Thesis (M.Sc.)--York University, 2005. Graduate Programme in Mathematics and Statistics. / Typescript. Includes bibliographical references (leaves 99-102). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url%5Fver=Z39.88-2004&res%5Fdat=xri:pqdiss &rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR11932

We study the collapse transition of a lattice based protein model including an explicit coarse-grained model of a solvent. This model accounts for explicit hydrophobic interactions, and it is studied by Monte Carlo simulation. The protein is modelled as self-avoiding random walk with nearest neighbor interactions on a two dimensional lattice. Without the solvent, universal quantities of the chain around the collapse transition temperature are well known. Hydrophobicity is then modelled through a lattice of solvent molecules in which each molecule can have Q states depending of an orientation variable. Only one state is energetically favored, when two neighboring solvent molecules are both in the same state of orientation. The monomers are placed in interstitial position of the solvent lattice, and are only allowed to occupy sites surrounded by solvent cells of the same orientation. The potential of mean force between two interstitial solute molecules is calculated, showing a solvent mediated attraction typical of hydrophobic interactions. We then show that this potential increases with the energy of hydrogen bond formation as it appears in the model, while its characteristic range decreases. More importantly, we show that the chain embedded in the solvent undergoes a collapse transition, with the temperature of the transition being shifted relative to that of the chain in isolation. We calculate several critical exponents near the collapse transition, and we observe that their values are not conserved in presence of the explicit solvent.

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