Length-dependent dynamics of microtubules
  Certain regulatory proteins influence the polymerization dynamics of microtubules by inducing catastrophe with a rate that depends on the microtubule length. Using a discrete formulation, here we show that, for a catastrophe rate proportional to the microtubule length, the steady-state probability distributions of length decay much faster with length than an exponential decay as seen in the absence of these proteins. 
Vandana Yadav and Sutapa Mukherji
physics.bio-ph cond-mat.soft cond-mat.stat-mech q-bio.SC