Because of thermal fluctuations, a polymer chain at room temperature will be bent. WLC and our model both predict that the molecule's observed conformations will be drawn from a certain probability distribution of shapes, obtained by combining bends distributed according to Boltzmann statistics with some energy function E(θ). Our task is to evaluate E(θ) from data.A comprehensive theory of DNA bending on short length scales must also include the twist degrees of freedom [1], as well as inhomogeneities from sequence [2,3]. Indeed, recent cyclization experiments suggest that the harmonic-elasticity model for the twist response of DNA also overstates the energetic cost of twist when curvature is high [4]. Thus, it seems likely that the twist energy function must be modified in a manner analogous to the one we have proposed for the bending energy. We leave this generalization to future work. For the random sequences studied here, we expect bending anisotropy to be a small effect for behavior on length scales greater than the helical pitch of 3.5 nm. Sequence dependent curvature, in natural DNA and in modified constructs with nonstandard bases, has been observed in AFM studies [5,6]; again we leave the extension of our model to include sequence to future work. A.2 Scale dependence in equilibrium statistical physicsHere we briefly elaborate on some ideas of scale dependence in equilibrium statistical physics, applied to our problem.The conformation of a macromolecule like DNA can usefully be described on any of several length scales. That is, when describing the molecule's behavior on a length scale ℓ exp larger than the size of individual atoms, we can often simplify our description by imagining the macromolecule to be composed

Over the past few years, it has become increasingly apparent that double-stranded RNA (dsRNA) plays a far greater role in the life cycle of a cell than previously expected. Numerous proteins, including helicases, polymerases, and nucleases interact specifically with the double helix of dsRNA. To understand the detailed nature of these dsRNA-protein interactions, the (bio)chemical, electrostatic, and mechanical properties of dsRNA need to be fully characterized. We present measurements of the persistence length of dsRNA using two different single-molecule techniques: magnetic tweezers and atomic force microscopy. We deduce a mean persistence length for long dsRNA molecules of 63.8 +/- 0.7 nm from force-extension measurements with the magnetic tweezers. We present atomic force microscopy images of dsRNA and demonstrate a new method for analyzing these, which yields an independent, yet consistent value of 62 +/- 2 nm for the persistence length. The introduction of these single-molecule techniques for dsRNA analysis opens the way for real-time, quantitative analysis of dsRNA-protein interactions.

The human DNA repair protein RAD51 is the crucial component of helical nucleoprotein filaments that drive homologous recombination. The molecular mechanistic details of how this structure facilitates the requisite DNA strand rearrangements are not known but must involve dynamic interactions between RAD51 and DNA. Here, we report the real-time kinetics of human RAD51 filament assembly and disassembly on individual molecules of both single- and double-stranded DNA, as measured using magnetic tweezers. The relative rates of nucleation and filament extension are such that the observed filament formation consists of multiple nucleation events that are in competition with each other. For varying concentration of RAD51, a Hill coefficient of 4.3 ± 0.5 is obtained for both nucleation and filament extension, indicating binding to dsDNA with a binding unit consisting of multiple (≥4) RAD51 monomers. We report Monte Carlo simulations that fit the (dis)assembly data very well. The results show that, surprisingly, human RAD51 does not form long continuous filaments on DNA. Instead each nucleoprotein filament consists of a string of many small filament patches that are only a few tens of monomers long. The high flexibility and dynamic nature of this arrangement is likely to facilitate strand exchange.

Recombinase proteins assembled into helical filaments on DNA are believed to be the catalytic core of homologous recombination. The assembly, disassembly and dynamic rearrangements of this structure must drive the DNA strand exchange reactions of homologous recombination. The sensitivity of eukaryotic recombinase activity to reaction conditions in vitro suggests that the status of bound nucleotide cofactors is important for function and possibly for filament structure. We analyzed nucleoprotein filaments formed by the human recombinase Rad51 in a variety of conditions on double-stranded and single-stranded DNA by scanning force microscopy. Regular filaments with extended double-stranded DNA correlated with active in vitro recombination, possibly due to stabilizing the DNA products of these assays. Though filaments formed readily on single-stranded DNA, they were very rarely regular structures. The irregular structure of filaments on single-stranded DNA suggests that Rad51 monomers are dynamic in filaments and that regular filaments are transient. Indeed, single molecule force spectroscopy of Rad51 filament assembly and disassembly in magnetic tweezers revealed protein association and disassociation from many points along the DNA, with kinetics different from those of RecA. The dynamic rearrangements of proteins and DNA within Rad51 nucleoprotein filaments could be key events driving strand exchange in homologous recombination.

The DNA strand-exchange reactions defining homologous recombination involve transient, nonuniform allosteric interactions between recombinase proteins and their DNA substrates. To study these mechanistic aspects of homologous recombination, we produced functional fluorescent human RAD51 recombinase and visualized recombinase interactions with single DNA molecules in both static and dynamic conditions. We observe that RAD51 nucleates filament formation at multiple sites on double-stranded DNA. This avid nucleation results in multiple RAD51 filament segments along a DNA molecule. Analysis of fluorescent filament patch size and filament kinks from scanning force microscopy (SFM) images indicate nucleation occurs minimally once every 500 bp. Filament segments did not rearrange along DNA, indicating tight association of the ATP-bound protein. The kinetics of filament disassembly was defined by activating ATP hydrolysis and following individual filaments in real time.

RecA, the key protein in homologous recombination, performs its actions as a helical filament on single-stranded DNA (ssDNA). ATP hydrolysis makes the RecA–ssDNA filament dynamic and is essential for successful recombination. RecA has been studied extensively by single-molecule techniques on double-stranded DNA (dsDNA). Here we directly probe the structure and kinetics of RecA interaction with its biologically most relevant substrate, long ssDNA molecules. We find that RecA ATPase activity is required for the formation of long continuous filaments on ssDNA. These filaments both nucleate and extend with a multimeric unit as indicated by the Hill coefficient of 5.4 for filament nucleation. Disassembly rates of RecA from ssDNA decrease with applied stretching force, corresponding to a mechanism where protein-induced stretching of the ssDNA aids in the disassembly. Finally, we show that RecA–ssDNA filaments can reversibly interconvert between an extended, ATP-bound, and a compressed, ADP-bound state. Taken together, our results demonstrate that ATP hydrolysis has a major influence on the structure and state of RecA filaments on ssDNA.

Homologous recombination, the exchange of strands between different DNA molecules, is essential for proper maintenance and accurate duplication of the genome. Using magnetic tweezers, we monitor RecA-driven homologous recombination of individual DNA molecules in real time. We resolve several key aspects of DNA structure during and after strand exchange. Changes in DNA length and twist yield helical parameters for the protein-bound three-stranded structure in conditions in which ATP was not hydrolyzed. When strand exchange was completed under ATP hydrolysis conditions that allow protein dissociation, a "D wrap" structure formed. During homologous recombination, strand invasion at one end and RecA dissociation at the other end occurred at the same rate, and our single-molecule analysis indicated that a region of only about 80 bp is actively involved in the synapsis at any time during the entire reaction involving a long ( approximately 1 kb) region of homology.

Nucleosome positioning dictates eukaryotic DNA compaction and access. To predict nucleosome positions in a statistical mechanics model, we exploited the knowledge that nucleosomes favor DNA sequences with specific periodically occurring dinucleotides. Our model is the first to capture both dyad position within a few base pairs, and free binding energy within 2 kBT, for all the known nucleosome positioning sequences. By applying Percus’s equation to the derived energy landscape, we isolate sequence effects on genome-wide nucleosome occupancy from other factors that may influence nucleosome positioning. For both in vitro and in vivo systems, three parameters suffice to predict nucleosome occupancy with correlation coefficients of respectively 0.74 and 0.66. As predicted, we find the largest deviations in vivo around transcription start sites. This relatively simple algorithm can be used to guide future studies on the influence of DNA sequence on chromatin organization.