Towards predicting Ca2+‐binding sites with different coordination numbers in proteins with atomic resolution

Ca²⁺‐binding sites in proteins exhibit a wide range of polygonal geometries that directly relate to an equally‐diverse set of biological functions. Although the highly‐conserved EF‐Hand motif has been studied extensively, non‐EF‐Hand sites exhibit much more structural diversity which has inhibited efforts to determine the precise location of Ca²⁺‐binding sites, especially for sites with few coordinating ligands. Previously, we established an algorithm capable of predicting Ca²⁺‐binding sites using graph theory to identify oxygen clusters comprised of four atoms lying on a sphere of specified radius, the center of which was the predicted calcium position. Here we describe a new algorithm, MUG (MUltiple Geometries), which predicts Ca²⁺‐binding sites in proteins with atomic resolution. After first identifying all the possible oxygen clusters by finding maximal cliques, a calcium center (CC) for each cluster, corresponding to the potential Ca²⁺ position, is located to maximally regularize the structure of the (cluster, CC) pair. The structure is then inspected by geometric filters. An unqualified (cluster, CC) pair is further handled by recursively removing oxygen atoms and relocating the CC until its structure is either qualified or contains fewer than four ligand atoms. Ligand coordination is then determined for qualified structures. This algorithm, which predicts both Ca²⁺ positions and ligand groups, has been shown to successfully predict over 90% of the documented Ca²⁺‐binding sites in three datasets of highly‐diversified protein structures with 0.22 to 0.49 Å accuracy. All multiple‐binding sites (i.e. sites with a single ligand atom associated with multiple calcium ions) were predicted, as were half of the low‐coordination sites (i.e. sites with less than four protein ligand atoms) and 14/16 cofactor‐coordinating sites. Additionally, this algorithm has the flexibility to incorporate surface water molecules and protein cofactors to further improve the prediction for low‐coordination and cofactor‐coordinating Ca²⁺‐binding sites. Proteins 2009. © 2008 Wiley‐Liss, Inc.     

Automated NMR resonance assignment strategy for RNA via the phosphodiester backbone based on high-dimensional through-bond APSY experiments

A fast, robust and reliable strategy for automated sequential resonance assignment for uniformly [¹³C, ¹⁵N]-labeled RNA via its phosphodiester backbone is presented. It is based on a series of high-dimensional through-bond APSY experiments: a 5D HCP-CCH COSY, a 4D H1′C1′CH TOCSY for ribose resonances, a 5D HCNCH for ribose-to-base connection, a 4D H6C6C5H5 TOCSY for pyrimidine resonances, and a 4D H8C8(C)C2H2 TOCSY for adenine resonances. The utilized pulse sequences are partially novel, and optimized to enable long evolution times in all dimensions. The highly precise APSY peak lists derived with these experiments could be used directly for reliable automated resonance assignment with the FLYA algorithm. This approach resulted in 98 % assignment completeness for all ¹³C–¹H, ¹⁵N1/9 and ³¹P resonances of a stem-loop with 14 nucleotides.     

Role of structural water for prediction of cation binding sites in apoproteins

Structures of many metal-binding proteins are often obtained without structural cations in their apoprotein forms. Missing cation coordinates are usually updated from structural templates constructed from many holoprotein structures. Such templates usually do not include structural water, the important contributor to the ion binding energy. Structural templates are also inconvenient for taking into account structural modifications around the binding site at apo-/holo- transitions. An approach based upon statistical potentials readily takes into account structural modifications associated with binding as well as contribution of structural water molecules. Here, we construct a set of statistical potentials for Mg²⁺, Ca²⁺, and Zn²⁺ contacting with protein atoms of a different type or structural water oxygens. Each type of the cations tends to form tight contacts with protein atoms of specific types. Structural water contributes relatively more into the binding pseudo-energy of Mg²⁺ and Ca²⁺ than of Zn²⁺. We have developed PIONCA (Protein-Ion Calculator), a fast CUDA GPGPU-based algorithm that predicts ion-binding sites in apoproteins. Comparative tests demonstrate that PIONCA outperforms most of the tools based on structural templates or docking. Our software can be also used for locating bound cations in holoprotein structures with missing cation heteroatoms. PIONCA is equipped with an interactive web interface based upon JSmol.     

KcsA 通道对Na+、K+及Rb+离子选择性的统计热力学研究

钾离子的通透率至少比钠离子的通透率大10000倍,这个问题至今没有很好地解决.为了在分子水平阐释钾离子通道的选择性机制,以KcsA钾通道X射线衍射结构为基础,采用密度泛函理论计算了不同离子在离子通道中的位能.计算结果表明,Rb+离子具有与K+离子相类似的位能曲线,但是其在通透过程遇到的位垒要比K+离子的位垒高,因而所对应的通透率也就小于钾离子的通透率,而钠离子的的通透率仅仅是钾离子通透率的0.0067%.文中所涉及的系统仅仅包含269个原子,而用分子动力学虽然也可以得到相近的结果,但是它的系统大小为41 000个原子.     

Free Energy Perturbations in Ribonuclease T1 Substrate Binding. A Study of the Influence of Simulation Length,Internal Degrees of Freedom and Structure in Free Energy Perturbations

Abstract

We have studied the reliability of free energy perturbation calculations with respect to simulation protocol and simulation length in a real biological system, the binding of two different ligands to wildtype Ribonuclease T ₁ (RNT1) and to a mutant of RNT1 with Glu-46 replaced by Gln (RNT1-Gln46). The binding of the natural substrate 3′ GMP has been compared with the binding of a fluorescent probe, 2-aminopurine 3′ mono phosphate (2AP3′MP). These simulations predict that the mutant binds 2AP3′MP better than 3′GMP. Four complete free energy perturbations were performed that form a closed loop of four free energy differences, which should sum up to zero. This could be used as a tool for searching for systematic errors that are not detected by standard forward ? backward perturbations. The perturbation between 2AP3′MP and 3′GMP is quite straightforward and similar to what has been done by other groups. The perturbation between Glu46 and Gln46 is much more complex, involving as many as twelve atoms and a change of charge. This perturbation needs much longer simulation time, 500-600 ps, than used in free energy perturbations before. The increased simulation time is needed both to reach an equilibrium and to include several phases of fluctuations of the observed parameters in the production run. The extremely long simulation time is not such a severe problem as much of the work might be done on several different machines in parallel and cheap workstations are excellent for these calculations. Problems may also occur with values of the coupling parameter Λ close to 0 or 1, due to the high mobility of atoms as well as insertion/deletion in a previously unoccupied space involved in the perturbation.     

Protein sequential resonance assignments by combinatorial enumeration using 13C alpha chemical shifts and their (i,i-1) sequential connectivities

The need for the structural characterization of proteins on a genomic scale has brought with it demands for new technology to speed the structure determination process. In NMR, one bottleneck is the sequential assignment of backbone resonances. In this paper, we explore the computational complexity of the sequential assignment problem using only ¹³C chemical shift data and C (i,i–1) sequential connectivity information, all of which can potentially be obtained from a single three-dimensional NMR spectrum. Although it is generally believed that there is too much ambiguity in such data to provide sufficient information for sequential assignment, we show that a straightforward combinatorial search algorithm can be used to find correct and unambiguous sequential assignments in a reasonable amount of CPU time for small proteins (approximately 80 residues or smaller) when there is little missing data. The deleterious effect of missing or spurious peaks and the dependence on match tolerances is also explored. This simple algorithm could be used as part of a semi-automated, interactive assignment procedure, e.g., to test partial manually determined solutions fo uniqueness and to extend these solutions.     

Influence of the completeness of chemical shift assignments on NMR structures obtained with automated NOE assignment

Reliable automated NOE assignment and structure calculation on the basis of a largely complete, assigned input chemical shift list and a list of unassigned NOESY cross peaks has recently become feasible for routine NMR protein structure calculation and has been shown to yield results that are equivalent to those of the conventional, manual approach. However, these algorithms rely on the availability of a virtually complete list of the chemical shifts. This paper investigates the influence of incomplete chemical shift assignments on the reliability of NMR structures obtained with automated NOESY cross peak assignment. The program CYANA was used for combined automated NOESY assignment with the CANDID algorithm and structure calculations with torsion angle dynamics at various degrees of completeness of the chemical shift assignment which was simulated by random omission of entries in the experimental ¹H chemical shift lists that had been used for the earlier, conventional structure determinations of two proteins. Sets of structure calculations were performed choosing the omitted chemical shifts randomly among all assigned hydrogen atoms, or among aromatic hydrogen atoms. For comparison, automated NOESY assignment and structure calculations were performed with the complete experimental chemical shift but under random omission of NOESY cross peaks. When heteronuclear-resolved three-dimensional NOESY spectra are available the current CANDID algorithm yields in the absence of up to about 10% of the experimental ¹H chemical shifts reliable NOE assignments and three-dimensional structures that deviate by less than 2 Å from the reference structure obtained using all experimental chemical shift assignments. In contrast, the algorithm can accommodate the omission of up to 50% of the cross peaks in heteronuclear- resolved NOESY spectra without producing structures with a RMSD of more than 2 Å to the reference structure. When only homonuclear NOESY spectra are available, the algorithm is slightly more susceptible to missing data and can tolerate the absence of up to about 7% of the experimental ¹H chemical shifts or of up to 30% of the NOESY peaks.Abbreviations: BmPBP^A – Bombyx mori pheromone binding protein form A; CYANA – combined assignment and dynamics algorithm for NMR applications; NMR – nuclear magnetic resonance; NOE – nuclear Overhauser effect; NOESY – NOE spectroscopy; RMSD – root-mean-square deviation; WmKT – Williopsis mrakii killer toxin     

A simple two-dimensional representation for the common secondary structural elements of polypeptides and proteins

A simple method is presented for projecting the conformation of extended secondary structure elements of peptides and proteins that extend over four C^αatoms onto a simple two-dimensional surface. A new set of two degrees of freedom is defined, a pseudo-dihedral involving four sequential C^αatoms, as well as the triple scalar product for the vectors describing the orientation of the three intervening peptide groups. The method provides a reduction in dimensionality, from the usual combination of multiple ϕ,ψ pairs to a single pair, yielding valuable information concerning the structure and dynamics of these important elements. The new two-dimensional surface is explored by reference to 63 selected protein crystal structures together with a comparison of model built peptides representing the common secondary structural elements. Dynamical aspects on this new surface are examined using a molecular dynamics trajectory of Basic Pancreatic Trypsin Inhibitor. © 1997 Wiley-Liss, Inc.     

HNCAN pulse sequences for sequential backbone resonance assignment across proline residues in perdeuterated proteins

A TROSY-based triple-resonance pulse scheme is described which correlates backbone ¹H and ¹⁵N chemical shifts of an amino acid residue with the ¹⁵N chemical shifts of both the sequentially preceding and following residues. The sequence employs ¹ J _NC and ² J _NC couplings in two sequential magnetization transfer steps in an `out-and-back' manner. As a result, N,N connectivities are obtained irrespective of whether the neighbouring amide nitrogens are protonated or not, which makes the experiment suitable for the assignment of proline resonances. Two different three-dimensional variants of the pulse sequence are presented which differ in sensitivity and resolution to be achieved in one of the nitrogen dimensions. The new method is demonstrated with two uniformly ²H/¹³C/¹⁵N-labelled proteins in the 30-kDa range.     

Improved 4D NMR experiments for the assignment of backbone nuclei in13C/15N labelled proteins

Summary We recently proposed a novel 4D NMR strategy for the assignment of backbone nuclei in¹³C/¹⁵N-labelled proteins (Boucher et al., 1992). Intra-residue (and many sequential) assignments are obtained from a HCANNH experiment, whereas sequential assignments are based on a complementary HCA(CO)NNH experiment. We present here new constant time 4D HCANNH, HCA(CO)NNH and HNCAHA experiments that are more sensitive. Some of the data were presented at the 33rd ENC held at Asilomar, California, U.S.A., in April 1992.     

Solution conformation of a heptadecapeptide comprising the DNA binding helix F of the cyclic AMP receptor protein of Escherichia coli. Combined use of 1H nuclear magnetic resonance and restrained molecular dynamics

A nuclear magnetic resonance study on a heptadecamer (17-mer) peptide comprising the DNA binding helix F of the cyclic AMP receptor protein of Escherichia coli is presented under solution conditions (viz. 40% (v/v) trifluorethanol) where it adopts an ordered helical structure as judged by circular dichroism. Using a combination of two-dimensional nuclear magnetic resonance techniques, complete resonance assignments are obtained in a sequential manner. From the two-dimensional nuclear Overhauser enhancement spectra, a set of 87 approximate distance restraints is derived and used as the basis for three-dimensional structure determination with a restrained molecular dynamics algorithm in which the interproton distances are incorporated into the total energy function of the system in the form of an additional effective potential term. The convergence properties of this approach are tested by starting from three different initial structures, namely an alpha-helix, a beta-strand and a 3-10 helix. In all three cases, convergence to an alpha-helical structure is achieved with a root mean square difference of less than 3 A for all atoms and less than 2 A for the backbone atoms.     

Amino acid type-selective backbone 1H-15N-correlations for Arg and Lys

Four novel amino acid type-selective triple resonance experiments to identify the backbone amino proton and nitrogen resonances of Arg and Lys and of their sequential neighbors in (¹³C,¹⁵N)-labeled proteins are presented: the R(i+1)-HSQC and R(i,i+1)-HSQC select signals originating from Arg side chains, the K(i+1)-HSQC and K(i,i+1)-HSQC select signals originating from Lys side chains. The selection is based on exploiting the characteristic chemical shifts of a pair of carbon atoms in Arg and Lys side chains using selective 90° pulses. The new experiments are recorded as two-dimensional ¹H-¹⁵N-correlations and their performance is demonstrated with the application to a protein domain of 83 amino acids.     

Soil CO2 emission estimated by different interpolation techniques

Soil CO₂ emissions are highly variable, both spatially and across time, with significant changes even during a one-day period. The objective of this study was to compare predictions of the diurnal soil CO₂ emissions in an agricultural field when estimated by ordinary kriging and sequential Gaussian simulation. The dataset consisted of 64 measurements taken in the morning and in the afternoon on bare soil in southern Brazil. The mean soil CO₂ emissions were significantly different between the morning (4.54 ??mol m^?2 s^?1) and afternoon (6.24 ??mol m^?2 s^?1) measurements. However, the spatial variability structures were similar, as the models were spherical and had close range values of 40.1 and 40.0 m for the morning and afternoon semivariograms. In both periods, the sequential Gaussian simulation maps were more efficient for the estimations of emission than ordinary kriging. We believe that sequential Gaussian simulation can improve estimations of soil CO₂ emissions in the field, as this property is usually highly non-Gaussian distributed.     

Intramolecular steric effects and hydrogen bonding in regular conformations of polyamino acids

A survey has been made, by using computer methods, of the types of helices which polypeptide chains can form, taking into account steric requirements and intramolecular hydrogen-bonding interactions. The influence on these two requirements, of small variations in the bond angles of the peptide residues, or of small changes in the overall dimensions of the helix (pitch and residues per turn), have been assessed for the special case of the α-helix. Criteria for the formation of acceptable hydrogen bonds have also been applied to helices of other types, viz., the 3, γ^?, ω^?, and π-helices. It was shown that the N? H … O and H … O? C angles in hydrogen bonds are sensitive to changes in either the NC^αC′ bond angle or in the rotational angles about the N? C^α and C^α? C′ bonds. However, the variants of the α-helix observed experimentally in myoglobin can all be constructed without distortion of the hydrogen bonds. For α-helices, the steric and hydrogen bonding requirements are more easily fulfilled with an NC^αC′ bond angle of 111°, rather than 109.5°. The decreased stability observed for the left-handed α-helix relative to the right-handed one for L -amino acids is due essentially only to interactions of the C^β atom of the side chains with atoms in adjacent peptide units in the backbone, and interactions with atoms in adjacent turns of the helical backbone are not significantly different in the two helices. Restrictions in the freedom of rotation of bulky side chains may have significant kinetic effects during the formation of the α-helix from the “random coil” state.     

Direct methods and residue type specific isotope labeling in NMR structure determination and model-driven sequential assignment

Direct methods in NMR based structure determination start from an unassigned ensemble of unconnected gaseous hydrogen atoms. Under favorable conditions they can produce low resolution structures of proteins. Usually a prohibitively large number of NOEs is required, to solve a protein structure ab-initio, but even with a much smaller set of distance restraints low resolution models can be obtained which resemble a protein fold. One problem is that at such low resolution and in the absence of a force field it is impossible to distinguish the correct protein fold from its mirror image. In a hybrid approach these ambiguous models have the potential to aid in the process of sequential backbone chemical shift assignment when ¹³C^β and ¹³C′ shifts are not available for sensitivity reasons. Regardless of the overall fold they enhance the information content of the NOE spectra. These, combined with residue specific labeling and minimal triple-resonance data using ¹³C^α connectivity can provide almost complete sequential assignment. Strategies for residue type specific labeling with customized isotope labeling patterns are of great advantage in this context. Furthermore, this approach is to some extent error-tolerant with respect to data incompleteness, limited precision of the peak picking, and structural errors caused by misassignment of NOEs. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Evaluation of an algorithm for the automated sequential assignment of protein backbone resonances: A demonstration of the connectivity tracing assignment tools (CONTRAST) software package

Summary The peptide sequential assignment algorithm presented here was implemented as a macro within the CONnectivity TRacing ASsignment Tools (CONTRAST) computer software package. The algorithm provides a semi- or fully automated global means of sequentially assigning the NMR backbone resonances of proteins. The program's performance is demonstrated here by its analysis of realistic computer-generated data for III^Glc, a 168-residue signal-transducing protein of Escherichia coli [Pelton et al. (1991) Biochemistry, 30, 10043–10057]. Missing experimental data (19 resonances) were generated so that a complete assignment set could be tested. The algorithm produces sequential assignments from appropriate peak lists of nD NMR data. It quantifies the ambiguity of each assignment and provides ranked alternatives. A best first approach, in which high-scoring local assignments are made before and in preference to lower scoring assignments, is shown to be superior (in terms of the current set of CONTRAST scoring routines) to approaches such as simulated annealing that seek to maximize the combined scores of the individual assignments. The robustness of the algorithm was tested by evaluating the effects of imposed frequency imprecision (scatter), added false signals (noise), missing peaks (incomplete data), and variation in userdefined tolerances on the performance of the algorithm.     

Computational experience with a parallel algorithm for tetrangle inequality bound smoothing

Determining molecular structure from interatomic distances is an important and challenging problem. Given a molecule with n atoms, lower and upper bounds on interatomic distances can usually be obtained only for a small subset of the atom pairs, using NMR. Given the bounds so obtained on the distances between some of the atom pairs, it is often useful to compute tighter bounds on all the pairwise distances. This process is referred to as bound smoothing. The initial lower and upper bounds for the pairwise distances not measured are usually assumed to be 0 and ∞. One method for bound smoothing is to use the limits imposed by the triangle inequality. The distance bounds so obtained can often be tightened further by applying the tetrangle inequality—the limits imposed on the six pairwise distances among a set of four atoms (instead of three for the triangle inequalities). The tetrangle inequality is expressed by the Cayley—Menger determinants. For every quadruple of atoms, each pass of the tetrangle inequality bound smoothing procedure finds upper and lower limits on each of the six distances in the quadruple. Applying the tetrangle inequalities to each of the ( ₄ ⁿ ) quadruples requires O(n ⁴) time. Here, we propose a parallel algorithm for bound smoothing employing the tetrangle inequality. Each pass of our algorithm requires O(n ³ log n) time on a CREW PRAM (Concurrent Read Exclusive Write Parallel Random Access Machine) with processors. An implementation of this parallel algorithm on the Intel Paragon XP/S and its performance are also discussed.     

An extended aqueous solvation model based on atom-weighted solvent accessible surface areas: SAWSA v2.0 model

A new method is proposed for calculating aqueous solvation free energy based on atom-weighted solvent accessible surface areas. The method, SAWSA v2.0, gives the aqueous solvation free energy by summing the contributions of component atoms and a correction factor. We applied two different sets of atom typing rules and fitting processes for small organic molecules and proteins, respectively. For small organic molecules, the model classified the atoms in organic molecules into 65 basic types and additionally. For small organic molecules we proposed a correction factor of hydrophobic carbon to account for the aggregation of hydrocarbons and compounds with long hydrophobic aliphatic chains. The contributions for each atom type and correction factor were derived by multivariate regression analysis of 379 neutral molecules and 39 ions with known experimental aqueous solvation free energies. Based on the new atom typing rules, the correlation coefficient (r) for fitting the whole neutral organic molecules is 0.984, and the absolute mean error is 0.40 kcal mol^–1, which is much better than those of the model proposed by Wang et al. and the SAWSA model previously proposed by us. Furthermore, the SAWSA v2.0 model was compared with the simple atom-additive model based on the number of atom types (NA). The calculated results show that for small organic molecules, the predictions from the SAWSA v2.0 model are slightly better than those from the atom-additive model based on NA. However, for macromolecules such as proteins, due to the connection between their molecular conformation and their molecular surface area, the atom-additive model based on the number of atom types has little predictive power. In order to investigate the predictive power of our model, a systematic comparison was performed on seven solvation models including SAWSA v2.0, GB/SA_1, GB/SA_2, PB/SA_1, PB/SA_2, AM1/SM5.2R and SM5.0R. The results showed that for organic molecules the SAWSA v2.0 model is better than the other six solvation models. For proteins, the model classified the atoms into 20 basic types and the predicted aqueous free energies of solvation by PB/SA were used for fitting. The solvation model based on the new parameters was employed to predict the solvation free energies of 38 proteins. The predicted values from our model were in good agreement with those from the PB/SA model and were much better than those given by the other four models developed for proteins.Figure The definition of hydrophobic carbons. Here CA, CB and CD are three carbon atoms; X represents a heteroatom. According to our definition, CB is a hydrophobic carbon, CA is not a hydrophobic carbon because a heteroatom is within four atoms and CD is not a hydrophobic carbon because CD is sp²- hydridized and in a six-member ring.Electronic Supplementary Material Supplementary material is available for this article at     

A simple way for sequential assignment in isotopically enriched proteins using a H(N)CACO correlation

Summary A simplified scheme for sequential assignment in isotopically enriched proteins is presented. It is based on the standard triple resonance experiments HNCO, HN(CO)CA, HNCA and a modified H(N)CACO correlation, in which both of the H^N connectivities to the CA/C pair of residue i and i-1 are observed. The H(N)CACO was tested on uniformly ¹³C/¹⁵N enriched P13 domain of mannose permease (31 kDa).     

A Fast Incremental Gaussian Mixture Model

This work builds upon previous efforts in online incremental learning, namely the Incremental Gaussian Mixture Network (IGMN). The IGMN is capable of learning from data streams in a single-pass by improving its model after analyzing each data point and discarding it thereafter. Nevertheless, it suffers from the scalability point-of-view, due to its asymptotic time complexity of O(NKD ³) for N data points, K Gaussian components and D dimensions, rendering it inadequate for high-dimensional data. In this work, we manage to reduce this complexity to O(NKD ²) by deriving formulas for working directly with precision matrices instead of covariance matrices. The final result is a much faster and scalable algorithm which can be applied to high dimensional tasks. This is confirmed by applying the modified algorithm to high-dimensional classification datasets.