Scaling laws and thermodynamic analysis for vascular branching of microvessels

When blood flows through small vessels, the two-phase nature of blood as a suspension of red cells (erythrocytes) in plasma cannot be neglected, and with decreasing vessel size, a homogeneous continuum model become less adequate in describing blood flow. Following the Haynes’ marginal zone theory, and viewing the flow as the result of concentric laminae of fluid moving axially, the present work provides models for fluid flow in dichotomous branching composed by larger and smaller vessels, respectively. Expressions for the branching sizes of parent and daughter vessels, that provides easier flow access, are obtained by means of a constrained optimization approach using the Lagrange multipliers. This study shows that when blood behaves as a Newtonian fluid, Hess – Murray law that states that the daughters-to-parent diameter ratio must equal to 2^(-1/3) is valid. However, when the nature of blood as a suspension becomes important, the expression for optimum branching diameters of vessels is dependent on the separation phase lengths. It is also shown that the same effect occurs for the relative lengths of daughters and parent vessels. For smaller vessels (e. g., arterioles and capillaries), it is found that the daughters-to-parent diameter ratio may varies from 0,741 to 0,849, and the daughters-to-parent length ratio varies from 0,260 to 2,42. For larger vessels (e. g., arteries), the daughters-to-parent diameter ratio and the daughters-to-parent length ratio range from 0,458 to 0,819, and from 0,100 to 6,27, respectively. In this paper, it is also demonstrated that the entropy generated when blood behaves as a single phase fluid (i. e., continuum viscous fluid) is greater than the entropy generated when the nature of blood as a suspension becomes important. Another important finding is that the manifestation of the particulate nature of blood in small vessels reduces entropy generation due to fluid friction, thereby maintaining the flow through dichotomous branching vessels at a relatively lower cost.

A new species and expanded distributions of freshwater Audouinella (Acrochaetiaceae, Rhodophyta) from Central Mexico and south-eastern Brazil

Eighteen collections of red-coloured Audouinella from Central Mexico and southeastern Brazil detected three species. The most common species, A. eugenea, is characterized by macroscopic thalli, the erect system consisting of filaments with cylindrical cells, undifferentiated into proximal and distal parts, and relatively large monosporangia (greater than or equal to 12.0 mum long). Spermatangia. and possible propagules were observed in some Mexican populations. This is the third Audouinella species observed to have gametangia and the first member of the Acrochaetiales with putative propagules. The second species, from Central Mexico, was characterized by the following features: macroscopic thalli, the erect system differentiated into proximal parts with cylindrical cells, unbranched or rarely branched, and distal parts with barrel-shaped cells, abundantly branched to form dense fascicles, with alternate or dichotomous branching, some at right-angles to the axis, and relatively large monosporangia (greater than or equal to 12.0 mum long). The morphologically distinct proximal and distal portions of the erect system, the latter forming dense fascicles, was a consistent character so far unknown in Audouinella; thus, we propose a new species, A. huastecana sp. nov. The third species is a microscopic epiphyte, A. meiospora, with a well-developed prostrate system composed of creeping and loosely aggregated filaments, and a short homogeneous erect system (less than or equal to 15 cells) of filaments with cylindrical or barrel-shaped cells and small monosporangia (less than or equal to 13.0 mum long). A. eugenea and A. meiospora are characterized for the first time from the Southern and Northern Hemispheres, respectively, both occurring mostly in areas of tropical or subtropical rainforests. A. meiospora is reported from new macroalgal hosts. A. eugenea and A. huastecana tended to occur in warm, alkaline waters with a high ion content that were moderate to fast flowing, whereas A. meiospora was not associated with particular habitats.

Unusual branching in the palm Euterpe edulis Mart

The unusual development of branches along the stem of Euterpe edulis is described for the first time. Branches originated at 2 to 190 cm from the ground. Ramified individuals and branches were able to produce reproductive structures and some branches produced roots. A plausible cause for the observed anomaly could be genetic problems due to small population sizes. The better agreement of this process can have a positive effect in the harvest of the heart of palm through the artificial induction of sprouts, what would prevent the death of the individual.

Alterations in growth and branching of Neurospora crassa caused by sub-inhibitory concentrations of antifungal agents

Six antifungal agents at subinhibitory concentrations were used for investigating their ability to affect the growth and branching in Neurospora crassa. Among the antifungals herein used, the azole agent ketoconazole at 0.5 mu g/ml inhibited radial growth more than fluconazole at 5.0 mu g/ml while amphotericin B at 0.05 mu g/ml was more effective than nystatin at 0.05 mu g/ml. Morphological alterations in hyphae were observed in the presence of griseofulvin, ketoconazole and terbinafine at the established concentrations. The antifungal agents were more effective on vegetative growth than on conidial germination. Terbinafine markedly reduced growth unit length (GU) by 54.89%, and caused mycelia to become hyperbranched. In all cases, there was a high correlation between hyphal length and number of tips (r > 0.9). All our results showed highly significant differences by ANOVA, (p < 0.001, alpha = 0.05). Considering that the hyphal tip is the main interface between the fungus and its environment/through which enzymes and toxins are secreted and nutrients absorbed, it would not be desirable to obtain a hyperbranched mycelia with inefficient doses of antifungal drugs.

The collision branching process

We consider a branching model, which we call the collision branching process (CBP), that accounts for the effect of collisions, or interactions, between particles or individuals. We establish that there is a unique CBP, and derive necessary and sufficient conditions for it to be nonexplosive. We review results on extinction probabilities, and obtain explicit expressions for the probability of explosion and the expected hitting times. The upwardly skip-free case is studied in some detail.

Quasispin graded-fermion formalism and gl(m vertical bar n)down arrow osp(m vertical bar n) branching rules

The graded-fermion algebra and quasispin formalism are introduced and applied to obtain the gl(m\n)down arrow osp(m\n) branching rules for the two- column tensor irreducible representations of gl(m\n), for the case m less than or equal to n(n > 2). In the case m < n, all such irreducible representations of gl(m\n) are shown to be completely reducible as representations of osp(m\n). This is also shown to be true for the case m=n, except for the spin-singlet representations, which contain an indecomposable representation of osp(m\n) with composition length 3. These branching rules are given in fully explicit form. (C) 1999 American Institute of Physics. [S0022-2488(99)04410-2].

Long-distance signalling and a mutational analysis of branching in pea

Four ramosus mutants with increased branching at basal and aerial nodes have been used to investigate the genetic regulation of bud outgrowth in Pisum sativum L. (garden pea). Studies of long-distance signalling, xylem sap cytokinin concentrations, shoot auxin level, auxin transport and auxin response are discussed. A model of branching control is presented that encompasses two graft-transmissible signals in addition to auxin and cytokinin. Mutants rms1 through rms4 are not deficient in indole-3-acetic acid (IAA) or in the basipetal transport of this hormone. Three of the four mutants, rms1, rms3 and rms4, have very reduced cytokinin concentrations in xylem sap from roots. This reduction in xylem sap cytokinin concentration appears to be caused by a property of the shoot and may be part of a feedback mechanism induced by an aspect of bud outgrowth. The shoot-to-root feedback signal is unlikely to be auxin itself, as auxin levels and transport are not correlated with xylem sap cytokinin concentrations in various intact and grafted mutant and wild-type plants. Rms1 and Rms2 act in shoot and rootstock to regulate the level or transport of graft-transmissible signals. Various grafting studies and double mutant analyses have associated Rms2 with the regulation of the shoot-to-root feedback signal. Rms1 is associated with a second unknown graft-transmissible signal that is postulated to move in the direction of root-to-shoot. Exogenous auxin appears to interact with both of the signals regulated by Rms1 and Rms2 in the inhibition of branching after decapitation. The action of Rms3 and Rms4 is less apparent at this stage, although both appear to act largely in the shoot.

The shoot controls zeatin riboside export from pea roots. Evidence from the branching mutant rms4

The rms4 mutant of pea (Pisum sativum L.) was used in grafting studies and cytokinin analyses of the root xylem sap to provide evidence that, at least for pea, the shoot can modify the import of cytokinins from the root. The rms4 mutation, which confers a phenotype with increased branching in the shoot, causes a very substantial decrease (down to 40-fold less) in the concentration of zeatin riboside (ZR) in the xylem sap of the roots. Results from grafts between wild-type (WT) and rms4 plants indicate that the concentration of cytokinins in the xylem sap of the roots is determined almost entirely by the genotype of the shoot. WT scions normalize the cytokinin concentration in the sap of rms4 mutant roots, whereas mutant scions cause WT roots to behave like those of self-grafted mutant plants. The mechanism whereby rms4 shoots of pea cause a down-regulation in the export of cytokinins from the roots is unknown at this time. However, our data provide evidence that the shoot transmits a signal to the roots and thereby controls processes involved in the regulation of cytokinin biosynthesis in the root.

The rms1 mutant of pea has elevated indole-3-acetic acid levels and reduced root-sap zeatin riboside content but increased branching controlled by graft-transmissible signal(s)

Rms1 is one of the series of five ramosus loci in pea (Pisum sativum L.) in which recessive mutant alleles confer increased branching at basal and aerial vegetative nodes. Shoots of the nonallelic rms1 and rms2 mutants are phenotypically similar in most respects. However, we found an up to 40-fold difference in root-sap zeatin riboside ([9R]Z) concentration between rms1 and rms2 plants. Compared with wild-type (WT) plants, the concentration of [9R]Z in rms1 root sap was very low and the concentration in rms2 root sap was slightly elevated. To our knowledge, the rms1 mutant is therefore the second ramosus mutant (rms4 being the first) to be characterized with low root-sap [9R]Z content. Like rms2, the apical bud and upper nodes of rms1 plants contain elevated indole-3-acetic acid levels compared with WT shoots. Therefore, the rms1 mutant demonstrates that high shoot auxin levels and low root-sap cytokinin levels are not necessarily correlated with increased apical dominance in pea. A graft-transmissible basis of action has been demonstrated for both mutants from reciprocal grafts between mutant and WT plants. Branching was also largely inhibited in rms1 shoots when grafted to rms2 rootstocks, but was not inhibited in rms2 shoots grafted to rms1 rootstocks. These grafting results are discussed, along with the conclusion that hormone-like signals other than auxin and cytokinin are also involved.

Dendritic branching patterns of pyramidal cells in the visual cortex of the new world marmoset monkey, with comparative notes on the old world macaque monkey

The basal dendritic arbors of 442 supragranular pyramidal cells in visual cortex of the marmoset monkey were compared by fractal analyses. As detailed in a previous study,(1) individual cells were injected with Lucifer Yellow and processed for a DAB reaction product. The basal dendritic arbors were drawn, in the tangential plane, and the fractal dimension (D) determined by the dilation method. The fractal dimensions were compared between cells in ten cortical areas containing cells involved in visual processing, including the primary visual area (Vi), the second visual area (V2), the dorsoanterior area (DA), the dorsomedial area (DM), the dorsolateral. area (DL), the middle temporal area (MT), the posterior parietal area (PP), the fundus of the superior temporal area (FST) and the caudal and rostral subdivisions of inferotemporal cortex (ITc and ITr, respectively). Of 45 pairwise interareal comparisons of the fractal dimension of neurones, 20 were significantly different. Moreover, comparison of data according to previously published visual processing pathways revealed a trend for cells with greater fractal dimensions in higher cortical areas. Comparison of the present results with those in homologous cortical areas in the macaque monkey(2) revealed some similarities between the two species. The similarity in the trends of D values of cells in both species may reflect developmental features which, result in different functional attributes.

Pyramidal neurones in macaque visual cortex: Interareal phenotypic variation of dendritic branching patterns

The basal dendritic arbors of over 500-layer III pyramidal neurones of the macaque cortex were compared by fractal analyses, which provides a measure of the space filling (or branching pattern) of dendritic arbors. Fractal values (D) of individual cells were compared between the cytochrome oxidase (CO)-rich blobs and CO-poor interblobs, of middle and upper layer III, and between sublaminae, in the primary visual area (Vi). These data were compared with those in the CO compartments in the second visual area (V2), and seven other extrastriate cortical areas. (V4, MT, LIP, 7a, TEO, TE and STP). There were significant differences in the fractal dimensions, and therefore the dendritic branching patterns, of cells in striate and extrastriate areas. Of the 55 possible pairwise comparisons of fractal dimension of neurones in different cortical areas (or CO compartments), 39 proved to be significantly different. The markedly different morphologies of pyramidal cells in the different cortical areas may be one of the features that determine the functional signatures of these cells by influencing the number of inputs received by, and propagation of potentials through, their dendritic arbors.

Long-distance signaling and the control of branching in the rms1 mutant of peal

The ramosus (rms) mutation (rms1) of pea (Pisum sativum) causes increased branching through modification of graft-transmissible signal(s) produced in rootstock and shoot. Additional grafting techniques have led us to propose that the novel signal regulated by Rms1 moves acropetally in shoots and acts as a branching inhibitor. Epicotyl interstock grafts showed that wild-type (WT) epicotyls grafted between rms1 scions and rootstocks can revert mutant scions to a WT non-branching phenotype. Mutant scions grafted together with mutant and WT rootstocks did not branch despite a contiguous mutant root-shoot system. The primary action of Rms1 is, therefore, unlikely to be to block transport of a branching stimulus from root to shoot. Rather, Rms1 may influence a long-distance signal that functions, directly or indirectly, as a branching inhibitor. It can be deduced that this signal moves acropetally in shoots because WT rootstocks inhibit branching in rms1 shoots, and although WT scions do not branch when grafted to mutant rootstocks, they do not inhibit branching in rms1 cotyledonary shoots growing from the same rootstocks. The acropetal direction of transport of the Rms1 signal supports previous evidence that the rms1 lesion is not in an auxin biosynthesis or transport pathway. The different branching phenotypes of WT and rms1 shoots growing from the same rms1 rootstock provides further evidence that the shoot has a major role in the regulation of branching and, moreover, that root-exported cytokinin is not the only graft-transmissible signal regulating branching in intact pea plants.

Mutational analysis of branching in pea. Evidence that Rms1 and Rms5 regulate the same novel signal

The fifth increased branching ramosus (rms) mutant, rms5, from pea (Pisum sativum), is described here for phenotype and grafting responses with four other rms mutants. Xylem sap zeatin riboside concentration and shoot auxin levels in rms5 plants have also been compared with rms1 and wild type (WT). Rms1 and Rms5 appear to act closely at the biochemical or cellular level to control branching, because branching was inhibited in reciprocal epicotyl grafts between rms5 or rms1 and WT plants, but not inhibited in reciprocal grafts between rms5 and rmsl seedlings. The weakly transgressive or slightly additive phenotype of the rmsl rms5 double mutant provides further evidence for this interaction. Like rms1, rms5 rootstocks have reduced xylem sap cytokinin concentrations, and rms5 shoots do not appear deficient in indole-3-acetic acid or 4-chloroindole-3-acetic acid. Rms1 and Rms5 are similar in their interaction with other Rms genes. Reciprocal grafting studies with rmsl, rms2, and rms5, together with the fact that root xylem sap cytokinin concentrations are reduced in rms1 and rms5 and elevated in rms2 plants, indicates that Rms1 and Rms5 may control a different pathway than that controlled by Rms2. Our studies indicate that Rms1 and Rms5 may regulate a novel graft-transmissible signal involved in the control of branching.

Promotion of motoneuron survival and branching in rapsyn-deficient mice

Inhibition of programmed cell death of motoneurons during embryonic development requires the presence of their target muscle and coincides with the initial stages of synaptogenesis. To evaluate the role of synapse formation on motoneuron survival during embryonic development, we counted the number of motoneurons in rapsyn-deficient mice. RaDsyn is a 43 kDa protein needed for the formation of postsynaptic specialisations at vertebrate neuromuscular synapses. Here we show that the rapsyn-deficient mice have a significant increase in the number of motoneurons in the brachial lateral motor column during the period of naturally occurring programmed cell death compared to their wild-type littermates. In addition, we observed an increase in intramuscular axonal branching in the rapsyn-deficient diaphragms compared to their wild-type littermates at embryonic day 18.5. These results suggest that deficits in the formation of the postsynaptic specialisation at the neuromuscular synapse, brought about by the absence of rapsyn, are sufficient to induce increases in both axonal branching and the survival of the innervating motoneuron. Moreover, these results support the idea that skeletal muscle activity through effective synaptic transmission and intramuscular axonal branching are major mechanisms that regulate motoneuron survival during development. (C) 2001 Wiley-Liss, Inc.