During the past decade, physical techniques such as optical
tweezers and atomic force microscopy were used to study the
mechanical properties of DNA at the single-molecule level.
Knowledge of DNA’s stretching and twisting properties now
permits these single-molecule techniques to be used in the
study of biological processes such as DNA replication and
*Department of Molecular and Cell Biology, †Department of Physics
and ‡Department of Chemistry, University of California, Berkeley,
CA 94720, USA
Current Opinion in Structural Biology 2000, 10:279–285
0959-440X/00/$ — see front matter
© 2000 Elsevier Science Ltd. All rights reserved.
atomic force microscopy
freely jointed chain
Until recently, physical and chemical studies of DNA were
performed in bulk, whereby large numbers of molecules
were sampled simultaneously. Inherent averaging in such
measurements makes it difficult to resolve the time-
dependent stresses and strains that develop in DNA
during the course of its biological reactions. Processes like
protein-induced DNA bending, induced-fit molecular
recognition between proteins and DNA, and the
mechanochemical energy transduction of DNA-binding
molecular motors were not directly accessible to study.
In the past decade, this situation has changed dramatically.
New methods to manipulate single molecules now offer
researchers the opportunity to directly measure the forces
generated in biochemical reactions and, even, to exert
external forces to alter the fate of these reactions.
The elastic behavior of dsDNA has been investigated in
various laboratories using a variety of forces, for example,
hydrodynamic drag [1–3], magnetic beads , glass nee-
dles  and optical traps [6,7]. Magnetic beads attached to
the ends of DNA by biotin–avidin can be pulled by exter-
nal magnets. These magnetic tweezers are a useful tool,
particularly in the range between 0.01 and 10 pN. Slightly
higher force regimes can be probed with optical tweezers,
which allow one to apply and sense forces on micron-sized
dielectric particles, such as plastic microspheres, in an
aqueous environment [8,9]. A trap is formed by focusing a
laser beam onto a micron-sized spot through a microscope
objective. A particle with an index of refraction higher than
that of the surrounding medium experiences a force equal
to the rate of change of momentum of the refracted trap-
ping beam. For a laser beam with a Gaussian profile, this
force attracts the bead and traps it at the center of the beam
near the focus. External forces acting on the bead can be
measured by observing either the particle position in the
trap or the corresponding deflection of the trapping beam.
Trapping forces typically range between 0.1 and 100 pN.
In atomic force microscopy (AFM), a tip at the end of a
flexible cantilever of known force constant is scanned over
the sample. Bending of the cantilever can be monitored by
the deflection of a laser beam reflected off its back [10,11].
If a molecule is attached between the tip and a surface, and
the tip is lifted upward, a force/extension curve can be
obtained. Typical forces range from 10 to 10,000 pN.
Complex behavior has been revealed by elasticity studies of
individual dsDNA molecules. In this case, the range of forces
applied to the molecule determines the nature and length
scale involved in the elastic response, with higher forces
probing shorter length units. So far, at least four different
force/extension regimes have been characterized for dsDNA.
The force/extension regimes of DNA
Entropic elasticity regime
A dsDNA molecule in solution bends and curves locally as
a result of thermal fluctuations. Such fluctuations shorten
the end-to-end distance of the molecule, even against an
applied force. This elastic behavior is thus purely entropic
in origin. Two models are often used to describe the
entropic elasticity of DNA. In the freely jointed chain
(FJC) model, the molecule is made up of rigid, orienta-
tionally independent Kuhn segments whose length, b, is a
measure of chain stiffness. The alignment of segments by
tension is described by the Boltzmann distribution. In the
inextensible worm-like chain (WLC) model, the molecule
is treated as a flexible rod of length L that curves smooth-
ly as a result of thermal fluctuations. The rod’s local
direction decorrelates at distance s along the curve accord-
ing to e–s/P, where the decay length, P, is the persistence
length of the chain. The stiffer the chain, the longer the
persistence length. For dsDNA in physiological salt, the
persistence length is approximately 50 nm. Forces of the
order kBT/P = 0.1 pN, where kBis the Boltzmann constant
and T is temperature, are required to align polymer seg-
ments with these dimensions.
Extension experiments have provided the strictest test to
date of these two models [4,6,7,12,13•]. Results, shown in
Figure 1, indicate that, even though the FJC model can
describe the behavior of dsDNA in the limit of low forces, it
Single-molecule studies of DNA mechanics
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