Twist propagation in dinucleosome arrays.

We present a Monte Carlo simulation study of the distribution and propagation of twist from one DNA linker to another for a two-nucleosome array subjected to externally applied twist. A mesoscopic model of the array that incorporates nucleosome geometry along with the bending and twisting mechanics of the linkers is employed and external twist is applied in stepwise increments to mimic quasistatic twisting of chromatin fibers. Simulation results reveal that the magnitude and sign of the imposed and induced twist on contiguous linkers depend strongly on their relative orientation. Remarkably, the relative direction of the induced and applied twist can become inverted for a subset of linker orientations-a phenomenon we refer to as "twist inversion". We characterize the twist inversion, as a function of relative linker orientation, in a phase diagram and explain its key features using a simple model based on the geometry of the nucleosome/linker complex. In addition to twist inversion, our simulations reveal "nucleosome flipping", whereby nucleosomes may undergo sudden flipping in response to applied twist, causing a rapid bending of the linker and a significant change in the overall twist and writhe of the array. Our findings shed light on the underlying mechanisms by which torsional stresses impact chromatin organization.

Coarse-Grained Brownian Dynamics Simulations of the 10-23 DNAzyme.

Deoxyribozymes (DNAzymes) are single-stranded DNA that catalyze nucleic acid biochemistry. Although a number of DNAzymes have been discovered by in vitro selection, the relationship between their tertiary structure and function remains unknown. We focus here on the well-studied 10-23 DNAzyme, which cleaves mRNA with a catalytic efficiency approaching that of RNase A. Using coarse-grained Brownian dynamics simulations, we find that the DNAzyme bends its substrate away from the cleavage point, exposing the reactive site and buckling the DNAzyme catalytic core. This hypothesized transition state provides microscopic insights into experimental observations concerning the size of the DNAzyme/substrate complex, the impact of the recognition arm length, and the sensitivity of the enzymatic activity to point mutations of the catalytic core. Upon cleaving the pertinent backbone bond in the substrate, we find that the catalytic core of the DNAzyme unwinds and the overall complex rapidly extends, in agreement with experiments on the related 8-17 DNAzyme. The results presented here provide a starting point for interpreting experimental data on DNAzyme kinetics, as well as developing more detailed simulation models. The results also demonstrate the limitations of using a simple physical model to understand the role of point mutations.

A boundary element method/Brownian dynamics approach for simulating DNA electrophoresis in electrically insulating microfabricated devices.

We present an approach for merging boundary element method (BEM) solutions of the electric field in electrically insulating complex geometries with Brownian dynamics (BD) simulations of DNA electrophoresis therein. Although a rote application of the standard BEM algorithm proves inaccurate and prohibitively expensive, we show that regularization of the near-wall electric field and an updating scheme commensurate with the characteristic length scale of the BD simulation furnishes a robust, efficient simulation protocol. The accuracy of the BEM-BD method is verified by simulating lambda-DNA collisions with an isolated, insulating cylindrical obstacle and comparing the results with equivalent BD simulations that employ the exact solution for the electric field. The computational overhead of our implementation of BEM-BD is comparable to an existing finite element method/BD approach. The BEM-BD algorithm is readily parallelized and well-suited to time-dependent and responsive electric fields, making it broadly applicable to simulating DNA electrophoresis in microfluidic devices.

Brownian dynamics simulations of single-stranded DNA hairpins.

We present a Brownian dynamics model which we use to study the kinetics and thermodynamics of single-stranded DNA hairpins, gaining insights into the role of stem mismatches and the kinetics rates underlying the melting transition. The model is a base-backbone type in which the DNA bases and sugar-phosphate backbone are represented as single units (beads) in the context of the Brownian dynamics simulations. We employ a minimal number of bead-bead interactions, leading to a simple computational scheme. To demonstrate the veracity of our model for DNA hairpins, we show that the model correctly captures the effects of base stacking, hydrogen bonding, and temperature on both the thermodynamics and the kinetics of hairpin formation and melting. When cast in dimensionless form, the thermodynamic results obtained from the present model compare favorably with default predictions of the m-fold server, although the present model is not sufficiently robust to provide dimensional results. The kinetic data at low temperatures indicate frequent but short-lived opening events, consistent with the measured chain end-to-end probability distribution. The model is also used to study the effect of base mismatches in the stem of the hairpin. With the parameters used here, the model overpredicts the relative shift in the melting temperature due to mismatches. The melting transition can be primarily attributed to a rapid increase in the hairpin opening rate rather than an equivalent decrease in the closing rate, in agreement with single-molecule experimental data.

Polymer deformation in Brownian ratchets: theory and molecular dynamics simulations.

We examine polymers in the presence of an applied asymmetric sawtooth (ratchet) potential which is periodically switched on and off, using molecular dynamics (MD) simulations with an explicit Lennard-Jones solvent. We show that the distribution of the center of mass for a polymer in a ratchet is relatively wide for potential well depths U0 on the order of several kBT. The application of the ratchet potential also deforms the polymer chains. With increasing U0 the Flory exponent varies from that for a free three-dimensional (3D) chain, nu=35 (U0=0), to that corresponding to a 2D compressed (pancake-shaped) polymer with a value of nu=34 for moderate U0. This has the added effect of decreasing a polymer's diffusion coefficient from its 3D value D3D to that of a pancaked-shaped polymer moving parallel to its minor axis D2D. The result is that a polymer then has a time-dependent diffusion coefficient D(t) during the ratchet off time. We further show that this suggests a different method to operate a ratchet, where the off time of the ratchet, toff, is defined in terms of the relaxation time of the polymer, tauR. We also derive a modified version of the Bader ratchet model [Bader, Proc. Natl. Acad. Sci. U.S.A. 96, 13165 (1999)] which accounts for this deformation and we present a simple expression to describe the time dependent diffusion coefficient D(t). Using this model we then illustrate that polymer deformation can be used to modulate polymer migration in a ratchet potential.

Combinatorial design of passive drug delivery platforms.

We introduce a novel computational approach to designing passive drug delivery systems based on porous materials such as hydrogels. Our approach uses three tools: a method to establish the exact release pattern from all possible loading sites inside a given hydrogel; a method to generate a large number of hydrogel structures to be tested numerically, and finally an optimization algorithm which leads to the selection of optimal hydrogel structures. Using this approach, we show that controlled release curves can be obtained by using a genetic algorithm for the optimization step. Strategies to generalize this approach to other systems are also discussed.

The theory of DNA separation by capillary electrophoresis.

The Human Genome has been sequenced in large part owing to the invention of capillary electrophoresis. Although this technology has matured enough to allow such amazing achievements, the physical mechanisms at play during separation have yet to be completely understood and optimized. Recently, new separation regimes and new physical mechanisms have been investigated. The use of free-flow electrophoresis and new modes of pulsed-field electrophoresis have been suggested, while we have observed a shift towards single nucleotide polymorphism analysis and microchip technologies. A strong theoretical basis remains essential for the efficient development of new methods.

Hierarchies in eukaryotic genome organization: Insights from polymer theory and simulations.

Eukaryotic genomes possess an elaborate and dynamic higher-order structure within the limiting confines of the cell nucleus. Knowledge of the physical principles and the molecular machinery that govern the 3D organization of this structure and its regulation are key to understanding the relationship between genome structure and function. Elegant microscopy and chromosome conformation capture techniques supported by analysis based on polymer models are important steps in this direction. Here, we review results from these efforts and provide some additional insights that elucidate the relationship between structure and function at different hierarchical levels of genome organization.

Theory of DNA electrophoresis (approximately 1999-2002(1/2)).

Over the last two decades, the introduction of new methods such as pulsed-field gel electrophoresis and capillary array electrophoresis has made it possible to map and sequence entire genomes, including our own. The development of these experimental methods has been helped by the progress of theoretical and computational sciences, and the interactions between these three modi operandi of modern science are still pushing the limits of our technologies. We now see a clear trend towards proteomics and microfluidic (even nanofluidic!) devices. In this review, we take a look at the progress of the field over the last 3 years using the glasses of the theoretical scientist and focusing mostly on new ideas and concepts. About a dozen different subfields are discussed and reviewed. We conclude by giving a commented list of some of the best review articles published over the last 2-3 years.