侵的两种不同生态策略。在此基础上,该研究还通过物种功能性状的多维超体积构建了外来植物与乡土群落间的相似性,提出了基于这种相似性的外来植物入侵预测的研究框架和基本流程。该模型框架的建立有助于理解外来植物的入侵机制,对外来植物的潜在入侵性预测提供了理论依据。当然,要实现外来植物能否成功入侵的准确预测,不仅依赖于功能性状的选择,还要考虑入侵的生境依赖性、空间尺度的重要性以及乡土群落的可入侵性等,未来的研究重点是通过控制实验对该模型进行验证和进一步完善。     

云南省凤仙花属(凤仙花科)2新记录种

报道了云南省凤仙花科(Balsaminaceae)凤仙花属(Impatiens L.)植物2新记录,即睫毛萼凤仙花(I.blepharosepala Pritz.ex Diels)和红雉凤仙花(I.oxyanthera Hook.f.),并提供了形态描述及其图片,凭证标本保存于重庆三峡学院生命科学与工程学院植物标本馆。该报道的睫毛萼凤仙花花色为白色,红雉凤仙花植株茎、叶皆被微柔毛,茎有分枝,小枝细,丰富了2个物种的形态描述。     

喜旱莲子草入侵群落土壤对植物生长的影响

分别以受喜旱莲子草(Alternanthera philoxeroides)入侵和未受喜旱莲子草入侵的当地植物群落土壤为生长基质,比较不同基质上入侵植物喜旱莲子草和同属的土著植物莲子草(A.sessilis)的生长指标,探讨喜旱莲子草入侵群落土壤对喜旱莲子草及莲子草生长的影响机制。结果表明,喜旱莲子草入侵群落土壤抑制了莲子草的生长,显著降低了根生物量、茎生物量和总生物;改变了形态特征,显著降低了分枝数量、茎长度、根长、根体积;减少了对根的生物量分配,显著抑制了根质量比与根冠比。喜旱莲子草入侵群落土壤对入侵植物喜旱莲子草的生物量、分枝数量、茎长度、根长、根体积没有显著的抑制作用,而显著增加了其叶片数量和叶质量比。这种效应将有利于喜旱莲子草在入侵地形成单优群落,表明土壤在喜旱莲子草成功入侵中起了重要作用。     

Which diameter and angle rule provides optimal flow patterns in a coronary bifurcation?

The branching angle and diameter ratio in epicardial coronary artery bifurcations are two important determinants of atherogenesis. Murray's cubed diameter law and bifurcation angle have been assumed to yield optimal flows through a bifurcation. In contrast, we have recently shown a 7/3 diameter law (HK diameter model), based on minimum energy hypothesis in an entire tree structure. Here, we derive a bifurcation angle rule corresponding to the HK diameter model and critically evaluate the streamline flow through HK and Murray-type bifurcations. The bifurcations from coronary casts were found to obey the HK diameter model and angle rule much more than Murray's model. A finite element model was used to investigate flow patterns for coronary artery bifurcations of various types. The inlet velocity and pressure boundary conditions were measured by ComboWire. Y-bifurcation of Murray type decreased wall shear stress-WSS (10%-40%) and created an increased oscillatory shear index-OSI in atherosclerosis-prone regions as compared with HK-type bifurcations. The HK-type bifurcations were found to have more optimal flow patterns (i.e., higher WSS and lower OSI) than Murray-type bifurcations which have been traditionally believed to be optimized. This study has implications for changes in bifurcation angles and diameters in percutaneous coronary intervention.     

Arterial bifurcations in the cardiovascular system of a rat

Arterial bifurcations in the cardiovascular system of a rat were studied, using a resin cast of the entire arterial tree. At each bifurcation, measurements were made of the diameters of the three vessels involved, the two branching angles, and the angle delta, which the parent artery makes with the plane containing the two branches. The results were found to be consistent with those reported previously in man and monkey. In addition, measurements of delta in the present study indicate that arterial bifurcations are mostly two dimensional.     

Modeling of branching structures of plants

Previous studies of branching structures generally focused on arteries. Four cost models minimizing total surface area, total volume, total drag and total power losses at a junction point have been proposed to study branching structures. In this paper, we highlight the branching structures of plants and examine which model fits data of branching structures of plants the best. Though the effect of light (e.g. phototropism) and other possible factors are not included in these cost models, a simple cost model with physiological significance, needs to be verified before further research on modeling of branching structures is conducted. Therefore, data are analysed in this paper to determine the best cost model. Branching structures of plants are studied by measuring branching angles and diameters of 234 junctions from four species of plants. The sample includes small junctions, large junctions, two- and three-dimensional junctions, junctions with three branches joining at a point and those with four branches joining at a point. First, junction exponents (x) were determined. Second, log-log plots indicate that model of volume minimization fits data better than other models. Third, one-sided t -tests were used to compare the fitness of four models. It is found that model of volume minimization fits data better than other cost models.     

Blood flow downstream of a two-dimensional bifurcation

Many cardiovascular lesions such as aneurysms, intimal cushions, and atherosclerotic plaques tend to occur near bifurcations. This suggests that hemodynamic factors may be involved. Since measuring devices (such as anemometers) are still too large to allow local measurements of flow disturbances, we have attempted to predict the nature of these factors mathematically. Biological variables include pulsatile flow of a nonNewtonian fluid in distensible branching vessels with different angles and flow rates. Our initial analysis considers the flow in a two-dimensional bifurcation with a symmetrical flow divider perfused with steady flow at variable Reynolds numbers. At all flows, high shear forces develop on either side of the flow divider (i.e. at the apex of the bifurcation). With high flows, regions of sluggish or reverse flow develop near the outer walls of the bifurcation. The analysis confirms that the flow at the apex is quite different from that at the outer angles and that the latter varies more with flow rate than the former.     

Modeling of Branching Patterns in Plants

A major determinant of plant architecture is the arrangement of branches around the stem, known as phyllotaxis. However, the specific form of branching conditions is not known. Here we discuss this question and suggest a branching model which seems to be in agreement with biological observations. Recently, a number of models connected with the genetic network or molecular biology regulation of the processes of pattern formation appeared. Most of these models consider the plant hormone, auxin, transport and distribution in the apical meristem as the main factors for pattern formation and phyllotaxis. However, all these models do not take into consideration the whole plant morphogenesis, concentrating on the events in the shoot or root apex. On the other hand, other approaches for modeling phyllotaxis, where the whole plant is considered, usually are mostly phenomenological, and due to it, do not describe the details of plant growth and branching mechanism. In this work, we develop a mathematical model and study pattern formation of the whole, though simplified, plant organism where the main physiological factors of plant growth and development are taken into consideration. We model a growing plant as a system of intervals, which we will consider as branches. We assume that the number and location of the branches are not given a priori, but appear and grow according to certain rules, elucidated by the application of mathematical modeling. Four variables are included in our model: concentrations of the plant hormones auxin and cytokinin, proliferation and growth factor, and nutrients—we observe a wide variety of plant forms and study more specifically the involvement of each variable in the branching process. Analysis of the numerical simulations shows that the process of pattern formation in plants depends on the interaction of all these variables. While concentrations of auxin and cytokinin determine the appearance of a new bud, its growth is determined by the concentrations of nutrients and proliferation factors. Possible mechanisms of apical domination in the frame of our model are discussed.     

Bistability and oscillations in chemical reaction networks

Bifurcation theory is one of the most widely used approaches for analysis of dynamical behaviour of chemical and biochemical reaction networks. Some of the interesting qualitative behaviour that are analyzed are oscillations and bistability (a situation where a system has at least two coexisting stable equilibria). Both phenomena have been identified as central features of many biological and biochemical systems. This paper, using the theory of stoichiometric network analysis (SNA) and notions from algebraic geometry, presents sufficient conditions for a reaction network to display bifurcations associated with these phenomena. The advantage of these conditions is that they impose fewer algebraic conditions on model parameters than conditions associated with standard bifurcation theorems. To derive the new conditions, a coordinate transformation will be made that will guarantee the existence of branches of positive equilibria in the system. This is particularly useful in mathematical biology, where only positive variable values are considered to be meaningful. The first part of the paper will be an extended introduction to SNA and algebraic geometry-related methods which are used in the coordinate transformation and set up of the theorems. In the second part of the paper we will focus on the derivation of bifurcation conditions using SNA and algebraic geometry. Conditions will be derived for three bifurcations: the saddle-node bifurcation, a simple branching point, both linked to bistability, and a simple Hopf bifurcation. The latter is linked to oscillatory behaviour. The conditions derived are sufficient and they extend earlier results from stoichiometric network analysis as can be found in (Aguda and Clarke in J Chem Phys 87:3461–3470, 1987; Clarke and Jiang in J Chem Phys 99:4464–4476, 1993; Gatermann et al. in J Symb Comput 40:1361–1382, 2005). In these papers some necessary conditions for two of these bifurcations were given. A set of examples will illustrate that algebraic conditions arising from given sufficient bifurcation conditions are not more difficult to interpret nor harder to calculate than those arising from necessary bifurcation conditions. Hence an increasing amount of information is gained at no extra computational cost. The theory can also be used in a second step for a systematic bifurcation analysis of larger reaction networks. We have added a dedication of the paper to K. Gatermann.     

Basal EDRF activity helps to keep the geometrical configuration of arterial bifurcations close to the Murray optimum

We have used X-ray microangiography to investigate the hypothesis that the potent endogenous vasodilator endothelium-derived relaxing factor (EDRF) contributes to the maintenance of "optimality" in vascular branching by modulating the diameters of the parent (D0) and daughter (D1 and D2) arteries at bifurcations. Five anatomically different types of bifurcation were studied in buffer-perfused rabbit ear preparations both under resting conditions and after pharmacological constriction by 5-hydroxytryptamine (5HT). A range of flow rates (1-5 ml min-1) was employed as release of EDRF from endothelial cells is stimulated by shear stress. Experimental data obtained in the presence and absence of EDRF activity were compared with theoretical predictions in three ways. (1) Junction exponents (x) were determined at each bifurcation from the equation Dx1 + Dx2 = Dx0, and their frequency distributions constructed. Murray (1926a, Proc. natn. Acad. Sci., U.S.A. 12, 207-214; 1926b, J. gen. Physiol. 9, 835-841.) proposed that x will be exactly 3 if power losses and intravascular volume are minimized simultaneously. In unconstricted preparations, either in the presence or absence of EDRF activity, and in preparations constricted by 0.1 microM 5HT in the presence of EDRF activity, the modes and medians of the frequency distributions of x were found to be close to 3 at all flow rates. In contrast, in 0.1 microM 5HT-constricted preparations in the absence of EDRF activity, no single mode common to all flow rates was apparent and medians were significantly larger at all flow rates. (2) Theoretically "optimal" branching angles were derived from experimental diameter measurements using four mathematical models which minimize respectively the total surface area, total volume, total drag (shear stress) and total power losses at bifurcations (Murray, 1926b). These calculated branching angles were then compared with actual branching angles. EDRF activity was found to be necessary for accurate prediction of branching angles by the minimum volume and power loss models in 5HT-constricted but not in resting preparations. (3) For each model or "minimization principle", there is an optimal mathematical relationship between the junction exponent, x, and the angle between daughter arteries, psi 12, at a bifurcation (Roy & Woldenberg, 1982, Bull. math. Biol. 44, 349-360.) Experimentally determined values of x and psi 12 agreed closely with those predicted both by the minimum volume and the minimum power loss principles, except again in 5HT-constricted preparations in the absence of EDRF activity.(ABSTRACT TRUNCATED AT 250 WORDS)     

Roots and calibers of the human coronary arteries

The anatomical structure of the coronary-aortic junctions in humans is studied by using corrosion casts of the coronary network. A model is proposed for the specification of these junctions in terms of vessel diameters and branching angles, and the model is used to produce morphological data on these junctions which hitherto have not been available. This anatomical model correlates poorly with the accepted theoretical model of arterial bifurcations in the cardiovascular system. The results suggest that the structure of the coronary-aortic junctions is very different from the structure of typical arterial bifurcations and, by implication, that the flow conditions under which they function are very different. A good understanding of these junctions is important in coronary bypass surgery, where the coronary-aortic junctions are emulated by creating a new anastomosis for the graft at the base of the ascending aorta, and in coronary artery disease, where atherosclerotic lesions occur not far from the coronary-aortic junctions.     

BRANCH GEOMETRY AND EFFECTIVE LEAF AREA: A STUDY OF TERMINAUA-BRANCHING PATTERN. 1. THEORETICAL TREES

Single lateral branches and branch tiers of Terminalia catappa L. are simulated and drawn by computer. Leaf clusters on the branches are approximated by discs, and the effective leaf areas are determined by use of Dirichlet domains. Theoretical optimal branching angles which produce the maximum effective leaf area are obtained from simulations. Symmetrical and asymmetrical branching angles are contrasted; the latter characterize real trees. Varying leaf disc radius and ratio of branch-unit lengths affects optimal branching angles, as does the symmetry of a tier of five branches. Leaf area indices for individual branches and branch tiers are given for all simulations. The number of branches in a tier has a major effect on leaf area index and effective leaf area. The theoretical optimal branching angles of many simulations are very close to the values observed in real trees of T. catappa. We conclude that the observed branching angles and number of branches in a tier of this species optimize light interception within constraints of a fixed pattern of branching, one that is widespread among tropical trees.     

Contribution a l’etude de la forme des plantes: discussion d’un modele de ramification

The problem of the forms of plants and models of branching are discussed using experimental data on the mistletoe. The number of branches by division, the distribution of divisions with regard to the number of branches per division and to the level of division, the geometrical characters of branches according to the level of division and the host, the stability of model are studied. One gives an interpretation of the model of branching as a model of growth.