Exact, constraint-based structure prediction in simple protein models

Die Arbeit untersucht die exakte Vorhersage der Struktur von Proteinen in dreidimensionalen, abstrakten Proteinmodellen; insbesondere wird ein exakter Ansatz zur Strukturvorhersage in den HP-Modellen (Lau und Dill, ACS, 1989) des kubischen und kubisch-flächenzentrierten Gitters entwickelt und diskutiert. Im Gegensatz zu heuristischen Methoden liefert das vorgestellte exakte Verfahren beweisbar korrekte Strukturen. HP-Modelle (Hydrophob, Polar) repräsentieren die Rückgratkonformation eines Proteins durch Gitterpunkte und berücksichti\-gen ausschließlich die hydrophobe Wechselwirkung als treibende Kraft bei der Ausbildung der Proteinstruktur. Wesentlich für die erfolgreiche Umsetzung des vorgestellten Verfahrens ist die Verwendung von constraint-basierten Techniken. Im Zentrum steht die Berechnung und Anwendung hydrophober Kerne für die Strukturvorhersage

Long Proteins with Unique Optimal Foldings in the H-P Model

It is widely accepted that (1) the natural or folded state of proteins is a global energy minimum, and (2) in most cases proteins fold to a unique state determined by their amino acid sequence. The H-P (hydrophobic-hydrophilic) model is a simple combinatorial model designed to answer qualitative questions about the protein folding process. In this paper we consider a problem suggested by Brian Hayes in 1998: what proteins in the two-dimensional H-P model have unique optimal (minimum energy) foldings? In particular, we prove that there are closed chains of monomers (amino acids) with this property for all (even) lengths; and that there are open monomer chains with this property for all lengths divisible by four.Comment: 22 pages, 18 figure

CPSP-tools – Exact and complete algorithms for high-throughput 3D lattice protein studies

<p>Abstract</p> <p>Background</p> <p>The principles of protein folding and evolution pose problems of very high inherent complexity. Often these problems are tackled using simplified protein models, e.g. lattice proteins. The CPSP-tools package provides programs to solve exactly and completely the problems typical of studies using 3D lattice protein models. Among the tasks addressed are the prediction of (all) globally optimal and/or suboptimal structures as well as sequence design and neutral network exploration.</p> <p>Results</p> <p>In contrast to stochastic approaches, which are not capable of answering many fundamental questions, our methods are based on fast, non-heuristic techniques. The resulting tools are designed for high-throughput studies of 3D-lattice proteins utilising the Hydrophobic-Polar (HP) model. The source bundle is freely available <abbrgrp><abbr bid="B1">1</abbr></abbrgrp>.</p> <p>Conclusion</p> <p>The CPSP-tools package is the first set of exact and complete methods for extensive, high-throughput studies of non-restricted 3D-lattice protein models. In particular, our package deals with cubic and face centered cubic (FCC) lattices.</p

Lattice and off-lattice side chain models of protein folding: Linear time structure prediction better than 86% of optimal

This paper considers the protein structure prediction problem for lattice and off-lattice protein folding models that explicitly represent side chains. Lattice models of proteins have proven extremely useful tools for reasoning about protein folding in unrestricted continuous space through analogy. This paper provides the first illustration of how rigorous algorithmic analyses of lattice models can lead to rigorous algorithmic analyses of off-lattice models. The authors consider two side chain models: a lattice model that generalizes the HP model (Dill 85) to explicitly represent side chains on the cubic lattice, and a new off-lattice model, the HP Tangent Spheres Side Chain model (HP-TSSC), that generalizes this model further by representing the backbone and side chains of proteins with tangent spheres. They describe algorithms for both of these models with mathematically guaranteed error bounds. In particular, the authors describe a linear time performance guaranteed approximation algorithm for the HP side chain model that constructs conformations whose energy is better than 865 of optimal in a face centered cubic lattice, and they demonstrate how this provides a 70% performance guarantee for the HP-TSSC model. This is the first algorithm in the literature for off-lattice protein structure prediction that has a rigorous performance guarantee. The analysis of the HP-TSSC model builds off of the work of Dancik and Hannenhalli who have developed a 16/30 approximation algorithm for the HP model on the hexagonal close packed lattice. Further, the analysis provides a mathematical methodology for transferring performance guarantees on lattices to off-lattice models. These results partially answer the open question of Karplus et al. concerning the complexity of protein folding models that include side chains

A hybrid approach to protein folding problem integrating constraint programming with local search

<p>Abstract</p> <p>Background</p> <p>The protein folding problem remains one of the most challenging open problems in computational biology. Simplified models in terms of lattice structure and energy function have been proposed to ease the computational hardness of this optimization problem. Heuristic search algorithms and constraint programming are two common techniques to approach this problem. The present study introduces a novel hybrid approach to simulate the protein folding problem using constraint programming technique integrated within local search.</p> <p>Results</p> <p>Using the face-centered-cubic lattice model and 20 amino acid pairwise interactions energy function for the protein folding problem, a constraint programming technique has been applied to generate the neighbourhood conformations that are to be used in generic local search procedure. Experiments have been conducted for a few small and medium sized proteins. Results have been compared with both pure constraint programming approach and local search using well-established local move set. Substantial improvements have been observed in terms of final energy values within acceptable runtime using the hybrid approach.</p> <p>Conclusion</p> <p>Constraint programming approaches usually provide optimal results but become slow as the problem size grows. Local search approaches are usually faster but do not guarantee optimal solutions and tend to stuck in local minima. The encouraging results obtained on the small proteins show that these two approaches can be combined efficiently to obtain better quality solutions within acceptable time. It also encourages future researchers on adopting hybrid techniques to solve other hard optimization problems.</p

Exploring the HP Model for Protein Folding

We explore the HP model not only on the square lattice as originally proposed by Ken Dill, but we also use the triangular lattice. We find upper and lower bounds on the number of self-avoiding walks. In the square lattice, we get O(b^n) for some b in [2.414, 3]. We count the number of all self-avoiding walks of length up to 16 in the square and triangular lattices by exhaustively listing them. We use these lists of self-avoiding walks to study two HP sequences, one of length 11, and the other of length 16. We show that the diameter of the convex hull of a conformation can be used as an estimate of the energy of the conformation. Our examples demonstrate that the same holds true for the area of the convex hull. Both of these measures can be easily computed for a given conformation