Distance-geometry calculation

A distance geometry calculation consists of two major parts. In the first, the distances are checked for consistency, using a set of inequalities that distances have to satisfy (this part is called bound smoothing ) in the second, distances are chosen randomly within these bounds, and the so-called metric matrix (Mij) is calculated. Embedding then converts this matrix to three-dimensional coordinates, using methods akin to principal component analysis [40]. 

There are many extensive reviews on metric matrix distance geometry [41-44], some of which provide illustrative examples [45,46]. In total, we can distinguish five steps in a distance geometry calculation ... 

Figure 3 Flow of a distance geometry calculation. On the left is shown the development of the data on the right, the operations, d , is the distance between atoms / and j Z. , and Ujj are lower and upper bounds on the distance Z. and ZZj, are the smoothed bounds after application of the triangle inequality is the distance between atom / and the geometric center N is the number of atoms (Mj,) is the metric matrix is the positional vector of atom / 2, is the first eigenvector of (M ,) with eigenvalue Xf,. V , r- , and ate the y-, and -coordinates of atom /. (1-5 correspond to the numbered list on pg. 258.)...

Widmer H, Widmer A, Braun W. Extensive distance geometry calculations with different noe calibrations - new criteria for structure selection applied to sandostatin and BPTI. J Biomol NMR 1993 3 307-324. 

Pogozheva ID, Lomize AL, Mosberg HI. Opioid receptor three-dimensional structures from distance geometry calculations with hydrogen bonding constraints. Biophys J 1998 75 612-634. 

Nerdal, W. and Andersen, 0.M., Intermolecular aromatic acid association of an anthocyanin (petanin) evidenced by two-dimensional nuclear Overhauser enhancement nuclear magnetic resonance experiments and distance geometry calculations, Phytochem. Anal, 3, 182, 1992. 

R. Morrison and D. Hare, /. Mol. Biol., 204, 483 (1988). Determining Stereospecific H Nuclear Magnetic Resonance Assignments from Distance Geometry Calculations. 

K. M. Banks, D. R. Hare, and B. R. Reid, Biochemistry, 28,6996 (1989). Three-Dimensional Solution Structure of a DNA Duplex Containing the Bel I Restriction Sequence Two-Dimensional NMR Studies, Distance Geometry Calculations, and Refinement by Back-Calculation of the NOESY Spectrum. 

E. Peggion, A. Bisello, M. Rosenblatt, M. Chorev, D. F. Mierke, Mono- and bicyclic analogs of parathyroid hormone-related protein. 2. Conformational analysis of antagonists by CD, NMR, and distance geometry calculations, Biochemistry 1997, 36, 3300-3307. 

Kobayashi, Y., Ohkubo, T., Kyogoku, Y., Sakakibara, S., Braun, W., and Go, N. (1989) Solution conformation of conotoxin GI determined by IH nuclear magnetic resonans spectroscopy and distance geometry calculations. Biochemistry 28, 4853-4860. 

Motta A, Patore A, Goud NA, and Castiglione Morelli MA. Solution Conformation of Salmon Calcitonin in Sodium Dodecyl Sulfate Micelles as Determined by Two-dimensional NMR and Distance Geometry Calculations. Biochemistry 1991 30 10444-10450. 

By examining the stmctures of the two microcystins as derived from the distance geometry calculations, many of the NOES could not be described using the standard method of applying the NOEs to one conformation. Distance violations approaching 1.0 A were observed, particularly for the residues located around the Mdha residue. The constraint that this residue introduces into the cyclic peptide is significant, and it could very well be the source of dynamics, fast on the NMR time-scale. With this in mind, we undertook the calculation of these two inhibitors of the protein phosphatases 1 and 2A using the ensemble approach. 

New proline-rich cyclic nanapeptides, cycloleonuripeptides A-D (344-347), showing cell growth inhibitory activity, have been isolated from the fruits of Leonurus heterophyllus (248). Their structures and conformations were elucidated by extensive 2D-NMR (248) and X-ray crystallographic analysis (249), and by distance geometry calculations (250) (Fig. 51). 

Eledoisin, peptide amide from the salivary glands of the cephalopod (Eledone moschata and E. aldrovandi) belonging to the tachykinin family. Its biological activities in vitro are similar to those of substance P. The solution structure has been studied by two-dimensional NMR spectroscopy and distance geometry calculations [V. Erspamer,... 

At the time Murata s study was reported, the solution structure of acyclic portions of the okadaic acid structure were not known despite extensive NOE measurements coupled with distance geometry calculations. Using Jhh coupling constants measured from E. COSY data and "Jch (" = 2, 3), determined predominantly from HETLOC spectra for the contiguous protonated carbon portions of the molecule and phase-sensitive HMBC data for segments containing quaternary carbons, Murata and co-workerswere able to successfully establish the solution structure of okadaic acid. 

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