New methodology for computer-aided modelling of biomolecular structure and dynamics. 1. Non-cyclic structures

A general methodology is proposed for the conformational modelling of biomolecular systems. The approach allows one: (i) to describe the system under investigation by an arbitrary set of internal variables, i.e., torsion angles, bond angles, and bond lengths; it offers a possibility to pass from the free structure to a completely fixed one with the number of variables from 3N to zero, respectively, where N is the number of atoms; (ii) to consider both, a single molecule and a complex of many molecules, (e.g., proteins, water, ligands, etc.) in terms of one universal model; (iii) to study the dynamics of the system using explicit analytical Lagrangian equations of motion, thus opening up possibilities for investigations of slow concerted motions such as domain oscillations in proteins etc.; (iv) to calculate the partial derivatives of various functions of conformation, e.g., the conformational energy or external constraints imposed, using a standard efficient procedure regardless of the variables and the structure of the system. The approach is meant to be used in various investigations concerning the conformations and dynamics of biomacromolecules.     

Improving consensus structure by eliminating averaging artifacts

Background  

Common structural biology methods (i.e., NMR and molecular dynamics) often produce ensembles of molecular structures. Consequently, averaging of 3D coordinates of molecular structures (proteins and RNA) is a frequent approach to obtain a consensus structure that is representative of the ensemble. However, when the structures are averaged, artifacts can result in unrealistic local geometries, including unphysical bond lengths and angles.     

Normal mode analysis as a method to derive protein dynamics information from the Protein Data Bank

Normal mode analysis (NMA) can facilitate quick and systematic investigation of protein dynamics using data from the Protein Data Bank (PDB). We developed an elastic network model-based NMA program using dihedral angles as independent variables. Compared to the NMA programs that use Cartesian coordinates as independent variables, key attributes of the proposed program are as follows: (1) chain connectivity related to the folding pattern of a polypeptide chain is naturally embedded in the model; (2) the full-atom system is acceptable, and owing to a considerably smaller number of independent variables, the PDB data can be used without further manipulation; (3) the number of variables can be easily reduced by some of the rotatable dihedral angles; (4) the PDB data for any molecule besides proteins can be considered without coarse-graining; and (5) individual motions of constituent subunits and ligand molecules can be easily decomposed into external and internal motions to examine their mutual and intrinsic motions. Its performance is illustrated with an example of a DNA-binding allosteric protein, a catabolite activator protein. In particular, the focus is on the conformational change upon cAMP and DNA binding, and on the communication between their binding sites remotely located from each other. In this illustration, NMA creates a vivid picture of the protein dynamics at various levels of the structures, i.e., atoms, residues, secondary structures, domains, subunits, and the complete system, including DNA and cAMP. Comparative studies of the specific protein in different states, e.g., apo- and holo-conformations, and free and complexed configurations, provide useful information for studying structurally and functionally important aspects of the protein.     

Mechanical force can fine-tune redox potentials of disulfide bonds

Mechanical force applied along a disulfide bond alters its rate of reduction. We here aimed at quantifying the direct effect of force onto the chemical reactivity of a sulfur-sulfur bond in contrast to indirect, e.g., steric or mechanistic, influences. To this end, we evaluated the dependency of a disulfide bond's redox potential on a pulling force applied along the system. Our QM/MM simulations of cystine as a model system take conformational dynamics and explicit solvation into account and show that redox potentials increase over the whole range of forces probed here (30-3320 pN), and thus even in the absence of a significant disulfide bond elongation (<500 pN). Instead, at low forces, dihedrals and angles, as the softer degrees of freedom are stretched, contribute to the destabilization of the oxidized state. We find physiological forces to be likely to tune the disulfide's redox potentials to an extent similar to the tuning within proteins by point mutations.     

Algorithmic Generation of Freely Jointed Hard Sphere Chains and Properties of Inertial Tensors

Abstract

A statistical algorithm, capable of generating a large number of freely jointed hard sphere chains, is presented. This is the first of a series of algorithms being developed to model unfolded proteins by different modes of hard sphere chains. The aim of these studies is to systematically investigate the effects of different factors, such as atomic radii, bond angles, torsion angles, chain length, etc., on the conformation of unfolded proteins and other random polymers. As continuous models, various types of hard sphere chains enable one to isolate the aforementioned factors one at a time for investigation and thus are advantageous over discrete lattice models. In particular, the freely jointed hard sphere chain model allows one to evaluate the excluded volume effect. As a first step in this endeavor, the average determinant D(N,r) and the average trace T(N, r) of the inertial tensor A of the random chains were calculated at various sphere radii r and chain lengths N. It is found that both the average determinant D(N,r) and the average trace T(N,r) scale linearly with chain length N. after logarithmic transformation. However, the critical exponent of D(N,r) increases with r faster than that of T(N,r) as a result of the non-commutativity between the det operator and the average operator < >. The significance of the algorithm and the results obtained on understanding random polypeptide chains are discussed.     

Analysis of disulphide bond connectivity patterns in protein tertiary structure

The analysis of disulphide bond containing proteins in the Protein Data Bank (PDB) revealed that out of 27,209 protein structures analyzed, 12,832 proteins contain at least one intra-chain disulphide bond and 811 proteins contain at least one inter-chain disulphide bond. The intra-chain disulphide bond containing proteins can be grouped into 256 categories based on the number of disulphide bonds and the disulphide bond connectivity patterns (DBCPs) that were generated according to the position of half-cystine residues along the protein chain. The PDB entries corresponding to these 256 categories represent 509 unique SCOP superfamilies. A simple web-based computational tool is made freely available at the website http://www.ccmb.res.in/bioinfo/dsbcp that allows flexible queries to be made on the database in order to retrieve useful information on the disulphide bond containing proteins in the PDB. The database is useful to identify the different SCOP superfamilies associated with a particular disulphide bond connectivity pattern or vice versa. It is possible to define a query based either on a single field or a combination of the following fields, i.e., PDB code, protein name, SCOP superfamily name, number of disulphide bonds, disulphide bond connectivity pattern and the number of amino acid residues in a protein chain and retrieve information that match the criterion. Thereby, the database may be useful to select suitable protein structural templates in order to model the more distantly related protein homologs/analogs using the comparative modeling methods.     

Projection Methods for the Analysis of Complex Motions in Macromolecules

Abstract

In studies of macromolecular dynamics it is often desirable to analyze complex motions in terms of a small number of coordinates. Only for simple types of motion, e.g., rigid-body motions, these coordinates can be easily constructed from the Cartesian atomic coordinates. This article presents an approach that is applicable to infinitesimal or approximately infinitesimal motions, e.g., Cartesian velocities, normal modes, or atomic fluctuations. The basic idea is to characterize the subspace of interesting motions by a set of (possibly linearly dependent) vectors describing elementary displacements, and then project the dynamics onto this subspace. Often the elementary displacements can be found by physical intuition. The restriction to small displacements facilitates the study of complicated coupled motions and permits the construction of collective-motion subspaces that do not correspond to any set of generalized coordinates.

As an example for this technique, we analyze the low-frequency normal modes of proteins up to ≈ 20 THz (600 cm^?1) in order to see what kinds of motions occupy which frequency range. This kind of analysis is useful for the interpretation of spectroscopic measurements on proteins, e.g., inelastic neutron scattering experiments.     

Algorithmic generation of freely jointed hard sphere chains and properties of their inertial tensors

A statistical algorithm, capable of generating a large number of freely jointed hard sphere chains, is presented. This is the first of a series of algorithms being developed to model unfolded proteins by different modes of hard sphere chains. The aim of these studies is to systematically investigate the effects of different factors, such as atomic radii, bond angles, torsion angles, chain length, etc., on the conformation of unfolded proteins and other random polymers. As continuous models, various types of hard sphere chains enable one to isolate the aforementioned factors one at a time for investigation and thus are advantageous over discrete lattice models. In particular, the freely jointed hard sphere chain model allows one to evaluate the excluded volume effect. As a first step in this endeavor, the average determinant D(N, r) and the average trace T(N, r) of the inertial tensor A of the random chains were calculated at various sphere radii r and chain lengths N. It is found that both the average determinant D(N, r) and the average trace T(N, r) scale linearly with chain length N after logarithmic transformation. However, the critical exponent of D(N, r) increases with r faster than that of T(N, r) as a result of the non-commutativity between the det operator and the average operator < >. The significance of the algorithm and the results obtained on understanding random polypeptide chains are discussed.     

Influence of the environment in the conformation of alpha-helices studied by protein database search and molecular dynamics simulations

The influence of the solvent on the main-chain conformation (phi and Psi dihedral angles) of alpha-helices has been studied by complementary approaches. A first approach consisted in surveying crystal structures of both soluble and membrane proteins. The residues of analysis were further classified as exposed to either the water (polar solvent) or the lipid (apolar solvent) environment or buried to the core of the protein (intermediate polarity). The statistical results show that the more polar the environment, the lower the value of phi(i) and the higher the value of Psi(i) are. The intrahelical hydrogen bond distance increases in water-exposed residues due to the additional hydrogen bond between the peptide carbonyl oxygen and the aqueous environment. A second approach involved nanosecond molecular dynamics simulations of poly-Ala alpha-helices in environments of different polarity: water to mimic hydrophilic environments that can form hydrogen bonds with the peptide carbonyl oxygen and methane to mimic hydrophobic environments without this hydrogen bond capabilities. These simulations reproduce similar effects in phi and Psi angles and intrahelical hydrogen bond distance and angle as observed in the protein survey analysis. The magnitude of the intrahelical hydrogen bond in the methane environment is stronger than in the water environment, suggesting that alpha-helices in membrane-embedded proteins are less flexible than in soluble proteins. There is a remarkable coincidence between the phi and Psi angles obtained in the analysis of residues exposed to the lipid in membrane proteins and the results from computer simulations in methane, which suggests that this simulation protocol properly mimic the lipidic cell membrane and reproduce several structural characteristics of membrane-embedded proteins. Finally, we have compared the phi and Psi torsional angles of Pro kinks in membrane protein crystal structures and in computer simulations.     

Pex, analytical tools for PDB files. II. H-Pex: noncanonical H-bonds in alpha-helices

We use the H-Pex (Thomas et al., this issue) to analyze the main chain interactions in 131 proteins. In antiparallel beta-sheets, the geometry of the N...O bond is: median N...O distances, 2.9 SA, C==O...N angles at 154 degrees and the C alpha--C==O...H angles are dispersed around 3 degrees. In some instances, the other side of the C==O axis is occupied by a HC alpha. As recently supported by Vargas et al. (J Am Chem Soc 2000;122:4750-4755) C alpha H...O and NH...O could cooperate to sheet stability. In alpha-helices, the main chain C==O interact with the NH of their n + 4 neighbor on one side, and with a C beta H or C gamma H on the other side. The median O...N distance (3.0 A) and C==N angle (147 degrees) suggest a canonical H-bond, but the C alpha--C==O...H dihedral angle invalidates this option, since the hydrogen attacks the oxygen at 122 degrees, i.e., between the sp(2) and pi orbitals. This supports that the H-bond is noncanonical. In many instances, the C gamma H or the C beta H of the n + 4 residue stands opposite to the NH with respect to the oxygen. Therefore, we propose that, in alpha-helices, the C gamma H or C beta H and the NH of the n + 4 residue hold the oxygen like an electrostatic pincher. Proteins 2001;43:37-44.     

Nonorthogonal tight-binding model with H–C–N–O parameterisation

A parametric nonorthogonal tight-binding model (NTBM1) with the set of parameters for H–C–N–O systems is presented. This model compares well with widely used semi-empirical AM1 and PM3/PM7 models but contains less fitting parameters per atom. All NTBM1 parameters are derived based on a criterion of the best agreement between the calculated and experimental values of bond lengths, valence angles and binding energies for various H–C–N–O molecules. Results for more than 200 chemical compounds are reported. Parameters are currently available for hydrogen, carbon, nitrogen, oxygen atoms and corresponding interatomic interactions. The model has a good transferability and can be used for both relaxation of large molecular systems (e.g., high-molecular compounds or covalent cluster complexes) and long-timescale molecular dynamics simulation (e.g., modelling of thermal decomposition processes). The program package based on this model is available for download at no cost from http://ntbm.info.     

An analysis of the class of gene regulatory functions implied by a biochemical model

Understanding the integrated behavior of genetic regulatory networks, in which genes regulate one another's activities via RNA and protein products, is emerging as a dominant problem in systems biology. One widely studied class of models of such networks includes genes whose expression values assume Boolean values (i.e., on or off). Design decisions in the development of Boolean network models of gene regulatory systems include the topology of the network (including the distribution of input- and output-connectivity) and the class of Boolean functions used by each gene (e.g., canalizing functions, post functions, etc.). For example, evidence from simulations suggests that biologically realistic dynamics can be produced by scale-free network topologies with canalizing Boolean functions. This work seeks further insights into the design of Boolean network models through the construction and analysis of a class of models that include more concrete biochemical mechanisms than the usual abstract model, including genes and gene products, dimerization, cis-binding sites, promoters and repressors. In this model, it is assumed that the system consists of N genes, with each gene producing one protein product. Proteins may form complexes such as dimers, trimers, etc. The model also includes cis-binding sites to which proteins may bind to form activators or repressors. Binding affinities are based on structural complementarity between proteins and binding sites, with molecular binding sites modeled by bit-strings. Biochemically plausible gene expression rules are used to derive a Boolean regulatory function for each gene in the system. The result is a network model in which both topological features and Boolean functions arise as emergent properties of the interactions of components at the biochemical level. A highly biased set of Boolean functions is observed in simulations of networks of various sizes, suggesting a new characterization of the subset of Boolean functions that are likely to appear in gene regulatory networks.     

The structure of the ends of α-helices in globular proteins: effect of additional hydrogen bonds and implications for helix formation

We prepared a set of about 2000 α-helices from a relational database of high-resolution three-dimensional structures of globular proteins, and identified additional main chain i ← i+3 hydrogen bonds at the ends of the helices (i.e., where the hydrogen bonding potential is not fulfilled by canonical i ← i+4 hydrogen bonds). About one-third of α-helices have such additional hydrogen bonds at the N-terminus, and more than half do so at the C-terminus. Although many of these additional hydrogen bonds at the C-terminus are associated with Schellman loops, the majority are not. We compared the dihedral angles at the termini of α-helices having or lacking the additional hydrogen bonds. Significant differences were found, especially at the C-terminus, where the dihedral angles at positions C2 and C1 in the absence of additional hydrogen bonds deviate substantially from those occurring within the α-helix. Using a novel approach we show how the structure of the C-terminus of the α-helix can emerge from that of constituent overlapping α-turns and β-turns, which individually show a variation in dihedral angles at different positions. We have also considered the direction of propagation of the α-helix using this approach. If one assumes that helices start as a single α-turn and grow by successive addition of further α-turns, the paths for growth in the N → C and C → N directions differ in a way that suggests that extension in the C → N direction is favored.     

Molecular modeling study of intercalation complexes of tricyclic carboxamides with d(CCGGCGCCGG)₂ and d(CGCGAATTCGCG)₂

Tricyclic dyes with different mesoatoms such as xanthenes (fluorescein, eosin) anthracenes and acridines (proflavine) approved by the Food and Drug Administration (FDA) for use in foods, pharmaceuticals and cosmetic preparations interact with DNA, and some of them do so through intercalation. Hyperchem 7.5, Spartan 04, Yasara 10.5.14 program packages and molecular modeling, molecular mechanics and dynamics techniques with the oligonucleotides d(CCGGCGCCGG)2 and d(CGCGAATTCGCG)2 were utilized in order to examine the mode of binding to DNA of a range of tricyclic carboxamides bearing N,N-dimethylaminoethyl side chain, i.e., 9-amino-DACA, anthracene, acridine-1-carboxamide, acridine-4-carboxamide (DACA), azacridine, phenazine, pyridoquinoxaline, oxopyridoquinoxaline, phenoxazine and xanthenone or N,N-dimethylaminobutyl moiety, i.e., phenazine and acridine. The bicyclic quinoline-8-carboxamide was also examined for comparison reasons. On the basis of our data, prerequisite for the interaction between protonated N,N-dimethylaminoethyl moiety and guanine is the formation of only one internal hydrogen bond between carboxamide and peri NH + in the case of 9-amino-DACA or peri N in the cases of DACA, azacridine, phenazine and pyridoquinoxaline. The presence of an additional internal hydrogen bond between oxygen carboxamide and protonated N,N-dimethylamino group in the cases of tricyclic systems bearing peri NH (phenoxazine) or O (xanthenone) group, prevents the interaction between side chain and guanine. Also, the formation of one internal hydrogen bond between oxygen carboxamide and protonated N,N-dimethylamino group inhibits the interaction between side chain and guanine in the case of acridine-1-carboxamide. Our findings are in accordance with previously reported results obtained from the kinetic studies of the binding of acridine and related tricyclic carboxamides to DNA.     

Quantifying Burial,the Transport of Matter from the Lake Biosphere to the Geosphere

Burial is one of the most fundamental processes in contexts of massbalance calculations for substances (such as nutrients, organics, metals and radionuclides) in lakes. Substances can leave a lake by two processes, outflow, i.e., the transport to a downstream system, and burial, i.e., the transport by sedimentation from the lake biosphere to the geosphere. This work gives for the first time, to there best of the author's knowledge, a review on the factors and processes regulating burial and presents a general model for burial. This approach accounts for bottom dynamic conditions (i.e., where areas of fine sediment erosion, transport and accumulation prevail), sedimentation, bioturbation, mineralisation, and the depth and age of the bioactive sediment layer. This approach has been critically tested with very good results for radiocesium, radiostrontium, many metals, calcium from liming and phosphorus, but it has not been presented before in a comprehensive way. This model for burial is meant to be used in massbalance models based on ordinary differential equations (i.e., box models) in contexts where burial is not a target y‐variable but a necessary model variable (an x‐variable). This means that there are also specific demands on this approach, e.g., it must be based on readily accessible driving variables so that it is not too difficult to use the model in practice within the context of an overall lake model. The factors influencing burial, e.g., the deposition of materials and the depth of the bioactive sediment layer, are also needed in calculations of sediment concentrations and to determine amounts of substances or pollutants in sediments. To carry out such calculations, one also needs information on sediment bulk density, water content and organic content. This paper also presents new empirical models for such calculations to be used in the new model for burial.     

DMS dynamics in the most oligotrophic subtropical zones of the global ocean

The influences of physico-chemical and biological processes on dimethylsulfide (DMS) dynamics in the most oligotrophic subtropical zones of the global ocean were investigated. As metrics for the dynamics of DMS and the so-called ‘summer DMS paradox’ of elevated summer concentrations when surface chlorophyll a (Chl) and particulate organic carbon (POC) levels are lowest, we used the DMS-to-Chl and DMS-to-POC ratios in the context of three independent and complementary approaches. Firstly, field observations of environmental variables (such as the solar radiation dose, phosphorus limitation of phytoplankton and bacterial growth) were used alongside discrete DMS, Chl and POC estimates extracted from global climatologies (i.e., a ‘station based’ approach). We then used monthly climatological data for DMS, Chl, and POC averaged over the biogeographic province wherein a given oligotrophic subtropical zone resides (i.e., a ‘province based’ approach). Finally we employed sensitivity experiments with a new DMS module coupled to the ocean general circulation and biogeochemistry model PISCES to examine the influence of various processes in governing DMS dynamics in oligotrophic regions (i.e., a ‘model based’ approach). We find that the ‘station based’ and ‘province based’ approaches yield markedly different results. Interestingly, the ‘province based’ approach suggests the presence of a ‘summer DMS paradox’ in most all of the oligotrophic regions we studied. In contrast, the ‘station based’ approach suggests that the ‘summer DMS paradox’ is only present in the Sargasso Sea and eastern Mediterranean. Overall, we found the regional differences in the absolute and relative concentrations of DMS between 5 of the most oligotrophic regions of the world’s oceans were better accounted for by their nutrient dynamics (specifically phosphorus limitation) than by physical factors often invoked, e.g., the solar radiation dose. Our ‘model based’ experiments suggest that it is the limitation of phytoplankton/bacterial production and bacterial consumption of DMS by pervasive phosphorus limitation that is responsible for the ‘summer DMS paradox’.     

A proteomic survey of rat cerebral cortical synaptosomes

Previous findings from our laboratory and others indicate that two-dimensional gel electrophoresis (2-DE) can be used to study protein expression in defined brain regions, but mainly the proteins which are present in high abundance in glia are readily detected. The current study was undertaken to determine the protein profile in a synaptosomal subcellular fraction isolated from the cerebral cortex of the rat. Both 2-DE and liquid chromatography - tandem mass spectrometry (LC-MS/MS) procedures were used to isolate and identify proteins in the synaptosomal fraction and accordingly >900 proteins were detected using 2-DE; the 167 most intense gel spots were isolated and identified with matrix-assisted laser desorption/ionization - time of flight peptide mass fingerprinting or LC-MS/MS. In addition, over 200 proteins were separated and identified with the LC-MS/MS "shotgun proteomics" technique, some in post-translationally modified form. The following classes of proteins associated with synaptic function were detected: (a) proteins involved in synaptic vesicle trafficking-docking (e.g., SNAP-25, synapsin I and II, synaptotagmin I, II, and V, VAMP-2, syntaxin 1A and 1B, etc.); (b) proteins that function as transporters or receptors (e.g., excitatory amino acid transporters 1 and 2, GABA transporter 1); (c) proteins that are associated with the synaptic plasma membrane (e.g., post-synaptic density-95/synapse-associated protein-90 complex, neuromodulin (GAP-43), voltage-dependent anion-selective channel protein (VDACs), sodium-potassium ATPase subunits, alpha 2 spectrin, septin 7, etc.); and (d) proteins that mediate intracellular signaling cascades that modulate synaptic function (e.g., calmodulin, calcium-calmodulin-dependent protein kinase subunits, etc.). Other identified proteins are associated with mitochondrial or general cytosolic function. Of the two proteins identified as endoplasmic reticular, both interact with the synaptic SNARE complex to regulate vesicle trafficking. Taken together, these results suggest that the integrity of the synaptosomes was maintained during the isolation procedure and that this subcellular fractionation technique enables the enrichment of proteins associated with synaptic function. The results also suggest that this experimental approach can be used to study the differential expression of multiple proteins involved in alterations of synaptic function.     

Characterization of beta-turn and Asx-turns mimicry in a model peptide: stabilization via C--H . . . O interaction

The chemical synthesis and single-crystal X-ray diffraction analysis of a model peptide, Boc-Thr-Thr-NH2 (1) comprised of proteinogenic residues bearing an amphiphilic Cbeta -stereogenic center, has been described. Interestingly, the analysis of its molecular structure revealed the existence of a distinct conformation that mimics a typical beta-turn and Asx-turns, i.e., the two Thr residues occupy the left- and right-corner positions. The main-chain torsion angles of the N- and C-terminal residues i.e., semiextended: phi = -68.9 degrees , psi = 128.6 degrees ; semifolded: phi = -138.1 degrees , psi = 2.5 degrees conformations, respectively, in conjunction with a gauche- disposition of the obligatory C-terminus Thr CgammaH3 group, characterize the occurrence of the newly described beta-turn- and Asx-turns-like topology. The preferred molecular structure is suggested to be stabilized by an effective nonconventional main-chain to side-chain Ci=O . . . H--Cgamma(i+2)-type intraturn hydrogen bond. Noteworthy, the observed topology of the resulting 10-membered hydrogen-bonded ring is essentially similar to the one perceived for a classical beta-turn and the Asx-turns, stabilized by a conventional intraturn hydrogen bond. Considering the signs as well as magnitudes of the backbone torsion angles and the orientation of the central peptide bond, the overall mimicked topology resembles the type II beta-turn or type II Asx-turns. An analysis of Xaa-Thr sequences in high-resolution X-ray elucidated protein structures revealed the novel topology prevalence in functional proteins (unpublished). In view of indubitable structural as well as functional importance of nonconventional interactions in bioorganic and biomacromolecules, we intend to highlight the participation of Thr CgammaH in the creation of a short-range C=O . . . H--Cgamma -type interaction in peptides and proteins.