Protein chemical shift prediction

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Protein chemical shift prediction is a branch of biomolecular nuclear magnetic resonance spectroscopy that aims to accurately calculate protein chemical shifts from protein coordinates. Protein chemical shift prediction was first attempted in the late 1960s using semi-empirical methods applied to protein structures solved by X-ray crystallography. [1] Since that time protein chemical shift prediction has evolved to employ much more sophisticated approaches including quantum mechanics, machine learning and empirically derived chemical shift hypersurfaces. [1] The most recently developed methods exhibit remarkable precision and accuracy.

Contents

Protein chemical shifts

NMR chemical shifts are often called the mileposts of nuclear magnetic resonance spectroscopy. Chemists have used chemical shifts for more than 50 years as highly reproducible, easily measured parameters to map out the covalent structure of small organic molecules. Indeed, the sensitivity of NMR chemical shifts to the type and character of neighbouring atoms, combined with their reasonably predictable tendencies has made them invaluable for both deciphering and describing the structure of thousands of newly synthesized or newly isolated compounds [1] [2] [3] [4] The same sensitivity to a variety of important protein structural features has made protein chemical shifts equally valuable to protein chemists and biomolecular NMR spectroscopists. [4] In particular, protein chemical shifts are sensitive not only to substituent or covalent atom effects (such as electronegativity, redox states or ring currents) but they are also sensitive to backbone torsion angles (i.e. secondary structure), hydrogen bonding, local atomic motions and solvent accessibility.

Importance of protein chemical shift prediction

Predicted or estimated protein chemical shifts can be used to assist with the chemical shift assignment process. This is especially true if a similar (or identical) protein structure has been solved by X-ray crystallography. In this case, the three-dimensional structure can be used to estimate what the NMR chemical shifts should be and thereby simplify the process of assigning the experimentally observed chemical shifts. Predicted/estimated protein chemical shifts can also be used to identify incorrect or mis-assignments, to correct mis-referenced or incorrectly referenced chemical shifts, to optimize protein structures via chemical shift refinement and to identify the relative contributions of different electronic or geometric effects to nucleus-specific shifts. [1] Protein chemical shifts can also be used to identify secondary structures, to estimate backbone torsion angles, to determine the location of aromatic rings, to assess cysteine oxidation states, to estimate solvent exposure and to measure backbone flexibility. [4]

Progress in chemical shift prediction programs

Significant progress in chemical shift prediction has been made through continuous improvements in our understanding of the key physico-chemical factors contributing to chemical shift changes. These improvements have also been helped along through significant computational advancements [5] [6] [7] [8] and the rapid expansion of biomolecular chemical shift databases [9] . [10] Over the past four decades, at least three different methods for calculating or predicting protein chemical shifts have emerged. The first is based on using sequence/structure alignment against protein chemical shift databases, the second is based on directly calculating shifts from atomic coordinates, and the third is based on using a combination of the two approaches. [1] [4]

The emergence of hybrid prediction methods

By early 2000, several research groups realized that protein chemical shifts could be more efficiently and accurately calculated by combining different methods together as shown in Figure 1. This led to the development of several programs and web servers that rapidly calculate protein chemical shifts when provided with protein coordinate data. [1] These “hybrid” programs, along with some of their features and URLs, are listed below in Table 1.

Summary of protein chemical shift prediction programs

Table 1: Currently available protein chemical shift prediction programs
NameMethodWebsite
SHIFTCALC [11] Hybrid – empirical chemical shift hypersurfaces in combination with semi-classical calculations https://archive.today/20140324204821/http://nmr.group.shef.ac.uk/NMR/mainpage.html
SHIFTS [12] Hybrid – QM chemical shift hypersurfaces combined with semi-classical calculations http://casegroup.rutgers.edu/qshifts/qshifts.htm
CheSHIFT [13] QM calculated chemical shift hypersurfaces http://cheshift.com/
SHIFTX [2] Hybrid – empirical chemical shift hypersurfaces in combination with semi-classical calculations http://shiftx.wishartlab.com
PROSHIFT [14] Neural network model using atomic parameters and sequence information http://www.meilerlab.org/index.php/servers/show?s_id=9
SPARTA [15] Hybrid - sequence and shift matching to a databases combined with semi-classical calculations http://spin.niddk.nih.gov/bax/software/SPARTA/index.html
SPARTA+ [16] Hybrid - sequence and shift matching to a databases combined with semi-classical calculations and artificial neural network http://spin.niddk.nih.gov/bax/software/SPARTA+/
CAMSHIFT [17] Distance-based method in combination with parameterized polynomial expansion https://web.archive.org/web/20140109151911/http://www-vendruscolo.ch.cam.ac.uk/camshift/camshift.php
SHIFTX2 [4] Hybrid – machine learning method using atomic parameters and combination with semi-classical calculations (SHIFTX+). Finally, using ensemble rules with sequence homology based prediction (SHIFTY+) http://www.shiftx2.ca

http://www.wishartlab.com

Performance comparison of modern protein chemical shift prediction programs

This table (Figure 2) lists the correlation coefficients between the experimentally observed backbone chemical shifts and the calculated/predicted backbone shifts for different chemical shift predictors using an identical test set of 61 test proteins.

Coverage and speed

Different methods have different levels of coverage and rates of calculation. Some methods only calculate or predict chemical shifts for backbone atoms (6 atom types). Some calculate chemical shifts for backbone and certain side chain atoms (C and N only) and still others are able to calculate shifts for all atoms (40 atom types). For chemical shift refinement there is a need for rapid calculation as thousands of structures are generated during a molecular dynamics or simulated annealing run and their chemical shifts must be calculated equally rapidly.

ProgramNo. of atom types predictedSpeed (seconds/100 residues)
SHIFTX270.59
SPARTA6 (backbone only)17.92
SPARTA+6 (backbone only)2.47
CamShift6 (backbone only)0.91
SHIFTS313.66
PROSHIFT4012.82
SHIFTX2402.10

All the computational speed tests for SPARTA, SPARTA+, SHIFTS, CamShift, SHIFTX and SHIFTX2 were performed on the same computer using the same set of proteins. The calculation speed reported for PROSHIFT is based on the response rate of its web server. [4]

See also

Related Research Articles

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<span class="mw-page-title-main">Residual dipolar coupling</span>

The residual dipolar coupling between two spins in a molecule occurs if the molecules in solution exhibit a partial alignment leading to an incomplete averaging of spatially anisotropic dipolar couplings.

<i>Journal of Biomolecular NMR</i> Academic journal

The Journal of Biomolecular NMR publishes research on technical developments and innovative applications of nuclear magnetic resonance spectroscopy for the study of structure and dynamic properties of biopolymers in solution, liquid crystals, solids and mixed environments. Some of the main topics include experimental and computational approaches for the determination of three-dimensional structures of proteins and nucleic acids, advancements in the automated analysis of NMR spectra, and new methods to probe and interpret molecular motions.

<span class="mw-page-title-main">CING (biomolecular NMR structure)</span>

In biomolecular structure, CING stands for the Common Interface for NMR structure Generation and is known for structure and NMR data validation.

The Re-referenced Protein Chemical shift Database (RefDB) is an NMR spectroscopy database of carefully corrected or re-referenced chemical shifts, derived from the BioMagResBank (BMRB). The database was assembled by using a structure-based chemical shift calculation program to calculate expected protein (1)H, (13)C and (15)N chemical shifts from X-ray or NMR coordinate data of previously assigned proteins reported in the BMRB. The comparison is automatically performed by a program called SHIFTCOR. The RefDB database currently provides reference-corrected chemical shift data on more than 2000 assigned peptides and proteins. Data from the database indicates that nearly 25% of BMRB entries with (13)C protein assignments and 27% of BMRB entries with (15)N protein assignments require significant chemical shift reference readjustments. Additionally, nearly 40% of protein entries deposited in the BioMagResBank appear to have at least one assignment error. Users may download, search or browse the database through a number of methods available through the RefDB website. RefDB provides a standard chemical shift resource for biomolecular NMR spectroscopists, wishing to derive or compute chemical shift trends in peptides and proteins.

SHIFTCOR is a freely available web server as well as a stand-alone computer program for protein chemical shift re-referencing. Chemical shift referencing is a particularly widespread problem in biomolecular NMR with up to 25% of existing NMR chemical shift assignments being improperly referenced. Some of these referencing problems can lead to systematic errors of between 1.0 to 2.5 ppm. Errors of this magnitude can play havoc with any attempt to compare assignments between proteins or to structurally interpret chemical shifts. Identifying which proteins are mis-assigned or improperly referenced can be challenging, as can correcting the errors once they are found. The SHIFTCOR program was designed to assist with identifying and fixing these chemical shift referencing problems. Specifically it compares, identifies, corrects and re-references 1H, 13C and 15N backbone chemical shifts of peptides and proteins by comparing the observed chemical shifts with the predicted chemical shifts derived from the 3D structure of the protein(s) of interest [1]. The predicted chemical shifts are calculated using the ShiftX program. The SHIFTCOR program was originally used to construct a database of properly re-referenced protein chemical shift assignments called RefDB. RefDB is a web-accessible database of more than 2000 correctly referenced protein chemical shift assignments. While originally available as a stand-alone program only, SHIFTCOR has since been released for general use as a web server.

<span class="mw-page-title-main">Random coil index</span> Protocol in biochemistry

Random coil index (RCI) predicts protein flexibility by calculating an inverse weighted average of backbone secondary chemical shifts and predicting values of model-free order parameters as well as per-residue RMSD of NMR and molecular dynamics ensembles from this parameter.

CS-ROSETTA is a framework for structure calculation of biological macromolecules on the basis of conformational information from NMR, which is built on top of the biomolecular modeling and design software called ROSETTA. The name CS-ROSETTA for this branch of ROSETTA stems from its origin in combining NMR chemical shift (CS) data with ROSETTA structure prediction protocols. The software package was later extended to include additional NMR conformational parameters, such as Residual Dipolar Couplings (RDC), NOE distance restraints, pseudocontact chemical shifts (PCS) and restraints derived from homologous proteins. This software can be used together with other molecular modeling protocols, such as docking to model protein oligomers. In addition, CS-ROSETTA can be combined with chemical shift resonance assignment algorithms to create a fully automated NMR structure determination pipeline. The CS-ROSETTA software is freely available for academic use and can be licensed for commercial use. A software manual and tutorials are provided on the supporting website https://csrosetta.chemistry.ucsc.edu/.

Triple resonance experiments are a set of multi-dimensional nuclear magnetic resonance spectroscopy (NMR) experiments that link three types of atomic nuclei, most typically consisting of 1H, 15N and 13C. These experiments are often used to assign specific resonance signals to specific atoms in an isotopically-enriched protein. The technique was first described in papers by Ad Bax, Mitsuhiko Ikura and Lewis Kay in 1990, and further experiments were then added to the suite of experiments. Many of these experiments have since become the standard set of experiments used for sequential assignment of NMR resonances in the determination of protein structure by NMR. They are now an integral part of solution NMR study of proteins, and they may also be used in solid-state NMR.

<span class="mw-page-title-main">Structure validation</span> Process of evaluating 3-dimensional atomic models of biomacromolecules

Macromolecular structure validation is the process of evaluating reliability for 3-dimensional atomic models of large biological molecules such as proteins and nucleic acids. These models, which provide 3D coordinates for each atom in the molecule, come from structural biology experiments such as x-ray crystallography or nuclear magnetic resonance (NMR). The validation has three aspects: 1) checking on the validity of the thousands to millions of measurements in the experiment; 2) checking how consistent the atomic model is with those experimental data; and 3) checking consistency of the model with known physical and chemical properties.

<span class="mw-page-title-main">GeNMR</span>

GeNMR method is the first fully automated template-based method of protein structure determination that utilizes both NMR chemical shifts and NOE -based distance restraints.

<span class="mw-page-title-main">CS23D</span>

CS23D is a web server to generate 3D structural models from NMR chemical shifts. CS23D combines maximal fragment assembly with chemical shift threading, de novo structure generation, chemical shift-based torsion angle prediction, and chemical shift refinement. CS23D makes use of RefDB and ShiftX.

<span class="mw-page-title-main">Chemical shift index</span> Laboratory technique

The chemical shift index or CSI is a widely employed technique in protein nuclear magnetic resonance spectroscopy that can be used to display and identify the location as well as the type of protein secondary structure found in proteins using only backbone chemical shift data The technique was invented by David S. Wishart in 1992 for analyzing 1Hα chemical shifts and then later extended by him in 1994 to incorporate 13C backbone shifts. The original CSI method makes use of the fact that 1Hα chemical shifts of amino acid residues in helices tends to be shifted upfield relative to their random coil values and downfield in beta strands. Similar kinds of upfield and downfield trends are also detectable in backbone 13C chemical shifts.

Nuclear magnetic resonance chemical shift re-referencing is a chemical analysis method for chemical shift referencing in biomolecular nuclear magnetic resonance (NMR). It has been estimated that up to 20% of 13C and up to 35% of 15N shift assignments are improperly referenced. Given that the structural and dynamic information contained within chemical shifts is often quite subtle, it is critical that protein chemical shifts be properly referenced so that these subtle differences can be detected. Fundamentally, the problem with chemical shift referencing comes from the fact that chemical shifts are relative frequency measurements rather than absolute frequency measurements. Because of the historic problems with chemical shift referencing, chemical shifts are perhaps the most precisely measurable but the least accurately measured parameters in all of NMR spectroscopy.

Protein chemical shift re-referencing is a post-assignment process of adjusting the assigned NMR chemical shifts to match IUPAC and BMRB recommended standards in protein chemical shift referencing. In NMR chemical shifts are normally referenced to an internal standard that is dissolved in the NMR sample. These internal standards include tetramethylsilane (TMS), 4,4-dimethyl-4-silapentane-1-sulfonic acid (DSS) and trimethylsilyl propionate (TSP). For protein NMR spectroscopy the recommended standard is DSS, which is insensitive to pH variations. Furthermore, the DSS 1H signal may be used to indirectly reference 13C and 15N shifts using a simple ratio calculation [1]. Unfortunately, many biomolecular NMR spectroscopy labs use non-standard methods for determining the 1H, 13C or 15N “zero-point” chemical shift position. This lack of standardization makes it difficult to compare chemical shifts for the same protein between different laboratories. It also makes it difficult to use chemical shifts to properly identify or assign secondary structures or to improve their 3D structures via chemical shift refinement. Chemical shift re-referencing offers a means to correct these referencing errors and to standardize the reporting of protein chemical shifts across laboratories.

Resolution by Proxy (ResProx) is a method for assessing the equivalent X-ray resolution of NMR-derived protein structures. ResProx calculates resolution from coordinate data rather than from electron density or other experimental inputs. This makes it possible to calculate the resolution of a structure regardless of how it was solved. ResProx was originally designed to serve as a simple, single-number evaluation that allows straightforward comparison between the quality/resolution of X-ray structures and the quality of a given NMR structure. However, it can also be used to assess the reliability of an experimentally reported X-ray structure resolution, to evaluate protein structures solved by unconventional or hybrid means and to identify fraudulent structures deposited in the PDB. ResProx incorporates more than 25 different structural features to determine a single resolution-like value. ResProx values are reported in Angstroms. Tests on thousands of X-ray structures show that ResProx values match very closely to resolution values reported by X-ray crystallographers. Resolution-by-proxy values can be calculated for newly determined protein structures using a freely accessible ResProx web server. This server accepts protein coordinate data and generates a resolution estimate for that input structure.

Probabilistic Approach for protein NMR Assignment Validation (PANAV) is a freely available stand-alone program that is used for protein chemical shift re-referencing. Chemical shift referencing is a problem in protein nuclear magnetic resonance as >20% of reported NMR chemical shift assignments appear to be improperly referenced. For certain nuclei these referencing issues can cause systematic chemical shift errors of between 1.0 and 2.5 ppm. Chemical shift errors of this magnitude often make it very difficult to compare NMR chemical shift assignments between proteins. It also makes it very hard to structurally interpret chemical shifts. Unlike most other chemical shift re-referencing tools PANAV employs a structure-independent protocol. That is, with PANAV there is no need to know the structure of the protein in advance of correcting any chemical shift referencing errors. This makes PANAV particularly useful for NMR studies involving novel or newly assigned proteins, where the structure has yet to be determined. Indeed, this scenario represents the vast majority of assignment cases in biomolecular NMR. PANAV uses residue-specific and secondary structure-specific chemical shift distributions that were calculated over short fragments of correctly referenced proteins to identify mis-assigned resonances. More specifically, PANAV compares the initial chemical shift assignments to the expected chemical shifts based on their local sequence and expected/predicted secondary structure. In this way, PANAV is able to identify and re-reference mis-referenced chemical shift assignments. PANAV can also identify potentially mis-assigned resonances as well. PANAV has been extensively tested and compared against a large number of existing re-referencing or mis-assignment detection programs. These assessments indicate that PANAV is equal to or superior to existing approaches.

PREDITOR is a freely available web-server for the prediction of protein torsion angles from chemical shifts. For many years it has been known that protein chemical shifts are sensitive to protein secondary structure, which in turn, is sensitive to backbone torsion angles. torsion angles are internal coordinates that can be used to describe the conformation of a polypeptide chain. They can also be used as constraints to help determine or refine protein structures via NMR spectroscopy. In proteins there are four major torsion angles of interest: phi, psi, omega and chi-1. Traditionally protein NMR spectroscopists have used vicinal J-coupling information and the Karplus relation to determine approximate backbone torsion angle constraints for phi and chi-1 angles. However, several studies in the early 1990s pointed out the strong relationship between 1H and 13C chemical shifts and torsion angles, especially with backbone phi and psi angles. Later a number of other papers pointed out additional chemical shift relationships with chi-1 and even omega angles. PREDITOR was designed to exploit these experimental observations and to help NMR spectroscopists easily predict protein torsion angles from chemical shift assignments. Specifically, PREDITOR accepts protein sequence and/or chemical shift data as input and generates torsion angle predictions for phi, psi, omega and chi-1 angles. The algorithm that PREDITOR uses combines sequence alignment, chemical shift alignment and a number of related chemical shift analysis techniques to predict torsion angles. PREDITOR is unusually fast and exhibits a very high level of accuracy. In a series of tests 88% of PREDITOR’s phi/psi predictions were within 30 degrees of the correct values, 84% of chi-1 predictions were correct and 99.97% of PREDITOR’s predicted omega angles were correct. PREDITOR also estimates the torsion angle errors so that its torsion angle constraints can be used with standard protein structure refinement software, such as CYANA, CNS, XPLOR and AMBER. PREDITOR also supports automated protein chemical shift re-referencing and the prediction of proline cis/trans states. PREDITOR is not the only torsion angle prediction software available. Several other computer programs including TALOS, TALOS+ and DANGLE have also been developed to predict backbone torsion angles from protein chemical shifts. These stand-alone programs exhibit similar prediction performance to PREDITOR but are substantially slower.

ShiftX is a freely available web server for rapidly calculating protein chemical shifts from protein X-ray coordinates. Protein chemical shift prediction is particularly useful in verifying protein chemical shift assignments, adjusting mis-referenced chemical shifts, refining NMR protein structures and assisting with the NMR assignment of unassigned proteins that have either had their structures determined by X-ray or NMR methods.

David S. Wishart is a Canadian researcher and a Distinguished University Professor in the Department of Biological Sciences and the Department of Computing Science at the University of Alberta. Wishart also holds cross appointments in the Faculty of Pharmacy and Pharmaceutical Sciences and the Department of Laboratory Medicine and Pathology in the Faculty of Medicine and Dentistry. Additionally, Wishart holds a joint appointment in metabolomics at the Pacific Northwest National Laboratory in Richland, Washington. Wishart is well known for his pioneering contributions to the fields of protein NMR spectroscopy, bioinformatics, cheminformatics and metabolomics. In 2011, Wishart founded the Metabolomics Innovation Centre (TMIC), which is Canada's national metabolomics laboratory.

References

  1. 1 2 3 4 5 6 7 8 9 10 11 Wishart, DS (Feb 2011). "Interpreting protein chemical shift data". Progress in Nuclear Magnetic Resonance Spectroscopy. 58 (1–2): 62–87. doi:10.1016/j.pnmrs.2010.07.004. PMID   21241884.
  2. 1 2 3 Neal, S; Nip AM; Zhang H; Wishart DS (Jul 2003). "Rapid and accurate calculation of protein 1H, 13C and 15 N chemical shifts". Journal of Biomolecular NMR. 26 (3): 215–240. doi:10.1023/A:1023812930288. PMID   12766419. S2CID   29425090.
  3. 1 2 Wishart, DS; Watson, M.S.; Boyko, R.F.; Sykes, B.D. (Dec 1997). "Automated 1H and 13C Chemical Shift Prediction Using the BioMagResBank". Journal of Biomolecular NMR. 10 (4): 329–336. doi:10.1023/A:1018373822088. PMID   9460240. S2CID   6004996.
  4. 1 2 3 4 5 6 Han, Beomsoo; Yifeng Liu; Simon Ginzinger; David Wishart (May 2011). "SHIFTX2: significantly improved protein chemical shift prediction". Journal of Biomolecular NMR. 50 (1): 43–57. doi:10.1007/s10858-011-9478-4. PMC   3085061 . PMID   21448735.
  5. ↑ Williamson, MP; Asakura, T (Jul 1997). "Protein Chemical Shifts" . Protein NMR Techniques. Methods in Molecular Biology. Vol. 60. pp.  53–69. doi:10.1385/0-89603-309-0:53. ISBN   978-0-89603-309-2. PMID   9276246.
  6. ↑ Case, DA (Oct 1998). "The use of chemical shifts and their anisotropies in biomolecular structure determination". Current Opinion in Structural Biology. 8 (5): 624–630. doi:10.1016/S0959-440X(98)80155-3. PMID   9818268.
  7. ↑ Case, DA (Apr 2000). "Interpretation of chemical shifts and coupling constants in macromolecules". Current Opinion in Structural Biology. 10 (2): 197–203. doi:10.1016/S0959-440X(00)00068-3. PMID   10753812.
  8. ↑ Wishart, DS; Case, DA (2001). "Use of Chemical Shifts in Macromolecular Structure Determination". Nuclear Magnetic Resonance of Biological Macromolecules Part A. Methods in Enzymology. Vol. 338. pp. 3–34. doi:10.1016/s0076-6879(02)38214-4. ISBN   9780121822392. PMID   11460554.
  9. ↑ Seavey, B.R.; Farr, E.A.; Westler, W.M. & Markley, J.L. (1991). "A relational database for sequence-specific protein NMR data". Journal of Biomolecular NMR. 1 (3): 217–236. doi:10.1007/BF01875516. PMID   1841696. S2CID   33755287.
  10. ↑ Zhang, H; Neal, S. & Wishart, D.S. (Mar 2003). "RefDB: A database of uniformly referenced protein chemical shifts". J. Biomol. NMR. 25 (3): 173–195. doi:10.1023/A:1022836027055. PMID   12652131. S2CID   12786364.
  11. ↑ Iwadate, M; Asakura T; Williamson MP (1999). "C-alpha and C-beta carbon-13 chemical shifts in proteins from an empirical database". J Biomol NMR. 13 (3): 199–211. doi:10.1023/A:1008376710086. PMID   10212983. S2CID   43991686.
  12. ↑ Xu, XP; Case DA (2001). "Automated prediction of 15N, 13Calpha, 13Cbeta and 13C′ chemical shifts in proteins using a density functional database". J Biomol NMR. 21 (4): 321–333. doi:10.1023/A:1013324104681. PMID   11824752. S2CID   665000.
  13. ↑ Vila, JA; Arnautova YA; Martin OA (2009). "Quantum-mechanics-derived 13Calpha chemical shift server (CheShift) for protein structure validation". Proc Natl Acad Sci USA. 106 (40): 16972–16977. Bibcode:2009PNAS..10616972V. doi: 10.1073/pnas.0908833106 . PMC   2761357 . PMID   19805131.
  14. ↑ Meiler, J (2003). "PROSHIFT: protein chemical shift prediction using artificial neural networks". J Biomol NMR. 26 (1): 25–37. doi:10.1023/A:1023060720156. PMID   12766400. S2CID   16360110.
  15. ↑ Shen, Y; Bax A (2007). "Protein backbone chemical shifts predicted from searching a database for torsion angle and sequence homology". J Biomol NMR. 38 (4): 289–302. doi:10.1007/s10858-007-9166-6. PMID   17610132. S2CID   12886163.
  16. ↑ Shen, Yang; Ad Bax (2010). "SPARTA+: a modest improvement in empirical NMR chemical shift prediction by means of an artificial neural network". J Biomol NMR. 48 (1): 13–22. doi:10.1007/s10858-010-9433-9. PMC   2935510 . PMID   20628786.
  17. ↑ Kohlhoff, KJ; Robustelli P; Cavalli A; Salvatella X; Vendruscolo M (2009). "Fast and accurate predictions of protein NMR chemical shifts from interatomic distances". J Am Chem Soc. 131 (39): 13894–13895. doi:10.1021/ja903772t. PMID   19739624.
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