PubMed Health⌕ Search
Home/Archive/PubMed

PubMed · 3958635

Spontaneous oscillations in two 2-component cells coupled by diffusion.

J C Alexander
View original source ↗Export metadata ↓

Abstract

Mathematical examples are presented of oscillators with two variables which do not oscillate in isolation, but which do oscillate stably when coupled with a twin via diffusion. Two examples are presented, the Lefever-Prigogine Brusselator and a system used to model glycolytic oscillations. The mathematical method is not the usual bifurcation theory, but rather a type of singular perturbation theory combined with bifurcation theory. For both examples, it is shown that all stationary solutions are unstable for appropriate parameter settings. In the case of the Brusselator, it is further shown that there exist limit cycles; i.e. stable oscillations, in this parameter range. A numerical example is presented.

Explore related subjects

Cell Physiological PhenomenaDiffusionGlycolysisKineticsMathematicsModels, BiologicalOscillometryJournal ArticleResearch Support, U.S. Gov't, Non-P.H.S.

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

J C Alexander. 1986. Spontaneous oscillations in two 2-component cells coupled by diffusion.. https://doi.org/10.1007/bf00276957

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related citations

PubMed2007

Neutral fitness landscapes in signalling networks.

Biological and technological systems process information by means of cascades of signals. Be they interacting genes, spiking neurons or electronic transistors, information travels across these systems, producing, for each set of external conditions, an appropriate response. In technology, circuits performing specific complex tasks are designed by humans. In biology, however, design has to be ruled out, confronting us with the question of how these systems could have arisen by accumulation of small changes. The key factor is the genotype-phenotype map. With the exception of RNA folding, not much is known about the exact nature of this mapping. Here, we show that structure of the genotype-phenotype map of simple feed-forward circuits is very close to the ones found in RNA; they have a large degree of neutrality, by which a circuit can be completely rewired keeping its input-output function intact, and there is a relatively small neighbourhood of a given circuit containing almost all the phenotypes.

Cell Physiological Phenomena↗
PubMed2007

Directed cell migration in the presence of obstacles.

BACKGROUND: Chemotactic movement is a common feature of many cells and microscopic organisms. In vivo, chemotactic cells have to follow a chemotactic gradient and simultaneously avoid the numerous obstacles present in their migratory path towards the chemotactic source. It is not clear how cells detect and avoid obstacles, in particular whether they need a specialized biological mechanism to do so. RESULTS: We propose that cells can sense the presence of obstacles and avoid them because obstacles interfere with the chemical field. We build a model to test this hypothesis and find that this naturally enables efficient at-a-distance sensing to be achieved with no need for a specific and active obstacle-sensing mechanism. We find that (i) the efficiency of obstacle avoidance depends strongly on whether the chemotactic chemical reacts or remains unabsorbed at the obstacle surface. In particular, it is found that chemotactic cells generally avoid absorbing barriers much more easily than non-absorbing ones. (ii) The typically low noise in a cell's motion hinders the ability to avoid obstacles. We also derive an expression estimating the typical distance traveled by chemotactic cells in a 3D random distribution of obstacles before capture; this is a measure of the distance over which chemotaxis is viable as a means of directing cells from one point to another in vivo. CONCLUSION: Chemotactic cells, in many cases, can avoid obstacles by simply following the spatially perturbed chemical gradients around obstacles. It is thus unlikely that they have developed specialized mechanisms to cope with environments having low to moderate concentrations of obstacles.

Cell Physiological Phenomena↗
PubMed2007

Thermodynamically feasible kinetic models of reaction networks.

The dynamics of biological reaction networks are strongly constrained by thermodynamics. An holistic understanding of their behavior and regulation requires mathematical models that observe these constraints. However, kinetic models may easily violate the constraints imposed by the principle of detailed balance, if no special care is taken. Detailed balance demands that in thermodynamic equilibrium all fluxes vanish. We introduce a thermodynamic-kinetic modeling (TKM) formalism that adapts the concepts of potentials and forces from irreversible thermodynamics to kinetic modeling. In the proposed formalism, the thermokinetic potential of a compound is proportional to its concentration. The proportionality factor is a compound-specific parameter called capacity. The thermokinetic force of a reaction is a function of the potentials. Every reaction has a resistance that is the ratio of thermokinetic force and reaction rate. For mass-action type kinetics, the resistances are constant. Since it relies on the thermodynamic concept of potentials and forces, the TKM formalism structurally observes detailed balance for all values of capacities and resistances. Thus, it provides an easy way to formulate physically feasible, kinetic models of biological reaction networks. The TKM formalism is useful for modeling large biological networks that are subject to many detailed balance relations.

Cell Physiological Phenomena↗