Twisting and untwisting a single DNA molecule covered by RecA protein

We study dsDNA-RecA interactions by exerting forces in the pN range on single DNA molecules while the interstrand topological state is controlled owing to a magnetic tweezers setup. We show that unwinding a duplex DNA molecule induces RecA polymerization even at moderate force. Once initial polymerization has nucleated, the extent of RecA coverage still depends on the degree of supercoiling: exerting a positive or negative torsional constraint on the fiber forces partial depolymerization, with a strikingly greater stability when ATPgammaS is used as a cofactor instead of ATP. This nucleofilament's sensitivity to topology might be a way for the bacterial cell to limit consumption of precious RecA monomers when DNA damage is addressed through homologous recombination repair.     

Distances as Degrees of Freedom

Abstract

Tertiary contact distance information of varying resolution for large biological molecules abounds in the literature. The results provided herein develop a framework by which information of this type can be used to reduce the allowable configuration space of a macromolecule. The approach combines graph theory and distance geometry. Large molecules are represented as simple, undirected graphs, with atoms, or groups, as vertices, and distances between them as edges. It is shown that determination of the exact structure of a molecule in three dimensions only requires the specification of all the distances in a single tetrahedron, and four distances to every other atom. This is 4N-10 distances which is a subset of the total N(N-l)/2 unique distances in a molecule consisting of N atoms. This requirement for only 4N-10 distances has serious implications for distance geometry implementations in which all N(N-l)/2 distances are specified by bounded random numbers. Such distance matrices represent overspecified systems which when solved lead to non-obvious distribution of any error caused by inherent contradictions in the input data. It is also shown that numerous valid subsets of 4N-10 distances can be constructed. It is thus possible to tailor a subset of distances using all known distances as degrees of freedom, and thereby reduce the configuration space of the molecule. Simple algebraic relationships are derived that relate sets of distances, and complicated rotations are avoided. These relationships are used to construct minimum, complete sets of distances necessary to specify the exact structure of the entire molecule in three dimensions from incomplete distance information, and to identify sets of inconsistent distances. The method is illustrated for the flexible structural types present in large ribosomal RNAs: 1.) A five-membered ring; 2.) a chemically bonded chain with its ends in contact (i.e., a hairpin loop); 3.) the spatial orientation of two separate molecules, and; 4.) an RNA helix that can have variation in individual base pairs, giving rise to global deviation from standardized helical forms.     

Symmetry and information content of chemical structures

A method, based on symmetry, is suggested for determining the information content of systems. A comparison has been made between the information for symmetry, topology, and chemical composition. The new information measure increases when the asymmetry of the molecules and the number of atoms in the latter increases. It can distinguish between different molecular conformations, and give a linear correlation with the absolute entropy for homologous series of chemical compounds.     

Distances as degrees of freedom

Tertiary contact distance information of varying resolution for large biological molecules abounds in the literature. The results provided herein develop a framework by which information of this type can be used to reduce the allowable configuration space of a macromolecule. The approach combines graph theory and distance geometry. Large molecules are represented as simple, undirected graphs, with atoms, or groups, as vertices, and distances between them as edges. It is shown that determination of the exact structure of a molecule in three dimensions only requires the specification of all the distances in a single tetrahedron, and four distances to every other atom. This is 4N-10 distances which is a subset of the total N(N-1)/2 unique distances in a molecule consisting of N atoms. This requirement for only 4N-10 distances has serious implications for distance geometry implementations in which all N(N-1)/2 distances are specified by bounded random numbers. Such distance matrices represent overspecified systems which when solved lead to non-obvious distribution of any error caused by inherent contradictions in the input data. It is also shown that numerous valid subsets of 4N-10 distances can be constructed. It is thus possible to tailor a subset of distances using all known distances as degrees of freedom, and thereby reduce the configuration space of the molecule. Simple algebraic relationships are derived that relate sets of distances, and complicated rotations are avoided. These relationships are used to construct minimum, complete sets of distances necessary to specify the exact structure of the entire molecule in three dimensions from incomplete distance information, and to identify sets of inconsistent distances. The method is illustrated for the flexible structural types present in large ribosomal RNAs: 1.) A five-membered ring; 2.) a chemically bonded chain with its ends in contact (i.e., a hairpin loop); 3.) the spatial orientation of two separate molecules, and; 4.) an RNA helix that can have variation in individual base pairs, giving rise to global deviation from standardized helical forms.     

Essentiality and damage in metabolic networks

Understanding the architecture of physiological functions from annotated genome sequences is a major task for postgenomic biology. From the annotated genome sequence of the microbe Escherichia coli, we propose a general quantitative definition of enzyme importance in a metabolic network. Using a graph analysis of its metabolism, we relate the extent of the topological damage generated in the metabolic network by the deletion of an enzyme to the experimentally determined viability of the organism in the absence of that enzyme. We show that the network is robust and that the extent of the damage relates to enzyme importance. We predict that a large fraction (91%) of enzymes causes little damage when removed, while a small group (9%) can cause serious damage. Experimental results confirm that this group contains the majority of essential enzymes. The results may reveal a universal property of metabolic networks.     

Thiol proteases. Comparative studies based on the high-resolution structures of papain and actinidin, and on amino acid sequence information for cathepsins B and H, and stem bromelain

An accurate three-dimensional structure is known for papain (1.65 A resolution) and actinidin (1.7 A). A detailed comparison of these two structures was performed to determine the effect of amino acid changes on the conformation. It appeared that, despite only 48% identity in their amino acid sequence, different crystallization conditions and different X-ray data collection techniques, their structures are surprisingly similar with a root-mean-square difference of 0.40 A between 76% of the main-chain atoms (differences less than 3 sigma). Insertions and deletions cause larger differences but they alter the conformation over a very limited range of two to three residues only. Conformations of identical side-chains are generally retained to the same extent as the main-chain conformation. If they do change, this is due to a modified local environment. Several examples are described. Spatial positions of hydrogen bonds are conserved to a greater extent than are the specific groups involved. The greatest structural similarity is found for the active site residues of papain and actinidin, for the internal water molecules and for the main-chain conformation of residues in alpha-helices and anti-parallel beta-sheet structure. This was reflected also in the similarity of the temperature factors. It suggests that the secondary structural elements form the skeleton of the molecule and that their interaction is the main factor in directing the fold of the polypeptide chain. Therefore, substitution of residues in the skeleton will, in general, have the most drastic effect on the conformation of the protein molecule. In papain and actinidin, some main-chain-side-chain hydrogen bonds are also strongly conserved and these may determine the folding of non-repetitive parts of the structure. Furthermore, we included primary structure information for three homologous thiol proteases: stem bromelain, and the cathepsins B and H. By combining the three-dimensional structural information for papain and actinidin with sequence homologies and identities, we conclude that the overall folding pattern of the polypeptide chain is grossly the same in all five proteases, and that they utilize the same catalytic mechanism.     

Graph theoretic topology of the Great but small Barrier Reef world

The transport of larvae between coral reefs is critical to the functioning of Australia’s Great Barrier Reef (GBR) because it determines recruitment rates and genetic exchange. One way of modelling the transport of larvae from one reef to another is to use information about currents. However the connectivity relationships of the entire system have not been fully examined. Graph theory provides a framework for the representation and analysis of connections via larval transport. In the past, the geometric arrangement (topology) of biological systems, such as food webs and neural networks, has revealed a common set of characteristics known as the ‘small world’ property. We use graph theory to examine and describe the topology and connectivity of a species living in 321 reefs in the central section of the GBR over 32 years. This section of the GBR can be described by a directional weighted graph, and we discovered that it exhibits scale-free small-world characteristics. The conclusion that the GBR is a small-world network for biological organisms is robust to variation in both the life history of the species modelled and yearly variation in hydrodynamics. The GBR is the first reported mesoscale biological small-world network.     

Topological information content and chemical reactions

The difference of the topological information content of two reacting molecules and that of their reaction products is calculated for several topological types of chemical reactions, illustrating the influence of the structure of the reagents and of the reaction product. It is shown that the change in the topological information content in a chemical reaction can be positive as well as negative, depending on the way the reagents approach each other and thus on the reaction product formed. A quantitative measure of structural specificity is introduced.     

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.     

A robust and efficient automated docking algorithm for molecular recognition.

A completely automated method is described for determining the most likely mode of binding of two (macro)molecules from the knowledge of their three-dimensional structures alone. The method is based on well-known graph theoretical techniques and has been used successfully to determine and rationalize the binding of a number of known macromolecular complexes. In this article we present results for a special case of the general molecular recognition problem--given the information concerning the particular atoms involved in the binding for one of the molecules, the algorithm can correctly identify the corresponding (contacting) atoms of the other molecule. The approach used can be easily extended to the general molecular recognition problem and requires the extraction of maximal common subgraphs. In these studies the docking of the macromolecules was achieved without the aid of computer graphics or other visual aids. The algorithm has been used to determine the correct mode of binding of a protein antigen to an antibody in approximately 100 min on a DEC micro VAX 3600.     

A high-order graph generating self-organizing structure

A large class of neural network models have their units organized in a lattice with fixed topology or generate their topology during the learning process. These network models can be used as neighborhood preserving map of the input manifold, but such a structure is difficult to manage since these maps are graphs with a number of nodes that is just one or two orders of magnitude less than the number of input points (i.e., the complexity of the map is comparable with the complexity of the manifold) and some hierarchical algorithms were proposed in order to obtain a high-level abstraction of these structures. In this paper a general structure capable to extract high order information from the graph generated by a large class of self-organizing networks is presented. This algorithm will allow to build a two layers hierarchical structure starting from the results obtained by using the suitable neural network for the distribution of the input data. Moreover the proposed algorithm is also capable to build a topology preserving map if it is trained using a graph that is also a topology preserving map.     

Fast flexible modeling of RNA structure using internal coordinates

Modeling the structure and dynamics of large macromolecules remains a critical challenge. Molecular dynamics (MD) simulations are expensive because they model every atom independently, and are difficult to combine with experimentally derived knowledge. Assembly of molecules using fragments from libraries relies on the database of known structures and thus may not work for novel motifs. Coarse-grained modeling methods have yielded good results on large molecules but can suffer from difficulties in creating more detailed full atomic realizations. There is therefore a need for molecular modeling algorithms that remain chemically accurate and economical for large molecules, do not rely on fragment libraries, and can incorporate experimental information. RNABuilder works in the internal coordinate space of dihedral angles and thus has time requirements proportional to the number of moving parts rather than the number of atoms. It provides accurate physics-based response to applied forces, but also allows user-specified forces for incorporating experimental information. A particular strength of RNABuilder is that all Leontis-Westhof basepairs can be specified as primitives by the user to be satisfied during model construction. We apply RNABuilder to predict the structure of an RNA molecule with 160 bases from its secondary structure, as well as experimental information. Our model matches the known structure to 10.2 Angstroms RMSD and has low computational expense.     

Topological Small-World Organization of the Fibroblastic Reticular Cell Network Determines Lymph Node Functionality

Fibroblastic reticular cells (FRCs) form the cellular scaffold of lymph nodes (LNs) and establish distinct microenvironmental niches to provide key molecules that drive innate and adaptive immune responses and control immune regulatory processes. Here, we have used a graph theory-based systems biology approach to determine topological properties and robustness of the LN FRC network in mice. We found that the FRC network exhibits an imprinted small-world topology that is fully regenerated within 4 wk after complete FRC ablation. Moreover, in silico perturbation analysis and in vivo validation revealed that LNs can tolerate a loss of approximately 50% of their FRCs without substantial impairment of immune cell recruitment, intranodal T cell migration, and dendritic cell-mediated activation of antiviral CD8⁺ T cells. Overall, our study reveals the high topological robustness of the FRC network and the critical role of the network integrity for the activation of adaptive immune responses.     

Calculation of protein conformations by proton-proton distance constraints. A new efficient algorithm

We have developed a method to determine the three-dimensional structure of a protein molecule from such a set of distance constraints as can be determined by nuclear magnetic resonance studies. The currently popular methods for distance geometry based on the use of the metric matrix are applicable only to small systems. The method developed here is applicable to large molecules, such as proteins, with all atoms treated explicitly. This method works in the space of variable dihedral angles and determines a three-dimensional structure by minimization of a target function. We avoid difficulties hitherto inherent in this type of approach by two new devices: the use of variable target functions; and a method of rapid calculation of the gradient of the target functions. The method is applied to the determination of the structures of a small globular protein, bovine pancreatic trypsin inhibitor, from several artificial sets of distance constraints extracted from the X-ray crystal structure of this molecule. When a good set of constraints was available for both short- and long-range distances, the crystal structure was regenerated nearly exactly. When some ambiguities, such as those expected in experimental information, are allowed, the protein conformation can be determined up to a few local deformations. These ambiguities are mainly associated with the low resolving power of the short-range information.