TRAVELING WAVES IN THE BUFFERED FITZHUGH—NAGUMO MODEL

In many physiologically important excitable systems, such as intracellular calcium dynamics, the diffusing variable is highly buffered. In addition, all physiological buffered excitable systems contain multiple buffers, with different affinities. It is thus important to understand the properties of wave solutions in excitable systems with multiple buffers, and to understand how multiple buffers interact. Under the assumption that buffering acts on a fast time scale, we derive a criterion for the existence of a traveling pulse with positive wave speed in the buffered FitzHugh—Nagumo model, a prototypical excitable system. This condition suggests that there exists a critical excitability corresponding to the excitability parameter a c such that, for systems with excitability above this critical excitability (the excitability parameter a ∈ (0, a c )), buffers cannot prevent the propagation of traveling pulses with positive wave speed, provided that the parameter ϵ ≪ 1. Further, buffers can speed up wave propagation if the diffusivity of the buffer increases. On the other hand, for systems with excitability below this critical excitability (the excitability parameter a ∈ (a c , 1/2)), we can find a critical dissociation constant (K = K(a)) such that buffers can be classified into two types: weak buffers (K ∈ (K(a), ∞)) and strong buffers (K ∈ (0, K(a))). It turns out that the wave properties are strongly affected by competition between strong buffers and weak buffers. Weak buffers not only can help the existence of waves, but also can speed up wave propagation if their diffusivity increases. In contrast, strong buffers can eliminate calcium waves if the product of their diffusivity and total concentration exceeds some critical value. Moreover, as the diffusivity of the strong buffer increases to some critical value, the waves slow down to zero. Finally, adding a sufficiently large amount of buffer, either strong or weak, can eliminate the wave.