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• Contents: Protein folding and disease
• Folding kinetics can have a biological impact
• Why use physical simulation?
• Primary challenges
• Possible models
• Building atomistic models
• Modern force fields
• Ways to treat water
• Implicit solvent models
• Critical evaluation of force fields
• The sampling challenge
• Grid computing methods for dynamics
• What is the role of chemical detail?
• Protein folding theories.

Computational structural biology is a field that involves modeling of physical interactions between complex biological macromolecules in the aqueous environment in the cell. We model the solvent (water) environment around biological macromolecules, to better understand the physical interactions needed to improve methods of protein structure prediction and, more generally, for the protein folding problem. In this thesis, we model the effect of solvent environment on protein structure refinement using implicit and explicit water models. Specifically we used the Generalized Born Surface Area (GBSA) implicit water model and the SPC and TIP4P explicit water models with the all-atom OPLS force field. We also used the knowledge-based (KB) statistical potential functions, derived from high-resolution X-ray crystals of protein structures. The KB potentials include the affect of solvent implicitly, in that the distribution of distances between atoms in protein crystals is effected by the water in the unit cell. These potentials and water models were tested for refinement of an extensive set of protein structures, using energy minimization and molecular dynamics. Energy minimization with GBSA outperformed KB potential energy minimization, in that large magnitude of refinement was observed. Energy minimization with KB potential was more consistent, in that it refined more protein structures than GBSA. We also tested our computationally inexpensive KB energy minimization in the refinement category at the eight world-wide experiments on Critical Assessment of techniques for protein Structure Prediction (CASP) that performed well. We performed a consistency test on the all the predicted protein structure models by all groups at CASP that improved streorechemistry and refined models for the best performing groups. This warrants the use of this simple and computationally inexpensive, but consistent refinement protocol to act as a natural "end" step for all participating groups at CASP. Accurate description of the water structure around the solute of interest could improve our understanding of various biological processes such as protein folding. We study the hydration of hydrophobic solutes of varying sizes (methane, benzene, cyclohexane and Buckminsterfullerene) with Molecular Dynamics (MD) simulations using a recently introduced state-of-the-art quantum general purpose quantum mechanical polarizable force field (QMPFF3) fitted solely to high-level quantum mechanical data at MP2/cc-pVTZ level with a simple model correction using CCSD(T) data for higher accuracy of aromatic carbon atom type. We ask how well the hydrophobic affect is represented in classical force fields when compared to a more rigorous quantum mechanical force field. Polarization increases ordered water structure, in that the imprint of the hydrophobic surface extends to long range effect (up to 10Å for Buckminsterfullerene). Similar surface water affects, with less ordering are also observed for classical force fields. Most of the water molecules point their dipole moment away from the hydrophobic solutes but often one OH bond points towards the hydrophobic solute surface. The major conclusion from this study is that a quantum mechanical force field increases the strength of the hydrophobic effect; this could have a profound affect on protein folding.

The discovery by Cech and coworkers that structured RNA molecules could catalyze specific reactions has revolutionized our understanding of RNA's role and place in the biological machinery of life. The notion of understanding RNA folding from a biophysical perspective means understanding the formation of RNA structure in terms of the basic physical forces at play. This thesis describes the the use of electrostatic and coarse grain simulations and associated experiments to investigate different features of RNA folding. Chapter 1 gives an brief introduction to RNA folding, the primary physical forces that influence its formation, and a review of recent advances in our understanding of structure formation in RNA. Chapters 2 and 3 comprise the next section of the thesis and detail advances in our understanding of electrostatic effects around nucleic acids, a topic of great importance in RNA folding. Specifically, chapter 2 presents the development of a size-modified Poisson-Boltzmann theory to help account for the effects of ionic size while chapter 3 presents a critical assessment of the Poisson-Boltzmann description of electrostatic relaxation in tethered duplex model systems. Chapter 4 highlights a general theoretical framework for understanding the combined effects of electrostatics and junction topology on RNA folding stability and specificity. The last section focuses on the use of coarse grained simulation to understand the role of junction topology in shaping the allowed conformational space of the Transactivation Response (TAR) element from the genome of the Human Immunodeficiency Virus (HIV). Though the last section is not, strictly speaking, a study of RNA folding, understanding RNA conformational motion is of critical importance to the question of structure acquisition in RNAs.

The dynamics of many biological processes of interest, such as the folding of a protein, are slow and complicated enough that a single molecular dynamics simulation trajectory of the entire process is difficult to obtain in any reasonable amount of time. Moreover, one such simulation may not be sufficient to develop an understanding of the mechanism of the process, and multiple simulations may be necessary. One approach to circumvent this computational barrier is the use of Markov state models. These models are useful because they can be constructed using data from a large number of shorter simulations instead of a single long simulation. This thesis presents a new Bayesian method for the construction of Markov models from simulation data. A Markov model is specified by (t, P, T), where t is the mesoscopic time step, P is a partition of configuration space into mesostates, and T is an N x N transition rate matrix for transitions between the mesostates in one mesoscopic time step, where N is the number of mesostates in P. The method presented here is different from previous Bayesian methods in several ways. 1. The method uses Bayesian analysis to determine the partition as well as the transition probabilities. 2. The method allows the construction of a Markov model for any chosen mesoscopic time scale t. 3. It constructs Markov models for which the diagonal elements of T are all equal to or greater than 0.5. Such a model will be called a 'consistent mesoscopic Markov model' (or CMMM). Such models have important advantages for providing an understanding of the dynamics on a mesoscopic time scale. The Bayesian method uses simulation data to find a posterior probability distribution for (P, T) for any chosen t. This distribution can be regarded as the Bayesian probability that the kinetics observed in the atomistic simulation data on the mesoscopic time scale t was generated by the CMMM specified by (P, T). An optimization algorithm is used to find the most probable CMMM for the chosen mesoscopic time step. We applied this method of Markov model construction to several toy systems (random walks in one and two dimensions) as well as the dynamics of alanine dipeptide in water and of trpzip2 in water. The resulting Markov state models were indeed successful in capturing the dynamics of our test systems on a variety of mesoscopic time scales.