Studying the thermal fluctuations of DNA molecules reveals not only a wealth of interesting equilibrium and nonequilibrium statistical mechanics, but is also of importance for understanding the dynamics of DNA in vivo. An instance of the latter is in the context of regulatory functions that require collaborative interactions of distant operator sites on the DNA molecule. These thermal fluctuations are extremely sensitive to mechanical constraints, such as supercoiling or mechanical tension in the DNA. The natural force scale fc on which these fluctuations are sensitive to tension is related to the persistence length lp by fc = kBT/lp = 80 fN, which is generally considered small for a crowded cellular environment. We are studying the dynamics of single DNA molecules under tension under equilibrium and non-equilibrium conditions using a modified scanning-line laser trap. This technique allows us to apply a constant force between 20 fN and 3 pN to a λ-DNA molecule while we study its behavior under two different conditions: 1) nonequilibrium studies in which we observe the relaxation trajectory of a highly extended DNA molecule as it returns to its equilibrium conformation against an applied optical force, and 2) equilibrium studies which measure fluctuations in the extension of the molecule about its mean with sub-millisecond time resolution as a function of its extension. In the nonequilibrium studies we find a marked deviation from predictions derived from the wormlike-chain (WLC) model for extended DNA molecules. In the equilibrium studies we compute the time-correlation functions of the fluctuations to determine their time constants, and model them with a simple bead-and-spring model. We observe a decrease of the fundamental time constant with increasing extension of the molecule. This suggests that the change in spring constant dominates changes in the intra-chain hydrodynamic coupling between segments as the Gaussian coil unravels into an extended conformation.
Studying the thermal fluctuations of DNA molecules reveals not only a wealth of interesting equilibrium and non-equilibrium statistical mechanics, but is also of importance for understanding the dynamics of DNA in vivo. An instance of the latter is in the context of regulatory functions that require collaborative interactions of distant operator sites on the DNA molecule. These thermal fluctuations are extremely sensitive to mechanical constraints, such as supercoiling or mechanical tension in the DNA. The natural force scale fc on which these fluctuations are sensitive to tension is related to the persistence length lp by fc = kBT/lp = 80 fN, which is generally considered small for a crowded cellular environment. We are studying the dynamics of single DNA molecules under tension under equilibrium conditions using a modified scanning-line laser trap. This technique allows us to apply a constant force between 20 fN and 3 pN to a λ-DNA molecule while we measure fluctuations of its extension with sub-millisecond time resolution. We compute the time-correlation functions of these fluctuations to determine their time constants, and model them with a simple bead-and-spring model. We observe a decrease of the fundamental time constant with increasing extension of the molecule. This suggests that the change in spring constant dominates changes in the intra-chain hydrodynamic coupling between segments as the Gaussian coil unravels into an extended conformation.
Optical tweezers are widely used to manipulate individual biomolecules. Conventionally, they hold a molecule at a constant extension while the restoring force of the molecule is measured. Many applications, however, require that the molecule be held under constant force while its extension is measured. We developed two all-optical trapping techniques that provide such constant-force conditions together with a fast extension measurement scheme. Our techniques are based on a scanning-line optical trap, which provides a one-dimensional flat optical potential well. A position-independent lateral force is generated either by a synchronous modulation of the laser intensity during the scan or the use of an asymmetrically shaped beam profile in the back focal plane of the microscope objective. The position of the trapped particle as a measure of the extension of an attached molecule is measured by monitoring the diffraction pattern of the forward-scattered laser light. The performance of these techniques, along with consideration for the design and calibration of the instrument is discussed.
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