A nonlinear parabolic-hyperbolic system for contact inhibition and a degenerate parabolic Fisher KPP equation

We consider a mathematical model describing population dynamics of normal and abnormal cell densities with contact inhibition of cell growth from a theoretical point of view. In the first part of this paper, we discuss the global existence of a solution satisfying the segregation property in one space dimension for general initial data. Here, the term segregation property means that the different types of cells keep spatially segregated when the initial densities are segregated. The second part is devoted to singular limit problems for solutions of the PDE system and traveling wave solutions, respectively. Actually, the contact inhibition model considered in this paper possesses quite similar properties to those of the Fisher-KPP equation. In particular, the limit problems reveal a relation between the contact inhibition model and the Fisher-KPP equation.journal articl

Measurement of the e+e-→D(*)+D(*)- cross sections

journal articl

マルチ チャネル オンジョウ サイゲン システム ニ オケル カンキョウ ヘンカ ニ テキオウテキナ ギャクフィルタ ノ カンワ シュホウ

奈良先端科学技術大学院大学修士(工学)master thesi

Single-Molecule Unidirectional Processive Movement along a Helical Polymer Chain in Non-aqueous Medium

In this work, a molecule “walking” along a single chain of a synthetic helical polymer, which is used as a rail on a substrate in an organic solvent at room temperature, is observed. The walking comprises the unidirectional processive movement of a short-chain molecule along a chiral helical chain in 3 nm steps, driven by Brownian motion and a tapping effect of the atomic force microscopy tip based on a flash ratchet mechanism. Furthermore, the rail consists of a long-chain substituted phenylacetylene polymer with pendant cholesteryl groups, along which the short-chain molecule can walk as a result of van der Waals interactions. The macromolecular motion is videoed using a fast-scanning atomic force microscope, and additionally, this phenomenon is also simulated by all-atom molecular dynamics calculations. On the basis of these results, we propose the principle of a polymer molecular motor. This is the first report of a synthetic walking machine of a chiral helical polymer driven by thermal fluctuation as an artificial life function

Synthesis and Direct Observation of Chiral Supramolecular Polymer of Porphyrin Having Cholesteryl Groups

We report the synthesis and microscopic investigations of two chiral helical porphyrin supramolecular polymers with different coordinating metals that are expected to be capable of serving as synthetic macromolecular motors driven by thermal fluctuations. Furthermore, based on their microscopic images, we propose a stepwise process for the formation of higher-order structures. These porphyrins formed completely different association states, and this was reflected in the marked differences in the shapes of the supramolecular polymers. The Cu-TChOAlaCPP supramolecular polymers formed H-aggregate rods in diisopropyl ether, then grew into superhelices and then into ribbons. On the other hand, Zn-TChOAlaCPP supramolecular polymers formed aggregates based on van der Waals interactions in diethyl ether, then grew into fibers and then grew into multiple-helices and ribbons. In addition, we imaged the interaction between long and short chains of the Cu-TChOAlaCPP supramolecular polymer by fast-scanning atomic force microscopy, and we indicated the availability as a macromolecular motor driven by thermal fluctuations

Synthesis and Direct Observation of Chiral Supramolecular Polymer of Porphyrin Having Cholesteryl Groups

We report the synthesis and microscopic investigations of two chiral helical porphyrin supramolecular polymers with different coordinating metals that are expected to be capable of serving as synthetic macromolecular motors driven by thermal fluctuations. Furthermore, based on their microscopic images, we propose a stepwise process for the formation of higher-order structures. These porphyrins formed completely different association states, and this was reflected in the marked differences in the shapes of the supramolecular polymers. The Cu-TChOAlaCPP supramolecular polymers formed H-aggregate rods in diisopropyl ether, then grew into superhelices and then into ribbons. On the other hand, Zn-TChOAlaCPP supramolecular polymers formed aggregates based on van der Waals interactions in diethyl ether, then grew into fibers and then grew into multiple-helices and ribbons. In addition, we imaged the interaction between long and short chains of the Cu-TChOAlaCPP supramolecular polymer by fast-scanning atomic force microscopy, and we indicated the availability as a macromolecular motor driven by thermal fluctuations

Chiral Amplification in π‑Conjugated Helical Polymers with Circularly Polarized Luminescence

A series of d-glucose-bound optically active π-conjugated polymers (poly-Tr) were synthesized by ternary copolymerization of 2,5-diiodothiophene with diethynyl monomers containing a chiral and an achiral biphenyl unit using the Sonogashira coupling reaction. The effect of the chiral and achiral biphenyl contents on the chiral amplification in the preferred-handed helix formation (“the sergeants and soldiers effect”) was investigated by comparing the circular dichroism (CD) and circularly polarized luminescence (CPL) intensities of poly-Tr to that of the corresponding helical polymer (poly-T) without an achiral biphenyl unit. We observed that even when the chiral biphenyl content in the copolymer was 50 mol % (poly-T0.50), its CD and CPL intensities were almost comparable to that of poly-T, demonstrating the amplification of the helicity

Single-Molecule Unidirectional Processive Movement along a Helical Polymer Chain in Non-aqueous Medium

In this work, a molecule “walking” along a single chain of a synthetic helical polymer, which is used as a rail on a substrate in an organic solvent at room temperature, is observed. The walking comprises the unidirectional processive movement of a short-chain molecule along a chiral helical chain in 3 nm steps, driven by Brownian motion and a tapping effect of the atomic force microscopy tip based on a flash ratchet mechanism. Furthermore, the rail consists of a long-chain substituted phenylacetylene polymer with pendant cholesteryl groups, along which the short-chain molecule can walk as a result of van der Waals interactions. The macromolecular motion is videoed using a fast-scanning atomic force microscope, and additionally, this phenomenon is also simulated by all-atom molecular dynamics calculations. On the basis of these results, we propose the principle of a polymer molecular motor. This is the first report of a synthetic walking machine of a chiral helical polymer driven by thermal fluctuation as an artificial life function

Enantioselective Permeation of Various Racemates through an Optically Active Poly{1-[dimethyl(10-pinanyl)silyl]-1-propyne} Membrane

Optical resolution of various racemates such as (±)-tryptophan and (±)-1,3-butanediol was achieved by permeation through a self-supporting membrane of (+)-poly{1-[dimethyl(10-pinanyl)silyl]-1-propyne} [(+)-poly(DPSP)] prepared by homopolymerization of (−)-1-[dimethyl(10-pinanyl)silyl]-1-propyne [(−)-DPSP]. Almost complete optical resolution (% ee of the permeate = 81−100% ee) was achieved at an initial period of concentration-driven permeation, and stable permeation with moderate permselectivity (% ee of the permeate = 12−54% ee) continued for more than 600 h. In addition, by permeation of vapor permeant such as evapomeation and pervaporation, higher permeation rates were attained maintaining high enantioselectivity. The sign of the enantiomer that predominantly permeated through a (+)-poly(DPSP) membrane was opposite to that through a (−)-poly(DPSP) membrane. In the permeation through a (+)-poly(DPSP) membrane of a solute or a solvent having a high affinity for (+)-poly(DPSP) and in the permeation through a membrane from the copolymer of (−)-DPSP with a small amount of 1-(trimethylsilyl)-1-propyne, their enantioselectivities were much lower. These findings suggest that the permeating route surrounding chiral pinanyl groups in a (+)-poly(DPSP) membrane that can enantioselectively separate various racemates was easily deformed by using a solute or solvent having a high affinity for (+)-poly(DPSP) or by removing a small amount of pinanyl groups