  DNA strand displacement, where a single-stranded nucleic acid invades a DNA
duplex, is pervasive in genomic processes and DNA engineering applications. The
kinetics of strand displacement have been studied in bulk; however, the
kinetics of the underlying strand exchange were obfuscated by a slow
bimolecular association step. Here, we use a novel single-molecule Fluorescence
Resonance Energy Transfer (smFRET) approach termed the "fission" assay to
obtain the full distribution of first passage times of unimolecular strand
displacement. At a frame time of 4.4 ms, the first passage time distribution
for a 14-nt displacement domain exhibited a nearly monotonic decay with little
delay. Among the eight different sequences we tested, the mean displacement
time was on average 35 ms and varied by up to a factor of 13. The measured
displacement kinetics also varied between complementary invaders and between
RNA and DNA invaders of the same base sequence except for T$\rightarrow$U
substitution. However, displacement times were largely insensitive to the
monovalent salt concentration in the range of 0.25 M to 1 M. Using a
one-dimensional random walk model, we infer that the single-step displacement
time is in the range of $\sim 30 \mu s$ to $\sim 300 \mu s$ depending on the
base identity. The framework presented here is broadly applicable to the
kinetic analysis of multistep processes investigated at the single-molecule
level.
