Lattice models of proteins have been extensively used to study protein thermodynamics, folding dynamics and evolution. Our study considers two different hydrophobic-polar (HP) models on the two-dimensional square lattice: the purely HP model and a model where a compactness-favoring term is added. We exhaustively enumerate all the possible structures in our models and perform the study of their corresponding folds, HP arrangements in space and shapes. The two models considered differ greatly in their numbers of structures, folds, arrangements, and shapes. Despite their differences both lattice models have distinctive protein-like features: (1) Shapes are compact in both models, especially when a compactness-favoring energy term is added. (2) The residue composition is independent of the chain length and is very close to 50% hydrophobic in both models, as we observe in real proteins. (3) Comparative modeling works well in both models, particularly in the more compact one. The fact that our models show protein-like features suggests that lattice models incorporate the fundamental physical principles of proteins. Our work supports the use of lattice models to study questions about proteins that require exactness and extensive calculations, such as protein design and evolution, which are often too complex and computationally demanding to be addressed with more detailed models.

The book gives a comprehensive review of the most advanced multiscale methods for protein structure prediction, computational studies of protein dynamics, folding mechanisms and macromolecular interactions. It approaches span a wide range of the levels of coarse-grained representations, various sampling techniques and variety of applications to biomedical and biophysical problems. This book is intended to be used as a reference book for those who are just beginning their adventure with biomacromolecular modeling but also as a valuable source of detailed information for those who are already experts in the field of biomacromolecular modeling and in related areas of computational biology or biophysics.

Protein folding stands as one of the major interdisciplinary challenges of the last fifteen years, involving biology, chemistry, medicine and physics. In this book solvent effects, and the related hydrophobic effect, on proteins are investigated. Using a simple lattice model of proteins, in which the solvent is semi-explicitly taken into account, thermodynamical quantities can be investigated and the crucial role the solvent plays in protein folding can be demonstrated. Of particular relevance is our observation that a simple model, in which the potential energy is described in terms of the interactions between amino-acids only, does not correctly reproduce solvent effects. Approaches like this, in which solvent effects are treated implicitly, are commonly employed in many of more sophisticated models for protein folding dynamics. Our results are then of great importance as they suggest the treatment of the solvent in these models may need to be re-examined.

Protein folding is studied within the context of two coarse-grained lattice models that separate all amino acids into only a few types. The hydrophobic-polar (HP) model is a simplified lattice protein model for simulating protein folding and for understanding many biological problems of interest. In this work, an "improved" model, the semi-flexible H0P model, was proposed by introducing a new type of "neutral" monomer, "0", i.e., neither hydrophobic nor polar and also taking into consideration the stiffness of bonds connecting monomers. Even though both models are highly simplified protein models, finding the lowest energy conformations and determining the density of states are extremely difficult. We applied replica-exchange Wang-Landau sampling with appropriate trial moves for determining the density of states of multiple HP and H0P proteins, from which the thermodynamic properties such as specific heat can be calculated. Moreover, we developed a heuristic method for determining the ground state degeneracy of lattice proteins, based on multicanonical sampling. It is applied during comprehensive studies of single-site mutations in specific lattice proteins with different sequences. The effects in which we are interested include structural changes in ground states, changes of ground state energy, degeneracy, and thermodynamic properties of the system. With respect to mutations, both extremely sensitive and insensitive positions in the protein sequence have been found. That is, ground state energies and degeneracies, as well as other thermodynamic and structural quantities may be either largely unaffected or may change significantly due to mutation. Moreover, comparison between the HP model and the semi-flexible H0P model have been performed based on two real proteins: Crambin and Ribonuclease A. We found that, compared with the HP model, the semi-flexible H0P model possesses significantly reduced ground state degeneracy, and rich folding signals as the proteins rearranging into native states from very compact structures at low temperatures. We calculated the free energy vs end-to-end distance as a function of temperature. The HP model shows a relatively shallow folding funnel and flat free energy minimum, reflecting the high degeneracy of the ground state. In contrast, the semi-flexible H0P model has a well developed, rough free energy funnel with a low degeneracy ground state. In both cases, folding funnels are asymmetric with temperature dependent shape.