Session X42: Focus Session: The Physics of Genome Folding II: Chromosomes and Nucleosomes

Polymer-nematic textures in spherical confinement: a coarse-grained model of DNA packing

Inspired to understand the complex spectrum of space-filling organizations the dsDNA genome within the capsid of bacterial viruses, we study a minimal, coarse-grained model of single chains densely-packed into a finite spherical volume. We build the three basic elements of the model--i) the absence of chain ends ii) the tendency of parallel-strand alignment and iii) a preference of uniform areal density of chain segments--into a polymer nematic theory for confined chains. Given the geometric constraints of the problem, we show that axially symmetric packings fall into one of three topologies: the coaxial spool; the simple solenoid; and the twisted-solenoid. Among these, only the twisted-solenoid fills the volume without the presence of line-like disclinations, or voids, and are therefore generically preferred in the incompressible limit. An analysis of the thermodynamic behavior of this simple model reveals a rich behavior, a generic sequence of phases from the empty state for small container sizes, to the coaxial spool configuration at intermediate sizes, ultimately giving way, via a second-order, symmetry-breaking transition, to the twisted-solenoid structure above a critical sphere size, which we estimate to be within the range of bacteriophage capsid dimensions.   

Conformational Fluctuations of Chromosomal DNA in \textit{E. coli}

We measured the conformational fluctuations of the bacterial chromosome in \textit{E. Coli in }vivo using fluorescence correlation spectroscopy (FCS). The chromosomal DNA was randomly decorated with a cell-permeable intercalating dye. Conformational fluctuations of the DNA move the fluorophores stochastically into the diffraction-limited excitation volume of a focused laser beam. The time correlation function of the fluorescence intensity reflects the underlying dynamics of the DNA on length scales down to $\sim $200 nm. A comparison between live cells and dead yet structurally intact cells shows identical fluctuation spectra for short time scales, yet substantial differences for frequencies below 100 Hz. Live cells show much stronger fluctuations in this regime. This observation points to the crucial importance of active molecular motor action, as opposed to passive thermal noise, in driving larger conformational fluctuations in the chromosomal DNA, in particular on length scales exceeding $\sim $500 nm.   

Spatial organization and dynamics of interphase yeast chromosomes

Understanding how the genome is spatially organized is an important problem in cell biology, due to its key roles in gene expression and DNA recombination. Here we report on a combined experimental and theoretical study of the organization and dynamics of yeast chromosome III which has a functional role in the yeast life cycle, in particular, it is responsible for mating type switching. By imaging two fluorescent markers, one at the spindle pole body (SPB) and the other proximal to the HML locus that is involved in DNA recombination during mating type switching, we measured the cell to cell distribution of distances and the mean square displacement between the markers as a function of time. We compared our experimental results with a random-walk polymer model that takes into account tethering and confinement of chromosomes in the nucleus, and found that the model recapitulates the observed spatial and temporal organization of chromosome III in yeast in quantitative detail. The polymer model makes specific predictions for mating-type switching in yeast, and suggests new experiments to test them.   

Reverse-engineering Chromatin Folding via The Gaussian Polymer Model

Recent technological advancements in techniques exploring chromatin conformation, such as 3C and its derivatives, provide us with information about contact frequency between chromatin segments. There is an urgent need for systematic methods of reconstructing folding patterns of the chromatin from such data. Dekker et al have previously summarized this experimental data in the form of a so-called `spatially averaged' conformation around which fluctuations occur. This would be accurate for regions where the chromatin is mostly frozen around one structure, but rather misleading for more dynamic euchromatin. To address the ill-posed problem of reconstruction of probability distribution from pairwise contact data, we propose a minimum relative entropy approach, which reduces to finding an interacting polymer model that reproduces the contact strengths, and allows for both very dynamic as well as frozen structures depending upon the indicated degree of interaction. While comparing contact frequencies computed from this model to observed data, we introduce the minimal number of interactions required as determined by criteria controlling model complexity. This technique allows us to reproduce known interactions for several biologically important regions like the beta-globin locus.   

Electrohydrodynamics of DNA in confinement

New methods of DNA sequencing aim to exploit the direct reading of individual DNA molecules. Such methods require one be able to elongate DNA molecules so that individual base-pairs may be accessed. In turn, this requires a detailed understanding of the mechanical and thermodynamic behavior of DNA, so that external manipulation and confinement successfully stretch the molecule. We aim to study the interplay between electrostatic and hydrodynamic interactions on the conformations of coarse-grained DNA through use of computer simulations with the general geometry Ewald-like method (GGEM), both in bulk and under geometric confinement.   

Susceptibilities to DNA Structural Transitions within Eukaryotic Genomes

We analyze the competitive transitions to alternate secondary DNA structures in a negatively supercoiled DNA molecule of kilobase length and specified base sequence. We use statistical mechanics to calculate the competition among all regions within the sequence that are susceptible to transitions to alternate structures. We use an approximate numerical method since the calculation of an exact partition function is numerically cumbersome for DNA molecules of lengths longer than hundreds of base pairs. This method yields accurate results in reasonable computational times. We implement algorithms that calculate the competition between transitions to denatured states and to Z-form DNA. We analyze these transitions near the transcription start sites (TSS) of a set of eukaryotic genes. We find an enhancement of Z-forming regions upstream of the TSS and a depletion of denatured regions around the start sites. We confirm that these finding are statistically significant by comparing our results to a set of randomized genes with preserved base composition at each position relative to the gene start sites. When we study the correlation of these transitions in orthologous mouse and human genes we find a clear evolutionary conservation of both types of transitions around the TSS.   

Mechanics of DNA Sticky End Joints

Cohesive DNA sticky ends along with synthesis of stable branched DNA molecules have enabled self assembly of versatile new DNA structures including DNA crystals. Sticky end joints are formed by pairing of complimentary unpaired bases at the end of two DNA molecules. In this work mechanics of the DNA sticky end joints is investigated by using molecular dynamics simulations. Effects of base sequence, joint length, and salt concentration on the mechanical behavior of the joints is studied. The results have implications in understanding the mechanics of DNA crystals and other structures containing sticky end joints.   

Statistical physics of nucleosome positioning and chromatin structure

Genomic DNA is packaged into chromatin in eukaryotic cells. The fundamental building block of chromatin is the nucleosome, a 147 bp-long DNA molecule wrapped around the surface of a histone octamer. Arrays of nucleosomes are positioned along DNA according to their sequence preferences and folded into higher-order chromatin fibers whose structure is poorly understood. We have developed a framework for predicting sequence-specific histone-DNA interactions and the effective two-body potential responsible for ordering nucleosomes into regular higher-order structures. Our approach is based on the analogy between nucleosomal arrays and a one-dimensional fluid of finite-size particles with nearest-neighbor interactions. We derive simple rules which allow us to predict nucleosome occupancy solely from the dinucleotide content of the underlying DNA sequences.Dinucleotide content determines the degree of stiffness of the DNA polymer and thus defines its ability to bend into the nucleosomal superhelix. As expected, the nucleosome positioning rules are universal for chromatin assembled in vitro on genomic DNA from baker's yeast and from the nematode worm C.elegans, where nucleosome placement follows intrinsic sequence preferences and steric exclusion. However, the positioning rules inferred from in vivo C.elegans chromatin are affected by global nucleosome depletion from chromosome arms relative to central domains, likely caused by the attachment of the chromosome arms to the nuclear membrane. Furthermore, intrinsic nucleosome positioning rules are overwritten in transcribed regions, indicating that chromatin organization is actively managed by the transcriptional and splicing machinery.   

Interrogating Nucleosome Positioning Through Coarse-Grain Molecular Simulation

Nucleosome positioning plays a crucial role in biology. As the fundamental unit in chromosome structure, the nucleosome core particle (NCP) binds to approximately 147 DNA base pairs. The location of bound NCPs in the genome, therefore, affects gene expression. The specific positioning of NCPs has been experimentally probed and competing viewpoints have been presented in the literature. Models for nucleosome positioning based on sequence-dependent flexibility (a genomic ``code" for nucleosome positioning) have been demonstrated to explain available experimental data. However, so do statistical models with no built-in sequence preference; the driving force for NCP positioning therefore remains an open question. We use a coarse-grain model for the NCP in combination with advanced sampling techniques to probe the sequence preference of NCPs. We present a method for determining the relative affinity of two DNA sequences for the NCP and use this method to compare high- and low-affinity sequences. We discuss several coarse-grain protein models with varying level of detail to examine the impact of model resolution on the agreement of our results with experimental evidence. We also investigate the dynamics of the NCP-DNA complex and their dependence on system characteristics.   

Dynamics of Histone Tails within Chromatin

Genetic information in humans is encoded within DNA molecules that is wrapped around histone octamer proteins and compacted into a highly conserved structural polymer, chromatin. The physical and material properties of chromatin appear to influence gene expression by altering the accessibility of proteins to the DNA. The tails of the histones are flexible domains that are thought to play a role in regulating DNA accessibility and compaction; however the molecular mechanisms for these phenomena are not understood. I will present CW-EPR studies on site directed spin labeled nucleosomes that probe the structure and dynamics of these histone tails within nucleosomes.