Monte Carlo approaches to the protein folding problem
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The excluded volume of a polymer is defined and calculated by Monte Carlo integration. The excluded volume for a polymer with another polymer of the same length scales as N1.74. These results agree with theoretical predictions about the behavior of polymers in the dilute solution regime. The conformation of a Lennard-Jones chain in water is investigated. The chains remain collapsed from the triple point until 590 K. The presence of water increases the Θ temperature for a Lennard-Jones chain in water, and the transition is sharper in water than in vacuum. These results are explained by the breaking of hydrogen bonds as the chain expands. The solvation properties of model hydrophobic and hydrophilic solutes in SPC/E water are calculated by Monte Carlo simulation. Poor solubility correlates with poor solute/water interaction. At room temperature, energy dominates the aqueous solubility rather than entropy. The large cavities in water are unexpected and explain why a hard sphere solute is more soluble in water than in other solvents. Hydrogen bonding causes water to aggregate into clusters that produce large cavities. Hydrophobic solutes are found to maintain the orientational order in water, whereas hydrophilic solutes alter it. The gas solubility of n-alkanes in water is unexpected. The solubility shows a minimum as the carbon number is increased at C11. Using Monte Carlo simulations, the solubility of model alkanes is measured. These simulations capture the experimental anomaly qualitatively and attribute it to a growing importance of favorable energetic interactions. Microscopic contributions to the chemical potential for this system are defined and calculated through simulation. Partial expansion of a Lennard-Jones chain in water is seen by Monte Carlo simulation. This behavior is explained by entropically favorable large cavities in water at low temperatures. Cavity size distributions of water and the Lennard-Jones fluid are calculated by simulation and contrasted. Water is different from other fluids in its propensity for large cavities at low temperatures.