Traveling Waves in Buffered Systems: Applications to Calcium Waves

Abstract

Traveling waves of calcium are widely observed under conditions where the free calcium is heavily buffered. It is thus of considerable physiological interest to determine the precise effects that buffers have on the properties of traveling waves. Since calcium waves are widely believed to be the result of the reaction and diffusion of calcium, we study the properties of traveling waves in simple reaction-diffusion equations in which the diffusing species is buffered. For the buffered bistable equation we derive a constraint on the model parameters in order for a traveling wave of excitation to exist, and we show that stationary buffers cannot eliminate traveling waves. When the buffer is of low affinity, a constant effective diffusion coefficient may be defined, but no effective diffusion coefficient can be defined for high affinity buffers. We derive an approximate expression for the wave speed, show numerically that this approximation applies for both high and low affinity buffers, and hence derive an a...