  Knots are entangled structures that cannot be untangled without a cut.
Topological stability of knots is one of the many examples of their important
properties that can be used in information storage and transfer. Knot dynamics
is important for understanding general principles of entanglement as knots
provide an isolated system where tangles are highly controlled and easily
manipulated. To unravel the dynamics of these entangled topological objects,
the first step is to identify the dominant motions that are uniquely guided by
knot structure and its complexity. We identify and classify motions into three
main groups -- orthogonal, aligned, and mixed motions, which often act in
unison, orchestrating the complex dynamics of knots. The balance between these
motions is what creates an identifiable signature for every knot. As knot
complexity increases, the carefully orchestrated dynamics is gradually
silenced, eventually reaching a state of topologically driven dynamical arrest.
Depending on their complexity, knots undergo a transition from nearly
stochastic motions to either non-random or even quasiperiodic dynamics before
culminating in dynamical arrest. Here, we show for the first time that
connectivity alone can lead to a topology-driven dynamical arrest in knots of
high complexity. Unexpectedly, we noticed that some knots undergo cooperative
motions as they reach higher complexity, uniquely modulating conformational
patterns of a given knot. Together, these findings demonstrate a link between
topology and dynamics, presenting applications to nanoscale materials.
