Comb models for transport along spiny dendrites

TL;DR

This chapter explores comb models to understand transport phenomena in spiny dendrites, demonstrating their ability to model anomalous diffusion, reaction-diffusion, and wave propagation mechanisms in neural structures.

Contribution

It introduces a comb-like structure as a paradigm for modeling transport in spiny dendrites, linking chaos theory, anomalous diffusion, and biological wave propagation.

Findings

Combs can model anomalous diffusion in dendrites.

Comb structures explain wave propagation failure.

Models relate to reaction-diffusion and Levy walks.

Abstract

This chapter is a contribution in the "Handbook of Applications of Chaos Theory" ed. by Prof. Christos H Skiadas. The chapter is organized as follows. First we study the statistical properties of combs and explain how to reduce the effect of teeth on the movement along the backbone as a waiting time distribution between consecutive jumps. Second, we justify an employment of a comb-like structure as a paradigm for further exploration of a spiny dendrite. In particular, we show how a comb-like structure can sustain the phenomenon of the anomalous diffusion, reaction-diffusion and L\'evy walks. Finally, we illustrate how the same models can be also useful to deal with the mechanism of ta translocation wave / translocation waves of CaMKII and its propagation failure. We also present a brief introduction to the fractional integro-differentiation in appendix at the end of the chapter.