Mathematical model for apical growth, septation, and branching of mycelial microorganisms

A mathematical model for apical growth, septation, and branching of mycelial microorganisms is presented. The model consists of two parts: the determinstic part of the model is based on fundamental cellular and physical mechanisms; it represents the kinetics for growth of hyphal tips and septation of apical as well as intercalary compartments. In regard to random occurrences of hyphal growth and branching, the stochastic part deals with branching processes, tip growth directions, and outgrowth orientations of branches. The model can explain the morphological development of mycelia up to the formation of pellets. The results, as predicted by the model, correspond very closely to those observed in experiments. In addition, some unmeasured states can be ascertained, such as the distribution functions of hyphal length (biomass) and tips along pellet radii.     

Aspergillus nidulans Septin AspB Plays Pre- and Postmitotic Roles in Septum, Branch, and Conidiophore Development

Members of the septin family of proteins act as organizational scaffolds in areas of cell division and new growth in a variety of organisms. Herein, we show that in the filamentous fungus Aspergillus nidulans, the septin AspB is important for cellular division, branching, and conidiation both pre- and postmitotically. AspB localizes postmitotically to the septation site with an underlying polarity that is evident as cytokinesis progresses. This localization at the septation site is dependent on actin and occurs before the cross-wall is visible. AspB localizes premitotically as a ring at sites of branching and secondary germ tube emergence. It is the only known branch site marker. In addition, AspB is found at several stages during the development of the asexual reproductive structure, the conidiophore. It localizes transiently to the vesicle/metula and metula/phialide interfaces, and persistently to the phialide/conidiospore interface. A temperature-sensitive mutant of AspB shows phenotypic abnormalities, including irregular septa, high numbers of branches, and immature asexual reproductive structures.     

Escherichia coli low-molecular-weight penicillin-binding proteins help orient septal FtsZ, and their absence leads to asymmetric cell division and branching

Escherichia coli cells lacking low-molecular-weight penicillin-binding proteins (LMW PBPs) exhibit morphological alterations that also appear when the septal protein FtsZ is mislocalized, suggesting that peptidoglycan modification and division may work together to produce cell shape. We found that in strains lacking PBP5 and other LMW PBPs, higher FtsZ concentrations increased the frequency of branched cells and incorrectly oriented Z rings by 10- to 15-fold. Invagination of these rings produced improperly oriented septa, which in turn gave rise to asymmetric cell poles that eventually elongated into branches. Branches always originated from the remnants of abnormal septation events, cementing the relationship between aberrant cell division and branch formation. In the absence of PBP5, PBP6 and DacD localized to nascent septa, suggesting that these PBPs can partially substitute for the loss of PBP5. We propose that branching begins when mislocalized FtsZ triggers the insertion of inert peptidoglycan at unusual positions during cell division. Only later, after normal cell wall elongation separates the patches, do branches become visible. Thus, a relationship between the LMW PBPs and cytoplasmic FtsZ ultimately affects cell division and overall shape.     

Tip growth of <Emphasis Type="Italic">Neurospora crassa</Emphasis> upon resource shortage: Disturbances of the coordination of elongation,branching, and septation

The characteristics of elongation, branching, septation, and nuclear morphology in hyphal tips (of ~400 μm in length) of the mycelial fungus Neurospora crassa isolated from the mycelium and cultivated for several hours have been investigated using intracellular fluorescent markers. The newly formed branches had the following characteristic features: (1) the predefined orientation was conserved, whereas the diameter decreased (from 10–20 to 6.5 ± 0.4 μm), as did the elongation rate (from 24 ± 1 to 6.7 ± 0.5 μm/min); (2) a disturbed branching pattern with abnormally large internodal distances (up to 1471 μm) and developmental arrest of part of the buds of lateral branches; and (3) a conserved septation pattern and a relatively constant length of hyphal segments (68 ± 2 μm). The size of the nucleus-free zone at the tip (5–33 μm) and the distance between the first septum and the growth point (210 ± 15 μm) in the daughter branches of the isolated fragments were almost the same as in hyphae connected to the mycelium, whereas the average distance between the growth point and the first lateral branch (492 ± 127 μm) and the variability of this parameter were higher in the isolated fragments. The morphology of the nuclei and the size of the nucleus-free zone near the growth point did not differ from those reported for normal vegetative hyphae of N. crassa. The experimental model developed may be used for the elucidation of details of molecular genetic mechanisms that underlie the regulation of interactions between the intracellular structures that provide tip growth of the hyphae in N. crassa.     

The Aspergillus nidulans putative kinase, KfsA (kinase for septation), plays a role in septation and is required for efficient asexual spore formation

In Aspergillus nidulans nuclear division and cytokinesis are coupled processes during asexual sporulation. Metulae, phialides and conidia contain a single nucleus. Here we describe the role of a putative Saccharomyces cerevisiae Kin4-related kinase, KfsA (kinase for septation) in the control of septum formation in A. nidulans. The kfsA deletion caused an increase in the number of conidiophores with septa in their stalks from 20% in wild type to 60% in the mutant strain. Interestingly, 7% of metulae contained two nuclei and the corresponding phialides remained anucleate, suggesting septum formation before proper segregation of nuclei. This points to a checkpoint control of KfsA, which prevents septum formation before nuclear separation. KfsA localized to the cortex and septa in hyphae and in conidiophores but not to the spindle-pole bodies, as it was shown for Kin4 in yeast. KfsA appeared at septa after actin disappeared, suggesting an additional role of KfsA late during septum formation.     

Branching is coordinated with mitosis in growing hyphae of Aspergillus nidulans

Filamentous fungi like Aspergillus nidulans can effectively colonize their surroundings by the formation of new branches along the existing hyphae. While growth conditions, chemical perturbations, and mutations affecting branch formation have received great attention during the last decades, the mechanisms that regulates branching is still poorly understood. In this study, a possible relation between cell cycle progression and branching was studied by testing the effect of a nuclei distribution mutation, cell cycle inhibitors, and conditional cell cycle mutations in combination with tip-growth inhibitors and varying substrate concentrations on branch initiation. Formation of branches was blocked after inhibition of nuclear division, which was not caused by a reduced growth rate. In hyphae of a nuclei distribution mutant branching was severely reduced in anucleated hyphae whereas the number of branches per hyphal length was linearly correlated to the concentration of nuclei, in the nucleated hyphae. In wild type cells, branching intensity was increased when the tip extension was reduced, and reduced when growing on poor substrates. In these situations, the hyphal concentration of nuclei was maintained and it is suggested that branching is correlated to cell cycle progression in order to maintain a minimum required cytoplasmic volume per nucleus and to avoid the formation of anucleated hyphae in the absence of nuclear divisions. The presented results further suggest the hyphal diameter as a key point through which the hyphal element regulates its branching intensity in response to the surrounding substrate concentrations.     

NUCLEAR BEHAVIOR,SEPTATION, AND HYPHAL GROWTH OF ALTERNARIA SOLANI

Nuclei of multinucleate hyphal tip cells divided almost synchronously. Nuclear division was followed by multiple septation during which the elongated hyphal tip cell was divided into several, generally multinucleate, cells. Within the same hypha a distinct growth pattern was not observed with respect to number, length, and nuclear number of cells formed with each successive nuclear division-septation cycle. Hyphal branches originated and received nuclei from hyphal tip cells.     

Quantitation of 3D ureteric branching morphogenesis in cultured embryonic mouse kidney

The growth and branching of the epithelial ureteric tree is critical for development of the permanent kidney (metanephros). Current methods of analysis of ureteric branching are mostly qualitative. We have developed a method for measuring the length of individual branches, and thereby the total length of the ureteric tree in 3 dimensions (3D). The method involves confocal microscopy of whole-mount immunostained metanephroi and computer-based image segmentation, skeletonisation and measurement. The algorithm performs semi-automatic segmentation of a set of confocal images and skeletonisation of the resulting binary object. Length measurements and number of branch points are automatically obtained. The final representation can be reconstructed providing a fully rotating 3D perspective of the skeletonised tree. After 36 h culture of E12 mouse metanephroi, the total length of the ureteric tree was 6103 +/- 291 microm (mean +/- SD), a four-fold increase compared with metanephroi cultured for just 6 h (1522 +/- 149 microm). Ureteric duct length increased at a rate of 153 microm/h over the first 30 h period and was maximal between 18 and 24 h at 325 microm/h. The distribution of branch lengths at the six time points studied was similar, suggesting tight control of ureteric lengthening and branching. This method will be of use in analysing ureteric growth in kidneys cultured in the presence of specific molecules suspected of regulating ureteric growth. The method can also be used to analyse in vivo kidneys and to quantify branching morphogenesis in other developing organs.     

In vivo studies on the nuclear behavior of the arbuscular mycorrhizal fungusGigaspora rosea grown under axenic conditions

Summary The distribution and fate of nuclei of the arbuscular-my-corrhizal fungusGigaspora rosea during late stages of axenic cultures were studied in fixed cultures by transmitted light, conventional and confocal laser scanning microscopy, and in live cultures with two-photon fluorescence microscopy. Mature specimens not yet showing apical septation displayed oval-shaped nuclei localized in lateral positions of the hypha all along the germ-tube length. Beside these, round-shaped nuclei were found to migrate along the central germ-tube core. Some (rare) germ-tube areas, delimited by septa and containing irregularly shaped, much brighter fluorescent nuclei were also found. Specimens that had just initiated the septation process after germ-tube growth arrest displayed round or oval-shaped nuclei in several portions of the germ tubes. These hyphal areas often alternated with other septa-delimited cytoplasmic clusters which contained distorted, brightly fluorescent nuclei. Completely septated specimens mostly lacked nuclei along their germ tubes. However, highly fluorescent chromatin masses appeared within remnants of cytoplasmic material, often compressed between close septa. Our results provide a first clear picture of the in vivo distribution of nuclei along arbuscular mycorrhizal fungal germ tubes issued from resting spores, and suggest that selective areas of their coenocytic hyphae are under specific, single nuclear control. They indicate as well that random autolytic processes occur along senescingG. rosea germ tubes, probably as a consequence of the absence of a host root signal for mycorrhizal formation. Finally, the data presented here allow us to envisage the fate of nuclei released by the germinating spore after nonsymbiotic fungal growth arrest.Abbreviations AM fungi arbuscular-mycorrhizal fungi - DAPI 4, 6-diamidino-2-phenylindole - FM fluorescence microscopy - CLSM confocal laser scanning microscopy - 2PM two-photon microscopy - PI propidium iodide - PMT photomultiplier tube     

A new slant to the Z ring and bacterial cell branch formation

Rod-shaped bacteria such as Escherichia coli accurately maintain their shape from generation to generation. The cytoskeletal proteins MreB and FtsZ, which respectively guide parallel growth of the sidewall and perpendicular growth of the division septum, are important to maintain a straight sidewall and uniformly rounded cell poles. FtsZ normally assembles into a ring at the cell midpoint, called the Z ring, which is oriented perpendicular to the cell's axis and is thus in perfect position to guide growth of a perpendicular septum. In this issue of Molecular Microbiology, Potluri et al. show that low molecular weight penicillin binding proteins, particularly PBP5, have a role in maintaining the perpendicular geometry of the Z ring and subsequent septum in E. coli. When these factors are absent or perturbed, division septa are readily deformed, which results in abnormal cell poles that often bifurcate over time to generate branches. The data suggest that cellular branching in E. coli is specifically induced by aberrant septation events caused by mis-oriented Z rings and not by deformation of a growing cell pole or emergence of new tips from the sidewall, which are likely mechanisms of branching in other bacterial families.     

Crown alterations induced by decline: a study of relationships between growth rate and crown morphology in beech (Fagus sylvatica L.)

One of the first symptoms expressed by declining trees is reduced growth in stem diameter and length increment. The possibility of a relationship between length increment and crown thinning in beech (Fagus sylvatica L.) was investigated by developing a computer model to simulate first order branching patterns of the apical 2 m of monopodially branching beech trees, 70–100 years old, for a range of length increment rates. The model was based on values for branching angle, main axis and branch length increment, number of branches produced per year and branch mortality rates for six healthy and declining trees. Shoot growth rates in the apical 2 m of the sample trees ranged from about 5 cm/year (decline class 3) to 43 cm/ year (healthy). Simulations of branching patterns in the apical 2 m of trees growing at different rates indicated that, when growth rate exceeded about 20 cm/year, total first order branch length and area explored were independent of growth rate. When growth rates fell below this value there was a reduction in total area explored and first order branch length due primarily to the formation of fewer branches. More acute branching angles contributed to a reduction in the area explored. Growth rate-related crown thinning could increase the risk of bark necrosis and secondary pathogen infection during dry and/or hot spells.     

Light and electron microscope study of unilateral mating between a secondary mutant and a wild-type strain ofSchizophyllum commune

Summary After hyphal fusions between the secondary mutant and wild-type strains ofSchizophyllum commune some of the fused hyphae show several nuclei per cell and dissolved septa. These hyphae are designated migration hyphae because they are evidently the main routes of nuclear exchange between the two strains. On the wild-type side of the mating the nuclei spread gradually from the main part of the migration hyphae into the side branches, which develop into an extensive network with many anastomoses. The first cells with pseudoclamps or clamp connections are observed in this network.On the mutant side of the mating the branching is less developed and the number of anastomoses is smaller. The cross walls of the septa are poorly dissolved, and nuclear aggregations occur in the hyphae. No development of clamp connections or pseudoclamps is observed. It is suggested that the unilateral mating response of the secondary mutant strain might possibly be caused by the failure of the septa in the mutant hyphae to dissolve, which inhibits the distribution of the nuclei into the side branches of migration hyphae.     

Maximal polar growth potential depends on the polarisome component AgSpa2 in the filamentous fungus Ashbya gossypii

We used actin staining and videomicroscopy to analyze the development from a spore to a young mycelium in the filamentous ascomycete Ashbya gossypii. The development starts with an initial isotropic growth phase followed by the emergence of germ tubes. The initial tip growth speed of 6-10 microm/h increases during early stages of development. This increase is transiently interrupted in response to the establishment of lateral branches or septa. The hyphal tip growth speed finally reaches a maximum of up to 200 micro/h, and the tips of these mature hyphae have the ability to split into two equally fast-growing hyphae. A search for A. gossypii homologs of polarisome components of the yeast Saccharomyces cerevisiae revealed a remarkable size difference between Spa2p of both organisms, with AgSpa2p being double as long as ScSpa2p due to an extended internal domain. AgSpa2 colocalizes with sites of polarized actin. Using time-lapse videomicroscopy, we show that AgSpa2p-GFP polarization is established at sites of branch initiation and then permanently maintained at hyphal tips. Polarization at sites of septation is transient. During apical branching the existing AgSpa2p-GFP polarization is symmetrically divided. To investigate the function of AgSpa2p, we generated two AgSPA2 mutants, a partial deletion of the internal domain alone, and a complete deletion. The mutations had an impact on the maximal hyphal tip growth speed, on the hyphal diameter, and on the branching pattern. We suggest that AgSpa2p is required for the determination of the area of growth at the hyphal tip and that the extended internal domain plays an important role in this process.     

On-line study of fungal morphology during submerged growth in a small flow-through cell

A flow-through cell is designed to measure the growth kinetics of hyphae of Aspergillus oryzae grown submerged in a well controlled environment. The different stages of the growth process are characterized, from the spore to the fully developed hyphal element with up to 60 branches and a total length lt up to 10,000 micrometer. Spore swelling is found to occur without change in the form of the spore (circularity index constant at about 1.06) and the spore volume probably increases exponentially. The germ tube appears after about 4 h. The branching frequency and the rate of germ tube extension is determined. After about 10 h growth at a glucose concentration of 250 mg L-1, 6-7 branches have been set, and both the total hyphal length lt and the number of tips increase exponentially with time. The specific growth rate of the hyphae is 0. 33 h-1 while the average rate of the extension of the growing tips approaches 55 micrometer h-1. The growth kinetics for all the branches on the main hypha have also been found. The main hypha and all the branches grow at a rate which can be modeled by saturation kinetics with respect to the branch length and with nearly equal final tip speeds (160 micrometer h-1). Branches set near the apical tip of the main hypha attain their final tip speed in the shortest time, i.e., the value of the saturation parameter is small. Finally, the influence of substrate (glucose) concentration cs on the values of the morphological parameters has been determined. It is found that saturation type kinetics can be used to describe the influence of cs on the growth. Experiments with recirculation of effluent from the cell back to the inlet strongly suggest that the fungus secretes an inducer for growth and branching.     

A model for hyphal growth and branching.

A mathematical model for hyphal growth and branching is described which relates cytological events within hyphae to mycelial growth kinetics. Essentially the model quantifies qualitative theories of hyphal growth in which it is proposed that vesicles containing wall precursors and/or enzymes required for wall synthesis are generated at a constant rate throughout a mycelium and travel to the tips of hyphae where they fuse with the plasma membrane, liberating their contents into the wall and increasing the surface area of the hypha to give elongation. The hypothesis that there is a duplication cycle in hyphae which is equivalent to the cell cycle observed in unicellular micro-organisms is also included in the model. Predictions from the model are compared with experimentally observed growth kinetics of mycelia of Geotrichum candidum and Aspergillus nidulans. The finite difference model which was constructed is capable of predicting changes in hyphal length and in the number and positions of branches and septa on the basis of changes in vesicle and nuclear concentration. Predictions were obtained using the model which were in good agreement with experimentally observed data.     

Model for Branch Initiation in Aspergillus nidulans Based on Measurements of Growth Parameters

The rate of hyphal elongation and the number of branches per hypha were measured on short sporelings of Aspergillus nidulans growing at different rates. The rate of elongation was proportional to total length in unbranched and branched hyphae. At each growth rate, the number of branches per hypha increased with increasing length and gave approximately straight-line graphs when plotted against length. The average number of branches per unit of hyphal length was quite different for the various growth rates and increased in direct proportion to the growth rate. The results are interpreted to mean that (i) growing tips have a maximum rate at which they can elongate and which is reached at hyphal lengths characteristic of the particular growth rate and (ii) a new branch is formed when the capacity of the hypha to elongate exceeds that of the existing tips.     

hyp loci control cell pattern formation in the vegetative mycelium of Aspergillus nidulans.

Aspergillus nidulans grows by apical extension of multinucleate cells called hyphae that are subdivided by the insertion of crosswalls called septa. Apical cells vary in length and number of nuclei, whereas subapical cells are typically 40 microm long with three to four nuclei. Apical cells have active mitotic cycles, whereas subapical cells are arrested for growth and mitosis until branch formation reinitiates tip growth and nuclear divisions. This multicellular growth pattern requires coordination between localized growth, nuclear division, and septation. We searched a temperature-sensitive mutant collection for strains with conditional defects in growth patterning and identified six mutants (designated hyp for hypercellular). The identified hyp mutations are nonlethal, recessive defects in five unlinked genes (hypA-hypE). Phenotypic analyses showed that these hyp mutants have aberrant patterns of septation and show defects in polarity establishment and tip growth, but they have normal nuclear division cycles and can complete the asexual growth cycle at restrictive temperature. Temperature shift analysis revealed that hypD and hypE play general roles in hyphal morphogenesis, since inactivation of these genes resulted in a general widening of apical and subapical cells. Interestingly, loss of hypA or hypB function lead to a cessation of apical cell growth but activated isotropic growth and mitosis in subapical cells. The inferred functions of hypA and hypB suggest a mechanism for coordinating apical growth, subapical cell arrest, and mitosis in A. nidulans.     

Growth Dynamics and Morphology of Annual Shoots, According to their Architectural Position, in Young Cedrus atlantica (Endl.) Manetti ex Carriere (Pinaceae)

The influence of shoot architectural position on growth andbranching pattern of young Cedrus atlantica (Endl.) Manettiex Carrière trees were studied. Extension growth andtype of axillary products (lateral bud, sylleptic short or longshoots) of annual shoots of increasing branching order (mainstem, branches and branchlets) were recorded weekly during the1993 growing season. Annual final shoot length, duration ofextension, and maximum extension rate decreased with increasingbranching order. Sylleptic axillary shoots occurred only onannual shoots of the main stem and branches and were producedwhen extension rate was at its highest. Differences in growthrate and final length of annual shoots, according to their architecturalposition, were related to differences in the total number anddiversity of types of sylleptic axillary shoots produced. Itis suggested that types and numbers of sylleptic axillary shootsproduced are linked with threshold values for both final lengthand extension rate of the parent shoot. Copyright 1999 Annalsof Botany Company Atlas cedar, extension growth, sylleptic branching, tree architecture, morphology.     

Uncontrolled septation in a cell division cycle mutant of the fission yeast Schizosaccharomyces pombe.

A temperature-sensitive Schizosaccharomyces pombe mutant, cdc16-116, has been isolated which undergoes uncontrolled septation during its cell division cycle. The mutant accumulates two types of cells after 3 h of growth at the restrictive temperature: (i) type I cells (85% of the population), which complete nuclear division and then form up to five septa between the divided nuclei; and (ii) type II cells (15% of the population), which form an asymmetrically situated septum in the absence of any nuclear division. cdc16-116 is a monogenic recessive mutation unlinked to any previously known cdc gene of S. pombe. It is not affected in a previously reported control by which septation is dependent upon completion of nuclear division. We propose the cdc16-116 is unable to complete septum formation and proceed to cell separation and is also defective in a control which prevents the manufacture of more than one septum in each cell cycle.     

Influence of applied electrical fields on yeast and hyphal growth of Candida albicans

Yeast cells of Candida albicans which had been attached to polylysine-coated microscope slides were induced to form buds or germ tubes in the presence of external electrical fields. The sites of budding and germ tube formation and the growth of germ tubes and hyphal branches were polarized preferentially towards the cathode. Buds were not converted to pseudohyphae or germ tubes by the field and the field had no effect on the positioning of nuclei or septa in the yeast cell or germ tube. Buds were less polarized than germ tubes at any given applied voltage. The polarization of buds reached a peak at an electrical field of 12 mV per cell. Polarization of germ tubes was biphasic, increasing rapidly with increasing field strengths up to 5 mV per cell, and then more slowly in stronger fields. An electrical field was only required for a fraction of the time taken for germ tubes to start to form, so cells retained a memory of experiencing an electrical field which influenced the selection of sites of evagination. Increasing the electrical field delayed the time of germ tube evagination and inhibited the rate of germ tube extension. Unlike previous findings with other filamentous fungi, germ tubes grew unidirectionally towards the cathode for extended periods and did not deviate to a perpendicular orientation. This result suggests that the septal pore of the filamentous form may have high electrical resistance and would act as an effective barrier to solute transport between intercalary compartments.