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--- exercises:2017_uzh_acpc2:prot_fol [2017/05/17 10:28] – [1. Task: Familiarize yourself] vrybkin
+++ exercises:2017_uzh_acpc2:prot_fol [2020/08/21 10:15] (current) – external edit 127.0.0.1
@@ Line 1: / Line 1: @@
 ====== 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.
+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, [[http://mackerell.umaryland.edu/charmm_ff.shtml]]
-====== Background ======
+===== 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 11: / Line 11: @@
 Here  $a$  and  $b$  are the initial and the final values of the collective variable. TI is a general method, which can be applied to a variety of processes, e.g. phase transitions, electron transfer etc.
-===== 1. Task: Familiarize yourself =====
+===== Task 1: Familiarize yourself =====
-Download the files. Open the **deca_ala.pdb** protein data bank format file with **vmd**.
+Download the files: {{ :exercises:2017_uzh_acpc2:deca_ala.tar.gz |}}
+''deca_ala.pdb'' (protein data base) file contains the coordinates
+''deca_ala.psf'' (protein structure file) file contains connectivity data
+''par_all27_prot_lipid.inp'' contains the force field parameters
+''md_1836.inp'' is the CP2K input file
+ Open the ''deca_ala.pdb'' protein data bank format file with **vmd**. Create a new representation for the protein, e.g. of type **Ribbon** to observe the alpha-helix.
+{{ :exercises:2017_uzh_acpc2:deca_ala.gif?400 |}}
+===== Task 2: Perform constrained MD simulations =====
+For that you have to run MD for different values of the distance between atoms 7 and 98, in each run it will be constrained. In the original file ''md_1836.inp'' it is set to  $18.36$  Å as is in the ''deca_ala.pdb'' file.
+   - Run CP2K with ''md_1836.inp''
+   - Copy ''md_1836.inp'' to smth. like ''md_1536.inp'';
+   - Modify the PROJECT_NAME and ''TARGET'' value in the ''CONSTRAINT'' section for a new value: here 15.36;
+   - Run CP2K with the new input file;
+   - Repeat for several values in the range  $15$  to  $20$  Å.
+<note tip>
+  * To avoid confusion, try to perfrom every task in a new directory
+  * You may increase or decrease the number of MD steps, which is set to 5000 in the file, to speed-up the calculation or else get a better statiscics.
+</note>
+==== Constraint section TO BE modified for constrained MD ====
+<code - constraint section>
+ &CONSTRAINT
+    &COLLECTIVE
+      COLVAR 1
+      INTERMOLECULAR
+      TARGET [angstrom] 18.36
+    &END COLLECTIVE
+    &LAGRANGE_MULTIPLIERS
+      COMMON_ITERATION_LEVELS 1
+    &END
+ &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>