Abstract
Ductile materials can absorb spikes in mechanical force, whereas brittle ones fail catastrophically. Here we develop a theory to quantify the kinetic ductility of single molecules from force spectroscopy experiments, relating force-spike resistance to the differential responses of the intact protein and the unfolding transition state to an applied mechanical force. We introduce a class of unistable one-dimensional potential surfaces that encompass previous models as special cases and continuously cover the entire range from ductile to brittle. Compact analytic expressions for force-dependent rates and rupture-force distributions allow us to analyze force-clamp and force-ramp pulling experiments. We find that the force-transmitting protein domains of filamin and titin are kinetically ductile when pulled from their two termini, making them resistant to force spikes. For the mechanostable muscle protein titin, a highly ductile model reconciles data over 10 orders of magnitude in force loading rate from experiment and simulation.