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Protein Folding in Solution
In this exercise, you will calculate the protein folding free energy in aqueous solution using thermodynamic integration, a method based on molecular dynamics (MD). The protein will be described by the empirical force field, CHARMM.
Background
A model protein you will have to deal with is the alanine decapeptide. The folding/unfolding will be achieved by fixing the distance between the end carbon atoms in the chain: atoms 7 and 98. This distance is called a collective variable. At each distance one runs the MD simulation (constrained MD) to extract the time-averaged forces acting on the collective variable, $F(x)$. Then, a free energy difference can be calculated via thermodynamic integration (TI):
\begin{equation} \Delta A = -\int_a^b F(x)\, dx \end{equation}