  Manipulation of temperature can be used to actuate DNA origami nano-hinges
containing gold nanoparticles. We develop a physical model of this system that
uses partition function analysis of the interaction between the nano-hinge and
nanoparticle to predict the probability that the nano-hinge is open at a given
temperature. The model agrees well with experimental data and predicts
experimental conditions that allow the actuation temperature of the nano-hinge
to be tuned over a range of temperatures from $30$${}^{\circ}\mathrm{C}$ to
$45$${}^{\circ}\mathrm{C}$. Additionally, the model reveals surprising physical
constraints on the system. This combination of physical insight and predictive
potential is likely to inform future designs that integrate nanoparticles into
dynamic DNA origami structures. Furthermore, our modeling approach could be
expanded to consider the incorporation, stability, and actuation of other types
of functional elements or actuation mechanisms integrated into nucleic acid
devices.
