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We calculate the solvation free energy of proteins in the tube model of Banavar and Maritan [ Rev. Mod. Phys. 75 23 (2003)] using morphological thermodynamics which is based on Hadwiger’s theorem of integral geometry. Thereby we extend recent results by Snir and Kamien [ Science 307 1067 (2005)] to hard-sphere solvents at finite packing fractions and obtain new conclusions. Depending on the solvent properties, parameter regions are identified where the β sheet, the optimal helix, or neither is favored.
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