Theoretical Analysis of the Stress Induced B-Z Transition in Superhelical DNA

We present a method to calculate the propensities of regions within a DNA molecule to transition from B-form to Z-form under negative superhelical stresses. We use statistical mechanics to analyze the competition that occurs among all susceptible Z-forming regions at thermodynamic equilibrium in a superhelically stressed DNA of specified sequence. This method, which we call SIBZ, is similar to the SIDD algorithm that was previously developed to analyze superhelical duplex destabilization. A state of the system is determined by assigning to each base pair either the B- or the Z-conformation, accounting for the dinucleotide repeat unit of Z-DNA. The free energy of a state is comprised of the nucleation energy, the sequence-dependent B-Z transition energy, and the energy associated with the residual superhelicity remaining after the change of twist due to transition. Using this information, SIBZ calculates the equilibrium B-Z transition probability of each base pair in the sequence. This can be done at any physiologically reasonable level of negative superhelicity. We use SIBZ to analyze a variety of representative genomic DNA sequences. We show that the dominant Z-DNA forming regions in a sequence can compete in highly complex ways as the superhelicity level changes. Despite having no tunable parameters, the predictions of SIBZ agree precisely with experimental results, both for the onset of transition in plasmids containing introduced Z-forming sequences and for the locations of Z-forming regions in genomic sequences. We calculate the transition profiles of 5 kb regions taken from each of 12,841 mouse genes and centered on the transcription start site (TSS). We find a substantial increase in the frequency of Z-forming regions immediately upstream from the TSS. The approach developed here has the potential to illuminate the occurrence of Z-form regions in vivo, and the possible roles this transition may play in biological processes

Bubble statistics and positioning in superhelically stressed DNA

We present a general framework to study the thermodynamic denaturation of double-stranded DNA under superhelical stress. We report calculations of position- and size-dependent opening probabilities for bubbles along the sequence. Our results are obtained from transfer-matrix solutions of the Zimm-Bragg model for unconstrained DNA and of a self-consistent linearization of the Benham model for superhelical DNA. The numerical efficiency of our method allows for the analysis of entire genomes and of random sequences of corresponding length ($10^6-10^9$ base pairs). We show that, at physiological conditions, opening in superhelical DNA is strongly cooperative with average bubble sizes of $10^2-10^3$ base pairs (bp), and orders of magnitude higher than in unconstrained DNA. In heterogeneous sequences, the average degree of base-pair opening is self-averaging, while bubble localization and statistics are dominated by sequence disorder. Compared to random sequences with identical GC-content, genomic DNA has a significantly increased probability to open large bubbles under superhelical stress. These bubbles are frequently located directly upstream of transcription start sites.Comment: to be appeared in Physical Review

Mechanics and Function of DNA Looping and Supercoiling.

DNA is an essential molecule that enables the storage and retrieval of genetic information. Since the discovery of its structure (double helix), the relationship between the molecule's structure and function has been studied extensively. Here we extend beyond the static structure and consider how the mechanical properties and dynamics influence its function. To do so, we exercise an elasto-dynamic rod model for DNA. By exercising this model, we study two biologically relevant systems. First, we study DNA looping by Lac repressor. Although this is a classic gene regulatory system, the mechanics of the DNA loop remain largely unknown. Therefore, we compute the effects of inter-operator length, intrinsic curvature, and protein flexibility on the energetics and topology these loops. We calculate that anti-parallel loops are energetically preferred, the elastic energy of a family of intrinsically curved DNA loops spans 5-12 kT, and identify the sensitivity of elastic energy to protein flexibility. Our computations compare favorably with published experimental data and motivate experimental work in the Kahn lab at the University of Maryland. Furthermore, we contribute an efficient method to analyze a large family of intrinsically curved DNA molecules and a method to account for Lac repressor flexibility in our rod model. In addition, we analyze cryo-EM images (obtained by the Stasiak lab at the Université de Lausanne) of DNA minicircles with similar lengths to the Lac repressor DNA loops. Second, we study the relaxation of DNA supercoils by topoisomerase. In doing so, we make advancements to the rod model and perform the first multi-scale model of supercoil relaxation by topoisomerase. Specifically, we contribute an efficient method to account for self contact and electrostatics in our elastic rod model. In our multi-scale simulation we couple our rod model with recent data (from MD simulations by the Andricioaei lab at the University of California - Irvine) that characterizes the the mechanics of topoisomerase. In doing so we gain insight into the dynamics of supercoil relaxation and make a first prediction of the relaxation time (0.1-1.0 μs).Ph.D.Mechanical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/75861/1/tlillian_1.pd

Dinucleotides as simple models of the base stacking-unstacking component of DNA 'breathing' mechanisms

14 pagesRegulatory protein access to the DNA duplex 'interior' depends on local DNA 'breathing' fluctuations, and the most fundamental of these are thermally-driven base stacking-unstacking interactions. The smallest DNA unit that can undergo such transitions is the dinucleotide, whose structural and dynamic properties are dominated by stacking, while the ion condensation, cooperative stacking and inter-base hydrogen-bonding present in duplex DNA are not involved. We use dApdA to study stacking-unstacking at the dinucleotide level because the fluctuations observed are likely to resemble those of larger DNA molecules, but in the absence of constraints introduced by cooperativity are likely to be more pronounced, and thus more accessible to measurement. We study these fluctuations with a combination of Molecular Dynamics simulations on the microsecond timescale and Markov State Model analyses, and validate our results by calculations of circular dichroism (CD) spectra, with results that agree well with the experimental spectra. Our analyses show that the CD spectrum of dApdA is defined by two distinct chiral conformations that correspond, respectively, to a Watson-Crick form and a hybrid form with one base in a Hoogsteen configuration. We find also that ionic structure and water orientation around dApdA play important roles in controlling its breathing fluctuations.This research was supported by a grant from the National Institute of Child Health and Human Development (5R01HD081 362-05) awarded to L.S. and N.B.A. The funding sources had no role in the study design, data collection and analysis, or submission process

MICROMECHANICS OF DNA UNDER SHARP BENDING

Ph.DDOCTOR OF PHILOSOPH

Molecular simulations of conformational transitions in biomolecules using a novel computational tool

The function of biological macromolecules is inherently linked to their complex conformational behaviour. As a consequence, the corresponding potential energy landscape encompasses multiple minima. Some of the intermediate structures between the initial and final states can be characterized by experimental techniques. Computer simulations can explore the dynamics of individual states and bring these together to rationalize the overall process. A novel method based on atomistic structure-based potentials in combination with the empirical valence bond theory (EVB-SBP) has been developed and implemented in the Amber package. The method has been successfully applied to explore various biological processes. The first application of the EVB-SBP approach involves the study of base flipping in B-DNA. The use of simple structurebased potentials are shown to reproduce structural ensembles of stable states obtained by using more accurate force field simulations. Umbrella sampling in conjunction with the energy gap reaction coordinate enables the study of alternative molecular pathways efficiently. The main application of the method is the study of the switching mechanism in a short bistable RNA. Molecular pathways, which connect the two stable states, have been elucidated, with particular interest to the characterisation of the transition state ensemble. In addition, NMR experiments have been performed to support the theoretical findings. Finally, a recent study of large-scale conformational transitions in protein kinases shows the general applicability of the method to different biomolecules

Computational Approaches to Simulation and Analysis of Large Conformational Transitions in Proteins

abstract: In a typical living cell, millions to billions of proteins—nanomachines that fluctuate and cycle among many conformational states—convert available free energy into mechanochemical work. A fundamental goal of biophysics is to ascertain how 3D protein structures encode specific functions, such as catalyzing chemical reactions or transporting nutrients into a cell. Protein dynamics span femtosecond timescales (i.e., covalent bond oscillations) to large conformational transition timescales in, and beyond, the millisecond regime (e.g., glucose transport across a phospholipid bilayer). Actual transition events are fast but rare, occurring orders of magnitude faster than typical metastable equilibrium waiting times. Equilibrium molecular dynamics (EqMD) can capture atomistic detail and solute-solvent interactions, but even microseconds of sampling attainable nowadays still falls orders of magnitude short of transition timescales, especially for large systems, rendering observations of such "rare events" difficult or effectively impossible. Advanced path-sampling methods exploit reduced physical models or biasing to produce plausible transitions while balancing accuracy and efficiency, but quantifying their accuracy relative to other numerical and experimental data has been challenging. Indeed, new horizons in elucidating protein function necessitate that present methodologies be revised to more seamlessly and quantitatively integrate a spectrum of methods, both numerical and experimental. In this dissertation, experimental and computational methods are put into perspective using the enzyme adenylate kinase (AdK) as an illustrative example. We introduce Path Similarity Analysis (PSA)—an integrative computational framework developed to quantify transition path similarity. PSA not only reliably distinguished AdK transitions by the originating method, but also traced pathway differences between two methods back to charge-charge interactions (neglected by the stereochemical model, but not the all-atom force field) in several conserved salt bridges. Cryo-electron microscopy maps of the transporter Bor1p are directly incorporated into EqMD simulations using MD flexible fitting to produce viable structural models and infer a plausible transport mechanism. Conforming to the theme of integration, a short compendium of an exploratory project—developing a hybrid atomistic-continuum method—is presented, including initial results and a novel fluctuating hydrodynamics model and corresponding numerical code.Dissertation/ThesisDoctoral Dissertation Physics 201