Distribution Of Branch Points Research Articles

LIKE EARLY STARVATION 1 and EARLY STARVATION 1 promote and stabilize amylopectin phase transition in starch biosynthesis.

Starch, the most abundant carbohydrate reserve in plants, primarily consists of the branched glucan amylopectin, which forms semi-crystalline granules. Phase transition from a soluble to an insoluble form depends on amylopectin architecture, requiring a compatible distribution of glucan chain lengths and a branch-point distribution. Here, we show that two starch-bound proteins, LIKE EARLY STARVATION 1 (LESV) and EARLY STARVATION 1 (ESV1), which have unusual carbohydrate-binding surfaces, promote the phase transition of amylopectin-like glucans, both in a heterologous yeast system expressing the starch biosynthetic machinery and in Arabidopsis plants. We propose a model wherein LESV serves as a nucleating role, with its carbohydrate-binding surfaces helping align glucan double helices to promote their phase transition into semi-crystalline lamellae, which are then stabilized by ESV1. Because both proteins are widely conserved, we suggest that protein-facilitated glucan crystallization may be a general and previously unrecognized feature of starch biosynthesis.

Spaces of algebraic measure trees and triangulations of the circle

In this paper we present with algebraic trees a novel notion of (continuum) trees which generalizes countable graph-theoretic trees to (potentially) uncountable structures. For that purpose we focus on the tree structure given by the branch point map which assigns to each triple of points their branch point. We give an axiomatic definition of algebraic trees, define a natural topology, and equip them with a probability measure on the Borel-$\sigma$-field.Under an order-separability condition, algebraic (measure) trees can be considered as tree structure equivalence classes of metric (measure) trees (i.e.\ subtrees of R-trees). Using Gromov-weak convergence (i.e.\ sample distance convergence) of the particular representatives given by the metric arising from the distribution of branch points, we define a metrizable topology on the space of equivalence classes of algebraic measure trees. In many applications, binary trees are of particular interest. We introduce on that subspace with the sample shape and the sample subtree mass convergence two additional, natural topologies. Relying on the connection to triangulations of the circle, we show that all three topologies are actually the same, and the space of binary algebraic measure trees is compact. To this end, we provide a formal definition of triangulations of the circle, and show that the coding map which sends a triangulation to an algebraic measure tree is a continuous surjection onto the subspace of binary algebraic non-atomic measure trees.

Effect of Branch Point Distribution on the Radius of Gyration in Batch Free‐Radical Polymerization with Chain Transfer to Polymer

AbstractFree‐radical polymerization is irreversible, and the primary chains formed earlier are expected to possess larger branching density compared with those formed later, leading to a branching density distribution (BDD) among primary chains. In addition to the BDD, the primary chain length distribution (CLD) may change during polymerization. For a primary CLD with a shift toward smaller chain length during polymerization, the expected g‐ratio for a given number k of branch points can be approximated reasonably well with that for the random branched polymers having the accumulated primary CLD. On the other hand, when the primary CLD moves toward larger chain length during polymerization, the expected g‐ratio may become smaller than the corresponding random branched polymers, due to an “unnatural” combination in the length of backbone and branch chains. The compactness of branched architecture could be controlled through the consideration of the maximum end‐to‐end path length.

Lower bounds and asymptotics of real double Hurwitz numbers

We study the real counterpart of double Hurwitz numbers, called real double Hurwitz numbers here. We establish a lower bound for these numbers with respect to their dependence on the distribution of branch points. We use it to prove, under certain conditions, existence of real Hurwitz covers as well as logarithmic equivalence of real and classical Hurwitz numbers. The lower bound is based on the \enquote{tropical} computation of real Hurwitz numbers in arXiv:1412.4235.

Distributions of Branch Points of Some Algebroid Functions

In this paper, we investigate the distribution of branch points of some algebroid functions with infinitely many branch points. A sufficient condition that algebroid function has infinitely many branch points is given. By the Ahlfors' theory of covering surfaces, we also obtain the relationship between the Borel cluster directions of branch points and the Borel directions.

Coarse‐Grained Dendrimers in a Good Solvent: Comparison of Monte Carlo Simulations, Self‐Consistent Field Theory, and a Hybrid Modeling Strategy

AbstractRecently, a hybrid method has been developed, wherein the positions of some polymer segments are constrained to a small volume. The volume's position is sampled with a Monte Carlo algorithm. The distribution of the remaining segments is determined with Scheutjens–Fleer self‐consistent field theory (SF‐SCF). This incorporates thermal fluctuations into the model. Here it is investigated whether this also leads to an improved treatment of the excluded volume interactions. Dendrimers, with f = 1⋅⋅⋅7 generations, g = 2⋅⋅⋅5 spacers per branch point, and spacers of 20 or 50 segments, are used as a model system. The focus is on the radius of gyration, the asphericity, the radial density, and the end point and first branch point distribution. As expected, both SCF methods underestimate the radius of gyration due to underestimating the short range excluded volume. The SF‐SCF model, however, also gives a slightly different scaling and, in contrast to the other models, also predicts a bimodal distribution for first generation branch points for large f and g. This difference is attributed to overestimating the excluded volume at long ranges. As the hybrid method does not show this, localizing just a few segments largely compensates this shortcoming in the SF‐SCF theory.

Distribution of branch points of some algebroid functions in the unit disc

In this paper, we study the distribution of values and branch points of some algebroid functions in the unit disc,. And we prove that the Borel cluster point of branch points is also a Borel point.

Molecular Genetic Analysis of Glucan Branching Enzymes from Plants and Bacteria in Arabidopsis Reveals Marked Differences in Their Functions and Capacity to Mediate Starch Granule Formation.

The major component of starch is the branched glucan amylopectin, the branching pattern of which is one of the key factors determining its ability to form semicrystalline starch granules. Here, we investigated the functions of different branching enzyme (BE) types by expressing proteins from maize (Zea mays BE2a), potato (Solanum tuberosum BE1), and Escherichia coli (glycogen BE [EcGLGB]) in Arabidopsis (Arabidopsis thaliana) mutant plants that are deficient in their endogenous BEs and therefore, cannot make starch. The expression of each of these three BE types restored starch biosynthesis to differing degrees. Full complementation was achieved using the class II BE ZmBE2a, which is most similar to the two endogenous Arabidopsis isoforms. Expression of the class I BE from potato, StBE1, resulted in partial complementation and high amylose starch. Expression of the glycogen BE EcGLGB restored only minimal amounts of starch production, which had unusual chain length distribution, branch point distribution, and granule morphology. Nevertheless, each type of BE together with the starch synthases and debranching enyzmes were able to create crystallization-competent amylopectin polymers. These data add to the knowledge of how the properties of the BE influence the final composition of starch and fine structure of amylopectin.

Single-Nucleotide Resolution Mapping of the Gossypium raimondii Transcriptome Reveals a New Mechanism for Alternative Splicing of Introns

Alternative splicing (AS) is a vital genetic mechanism that enhances the diversity of eukaryotic transcriptomes. Here, we generated 8.3 Gb high-quality RNA-sequencing data from cotton (Gossypium raimondii) and performed a systematic, comparative analysis of AS events. We mapped 85% of the RNA-sequencing data onto the reference genome and identified 154368 splice junctions with 16437 as events in 10197 genes. Intron retention constituted the majority (40%) of all AS events in G. raimondii. Comparison across 11 eukaryote species showed that intron retention is the most common AS type in higher plants. Although transposable elements (TEs) were found in only 2.9% of all G. raimondii introns, they are present in 43% of the retained introns, suggesting that TE-insertion may be an important mechanism for intron retention during AS. The majority of the TE insertions are concentrated 0-40 nt upstream of the 3'-splice site, substantially altering the distribution of branch points from preferred positions and reducing the efficiency of intron splicing by decreasing RNA secondary structure flexibility. Our data suggest that TE-insertion-induced changes in branch point-site distribution are important for intron retention-type AS. Our findings may help explain the vast differences in intron-retention frequencies between vertebrates and higher plants.

Behavior of hyperbranched polymers in solutions

Hyperbranched polycarbosilanes are investigated by the methods of molecular hydrodynamics and optics. Dependences of the hydrodynamic and conformational properties of these polymers on their molecular mass, the length of linear chains between branching points, and the chemical structure of end groups are analyzed. The hydrodynamic behavior of hyperbranched polycarbosilanes is explained by the fact that the dimensions of their macromolecules are compact and their shape is close to spherical. The convolution of chains between branching points becomes more pronounced with an increase in their length and a decrease in the molecular mass of the polymer. When end fluorinated groups are incorporated into the hyperbranched polycarbosilane, in thermodynamically good solvents and θ solvents, hydrodynamic characteristics change apparently owing to a change in the density of macromolecules in solution. In a poor solvent, the compaction of fluorinated macromolecules and a reduction in their shape asymmetry are observed. At a fixed branching degree, the hydrodynamic properties of hyperbranched polymers depend on the structural regularity of their macromolecules: In terms of hydrodynamic properties, the hyperbranched polycarbosilane with a degree of branching of 1 and a random distribution of branching points within the volume of a macro-molecule is appreciably different from a dendrimer of the same chemical nature and is close to polycarbosilanes with a degree of branching of 0.5.

Advanced Monte Carlo Algorithm for the Atomistic Simulation of Short- and Long-Chain Branched Polymers: Implementation for Model H-Shaped, A3AA3 Multiarm (Pom-Pom), and Short-Chain Branched Polyethylene Melts

We present a powerful connectivity-altering Monte Carlo (MC) algorithm for simulating atomistically detailed models of long- and short-chain branched polymers. Based on a mix of advanced and simple moves, the algorithm allows the robust simulation of chain systems with a variety of molecular architectures: H-shaped, A3AA3 multiarm (pom-pom), and short-chain branched (SCB) ones. For the H-shaped and A3AA3 architectures (A denotes the backbone and A the arm), in particular, the recently developed intermolecular double bridging (DB) move effecting a new bridging between the chain backbones or the branches of two different chains and the intramolecular double rebridging (IDR) move effecting a new bridging between two branches of the same chain [Karayiannis et al. J. Chem. Phys. 2003, 118, 2451] are shown to provide a robust sampling of their structural and conformational characteristics at the chain level. The double concerted rotation (d-CONROT) and H-shaped branch rebridging (H-BR) moves, on the other hand, which are important in relaxing internal degrees of freedom in the chain and the local structure around branch points, allow complete equilibration at the segmental level, which is prerequisite for the correct prediction of the volumetric and packing properties of the simulated systems. For the case of SCB polymers, a continuum configurational bias move for branched polymers (Br-CCB) has been designed capable of sampling changes in the atomic coordinates in the vicinity of branch points. Along with an effective implementation of the conventional end-bridging (EB) move, this has resulted in a powerful method for simulating SCB polymers with a prespecified distribution of branch points along the chain and given (i.e., fixed) number of carbon atoms per branch. To deal with polydispersity in the simulated systems, the algorithm is executed in a semigrand canonical ensemble by making use of the set of chain relative chemical potentials which for a bulk, linear system produces a uniform distribution of chain lengths [Pant and Theodorou Macromolecules 1995, 28, 7224]. Consistent with recent considerations by Ramos et al. [Macromolecules 2007, 40, 9640], two different chain length distributions should be simultaneously controlled in the course of the simulation for branched systems. The new, generalized MC algorithm is capable of thoroughly equilibrating model H-shaped, multiarm A3AA3, and SCB polymers at all length scales and adequately sampling fluctuations in their structural, volumetric, and conformational properties. Overall, we find that branched polymers are characterized by a stiffer conformation than linear analogues of the same total chain length. For the H-shaped and A3AA3 architectures, in particular, we have observed that each dangling arm exerts an entropically driven tensile force on the chain crossbar (the part of the chain between the two branch points), causing significant chain stretching. Our results extend the previous works of Karayiannis et al. [J. Chem. Phys. 2003, 118, 2451] on the simulation of H-shaped polymers to A3AA3 PE polymers and of Ramos et al. [Macromolecules 2007, 40, 9640] on the simulation of model ethylene−1-hexene copolymers to copolymers with longer α-olefinic side groups, such as the ethylene−1-octene and ethylene−1-decene ones.

Glucan, water dikinase phosphorylates crystalline maltodextrins and thereby initiates solubilization

Starch phosphorylation by glucan, water dikinase (GWD; EC 2.7.9.4) is an essential step in the breakdown of native starch particles, but the underlying mechanisms have remained obscure. In this paper, the initial reactions of starch degradation were analyzed using crystallized maltodextrins as model carbohydrates. As revealed by X-ray diffraction analysis, the crystallized maltodextrins represent the B-type starch allomorph. Recombinant GWD phosphorylated crystalline maltodextrins with a high specific activity (55-60 nmol mg-1 protein min-1), but exhibited very little activity with the same maltodextrins that had been solubilized by heat treatment. Recombinant phosphoglucan, water dikinase (PWD; EC 2.7.9.5) utilized the crystalline maltodextrins only when pre-phosphorylated by GWD. Phosphorylation of crystalline maltodextrins, as catalyzed by GWD, initiated solubilization of neutral as well as phosphorylated glucans. In both the insoluble and the soluble state, mono-, di- and triphosphorylated alpha-glucans were observed, with wide and overlapping ranges of degree of polymerization. Thus, the substrate specificity of the GWD is defined by the physical arrangement of alpha-glucans rather than by structural parameters, such as the distribution of branching points or degree of polymerization. Unlike GWD and PWD, recombinant beta-amylase isozyme 3 (BAM3), which has been shown to be essential for plastidial starch degradation, preferentially degraded soluble maltodextrins rather than crystallized glucans. In summary, two conclusions were reached. Firstly, carbohydrate targets of GWD are primarily defined by the molecular order of glucan helices. Secondly, GWD-catalyzed phosphorylation mediates the phase transition of glucans from a highly ordered to a less ordered and hydrated state.

Microphase separation of double-grafted copolymers (centipedes) with gradient, random, and regular sequence of the branch points

We propose a theory of microphase separation of the double-grafted copolymer melts with different types of branch point distribution. It is shown that copolymers with gradient sequence of the branch points form a microstructure easier (at smaller values of the Flory-Huggins parameters) than equivalent copolymers with random or regular sequences. Two characteristic types of the microphase separation, "diblock-" and "comblike" are predicted. Due to the existence of the two characteristic length scales (the length of the backbone and the length of the side chains), the two-scale switching is possible.

Corrigendum

The Plant JournalVolume 45, Issue 5 p. 870-870 Free Access Corrigendum First published: 07 February 2006 https://doi.org/10.1111/j.1365-313X.2006.02708.xAboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Volume 41, Number 6, March 2005, pages 815–830, Delatte et al. The first paragraph of the Results section states: ‘The three genes encoding isoamylase-like proteins annotated in the Arabidopsis genome are AtISA1 (At2g39930, GenBank accession ATAF2109), AtISA2 (At1g03310, Gen-Bank accession AC005278) and AtISA3 (At4g09020, GenBank accession AC005359). Full-length cDNAs from these genes have been isolated (AY139980, BT000443 and AY091058 respectively). All three proteins contain predicted N-terminal chloroplast transit peptides (ChloroP; Emanuelsson et al., 1999). We obtained a line (SALK_029442)…’ The authors would like to make clear that the SALK line identifier in parenthesis is incorrect. The correct identifier is SALK_042704. We apologise to our readers for this mistake. Reference Delatte, T., Trevisan, M., Parker, M.L., Zeeman, S.C. (2005) Arabidopsis mutants Atisa1 and Atisa2 have identical phenotypes and lack the same multimeric isoamylase, which influences the branch point distribution of amylopectin during starch synthesis. The Plant Journal, 41, 815– 830. Volume45, Issue5March 2006Pages 870-870 ReferencesRelatedInformation

Arabidopsis mutants Atisa1 and Atisa2 have identical phenotypes and lack the same multimeric isoamylase, which influences the branch point distribution of amylopectin during starch synthesis

The aim of this work was to evaluate the function of isoamylase in starch granule biosynthesis in Arabidopsis leaves. A reverse-genetic approach was used to knockout AtISA1, one of three genes in Arabidopsis encoding isoamylase-type debranching enzymes. The mutant (Atisa1-1) lacks functional AtISA1 transcript and the major isoamylase activity (detected by native gels) in crude extracts of leaves. The same activity is abolished by mutation at the DBE1 locus, which encodes a second isoamylase-type protein, AtISA2. This is consistent with the idea that ISA1 and ISA2 proteins are subunits of the same enzyme in vivo. Atisa1-1, Atisa2-1 (dbe1), and the Atisa1-1/Atisa2-1 double mutant all have identical phenotypes. Starch content is reduced compared with the wild type but substantial quantities of the soluble glucan phytoglycogen are produced. The amylopectin of the remaining starch and the phytoglycogen in the mutants are structurally related to each other and differ from wild-type amylopectin. Electron micrographs reveal that the phytoglycogen-accumulating phenotype is highly tissue-specific. Phytoglycogen accumulates primarily in the plastids of the palisade and spongy mesophyll cells. Remarkably, other cell types appear to accumulate only starch, which is normal in appearance but is altered in structure. As phytoglycogen accumulates during the day, its rate of accumulation decreases, its structure changes and intermediates of glucan breakdown accumulate, suggesting that degradation occurs simultaneously with synthesis. We conclude that the AtISA1/AtISA2 isoamylase influences glucan branching pattern, but that this may not be the primary determinant of partitioning between crystalline starch and soluble phytoglycogen.

Thermodynamic considerations of starch functionality in foods

Functionality of starch macromolecules is considered from the viewpoint of their thermodynamic properties. The thermodynamic incompatibility, self-association and inclusion complexing of starch macromolecules are important for food formulation and digestion. Helical conformations of starch macromolecules increase their co-solubility with other biopolymers (molecular mimicry) and influence the thermodynamic activity of other macromolecules (molecular symbiosis). Molecular mimicry and molecular symbiosis are the basis of many biological functions, phase behaviour and rheology of biopolymer mixtures. Rotation of starch granules in shear flow (producing a ball-bearing effect) contributes to the fat-like texture of foods. Branched exopolysaccharides could be an evolutional predecessor of starch granules. Amylopectin-like exopolysaccharides form a biopolymer solution layer around the cell, which is not accessible to foreign macromolecules due to biopolymer incompatibility underlying a non-specific defence of the cell. However, this biopolymer solution around cells remains perfectly accessible to nutrients of low molecular weight allowing for necessary cell nutrition. This barrier solution layer of exopolysaccharides could then be regarded as a protective and alimentary capsule surrounding the cell. The principle of incompatibility of exopolysaccharide fractions could be extended to provide a mechanism by which exopolysaccharides leaving the cell are responsible for binding and evacuating metabolites. This binding of undesirable metabolites is analogous to the binding of self-antigens and in a molecular sense precedes the evolutionary development of a similar result: specific immunity. A colony of cells is formed as the assembly of individual cells with their surrounding exopolysaccharide solutions separated from the medium by the interfacial layer. The overlap of the interfacial layers produces a three-dimensional network of canals that would assist the diffusional transportation of nutrients from a larger surrounding area. At the level of individual cells, the thermodynamic properties of amylopectin-like exopolysaccharides predict the binding of nutrients within their helical structure by inclusion complexing. Carrying them to the surface of the cell would then produce an octopus-like effect of facilitated transport. The capacity of starch macromolecules to bind lipids and other hydrophobic ligands leads to a decrease in the rate of enzymatic hydrolyses of inclusion complexes, which would extend the contribution of the exopolysaccharide layer to the nutrition of the cell. An increase in concentration of cells and their competition for the exopolysaccharides as a source of energy could result in the accumulation of dietary energy reserve inside the cells in the form of starch-like granules. Like globular proteins, the primary structure of amylopectin (branch point distribution and side-chain lengths) appears to be responsible for the secondary and tertiary structure of macromolecules and the structure–function relationship in starch granules.

Effects of dendritic morphology on CA3 pyramidal cell electrophysiology: a simulation study

We investigated the effect of morphological differences on neuronal firing behavior within the hippocampal CA3 pyramidal cell family by using three-dimensional reconstructions of dendritic morphology in computational simulations of electrophysiology. In this paper, we report for the first time that differences in dendritic structure within the same morphological class can have a dramatic influence on the firing rate and firing mode (spiking versus bursting and type of bursting). Our method consisted of converting morphological measurements from three-dimensional neuroanatomical data of CA3 pyramidal cells into a computational simulator format. In the simulation, active channels were distributed evenly across the cells so that the electrophysiological differences observed in the neurons would only be due to morphological differences. We found that differences in the size of the dendritic tree of CA3 pyramidal cells had a significant qualitative and quantitative effect on the electrophysiological response. Cells with larger dendritic trees: (1) had a lower burst rate, but a higher spike rate within a burst, (2) had higher thresholds for transitions from quiescent to bursting and from bursting to regular spiking and (3) tended to burst with a plateau. Dendritic tree size alone did not account for all the differences in electrophysiological responses. Differences in apical branching, such as the distribution of branch points and terminations per branch order, appear to effect the duration of a burst. These results highlight the importance of considering the contribution of morphology in electrophysiological and simulation studies.

Dimensions of branched polymers formed in simultaneous long‐chain branching and random scission

AbstractIn free‐radical olefin polymerizations, the polymer‐transfer reactions could lead to chain scission as well as the formation of long‐chain branches. The Monte Carlo simulation for free‐radical polymerization that involves simultaneous long‐chain branching and random scission is used to investigate detailed branched structure. The relationship between the mean‐square radius of gyration 〈s2〉 and degree of polymerization P as well as that between the branching density and P is the same for both with and without random scission reactions—at least for smaller frequencies of scission reactions. The 〈s2〉 values were larger than those calculated from the Zimm–Stockmayer (Z‐S) equation in which random distribution of branch points is assumed, and therefore, the Z‐S equation may not be applied for low‐density polyethylenes. The elution curves of size exclusion chromatography were also simulated. The molecular weight distribution (MWD) calibrated relative to standard linear polymers is much narrower than the true MWD, and high molecular weight tails are clearly underestimated. A simplified method to estimate the true MWD from the calibrated MWD data is proposed. The MWD obtained with a light scattering photometer in which the absolute weight‐average molecular weight of polymers at each retention volume is determined directly is considered a reasonable estimate of the true MWD. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2960–2968, 2001

Polymer Chain Buildup and Network Formation of Imidazole-Cured Epoxy/Phenol Resins

A new algorithm of Monte Carlo (MC) simulation has been proposed for the imidazole/epoxy/phenol resin system. The strategy of the MC method is divided into two steps: the first is deciding the type of reaction mechanism, and then choosing the reacting functional groups. The structural properties corresponding to the conversion change, such as the average molecular weight, the molecular weight distribution, the sol−gel fraction, and the branch point distribution of the sol part can be simulated by this method. The BPA molar ratio seems the most important factor in this system. Because it dominates the final structure of the cured resins, either linear or branched. The theoretical results were compared and verified by the gel permeation chromatography and the sol extraction analysis. Both theoretical and experimental results coincide with each other very successfully.

On the non-random nature of amylopectin branching

The cluster model of amylopectin (AP) provides a useful conceptual basis for understanding of the structure of the molecule, and this model guides current thinking related to AP biosynthesis and physical behavior. The chain length profile of constituent linear regions of the molecule is commonly determined, and the cluster model guides the interpretation of results with an emphasis on the clustering of the linear regions of these chains. Less attention has been given to the related but distinct question of the clustering of the branch points in AP, perhaps because this work is methodologically more difficult than for determination of the chain length profile and interpretation of the results is less straightforward. However, the unique aspect of AP is that its branching is non-random, and the physical properties of AP may be considered to result from this unique structure. This review addresses the available information on the distribution of branch points in AP. Emphasis on this aspect of the cluster model has ramifications for future research on AP biosynthesis and AP physical behavior.