What is the optimal shape of an axon?

Antoine Henrot (1, 2) , Yannick Privat (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 CORIDA - Robust control of infinite dimensional systems and applications

What is the optimal shape of an axon? Of course, optimality refers to some particular criterion. In this paper, we look at the case of an axon tapered at one end and connected at the other end to a soma. The electrical potential in the fiber follows the classical cable equations as established by W. Rall. We are interested in the shape of the axon which minimizes either the attenuation in time of the potential or the attenuation in space. In both cases, we prove that the cylindrical shape is optimal.

Mots clés: optimal shape; cable equation; axon; eigenvalue problem

Domaines: Equations aux dérivées partielles [math.AP]; Optimisation et contrôle [math.OC]; Morphogenèse

Antoine Henrot, Yannick Privat. What is the optimal shape of an axon?. 2007. ⟨hal-00128444v1⟩