Anomalous transport and nonlinear reactions in spiny dendrites / Fedotov Sergei,Al-Shamsi Hamed,Ivanov Alexey,Zubarev Andrey // PHYSICAL REVIEW E. - 2010. - V. 82, l. 4, 1.

ISSN/EISSN:

1539-3755 / 1550-2376

Type:

Article

Abstract:

We present a mesoscopic description of the anomalous transport and reactions of particles in spiny dendrites. As a starting point we use two-state Markovian model with the transition probabilities depending on residence time variable. The main assumption is that the longer a particle survives inside spine, the smaller becomes the transition probability from spine to dendrite. We extend a linear model presented in Fedotov et al. {[}Phys. Rev. Lett. 101, 218102 (2008)] and derive the nonlinear Master equations for the average densities of particles inside spines and parent dendrite by eliminating residence time variable. We show that the flux of particles between spines and parent dendrite is not local in time and space. In particular the average flux of particles from a population of spines through spines necks into parent dendrite depends on chemical reactions in spines. This memory effect means that one cannot separate the exchange flux of particles and the chemical reactions inside spines. This phenomenon does not exist in the Markovian case. The flux of particles from dendrite to spines is found to depend on the transport process inside dendrite. We show that if the particles inside a dendrite have constant velocity, the mean particle's position < x(t)> increases as t(mu) with mu < 1 (anomalous advection). We derive a fractional advection-diffusion equation for the total density of particles.

Author keywords:

RANDOM-WALKS; ACTIVE SPINES; DIFFUSION; MODEL; SYSTEMS; WAVES; SUPERDIFFUSION; EQUATIONS; CABLE

DOI:

10.1103/PhysRevE.82.041103

Web of Science ID:

ISI:000282570900001

Соавторы в МНС:

Другие поля

Поле	Значение
Month	OCT 6
Publisher	AMER PHYSICAL SOC
Address	ONE PHYSICS ELLIPSE, COLLEGE PK, MD 20740-3844 USA
Language	English
Article-Number	041103
EISSN	1550-2376
Keywords-Plus	RANDOM-WALKS; ACTIVE SPINES; DIFFUSION; MODEL; SYSTEMS; WAVES; SUPERDIFFUSION; EQUATIONS; CABLE
Research-Areas	Physics
Web-of-Science-Categories	Physics, Fluids \& Plasmas; Physics, Mathematical
ResearcherID-Numbers	Fedotov, Sergei/H-5880-2012 Ivanov, Alexey/E-4442-2011 Zubarev, Adrey/B-4752-2014
ORCID-Numbers	Ivanov, Alexey/0000-0001-8239-4039
Funding-Acknowledgement	{[}GammaK N02-740-11-5172]
Funding-Text	This research was supported by the Grant Gamma K N02-740-11-5172 ``Anomalous transport in biological and chemical systems.{''}
Number-of-Cited-References	52
Usage-Count-Since-2013	8
Journal-ISO	Phys. Rev. E
Doc-Delivery-Number	659MP