Chemical distance geometry: Current realization and future projection

Since the 1988 monograph “Distance Geometry and Molecular Conformation” by Crippen and Havel, there have been significant changes in the application of distance geometry to problems of chemical interest. This review attempts to outline what the current state of the art is, in both the underlying mathematical methods and chemical applications, and to indicate future developments. Rather than go into details concerning algorithms and theorems, the emphasis is on defining the kinds of problems we can solve or would like to, and then guiding the interested reader to the recent literature. Special emphasis is given to the problem of determining macromolecular conformation in solution by NMR, including energy functions, and dealing with conformational flexibility.

[1]  A. Pardi,et al.  Limited sampling of conformational space by the distance geometry algorithm: implications for structures generated from NMR data. , 1989, Biochemistry.

[2]  W. Glunt,et al.  An alternating projection algorithm for computing the nearest euclidean distance matrix , 1990 .

[3]  G. Crippen,et al.  Linearized embedding: A new metric matrix algorithm for calculating molecular conformations subject to geometric constraints , 1989 .

[4]  H Oschkinat,et al.  Improved strategies for the determination of protein structures from NMR data: The solution structure of acyl carrier protein , 1989, FEBS letters.

[5]  J H Prestegard,et al.  A dynamic model for the structure of acyl carrier protein in solution. , 1989, Biochemistry.

[6]  Gordon M. Crippen,et al.  Combined use of stereospecific deuteration, NMR, distance geometry, and energy minimization for the conformational analysis of the highly .delta. opioid receptor selective peptide [D-Pen2,D-Pen5]enkephalin , 1990 .

[7]  W. V. van Gunsteren,et al.  Time-averaged nuclear Overhauser effect distance restraints applied to tendamistat. , 1990, Journal of molecular biology.

[8]  H. Kushner Asymptotic global behavior for stochastic approximation and diffusions with slowly decreasing noise effects: Global minimization via Monte Carlo , 1987 .

[9]  K. Wuethrich,et al.  The development of nuclear magnetic resonance spectroscopy as a technique for protein structure determination , 1989 .

[10]  Gordon M. Crippen,et al.  Conformational analysis by energy embedding , 1982 .

[11]  G. M. Crippen,et al.  Why energy embedding works , 1987 .

[12]  Gordon M. Crippen,et al.  Distance Geometry and Molecular Conformation , 1988 .

[13]  Leonard M. Blumenthal,et al.  Theory and applications of distance geometry , 1954 .

[14]  Timothy F. Havel,et al.  Computational experience with an algorithm for tetrangle inequality bound smoothing. , 1989, Bulletin of mathematical biology.

[15]  R. Levy,et al.  Solution structures of proteins from NMR data and modeling: alternative folds for neutrophil peptide 5. , 1989, Biochemistry.

[16]  I. Kuntz,et al.  [9] Distance geometry , 1989 .

[17]  H A Scheraga,et al.  An approach to the multiple-minima problem in protein folding by relaxing dimensionality. Tests on enkephalin. , 1987, Journal of molecular biology.

[18]  M. Summers,et al.  High-resolution structure of an HIV zinc fingerlike domain via a new NMR-based distance geometry approach. , 1990, Biochemistry.

[19]  P. Kollman,et al.  Computer simulation studies of spherands, crowns and porphyrins: application of computer graphics, distance geometry, molecular mechanics and molecular dynamics approaches , 1989 .

[20]  G M Crippen,et al.  Energy embedding of trypsin inhibitor , 1982, Biopolymers.

[21]  T. Cross,et al.  A method for the analytic determination of polypeptide structure using solid state nuclear magnetic resonance: The ‘‘metric method’’ , 1990 .

[22]  K. Wüthrich Protein structure determination in solution by nuclear magnetic resonance spectroscopy. , 1989, Science.

[23]  R. Kaptein,et al.  Determination of biomolecular structures from proton-proton NOE's using a relaxation matrix approach , 1988 .

[24]  B. Hendrickson The Molecular Problem: Determining Conformation from Pairwise Distances , 1990 .

[25]  K. Wüthrich NMR of proteins and nucleic acids , 1988 .

[26]  P. Chiang,et al.  Distance geometry of alpha-substituted 2,2-diphenylpropionate antimuscarinics. , 1989, Molecular pharmacology.

[27]  H A Scheraga,et al.  An approach to the multiple-minima problem by relaxing dimensionality. , 1986, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Gordon M. Crippen,et al.  Global energy minimization by rotational energy embedding , 1990, J. Chem. Inf. Comput. Sci..

[29]  A. Gronenborn,et al.  Determination of three‐dimensional structures of proteins from interproton distance data by hybrid distance geometry‐dynamical simulated annealing calculations , 1988, FEBS letters.

[30]  G. M. Crippen,et al.  Use of augmented Lagrangians in the calculation of molecular conformations by distance geometry , 1988, J. Chem. Inf. Comput. Sci..

[31]  M. Billeter,et al.  Restrained energy refinement with two different algorithms and force fields of the structure of the α‐amylase inhibitor tendamistat determined by nmr in solution , 1990 .

[32]  Timothy F. Havel,et al.  The sampling properties of some distance geometry algorithms applied to unconstrained polypeptide chains: A study of 1830 independently computed conformations , 1990, Biopolymers.

[33]  A. Gronenborn,et al.  Determination of three‐dimensional structures of proteins from interproton distance data by dynamical simulated annealing from a random array of atoms Circumventing problems associated with folding , 1988, FEBS letters.

[34]  G. Fox,et al.  Distances as degrees of freedom. , 1989, Journal of biomolecular structure & dynamics.