Are buffers boring? Uniqueness and asymptotical stability of traveling wave fronts in the buffered bistable system

Traveling waves of calcium are widely observed under the condition that the free cytosolic calcium is buffered. Thus it is of physiological interest to determine how buffers affect the properties of calcium waves. Here we summarise and extend previous results on the existence, uniqueness and stability of traveling wave solutions of the buffered bistable equation, which is the simplest possible model of the upstroke of a calcium wave. Taken together, the results show that immobile buffers do not change the existence, uniqueness or stability of the traveling wave, while mobile buffers can eliminate a traveling wave. However, if a wave exists in the latter case, it remains unique and stable.