Principal-components analysis of shape fluctuations of single DNA molecules

Adam E. Cohen* and
W. E. Moerner

Department of Chemistry, Stanford University, Stanford, CA 94305

Edited by Robert J. Silbey, Massachusetts Institute of Technology, Cambridge, MA, and approved March 15, 2007 (received for review October 25, 2006)

Abstract

Thermal fluctuations agitate molecules in solution over a broad range of times and distances. By passively watching the shape fluctuations of a thermally driven biomolecule, one can infer properties of the underlying interactions that determine the motion. We applied this concept to single molecules of fluorescently labeled λ-DNA, a key model system for polymer physics. In contrast to most other single-molecule DNA experiments, we examined the unstretched, equilibrium state of DNA by using an anti-Brownian electrokinetic trap to confine the center of mass of the DNA without perturbing its internal dynamics. We analyze the long-wavelength conformational normal modes, calculate their spring constants, and measure linear and nonlinear couplings between modes. The modes show strong signs of nonlinear hydrodynamics, a feature of the underlying equations of polymer dynamics that has not previously been reported and is neglected in the widely used Rouse and Zimm approximations.

Footnotes

*To whom correspondence should be sent at the present address:
Department of Chemistry, 12 Oxford Street, Harvard University, Cambridge, MA 02138.
E-mail: acohen{at}post.harvard.edu
Author contributions: A.E.C. and W.E.M. designed research; A.E.C. performed research; A.E.C. contributed new reagents/analytic tools; A.E.C. analyzed data; and A.E.C. and W.E.M. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
This article contains supporting information online at www.pnas.org/cgi/content/full/0610396104/DC1.
Abbreviations:

HI,

hydrodynamic interaction;

ABEL,

anti-Brownian electrokinetic;

PC,

principal component;

PCA,

principal-components analysis.