Enzyme rates are usually considered to be dependent on local properties of the molecules involved in reactions. However, for large molecules, distant constraints might affect reaction rates by affecting dynamics leading to transition states. In single-molecule experiments we have found that enzymes that relax DNA torsional stress display rates that depend strongly on how the distant ends of the molecule are constrained; experiments with different-sized particles tethered to the end of 10-kb DNAs reveal enzyme rates inversely correlated with particle drag coefficients. This effect can be understood in terms of the coupling between molecule extension and local molecular stresses: The rate of bead thermal motion controls the rate at which transition states are visited in the middle of a long DNA. Importantly, we have also observed this effect for reactions on unsupercoiled DNA; other enzymes show rates unaffected by bead size. Our results reveal a unique mechanism through which enzyme rates can be controlled by constraints on macromolecular or supramolecular substrates.DNA topology | DNA-protein interactions | enzyme kinetics | molecular friction | single-molecule biophysics Q uantification of enzyme rates is fundamental to mechanistic understanding of life processes. One often considers rates of enzyme activity to be dependent on properties of the molecules near the reaction site. However, conformational fluctuations of large molecules can be controlled by distant constraints on a molecule, which might in turn control activities of enzymes along that molecule that rely on conformational fluctuations of their substrates to reach their transition states. Large DNA molecules provide a prime candidate for realization of this effect. Tethering the ends of a chromosomal domain will constrain bending and twisting fluctuations of the DNA between the tether points. Changes in the tethering constraints will change the conformational kinetics of the intervening DNA, conceivably modifying rates of enzymes acting along it.Here, we report in vitro single-molecule experiments showing this effect, through direct observation of variation of DNA-acting enzyme rates with changes in DNA end constraints. Our main focus is on enzymes that processively relax DNA supercoiling, although we have observed similar effects for single-step reactions on unsupercoiled DNAs. Single-DNA experiments (Fig. 1A) permit real-time observation of nucleic acid-acting enzyme activities, including those that change DNA supercoiling (1, 2). Such experiments are conveniently carried out using "magnetic tweezers," where a paramagnetic bead attached to the end of the molecule is pulled by a constant force via a magnetic field gradient. Rotation of the magnets allows DNA to be supercoiled, reducing DNA extension (3) (Fig. 1A). This allows enzyme cleavage of one or both strands of a dsDNA to be observed (1, 2, 4) (Fig. 1B). When cleavage occurs, the particle at the end of the DNA moves as linking number is relaxed. We note that the bead orientation is fixed durin...