Biomedical subjects

Damián E Strier

Publications and source records attributed to Damián E Strier.

3 recordsLinked to original sources

PubMed2004

Role of complexing agents in the appearance of Turing patterns.

In this paper we study a four-species reaction-diffusion system where Turing patterns are stabilized by the presence of fast reversible reactions between the morphogens and two different mobile complexing agents (CAs) that are not necessarily in excess. We provide a quantitative explanation of how the interaction with the CA changes the size of the Turing space making it possible to observe patterns even in a region where the free diffusion coefficients of the relevant species are equal, as is usually the case in real systems. Our analytical treatment gives a series of mathematical relations that can be helpful for those designing experiments where Turing patterns are expected to appear. We also show how the mobility of CAs affect the characteristic size of the pattern. Finally, we provide an example of biological interest in order to illustrate the main procedures and results.

Biophysics↗

PubMed2003

Saltatory and continuous calcium waves and the rapid buffering approximation.

Calcium waves propagate inside cells due to a regenerative mechanism known as calcium-induced calcium release. Buffer-mediated calcium diffusion in the cytosol plays a crucial role in the process. However, most models of calcium waves either treat buffers phenomenologically or assume that they are in equilibrium with calcium (the rapid buffering approximation). In this article we address the issue of whether this approximation provides a good description of wave propagation. We first compare the timescales present in the problem, and determine the situations in which the equilibrium hypothesis fails. We then present a series of numerical studies based on the simple fire-diffuse-fire model of wave propagation. We find that the differences between the full and reduced descriptions may lead to errors that are above experimental resolution even for relatively fast buffers in the case of saltatory waves. Conversely, in the case of continuous waves, the approximation may give accurate results even for relatively slow buffers.

Biophysics↗

PubMed2002

Slow time evolution of two-time-scale reaction-diffusion systems: the physical origin of nondiffusive transport.

We study, from a mesoscopic point of view, the slow time-scale dynamics of a mixture of chemicals in which there is a chemical reaction that occurs much faster than all other processes, including diffusion. For a simple paradigmatic model reaction, it is possible to find a reduced set of dynamical equations analytically. This procedure, which yields the same mean field equations as the macroscopic approach described by Strier and Dawson [J. Chem. Phys, 112, 825 (2000)], clarifies the physical origin of some of the terms that appear in the reduced reaction-diffusion equations, such as "negative density dependent cross diffusion terms," whose actual meaning is hard to assess within the macroscopic framework. We also present a two-time-scale reactive lattice gas automaton with which it is possible to check the validity of the analytical results and the conditions under which the reduced description holds. Using this lattice gas we also show how the differential interaction with immobile species can give rise to the formation of stable Turing patterns in a system where all the other chemicals diffuse approximately at the same rate.

Journal Article↗