Traveling Salesman Finds Random Walk: A Curve Reconstruction Algorithm for Supercoiled DNA.

DNA supercoiling plays an important role in a variety of cellular processes, including transcription, replication, and DNA compaction. To fully understand these processes, we must uncover and characterize the dynamics of supercoiled DNA. However, supercoil dynamics are difficult to access because of the wide range of relevant length and timescales. In this work, we present an algorithm to reconstruct the arrangement of identical fluorescent particles distributed around a circular DNA molecule, given their three-dimensional trajectories through time. We find that this curve reconstruction problem is analogous to solving the traveling salesman problem. We demonstrate that our approach converges to the correct arrangement with a sufficiently long observation time. In addition, we show that the time required to accurately reconstruct the fluorophore arrangement is reduced by increasing the fluorophore density or reducing the level of supercoiling. This curve reconstruction algorithm, when paired with next-generation super-resolution imaging systems, could be used to access and thereby advance our understanding of supercoil dynamics.

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.

Structural ensemble and dynamics of toroidal-like DNA shapes in bacteriophage ϕ29 exit cavity.

In the bacteriophage ϕ29, DNA is packed into a preassembled capsid from which it ejects under high pressure. A recent cryo-EM reconstruction of ϕ29 revealed a compact toroidal DNA structure (30-40 basepairs) lodged within the exit cavity formed by the connector-lower collar protein complex. Using multiscale models, we compute a detailed structural ensemble of intriguing DNA toroids of various lengths, all highly compatible with experimental observations. In particular, coarse-grained (elastic rod) and atomistic (molecular dynamics) models predict the formation of DNA toroids under significant compression, a largely unexplored state of DNA. Model predictions confirm that a biologically attainable compressive force of 25 pN sustains the toroid and yields DNA electron density maps highly consistent with the experimental reconstruction. The subsequent simulation of dynamic toroid ejection reveals large reactions on the connector that may signal genome release.

FRET studies of a landscape of Lac repressor-mediated DNA loops.

DNA looping mediated by the Lac repressor is an archetypal test case for modeling protein and DNA flexibility. Understanding looping is fundamental to quantitative descriptions of gene expression. Systematic analysis of LacI•DNA looping was carried out using a landscape of DNA constructs with lac operators bracketing an A-tract bend, produced by varying helical phasings between operators and the bend. Fluorophores positioned on either side of both operators allowed direct Förster resonance energy transfer (FRET) detection of parallel (P1) and antiparallel (A1, A2) DNA looping topologies anchored by V-shaped LacI. Combining fluorophore position variant landscapes allows calculation of the P1, A1 and A2 populations from FRET efficiencies and also reveals extended low-FRET loops proposed to form via LacI opening. The addition of isopropyl-ß-D-thio-galactoside (IPTG) destabilizes but does not eliminate the loops, and IPTG does not redistribute loops among high-FRET topologies. In some cases, subsequent addition of excess LacI does not reduce FRET further, suggesting that IPTG stabilizes extended or other low-FRET loops. The data align well with rod mechanics models for the energetics of DNA looping topologies. At the peaks of the predicted energy landscape for V-shaped loops, the proposed extended loops are more stable and are observed instead, showing that future models must consider protein flexibility.

DNA modeling reveals an extended lac repressor conformation in classic in vitro binding assays.

Protein-mediated DNA looping, such as that induced by the lactose repressor (LacI) of Escherichia coli, is a well-known gene regulation mechanism. Although researchers have given considerable attention to DNA looping by LacI, many unanswered questions about this mechanism, including the role of protein flexibility, remain. Recent single-molecule observations suggest that the two DNA-binding domains of LacI are capable of splaying open about the tetramerization domain into an extended conformation. We hypothesized that if recent experiments were able to reveal the extended conformation, it is possible that such structures occurred in previous studies as well. In this study, we tested our hypothesis by reevaluating two classic in vitro binding assays using a computational rod model of DNA. The experiments and computations evaluate the looping of both linear DNA and supercoiled DNA minicircles over a broad range of DNA interoperator lengths. The computed energetic minima align well with the experimentally observed interoperator length for optimal loop stability. Of equal importance, the model reveals that the most stable loops for linear DNA occur when LacI adopts the extended conformation. In contrast, for DNA minicircles, optimal stability may arise from either the closed or the extended protein conformation depending on the degree of supercoiling and the interoperator length.

A multiscale dynamic model of DNA supercoil relaxation by topoisomerase IB.

In this study, we report what we believe to be the first multiscale simulation of the dynamic relaxation of DNA supercoils by human topoisomerase IB (topo IB). We leverage our previous molecular dynamics calculations of the free energy landscape describing the interaction between a short DNA fragment and topo IB. Herein, this landscape is used to prescribe boundary conditions for a computational, elastodynamic continuum rod model of a long length of supercoiled DNA. The rod model, which accounts for the nonlinear bending, twisting, and electrostatic interaction of the (negatively charged) DNA backbone, is extended to include the hydrodynamic drag induced by the surrounding physiological buffer. Simulations for a 200-bp-long DNA supercoil in complex with topo IB reveal a relaxation timescale of ∼0.1-1.0 µs. The relaxation follows a sequence of cascading reductions in the supercoil linking number (Lk), twist (Tw), and writhe (Wr) that follow companion cascading reductions in the supercoil elastic and electrostatic energies. The novel (to our knowledge) multiscale modeling method may enable simulations of the entire experimental setup that measures DNA supercoiling and relaxation via single molecule magnetic trapping.

Computational analysis of looping of a large family of highly bent DNA by LacI.

Sequence-dependent intrinsic curvature of DNA influences looping by regulatory proteins such as LacI and NtrC. Curvature can enhance stability and control shape, as observed in LacI loops formed with three designed sequences with operators bracketing an A-tract bend. We explore geometric, topological, and energetic effects of curvature with an analysis of a family of highly bent sequences, using the elastic rod model from previous work. A unifying straight-helical-straight representation uses two phasing parameters to describe sequences composed of two straight segments that flank a common helically supercoiled segment. We exercise the rod model over this two-dimensional space of phasing parameters to evaluate looping behaviors. This design space is found to comprise two subspaces that prefer parallel versus anti-parallel binding topologies. The energetic cost of looping varies from 4 to 12 kT. Molecules can be designed to yield distinct binding topologies as well as hyperstable or hypostable loops and potentially loops that can switch conformations. Loop switching could be a mechanism for control of gene expression. Model predictions for linking numbers and sizes of LacI-DNA loops can be tested using multiple experimental approaches, which coupled with theory could address whether proteins or DNA provide the observed flexibility of protein-DNA loops.