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Abstract:
The existence and properties of intracellular waves of increased free cytoplasmic calcium concentration (calcium waves) are strongly affected by the binding and unbinding of calcium ions to a multitude of different buffers in the cell. These buffers can be mobile or immobile and, in general, have multiple binding sites that are not independent. Previous theoretical studies have focused on the case when each buffer molecule binds a single calcium ion. In this study, we analyze how calcium waves are affected by calcium buffers with two non-independent binding sites, and show that the interactions between the calcium binding sites can result in the emergence of new behaviors. In particular, for certain combinations of kinetic parameters, the profiles of buffer molecules with one calcium ion bound can be non-monotone.

Keywords:
Reaction-diffusion systems, Buffered calcium systems

Abstract:
Traveling waves form a basic class of solutions to reaction–diffusion equations, which can describe a large number of phenomena. The basic property characterizing traveling wave solutions is their speed of propagation. In this study we analyze its dependence on the diffusivities of the interacting agents. We show that this dependence is subject to some relations, which can be derived by simple scaling properties. We augment our findings by an investigation of reaction–diffusion systems describing intercellular calcium dynamics in the presence of buffer molecules. We establish some mathematical results concerning the behavior of the velocity of traveling waves in the case of fast buffer kinetics, (paying special attention to the vicinity of zero speed), and present outcomes of numerical simulations showing how complicated the interplay between the diffusion coefficients of calcium and buffering molecules can be, especially in models with more than one kind of buffer molecules.

Keywords:
reaction-diffusion equations, traveling waves, Euler’s homogeneous function theorem, buffered calcium systems