Convective-diffusive model of two-dimensional root growth and proliferation

Simulations of crop productivity and environmental quality depend strongly on the root activity model used. Flexible, generic root system models are needed that can easily be coupled to various process-based soil models and can easily be modified to test various hypotheses about how roots respond to their environment. In this paper, we develop a convective-diffusive model of root growth and proliferation, and use it to test some of these hypotheses with data on the growth of roots on potted chrysanthemum cuttings. The proliferation of roots is viewed as a result of a diffusion-like gradient-driven propagation in all directions and convection-like propagation downwards caused by geotropism. The finite element method was used to solve the boundary problem for the convective-diffusive equation. To test hypotheses, we wrote modules in a way that caused a test parameter to be zero, should the hypothesis be rejected. These modules were added or removed to test each hypothesis in turn and in various combinations. The model explained 92% of the variation in the experimental data of Chen and Lieth (1993) on root growth of potted chrysanthemum cuttings. For this dataset the following hypotheses were accepted: (1) root diffusivity (colonization of new soil) did not depend on root density, (2) there was no geotropic trend in root development, (3) potential root growth increased linearly with root density, (4) there were (at least) two classes of roots with different rates of growth and proliferation, and (5) potential root growth rate decreased with distance from the plant stem base.     

Simulated Low-gravity Environments and Respiratory Metabolism in Avena Seedlings

Using horizontal and vertical axis clinostats and sand-grown oat seedlings (Avena sativa), it was found that horizontal clinostat rotation at 2 rpm increased respiration and inorganic and organic phosphorus content of seedlings. Increased coleoptile geotropism and root growth are attributed to rotational nullification of the directional component of the gravitational stimulus. These growth modifications are mechanistically explicable by the relationship between plant metabolism and auxin concentration in these organs.     

Auxin and the response of pea roots to auxin transport inhibitors: morphactin

The auxin transport inhibitor methyl-2-chloro-9-hydroxyfluorene-9-carboxylate (CFM), a morphactin, inhibits negative geotropism, causes cellular swelling, and induces root hair formation in roots of intact Pisum sativum L. seedlings. In excised pea root tips, CFM inhibits elongation more than increase in fresh weight (swell ratio = 1.3 at 20 mum CFM). CFM growth inhibition was expressed in the presence of ethylene. Indoleacetic acid (IAA) prevented the expression of CFM growth inhibition possibly because IAA inhibited the accumulation of CFM into the tissue sections. CFM inhibited the accumulation of IAA and 2,4-dichlorophenoxyacetic acid into excised root tips. Applying Leopold's (1963. Brookhaven Symp. Biol. 16: 218-234) model for polar auxin transport, this result suggests a possible explanation for CFM inhibition of geotropism in pea roots, i.e. disruption of auxin transport by interfering with auxin binding.     

Inhibitors of the geotropic response in plants: A correlation of molecular structures

Selected compounds from several groups of chemicals known to affect the root geotropic response in plants have been assessed for their effects on both stem and root geotropism in cress seedlings in order to compare their relative activities. It is suggested that a class of compound which affects geotropism can be distinguished, and that the molecular requirements for its activity can be tentatively defined. It is suggested that an ortho carboxylic acid function attached to an aromatic ring, which is separated by a conjugated system of atoms from a second aromatic ring, is required for high activity. Substituents on the second aromatic ring increase activity if they assist in the achievement of a minimum molecular size.     

Relations between root length densities and root intersections with horizontal and vertical planes using root growth modelling in 3-dimensions

The root growth simulation model of Diggle (ROOTMAP; 1988) was modified to allow the numerical output of data on root intersections with horizontal and vertical planes. ROOTMAP was used to generate two three-dimensional model structures of fibrous root systems. The lateral roots were oriented randomly (geotropism index=0) but the main axes were positively gravitropic (geotropism index=0.6). The mean density of root intersections (n, cm^-2) with the sides of a series of 5×5×5 cm cubic volumes was related approximately linearly to the root length density (L_t cm^-2) within each volume by the equation L_t=2.3n (correlation coefficient, r=0.981). This compared with the relation of L_t=2n predicted theoretically for randomly oriented lines (Melhuish and Lang, 1968). Root length density was related to the intersection density by the equation L_t=2.43n_v (r=0.940) for the vertical faces and L_t=1.88n_h (r=0.984) for the horizontal faces. L_t/n_v was greater than L_t/n_h because of the preferential vertical orientation of the main root axes. The Melhuish and Lang (1968) equation does not generally give accurate prediction of root length density from field experiment data. Under field conditions, values have been reported in the ranges of 1.4 to 16 for L_t/n_h, and 3.8 to 9 for L_t/n_v. The most likely explanation for this difference is that only a small proportion (e.g. about 20–30%) of the actual number of roots are counted using the core-break and root mapping (including the trench wall) methods, due to the practical experimental difficulties of identifying individual fine roots under field conditions. Detailed experimental studies are needed to identify what portion of the root system is recorded using these field techniques (e.g. whether the main root axes are counted while the fine lateral roots remain undetected). Three-dimensional models of root growth provide a new method of studying the relations between L_t, n_v and n_h for root systems generated stochastically according to known geometrical rules. Using these models it will be possible to determine the effects of the degree of gravitropism and of root branching on the value and on the variability of L_t/n_h and L_t/n_v. The effectiveness of the statistical corrections that have been developed to correct for non-random root orientation can also be evaluated, as can the effects of sample position.     

Root geotropism and the role of growth regulators from the cap: a re-examination

Abstract. It is widely believed that the root cap participates in geotropism by acting both as a sensor of the direction of gravity and as a source of at least one regulator of root growth, which may be abscisic acid (ABA). It has been suggested that this regulator accumulates within the prospective concave (or lower) half of the root and there causes a retardation of growth that brings about bending. A re-examination of the evidence upon which this inhibitor hypothesis of geotropic control is based reveals that (1) it is derived almost entirely from microsurgical studies and the deductions from such experiments still require corro-orations from analyses of inhibitor content and action; (2) the evidence that ABA is the inhibitor seems poor at present; (3) in maize and lentil, two well-studied species, geocurvature is probably a consequence of accelerated growth within the prospective convex (or upper) half rather than inhibited growth within the concave (or lower) half; (4) the geotropic signal from the cap may be one that redirects a pre-existing basipetal flow of inhibitor away from the upper     

ABA promotes quiescence of the quiescent centre and suppresses stem cell differentiation in the Arabidopsis primary root meristem

It is well known that abscisic acid (ABA) can halt meristems for long periods without loss of meristem function, and can also promote root growth at low concentrations, but the mechanisms underlying such regulation are largely unknown. Here we show that ABA promotes stem cell maintenance in Arabidopsis root meristems by both promoting the quiescence of the quiescent centre (QC) and suppressing the differentiation of stem cells and their daughters. We demonstrate that these two mechanisms of regulation by ABA involve distinct pathways, and identify components in each pathway. Our findings demonstrate a cellular mechanism for a positive role for ABA in promoting root meristem maintenance and root growth in Arabidopsis.     

Endogenous and exogenous auxin in the control of root growth

The endogenous indol-3yl-acetic acid (IAA) of detipped apical segments from roots of maize (cv ORLA) was greatly reduced by an exodiffusion technique which depended upon the preferential acropetal transport of the phytohormone into buffered agar. When IAA was applied to the basal cut ends of freshly prepared root segments only growth inhibitions were demonstrable but after the endogenous auxin concentration had been reduced by the exodiffusion technique it became possible to stimulate growth by IAA application. The implications of the interaction between exogenous and endogenous IAA in the control of root segment growth are discussed with special reference to the role of endogenous IAA in the regulation of root growth and geotropism.Abbreviations IAA indol-3yl-acetic acid - GC-MS gas chromatography-mass spectrometry     

高等植物的PCD研究进展(一)

植物细胞程序性死亡(programmed cell death,PCD)已成为当前生物学的研究热点之一。植物PCD普遍存在于植物器官和个体生长发育过程及与环境相互作用过程中,具有重要的生物学意义。在高等植物生长发育过程中,根冠细胞、导管细胞、绒毡层细胞、胚乳细胞、胚柄细胞、糊粉细胞、大孢子细胞、助细胞和反足细胞等细胞在一定程度上均发生了PCD。另外,衰老也涉及PCD。本文综述了最近几年来与发育有关的PCD研究进展,主要包括高等植物细胞死亡的形式、起因及其PCD的形态、生化特征及高等植物营养器官(根、茎和叶)和生殖器官(花、果实和种子)在其生长发育过程中的PCD。文章最后还对植物PCD的进化和生物学意义作了进一步的讨论。 Abstract：Plant programmed cell death(PCD),the details of which are becoming a focus of intensive research in biology, is a ubiquitous phenomenon and plays an improtant biological role in the develpoment of organs and whole organisms and in interactions with the environment.During higher plant development,root cap cells,tracheary elements(TEs),tapetalcells,endosperm cells,suspensor cells,aleurone cells,megaspore cells,help cells and antipodal cells,etc.undergo PCD to some degree.In addition,senescence also involves PCD.This paper mainly reviewed PCD research progress in higher plant development in recent years,including forms and causes of cell death and PCD morphological and biochemical features in higher plants;PCD in development of nutritive organs(root ,stem and leaf) and reproductive organs(flower ,fruit and seed),evolution and biological rloes of plant PCD were further discussed in the paper.     

Random Search Algorithm for Solving the Nonlinear Fredholm Integral Equations of the Second Kind

In this paper, a randomized numerical approach is used to obtain approximate solutions for a class of nonlinear Fredholm integral equations of the second kind. The proposed approach contains two steps: at first, we define a discretized form of the integral equation by quadrature formula methods and solution of this discretized form converges to the exact solution of the integral equation by considering some conditions on the kernel of the integral equation. And then we convert the problem to an optimal control problem by introducing an artificial control function. Following that, in the next step, solution of the discretized form is approximated by a kind of Monte Carlo (MC) random search algorithm. Finally, some examples are given to show the efficiency of the proposed approach.     

Interactions between bacterial diazotrophs and non-legume dicots: Arabidopsis thaliana as a model plant

When interactions between diazotrophic bacteria and non-legume plants are studied within the context of trying to extend biological nitrogen fixation to non-legume crops, an important first step is to establish reproducible internal colonization at high frequency of these plants. Using Azorhizobium caulinodans ORS571 (which induces stem and root nodules on the tropical legume Sesbania rostrata), tagged with a constitutively expressed lacZ reporter gene, we have studied the possibilities of internal colonization of the root system of the model dicot Arabidopsis thaliana. ORS571 was found to be able to enter A. thaliana roots after first colonizing lateral root cracks (LRCs), at the points of emergence of lateral roots. Cytological studies showed that after LRC colonization, bacteria moved into the intercellular space between the cortical and endodermal cell layers of roots. In our experimental conditions, this LRC and intercellular colonization are reproducible and occur at high frequency, although the level of colonization at each site is low. The flavonoids naringenin and daidzein, at low concentrations, were found to significantly stimulate (at the p=0.01 level) the frequency of LRC and intercellular colonization of A. thaliana roots by A. caulinodans. The role in colonization of the structural nodABC genes, as well as the regulatory gene nodD, was studied and it was found that both colonization and flavonoid stimulation of colonization are nod gene-independent. These systems should now enable the various genetic and physiological factors which are limiting both for rhizobial colonization and for endophytic nitrogen fixation in non-legumes, to be investigated. In particular, the use of A. thaliana, which has many advantages over other plants for molecular genetic studies, to study interactions between diazotrophic bacteria and non-legume dicots, should provide the means of identifying and understanding the mechanisms by which plant genes are involved in these interactions.     

Modelling root structure and stability

Summary Seven fully excavated 16 year-old root systems of Sitka spruce were analysed. All roots in excess of 1 cm diameter at their origin on the stumps were analysed, data being collected until root diameter declined to less than 0.5 cm.Root morphology and distribution was identified as a balance between systematic biological mechanisms and their disruption by environmental factors, particularly changes of soil density and soil surface contours. The biological mechanisms have been modelled and the model is capable of simulating root systems in response to a few simple input variablese.g. the number of roots originating at stumps, stem ratius, total number of roots of all ordersetc.Additionally equations have been developed to estimate the distribution of root diameter, and root weight at all distances from tree stems and a similar equation permits the estimation of tree diameter at chosen heights. These latter estimates being utilized to calculate the turning moment of stems when blown by the wind.The influence of the wind on turning moment is explored for simulated root systems of differing strength and gross morphology.     

Absorptive root area and stem resistivity in whole trees of contrasting structure and size – improvement of methods

Aims

The study was focused on comparing the results of the three instrumental methods applied simultaneously for root studies in several tree species representing contrasting situations: root systems of different structure and stems of a wide range of diameters (especially when considering their resistivity). We want to learn properties of the methods, make some improvements and test their validity, before they will be applied to a large series of trees at the stand level.

Material and methods

Douglas fir (Pseudotsuga menziessii (Mirbel) Franco) with very asymmetric root system and Blue spruce (Picea pungens Engelm.) with homogeneous root system growing in the Mendel University Training Forest Enterprise in K?tiny, were selected as the main sample trees. Three variants of stem impedance measurements needed for absorptive root area estimates were applied to an additional series of over 20 trees. In order to characterize vertical and circumferential (around stem) root distribution we applied (1) the sap flow radial patterns measured by the multi-point sensors based on the heat field deformation (HFD) method, and (2) a modified earth impedance (MEI) method from the group of thermodynamic and electric measuring methods and finally we (3) almost harmlessly excavated the whole root system by supersonic air stream. Three steps of absorptive root area measurements were improved: (a) Impact of stem impedance was almost eliminated, (b) Excessive variation of stem impedance values measured too close to stems (in a place with the most heterogeneous materials) was compensated by extrapolation of several close points, (c) Impact of high curvature of small stems was determined and eliminated by an equation.

Results

All the methods gave similar results when considering differences between individual trees as well as between stem sides. Sap flow density was interesting when expressed per measured absorptive root area and leaf area. Experimental data of main and additional sample trees confirmed validity of relationship, which can be applied to improve stem resistivity especially in small trees.

Conclusions

Results indicated, that all the instrumental methods are field applicable and suitable for quantitative measurements, when specific properties of the methods and stem macrostructure are taken into account. Soil electric parameters characterize the important properties related to presence of cracks, water content, and ion concentration, which are being analyzed now.     

General proof of the validity of a new tensor equation of plant growth

Plant cell/organ growth may be partly described by a local tensor equation. We provide a mathematical proof that the Lockhart (global) equation is the diagonal component of this tensor equation.     

Modeling and Dynamical Analysis of Virus-Triggered Innate Immune Signaling Pathways

The investigation of the dynamics and regulation of virus-triggered innate immune signaling pathways at a system level will enable comprehensive analysis of the complex interactions that maintain the delicate balance between resistance to infection and viral disease. In this study, we developed a delayed mathematical model to describe the virus-induced interferon (IFN) signaling process by considering several key players in the innate immune response. Using dynamic analysis and numerical simulation, we evaluated the following predictions regarding the antiviral responses: (1) When the replication ratio of virus is less than 1, the infectious virus will be eliminated by the immune system’s defenses regardless of how the time delays are changed. (2) The IFN positive feedback regulation enhances the stability of the innate immune response and causes the immune system to present the bistability phenomenon. (3) The appropriate duration of viral replication and IFN feedback processes stabilizes the innate immune response. The predictions from the model were confirmed by monitoring the virus titer and IFN expression in infected cells. The results suggest that the balance between viral replication and IFN-induced feedback regulation coordinates the dynamical behavior of virus-triggered signaling and antiviral responses. This work will help clarify the mechanisms of the virus-induced innate immune response at a system level and provide instruction for further biological experiments.     

A probabilistic view on the deterministic mutation–selection equation: dynamics,equilibria, and ancestry via individual lines of descent

We reconsider the deterministic haploid mutation–selection equation with two types. This is an ordinary differential equation that describes the type distribution (forward in time) in a population of infinite size. This paper establishes ancestral (random) structures inherent in this deterministic model. In a first step, we obtain a representation of the deterministic equation’s solution (and, in particular, of its equilibria) in terms of an ancestral process called the killed ancestral selection graph. This representation allows one to understand the bifurcations related to the error threshold phenomenon from a genealogical point of view. Next, we characterise the ancestral type distribution by means of the pruned lookdown ancestral selection graph and study its properties at equilibrium. We also provide an alternative characterisation in terms of a piecewise-deterministic Markov process. Throughout, emphasis is on the underlying dualities as well as on explicit results.

     

Therapeutic resistance and cancer recurrence mechanisms: Unfolding the story of tumour coming back

Cancer recurrence is believed to be one of the major reasons for the failure of cancer treatment strategies. This biological phenomenon could arise from the incomplete eradication of tumour cells after chemo- and radiotherapy. Recent developments in the design of models reflecting cancer recurrence and in vivo imaging techniques have led researchers to gain a deeper and more detailed insight into the mechanisms underlying tumour relapse. Here, we provide an overview of three important drivers of recurrence including cancer stem cells (CSCs), neosis, and phoenix rising. The survival of cancer stem cells is well recognized as one of the primary causes of therapeutic resistance in malignant cells. CSCs have a relatively latent metabolism and show resistance to therapeutic agents through a variety of routes. Neosis has proven to be as an important mechanism behind tumour self-proliferation after treatment which gives rise to the expansion of tumour cells in the injured site via production of Raju cells. Phoenix rising is a pro-recurrence pathway through which apoptotic cancer cells send strong signals to the neighbouring diseased cells leading to their multiplication. The mechanisms involved in therapeutic resistance and tumour recurrence have not yet been fully understood and mostly remain unexplained. Without doubt, an improved understanding of the cellular machinery contributing to recurrence will pave the way for the development of novel, sophisticated and effective anti-tumour therapeutic strategies which can eradicate tumour without the threat of relapse.     

基于脉冲扰动作用下的一个捕食者-食饵模型的动力学性质

基于害虫的生物控制和化学控制策略,考虑到化学杀虫剂对天敌的影响,利用脉冲微分方程建立了在不同的固定时刻分别喷洒杀虫剂和释放天敌的具有依氏(Ivlev)功能性反应的捕食者-食饵脉冲动力系统．证明了当脉冲周期小于某个临界值时,系统存在一个渐近稳定的害虫根除周期解,否则系统是持续生存的．通过分析表明如果采取有效的化学控制策略,那么这种综害虫合控制策略更有效．     

The Dynamics of Root Growth: A Geometric Model

A new model for macroscopic root growth based on a dynamical Riemannian geometry is presented. Assuming that the thickness of the root is much less than its length, the model is restricted to growth in one dimension (1D). We treat 1D tissues as continuous, deformable, growing geometries for sizes larger than 1 mm. The dynamics of the growing root are described by a set of coupled tensor equations for the metric of the tissue and velocity field of material transport in non-Euclidean space. These coupled equations represent a novel feedback mechanism between growth and geometry. We compare 1D numerical simulations of these tissue growth equations to two measures of root growth. First, sectional growth along the simulated root shows an elongation zone common to many species of plant roots. Second, the relative elemental growth rate calculated in silico exhibits spatio-temporal dynamics recently characterized in high-resolution root growth studies but which thus far lack a biological hypothesis to explain them. In our model, these dynamics are a direct consequence of considering growth as both a geometric reaction–diffusion process and expansion due to a distributed source of new materials.     

Abscisic acid levels in the root tips of seven Zea mays varieties

Seven varieties of Zea mays were analysed for cis-abscisic acid (ABA) and trans-ABA levels in the primary root tips by a stable isotope dilution technique. Differences in ABA levels were observed between the first 1 mm apical segments of the different varieties. No trans-ABA could be detected. In the next 2 mm ofthe root segments, the amount of ABA did not vary very much from one variety to another. The levels of ABA might very well reflect the growth reactivity of the root tips towards geotropism and light.