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We have exactly enumerated all sequences and conformations of HP proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the hydrophobic-polar (HP) model, where only two types of monomers are…

In the framework of a lattice-model study of protein folding, we investigate the interplay between designability, thermodynamic stability, and kinetics. To be ``protein-like'', heteropolymers must be thermodynamically stable, stable against…

A simple lattice model for proteins that allows for distinct sizes of the amino acids is presented. The model is found to lead to a significant number of conformations that are the unique ground state of one or more sequences or encodable.…

We study the thermodynamic behavior of a simple off-lattice model for protein folding. The model is two-dimensional and has two different ``amino acids''. Using numerical simulations of all chains containing eight or ten monomers, we…

A general strategy is described for finding which amino acid sequences have native states in a desired conformation (inverse design). The approach is used to design sequences of 48 hydrophobic and polar aminoacids on three-dimensional…

Folding properties of a two-dimensional toy protein model containing only two amino-acid types, hydrophobic and hydrophilic, respectively, are analyzed. An efficient Monte Carlo procedure is employed to ensure that the ground states are…

The number of protein structures is far less than the number of sequences. By imposing simple generic features of proteins (low energy and compaction) on all possible sequences we show that the structure space is sparse compared to the…

Lattice models, for their coarse-grained nature, are best suited for the study of the ``designability problem'', the phenomenon in which most of the about 16,000 proteins of known structure have their native conformations concentrated in a…

We discuss recent theoretical developments in the study of simple lattice models of proteins. Such models are designed to understand general features of protein structures and mechanism of folding. Among the topics covered are (i) the use…

We propose a general method for predicting potentially good folders from a given number of amino acid sequences. Our approach is based on the calculation of the rate of convergence of each amino acid chain towards the native structure using…

The concept of the reduced set of contact maps is introduced. Using this concept we find the ground state candidates for Hydrophobic-Polar lattice model on a two dimensional square lattice. Using these results we exactly enumerate the…

The precise sequence of aminoacids plays a central role in the tertiary structure of proteins and their functional properties. The Hydrophobic-Polar lattice models have provided valuable insights regarding the energy landscape. We…

The intricate three-dimensional geometries of protein tertiary structures underlie protein function and emerge through a folding process from one-dimensional chains of amino acids. The exact spatial sequence and configuration of amino…

We study folding dynamics of protein-like sequences on square lattice using physical move set that exhausts all possible conformational changes. By analytically solving the master equation, we follow the time-dependent probabilities of…

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…

The hydrophobic/polar HP model on the square lattice has been widely used to investigate basics of protein folding. In the cases where all designing sequences (sequences with unique ground states) were enumerated without restrictions on the…

All known terrestrial proteins are coded as continuous strings of ~20 amino acids. The patterns formed by the repetitions of elements in groups of finite sequences describes the natural architectures of protein families. We present a method…

In order to extend the results obtained with minimal lattice models to more realistic systems, we study a model where proteins are described as a chain of 20 kinds of structureless amino acids moving in a continuum space and interacting…

Making use of a simplified model for protein folding, it can be shown that conformations which are particularly stable when their energy is minimized with respect to amino acid sequence (in the sense that they display a large energy gap to…

We present an algorithm for the exhaustive enumeration of all monomer sequences and conformations of short lattice proteins as described by the hydrophobic-polar (HP) model. The algorithm is used for an exact identification of all designing…