Microtubule Dynamic Instability

GTP-cap model: stochastic catastrophe & rescue events (Mitchison & Kirschner 1984)

Growth/Shrink Rates

Growth rate v+ (μm/min) 1.5

Shrink rate v- (μm/min) 8.0

Transition Rates

Catastrophe f_c (min⁻¹) 0.08

Rescue f_r (min⁻¹) 0.10

State

Length (μm): 0.00

Phase: Growing

Catastrophes: 0

Rescues: 0

Dynamic Instability of Microtubules

Microtubules (MTs) alternate stochastically between growing (polymerisation) and rapidly shrinking (depolymerisation) phases — a phenomenon discovered by Mitchison & Kirschner in 1984. The switch is governed by a GTP-tubulin cap: when the cap is lost, rapid depolymerisation ("catastrophe") ensues; reassembly of a cap triggers "rescue".

The steady-state length distribution is exponential: P(L) ∝ exp(−L/⟨L⟩) with ⟨L⟩ = v+·v−/(f_c·v− − f_r·v+) in the bounded phase. The unbounded growth phase requires f_c·v− < f_r·v+ — catastrophe rate too small to confine the MT.

Dynamic instability is critical for chromosome capture during mitosis: the kinetochore exploits catastrophe to create pulling forces via a Brownian ratchet mechanism.