88 research outputs found
Effective nonlocal kernels on Reaction-diffusion networks
A new method to derive an essential integral kernel from any given
reaction-diffusion network is proposed. Any network describing metabolites or
signals with arbitrary many factors can be reduced to a single or a simpler
system of integro-differential equations called "effective equation" including
the reduced integral kernel (called "effective kernel" ) in the convolution
type. As one typical example, the Mexican hat shaped kernel is theoretically
derived from two component activator-inhibitor systems. It is also shown that a
three component system with quite different appearance from activator-inhibitor
systems is reduced to an effective equation with the Mexican hat shaped kernel.
It means that the two different systems have essentially the same effective
equations and that they exhibit essentially the same spatial and temporal
patterns. Thus, we can identify two different systems with the understanding in
unified concept through the reduced effective kernels. Other two applications
of this method are also given: Applications to pigment patterns on skins (two
factors network with long range interaction) and waves of differentiation
(called proneural waves) in visual systems on brains (four factors network with
long range interaction). In the applications, we observe the reproduction of
the same spatial and temporal patterns as those appearing in pre-existing
models through the numerical simulations of the effective equations
Elevated levels of tissue inhibitor of metalloproteinases (TIMPS) in human hepatocellular carcinomas
Renormalization-group Method for Reduction of Evolution Equations; invariant manifolds and envelopes
The renormalization group (RG) method as a powerful tool for reduction of
evolution equations is formulated in terms of the notion of invariant
manifolds. We start with derivation of an exact RG equation which is analogous
to the Wilsonian RG equations in statistical physics and quantum field theory.
It is clarified that the perturbative RG method constructs invariant manifolds
successively as the initial value of evolution equations, thereby the meaning
to set is naturally understood where is the arbitrary initial
time. We show that the integral constants in the unperturbative solution
constitutes natural coordinates of the invariant manifold when the linear
operator in the evolution equation has no Jordan cell; when has a
Jordan cell, a slight modification is necessary because the dimension of the
invariant manifold is increased by the perturbation. The RG equation determines
the slow motion of the would-be integral constants in the unperturbative
solution on the invariant manifold. We present the mechanical procedure to
construct the perturbative solutions hence the initial values with which the RG
equation gives meaningful results. The underlying structure of the reduction by
the RG method as formulated in the present work turns out to completely fit to
the universal one elucidated by Kuramoto some years ago. We indicate that the
reduction procedure of evolution equations has a good correspondence with the
renormalization procedure in quantum field theory; the counter part of the
universal structure of reduction elucidated by Kuramoto may be the Polchinski's
theorem for renormalizable field theories. We apply the method to interface
dynamics such as kink-anti-kink and soliton-soliton interactions in the latter
of which a linear operator having a Jordan-cell structure appears.Comment: 67 pages. No figures. v2: Additional discussions on the unstable
motion in the the double-well potential are given in the text and the
appendix added. Some references are also added. Introduction is somewhat
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Improvement in organophosphorus hydrolase activity of cell surface-engineered yeast strain using Flo1p anchor system
Organophosphorus hydrolase (OPH) hydrolyzes organophosphorus esters. We constructed the yeast-displayed OPH using Flo1p anchor system. In this system, the N-terminal region of the protein was fused to Flo1p and the fusion protein was displayed on the cell surface. Hydrolytic reactions with paraoxon were carried out during 24 h of incubation of OPH-displaying cells at 30°C. p-Nitrophenol produced in the reaction mixture was detected by HPLC. The strain with highest activity showed 8-fold greater OPH activity compared with cells engineered using glycosylphosphatidylinositol anchor system, and showed 20-fold greater activity than Escherichia coli using the ice nucleation protein anchor system. These results indicate that Flo1p anchor system is suitable for display of OPH in the cell surface-expression systems
Linearized Stability Analysis of Stationary Solutions for Surface Diffusion with Boundary Conditions
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