Force-extension (F-x) relationships were measured for single molecules
of DNA under a variety of buffer conditions, using an optical trappin
g interferometer modified to incorporate feedback control. One end of
a single DNA molecule was fixed to a coverglass surface by means of a
stalled RNA polymerase complex. The other end was linked to a microsco
pic bead, which was captured and held in an optical trap. The DNA was
subsequently stretched by moving the coverglass with respect to the tr
ap using a piezo-driven stage, while the position of the bead was reco
rded at nanometer-scale resolution. An electronic feedback circuit was
activated to prevent bead movement beyond a preset clamping point by
modulating the light intensity, altering the trap stiffness dynamicall
y. This arrangement permits rapid determination of the F-x relationshi
p for individual DNA molecules as short as similar to 1 mu m with unpr
ecedented accuracy, subjected to both low(similar to 0.1 pN) and high
(similar to 50 pN) loads: complete data sets are acquired in under a m
inute. Experimental F-x relationships were fit over much of their rang
e by entropic elasticity theories based on worm-like chain models. Fit
s yielded a persistence length, L(P), of similar to 47 nm in a buffer
containing 10 mM Na+, Multivalent cations, such as Mg2+ or spermidine(
3+), reduced L(P) to similar to 40 nm. Although multivalent ions shiel
d most of the negative charges on the DNA backbone, they did not furth
er reduce L(P) significantly, suggesting that the intrinsic persistenc
e length remains close to 40 nm. An elasticity theory incorporating bo
th enthalpic and entropic contributions to stiffness fit the experimen
tal results extremely well throughout the full range of extensions and
returned an elastic modulus of similar to 1100 pN.