Determining protein-induced DNA bending in force-extension experiments: theoretical analysis

Single-molecule dynamics of DNA gyrase in evolutionarily distant bacteria Mycobacterium tuberculosis and Escherichia coli

DNA gyrase is an essential nucleoprotein motor present in all bacteria and is a major target for antibiotic treatment of Mycobacterium tuberculosis (MTB) infection. Gyrase hydrolyzes ATP to add negative supercoils to DNA using a strand passage mechanism that has been investigated using biophysical and biochemical approaches. To analyze the dynamics of substeps leading to strand passage, single-molecule rotor bead tracking (RBT) has been used previously to follow real-time supercoiling and conformational transitions in Escherichia coli (EC) gyrase. However, RBT has not yet been applied to gyrase from other pathogenically relevant bacteria, and it is not known whether substeps are conserved across evolutionarily distant species. Here, we compare gyrase supercoiling dynamics between two evolutionarily distant bacterial species, MTB and EC. We used RBT to measure supercoiling rates, processivities, and the geometries and transition kinetics of conformational states of purified gyrase proteins in complex with DNA. Our results show that E. coli and MTB gyrases are both processive, with the MTB enzyme displaying velocities ∼5.5× slower than the EC enzyme. Compared with EC gyrase, MTB gyrase also more readily populates an intermediate state with DNA chirally wrapped around the enzyme, in both the presence and absence of ATP. Our substep measurements reveal common features in conformational states of EC and MTB gyrases interacting with DNA but also suggest differences in populations and transition rates that may reflect distinct cellular needs between these two species.

Dynamic coupling between conformations and nucleotide states in DNA gyrase

Gyrase is an essential bacterial molecular motor that supercoils DNA using a conformational cycle in which chiral wrapping of > 100 base pairs confers directionality on topoisomerization. To understand the mechanism of this nucleoprotein machine, global structural transitions must be mapped onto the nucleotide cycle of ATP binding, hydrolysis and product release. Here we investigate coupling mechanisms using single-molecule tracking of DNA rotation and contraction during Escherichia coli gyrase activity under varying nucleotide conditions. We find that ADP must be exchanged for ATP to drive the rate-limiting remodeling transition that generates the chiral wrap. ATP hydrolysis accelerates subsequent duplex strand passage and is required for resetting the enzyme and recapturing transiently released DNA. Our measurements suggest how gyrase coordinates DNA rearrangements with the dynamics of its ATP-driven protein gate, how the motor minimizes futile cycles of ATP hydrolysis and how gyrase may respond to changing cellular energy levels to link gene expression with metabolism.

Simulation of DNA Supercoil Relaxation

Several recent single-molecule experiments observe the response of supercoiled DNA to nicking endonucleases and topoisomerases. Typically in these experiments, indirect measurements of supercoil relaxation are obtained by observing the motion of a large micron-sized bead. The bead, which also serves to manipulate DNA, experiences significant drag and thereby obscures supercoil dynamics. Here we employ our discrete wormlike chain model to bypass experimental limitations and simulate the dynamic response of supercoiled DNA to a single strand nick. From our simulations, we make three major observations. First, extension is a poor dynamic measure of supercoil relaxation; in fact, the linking number relaxes so fast that it cannot have much impact on extension. Second, the rate of linking number relaxation depends upon its initial partitioning into twist and writhe as determined by tension. Third, the extensional response strongly depends upon the initial position of plectonemes.

Gold rotor bead tracking for high-speed measurements of DNA twist, torque and extension

Simultaneous measurements of DNA twist and extension have been used to measure physical properties of the double helix and to characterize structural dynamics and mechanochemistry in nucleoprotein complexes. However, the spatiotemporal resolution of twist measurements has been limited by the use of angular probes with large rotational drags, preventing the detection of short-lived intermediates or small angular steps. Here we introduce AuRBT, demonstrating a >100X improvement in time resolution over previous techniques. AuRBT employs gold nanoparticles as bright low-drag rotational and extensional probes, relying on instrumentation that combines magnetic tweezers with objective-side evanescent darkfield microscopy. In an initial application to molecular motor mechanism, we have examined the high-speed structural dynamics of DNA gyrase, revealing an unanticipated transient intermediate. AuRBT also enables direct measurements of DNA torque with >50X shorter integration times than previous techniques; here we demonstrate high-resolution torque spectroscopy by mapping the conformational landscape of a Z-forming DNA sequence.

DNA phosphate crowding correlates with protein cationic side chain density and helical curvature in protein/DNA crystal structures

Sequence-specific binding of proteins to their DNA targets involves a complex spectrum of processes that often induce DNA conformational variation in the bound complex. The forces imposed by protein binding that cause the helical deformations are intimately interrelated and difficult to parse or rank in importance. To investigate the role of electrostatics in helical deformation, we quantified the relationship between protein cationic residue density (Cpc) and DNA phosphate crowding (Cpp). The correlation between Cpc and Cpp was then calculated for a subset of 58 high resolution protein-DNA crystal structures. Those structures containing strong Cpc/Cpp correlation (>±0.25) were likely to contain DNA helical curvature. Further, the correlation factor sign predicted the direction of helical curvature with positive (16 structures) and negative (seven structures) correlation containing concave (DNA curved toward protein) and convex (DNA curved away from protein) curvature, respectively. Protein-DNA complexes without significant Cpc/Cpp (36 structures) correlation (-0.25<0<0.25) tended to contain DNA without significant curvature. Interestingly, concave and convex complexes also include more arginine and lysine phosphate contacts, respectively, whereas linear complexes included essentially equivalent numbers of Lys/Arg phosphate contacts. Together, these findings suggest an important role for electrostatic interactions in protein-DNA complexes involving helical curvature.

Recent developments in single-molecule DNA mechanics

Over the past two decades, measurements on individual stretched and twisted DNA molecules have helped define the basic elastic properties of the double helix and enabled real-time functional assays of DNA-associated molecular machines. Recently, new magnetic tweezers approaches for simultaneously measuring freely fluctuating twist and extension have begun to shed light on the structural dynamics of large nucleoprotein complexes. Related technical advances have facilitated direct measurements of DNA torque, contributing to a better understanding of abrupt structural transitions in mechanically stressed DNA. The new measurements have also been exploited in studies that hint at a developing synergistic relationship between single-molecule manipulation and structural DNA nanotechnology.

ATP binding controls distinct structural transitions of Escherichia coli DNA gyrase in complex with DNA

DNA gyrase is a molecular motor that harnesses the free energy of ATP hydrolysis to introduce negative supercoils into DNA. A critical step in this reaction is the formation of a chiral DNA wrap. Here we observe gyrase structural dynamics using a single-molecule assay in which gyrase drives the processive, stepwise rotation of a nanosphere attached to the side of a stretched DNA molecule. Analysis of rotational pauses and measurements of DNA contraction reveal multiple ATP-modulated structural transitions. DNA wrapping is coordinated with the ATPase cycle and proceeds by way of an unanticipated structural intermediate that dominates the kinetics of supercoiling. Our findings reveal a conformational landscape of loosely coupled transitions funneling the motor toward productive energy transduction, a feature that may be common to the reaction cycles of other DNA and protein remodeling machines.

Tightness of knots in a polymer chain

It was predicted recently that sufficiently complex knots on a linear wormlike chain can have a metastable size, preventing their spontaneous expansion. We tested this prediction via computer simulations for 7(1) and 10(151) knots. We calculated the equilibrium distributions of knot size S for both knots. By using the umbrella sampling, we were able to obtain the distributions over a wide range of S values. The distributions were converted into the dependencies of the free energy on the knot size. The obtained free energy profiles have no pronounced local minima, so there are no metastable knot sizes for these knots. We also performed Brownian dynamics simulation of 7(1) knot relaxation that started from a very tight knot conformation. The simulation showed that knot expansion is a fast process compared to knot displacement along the chain contour by diffusion.