373 research outputs found
Model of the Belousov-Zhabotinsky reaction
The article describes results of the modified model of the
Belousov-Zhabotinsky reaction, which resembles rather well the limit set
observed upon experimental performance of the reaction in the Petri dish. We
discuss the concept of the ignition of circular waves and show that only the
asymmetrical ignition leads to the formation of spiral structures. From the
qualitative assumptions on the behavior of dynamic systems, we conclude that
the Belousov-Zhabotinsky reaction likely forms a regular grid.Comment: 17 pages, 12 figure
Structural instability in an autophosphorylating kinase switch
We analyse a simple kinase model that exhibits bistability when there is no protein turnover, and show analytically that the property of being bistable is not necessarily conserved when degradation and synthesis of the kinase are taken into account
Phase Transitions for Belousov-Zhabotinsky Reactions
The main objective of this article is to study the dynamic phase transitions
associated with the spatial-temporal oscillations of the BZ reactions, given by
Field, Koros and Noyes, also referred as the Oregonator. Two criteria are
derived to determine 1) existence of either multiple equilibria or
spatiotemporal oscillations, and 2) the types of transitions. These criteria
gives a complete characterization of the dynamic transitions of the BZ systems
from the homogeneous states. The analysis is carried out using a dynamic
transition theory developed recently by the authors, which has been
successfully applied to a number of problems in science
Reaction–diffusion chemistry implementation of associative memory neural network
Unconventional computing paradigms are typically very difficult to program. By implementing efficient parallel control architectures such as artificial neural networks, we show that it is possible to program unconventional paradigms with relative ease. The work presented implements correlation matrix memories (a form of artificial neural network based on associative memory) in reaction–diffusion chemistry, and shows that implementations of such artificial neural networks can be trained and act in a similar way to conventional implementations
Stochastic Turing patterns in the Brusselator model
A stochastic version of the Brusselator model is proposed and studied via the
system size expansion. The mean-field equations are derived and shown to yield
to organized Turing patterns within a specific parameters region. When
determining the Turing condition for instability, we pay particular attention
to the role of cross diffusive terms, often neglected in the heuristic
derivation of reaction diffusion schemes. Stochastic fluctuations are shown to
give rise to spatially ordered solutions, sharing the same quantitative
characteristic of the mean-field based Turing scenario, in term of excited
wavelengths. Interestingly, the region of parameter yielding to the stochastic
self-organization is wider than that determined via the conventional Turing
approach, suggesting that the condition for spatial order to appear can be less
stringent than customarily believed.Comment: modified version submitted to Phys Rev. E. 5. 3 Figures (5 panels)
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The Stability of a Stochastic CaMKII Switch: Dependence on the Number of Enzyme Molecules and Protein Turnover
Molecular switches have been implicated in the storage of information in biological systems. For small structures such as synapses, these switches are composed of only a few molecules and stochastic fluctuations are therefore of importance. Such fluctuations could potentially lead to spontaneous switch reset that would limit the lifetime of information storage. We have analyzed a model of the calcium/calmodulin-dependent protein kinase II (CaMKII) switch implicated in long-term memory in the nervous system. The bistability of this switch arises from autocatalytic autophosphorylation of CaMKII, a reaction that is countered by a saturable phosphatase-1-mediated dephosphorylation. We sought to understand the factors that control switch stability and to determine the functional relationship between stability and the number of molecules involved. Using Monte Carlo simulations, we found that the lifetime of states of the switch increase exponentially with the number of CaMKII holoenzymes. Switch stability requires a balance between the kinase and phosphatase rates, and the kinase rate must remain high relative to the rate of protein turnover. Thus, a critical limit on switch stability is set by the observed turnover rate (one per 30 h on average). Our computational results show that, depending on the timescale of fluctuations in enzyme numbers, for a switch composed of about 15 CaMKII holoenzymes, the stable persistent activation can span from a few years to a human lifetime
Riding a Spiral Wave: Numerical Simulation of Spiral Waves in a Co-Moving Frame of Reference
We describe an approach to numerical simulation of spiral waves dynamics of
large spatial extent, using small computational grids.Comment: 15 pages, 14 figures, as accepted by Phys Rev E 2010/03/2
Computational Modalities of Belousov-Zhabotinsky Encapsulated Vesicles
We present both simulated and partial empirical evidence for the
computational utility of many connected vesicle analogs of an encapsulated
non-linear chemical processing medium. By connecting small vesicles containing
a solution of sub-excitable Belousov-Zhabotinsky (BZ) reaction, sustained and
propagating wave fragments are modulated by both spatial geometry, network
connectivity and their interaction with other waves. The processing ability is
demonstrated through the creation of simple Boolean logic gates and then by the
combination of those gates to create more complex circuits
Thermal switch of oscillation frequency in belousov- zhabotinsky liquid marbles
© 2019 The Authors. External control of oscillation dynamics in the Belousov- Zhabotinsky (BZ) reaction is important for many applications including encoding computing schemes. When considering the BZ reaction, there are limited studies dealing with thermal cycling, particularly cooling, for external control. Recently, liquid marbles (LMs) have been demonstrated as a means of confining the BZ reaction in a system containing a solid-liquid interface. BZ LMs were prepared by rolling 50 ml droplets in polyethylene (PE) powder. Oscillations of electrical potential differences within the marble were recorded by inserting a pair of electrodes through the LM powder coating into the BZ solution core. Electrical potential differences of up to 100mV were observed with an average period of oscillation ca 44 s. BZ LMs were subsequently frozen to 218C to observe changes in the frequency of electrical potential oscillations. The frequency of oscillations reduced upon freezing to 11mHz cf. 23 mHz at ambient temperature. The oscillation frequency of the frozen BZ LM returned to 23 mHz upon warming to ambient temperature. Several cycles of frequency fluctuations were able to be achieved
Quasiperiodic Patterns in Boundary-Modulated Excitable Waves
We investigate the impact of the domain shape on wave propagation in
excitable media. Channelled domains with sinusoidal boundaries are considered.
Trains of fronts generated periodically at an extreme of the channel are found
to adopt a quasiperiodic spatial configuration stroboscopically frozen in time.
The phenomenon is studied in a model for the photo-sensitive
Belousov-Zabotinsky reaction, but we give a theoretical derivation of the
spatial return maps prescribing the height and position of the successive
fronts that is valid for arbitrary excitable reaction-diffusion systems.Comment: 4 pages (figures included
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