  We present a general stochastic dynamic model of a cluster of biological
complexes with fluctuating dissociation and association rates. The master
equation has analytical solutions in two limiting cases: the vanishing force
with reflecting boundary condition and slow reaction limit. In particular, the
latter can describe the dynamics of a catch-slip bond cluster under a constant
force. We find that if the rebinding rate vanishes, the size of the cluster
matters little to the cluster lifetime within the whole catch force regime. The
large cluster rapidly decays and single catch bond governs the final dynamic
behaviors of the cluster. The catch behavior would be further amplified in the
presence of large nonvanishing rebinding rates.
