Multivalued Functions, Branch Points, and Cuts

Branching filaments with striking perpendicularity form when actin polymerizes in the presence of macrophage actin-binding protein. Actin-binding protein molecules are visible at the branch points. Compared with actin polymerized in the absence of actin-binding proteins, not only do the filaments branch but the average length of the actin filaments decreases from 3.2 to 0.63 micrometer. Arrowhead complexes formed by addition of heavy meromyosin molecules to the branching actin filaments point toward the branch points. Actin-binding protein also accelerates the onset of actin polymerization. All of these findings show that actin filaments assemble from nucleating sites on actin-binding protein dimers. A branching polymerization of actin filaments from a preexisting lattice of actin filaments joined by actin-binding protein molecules could generate expansion of cortical cytoplasm in amoeboid cells.

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An airfoil theory of bifurcating laminar separation from thin obstacles

Journal of Fluid Mechanics ◽

10.1017/s0022112090000428 ◽

1990 ◽

Vol 216 ◽

pp. 255-284 ◽

Cited By ~ 4

Author(s):

C. J. Lee ◽

H. K. Cheng

Keyword(s):

Boundary Layer ◽

Reynolds Number ◽

Steady State ◽

Steady State Solution ◽

Equation System ◽

Branch Points ◽

Laminar Separation ◽

Kutta Condition ◽

Numerical Studies ◽

Steady State Solutions

Global interaction of the boundary layer separating from an obstacle with resulting open/closed wakes is studied for a thin airfoil in a steady flow. Replacing the Kutta condition of the classical theory is the breakaway criterion of the laminar triple-deck interaction (Sychev 1972; Smith 1977), which, together with the assumption of a uniform wake/eddy pressure, leads to a nonlinear equation system for the breakaway location and wake shape. The solutions depend on a Reynolds numberReand an airfoil thickness ratio or incidence τ and, in the domain$Re^{\frac{1}{16}}\tau = O(1)$considered, the separation locations are found to be far removed from the classical Brillouin–Villat point for the breakaway from a smooth shape. Bifurcations of the steady-state solution are found among examples of symmetrical and asymmetrical flows, allowing open and closed wakes, as well as symmetry breaking in an otherwise symmetrical flow. Accordingly, the influence of thickness and incidence, as well as Reynolds number is critical in the vicinity of branch points and cut-off points where steady-state solutions can/must change branches/types. The study suggests a correspondence of this bifurcation feature with the lift hysteresis and other aerodynamic anomalies observed from wind-tunnel and numerical studies in subcritical and high-subcriticalReflows.

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Different Angiogenic Potentials of Mesenchymal Stem Cells Derived from Umbilical Artery, Umbilical Vein, and Wharton’s Jelly

Stem Cells International ◽

10.1155/2017/3175748 ◽

2017 ◽

Vol 2017 ◽

pp. 1-15 ◽

Cited By ~ 9

Author(s):

Lu Xu ◽

Jianjun Zhou ◽

Jingyu Liu ◽

Yong Liu ◽

Lei Wang ◽

...

Keyword(s):

Stem Cells ◽

Mesenchymal Stem Cells ◽

Umbilical Vein ◽

Wharton’S Jelly ◽

Tube Length ◽

Branch Points ◽

Differentiation Potential ◽

Wharton's Jelly ◽

Allogeneic Cell Therapy ◽

Perivascular Stem Cells

Human mesenchymal stem cells derived from the umbilical cord (UC) are a favorable source for allogeneic cell therapy. Here, we successfully isolated the stem cells derived from three different compartments of the human UC, including perivascular stem cells derived from umbilical arteries (UCA-PSCs), perivascular stem cells derived from umbilical vein (UCV-PSCs), and mesenchymal stem cells derived from Wharton’s jelly (WJ-MSCs). These cells had the similar phenotype and differentiation potential toward adipocytes, osteoblasts, and neuron-like cells. However, UCA-PSCs and UCV-PSCs had more CD146+ cells than WJ-MSCs (P<0.05). Tube formation assay in vitro showed the largest number of tube-like structures and branch points in UCA-PSCs among the three stem cells. Additionally, the total tube length in UCA-PSCs and UCV-PSCs was significantly longer than in WJ-MSCs (P<0.01). Microarray, qRT-PCR, and Western blot analysis showed that UCA-PSCs had the highest expression of the Notch ligand Jagged1 (JAG1), which is crucial for blood vessel maturation. Knockdown of Jagged1 significantly impaired the angiogenesis in UCA-PSCs. In summary, UCA-PSCs are promising cell populations for clinical use in ischemic diseases.

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Asymptotics of Hermite-Pade Rational Approximants for Two Analytic Functions with Separated Pairs of Branch Points (Case of Genus 0)

International Mathematics Research Papers ◽

10.1093/imrp/rpm007 ◽

2010 ◽

Cited By ~ 17

Author(s):

A. I. Aptekarev ◽

A. B. J. Kuijlaars ◽

W. Van Assche

Keyword(s):

Analytic Functions ◽

Branch Points ◽

Rational Approximants

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THE WATER-SOLUBLE POLYSACCHARIDES OF DERMATOPHYTES: IV. GALACTOMANNANS I FROM TRICHOPHYTON GRANULOSUM, TRICHOPHYTON INTERDIGITALE, MICROSPORUM QUINCKEANUM, TRICHOPHYTON RUBRUM, AND TRICHOPHYTON SCHÖNLEINII

Canadian Journal of Chemistry ◽

10.1139/v65-005 ◽

1965 ◽

Vol 43 (1) ◽

pp. 30-39 ◽

Cited By ~ 46

Author(s):

C. T. Bishop ◽

M. B. Perry ◽

F. Blank ◽

F. P. Cooper

Keyword(s):

Aqueous Solutions ◽

Copper Complexes ◽

Trichophyton Rubrum ◽

Periodate Oxidation ◽

Structural Features ◽

Water Soluble ◽

Major Constituent ◽

Branch Points ◽

Terminal Units ◽

Hydrolysis Of

A group of polysaccharides, called galactomannans I, were precipitated as their insoluble copper complexes from aqueous solutions of the crude polysaccharides obtained from each of the organisms designated in the title. The five galactomannans I were homogeneous under conditions of electrophoresis and ultracentrifugation and had high positive specific rotations. The major constituent monosaccharide was D-mannose; amounts of D-galactose ranged from nil for the polysaccharide from T. rubrum to 13% for that from T. schönleinii. Methylation and hydrolysis of the five galactomannans I yielded varying amounts of the following: 2,3,5,6-tetra-O-methyl-D-galactose (not present in the products from T. rubrum), 2,3,4,6-tetra-O-methyl-D-mannose, 2,3,4-tri-O-methyl-D-mannose, 2,4,6-tri-O-methyl-D-mannose, 3,4-di-O-methyl-D-mannose, and 3,5-di-O-methyl-D-mannose. Periodate oxidation results agreed with the methylation studies. The gross structural features of each galactomannan I appear to be the same, namely, a basic chain of 1 → 6 linked α-D-mannopyranose units for approximately every 22 of which there is a 1 → 3 linked α-D-mannopyranose residue. Branch points occur along the 1 → 6 linked chain at the C2 positions of the D-mannopyranose units and once in every 45 units at the C2 position of a 1 → 6 linked D-mannofuranose residue. The D-galactose in the polysaccharides is present exclusively as non-reducing terminal furanose units; non-reducing terminal units of D-mannopyranose are also present. The variations in the identities and relative amounts of the non-reducing terminal units were the only apparent differences in the gross structural features within this group of polysaccharides.

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