Efficient Algorithms for Finding Maximum and Maximal Cliques and Their Applications

The problem of finding a maximum clique or enumerating all maximal cliques is very important and has been explored in several excellent survey papers. Here, we focus our attention on the step-by-step examination of a series of branch-and-bound depth-first search algorithms: Basics, MCQ, MCR, MCS, and MCT. Subsequently, as with the depth-first search as above, we present our algorithm, CLIQUES, for enumerating all maximal cliques. Finally, we describe some of the applications of the algorithms and their variants in bioinformatics, data mining, and other fields

A Peaceman-Rachford Splitting Method for the Protein Side-Chain Positioning Problem

We formulate a doubly nonnegative (DNN) relaxation of the protein side-chain positioning (SCP) problem. We take advantage of the natural splitting of variables that stems from the facial reduction technique in the semidefinite relaxation, and we solve the relaxation using a variation of the Peaceman-Rachford splitting method. Our numerical experiments show that we solve all our instances of the SCP problem to optimality

Computational Protein Design Using AND/OR Branch-and-Bound Search

The computation of the global minimum energy conformation (GMEC) is an important and challenging topic in structure-based computational protein design. In this paper, we propose a new protein design algorithm based on the AND/OR branch-and-bound (AOBB) search, which is a variant of the traditional branch-and-bound search algorithm, to solve this combinatorial optimization problem. By integrating with a powerful heuristic function, AOBB is able to fully exploit the graph structure of the underlying residue interaction network of a backbone template to significantly accelerate the design process. Tests on real protein data show that our new protein design algorithm is able to solve many prob- lems that were previously unsolvable by the traditional exact search algorithms, and for the problems that can be solved with traditional provable algorithms, our new method can provide a large speedup by several orders of magnitude while still guaranteeing to find the global minimum energy conformation (GMEC) solution.Comment: RECOMB 201

A protein-dependent side-chain rotamer library

<p>Abstract</p> <p>Background</p> <p>Protein side-chain packing problem has remained one of the key open problems in bioinformatics. The three main components of protein side-chain prediction methods are a rotamer library, an energy function and a search algorithm. Rotamer libraries summarize the existing knowledge of the experimentally determined structures quantitatively. Depending on how much contextual information is encoded, there are backbone-independent rotamer libraries and backbone-dependent rotamer libraries. Backbone-independent libraries only encode sequential information, whereas backbone-dependent libraries encode both sequential and locally structural information. However, side-chain conformations are determined by spatially local information, rather than sequentially local information. Since in the side-chain prediction problem, the backbone structure is given, spatially local information should ideally be encoded into the rotamer libraries.</p> <p>Methods</p> <p>In this paper, we propose a new type of backbone-dependent rotamer library, which encodes structural information of all the spatially neighboring residues. We call it protein-dependent rotamer libraries. Given any rotamer library and a protein backbone structure, we first model the protein structure as a Markov random field. Then the marginal distributions are estimated by the inference algorithms, without doing global optimization or search. The rotamers from the given library are then re-ranked and associated with the updated probabilities.</p> <p>Results</p> <p>Experimental results demonstrate that the proposed protein-dependent libraries significantly outperform the widely used backbone-dependent libraries in terms of the side-chain prediction accuracy and the rotamer ranking ability. Furthermore, without global optimization/search, the side-chain prediction power of the protein-dependent library is still comparable to the global-search-based side-chain prediction methods.</p

How interface geometry dictates water's thermodynamic signature in hydrophobic association

As a common view the hydrophobic association between molecular-scale binding partners is supposed to be dominantly driven by entropy. Recent calorimetric experiments and computer simulations heavily challenge this established paradigm by reporting that water's thermodynamic signature in the binding of small hydrophobic ligands to similar-sized apolar pockets is enthalpy-driven. Here we show with purely geometric considerations that this controversy can be resolved if the antagonistic effects of concave and convex bending on water interface thermodynamics are properly taken into account. A key prediction of this continuum view is that for fully complementary binding of the convex ligand to the concave counterpart, water shows a thermodynamic signature very similar to planar (large-scale) hydrophobic association, that is, enthalpy-dominated, and hardly depends on the particular pocket/ligand geometry. A detailed comparison to recent simulation data qualitatively supports the validity of our perspective down to subnanometer scales. Our findings have important implications for the interpretation of thermodynamic signatures found in molecular recognition and association processes. Furthermore, traditional implicit solvent models may benefit from our view with respect to their ability to predict binding free energies and entropies.Comment: accepted for publication in J. Stat. Phys., special issue on water&associated liquid