87 research outputs found
Condensation of anhydrides or dicarboxylic acids with compounds containing active methylene groups. Part 1: Condensation of phthalic anhydride with acetoacetic and malonic ester
Phthalic anhydride was condensed with acetoacetic ester in acetic anhydride and triethylamine solution, and when phthalyl chloride was reacted with sodium acetoacetic ester compounds were formed of the phthalide and indandione series: phthalylacetoacetic ester and a derivative of indan-1,3-dione which after boiling with hydrochloric acid yielded indan-1,3-dione. Phthalylmalonic ester was obtained from phthalic anhydride and malonic ester in the presence of triethylamine
Creation and Reproduction of Model Cells with Semipermeable Membrane
A high activity of reactions can be confined in a model cell with a
semipermeable membrane in the Schl\"ogl model. It is interpreted as a model of
primitive metabolism in a cell. We study two generalized models to understand
the creation of primitive cell systems conceptually from the view point of the
nonlinear-nonequilibrium physics. In the first model, a single-cell system with
a highly active state confined by a semipermeable membrane is spontaneously
created from an inactive homogeneous state by a stochastic jump process. In the
second model, many cell structures are reproduced from a single cell, and a
multicellular system is created.Comment: 11 pages, 7 figure
Reaction-Diffusion System in a Vesicle with Semi-Permeable Membrane
We study the Schloegl model in a vesicle with semi-permeable membrane. The
diffusion constant takes a smaller value in the membrane region, which prevents
the outflow of self-catalytic product. A nonequilibrium state is stably
maintained inside of the vesicle. Nutrients are absorbed and waste materials
are exhausted through the membrane by diffusion. It is interpreted as a model
of primitive metabolism in a cell.Comment: 8 pages, 6 figure
Breathing Current Domains in Globally Coupled Electrochemical Systems: A Comparison with a Semiconductor Model
Spatio-temporal bifurcations and complex dynamics in globally coupled
intrinsically bistable electrochemical systems with an S-shaped current-voltage
characteristic under galvanostatic control are studied theoretically on a
one-dimensional domain. The results are compared with the dynamics and the
bifurcation scenarios occurring in a closely related model which describes
pattern formation in semiconductors. Under galvanostatic control both systems
are unstable with respect to the formation of stationary large amplitude
current domains. The current domains as well as the homogeneous steady state
exhibit oscillatory instabilities for slow dynamics of the potential drop
across the double layer, or across the semiconductor device, respectively. The
interplay of the different instabilities leads to complex spatio-temporal
behavior. We find breathing current domains and chaotic spatio-temporal
dynamics in the electrochemical system. Comparing these findings with the
results obtained earlier for the semiconductor system, we outline bifurcation
scenarios leading to complex dynamics in globally coupled bistable systems with
subcritical spatial bifurcations.Comment: 13 pages, 11 figures, 70 references, RevTex4 accepted by PRE
http://pre.aps.or
Diffusive coupling can discriminate between similar reaction mechanisms in an allosteric enzyme system
<p>Abstract</p> <p>Background</p> <p>A central question for the understanding of biological reaction networks is how a particular dynamic behavior, such as bistability or oscillations, is realized at the molecular level. So far this question has been mainly addressed in well-mixed reaction systems which are conveniently described by ordinary differential equations. However, much less is known about how molecular details of a reaction mechanism can affect the dynamics in diffusively coupled systems because the resulting partial differential equations are much more difficult to analyze.</p> <p>Results</p> <p>Motivated by recent experiments we compare two closely related mechanisms for the product activation of allosteric enzymes with respect to their ability to induce different types of reaction-diffusion waves and stationary Turing patterns. The analysis is facilitated by mapping each model to an associated complex Ginzburg-Landau equation. We show that a sequential activation mechanism, as implemented in the model of Monod, Wyman and Changeux (MWC), can generate inward rotating spiral waves which were recently observed as glycolytic activity waves in yeast extracts. In contrast, in the limiting case of a simple Hill activation, the formation of inward propagating waves is suppressed by a Turing instability. The occurrence of this unusual wave dynamics is not related to the magnitude of the enzyme cooperativity (as it is true for the occurrence of oscillations), but to the sensitivity with respect to changes of the activator concentration. Also, the MWC mechanism generates wave patterns that are more stable against long wave length perturbations.</p> <p>Conclusions</p> <p>This analysis demonstrates that amplitude equations, which describe the spatio-temporal dynamics near an instability, represent a valuable tool to investigate the molecular effects of reaction mechanisms on pattern formation in spatially extended systems. Using this approach we have shown that the occurrence of inward rotating spiral waves in glycolysis can be explained in terms of an MWC, but not with a Hill mechanism for the activation of the allosteric enzyme phosphofructokinase. Our results also highlight the importance of enzyme oligomerization for a possible experimental generation of Turing patterns in biological systems.</p
Non-smooth feedback control for BelousovâZhabotinskii reactionâdiffusion equations: semi-analytical solutions
Fronts and pulses in an enzymatic reaction catalyzed by glucose oxidase
Waves and patterns in living systems are often driven by biochemical reactions with enzymes as catalysts and regulators. We present a reactionâdiffusion system catalyzed by the enzyme glucose oxidase that exhibits traveling wave patterns in a spatially extended medium. Fronts and pulses propagate as a result of the coupling between the enzyme-catalyzed autocatalytic production and diffusion of hydrogen ions. A mathematical model qualitatively explains the experimental observations
Quaternary Cross-Diffusion in Water-in-Oil Microemulsions Loaded with a Component of the BelousovâZhabotinsky Reaction
Oscillatory Clusters in the Periodically Illuminated, Spatially Extended Belousov-Zhabotinsky Reaction
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