Dynamics of single molecules of DNA (with W. E. Moerner, Stanford)
Many single-molecule experiments have focused on the shape and dynamics of DNA tethered to a surface or stretched between a pair of beads, but much less attention has been paid to the dynamics of single molecules in their free-solution, relaxed, conformation. We used the ABEL trap to immobilize single molecules l-DNA and to study the internal dynamics of trapped molecules. We labeled the DNA with the intercalating dye YOYO-1. This dye lights up the molecule like a string of Christmas lights. Then we took ~60,000 frames of high speed video of single molecules fluctuating in the trap.
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This movie shows a typical piece of data. |
We analyzed these images to learn about:
- The average shape of a molecule of DNA
- The deviations about this average shape
- The dynamics of how one shape becomes another shape
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We learned that the average distribution of mass about the center of mass does not follow a Gaussian distribution. A simple analytical model quantitatively agrees with the observed distribution. The key concept is that each piece of the DNA follows a Gaussian distribution about the center of mass, but different pieces follow different distributions (the ends wander further from the center of mass than does the middle). The total density distribution is the sum of many Gaussians of different widths, and thus is not Gaussian--even in the complete absence of excluded volume or other non-ideal interactions. The figure shows a cross-section of the time-averaged density distribution, a fit to a Gaussian, and a fit to the model that includes the contributions from each element of the DNA chain. The formula for the fit is given in our PRL paper on DNA. |
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By performing Principal Components Analysis (PCA) we decomposed the shape fluctuations into a set of normal modes, akin to the vibrational modes of a drumhead. We developed an analytical model for these principal components that quantitatively agrees with our data. The eigenvalue associated with each principal component is a measure of the entropic stiffness of the DNA in that mode. The eigenvalues and the comparison to theory are discussed in our PNAS paper on DNA. |
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Although our data is limited to 2-D projections of the 3-D conformation of the DNA, the model can easily be extended to any number of dimensions. Below is an image of the principal components of a random walk in 3-D. PCA provides a powerful tool for describing the variability in random walks, and this technique might be useful in a fields outside of polymer physics. |
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How does one shape fluctuation become another? To address this question we looked at the cross-correlation of fluctuations at one position and time with the fluctuations at some other position and some other time. These cross-correlations are related to the internal mechanical response of the polymer by the fluctuation-dissipation theorem. Thus we were able to probe the mechanical response of DNA without ever actually touching it: we relied on thermal fluctuations to provide all possible perturbations to the molecule, and then filtered the data to extract information about any particular perturbation of interest. The movies show the relaxation response for perturbations arising at different points in the DNA. |
By analyzing the dynamics of the shape fluctuations in the basis of Principal Components we showed that the dynamics are influenced by nonlinear hydrodynamic interactions between the fluctuating segments.
Documentation:
- Adam Cohen, W. E. Moerner: Principal Components Analysis of shape fluctuations of single DNA molecules, PNAS, 104, 12622-12627, 31 July 2007. Journal link and Supporting Material and Movies.
- Adam Cohen, W. E. Moerner: Internal mechanical response of a polymer in solution, Phys. Rev. Lett., 98, 116001 (2007). Supplementary material.