Principal-components analysis of shape fluctuations of single DNA molecules

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 -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 longwavelength 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.DNA dynamics ͉ single molecule ͉ hydrodynamic interactions ͉ polymer physics T he simplest model of a linear polymer is a chain of beads joined by springs. In the Rouse model (1), each bead is a Brownian diffuser with the same drag and diffusion coefficients it would have in the absence of other beads. This model neglects the fact that each bead is subject to the time-varying flow fields produced by the other diffusing beads. This hydrodynamic interaction (HI) renders the underlying dynamics nonlinear. The Zimm model (2) includes hydrodynamics but restores linearity through a mean-field approximation: each bead is made to interact with the average conformation of its neighbors. Subsequent work has applied sophisticated mathematical techniques to calculate corrections resulting from fluctuating hydrodynamics (3-5), but the overall significance of internal HIs to polymer dynamics remains unresolved (6).The HI is the dominant long-range force for biomolecules in aqueous buffers: it couples motion of one part of a molecule to motion of possibly remote parts of the same molecule. Thus, understanding HIs is crucial to understanding the rates of molecular events that involve large-scale conformational change such as folding of proteins and RNA, packaging of DNA, motion of molecular motors, and motion of DNA-binding proteins.Long before polymers were studied at the single-molecule level, many clever experiments applied light scattering and neutron scattering as indirect probes of polymer dynamics (7,8). However, these experiments were (i) limited to probing only the lowest one or two internal relaxations and (ii) only yielded second-order ensemble-averaged correlation functions without measuring the entire distribution of underlying states. This second property of scattering techniques makes them insensitive to deviations from the linearized Zimm theory.Higgins and Benoit (9) and Quake et al. (10) used laser tweezers to study the dynamics of partially extended DNA in solution yet failed to find deviations from the Zimm theory. This negative result is not s...

Polymer Dynamics, Fluorescence Correlation Spectroscopy, and the Limits of Optical Resolution

“…[1][2][3][4][5]. However, this single-molecule imaging approach is restricted to the study of polymers which are larger in size than the diffraction limit of the imaging optics.…”

Redox cycling and kinetic analysis of single molecules of solution-phase nitrite reductase

“…This scheme results in the confinement of the object in a spatially homogeneous excitation volume for multiple seconds without immobilization and can be applied to single biomolecules substantially smaller than the large dielectric beads that are trapped with optical tweezers. We have previously used the ABEL trap to study conformational dynamics of single photosynthetic antenna proteins (6) and fluorescently labeled DNA molecules (12).…”

Controlling Brownian motion of single protein molecules and single fluorophores in aqueous buffer

“…This latency set a lower bound of 20 nm on the diameter of objects that could be trapped in water (although smaller objects could be trapped by increasing the viscosity of the solution [14]). With this software-based ABEL trap it was possible to observe the shape fluctuations of single DNA molecules in free solution [15,16] and to control the motion of nanoparticles subject to arbitrary force-fields [17].…”