Konstantin V. Klenin

A Brownian dynamics program for the simulation of linear and circular DNA and other wormlike chain polyelectrolytes.

For the interpretation of solution structural and dynamic data of linear and circular DNA molecules in the kb range, and for the prediction of the effect of local structural changes on the global conformation of such DNAs, we have developed an efficient and easy way to set up a program based on a second-order explicit Brownian dynamics algorithm. The DNA is modeled by a chain of rigid segments interacting through harmonic spring potentials for bending, torsion, and stretching. The electrostatics are handled using precalculated energy tables for the interactions between DNA segments as a function of relative orientation and distance. Hydrodynamic interactions are treated using the Rotne-Prager tensor. While maintaining acceptable precision, the simulation can be accelerated by recalculating this tensor only once in a certain number of steps.

Computation of writhe in modeling of supercoiled DNA.

We describe four previously unpublished methods allowing the computation of the writhe for a supercoiled DNA molecule modeled by a polymer chain consisting of straight segments. These methods are compared with each other in terms of computational efficiency and the scope of their applicability is discussed.

Salt-dependent DNA superhelix diameter studied by small angle neutron scattering measurements and Monte Carlo simulations.

Using small angle neutron scattering we have measured the static form factor of two different superhelical DNAs, p1868 (1868 bp) and pUC18 (2686 bp), in dilute aqueous solution at salt concentrations between 0 and 1.5 M Na+ in 10 mM Tris at 0% and 100% D2O. For both DNA molecules, the theoretical static form factor was also calculated from an ensemble of Monte Carlo configurations generated by a previously described model. Simulated and measured form factors of both DNAs showed the same behavior between 10 and 100 mM salt concentration: An undulation in the scattering curve at a momentum transfer q = 0.5 nm-1 present at lower concentration disappears above 100 mM. The position of the undulation corresponds to a distance of approximately 10-20 nm. This indicated a change in the DNA superhelix diameter, as the undulation is not present in the scattering curve of the relaxed DNA. From the measured scattering curves of superhelical DNA we estimated the superhelix diameter as a function of Na+ concentration by a quantitative comparison with the scattering curve of relaxed DNA. The ratio of the scattering curves of superhelical and relaxed DNA is very similar to the form factor of a pair of point scatterers. We concluded that the distance of this pair corresponds to the interstrand separation in the superhelix. The computed superhelix diameter of 16.0 +/- 0.9 nm at 10 mM decreased to 9.0 +/- 0.7 nm at 100 mM salt concentration. Measured and simulated scattering curves agreed almost quantitatively, therefore we also calculated the superhelix diameter from the simulated conformations. It decreased from 18.0 +/- 1.5 nm at 10 mM to 9.4 +/- 1.5 nm at 100 mM salt concentration. This value did not significantly change to lower values at higher Na+ concentration, in agreement with results obtained by electron microscopy, scanning force microscopy imaging in aqueous solution, and recent MC simulations, but in contrast to the observation of a lateral collapse of the DNA superhelix as indicated by cryo-electron microscopy studies.

Looping Dynamics of Linear DNA Molecules and the Effect of DNA Curvature: A Study by Brownian Dynamics Simulation

A Brownian dynamics (BD) model described in the accompanying paper (Klenin, K., H. Merlitz, and J. Langowski. 1998. A Brownian dynamics program for the simulation of linear and circular DNA, and other wormlike chain polyelectrolytes. Biophys. J. 74:000-000) has been used for computing the end-to-end distance distribution function, the cyclization probability, and the cyclization kinetics of linear DNA fragments between 120 and 470 basepairs with optional insertion of DNA bends. Protein-mediated DNA loop formation was modeled by varying the reaction distance for cyclization between 0 and 10 nm. The low cyclization probability of DNA fragments shorter than the Kuhn length (300 bp) is enhanced by several orders of magnitude when the cyclization is mediated by a protein bridge of 10 nm diameter, and/or when the DNA is bent. From the BD trajectories, end-to-end collision frequencies were computed. Typical rates for loop formation of linear DNAs are 1.3 x 10(3) s(-1) (235 bp) and 4.8 x 10(2) s(-1) (470 bp), while the insertion of a 120 degree bend in the center increases this rate to 3.0 x 10(4) s(-1) (235 bp) and 5.5 x 10(3) s(-1) (470 bp), respectively. The duration of each encounter is between 0.05 and 0.5 micros for these DNAs. The results are discussed in the context of the interaction of transcription activator proteins.

Facilitated diffusion of DNA-binding proteins

The diffusion-controlled limit of reaction times for site-specific DNA-binding proteins is derived from first principles. We follow the generally accepted concept that a protein propagates via two competitive modes, a three-dimensional diffusion in space and a one-dimensional sliding along the DNA. However, our theoretical treatment of the problem is new. The accuracy of our analytical model is verified by numerical simulations. The results confirm that the unspecific binding of protein to DNA, combined with sliding, is capable to reduce the reaction times significantly.

Branched DNA That Forms a Solid at 95 °C

Control over the structure of materials may be achieved by using predictable interactions, such as base pairing. Base pairing between DNA strands is emerging as one of the most versatile design principles of nanoconstruction. A range of hybridization and folding motifs of linear and circular DNA have been reported. The flexibility of the design has been further expanded by linking oligonucleotides to synthetic branching elements or “cores”. 5] The resulting construct can have properties not found in natural DNA. This includes DNA-coated gold nanoparticles that assemble into three-dimensional aggregates, the melting transitions of which are exceptionally sharp. Nanoparticle size and linker structure affect the association behavior, and crystallization may be induced in favorable cases. For DNA hybrids with organic cores, the effect of linking the DNA to a branching element can be more dramatic still. Four-arm hybrid 1 (Scheme 1) with its tetrahedral core was recently shown to assemble into a macroscopic material, even though its oligonucleotide arms are just dimers. The assembly process is sequence specific, as demonstrated by mismatch controls, but the UV-melting transitions are broad, not sharp as in the case of gold nanoparticles. Shortly after the publication of the unusually stable assemblies of 1, the first designed DNA crystals were reported. The fact that the association of the rigid triangle motifs that serve as rigid “cores” in these crystals is also driven by no more than dimer “sticky ends” again suggests that the rules for 3D construction of periodic assemblies are quite different from those of linear DNA.

Modelling proteins: conformational sampling and reconstruction of folding kinetics.

In the last decades biomolecular simulation has made tremendous inroads to help elucidate biomolecular processes in-silico. Despite enormous advances in molecular dynamics techniques and the available computational power, many problems involve long time scales and large-scale molecular rearrangements that are still difficult to sample adequately. In this review we therefore summarise recent efforts to fundamentally improve this situation by decoupling the sampling of the energy landscape from the description of the kinetics of the process. Recent years have seen the emergence of many advanced sampling techniques, which permit efficient characterisation of the relevant family of molecular conformations by dispensing with the details of the short-term kinetics of the process. Because these methods generate thermodynamic information at best, they must be complemented by techniques to reconstruct the kinetics of the process using the ensemble of relevant conformations. Here we review recent advances for both types of methods and discuss their perspectives to permit efficient and accurate modelling of large-scale conformational changes in biomolecules. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Computational analysis of the chiral action of type II DNA topoisomerases

It was found recently that bacterial type II DNA topoisomerase, topo IV, is much more efficient in relaxing (+) DNA supercoiling than (-) supercoiling. This means that the DNA-enzyme complex is chiral. This chirality can appear upon binding the first segment that participates in the strand passing reaction (G segment) or only after the second segment (T segment) joins the complex. The former possibility is analyzed here. We assume that upon binding the enzyme, the G segment forms a part of left-handed helical turn. This model is an extension of the hairpin model introduced earlier to explain simplification of DNA topology by these enzymes. Using statistical-mechanical simulation of DNA properties, we estimated different consequences of the model: (1) relative rates of relaxation of (+) and (-) supercoiling by the enzyme; (2) the distribution of positions of the G segment in supercoiled molecules; (3) steady-state distribution of knots in circular molecules created by the topoisomerase; (4) the variance of topoisomer distribution created by the enzyme; (5) the effect of (+) and (-) supercoiling on the binding topo II with G segment. The simulation results are capable of explaining nearly all available experimental data, at least semiquantitatively. A few predictions obtained in the model analysis can be tested experimentally.

Kinetics of Site–Site Interactions in Supercoiled DNA with Bent Sequences

A curved DNA segment is known to adopt a preferred end loop localization in superhelical (sc) DNA and thus may organize the overall conformation of the molecule. Through this process it influences the probability of site juxtaposition. We addressed the effect of a curvature on site-site interactions quantitatively by measuring the kinetics of cross-linking of two biotinylated positions in scDNA by streptavidin. The DNA was biotinylated at either symmetric or asymmetric positions with respect to a curved insert via triplex-forming oligonucleotides (TFOs) modified with biotin. We used a quench-flow device to mix the DNA with the protein and scanning force microscopy to quantify the reaction products. As a measure of the interaction probability, rate constants of cross-linking and local concentrations j(M) of one biotinylated site in the vicinity of the other were determined and compared to Monte Carlo simulations for corresponding DNAs. In good agreement with the simulations, a j(M) value of 1.74 microM between two sites 500bp apart was measured for an scDNA without curvature. When a curvature was centered between the sites, the interaction probability increased about twofold over the DNA without curvature, significantly less than expected from the simulations. However, the relative differences of the interaction probabilities due to varied biotin positions with respect to the curvature agreed quantitatively with the theory.

Derivatives of molecular surface area and volume: Simple and exact analytical formulas

The computational effort of biomolecular simulations can be significantly reduced by means of implicit solvent models in which the energy generally contains a correction depending on the surface area and/or the volume of the molecule. In this article, we present simple derivation of exact, easy‐to‐use analytical formulas for these quantities and their derivatives with respect to atomic coordinates. In addition, we provide an efficient, linear‐scaling algorithm for the construction of the power diagram required for practical implementation of these formulas. Our approach is implemented in a C++ header‐only template library.