Local deformation studies of chain molecules: differential conditions for changes of dihedral angles

New first and second-order differential equations for changes of dihedral angles characterizing local deformations of chain molecules with fixed bond lengths and bond angles are derived. Two methods for integrating the differential relations are given. The proposed method is used to generate a path of locally deformed conformations around a β-turn region of a small protein, bovine pancreatic trypsin inhibitor. The variable regions change their conformations by more than 3 Å root-mean-square distance value whereas the fixed regions stay within 0.02 Å. Possible applications of this method are in the field of computer graphics, Monte Carlo simulations, and energy minimization calculations of chain molecules.     

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.     

Refined models for computer calculations in protein engineering. Calibration and testing of atomic potential functions compatible with more efficient calculations

A reappraisal has been made of interatomic potential functions for protein structure calculations using the all-atom approximation (except CH, CH2 and CH3, which are treated as "united atoms"). Some key problems are identified and treated. The potential functions are somewhat novel in form and consistent with more efficient and robust folding algorithms. In addition, the potentials are calibrated for for the rigid geometry approximation, since use of fixed standard bond lengths and valence angles (and fixed trans planar peptide groups) reduces the number of conformational variables and saves a great deal of computer time. Though these algorithms demand the use of potential functions of this special type, these functions can be readily implemented in more classical programs for the conformational analysis of proteins. They are calibrated or tested against a large body of experimental data, including extended basis set ab initio, quantum mechanical calculations, nuclear magnetic resonance spectroscopic data and dipole moment data for di- and oligopeptides, characteristic ratio data for random coil homopolypeptides, extensive data from peptide solubility studies, and experimental structures of polyalanine fibres and globular proteins. This paper will form the basis of a further report, which will include investigations of how water might be more realistically represented subject to the computing power available.     

Sculpting proteins interactively: continual energy minimization embedded in a graphical modeling system.

We describe a new paradigm for modeling proteins in interactive computer graphics systems--continual maintenance of a physically valid representation, combined with direct user control and visualization. This is achieved by a fast algorithm for energy minimization, capable of real-time performance on all atoms of a small protein, plus graphically specified user tugs. The modeling system, called Sculpt, rigidly constrains bond lengths, bond angles, and planar groups (similar to existing interactive modeling programs), while it applies elastic restraints to minimize the potential energy due to torsions, hydrogen bonds, and van der Waals and electrostatic interactions (similar to existing batch minimization programs), and user-specified springs. The graphical interface can show bad and/or favorable contacts, and individual energy terms can be turned on or off to determine their effects and interactions. Sculpt finds a local minimum of the total energy that satisfies all the constraints using an augmented Lagrange-multiplier method; calculation time increases only linearly with the number of atoms because the matrix of constraint gradients is sparse and banded. On a 100-MHz MIPS R4000 processor (Silicon Graphics Indigo), Sculpt achieves 11 updates per second on a 20-residue fragment and 2 updates per second on an 80-residue protein, using all atoms except non-H-bonding hydrogens, and without electrostatic interactions. Applications of Sculpt are described: to reverse the direction of bundle packing in a designed 4-helix bundle protein, to fold up a 2-stranded beta-ribbon into an approximate beta-barrel, and to design the sequence and conformation of a 30-residue peptide that mimics one partner of a protein subunit interaction. Computer models that are both interactive and physically realistic (within the limitations of a given force field) have 2 significant advantages: (1) they make feasible the modeling of very large changes (such as needed for de novo design), and (2) they help the user understand how different energy terms interact to stabilize a given conformation. The Sculpt paradigm combines many of the best features of interactive graphical modeling, energy minimization, and actual physical models, and we propose it as an especially productive way to use current and future increases in computer speed.     

Program for the visualization and interactive study of molecules on a calligraphic display system

Mops is a computer program for the visualization and interactive analysis of crystallographic and molecular structures on a calligraphic PS 300 display system. This system allows the interactive display of bond lengths, bond angles and torsion angles with colour coding of atom types as well as crystalline packing interactions. Mops is also capable of easily drawing a chosen image on the screen using the Ortep program. This facility allows the very fast preparation of slides or illustrations.     

Solution structure and dynamics of the central CCP module pair of a poxvirus complement control protein

The complement control protein (CCP) module (also known as SCR, CCP or sushi domain) is prevalent amongst proteins that regulate complement activation. Functional and mutagenesis studies have shown that in most cases two or more neighbouring CCP modules form specific binding sites for other molecules. Hence the orientation in space of a CCP module with respect to its neighbours and the flexibility of the intermodular junction are likely to be critical for function. Vaccinia virus complement control protein (VCP) is a complement regulatory protein composed of four tandemly arranged CCP modules. The solution structure of the carboxy-terminal half of this protein (CCP modules 3 and 4) has been solved previously. The structure of the central portion (modules 2 and 3, VCP approximately 2,3) has now also been solved using NMR spectroscopy at 37 degrees C. In addition, the backbone dynamics of VCP approximately 2,3 have been characterised by analysis of its (15)N relaxation parameters. Module 2 has a typical CCP module structure while module 3 in the context of VCP approximately 2,3 has some modest but significant differences in structure and dynamics to module 3 within the 3,4 pair. Modules 2 and 3 do not share an extensive interface, unlike modules 3 and 4. Only two possible NOEs were identified between the bodies of the modules, but a total of 40 NOEs between the short intermodular linker of VCP approximately 2,3 and the bodies of the two modules determines a preferred, elongated, orientation of the two modules in the calculated structures. The anisotropy of rotational diffusion has been characterised from (15)N relaxation data, and this indicates that the time-averaged structure is more compact than suggested by (1)H-(1)H NOEs. The data are consistent with the presence of many intermodular orientations, some of which are kinked, undergoing interconversion on a 10(-8)-10(-6) second time-scale. A reconstructed representation of modules 2-4 allows visualisation of the spatial arrangement of the 11 substitutions that occur in the more potent complement inhibitor from Variola (small pox) virus.     

Validation of nuclear magnetic resonance structures of proteins and nucleic acids: hydrogen geometry and nomenclature

A statistical analysis is reported of 1,200 of the 1,404 nuclear magnetic resonance (NMR)-derived protein and nucleic acid structures deposited in the Protein Data Bank (PDB) before 1999. Excluded from this analysis were the entries not yet fully validated by the PDB and the more than 100 entries that contained < 95% of the expected hydrogens. The aim was to assess the geometry of the hydrogens in the remaining structures and to provide a check on their nomenclature. Deviations in bond lengths, bond angles, improper dihedral angles, and planarity with respect to estimated values were checked. More than 100 entries showed anomalous protonation states for some of their amino acids. Approximately 250,000 (1.7%) atom names differed from the consensus PDB nomenclature. Most of the inconsistencies are due to swapped prochiral labeling. Large deviations from the expected geometry exist for a considerable number of entries, many of which are average structures. The most common causes for these deviations seem to be poor minimization of average structures and an improper balance between force-field constraints for experimental and holonomic data. Some specific geometric outliers are related to the refinement programs used. A number of recommendations for biomolecular databases, modeling programs, and authors submitting biomolecular structures are given.     

蛋白质结构与功能研究中的分子模拟技术

分子模拟技术为蛋白质的研究提供了一种崭新的手段,在理论上解决了结构预测和功能分析以及蛋白质工程实施方面所面临的难题。它在蛋白质的结构预测和模建工作中占有举足轻重的地位,实现了生物技术与计算机技术的完美结合。本文简要阐述了该技术的基本步骤和工作原理,并以目前应用最广的生物大分子领域的商品化分子模拟软件Accelrys公司基于Linux系统开发的InsightII为例,介绍了相关程序模块的功能和作用,同时结合该技术在蛋白质的结构预测和模建、结构与功能关系分析、分子设计等过程中的开发与应用,加以具体说明和展望。     

Crystallographic structure refinement of Chromatium high potential iron protein at two Angstroms resolution.

The structure of Chromatium high potential iron protein (HiPIP) has been refined by semiautomatic Fo-Fc (observed minus calculated structure amplitude Fourier methods to a convential R index, R=sum of the absolute value of Fo-Fc divided by the sum of Fo, of 24.7% for a model in which bond distances and angles are constrained to standard values. Bond length and angle constraints were applied only intermittenly during the computations. At a late stage of the refinement, atomic parameters for only the Fe4S4 cluster plus the 4 associated cystein S-gamma atoms were adjusted by least squares methods and kept fixed during the rest of the refinement. The refined model consists of 625 of the 632 nonhydrogen atoms in the protein plus 75 water molecules. Seven side chain atoms could not be located in the final electron density map. A computer program rather than visual inspection was used wherever possible in the refinement: for locating water molecules, for removing water molecules that too closely approach other atoms, for deleting atoms that lay in regions of low electron density, and for evaluating the progress of refinement. Fo-Fc Fourier refinement is sufficiently economical to be applied routinely in protein crystal structure determinations. The complete HiPIP refinement required approximately 12 hours of CDC 3600 computer time and cost less than $3000 starting from a "trial structure," based upon multipe isomorphoous replacement phases, which gave an R of 43%...     

Refined crystal structure (2.3 A) of a double-headed winged bean alpha-chymotrypsin inhibitor and location of its second reactive site.

The crystal structure of a double-headed alpha-chymotrypsin inhibitor, WCI, from winged bean seeds has now been refined at 2.3 A resolution to an R-factor of 18.7% for 9,897 reflections. The crystals belong to the hexagonal space group P6(1)22 with cell parameters a = b = 61.8 A and c = 212.8 A. The final model has a good stereochemistry and a root mean square deviation of 0.011 A and 1.14 degrees from ideality for bond length and bond angles, respectively. A total of 109 ordered solvent molecules were localized in the structure. This improved structure at 2.3 A led to an understanding of the mechanism of inhibition of the protein against alpha-chymotrypsin. An analysis of this higher resolution structure also helped us to predict the location of the second reactive site of the protein, about which no previous biochemical information was available. The inhibitor structure is spherical and has twelve anti-parallel beta-strands with connecting loops arranged in a characteristic beta-trefoil fold common to other homologous serine protease inhibitors in the Kunitz (STI) family as well as to some non homologous functionally unrelated proteins. A wide variation in the surface loop regions is seen in the latter ones.     

Refined crystal structure of carboxypeptidase A at 1.54 A resolution

The crystal structure of bovine carboxypeptidase A (Cox) has been refined at 1.54 A resolution using the restrained least-squares algorithm of Hendrickson & Konnert (1981). The crystallographic R factor (formula; see text) for structure factors calculated from the final model is 0.190. Bond lengths and bond angles in the carboxypeptidase A model have root-mean-square deviations from ideal values of 0.025 A and 3.6 degrees, respectively. Four examples of a reverse turn like structure (the "Asx" turn) requiring an aspartic acid or asparagine residue are observed in this structure. The Asx turn has the same number of atoms as a reverse turn, but only one peptide bond, and the hydrogen bond that closes the turn is between the Asx side-chain CO group and a main-chain NH group. The distributions of CO-N and NH-O hydrogen bond angles in the alpha-helices and beta-sheet structures of carboxypeptidase A are centered about 156 degrees. A total of 192 water molecules per molecule of enzyme are included in the final model. Unlike the hydrogen bonding geometry observed in the secondary structure of the enzyme, the CO-O(wat) hydrogen bond angle is distributed about 131 degrees, indicating the role of the lone pair electrons of the carbonyl oxygen in the hydrogen bond interaction. Twenty four solvent molecules are observed buried within the protein. Several of these waters are organized into hydrogen-bonded chains containing up to five waters. The average temperature factor for atoms in carboxypeptidase A is 8 A2, and varies from 5 A2 in the center of the protein, to over 30 A2 at the surface.     

一种研究蛋白质晶体中分子堆积的图形程序—PACKING

在蛋白质晶体结构研究中常需分析分子在晶胞内的堆积,本文介绍一种用于IRIS-4D计算机的图形软件,可显示分子在晶胞中的堆积图形、计算原子之间的距离和键角等,进行分子置换、模拟不同的分子堆积模型。     

Relaxation of backbone bond geometry improves protein energy landscape modeling

A key issue in macromolecular structure modeling is the granularity of the molecular representation. A fine‐grained representation can approximate the actual structure more accurately, but may require many more degrees of freedom than a coarse‐grained representation and hence make conformational search more challenging. We investigate this tradeoff between the accuracy and the size of protein conformational search space for two frequently used representations: one with fixed bond angles and lengths and one that has full flexibility. We performed large‐scale explorations of the energy landscapes of 82 protein domains under each model, and find that the introduction of bond angle flexibility significantly increases the average energy gap between native and non‐native structures. We also find that incorporating bonded geometry flexibility improves low resolution X‐ray crystallographic refinement. These results suggest that backbone bond angle relaxation makes an important contribution to native structure energetics, that current energy functions are sufficiently accurate to capture the energetic gain associated with subtle deformations from chain ideality, and more speculatively, that backbone geometry distortions occur late in protein folding to optimize packing in the native state.     

Conformational analysis of molecular chains using nano-kinematics

We present algorithms for 3–D manipulation and conforma–tionalanalysis of molecular chains, when bond lengths, bond anglesand related dihedral angles remain fixed. These algorithms areuseful for local deformations of linear molecules, exact ringclosure in cyclic molecules and molecular embedding for shortchains. Other possible applications include structure prediction,protein folding, conformation energy analysis and 3D molecularmatching and docking. The algorithms are applicable to all serialmolecular chains and make no asssumptions about their geometry.We make use of results on direct and inverse kinematics fromrobotics and mechanics literature and show the correspondencebetween kinematics and conformational analysis of molecules.In particular, we pose these problems algebraically and computeall the solutions making use of the structure of these equationsand matrix computations. The algorithms have been implementedand perform well in practice. In particular, they take tensof milliseconds on current workstations for local deformationsand chain closures on molecular chains consisting of six orfewer rotatable dihedral angles     

Role of amino acid properties to determine backbone tau(N-Calpha-C') stretching angle in peptides and proteins

The analysis of the basic geometry of amino acid residues of protein structures has demonstrated the invariability of all the bond lengths and bond angles except for tau, the backbone N-Calpha-C' angle. This angle can be widened or contracted significantly from the tetrahedral geometry to accommodate various other strains in the structure. In order to accurately determine the cause for this deviation, a survey is made for the tau angles using the peptide structures and the ultrahigh resolution protein structures. The average deviation of N-Calpha-C' angles from tetrahedral geometry for each amino acid in all the categories were calculated and then correlated with forty-eight physiochemical, energetic and conformational properties of amino acids. Linear and multiple regression analysis were carried out between the amino acid deviation and the 48 properties. This study confirms the deviation of tau angles in both the peptide and protein structures but similar forces do not influence them. The peptide structures are influenced by physical properties whereas as expected the conformational properties influence the protein structures. And it is not any single property that dominates the deviation but the combination of different factors contributes to the tau angle deviation.     

Tuna cytochrome c at 2.0 A resolution. III. Coordinate optimization and comparison of structures.

Optimum coordinate sets have been obtained for ferrocytochrome c and the two symmetry-independent molecules of ferricytochrome c from tuna at 2.0 A resolution by making the best fit of models with standard bond lengths and angles to the experimental electron density maps (1977) J. Biol. Chem. 252, 759-785, as a preliminary to full refinement with 1.5 A data. Both the Diamond model-building programs and locally developed minicomputer routines were tried, with the latter preferred for economy and ease of operation, although both gave satisfactory results. Atomic coordinates are available on microfiche or from the Brookhaven Protein Data Bank. Using the two ferricytochrome molecules as a control, no differences between oxidized and reduced cytochrome molecules can be seen that are outside the probable limits of accuracy of the 2.0 A analysis. Rotation and subtractive difference map comparisons also show no conformation changes. If believable differences do appear in the course of the 1.5 A refinement now underway, these should be no more than minor breathing of main chain or adjustment of side chains.     

Shape-dependent control of cell growth, differentiation, and apoptosis: switching between attractors in cell regulatory networks

Development of characteristic tissue patterns requires that individual cells be switched locally between different phenotypes or "fates;" while one cell may proliferate, its neighbors may differentiate or die. Recent studies have revealed that local switching between these different gene programs is controlled through interplay between soluble growth factors, insoluble extracellular matrix molecules, and mechanical forces which produce cell shape distortion. Although the precise molecular basis remains unknown, shape-dependent control of cell growth and function appears to be mediated by tension-dependent changes in the actin cytoskeleton. However, the question remains: how can a generalized physical stimulus, such as cell distortion, activate the same set of genes and signaling proteins that are triggered by molecules which bind to specific cell surface receptors. In this article, we use computer simulations based on dynamic Boolean networks to show that the different cell fates that a particular cell can exhibit may represent a preprogrammed set of common end programs or "attractors" which self-organize within the cell's regulatory networks. In this type of dynamic network model of information processing, generalized stimuli (e.g., mechanical forces) and specific molecular cues elicit signals which follow different trajectories, but eventually converge onto one of a small set of common end programs (growth, quiescence, differentiation, apoptosis, etc.). In other words, if cells use this type of information processing system, then control of cell function would involve selection of preexisting (latent) behavioral modes of the cell, rather than instruction by specific binding molecules. Importantly, the results of the computer simulation closely mimic experimental data obtained with living endothelial cells. The major implication of this finding is that current methods used for analysis of cell function that rely on characterization of linear signaling pathways or clusters of genes with common activity profiles may overlook the most critical features of cellular information processing which normally determine how signal specificity is established and maintained in living cells.