Nonatomic solvent-driven Voronoi tessellation of proteins: an open tool to analyze protein folds

Back in time to the Gly-rich prototype of the phosphate binding elementary function

Binding of nucleotides and their derivatives is one of the most ancient elementary functions dating back to the Origin of Life. We review here the works considering one of the key elements in binding of (di)nucleotide-containing ligands - phosphate binding. We start from a brief discussion of major participants, conditions, and events in prebiotic evolution that resulted in the Origin of Life. Tracing back to the basic functions, including metal and phosphate binding, and, potentially, formation of primitive protein-protein interactions, we focus here on the phosphate binding. Critically assessing works on the structural, functional, and evolutionary aspects of phosphate binding, we perform a simple computational experiment reconstructing its most ancient and generic sequence prototype. The profiles of the phosphate binding signatures have been derived in form of position-specific scoring matrices (PSSMs), their peculiarities depending on the type of the ligands have been analyzed, and evolutionary connections between them have been delineated. Then, the apparent prototype that gave rise to all relevant phosphate-binding signatures had also been reconstructed. We show that two major signatures of the phosphate binding that discriminate between the binding of dinucleotide- and nucleotide-containing ligands are GxGxxG and GxxGxG, respectively. It appears that the signature archetypal for dinucleotide-containing ligands is more generic, and it can frequently bind phosphate groups in nucleotide-containing ligands as well. The reconstructed prototype's key signature GxGGxG underlies the role of glycine residues in providing flexibility and interactions necessary for binding the phosphate groups. The prototype also contains other ancient amino acids, valine, and alanine, showing versatility towards evolutionary design and functional diversification.

Analyses of displacements resulting from a point mutation in proteins

The effects of a single residue substitution on the protein backbone are frequently quite small and there are many other potential sources of structural variation for protein. We present here a methodology considering different sources of distortions in order to isolate the very effect of the mutation. To validate our methodology, we consider a well-studied family with many single mutants: the human lysozyme. Most of the perturbations are expected to be at the very localisation of the mutation, but in many cases the effects are propagated at long range. We show that the distances between the mutated residue and the 5% most disturbed residues exponentially decreases. One third of the affected residues are in direct contact with the mutated position; the remaining two thirds are potential allosteric effects. We confirm the reliability of the residues identified as significantly perturbed by comparing our results to experimental studies. We confirm with the present method all the previously identified perturbations. This study shows that mutations have long-range impact on protein backbone that can be detected, although the displacement of the affected atoms is small.

Oncogenesis, lipids rafts and liquid crystals: A nanoscopic supplementary field for applied researches and a new hope of advances in cancer

Liquid crystals (LC) are an intermediate state between an ordered crystalline solid and a more disordered liquid. LCs (or mesophases) are ubiquitous in living systems, optimizing multiple biological functions that could not operate in purely solid or liquid environments as both mobility and organization are needed. One of us recently suggested that there is an information vector, shared by neurodegenerative and infectious pathologies, to be found within lipid rafts in an ordered liquid (Lo) form mediated by cholesterol. Here we extend this underlying mechanism to oncogenic processes. The specificity of our approach lies in highlighting the direct involvement of liquid crystals in early carcinogenic processes, by identifying specific metabolic pathways, with the intention of focusing research effort on this level, now that this has become technically feasible. Exploring LCs in living bodies reveals links between numerous oncogenic mechanisms. The approach is based on the geometric properties of amphiphilic (hydrophilic and lipophilic) plasma and intracellular membranes, the phospholipids of which are an example of the lamellar LC phase. These LCs underlie cell signaling and signaling pathways disorders at membrane level: consequently, they are directly concerned with deregulation underlying many cancerous processes. We demonstrate the implication of cancer cell membranes mesophases. That is in the membranes mesophases that are initiated most of metabolic pathways, leading to downstream pathogenic intracellular mechanisms. The concepts of order and of symmetry, in the mathematical sense, involved in condensed matter accompany informed adaptive supramolecular chemical processes in forming self-organizing mesogenic molecular assemblies. Multidisciplinary teamwork combining knowledge from different fields holds out the hope of therapeutic progress upstream of irreversible cancerous processes, while conserving the physiological integrity of the cells themselves.

Neurodegenerative diseases, infectious pathologies and liquid crystals: Hypothesis of a common information vector involving a multidisciplinary approach

The existence of an information vector common to very different pathologies is the hypothesis of one of us, the argumentation and discussion of which we present here. It is a mesomorphic state of material called liquid crystal. The liquid-ordered (Lo) phase, made up of membrane rafts mediated by cholesterol, lies at the center of our concept. This mesophase is either preexistent and then modified by the pathogenic process, or initiated by the latter. The most notable disorders involved are Alzheimer's, Parkinson's, Charcot and Creutzfeldt-Jakob diseases, flu-like illnesses and acquired immunodeficiency syndrome (AIDS), although this list may well be extended to include other anisotropic, birefringent amyloid proteinopathies, which have properties compatible with those of liquid crystals. Incidentally, numerous conventional infectious pathologies can also induce a mesomorphic state in cell membranes. It has already been established that mesophases contain the chemical information transmitted from the intramolecular microscopic level, where covalent bonds are applied. Information is then transmitted at the intermolecular macroscopic level, where it is made up of informed, self-organized collections. Electrostatic interactions, coordination of metallic ions, van der Waals forces and donor-acceptor interactions of hydrogen bonding all come into play. These reactions are produced notably in the nanodomains enriched by cholesterol and sphingolipids. Lipids in the cell membrane are where the phase separations favoring elastic hydrodynamic instabilities conducive to the Lo phase take place. In addition, perturbations of the mesomorphic states of membrane rafts due, for example, to lipid dysfunction-even mild ones-with an intracerebral or generalized location could bring about a displacement of thermodynamic equilibrium favoring the initiation and progression of the pathologies under consideration here. Indeed, the most recent work has rendered our hypothesis highly probable. Moreover, our hypothesis is supported by medical and biological observations arising essentially from biophysics and widely documented in the literature. Thus, these facts expand the number of diagnostic and therapeutic perspectives that could be evoked and perhaps even demand exploration.

Basic units of protein structure, folding, and function

Study of the hierarchy of domain structure with alternative sets of domains and analysis of discontinuous domains, consisting of remote segments of the polypeptide chain, raised a question about the minimal structural unit of the protein domain. The hypothesis on the decisive role of the polypeptide backbone in determining the elementary units of globular proteins have led to the discovery of closed loops. It is reviewed here how closed loops form the loop-n-lock structure of proteins, providing the foundation for stability and designability of protein folds/domain and underlying their co-translational folding. Simplified protein sequences are considered here with the aim to explore the basic principles that presumably dominated the folding and stability of proteins in the early stages of structural evolution. Elementary functional loops (EFLs), closed loops with one or few catalytic residues, are, in turn, units of the protein function. They are apparent descendants of the prebiotic ring-like peptides, which gave rise to the first functional folds/domains being fused in the beginning of the evolution of protein structure. It is also shown how evolutionary relations between protein functional superfamilies and folds delineated with the help of EFLs can contribute to establishing the rules for design of desired enzymatic functions. Generalized descriptors of the elementary functions are proposed to be used as basic units in the future computational design.

A novel evaluation of residue and protein volumes by means of Laguerre tessellation

Amino acids control the protein folding process and maintain its functional fold. This study underlines the interest of the Laguerre tessellation to determine relevant amino acid volumes in proteins. Previous studies used a limited number of proteins and only buried residues. The present computations improve the method and results on three main points: (i) a large, high-quality updated and refined data bank of proteins is used; (ii) all residues are taken into account, including those at the protein surface, thanks to (iii) the addition of a realistic solvent. The new values of the average and standard deviation of amino acid volumes show significant corrections with respect to previous studies. Another issue of the method is the polyhedral protein/water interface area (PIA) which quantifies the exposure of atoms or residues to the solvent. We propose this PIA as a new, parameter-free, alternative for measuring accessibility. The comparison with NACCESS is satisfactory; however, the methods disagree in pointing out buried residues: where NACCESS evaluates to zero, the exposure given by PIA ranges from 0 to 20%. Variations of average residue volumes have been analyzed under several conditions, e.g., how they depend on protein size and on secondary structure environments. As it is based on strong mathematical grounds and on numerous high-quality protein structures, our work gives a reliable methodology and up-to-date values of amino acid volumes and surface accessibility.

The tumour necrosis factor as a mediator of vessel inflammation: importance of exposed receptor residues for its neutralization

BACKGROUND

The analysis of the macromolecular tumour necrosis factor (TNF)-receptor interface helps to understand the antigenicity of this inflammatory protein.

METHOD

The calculations are based on structural data from the protein database. The residues of the macromolecular interface are identified in the interface contact matrix, a plot of pair-wise interactions between adjacent residues in the TNF-receptor complex. Starting from the matrix elements, the most exposed residues of the receptor, together with their relative contribution to the interface, are determined. This is done by Voronoi tessellation, a unique and well defined partition of the protein into polyhedral cells defining the proprietary space of the associated amino acid and its contact faces with neighboured residue cells.

RESULTS

Several interfacial receptor residues, contributing with a total amount of 63% to the macromolecular interface, could be identified.

CONCLUSION

Based on the assumption that residues with higher interfacial exposure values are playing the most important role in TNF-receptor complex, they will be the original material for further developments in engineering more efficient TNF blockers.

Characterization of non-trivial neighborhood fold constraints from protein sequences using generalized topohydrophobicity

Prediction of key features of protein structures, such as secondary structure, solvent accessibility and number of contacts between residues, provides useful structural constraints for comparative modeling, fold recognition, ab-initio fold prediction and detection of remote relationships. In this study, we aim at characterizing the number of non-trivial close neighbors, or long-range contacts of a residue, as a function of its “topohydrophobic” index deduced from multiple sequence alignments and of the secondary structure in which it is embedded. The “topohydrophobic” index is calculated using a two-class distribution of amino acids, based on their mean atom depths. From a large set of structural alignments processed from the FSSP database, we selected 1485 structural sub-families including at least 8 members, with accurate alignments and limited redundancy. We show that residues within helices, even when deeply buried, have few non-trivial neighbors (0–2), whereas β-strand residues clearly exhibit a multimodal behavior, dominated by the local geometry of the tetrahedron (3 non-trivial close neighbors associated with one tetrahedron; 6 with two tetrahedra). This observed behavior allows the distinction, from sequence profiles, between edge and central β-strands within β-sheets. Useful topological constraints on the immediate neighborhood of an amino acid, but also on its correlated solvent accessibility, can thus be derived using this approach, from the simple knowledge of multiple sequence alignments.

From protein sequence space to elementary protein modules

The formatted protein sequence space is built from identical size fragments of prokaryotic proteins (112 complete proteomes). Connecting sequence-wise similar fragments (points in the space) results in the formation of numerous networks, that combine sometimes different types of proteins sharing, though, fragments with similar or distantly related sequences. The networks are mapped on individual protein sequences revealing distinct regions (modules) associated with prominent networks with well-defined functional identities. Presence of multiple sites of sequence conservation (modules) in a given protein sequence suggests that the annotated protein function may be decomposed in "elementary" subfunctions of the respective modules. The modules correspond to previously discovered conserved closed loop structures and their sequence prototypes.

Pocket extraction on proteins via the Voronoi diagram of spheres

Proteins consist of atoms. Given a protein, the automatic recognition of depressed regions, called pockets, on the surface of proteins is important for protein-ligand docking and facilitates fast development of new drugs. Recently, computational approaches have emerged for recognizing pockets from the geometrical point of view. Presented in this paper is a geometric method for the pocket recognition which is based on the Voronoi diagram for atoms. Given a Voronoi diagram, the proposed algorithm transforms the atomic structure to meshes which contain the information of the proximity among atoms, and then recognizes depressions on the surface of a protein using the meshes.

An algorithm for three-dimensional Voronoi S-network

The paper presents an algorithm for calculating the three-dimensional Voronoi-Delaunay tessellation for an ensemble of spheres of different radii (additively-weighted Voronoi diagram). Data structure and output of the algorithm is oriented toward the exploration of the voids between the spheres. The main geometric construct that we develop is the Voronoi S-network (the network of vertices and edges of the Voronoi regions determined in relation to the surfaces of the spheres). General scheme of the algorithm and the key points of its realization are discussed. The principle of the algorithm is that for each determined site of the network we find its neighbor sites. Thus, starting from a known site of the network, we sequentially find the whole network. The starting site of the network is easily determined based on certain considerations. Geometric properties of ensembles of spheres of different radii are discussed, the conditions of applicability and limitations of the algorithm are indicated. The algorithm is capable of working with a wide variety of physical models, which may be represented as sets of spheres, including computer models of complex molecular systems. Emphasis was placed on the issue of increasing the efficiency of algorithm to work with large models (tens of thousands of atoms). It was demonstrated that the experimental CPU time increases linearly with the number of atoms in the system, O(n).

Comprehensive statistical analysis of residues interaction specificity at protein-protein interfaces

We calculated interchain contacts on the atomic level for nonredundant set of 4602 protein-protein interfaces using an unbiased Voronoi-Delaune tessellation method, and made 20x20 residue contact matrixes both for homodimers and heterocomplexes. The area of contacts and the distance distribution for these contacts were calculated on both the residue and the atomic levels. We analyzed residue area distribution and showed the existence of two types of interresidue contacts: stochastic and specific. We also derived formulas describing the distribution of contact area for stochastic and specific interactions in parametric form. Maximum pairing preference index was found for Cys-Cys contacts and for oppositely charged interactions. A significant difference in residue contacts was observed between homodimers and heterocomplexes. Interfaces in homodimers were enriched with contacts between residues of the same type due to the effects of structure symmetry.

Walking through the protein sequence space: Towards new generation of the homology modeling

A new method is proposed to reveal apparent evolutionary relationships between protein fragments with similar 3D structures by finding "intermediate" sequences in the proteomic database. Instead of looking for homologies and intermediates for a whole protein domain, we build a chain of intermediate short sequences, which allows one to link similar structural modules of proteins belonging to the same or different families. Several such chains of intermediates can be combined into an evolutionary tree of structural protein modules. All calculations were made for protein fragments of 20 aa residues. Three evolutionary trees for different module structures are described. The aim of the paper is to introduce the new method and to demonstrate its potential for protein structural predictions. The approach also opens new perspectives for protein evolution studies.

Spectral properties of contact matrix: application to proteins

A protein can be modelled by a set of points representing its amino acids. Topologically, this set of points is entirely defined by its contact matrix (adjacency matrix in graph theory). The contact matrix characterizing the relation between neighboring amino acids is deduced from Voronoi or Laguerre decomposition. This method allows contact matrices to be defined without any arbitrary cut-off that could induce arbitrary effects. Eigenvalues of these matrices are related with elementary excitations in proteins. We present some spectral properties of these matrices that reflect global properties of proteins. The eigenvectors indicate participation of each amino acids to the excitation modes of the proteins. It is interesting to compare the protein modelled as a close packing of amino acids, with a random close packing of spheres. The main features of the protein are those of a packing, a result that confirms the importance of the dense packing model for proteins. Nevertheless there are some properties, specific to the hierarchical organization of the protein: the primary chain order, the secondary structures and the domain structures.

Voronoi and Voronoi-related tessellations in studies of protein structure and interaction

The three-dimensional structure of a protein can be modeled by a set of polyhedra drawn around its atoms or residues. The tessellation invented by Voronoi in 1908, and other tessellations of space derived from it, provide versatile representations of three-dimensional structures. In recent years, they have been used to investigate a series of issues relating to proteins: atom and residue volumes, packing, folding, interactions and binding.

A docking analysis of the statistical physics of protein–protein recognition

We describe protein-protein recognition within the frame of the random energy model of statistical physics. We simulate, by docking the component proteins, the process of association of two proteins that form a complex. We obtain the energy spectrum of a set of protein-protein complexes of known three-dimensional structure by performing docking in random orientations and scoring the models thus generated. We use a coarse protein representation where each amino acid residue is replaced by its Voronoï cell, and derive a scoring function by applying the evolutionary learning program ROGER to a set of parameters measured on that representation. Taking the scores of the docking models to be interaction energies, we obtain energy spectra for the complexes and fit them to a Gaussian distribution, from which we derive physical parameters such as a glass transition temperature and a specificity transition temperature.

Computer simulation study of intermolecular voids in unsaturated phosphatidylcholine lipid bilayers

Computer simulation of the liquid crystalline phase of five different hydrated unsaturated phosphadidylcholine (PC) lipid bilayers, i.e., membranes built up by 18:0/18:1omega9cis PC, 18:0/18:2omega6cis PC, 18:0/18:3omega3cis PC, 18:0/20:4omega6cis PC, and 18:0/22:6omega3cis PC molecules have been performed on the isothermal-isobaric ensemble at 1 atm and 303 K. (The notation n:domegapcis specifies the lipid tails: n refers to the total number of carbon atoms in the chain, d is the number of the methylene-interrupted double bonds, p denotes the number of carbons between the chain terminal CH(3) group and the nearest double bond, and cis refers to the conformation around the double bonds.) The characteristics of the free volume in these systems have been analyzed by means of a generalized version of the Voronoi-Delaunay method [M. G. Alinchenko et al., J. Phys. Chem. B 108, 19056 (2004)]. As a reference system, the hydrated bilayer of the saturated 14:014:0 PC molecules (dimyristoylphosphatidylcholine) has also been analyzed. It has been found that the profiles of the fraction of the free volume across the membrane exhibit a rather complex pattern. This fine structure of the free volume fraction profiles can be interpreted by dividing the membrane into three separate major zones (i.e., zones of the aqueous, polar, and apolar parts of the membrane) and defining five subzones within these zones according to the average position of various atomic groups in the membrane. The fraction of the free volume in the middle of the membrane is found to increase with increasing unsaturation of the sn-2 chain of the lipid molecule. This is due to the fact that with increasing number of methylene-interrupted double bonds the lipid tails become more flexible, and hence they do not extend to the middle of the membrane. It is found that there are no broad enough preformed channels in the bilayers through which small penetrants, such as water molecules, can readily go through; however, the existing channels can largely facilitate the permeation of these molecules.

Voro3D: 3D Voronoi tessellations applied to protein structures

Voro3D is an original easy-to-use tool, which provides a brand new point of view on protein structures through the three-dimensional (3D) Voronoi tessellations. To construct the Voronoi cells associated with each amino acid by a number of different tessellation methods, Voro3D uses a protein structure file in the PDB format as an input. After calculation, different structural properties of interest like secondary structures assignment, environment accessibility and exact contact matrices can be derived without any geometrical cut-off. Voro3D provides also a visualization of these tessellations superimposed on the associated protein structure, from which it is possible to model a polygonal protein surface using a model solvent or to quantify, for instance, the contact areas between a protein and a ligand.

AVAILABILITY

The software executable file for PC using Windows 98, 2000, NT, XP can be freely downloaded at http://www.lmcp.jussieu.fr/~mornon/voronoi.html

CONTACT

franck.dupuis@sanofi-aventis.com; jean-paul-mornon@imcp.jussieu.fr.

Protein secondary structure assignment through Voronoï tessellation

We present a new automatic algorithm, named VoTAP (Voronoï Tessellation Assignment Procedure), which assigns secondary structures of a polypeptide chain using the list of alpha-carbon coordinates. This program uses three-dimensional Voronoï tessellation. This geometrical tool associates with each amino acid a Voronoï polyhedron, the faces of which unambiguously define contacts between residues. Thanks to the face area, for the contacts close together along the primary structure (low-order contacts) a distinction is made between strong and normal ones. This new definition yields new contact matrices, which are analyzed and used to assign secondary structures. This assignment is performed in two stages. The first one uses contacts between residues close together along the primary structure and is based on data collected on a bank of 282 well-refined nonredundant structures. In this bank, associations were made between the prints defined by these low-order contacts and the assignments performed by different automatic methods. The second step focuses on the strand assignment and uses contacts between distant residues. Comparison with several other automatic assignment methods are presented, and the influence of resolution on the assignment is investigated.

Evolutionary aspects of protein structure and folding

The traditional reconstruction of molecular events of the past based on sequence conservation becomes very vague beyond one to two billion years ago. There are certain molecular features, however, such as polymer flexibility and loop closure, that are conserved merely because of their physical nature. This allows one to penetrate the earliest stages of protein evolution.