emDNA - A Tool for Modeling Protein-decorated DNA Loops and Minicircles at the Base-pair Step Level.

Computational modeling of nucleic acids plays an important role in molecular biology, enhancing our general understanding of the relationship between structure and function. Biophysical studies have provided a wealth of information on how double-helical DNA responds to proteins and other molecules in its local environment but far less understanding of the larger scale structural responses found in protein-decorated loops and minicircles. Current computational models of DNA range from detailed all-atom molecular dynamics studies, which produce rich time and spatially dependent depictions of small DNA fragments, to coarse-grained simulations, which sacrifice detailed physical and chemical information to treat larger-scale systems. The treatment of DNA used here, at the base-pair step level with rigid-body parameters, allows one to develop models hundreds of base pairs long from local, sequence-specific features found from experiment. The emDNA software takes advantage of this framework, producing optimized structures of DNA at thermal equilibrium with built-in or user-generated elastic models. The program, in combination with the case studies included in this article, allows users of any skill level to develop and investigate mesoscale models of their own design. The functionality of emDNA includes a tool to incorporate experiment-specific configurations, e.g., protein-bound and/or melted DNA from known high-resolution structures, within higher-order 3D models by fixing the orientation and position of user-specified base pairs. The software provides a new avenue into multiscale genetic modeling, giving a wide range of users a deeper understanding of DNA mesoscale organization and the opportunity to pose new questions in genetic research. The publicly available emDNA software, including build instructions and usage information, is available on GitHub (https://nicocvn.github.io/emDNA/).

Synergy between Protein Positioning and DNA Elasticity: Energy Minimization of Protein-Decorated DNA Minicircles.

The binding of proteins onto DNA contributes to the shaping and packaging of the genome as well as to the expression of specific genetic messages. With a view to understanding the interplay between the presence of proteins and the deformation of DNA involved in such processes, we developed a new method to minimize the elastic energy of DNA fragments at the mesoscale level. Our method makes it possible to obtain the optimal pathways of protein-decorated DNA molecules for which the terminal base pairs are spatially constrained. We focus in this work on the deformations induced by selected architectural proteins on circular DNA. We report the energy landscapes of DNA minicircles subjected to different levels of torsional stress and containing one or two proteins as functions of the chain length and spacing between the proteins. Our results reveal cooperation between the elasticity of the double helix and the structural distortions of DNA induced by bound proteins. We find that the imposed mechanical stress influences the placement of proteins on DNA and that the proteins, in turn, modulate the mechanical stress and thereby broadcast their presence along DNA.

Parallels between DNA and collagen - comparing elastic models of the double and triple helix.

Multi-stranded helices are widespread in nature. The interplay of polymeric properties with biological function is seldom discussed. This study probes analogies between structural and mechanical properties of collagen and DNA. We modeled collagen with Eulerian rotational and translational parameters of adjacent rungs in the triple-helix ladder and developed statistical potentials by extracting the dispersion of the parameters from a database of atomic-resolution structures. The resulting elastic model provides a common quantitative way to describe collagen deformations upon interacting with integrins or matrix metalloproteinase and DNA deformations upon protein binding. On a larger scale, deformations in Type I collagen vary with a periodicity consistent with the D-periodic banding of higher-order fibers assemblies. This indicates that morphologies of natural higher-order collagen packing might be rooted in the characteristic deformation patterns.

Nucleosome-free DNA regions differentially affect distant communication in chromatin.

Communication between distantly spaced genomic regions is one of the key features of gene regulation in eukaryotes. Chromatin per se can stimulate efficient enhancer-promoter communication (EPC); however, the role of chromatin structure and dynamics in this process remains poorly understood. Here we show that nucleosome spacing and the presence of nucleosome-free DNA regions can modulate chromatin structure/dynamics and, in turn, affect the rate of EPC in vitro and in silico. Increasing the length of internucleosomal linker DNA from 25 to 60 bp results in more efficient EPC. The presence of longer nucleosome-free DNA regions can positively or negatively affect the rate of EPC, depending upon the length and location of the DNA region within the chromatin fiber. Thus the presence of histone-free DNA regions can differentially affect the efficiency of EPC, suggesting that gene regulation over a distance could be modulated by changes in the length of internucleosomal DNA spacers.

Contributions of Sequence to the Higher-Order Structures of DNA.

One of the critical unanswered questions in genome biophysics is how the primary sequence of DNA bases influences the global properties of very-long-chain molecules. The local sequence-dependent features of DNA found in high-resolution structures introduce irregularities in the disposition of adjacent residues that facilitate the specific binding of proteins and modulate the global folding and interactions of double helices with hundreds of basepairs. These features also determine the positions of nucleosomes on DNA and the lengths of the interspersed DNA linkers. Like the patterns of basepair association within DNA, the arrangements of nucleosomes in chromatin modulate the properties of longer polymers. The intrachromosomal loops detected in genomic studies contain hundreds of nucleosomes, and given that the simulated configurations of chromatin depend on the lengths of linker DNA, the formation of these loops may reflect sequence-dependent information encoded within the positioning of the nucleosomes. With knowledge of the positions of nucleosomes on a given genome, methods are now at hand to estimate the looping propensities of chromatin in terms of the spacing of nucleosomes and to make a direct connection between the DNA base sequence and larger-scale chromatin folding.

What controls DNA looping?

The looping of DNA provides a means of communication between sequentially distant genomic sites that operate in tandem to express, copy, and repair the information encoded in the DNA base sequence. The short loops implicated in the expression of bacterial genes suggest that molecular factors other than the naturally stiff double helix are involved in bringing the interacting sites into close spatial proximity. New computational techniques that take direct account of the three-dimensional structures and fluctuations of protein and DNA allow us to examine the likely means of enhancing such communication. Here, we describe the application of these approaches to the looping of a 92 base-pair DNA segment between the headpieces of the tetrameric Escherichia coli Lac repressor protein. The distortions of the double helix induced by a second protein--the nonspecific nucleoid protein HU--increase the computed likelihood of looping by several orders of magnitude over that of DNA alone. Large-scale deformations of the repressor, sequence-dependent features in the DNA loop, and deformability of the DNA operators also enhance looping, although to lesser degrees. The correspondence between the predicted looping propensities and the ease of looping derived from gene-expression and single-molecule measurements lends credence to the derived structural picture.

Effect of the boundary conditions and influence of the rotational inertia on the vibrational modes of an elastic ring.

We present the small-amplitude vibrations of a circular elastic ring with periodic and clamped boundary conditions. We model the rod as an inextensible, isotropic, naturally straight Kirchhoff elastic rod and obtain the vibrational modes of the ring analytically for periodic boundary conditions and numerically for clamped boundary conditions. Of particular interest are the dependence of the vibrational modes on the torsional stress in the ring and the influence of the rotational inertia of the rod on the mode frequencies and amplitudes. In rescaling the Kirchhoff equations, we introduce a parameter inversely proportional to the aspect ratio of the rod. This parameter makes it possible to capture the influence of the rotational inertia of the rod. We find that the rotational inertia has a minor influence on the vibrational modes with the exception of a specific category of modes corresponding to high-frequency twisting deformations in the ring. Moreover, some of the vibrational modes over or undertwist the elastic rod depending on the imposed torsional stress in the ring.

Weak operator binding enhances simulated Lac repressor-mediated DNA looping.

The 50th anniversary of Biopolymers coincides closely with the like celebration of the discovery of the Escherichia coli (lac) lactose operon, a classic genetic system long used to illustrate the influence of biomolecular structure on function. The looping of DNA induced by the binding of the Lac repressor protein to sequentially distant operator sites on DNA continues to serve as a paradigm for understanding long-range genomic communication. Advances in analyses of DNA structures and in incorporation of proteins in computer simulations of DNA looping allow us to address long-standing questions about the role of protein-mediated DNA loop formation in transcriptional control. Here we report insights gained from studies of the sequence-dependent contributions of the natural lac operators to Lac repressor-mediated DNA looping. Novel superposition of the ensembles of protein-bound operator structures derived from NMR measurements reveals variations in DNA folding missed in conventional structural alignments. The changes in folding affect the predicted ease with which the repressor induces loop formation and the ways that DNA closes between the protein headpieces. The peeling of the auxiliary operators away from the repressor enhances the formation of loops with the 92-bp wildtype spacing and hints of a structural reason behind their weak binding.

Insights into Gene Expression and Packaging from Computer Simulations.

Within the nucleus of each cell lies DNA - an unfathomably long, twisted, and intricately coiled molecule - segments of which make up the genes that provide the instructions that a cell needs to operate. As we near the 60(th) anniversary of the discovery of the DNA double helix, crucial questions remain about how the physical arrangement of the DNA in cells affects how genes work. For example, how a cell stores the genetic information inside the nucleus is complicated by the necessity of maintaining accessibility to DNA for genetic processing. In order to gain insight into the roles played by various proteins in reading and compacting the genome, we have developed new methodologies to simulate the dynamic, three-dimensional structures of long, fluctuating, protein-decorated strands of DNA. Our a priori approach to the problem allows us to determine the effects of individual proteins and their chemical modifications on overall DNA structure and function. Here we present our recent treatment of the communication between regulatory proteins attached to precisely constructed stretches of chromatin. Our simulations account for the enhancement in communication detected experimentally on chromatin compared to protein-free DNA of the same chain length as well as the critical roles played by the cationic 'tails' of the histone proteins in this signaling. The states of chromatin captured in the simulations offer new insights into the ways that the DNA, histones, and regulatory proteins contribute to long-range communication along the genome.

Internucleosomal interactions mediated by histone tails allow distant communication in chromatin.

Action across long distances on chromatin is a hallmark of eukaryotic transcriptional regulation. Although chromatin structure per se can support long-range interactions, the mechanisms of efficient communication between widely spaced DNA modules in chromatin remain a mystery. The molecular simulations described herein suggest that transient binary internucleosomal interactions can mediate distant communication in chromatin. Electrostatic interactions between the N-terminal tails of the core histones and DNA enhance the computed probability of juxtaposition of sites that lie far apart along the DNA sequence. Experimental analysis of the rates of communication in chromatin constructs confirms that long-distance communication occurs efficiently and independently of distance on tail-containing, but not on tailless, chromatin. Taken together, our data suggest that internucleosomal interactions involving the histone tails are essential for highly efficient, long-range communication between regulatory elements and their targets in eukaryotic genomes.

Characterization of the geometry and topology of DNA pictured as a discrete collection of atoms.

The structural and physical properties of DNA are closely related to its geometry and topology. The classical mathematical treatment of DNA geometry and topology in terms of ideal smooth space curves was not designed to characterize the spatial arrangements of atoms found in high-resolution and simulated double-helical structures. We present here new and rigorous numerical methods for the rapid and accurate assessment of the geometry and topology of double-helical DNA structures in terms of the constituent atoms. These methods are well designed for large DNA datasets obtained in detailed numerical simulations or determined experimentally at high-resolution. We illustrate the usefulness of our methodology by applying it to the analysis of three canonical double-helical DNA chains, a 65-bp minicircle obtained in recent molecular dynamics simulations, and a crystallographic array of protein-bound DNA duplexes. Although we focus on fully base-paired DNA structures, our methods can be extended to treat the geometry and topology of melted DNA structures as well as to characterize the folding of arbitrary molecules such as RNA and cyclic peptides.