Exhaustive enumeration of protein conformations using experimental restraints

Abstract

We present an efficient new algorithm that enumerates all possible conformations of a protein that satisfy a given set of distance restraints. Rapid growth of all possible self-avoiding conformations on the diamond lattice provides construction of a-carbon representations of a protein fold. We investigated the dependence of the number of conformations on pairwise distance restraints for the proteins crambin, pancreatic trypsin inhibitor, and ubiquitin. Knowledge of between one and two contacts per monomer is shown to be sufficient to restrict the number of candidate structures to approximately 1 , OOO conformations. Pairwise RMS deviations of atomic position comparisons between pairs of these 1,000 structures revealed that these conformations can be grouped into about 25 families of structures. These results suggest a new approach to assessing alternative protein folds given a very limited number of distance restraints. Such restraints are available from several experimental techniques such as NMR, NOESY, energy transfer fluorescence spectroscopy, and crosslinking experiments. This work focuses on exhaustive enumeration of protein structures with emphasis on the possible use of NOESY-determined distance restraints.Keywords: lattice models of proteins; NMR restraints; protein folding; protein structure prediction Determining the solution structure of proteins from highresolution NMR data by restrained molecular dynamical simulated annealing (MDSA) uses distance information determined from NOE data (Briinger et al

Fidelity of the Protein Structure Reconstruction from Inter-Residue Proximity Constraints

“…Therefore, an important question is, What is the minimal number of inter-residue constraints needed to determine the fold of a protein? Both analytical 20 and computational 21 efforts have been devoted to addressing related problems in early studies in the context of general polymer theory and lattice protein models. The simplifications of polymer/protein models used in these studies are not directly extendable to real proteins.…”

Reduced models of proteins and their applications

“…For very simple discrete models, all conformations could be enumerated [20,76,96,141,[255][256][257][258][259][260] and an exact analysis of the model thermodynamics performed [20,261]. Structure and thermodynamics of more complex models are studied via classical molecular dynamics [262 -267] (MD), Monte Carlo (MC) methods [26,109,129,158 -160,167,168, 237,239,268-274], genetic algorithms and hybrid combinations of these methods [275].…”

“…Simple lattice and off lattice models of real proteins were studied not only for the sake of test structure predictions but also to elucidate effects of various interactions on protein folding dynamics [9,174] and thermodynamics [136,266] or the role of structural restraints on the modeled structures [76].…”

“…Recently, a very sophisticated method for such enumerations has been developed [256 -259]. Sometimes the enumeration of conformational states could be extended onto somewhat more complex models [76,141]. The problems addressed in the context of 'simple exact' [20] models include: the fundamentals of hydrophobic collapse [293] and some elements of folding kinetics [115, 145-147,232,255,294 -298], design of foldable sequences with a unique ground state and the requirements of the twostate cooperativity of the folding process [23 -25,299,300].…”

“…It is still impractical (due to enormous computational cost) to simulate a full folding process of even relatively small proteins using detailed molecular models [72]. Related to ab initio protein structure prediction is model building based on fragmentary experimental data [73]-for example starting from NMR assigned secondary structure (partial or complete) and/or from a small number of known side chain contacts from NMR [74][75][76] or other experiments [77] as crosslink walks or tryptophan fluorescence. Building good molecular models from electron microscopy still remains a big challenge and may also benefit from the application of properly designed reduced models in the near future.…”