Eur. Phys. J. E (2012) 35: 101
https://doi.org/10.1140/epje/i2012-12101-3

Regular Article

Microtubule length dependence of motor traffic in cells

Laboratory of Mathematics for Nonlinear Science, Shanghai Key Laboratory for Contemporary Applied Mathematics, Centre for Computational System Biology, School of Mathematical Sciences, Fudan University, 200433, Shanghai, China

^* e-mail: xyz@fudan.edu.cn

Received: 23 May 2012
Revised: 4 August 2012
Accepted: 14 September 2012
Published online: 11 October 2012

Abstract

Motor proteins in living cells, such as kinesin and dynein, can move processively along the microtubule (MT), and can also detach from or attach to MT stochastically. Experiments found that the traffic of motors along MT may be jammed; thus various theoretical models were designed to understand this process. However, previous studies mainly focused on motor attachment/detachment rate dependent properties. Leduc et al. recently found that the traffic jam of motor protein Kip3 depends on MT length (Proc. Natl. Acad. Sci. U.S.A. 109, 6100 (2012)). Therefore, this study discusses the MT length-dependent properties of motor traffic. The results showed that MT length has one critical value N _c ; a traffic jam occurs only when MT length N > N _c . The jammed MT length increases with total MT length N , whereas the non-jammed MT length may not change monotonically with N . The critical value N_c increases with motor detachment rate from MT, but decreases with motor attachment rate to MT. Therefore, the traffic of motors will be more likely to be jammed when the MT is long, motor detachment rate is high, and motor detachment rate is low.