Flexible histone tails in a new mesoscopic oligonucleosome model

We describe a new mesoscopic model of oligonucleosomes that incorporates flexible histone tails. The nucleosome cores are modeled using the discrete surface-charge optimization model, which treats the nucleosome as an electrostatic surface represented by hundreds of point charges; the linker DNAs are treated using a discrete elastic chain model; and the histone tails are modeled using a bead/chain hydrodynamic approach as chains of connected beads where each bead represents five protein residues. Appropriate charges and force fields are assigned to each histone chain so as to reproduce the electrostatic potential, structure, and dynamics of the corresponding atomistic histone tails at different salt conditions. The dynamics of resulting oligonucleosomes at different sizes and varying salt concentrations are simulated by Brownian dynamics with complete hydrodynamic interactions. The analyses demonstrate that the new mesoscopic model reproduces experimental results better than its predecessors, which modeled histone tails as rigid entities. In particular, our model with flexible histone tails: correctly accounts for salt-dependent conformational changes in the histone tails; yields the experimentally obtained values of histone-tail mediated core/core attraction energies; and considers the partial shielding of electrostatic repulsion between DNA linkers as a result of the spatial distribution of histone tails. These effects are crucial for regulating chromatin structure but are absent or improperly treated in models with rigid histone tails. The development of this model of oligonucleosomes thus opens new avenues for studying the role of histone tails and their variants in mediating gene expression through modulation of chromatin structure.     

Calculation of the solution properties of flexible macromolecules: methods and applications

While the prediction of hydrodynamic properties of rigid particles is nowadays feasible using simple and efficient computer programs, the calculation of such properties and, in general, the dynamic behavior of flexible macromolecules has not reached a similar situation. Although the theories are available, usually the computational work is done using solutions specific for each problem. We intend to develop computer programs that would greatly facilitate the task of predicting solution behavior of flexible macromolecules. In this paper, we first present an overview of the two approaches that are most practical: the Monte Carlo rigid-body treatment, and the Brownian dynamics simulation technique. The Monte Carlo procedure is based on the calculation of properties for instantaneous conformations of the macromolecule that are regarded as if they were instantaneously rigid. We describe how a Monte Carlo program can be interfaced to the programs in the HYDRO suite for rigid particles, and provide an example of such calculation, for a hypothetical particle: a protein with two domains connected by a flexible linker. We also describe briefly the essentials of Brownian dynamics, and propose a general mechanical model that includes several kinds of intramolecular interactions, such as bending, internal rotation, excluded volume effects, etc. We provide an example of the application of this methodology to the dynamics of a semiflexible, wormlike DNA.     

Sequence Dependencies of DNA Deformability and Hydration in the Minor Groove

DNA deformability and hydration are both sequence-dependent and are essential in specific DNA sequence recognition by proteins. However, the relationship between the two is not well understood. Here, systematic molecular dynamics simulations of 136 DNA sequences that differ from each other in their central tetramer revealed that sequence dependence of hydration is clearly correlated with that of deformability. We show that this correlation can be illustrated by four typical cases. Most rigid basepair steps are highly likely to form an ordered hydration pattern composed of one water molecule forming a bridge between the bases of distinct strands, but a few exceptions favor another ordered hydration composed of two water molecules forming such a bridge. Steps with medium deformability can display both of these hydration patterns with frequent transition. Highly flexible steps do not have any stable hydration pattern. A detailed picture of this correlation demonstrates that motions of hydration water molecules and DNA bases are tightly coupled with each other at the atomic level. These results contribute to our understanding of the entropic contribution from water molecules in protein or drug binding and could be applied for the purpose of predicting binding sites.     

An automated computer vision and roboticsbased technique for 3-D flexible biomolecular docking and matching

The generation of binding modes between two molecules, alsoknown as molecular docking, is a key problem in rational drugdesign and biomolecular recognition. Docking a ligand, e.g.,a drug molecule or a protein molecule, to a protein receptor,involves recognition of molecular surfaces as molecules interactat their surface. Recent studies report that the activity ofmany molecules induces conformational transitions by ‘hinge-bending’,which involves movements of relatively rigid parts with respectto each other. In ligand–receptor binding, relative rotationalmovements of molecu–lar substructures about their commonhinges have been observed. For automatically predicting flexiblemolecular interactions, we adapt a new technique developed inComputer Vision and Robotics for the efficient recognition ofpartially occluded articulated objects. These type of objectsconsist of rigid parts which are connected by rotary joints(hinges). Our approach is based on an extension and generalizationof the Geometric Hashing and Generalized Hough Transform paradigmfor rigid object recognition. Unlike other techniques whichmatch each part individually, our approach exploits forcefullyand efficiently enough the fact that the different rigid partsdo belong to the same flexible molecule. We show experimentalresults obtained by an implementation of the algorithm for rigidand flexible docking. While the ‘correct’, crystal–boundcomplex is obtained with a small RMSD, additional, predictive‘high scoring’ binding modes are generated as well.The diverse applications and implications of this general, powerfultool are discussed     

X-ray analysis of Mycobacterium smegmatis Dps and a comparative study involving other Dps and Dps-like molecules

The structure of the DNA binding protein from starved cells from Mycobacterium smegmatis has been determined in three crystal forms and has been compared with those of similar proteins from other sources. The dodecameric molecule can be described as a distorted icosahedron. The interfaces among subunits are such that the dodecameric molecule appears to have been made up of stable trimers. The situation is similar in the proteins from Escherichia coli and Agrobacterium tumefaciens, which are closer to the M.smegmatis protein in sequence and structure than those from other sources, which appear to form a dimer first. Trimerisation is aided in the three proteins by the additional N-terminal stretches that they possess. The M.smegmatis protein has an additional C-terminal stretch compared to other related proteins. The stretch, known to be involved in DNA binding, is situated on the surface of the molecule. A comparison of the available structures permits a delineation of the rigid and flexible regions in the molecule. The subunit interfaces around the molecular dyads, where the ferroxidation centres are located, are relatively rigid. Regions in the vicinity of the acidic holes centred around molecular 3-fold axes, are relatively flexible. So are the DNA binding regions. The crystal structures of the protein from M.smegmatis confirm that DNA molecules can occupy spaces within the crystal without disturbing the arrangement of the protein molecules. However, contrary to earlier suggestions, the spaces do not need to be between layers of protein molecules. The cubic form provides an arrangement in which grooves, which could hold DNA molecules, criss-cross the crystal.     

Flexible structural comparison allowing hinge-bending, swiveling motions

We present an efficient method for flexible comparison of protein structures, allowing swiveling motions. In all currently available methodologies developed and applied to the comparisons of protein structures, the molecules are considered to be rigid objects. The method described here extends and generalizes current approaches to searches for structural similarity between molecules by viewing proteins as objects consisting of rigid parts connected by rotary joints. During the matching, the rigid subparts are allowed to be rotated with respect to each other around swiveling points in one of the molecules. This technique straightforwardly detects structural motifs having hinge(s) between their domains. Whereas other existing methods detect hinge-bent motifs by initially finding the matching rigid parts and subsequently merging these together, our method automatically detects recurring substructures, allowing full 3 dimensional rotations about their swiveling points. Yet the method is extremely fast, avoiding the time-consuming full conformational space search. Comparison of two protein structures, without a predefinition of the motif, takes only seconds to one minute on a workstation per hinge. Hence, the molecule can be scanned for many potential hinge sites, allowing practically all C(alpha) atoms to be tried as swiveling points. This algorithm provides a highly efficient, fully automated tool. Its complexity is only O(n2), where n is the number of C(alpha) atoms in the compared molecules. As in our previous methodologies, the matching is independent of the order of the amino acids in the polypeptide chain. Here we illustrate the performance of this highly powerful tool on a large number of proteins exhibiting hinge-bending domain movements. Despite the motions, known hinge-bent domains/motifs which have been assembled and classified, are correctly identified. Additional matches are detected as well. This approach has been motivated by a technique for model based recognition of articulated objects originating in computer vision and robotics.     

Code domains in tandem repetitive DNA sequence structures

Traditionally, many people doing research in molecular biology attribute coding properties to a given DNA sequence if this sequence contains an open reading frame for translation into a sequence of amino acids. This protein coding capability of DNA was detected about 30 years ago. The underlying genetic code is highly conserved and present in every biological species studied so far. Today, it is obvious that DNA has a much larger coding potential for other important tasks. Apart from coding for specific RNA molecules such as rRNA, snRNA and tRNA molecules, specific structural and sequence patterns of the DNA chain itself express distinct codes for the regulation and expression of its genetic activity. A chromatin code has been defined for phasing of the histone-octamer protein complex in the nucleosome. A translation frame code has been shown to exist that determines correct triplet counting at the ribosome during protein synthesis. A loop code seems to organize the single stranded interaction of the nascent RNA chain with proteins during the splicing process, and a splicing code phases successive 5' and 3' splicing sites. Most of these DNA codes are not exclusively based on the primary DNA sequence itself, but also seem to include specific features of the corresponding higher order structures. Based on the view that these various DNA codes are genetically instructive for specific molecular interactions or processes, important in the nucleus during interphase and during cell division, the coding capability of tandem repetitive DNA sequences has recently been reconsidered.     

Multiscale modeling of macromolecular conformational changes combining concepts from rigidity and elastic network theory

The development of a two-step approach for multiscale modeling of macromolecular conformational changes is based on recent developments in rigidity and elastic network theory. In the first step, static properties of the macromolecule are determined by decomposing the molecule into rigid clusters by using the graph-theoretical approach FIRST and an all-atom representation of the protein. In this way, rigid clusters are not limited to consist of residues adjacent in sequence or secondary structure elements as in previous studies. Furthermore, flexible links between rigid clusters are identified and can be modeled as such subsequently. In the second step, dynamical properties of the molecule are revealed by the rotations-translations of blocks approach (RTB) using an elastic network model representation of the coarse-grained protein. In this step, only rigid body motions are allowed for rigid clusters, whereas links between them are treated as fully flexible. The approach was tested on a data set of 10 proteins that showed conformational changes on ligand binding. For efficiency, coarse-graining the protein results in a remarkable reduction of memory requirements and computational times by factors of 9 and 27 on average and up to 25 and 125, respectively. For accuracy, directions and magnitudes of motions predicted by our approach agree well with experimentally determined ones, despite embracing in extreme cases >50% of the protein into one rigid cluster. In fact, the results of our method are in general comparable with when no or a uniform coarse-graining is applied; and the results are superior if the movement is dominated by loop or fragment motions. This finding indicates that explicitly distinguishing between flexible and rigid regions is advantageous when using a simplified protein representation in the second step. Finally, motions of atoms in rigid clusters are also well predicted by our approach, which points to the need to consider mobile protein regions in addition to flexible ones when modeling correlated motions.     

FlexProt: alignment of flexible protein structures without a predefinition of hinge regions.

FlexProt is a novel technique for the alignment of flexible proteins. Unlike all previous algorithms designed to solve the problem of structural comparisons allowing hinge-bending motions, FlexProt does not require an a priori knowledge of the location of the hinge(s). FlexProt carries out the flexible alignment, superimposing the matching rigid subpart pairs, and detects the flexible hinge regions simultaneously. A large number of methods are available to handle rigid structural alignment. However, proteins are flexible molecules, which may appear in different conformations. Hence, protein structural analysis requires algorithms that can deal with molecular flexibility. Here, we present a method addressing specifically a flexible protein alignment task. First, the method efficiently detects maximal congruent rigid fragments in both molecules. Transforming the task into a graph theoretic problem, our method proceeds to calculate the optimal arrangement of previously detected maximal congruent rigid fragments. The fragment arrangement does not violate the protein sequence order. A clustering procedure is performed on fragment-pairs which have the same 3-D rigid transformation regardless of insertions and deletions (such as loops and turns) which separate them. Although the theoretical worst case complexity of the algorithm is O(n(6)), in practice FlexProt is highly efficient. It performs a structural comparison of a pair of proteins 300 amino acids long in about seven seconds on a standard desktop PC (400 MHz Pentium II processor with 256MB internal memory). We have performed extensive experiments with the algorithm. An assortment of these results is presented here. FlexProt can be accessed via WWW at bioinfo3d.cs.tau.ac.il/FlexProt/.     

Structure, flexibility, and mechanism of the Bacillus stearothermophilus RecU Holliday junction resolvase

Here we report a high resolution structure of RecU-Holliday junction resolvase from Bacillus stearothermophilus. The functional unit of RecU is a homodimer that contains a "mushroom" like structure with a rigid cap and two highly flexible loops extending outwards. These loops appear to be highly flexible/dynamic, and presumably are directly involved in DNA binding and holding it for catalysis. Structural modifications of both the protein and DNA upon their interaction are essential for catalysis. An Mg2+ ion is present in each of the two active sites in this homodimeric enzyme, and two water molecules are coordinated with each Mg2+ ion. Our data are consistent with one of these water molecules acting as a nucleophile and the other as a general acid. The identities of the general base and general acid involved in catalysis and the Lewis acid that stabilizes the pentacovalent transition state phosphate ion are proposed. A model for the RecU-Holliday junction DNA complex is also proposed and discussed in the context of DNA binding and cleavage.     

HingeProt: automated prediction of hinges in protein structures

Proteins are highly flexible molecules. Prediction of molecular flexibility aids in the comprehension and prediction of protein function and in providing details of functional mechanisms. The ability to predict the locations, directions, and extent of molecular movements can assist in fitting atomic resolution structures to low-resolution EM density maps and in predicting the complex structures of interacting molecules (docking). There are several types of molecular movements. In this work, we focus on the prediction of hinge movements. Given a single protein structure, the method automatically divides it into the rigid parts and the hinge regions connecting them. The method employs the Elastic Network Model, which is very efficient and was validated against a large data set of proteins. The output can be used in applications such as flexible protein-protein and protein-ligand docking, flexible docking of protein structures into cryo-EM maps, and refinement of low-resolution EM structures. The web server of HingeProt provides convenient visualization of the results and is available with two mirror sites at http://www.prc.boun.edu.tr/appserv/prc/HingeProt3 and http://bioinfo3d.cs.tau.ac.il/HingeProt/.     

Chromatin reconstitution on small DNA rings. V. DNA thermal flexibility of single nucleosomes.

The thermal flexibility of DNA minicircles reconstituted with single nucleosomes was measured relative to the naked minicircles. The measurement used a new method based on the electrophoretic properties of these molecules, whose mobility strongly depended on the DNA writhe, either of the whole minicircle, when naked, or of the extranucleosomal loop, when reconstituted. The experiment was as follows. The DNA length was first increased by one base-pair (bp), and the correlative shift in mobility resulting from the altered DNA writhe was recorded. Second, the gel temperature was increased so that the former mobility was restored. Under these conditions, the untwisting of the thermally flexible DNA due to the temperature shift exactly compensates for the increase in the DNA mean twist number resulting from the one bp addition. The relative thermal flexibility was then calculated as the ratio between the increases in temperature measured for the naked and the reconstituted DNAs, respectively. The figure, 0.69 (+/- 0.07), was used to derive the length of DNA in interaction with the histones, 109 (+/- 25) bp. Such length was in good agreement with the mean value of 115 bp we have previously obtained from the distribution of the angles between DNAs at the entrance and exit of similar nucleosomes measured from high resolution electron microscopy. This consistency further reinforces our previous conclusion that minicircle-reconstituted nucleosomes, with 1.3(109/83) to 1.4(115/83) turns of superhelical DNA, show no crossing of entering and exiting DNAs when the loop is in its most probable configuration, and therefore, that these nucleosomes behave topologically as "single-turn" particles. The present data are also within the range of values, 50 to 100 bp of thermally rigid DNA per nucleosome, obtained by others for yeast plasmid chromatin, suggesting that the "single-turn" particle notion may be extended to this particular case of naturally-occurring H1-free chromatin. However, these data are quite different from the 230 bp figure derived from thermal measurements of reconstituted H1-free minichromosomes. It is proposed that nucleosome interactions occurring in this chromatin, but not in yeast chromatin, may be partly responsible for the discrepancy.     

Topological constraints strongly affect chromatin reconstitution in silico

The fundamental building block of chromatin, and of chromosomes, is the nucleosome, a composite material made up from DNA wrapped around a histone octamer. In this study we provide the first computer simulations of chromatin self-assembly, starting from DNA and histone proteins, and use these to understand the constraints which are imposed by the topology of DNA molecules on the creation of a polynucleosome chain. We take inspiration from the in vitro chromatin reconstitution protocols which are used in many experimental studies. Our simulations indicate that during self-assembly, nucleosomes can fall into a number of topological traps (or local folding defects), and this may eventually lead to the formation of disordered structures, characterised by nucleosome clustering. Remarkably though, by introducing the action of topological enzymes such as type I and II topoisomerase, most of these defects can be avoided and the result is an ordered 10-nm chromatin fibre. These findings provide new insight into the biophysics of chromatin formation, both in the context of reconstitution in vitro and in terms of the topological constraints which must be overcome during de novo nucleosome formation in vivo, e.g. following DNA replication or repair.