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--- exercises:2017_uzh_acpc2:prot_fol [2017/05/17 12:27] – [Task 2: Perform constrained MD simulations] vrybkin
+++ exercises:2017_uzh_acpc2:prot_fol [2020/08/21 10:15] (current) – external edit 127.0.0.1
@@ Line 3: / Line 3: @@
 ===== 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):
+A model protein you will have to deal with is the alanine decapeptide. The folding/unfolding will be achieved by stretching/compressing the chain and fixing the distance between the end carbon atoms in it: 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}
@@ Line 53: / Line 53: @@
  &END CONSTRAINT
 </code>
+===== Task 3: Evaluate the free energy difference =====
+⇒ Each constrained MD will produce a ''.LagrangeMultLog''-files, which look like this:
+<code>
+Shake  Lagrangian Multipliers:           -63.547262596
+Rattle Lagrangian Multipliers:            63.240598387
+Shake  Lagrangian Multipliers:            -0.326901815
+Rattle Lagrangian Multipliers:            -0.318145579
+</code>
+<note warning>
+Make sure that you get the units right. The Largange multipliers are written in atomic units (Hartree/bohr), while the distances are in Angstrom.
+</note>
+  * From these files you can calculate the average Lagrange multiplier of the Shake-algorithm like this:
+<code>
+grep Shake yourprojectname.LagrangeMultLog | awk '{c++ ; s=s+$4}END{print s/c}'
+</code>
+  * The average Lagrange multiplier is the average force  $F(x)$  required to constrain the atoms at the distance  $x$ .
+  * From these forces the free energy difference can be obtained via TI (see **Background**)
+<note tip>
+  * Calculate  $\Delta A$  numerically using the trapezoidal rule (or equivalent) with EXCEL, ORIGIN or any scripting language.
+</note>