Principles of sequence-dependent flexure of DNA

The curvature of a bent rod may be defined in several different, but equivalent ways. The best way of describing the curvature of double-helical DNA is by an angle of turning per base step. Curvature comes mainly from the angle of roll between successive base-pairs, and this is defined as positive when the angle opens up on the minor groove side of the bases. DNA forms a plane curve if the roll angle values along the molecule alternate periodically between positive and negative, with a complete period equal to the helical repeat. It is known from studies of crystallized oligomers that the roll angles for particular dinucleotide steps have preferred values, or lie in preferred ranges of values. Therefore the formation of a plane curve will be easier with some base sequences of DNA than with others. We set up a computer algorithm for determining the ease with which DNA of given sequence will adopt a curved form. The algorithm has two different sets of constants: in model 1 the base step parameters come from an inspection of crystallized oligomers, and in model 2 data from a statistical survey of the incidence of dinucleotide steps in a large number of samples of chicken erythrocyte core DNA is incorporated. Both forms of the algorithm successfully locate the dyad of the nucleosome sequence (modulo 10) in a frog gene, and suggest strongly that sequence-dependent flexural properties of DNA play a part in the recognition of binding sites by nucleosome cores.     

A nonlinear mixed-effect mixture model for functional mapping of dynamic traits

Functional mapping has emerged as a next-generation statistical tool for mapping quantitative trait loci (QTL) that affect complex dynamic traits. In this article, we incorporated the idea of nonlinear mixed-effect (NLME) models into the mixture-based framework of functional mapping, aimed to generalize the spectrum of applications for functional mapping. NLME-based functional mapping, implemented with the linearization algorithm based on the first-order Taylor expansion, can provide reasonable estimates of QTL genotypic-specific curve parameters (fixed effect) and the between-individual variation of these parameters (random effect). Results from simulation studies suggest that the NLME-based model is more general than traditional functional mapping. The new model can be useful for the identification of the ontogenetic patterns of QTL genetic effects during time course.     

A deformation energy model reveals sequence-dependent property of nucleosome positioning

Chromosoma - We present a deformation energy model for predicting nucleosome positioning, in which a position-dependent structural parameter set derived from crystal structures of nucleosomes was...     

DNA sequence-dependent positioning of the linker histone in a nucleosome: A single-pair FRET study

Linker histones (LHs) bind to nucleosomes with their globular domain (gH) positioned in either an on- or an off-dyad binding mode. Here, we study the effect of the linker DNA (L-DNA) sequence on the binding of a full-length LH, Xenopus laevis H1.0b, to a Widom 601 nucleosome core particle (NCP) flanked by two 40 bp long L-DNA arms, by single-pair FRET spectroscopy. We varied the sequence of the 11 bp of L-DNA adjoining the NCP on either side, making the sequence either A-tract, purely GC, or mixed with 64% AT. The labeled gH consistently exhibited higher FRET efficiency with the labeled L-DNA containing the A-tract than that with the pure-GC stretch, even when the stretches were swapped. However, it did not exhibit higher FRET efficiency with the L-DNA containing 64% AT-rich mixed DNA when compared to the pure-GC stretch. We explain our observations with a model that shows that the gH binds on dyad and that two arginines mediate recognition of the A-tract via its characteristically narrow minor groove. To investigate whether this on-dyad minor groove-based recognition was distinct from previously identified off-dyad major groove-based recognition, a nucleosome was designed with A-tracts on both the L-DNA arms. One A-tract was complementary to thymine and the other to deoxyuridine. The major groove of the thymine-tract was lined with methyl groups that were absent from the major groove of the deoxyuridine tract. The gH exhibited similar FRET for both these A-tracts, suggesting that it does not interact with the thymine methyl groups exposed on the major groove. Our observations thus complement previous studies that suggest that different LH isoforms may employ different ways of recognizing AT-rich DNA and A-tracts. This adaptability may enable the LH to universally compact scaffold-associated regions and constitutive heterochromatin, which are rich in such sequences.     

Role of DNA flexibility in sequence-dependent activity of uracil DNA glycosylase

Uracil DNA glycosylase (UDG) is a base excision repair enzyme that specifically recognizes and removes uracil from double- or single-stranded DNA. The efficiency of the enzyme depends on the DNA sequence surrounding the uracil. Crystal structures of UDG in complex with DNA reveal that the DNA is severely bent and distorted in the region of the uracil. This suggests that the sequence-dependent efficiency of the enzyme may be related to the energetic cost of DNA distortion in the process of specific damage recognition. To test this hypothesis, molecular dynamics simulations were performed on two sequences representing extreme cases of UDG efficiency, AUA/TAT (high efficiency) and GUG/CAC (low efficiency). Analysis of the simulations shows that the effective bending force constants are lower for the AUA/TAT sequence, indicating that this sequence is more flexible than the GUG/CAC sequence. Fluorescence lifetimes of the adenine analogue 2-aminopurine (2AP), replacing adenine opposite the uracil, are shorter in the context of the AUA/TAT sequence, indicating more dynamic base-base interaction and greater local flexibility than in the GUG/CAC sequence. Furthermore, the K(M) of Escherichia coli UDG for the AUA/TAT sequence is 10-fold smaller than that for the GUG/CAC sequence, while the k(cat) is only 2-fold smaller. This indicates that differences in UDG efficiency largely arise from differences in binding and not catalysis. These results link directly flexibility near the damaged DNA site with the efficiency of DNA repair.     

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.     

A theoretical model for the prediction of sequence-dependent nucleosome thermodynamic stability

A theoretical model for predicting nucleosome thermodynamic stability in terms of DNA sequence is advanced. The model is based on a statistical mechanical approach, which allows the calculation of the canonical ensemble free energy involved in the competitive nucleosome reconstitution. It is based on the hypothesis that nucleosome stability mainly depends on the bending and twisting elastic energy to transform the DNA intrinsic superstructure into the nucleosomal structure. The ensemble average free energy is calculated starting from the intrinsic curvature, obtained by integrating the dinucleotide step deviations from the canonical B-DNA and expressed in terms of a Fourier series, in the framework of first-order elasticity. The sequence-dependent DNA flexibility is evaluated from the differential double helix thermodynamic stability. A large number of free-energy experimental data, obtained in different laboratories by competitive nucleosome reconstitution assays, are successfully compared to the theoretical results. They support the hypothesis that the stacking energies are the major factor in DNA rigidity and could be a measure of DNA stiffness. A dual role of DNA intrinsic curvature and flexibility emerges in the determination of nucleosome stability. The difference between the experimental and theoretical (elastic) nucleosome-reconstitution free energy for the whole pool of investigated DNAs suggests a significant role for the curvature-dependent DNA hydration and counterion interactions, which appear to destabilize nucleosomes in highly curved DNAs. This model represents an attempt to clarify the main features of the nucleosome thermodynamic stability in terms of physical-chemical parameters and suggests that in molecular systems with a large degree of complexity, the average molecular properties dominate over the local features, as in a statistical ensemble.     

Theoretical study of sequence-dependent nanopore unzipping of DNA

We theoretically investigate the unzipping of DNA electrically driven through a nanometer-size pore. Taking the DNA base sequence explicitly into account, the unpairing and translocation process is described by a biased random walk in a one-dimensional energy landscape determined by the sequential basepair opening. Distributions of translocation times are numerically calculated as a function of applied voltage and temperature. We show that varying these two parameters changes the dynamics from a predominantly diffusive behavior to a dynamics governed by jumps over local energy barriers. The work suggests experimentally studying sequence effects, by comparing the average value and standard deviation of the statistical distribution of translocation times.     

Computation of a stabilizing set of feedback matrices of a large-scale nonlinear musculoskeletal dynamic model

The purpose of this study is to present a general mathematical framework to compute a set of feedback matrices which stabilize an unstable nonlinear anthropomorphic musculoskeletal dynamic model. This method is activity specific and involves four fundamental stages. First, from muscle activation data (input) and motion degrees-of-freedom (output) a dynamic experimental model is obtained using system identification schemes. Second, a nonlinear musculoskeletal dynamic model which contains the same number of muscles and degrees-of-freedom and best represents the activity being considered is proposed. Third, the nonlinear musculoskeletal model (anthropomorphic model) is replaced by a family of linear systems, parameterized by the same set of input/output data (nominal points) used in the identification of the experimental model. Finally, a set of stabilizing output feedback matrices, parameterized again by the same set of nominal points, is computed such that when combined with the anthropomorphic model, the combined system resembles the structural form of the experimental model. The method is illustrated in regard to the human squat activity.     

A fully nonlinear viscohyperelastic model for the brain tissue applicable to dynamic rates

Understanding the mechanical response of the brain to external loadings is of critical importance in investigating the pathological conditions of this tissue during injurious conditions. Such injurious loadings may occur at high rates, for example among others, during road traffic or sport accidents, falls, or due to explosions. Hence, investigating the injury mechanism and design of protective devices for the brain requires constitutive modeling of this tissue at such rates. Accordingly, this paper is aimed at critically investigating the physical background for viscohyperelastic modeling of the brain tissue with scrutinizing the elastic fields pertinent to large, time dependent deformations, and developing a fully nonlinear multimode Maxwell model that can mathematically explain such deformations. The proposed model can be calibrated using the simple monotonic uniaxial deformation of the sample extracted from the tissue, and does not require additional information from relaxation or creep experiments. The performance of the proposed model is examined using the experimental results of two different studies, which reveals a desirable agreement. The usefulness, limitations, and future developments of the proposed model are discussed in this paper.     

Attenuation of DNA-protein interactions associated with intrinsic, sequence-dependent DNA curvature.

Inherently curved DNA segments, associated with short runs of adenines, have been identified in many gene regulatory regions, yet their physiological significance remains unknown. The observations reported in this study indicate that intrinsically bent nucleic acid fragments are characterized by substantially attenuated affinities toward DNA-binding proteins involved in structural functions, such as H1 histone and protamine, as well as toward various DNA-modifying enzymes including ligases and exo- and endonucleases. Two mechanisms might be responsible for the altered binding properties. According to the first mechanism, the attenuated binding affinities and the bending represent two independent consequences of the unique structural parameters exhibited by A-tracts. Indeed, analysis of the degradation products obtained upon exposure of the curved sequences to various chemical nucleases points toward the narrowing of the DNA minor groove, a conformational modulation known to characterize A-tracts and to run along the axially-bent motifs, as a potential determinant of the observed binding attenuation. Alternatively, the conformational constraints which result from the stable bending might act to modulate the strength of DNA-protein interactions. Although the factor directly responsible for the altered binding affinities revealed by the bent sequences cannot as yet be conclusively resolved, it is proposed that a reiteration of this specific factor, being either an A-tract or a bend, in phase with the DNA helical repeat acts to amplify the modulation of the binding.(ABSTRACT TRUNCATED AT 250 WORDS)     

A dynamic stochastic model for DNA replication initiation in early embryos

Background

Eukaryotic cells seem unable to monitor replication completion during normal S phase, yet must ensure a reliable replication completion time. This is an acute problem in early Xenopus embryos since DNA replication origins are located and activated stochastically, leading to the random completion problem. DNA combing, kinetic modelling and other studies using Xenopus egg extracts have suggested that potential origins are much more abundant than actual initiation events and that the time-dependent rate of initiation, I(t), markedly increases through S phase to ensure the rapid completion of unreplicated gaps and a narrow distribution of completion times. However, the molecular mechanism that underlies this increase has remained obscure.

Methodology/Principal Findings

Using both previous and novel DNA combing data we have confirmed that I(t) increases through S phase but have also established that it progressively decreases before the end of S phase. To explore plausible biochemical scenarios that might explain these features, we have performed comparisons between numerical simulations and DNA combing data. Several simple models were tested: i) recycling of a limiting replication fork component from completed replicons; ii) time-dependent increase in origin efficiency; iii) time-dependent increase in availability of an initially limiting factor, e.g. by nuclear import. None of these potential mechanisms could on its own account for the data. We propose a model that combines time-dependent changes in availability of a replication factor and a fork-density dependent affinity of this factor for potential origins. This novel model quantitatively and robustly accounted for the observed changes in initiation rate and fork density.

Conclusions/Significance

This work provides a refined temporal profile of replication initiation rates and a robust, dynamic model that quantitatively explains replication origin usage during early embryonic S phase. These results have significant implications for the organisation of replication origins in higher eukaryotes.     

A simple Markov model of sodium channels with a dynamic threshold

Characteristics of action potential generation are important to understanding brain functioning and, thus, must be understood and modeled. It is still an open question what model can describe concurrently the phenomena of sharp spike shape, the spike threshold variability, and the divisive effect of shunting on the gain of frequency-current dependence. We reproduced these three effects experimentally by patch-clamp recordings in cortical slices, but we failed to simulate them by any of 11 known neuron models, including one- and multi-compartment, with Hodgkin-Huxley and Markov equation-based sodium channel approximations, and those taking into account sodium channel subtype heterogeneity. Basing on our voltage-clamp data characterizing the dependence of sodium channel activation threshold on history of depolarization, we propose a 3-state Markov model with a closed-to-open state transition threshold dependent on slow inactivation. This model reproduces the all three phenomena. As a reduction of this model, a leaky integrate-and-fire model with a dynamic threshold also shows the effect of gain reduction by shunt. These results argue for the mechanism of gain reduction through threshold dynamics determined by the slow inactivation of sodium channels.     

Statistical mechanics of sequence-dependent circular DNA and its application for DNA cyclization

DNA cyclization is potentially the most powerful approach for systematic quantitation of sequence-dependent DNA bending and flexibility. We extend the statistical mechanics of the homogeneous DNA circle to a model that considers discrete basepairs, thus allowing for inhomogeneity, and apply the model to analysis of DNA cyclization. The theory starts from an iterative search for the minimum energy configuration of circular DNA. Thermodynamic quantities such as the J factor, which is essentially the ratio of the partition functions of circular and linear forms, are evaluated by integrating the thermal fluctuations around the configuration under harmonic approximation. Accurate analytic expressions are obtained for equilibrium configurations of homogeneous circular DNA with and without bending anisotropy. J factors for both homogeneous and inhomogeneous DNA are evaluated. Effects of curvature, helical repeat, and bending and torsional flexibility in DNA cyclization are analyzed in detail, revealing that DNA cyclization can detect as little as one degree of curvature and a few percent change in flexibility. J factors calculated by our new approach are well consistent with Monte Carlo simulations, whereas the new theory has much greater efficiency in computations. Simulation of experimental results has been demonstrated.     

Predicting sequence-dependent melting stability of short duplex DNA oligomers

Many important applications of DNA sequence-dependent hybridization reactions have recently emerged. This has sparked a renewed interest in analytical calculations of sequence-dependent melting stability of duplex DNA. In particular, for many applications it is often desirable to accurately predict the transition temperature, or t_m, of short duplex DNA oligomers (∼ 20 base pairs or less) from their sequence and concentration. The thermodynamic analytical method underlying these predictive calculations is based on the nearest-neighbor model. At least 11 sets of nearest-neighbor sequence-dependent thermodynamic parameters for DNA have been published. These sets are compared. Use of the nearest-neighbor sets in predicting t_m from the DNA sequence is demonstrated, and the ability of the nearest-neighbor parameters to provide accurate predictions of experimental t_m's of short duplex DNA oligomers is assessed. © 1998 John Wiley & Sons, Inc. Biopoly 44: 217–239, 1997     

The mechanics behind DNA sequence-dependent properties of the nucleosome

Chromatin organization and composition impart sophisticated regulatory features critical to eukaryotic genomic function. Although DNA sequence-dependent histone octamer binding is important for nucleosome activity, many aspects of this phenomenon have remained elusive. We studied nucleosome structure and stability with diverse DNA sequences, including Widom 601 derivatives with the highest known octamer affinities, to establish a simple model behind the mechanics of sequence dependency. This uncovers the unique but unexpected role of TA dinucleotides and a propensity for G|C-rich sequence elements to conform energetically favourably at most locations around the histone octamer, which rationalizes G|C% as the most predictive factor for nucleosome occupancy in vivo. In addition, our findings reveal dominant constraints on double helix conformation by H3-H4 relative to H2A-H2B binding and DNA sequence context-dependency underlying nucleosome structure, positioning and stability. This provides a basis for improved prediction of nucleosomal properties and the design of tailored DNA constructs for chromatin investigations.     

A nonlinear mathematical model of DNA and its use in calculating neutron scatter

A simple nonlinear mathematical model is applied to calculate spectrum of inelastic coherent scattering of neutrons by DNA.