Abstract:A new, computationally efficient Monte Carlo approach has been developed to estimate the ring-closure properties of short, realistically modeled DNA chains. The double helix is treated at the level of base-pair steps using an elastic potential that accounts for the sequencedependent variability in the intrinsic structure and elastic moduli of the base-pair steps, including the known coupling of conformational variables. Rather than using traditional Metropolis-Monte Carlo techniques to generate representative configurations, a Gaussian sampling method is introduced to construct three-dimensional structures from linear combinations of the rigid-body parameters defining the relative orientation and displacement of successive base pairs. The computation of the J factor, the well-known ratio of the equilibrium constants for cyclization vs bimolecular association of a linear molecule, takes into account restrictions on the displacement and directions of the base pairs joined in ring closure, including the probability that the end-toend vector is null and the terminal base pairs coincide. The increased sample sizes needed to assess the likelihood that very short chains satisfy these criteria are attained using the Alexandrowicz half-chain sampling enhancement technique in combination with selective linkage of the two-half-chain segments. The method is used to investigate the cyclization properties of arbitrary-length DNA with greatly enhanced sampling sizes, i.e., O(10 14 ) configurations, and to estimate J factors lower than 0.1 pM with high accuracy. The methodology has been checked against classic theoretical predictions of the cyclization properties of an ideal, inextensible, naturally straight, DNA elastic rod and then applied to investigate the extent to which one can account for the unexpectedly large J factors of short DNA chains without the need to invoke significant distortions of double helical structure. Several well-known structural features of DNAs including the presence of intrinsic curvature, roll-twist coupling, or enhanced pyrimidine-purine deformabilitysbring the computed J factors in line with the observed data. Moreover, periodically distributed roll-twist coupling reduces the magnitude of oscillations in J, seen in plots of J vs chain length, to the extent found experimentally.

The E. coli Lac repressor is the classic textbook example of a protein that attaches to widely spaced sites along a genome and forces the intervening DNA into a loop. The short loops implicated in the regulation of the lac operon suggest the involvement of factors other than DNA and repressor in gene control. The molecular simulations presented here examine two likely structural contributions to the in-vivo looping of bacterial DNA: the distortions of the double helix introduced upon association of the highly abundant, nonspecific nucleoid protein HU and the large-scale deformations of the repressor detected in low-resolution experiments. The computations take account of the three-dimensional arrangements of nucleotides and amino acids found in crystal structures of DNA with the two proteins, the natural rest state and deformational properties of protein-free DNA, and the constraints on looping imposed by the conformation of the repressor and the orientation of bound DNA. The predicted looping propensities capture the complex, chain-length-dependent variation in repression efficacy extracted from gene expression studies and in vitro experiments and reveal unexpected chain-length-dependent variations in the uptake of HU, the deformation of repressor, and the folding of DNA. Both the opening of repressor and the presence of HU, at levels approximating those found in vivo, enhance the probability of loop formation. HU affects the global organization of the repressor and the opening of repressor influences the levels of HU binding to DNA. The length of the loop determines whether the DNA adopts antiparallel or parallel orientations on the repressor, whether the repressor is opened or closed, and how many HU molecules bind to the loop. The collective behavior of proteins and DNA is greater than the sum of the parts and hints of ways in which multiple proteins may coordinate the packaging and processing of genetic information.

The histone-like HU (heat unstable) protein plays a key role in the organization and regulation of the Escherichia coli genome. The nonspecific nature of HU binding to DNA complicates analysis of the mechanism by which the protein contributes to the looping of DNA. Conventional models of the looping of HU-bound duplexes attribute the changes in biophysical properties of DNA brought about by the random binding of protein to changes in the effective parameters of an ideal helical wormlike chain. Here, we introduce a novel Monte Carlo approach to study the effects of nonspecific HU binding on the configurational properties of DNA directly. We randomly decorated segments of an ideal double-helical DNA with HU molecules that induce the bends and other structural distortions of the double helix find in currently available X-ray structures. We find that the presence of HU at levels approximating those found in the cell reduces the persistence length by roughly threefold compared with that of naked DNA. The binding of protein has particularly striking effects on the cyclization properties of short duplexes, altering the dependence of ring closure on chain length in a way that cannot be mimicked by a simple wormlike model and accumulating at higher-than-expected levels on successfully closed chains. Moreover, the uptake of protein on small minicircles depends on chain length, taking advantage of the HU-induced deformations of DNA structure to facilitate ligation. Circular duplexes with bound HU show much greater propensity than protein-free DNA to exist as negatively supercoiled topoisomers, suggesting a potential role of HU in organizing the bacterial nucleoid. The local bending and undertwisting of DNA by HU, in combination with the number of bound proteins, provide a structural rationale for the condensation of DNA and the observed expression levels of reporter genes in vivo.

A theoretical framework is presented to model ion and DNA translocation across a nanopore confinement under an applied electric field. A combined Grand Canonical Monte Carlo Brownian Dynamics (GCMC/BD) algorithm offers a general approach to study ion permeation through wide molecular pores with a direct account of ion–ion and ion–DNA correlations. This work extends previously developed theory by incorporating the recently developed coarse-grain polymer model of DNA by de Pablo and colleagues [Knotts, T. A.; Rathore, N.; Schwartz, D. C.; de Pablo, J. J. J. Chem. Phys. 2007, 126] with explicit ions for simulations of polymer dynamics. Atomistic MD simulations were used to guide model developments. The power of the developed scheme is illustrated with studies of single-stranded DNA (ss-DNA) oligomer translocation in two model cases: a cylindrical pore with a varying radius and a well-studied experimental system, the staphylococcal α-hemolysin channel. The developed model shows good agreement with experimental data for model studies of two homopolymers: ss-poly(dA)n and ss-poly(dC)n. The developed protocol allows for direct evaluation of different factors (charge distribution and pore shape and size) controlling DNA translocation in a variety of nanopores.