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.

Protein folding is a fundamental problem in modern structural biology. The nature of the problem poses challenges to the understanding of the process via computer simulations. One of the challenges in the computer simulation of proteins at the atomic level is the efficiency of sampling conformational space. Replica exchange (RE) methods are widely employed to alleviate the difficulty. To study how to best employ RE to protein folding and binding problems, we constructed a kinetic network model for RE studies of protein folding and used this simplified model to carry out "simulations of simulations" to analyze how the underlying temperature dependence of the conformational kinetics and the basic parameters of RE all interact to affect the number of folding transitions observed. When protein folding follows anti-Arrhenius kinetics, we observe a speed limit for the number of folding transitions observed at the low temperature of interest, which depends on the maximum of the harmonic mean of the folding and unfolding transition rates at high temperature. The efficiency of temperature RE was also studied on a more complicated and realistic continuous two-dimensional potential. Comparison of the efficiencies obtained using the continuous and discrete models makes it possible to identify non-Markovian effects which slow down equilibration of the RE ensemble on the more complex continuous potential. In particular, the efficiency of RE is limited by the timescale of conformational relaxation within free energy basins. The other challenges we are facing in all-atom simulations is to obtain meaningful information on the slow kinetics and pathways of folding. We present a kinetic network model which recover the kinetics using RE-generated states as the nodes of a kinetic network. Choosing the appropriate neighbors and the microscopic rates between the neighbors, the correct kinetics of the system can be recovered by running a simulation on the network.

The book will discuss classes of proteins and their folding, as well as the involvement of bioinformatics in solving the protein folding problem. In vivo and in vitro folding mechanisms are examined, as well as the failures of in vitro folding, a mechanism helpful in understanding disease caused by misfolding. The role of energy landscapes is also discussed and the computational approaches to these landscapes.

Since the first attempts to model proteins on a computer began almost thirty years ago, our understanding of protein structure and dynamics has dramatically increased. Spectroscopic measurement techniques continue to improve in resolution and sensitivity, allowing a wealth of information to be obtained with regard to the kinetics of protein folding and unfolding, and complementing the detailed structural picture of the folded state. Concurrently, algorithms, software, and computational hardware have progressed to the point where both structural and kinetic problems may be studied with a fair degree of realism. Despite these advances, many major challenges remain in understanding protein folding at both the conceptual and practical levels. Computational Methods for Protein Folding seeks to illuminate recent advances in computational modeling of protein folding in a way that will be useful to physicists, chemists, and chemical physicists. Covering a broad spectrum of computational methods and practices culled from a variety of research fields, the editors present a full range of models that, together, provide a thorough and current description of all aspects of protein folding. A valuable resource for both students and professionals in the field, the book will be of value both as a cutting-edge overview of existing information and as a catalyst for inspiring new studies. Computational Methods for Protein Folding is the 120th volume in the acclaimed series Advances in Chemical Physics, a compilation of scholarly works dedicated to the dissemination of contemporary advances in chemical physics, edited by Nobel Prize-winner Ilya Prigogine.

A solution to the protein folding problem has eluded researchers for more than 30 years. The stakes are high. Such a solution will make 40,000 more tertiary structures available for immediate study by translating the DNA sequence information in the sequence databases into three-dimensional protein structures. This translation will be indispensable for the analy sis of results from the Human Genome Project, de novo protein design, and many other areas of biotechnological research. Finally, an in-depth study of the rules of protein folding should provide vital clues to the protein fold ing process. The search for these rules is therefore an important objective for theoretical molecular biology. Both experimental and theoretical ap proaches have been used in the search for a solution, with many promising results but no general solution. In recent years, there has been an exponen tial increase in the power of computers. This has triggered an incredible outburst of theoretical approaches to solving the protein folding problem ranging from molecular dynamics-based studies of proteins in solution to the actual prediction of protein structures from first principles. This volume attempts to present a concise overview of these advances. Adrian Roitberg and Ron Elber describe the locally enhanced sam pling/simulated annealing conformational search algorithm (Chapter 1), which is potentially useful for the rapid conformational search of larger molecular systems.