This paper provides a consistent approach (within a one-dimensional approxi
mation) to the description of the evolution of the microtubule length at bo
th low- and high-density concentrations. We derive general master-type equa
tions which are based on the key chemical reactions involved in the assembl
y and disassembly of microtubules. The processes included are: polymerizati
on and depolymerization of a single protein dimer, catastrophic disassembly
affecting an a piori arbitrary number of dimers, and a rescue event. Solut
ions of the derived equations are compared with the existing experimental d
ata. Important conclusions linking the emergence of bell-shaped histograms
with the nature of catastrophe and rescue phenomena are drawn. Finally, we
briefly discuss the emergence of coherent phenomena in microtubule polymeri
zation, i.e., a transition to collective oscillations in the assembly and d
isassembly effects. (C) 1999 Elsevier Science S.A. All rights reserved.