### Abstract

Calcium buffers are large proteins that act as binding sites for free cytosolic calcium. Since a large fraction of cytosolic calcium is bound to calcium buffers, calcium waves are widely observed under the condition that free cytosolic calcium is heavily buffered. In addition, all physiological buffered excitable systems contain multiple buffers with different affinities. It is thus important to understand the properties of waves in excitable systems with the inclusion of buffers. There is an ongoing controversy about whether or not the addition of calcium buffers into the system always slows down the propagation of calcium waves. To solve this controversy, we incorporate the buffering effect into the generic excitable system, the FitzHugh-Nagumo model, to get the buffered FitzHugh-Nagumo model, and then to study the effect of the added buffer with large diffusivity on traveling waves of such a model in one spatial dimension. We can find a critical dissociation constant (K = K(a)) characterized by system excitability parameter a such that calcium buffers can be classified into two types: weak buffers (K ∈ K(a), ∞) and strong buffers (K ∈ (0, K(a)). We analytically show that the addition of weak buffers or strong buffers but with its total concentration b_{0}^{1}. below some critical total concentration b_{0}^{1,c} into the system can generate a traveling wave of the resulting system which propagates faster than that of the origin system, provided that the diffusivity D_{1} of the added buffers is sufficiently large. Further, the magnitude of the wave speed of traveling waves of the resulting system is proportional to √D_{1} as D_{1} → ∞. In contrast, the addition of strong buffers with the total concentration b_{0}^{1}>b_{0}^{1,c} into the system may not be able to support the formation of a biologically acceptable wave provided that the diffusivity D_{1} of the added buffers is sufficiently large.

Original language | English |
---|---|

Pages (from-to) | 1587-1632 |

Number of pages | 46 |

Journal | Journal of Mathematical Biology |

Volume | 67 |

Issue number | 6-7 |

DOIs | |

Publication status | Published - 2013 Dec 1 |

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### Keywords

- Buffer
- Buffered FitzHugh-Nagumo model
- Calcium
- Traveling wave

### ASJC Scopus subject areas

- Modelling and Simulation
- Agricultural and Biological Sciences (miscellaneous)
- Applied Mathematics

### Cite this

**Do calcium buffers always slow down the propagation of calcium waves?** / Tsai, Je-Chiang.

Research output: Contribution to journal › Article

*Journal of Mathematical Biology*, vol. 67, no. 6-7, pp. 1587-1632. https://doi.org/10.1007/s00285-012-0605-y

}

TY - JOUR

T1 - Do calcium buffers always slow down the propagation of calcium waves?

AU - Tsai, Je-Chiang

PY - 2013/12/1

Y1 - 2013/12/1

N2 - Calcium buffers are large proteins that act as binding sites for free cytosolic calcium. Since a large fraction of cytosolic calcium is bound to calcium buffers, calcium waves are widely observed under the condition that free cytosolic calcium is heavily buffered. In addition, all physiological buffered excitable systems contain multiple buffers with different affinities. It is thus important to understand the properties of waves in excitable systems with the inclusion of buffers. There is an ongoing controversy about whether or not the addition of calcium buffers into the system always slows down the propagation of calcium waves. To solve this controversy, we incorporate the buffering effect into the generic excitable system, the FitzHugh-Nagumo model, to get the buffered FitzHugh-Nagumo model, and then to study the effect of the added buffer with large diffusivity on traveling waves of such a model in one spatial dimension. We can find a critical dissociation constant (K = K(a)) characterized by system excitability parameter a such that calcium buffers can be classified into two types: weak buffers (K ∈ K(a), ∞) and strong buffers (K ∈ (0, K(a)). We analytically show that the addition of weak buffers or strong buffers but with its total concentration b01. below some critical total concentration b01,c into the system can generate a traveling wave of the resulting system which propagates faster than that of the origin system, provided that the diffusivity D1 of the added buffers is sufficiently large. Further, the magnitude of the wave speed of traveling waves of the resulting system is proportional to √D1 as D1 → ∞. In contrast, the addition of strong buffers with the total concentration b01>b01,c into the system may not be able to support the formation of a biologically acceptable wave provided that the diffusivity D1 of the added buffers is sufficiently large.

AB - Calcium buffers are large proteins that act as binding sites for free cytosolic calcium. Since a large fraction of cytosolic calcium is bound to calcium buffers, calcium waves are widely observed under the condition that free cytosolic calcium is heavily buffered. In addition, all physiological buffered excitable systems contain multiple buffers with different affinities. It is thus important to understand the properties of waves in excitable systems with the inclusion of buffers. There is an ongoing controversy about whether or not the addition of calcium buffers into the system always slows down the propagation of calcium waves. To solve this controversy, we incorporate the buffering effect into the generic excitable system, the FitzHugh-Nagumo model, to get the buffered FitzHugh-Nagumo model, and then to study the effect of the added buffer with large diffusivity on traveling waves of such a model in one spatial dimension. We can find a critical dissociation constant (K = K(a)) characterized by system excitability parameter a such that calcium buffers can be classified into two types: weak buffers (K ∈ K(a), ∞) and strong buffers (K ∈ (0, K(a)). We analytically show that the addition of weak buffers or strong buffers but with its total concentration b01. below some critical total concentration b01,c into the system can generate a traveling wave of the resulting system which propagates faster than that of the origin system, provided that the diffusivity D1 of the added buffers is sufficiently large. Further, the magnitude of the wave speed of traveling waves of the resulting system is proportional to √D1 as D1 → ∞. In contrast, the addition of strong buffers with the total concentration b01>b01,c into the system may not be able to support the formation of a biologically acceptable wave provided that the diffusivity D1 of the added buffers is sufficiently large.

KW - Buffer

KW - Buffered FitzHugh-Nagumo model

KW - Calcium

KW - Traveling wave

UR - http://www.scopus.com/inward/record.url?scp=84887460975&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84887460975&partnerID=8YFLogxK

U2 - 10.1007/s00285-012-0605-y

DO - 10.1007/s00285-012-0605-y

M3 - Article

VL - 67

SP - 1587

EP - 1632

JO - Journal of Mathematical Biology

JF - Journal of Mathematical Biology

SN - 0303-6812

IS - 6-7

ER -