In this paper we address the problem of comparing and classifying protein surfaces through a kernelized version of the Softassign
graph-matching algorithm. Preliminary experiments with random-generated graphs have suggested that weighting the quadratic
cost function of Softassign with information coming from the computation of diffusion kernels on graphs attenuate the performance
decay with increasing noise levels. Our experimental results show that this approach yields a useful similarity measure to
cluster proteins with similar structure, to automatically find prototypical graphs representing families of proteins and also
to classify proteins in terms of their distance to these prototypes. We also show that the role of kernel-based information
is to smooth the obtained matching fields, which in turn results in noise-free prototype estimation.
[Show abstract][Hide abstract] ABSTRACT: The docking field has come of age. The time is ripe to present the principles of docking, reviewing the current state of the field. Two reasons are largely responsible for the maturity of the computational docking area. First, the early optimism that the very presence of the "correct" native conformation within the list of predicted docked conformations signals a near solution to the docking problem, has been replaced by the stark realization of the extreme difficulty of the next scoring/ranking step. Second, in the last couple of years more realistic approaches to handling molecular flexibility in docking schemes have emerged. As in folding, these derive from concepts abstracted from statistical mechanics, namely, populations. Docking and folding are interrelated. From the purely physical standpoint, binding and folding are analogous processes, with similar underlying principles. Computationally, the tools developed for docking will be tremendously useful for folding. For large, multidomain proteins, domain docking is probably the only rational way, mimicking the hierarchical nature of protein folding. The complexity of the problem is huge. Here we divide the computational docking problem into its two separate components. As in folding, solving the docking problem involves efficient search (and matching) algorithms, which cover the relevant conformational space, and selective scoring functions, which are both efficient and effectively discriminate between native and non-native solutions. It is universally recognized that docking of drugs is immensely important. However, protein-protein docking is equally so, relating to recognition, cellular pathways, and macromolecular assemblies. Proteins function when they are bound to other molecules. Consequently, we present the review from both the computational and the biological points of view. Although large, it covers only partially the extensive body of literature, relating to small (drug) and to large protein-protein molecule docking, to rigid and to flexible. Unfortunately, when reviewing these, a major difficulty in assessing the results is the non-uniformity in the formats in which they are presented in the literature. Consequently, we further propose a way to rectify it here.
Proteins Structure Function and Bioinformatics 06/2002; 47(4):409-43. DOI:10.1002/prot.10115 · 2.63 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The contributions of this article are twofold. First, we develop a new nonquadratic energy function for graph matching. The starting point is a recently reported mixture model that gauges relational consistency using a series of exponential functions of the Hamming distances between graph neighborhoods. We compute the effective neighborhood potentials associated with the mixture model by identifying the single probability function of zero Kullback divergence. This new energy function is simply a weighted sum of graph Hamming distances. The second contribution is to locate matches by graduated assignment. Rather than solving the mean-field saddle-point equations, which are intractable for our nonquadratic energy function, we apply the soft-assign ansatz to the derivatives of our energy function. Here we introduce a novel departure from the standard graduated assignment formulation of graph matching by allowing the connection strengths of the data graph to update themselves. The aim is to provide a means by which the structure of the data graph can be updated so as to rectify structural errors. The method is evaluated experimentally and is shown to outperform its quadratic counterpart.
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