  We develop a formalism for single molecule dynamic force spectroscopy to map
the energy landscape of protein-protein complex ($P_1$$P_2$). The joint
distribution $P(\tau_1,\tau_2)$ of unbinding lifetimes $\tau_1$ and $\tau_2$
measurable in a compression-tension cycle, which accounts for the internal
relaxation dynamics of the proteins under tension, shows that the histogram of
$\tau_1$ is not Poissonian. The theory is applied to the forced unbinding of
protein $P_1$, modeled as a wormlike chain, from $P_1$$P_2$. We propose a new
class of experiments which can resolve the effect of internal protein dynamics
on the unbinding lifetimes.
