The strength or weakness of an algorithm is ultimately governed by the confidence of its result. When the domain of the problem is large (e.g. traversal of a high-dimensional space), a perfect solution cannot be obtained, so approximations must be made. These approximations often lead to a reported quantity of interest (QOI) which varies between runs, decreasing the confidence of any single run. When the algorithm further computes this final QOI based on uncertain or noisy data, the variability (or lack of confidence) of the final QOI increases. Unbounded, these two sources of uncertainty (algorithmic approximations and uncertainty in input data) can result in a reported statistic that has low correlation with ground truth. In biological applications, this is especially applicable, as the search space is generally approximated at least to some degree (e.g. a high percentage of protein structures are invalid or energetically unfavorable) and the explicit conversion from continuous to discrete space for protein representation implies some uncertainty in the input data. This research applies uncertainty quantification techniques to the difficult protein-protein docking problem, first showing the variability that exists in existing software, and then providing a method for computing probabilistic certificates in the form of Chernoff-like bounds. Finally, this paper leverages these probabilistic certificates to accurately bound the uncertainty in docking from two docking algorithms, providing a QOI that is both robust and statistically meaningful.
Amadei al @cite_18 suggested it was possible to separate the protein configurational space into two subspaces, the essential'' subspace (only a few degrees of freedom that give rise to the large-scale motions of the protein) and the physically constrained'' subspace, consisting of largely Gaussian motion. Thus, identifying a small number of hinge'' residues that give rise to the 'essential' subspace has been the focus of another group of work. Shamsuddin al @cite_17 constructed @math basis vectors to define the motion of rigid bodies joined by hinge residues, HingeProt @cite_1 is a popular method for identifying hinges using cross-correlation of movements from a normal modes analysis (NMA).
@cite_18 @cite_1 @cite_17
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Analysis of extended molecular dynamics (MD) simulations of several proteins in aquous solutions reveals that it is possible to separate the configurational space into two subspaces: (1) an ‘essential’ subspace containing only a few degrees of freedom in which anharmonic motion occurs that comprises most of the positional fluctuations; and (2) the remaining space in which the motion has a narrow Gaussian distribution and which can be considered as ‘physically constrained’. Here we present a novel technique for the alignment of flexible proteins. The method does not require an a priori knowledge of the flexible hinge regions. The FlexProt algorithm simultaneously detects the hinge regions and aligns the rigid subparts of the molecules. Our technique is not sensitive to insertions and deletions. Numerous methods have been developed to solve rigid structural comparisons. Unlike FlexProt, all previously developed methods designed to solve the protein flexible alignment require an a priori knowledge of the hinge regions. The FlexProt method is based on 3-D pattern-matching algorithms combined with graph theoretic techniques. The algorithm is highly efficient. For example, it performs a structural comparison of a pair of proteins with 300 amino acids in about 7 s on a 400-MHz desktop PC. We provide experimental results obtained with this algorithm. First, we flexibly align pairs of proteins taken from the database of motions. These are extended by taking additional proteins from the same SCOP family. Next, we present some of the results obtained from exhaustive all-against-all flexible structural comparisons of 1329 SCOP family representatives. Our results include relatively high-scoring flexible structural alignments between the C-terminal merozoite surface protein vs. tissue factor; class II aminoacyl-tRNA synthase, histocompatibility antigen vs. neonatal FC receptor; tyrosine-protein kinase C-SRC vs. haematopoetic cell kinase (HCK); tyrosine-protein kinase C-SRC vs. titine protein (autoinhibited serine kinase domain); and tissue factor vs. hormone-binding protein. These are illustrated and discussed, showing the capabilities of this structural alignment algorithm, which allows un-predefined hinge-based motions. Proteins 2002;48:242–256. © 2002 Wiley-Liss, Inc. Abstract Two major components are required for a successful prediction of the three-dimensional structure of peptides and proteins: an efficient global optimization procedure which is capable of finding an appropriate local minimum for the strongly anisotropic function of hundreds of variables, and a set of free energy components for a protein molecule in solution which are computationally inexpensive enough to be used in the search procedure, yet sufficiently accurate to ensure the uniqueness of the native conformation. We here found an efficient way to make a random step in a Monte Carlo procedure given knowledge of the energy or statistical properties of conformational subspaces (e.g. φ-ψ zones or side-chain torsion angles). This biased probability Monte Carlo (BPMC) procedure randomly selects the subspace first, then makes a step to a new random position independent of the previous position, but according to the predefined continuous probability distribution. The random step is followed by a local minimization in torsion angle space. The positions, sizes and preferences for high-probability zones on φ-ψ maps and χ-angle maps were calculated for different residue types from the representative set of 191 and 161 protein 3D-structures, respectively. A fast and precise method to evaluate the electrostatic energy of a protein in solution is developed and combined with the BPMC procedure. The method is based on the modified spherical image charge approximation, efficiently projected onto a molecule of arbitrary shape. Comparison with the finite-difference solutions of the Poisson-Boltzmann equation shows high accuracy for our approach. The BPMC procedure is applied successfully to the structure prediction of 12- and 16-residue synthetic peptides and the determination of protein structure from NMR data, with the immunoglobulin binding domain of streptococcal protein G as an example. The BPMC runs display much better convergence properties than the non-biased simulations. The advantage of a true global optimization procedure for NMR structure determination is its ability to cope with local minima originating from data errors and ambiguities in NMR data. Elastic network models have been successful in elucidating the largest scale collective motions of proteins. These models are based on a set of highly coupled springs, where only the close neighboring amino acids interact, without any residue specificity. Our objective here is to determine whether the equivalent cooperative motions can be obtained upon further coarse-graining of the protein structure along the backbone. The influenza virus hemagglutinin A (HA), composed of N = 1509 residues, is utilized for this analysis. Elastic network model calculations are performed for coarse-grained HA structures containing only N 2, N 10, N 20, and N 40 residues along the backbone. High correlations (>0.95) between residue fluctuations are obtained for the first dominant (slowest) mode of motion between the original model and the coarse-grained models. In the case of coarse-graining by a factor of 1 40, the slowest mode shape for HA is reconstructed for all residues by successively selecting different subsets of residues, shifting one residue at a time. The correlation for this reconstructed first mode shape with the original all-residue case is 0.73, while the computational time is reduced by about three orders of magnitude. The reduction in computational time will be much more significant for larger targeted structures. Thus, the dominant motions of protein structures are robust enough to be captured at extremely high levels of coarse-graining. And more importantly, the dynamics of extremely large complexes are now accessible with this new methodology.