Simulation of growth of a filamentous fungus in 3 dimensions

The tridimensional growth of a filamentous fungus was simulated, based on a model for the evolution of the microscopic morphology of Trichoderma reesei. When supplemented with a spatial representation of growth, the model correctly simulates the evolution from a single spore to a pellet. Diffusion of oxygen is included in the model. The simulated tridimensional structures have a fractal nature; and the fractal dimension, determined by a box-counting method, increases during growth. The fractal dimension only depends on the mass of the pellet and is not affected by model parameters such as tip extension rate and branching frequency. Realistic pictures are obtained and the radius of the pellet increases at a constant rate. The influence of model parameters (tip extension rate, branching frequency, minimum porosity) on dissolved oxygen concentration profiles, biomass concentration profiles, rate at which the pellet diameter increases, and the evolution of the fractal dimension was determined. The dissolved oxygen profiles were found to be very different from the profiles, obtained by assuming a homogenous biomass distribution within the pellet. Finally, the formation of pellets from spore aggregates is calculated and the size of the spore aggregate is found to only influence the time needed before the appearance of a pellet and not its morphology. (c) 1997 John Wiley & Sons, Inc.     

On the rate of budding and proximal attenuation of the graptoloid rhabdosome

Earlier models of the morphogenesis in graptoloid colonies can be improved by taking into account the rate of growth and budding. It is assumed that both these factors are controlled by a specific function of the morphogen, here called for convenience the blastogen , and both are responsible for the attenuation of the proximal part of the rhabdosome. The permanence of this attenuation may theoretically be explained by the universal advantage of differentiation between the proximal and the distal part of the colony. Some aspects of possible adaptive significance of such colony organization are discussed. □ Graptoloid colonies, morphogenesis, mathematical model.     

Tests of a cellular model for constant branch distribution in the filamentous fungus Neurospora crassa

The growth of mycelial fungi is characterized by the highly polarized extension of hyphal tips and the formation of subapical branches, which themselves extend as new tips. In Neurospora crassa, tip growth and branching are crucial elements for this saprophyte in the colonization and utilization of organic substrates. Much research has focused on the mechanism of tip extension, but a cellular model that fully explains the known phenomenology of branching by N. crassa has not been proposed. We described and tested a model in which the formation of a lateral branch in N. crassa was determined by the accumulation of tip-growth vesicles caused by the excess of the rate of supply over the rate of deposition at the apex. If both rates are proportional to metabolic rate, then the model explains the known lack of dependence of branch interval on growth rate. We tested the model by manipulating the tip extension rate, first by shifting temperature in both the wild type and hyperbranching (colonial) mutants and also by observing the behavior of both tipless colonies and colonyless tips. We found that temperature shifts in either direction result in temporary changes in branching. We found that colonyless tips also pass through a temporary transition phase of branching. The tipless colonies produced a cluster of new tips near the point of damage. We also found that branching in colonial mutants is dependent on growth rate. The results of these tests are consistent with a model of branching in which branch initiation is controlled by the dynamics of tip growth while being independent of the actual rate of this growth.     

Tests of a Cellular Model for Constant Branch Distribution in the Filamentous Fungus Neurospora crassa

The growth of mycelial fungi is characterized by the highly polarized extension of hyphal tips and the formation of subapical branches, which themselves extend as new tips. In Neurospora crassa, tip growth and branching are crucial elements for this saprophyte in the colonization and utilization of organic substrates. Much research has focused on the mechanism of tip extension, but a cellular model that fully explains the known phenomenology of branching by N. crassa has not been proposed. We described and tested a model in which the formation of a lateral branch in N. crassa was determined by the accumulation of tip-growth vesicles caused by the excess of the rate of supply over the rate of deposition at the apex. If both rates are proportional to metabolic rate, then the model explains the known lack of dependence of branch interval on growth rate. We tested the model by manipulating the tip extension rate, first by shifting temperature in both the wild type and hyperbranching (colonial) mutants and also by observing the behavior of both tipless colonies and colonyless tips. We found that temperature shifts in either direction result in temporary changes in branching. We found that colonyless tips also pass through a temporary transition phase of branching. The tipless colonies produced a cluster of new tips near the point of damage. We also found that branching in colonial mutants is dependent on growth rate. The results of these tests are consistent with a model of branching in which branch initiation is controlled by the dynamics of tip growth while being independent of the actual rate of this growth.     

Proximal structure and development in the Ordovician graptolite Parisograptus Chen and Zhang, 1996

The proximal development of Parisograptus Chen and Zhang is described from three–dimensionally preserved specimens. The unique development features an origin of proximal thecae like a string of pearls vertically upon each other on the reverse side of the rhabdosome with the dorsal sides of the initial stipes placed side by side. The development differs strongly from that found in the superficially similar Arienigraptus in which the first thecal pairs grow downwards side by side, even though the rhabdosome shapes are quite similar. It represents a first step towards the development of a completely biserial rhabdosome and eventually leads to the biserial, monopleural glossograptids.     

桃树修剪分枝模式的模拟

在不同修剪手法下,对栽培桃树(Prunuspersica(L.)Batsch)不同母枝上的分枝模式进行了比较研究.从分枝模式来看:修剪后的母枝基本由3个不同的区域组成,基部是不萌发的潜伏芽形成的未分枝区域;中部是延迟分枝和多次分枝组成的分枝区域(主要的枝条类型有短枝、长枝和多次枝);顶部是被剪除的部分.我们通过隐式半马尔可夫模型来模拟这一分枝模式,主要是定量描述1次枝和多次枝在母枝上的数量及其分布状况.在上述模型中,未分枝区、延迟分枝区和多次分枝区称为瞬时态,被剪除的部分称为吸收态.模拟的结果与观察的结果进行对比后发现,两者具有很好的一致性.这说明隐式半马尔可夫模型是模拟植物分枝过程的一种有效方法,尽管隐式半马尔可夫链模型只是一个描述性的模型,但仍能对其所描述的生物现象进行解释,在预测修剪手法对母枝分枝模式影响方面比传统的方法具有明显的优势.本研究结果是建立三维虚拟桃树树冠分枝结构的基础.     

Growth velocities of branched actin networks

The growth of an actin network against an obstacle that stimulates branching locally is studied using several variants of a kinetic rate model based on the orientation-dependent number density of filaments. The model emphasizes the effects of branching and capping on the density of free filament ends. The variants differ in their treatment of side versus end branching and dimensionality, and assume that new branches are generated by existing branches (autocatalytic behavior) or independently of existing branches (nucleation behavior). In autocatalytic models, the network growth velocity is rigorously independent of the opposing force exerted by the obstacle, and the network density is proportional to the force. The dependence of the growth velocity on the branching and capping rates is evaluated by a numerical solution of the rate equations. In side-branching models, the growth velocity drops gradually to zero with decreasing branching rate, while in end-branching models the drop is abrupt. As the capping rate goes to zero, it is found that the behavior of the velocity is sensitive to the thickness of the branching region. Experiments are proposed for using these results to shed light on the nature of the branching process.     

Genetically controlled cortical tissue deposition inNormalograptus scalaris (Hisinger, 1837)

A specimen ofNormalograptus scalaris (Hisinger) from the Llandovery of Dalarna, Sweden, shows a highly asymmetrical rhabdosome in which one stipe was abandoned at an early stage in the growth of the colony. The surface of the rhabdosome is thickly covered by cortical tissue, but the remaining dorsal side of the second stipe is left free. Even though the symmetry of the colony is strongly distorted, it survived for a considerable time. It is suggested that this unusual development involved genetic control of cortical tissue deposition in the graptolite colony.      

Population structure of graptolite assemblages

Graptolite rhabdosomes display a diverse suite of morphologies. The range of morphotypes present within most moderate- to high-diversity assemblages from the Ordovician and Silurian is similar, despite the different taxonomic composition of the faunas at different times. Survivorship analyses of graptolite faunas from the Ordovician and Silurian demonstrate strong similarities in the mortality rates of unrelated graptolites of similar functional morphology. They also show a strong correlation between decreasing mortality rates among more mature colonies with increasing rhabdosome complexity. This similarity in both functional morphology and life history of graptolites suggests that they lived within a very stable planktic community structure.     

Choline: Its role in the growth of filamentous fungi and the regulation of mycelial morphology

Abstract Choline is an essential metabolite for the growth of filamentous fungi. It occurs most notably as a component of the major membrane phospholipid, phosphatidyl choline (lecithin), and fulfills a major role in sulphate metabolism in the form of choline- o -sulphate in many species. Choline is usually synthesised endogenously, but exogenous choline can also be taken up, either to compensate for metabolic deficiencies in choline-requiring mutants such as those of Aspergillus nidulans and Neurospora crassa , or as a normal function by species such as Fusarium graminearum which do not require added choline for growth. F. graminearum has a highly specific constitutive uptake system for this purpose. Recent studies have begun to indicate that choline also plays an important role in hyphal and mycelial morphology. Over a wide range of concentrations, choline influences mycelial morphology, apparently influences mycelial morphology, apparently by controlling branch initiation. At high concentrations of added choline, branching is inhibited but specific growth rate is unaffected, leading to the production of rapidly extending, sparsely branched mycelia. Reduction of choline concentration allows a progressive increase in branching. Additionally, in choline-requiring mutants which have a very reduced content of choline, multiple tip-formation and apical branching occurs. Just prior to cessation of growth in choline-starved cultures of A. nidulans choline-requiring mutants, hyphal morphology changes due to a brief phase of unpolarised growth to produce spherical swellings called ballons, at or near hyphal apices. The precise mechanism by which choline affects fungal morphology is not yet known, although in A. nidulans it appears to be at least partially due to the influence of membrane composition on the synthesis of the hyphal wall polymer chitin. Several hypotheses for the possible mode of action of choline in affecting fungal morphology are discussed here.     

Conversion of fibrinogen to fibrin. The correlation between clotting kinetics and morphology of fibrin polymerized in different solvent media

The morphology of fibrin strongly depends on solvent medium, as shown by clotting experiments carried out in the presence of different salts. The clots were characterized by electron microscopy and spectrophotometric methods; the kinetics of gelation were determined. In the presence of electrolytes which strongly delay clotting, the strands are thin and few branching points are observed; opposite morphological changes are induced by salts which act as accelerating agents. On the basis of this correlation, and of previous data on the structure of fibrin, a kinetic model of the self-assembly process is outlined. It accounts well for the observed solvent effects on the morphology of the network. An important result emerging from our experiments is that the fibers undergo branching prior to gelation. Branching points arise from the defective growth of the fibers; a simple explanation of the occurrence of branching may be obtained by our self-assembly model.     

Key differences between lateral and apical branching in hyphae of Neurospora crassa

We examined in fine detail growth kinetics and intracellular events during lateral and apical branching in hyphae of Neurospora crassa. By high-resolution video-enhanced light microscopy, we found remarkable differences in the events preceding lateral vs apical branching. While apical branching involved a significant disturbance in the apical growth of the parental hypha, lateral branching occurred without any detectable alterations in the growth of the parental hypha. Prior to the emergence of a lateral branch, an incipient Spitzenk?rper was formed about 12-29 microm behind the apex. Lateral branch formation did not interfere with the elongation rate of the primary hypha, the shape of its apex or the behavior of its Spitzenk?rper. In sharp contrast, apical branching was preceded by marked changes in physiology and morphology of the parental hypha and by a sharp drop in elongation rate. The sequence involved a cytoplasmic contraction, followed by a retraction, dislocation, and disappearance of the Spitzenk?rper; hyphal elongation decreased sharply and a transient phase of isotropic growth caused the hyphal apex to round up. Growth resumed with the formation of two or more apical branches, each one with a Spitzenk?rper formed by gradual condensation of phase-dark material (vesicles) around an invisible nucleation site. The observed dissimilarities between lateral and apical branching suggest that these morphogenetic pathways are triggered differently. Whereas apical branching may be traced to a sudden discrete disruption in cytoplasmic organization (cytoplasmic contraction), the trigger of lateral branching probably stems from the subapical accumulation of wall precursors (presumably vesicles) reaching a critical concentration.     

Polyp oriented modelling of coral growth

The morphogenesis of colonial stony corals is the result of the collective behaviour of many coral polyps depositing coral skeleton on top of the old skeleton on which they live. Yet, models of coral growth often consider the polyps as a single continuous surface. In the present work, the polyps are modelled individually. Each polyp takes up resources, deposits skeleton, buds off new polyps and dies. In this polyp oriented model, spontaneous branching occurs. We argue that branching is caused by a so called “polyp fanning effect” by which polyps on a convex surface have a competitive advantage relative to polyps on a flat or concave surface. The fanning effect generates a more potent branching mechanism than the Laplacian growth mechanism that we have studied previously (J. Theor. Biol. 224 (2003) 153). We discuss the application of the polyp oriented model to the study of environmentally driven morphological plasticity in stony corals. In a few examples we show how the properties of the individual polyps influence the whole colony morphology. In our model, the spacing of polyps influences the thickness of coral branches and the overall compactness of the colony. Density variations in the coral skeleton may also be important for the whole colony morphology, which we address by studying two variants of the model. Finally, we discuss the importance of small scale resource translocation in the coral colony and its effects on the morphology of the colony.     

ISOLATED GRAPTOLITES FROM THE LITUIGRAPTUS CONVOLUTUS BIOZONE (SILURIAN, LLANDOVERY) OF DALARNA, SWEDEN

Abstract:  Isolated material of 13 graptolite species from the Aeronian (middle Llandovery) Lituigraptus convolutus Biozone is described. A considerable amount of late astogenetic peridermal thickening is revealed in Normalograptus scalaris and Rivagraptus bellulus . As a result, in the former, thecal morphology is modified from climacograptid to pseudoglyptograptid; in both species, the virgella becomes robust. In Metaclimacograptus minimus and Me. sp., it is shown that the dorsal metathecal wall forms the genicular hood, whereas in N. nikolayevi , the infragenicular wall of the succeeding theca forms the distal thecal apertural margin. Pribylograptus argutus exhibits typical pribylograptid thecae along the length of the available rhabdosome fragments. Characters differentiating Campograptus lobiferus from C. harpago include the greater dorso-ventral width and more rapid increase in dorso-ventral width of the former and the greater recurving of distal thecae and presence of thecal spines/processes on all thecae of the latter. Lituigraptus convolutus has rastritiform thecae proximally; thecal apertures throughout the rhabdosome are crescentic and laterally expanded.     

Dynamic modeling of branching morphogenesis of ureteric bud in early kidney development

In the early kidney development, a simple epithelial tube called ureteric bud is derived from the intermediate mesoderm and undergoes a complex process of growth and terminal bifid branching. The branching of the ureteric bud is achieved by different cellular behaviors including cell proliferation and chemotaxis. In this paper, we examine how the branching morphology depends on different physical or chemical factors by constructing a cell-based model to describe the simple tube branching in the early kidney development. We conclude that a proper balance between growth speed of epithelial sheet due to cell proliferation and cell mobility due to chemotaxis is necessary to realize the development of normal Y-shaped pattern. When cell proliferation is fast compared to chemotaxis, kinked pattern is formed, and when cell proliferation is slow, bloated pattern is formed. These are consistent with experimental observations in different morphological anomalies of mutants. We show that the different branching patterns are accurately predicted by growth-chemotaxis ratio.     

桃树修剪分枝模式的模拟

在不同修剪手法下,对栽培桃树(Prunuspersica(L.)Batsch)不同母枝上的分枝模式进行了比较研究。从分枝模式来看修剪后的母枝基本由3个不同的区域组成,基部是不萌发的潜伏芽形成的未分枝区域;中部是延迟分枝和多次分枝组成的分枝区域(主要的枝条类型有短枝、长枝和多次枝);顶部是被剪除的部分。我们通过隐式半马尔可夫模型来模拟这一分枝模式,主要是定量描述1次枝和多次枝在母枝上的数量及其分布状况。在上述模型中,未分枝区、延迟分枝区和多次分枝区称为瞬时态,被剪除的部分称为吸收态。模拟的结果与观察的结果进行对比后发现,两者具有很好的一致性。这说明隐式半马尔可夫模型是模拟植物分枝过程的一种有效方法,尽管隐式半马尔可夫链模型只是一个描述性的模型,但仍能对其所描述的生物现象进行解释,在预测修剪手法对母枝分枝模式影响方面比传统的方法具有明显的优势。本研究结果是建立三维虚拟桃树树冠分枝结构的基础。     

Morphogenesis of the branching reef coral Madracis mirabilis

Understanding external deciding factors in growth and morphology of reef corals is essential to elucidate the role of corals in marine ecosystems, and to explain their susceptibility to pollution and global climate change. Here, we extend on a previously presented model for simulating the growth and form of a branching coral and we compare the simulated morphologies to three-dimensional (3D) images of the coral species Madracis mirabilis. Simulation experiments and isotope analyses of M. mirabilis skeletons indicate that external gradients of dissolved inorganic carbon (DIC) determine the morphogenesis of branching, phototrophic corals. In the simulations we use a first principle model of accretive growth based on local interactions between the polyps. The only species-specific information in the model is the average size of a polyp. From flow tank and simulation studies it is known that a relatively large stagnant and diffusion dominated region develops within a branching colony. We have used this information by assuming in our model that growth is entirely driven by a diffusion-limited process, where DIC supply represents the limiting factor. With such model constraints it is possible to generate morphologies that are virtually indistinguishable from the 3D images of the actual colonies.     

Relationships between phosphatidylcholine content, chitin synthesis, growth, and morphology of Aspergillus nidulans choC

The phosphatidylcholine (PC) content of Aspergillus nidulans choC was varied by growing the auxotroph in medium containing various concentrations of choline chloride. Direct linear correlations were observed between PC content and in vivo chitin synthase activity, between in vivo chitin synthase activity and mean hyphal extension rate, and between mean hyphal extension rate and hyphal growth unit length; hyphal growth unit length is a measure of hyphal branching. Further, there was a correlation between PC content and colony radial growth rate. Thus, membrane composition is an important determinant of both hyphal (and colony) extension rate and mycelial morphology.