We present performance-guaranteed approximation algorithms for the protein folding problem in the hydrophobic-hydrophilic model (Dill, 1985). Our algorithms are the first approximation algorithms in the literature with guaranteed performance for this model (Dill, 1994). The hydrophobic-hydrophilic model abstracts the dominant force of protein folding: the hydrophobic interaction. The protein is modeled as a chain of amino acids of length n that are of two types; H (hydrophobic, i.e., nonpolar) and P (hydrophilic, i.e., polar). Although this model is a simplification of more complex protein folding models, the protein folding structure prediction problem is notoriously difficult for this model. Our algorithms have conformation that has linear (3n) or quadratic time and achieve a three-dimensional protein a guaranteed free energy no worse than three-eighths of optimal. This result answers the open problem of Ngo et al. (1994) about the possible existence of an efficient approximation algorithm with guaranteed performance for protein structure prediction in any well-studied model of protein folding. By achieving speed and near-optimality simultaneously, our algorithms rigorously capture salient features of the recently proposed framework of protein folding by Sali et al. (1994). Equally important, the final conformations of our algorithms have significant secondary structure (antiparallel sheets, ^-sheets, compact hydrophobic core). Furthermore, hypothetical folding pathways can be described for our algorithms that fit within the framework of diffusion-collision protein folding proposed by Karplus and Weaver (1979). Computational limitations of algorithms that compute the optimal conformation have restricted their applicability to short sequences (length < 90). Because our algorithms trade computational accuracy for speed, they can construct near-optimal conformations in linear time for sequences of any size. 1.

Three open problems on folding/unfolding are discussed: (1) Can every convex polyhedron be cut along edges and unfolded at to a single nonoverlapping piece? (2) Given gluing instructions for a polygon, construct the unique 3D convex polyhedron to which itfolds. (3) Can every planar polygonal chain be straightened?

The evolution of RNA molecules in replication assays, viroids and RNA viruses can be viewed as an adaptation process on a 'fitness' landscape. The dynamics of evolution is hence tightly linked to the structure of the underlying landscape. Global features of landscapes can be described by statistical measures like number of optima, lengths of walks, and correlation functions. The evolution of a quasispecies on such landscapes exhibits three dynamical regimes depending on the replication fidelity: Above the "localization threshold" the population is centered around a (local) optimum. Between localization and "dispersion threshold" the population is still centered around a consensus sequence, which, however, changes in time. For very large mutation rates the population spreads in sequence space like a gas. The critical mutation rates separating the three domains depend strongly on characteristics properties of the fitness landscapes. Statistical characteristics of RNA landscapes are acces...

The protein structure prediction problem is one of the most (if not the most) important problem in computational biology. This problem consists of nding the conformation of a protein with minimal energy. Because of the complexity of this problem, simplied models like Dill's HP-lattice model [15, 16] have become a major tool for investigating general properties of protein folding. Even for this simplied model, the structure prediction problem has been shown to be NP-complete [5, 7]. We describe a constraint formulation of the HP-model structure prediction problem, and present the basic constraints and search strategy. Of course, the simple formulation would not lead to an ecient algorithm. We therefore describe redundant constraints to prune the search tree. Furthermore, we need bounding function for the energy of an HP-protein. We introduce a new lower bound based on partial knowledge about the nal conformation (namely the distribution of H-monomers to layers). 1 Intr...

Discretized models of biopolymer structures can be used not only as approximations of the actual spatial structures but also as a computationally feasible approach to the generic features of the sequence-structure relationships. We review the combinatorics of nucleic acid secondary structures as well as lattice models of proteins, and show how properties such as the existence of extended neutral networks or shape space covering can be explained on this basis.

We present an "ab initio" method that tries to determine the tertiary structure of unknown proteins by modelling the folding process without using potentials extracted from known protein structures. We have been able to obtain appropriate matrices of folding potentials, i.e. 'forces' able to drive the folding process to produce correct tertiary structures, using a genetic algorithm. Some initial simulations that try to simulate the folding process of a fragment of the crambin that results in an alpha-helix, have yielded good results. We discuss some general implications of an Artificial Life approach to protein folding which makes an attempt at simulating the actual folding process rather than just trying to predict its final result.

We present a global search technique for finding the minimal conformation of a sequence in Dill's HP-lattice model [5, 6]. The HP-lattice model is a simplified model of proteins, that has become a major tool for investigating general properties of protein folding. The search technique uses constraint programming for efficiently pruning the search tree. We state the problem of structure prediction in the HP-lattice model and describe our implementation using the Oz-system [7]. 1 Introduction The protein folding problem is one of the major unsolved problems in computational biology. For this reason, simplified models have been introduced, which became a major tool for investigating general properties of protein folding. An important class of simplified models are the so-called lattice models. The simplifications used in this class of models are (1) monomers (or residues) are represented using a unified size (2) bond length is unified (3) the positions of the monomers are restricted to p...

A computer model of protein aggregation competing with productive folding is proposed. Our model adapts techniques from lattice Monte Carlo studies of protein folding to the problem of aggregation. However, rather than starting with a single string of residues, we allow independently folding strings to undergo collisions and consider their interactions in dierent orientations. We rst present some background into the nature and signicance of protein aggregation and the use of lattice Monte Carlo simulations in understanding other aspects of protein folding. The results of a series of simulation experiments involving simple versions of the model illustrate the importance of considering aggregation in simulations of protein folding and provide some preliminary understanding of the characteristics of the model. Finally, we discuss the value of the model in general and of our particular design decisions and experiments. We conclude that computer simulation techniques developed to study p...

contact areas versus atom type in a database of non-homologous protein 25 rue du Docteur Roux structures. The atomic environment is characterized by the surface area 75015 Paris, France accessible to solvent and the surface of contacts with polar and non-polar 2 atoms. Four types of atoms are considered, namely neutral polar atoms from UPR 003 Cancérogénèse et protein backbones and from protein side-chains, non-polar atoms and Mutagénèse Moléculaire et charged atoms. Potential energies �Ej(E) are defined from the preference for Structurale du CNRS an atom of type j to be in a given environment E compared to the expected Boulevard Sébastien Brant value if everything was random; Boltzmann’s law is then used to transform 67400 Illkirch Graffenstaden these preferences into energies. These new potentials very clearly France discriminate misfolded from correct structural models. The performance of these potentials are critically assessed by monitoring the recognition of the native fold among a large number of alternative structural folding types (the hide-and-seek procedure), as well as by testing if the native sequence can be recovered from a large number of randomly shuffled sequences for a given 3D fold (a procedure similar to the inverse folding problem). We suggest that these potentials reflect the atomic short range non-local interactions in proteins. To characterise atomic solvation alone, similar potentials were derived as a function of the percentage of solvent-accessible area alone. These energies were found to agree reasonably well with the solvation formalism of Eisenberg and McLachlan.

It has been noted that natural proteins adapt only a limited number of folds. The question why and how nature selected these small number of folds has intrigued several investigators. With the use of simple models of protein folding, we demonstrate systematically that there is a "designability principle" behind nature's selection of protein folds. The designability of a structure (fold) is measured by the number of sequences that can design the structure-- that is, sequences that possess the structure as their unique ground state. Structures differ drastically in terms of their designability. A small number of highly designable structures emerge with a number of associated sequences much larger than the average. These highly designable structures possess Present address: Max Planck Institut fur Gravitationsphysik, Albert-Einstein-Institut, Schlaatzweg 1, 14473 Potsdam, Germany y Present address: Department of Biochemistry and Biophysics, University of California at San Francisco, San Francisco, CA 94143, USA z Present address: Centre de Recherches sur les Tr`es basses temp'eratures (CRTBT), BP 166X, 38042 Grenoble C'edex, France x Present address: Department of Physics, George Washington University, Washington, D.C. 20052, USA Corresponding author: tang@research.nj.nec.com 1 "proteinlike" secondary structures, motifs, and even tertiary symmetries. In addition, they are thermodynamically more stable and fold faster than other structures. These results suggest that protein structures are selected in nature because they are readily designed and stable against mutations, and that such a selection simultaneously leads to thermodynamic stability. Keywords: Protein folding; Lattice models; Off-lattice models; Enumeration; Designability I.