# 1.1 Assignment 2: performing rotations  (Page 4/4)

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## Ranking by energy

Protein conformations are not only geometric objects but are characterized by energetic stability. You have seenthat there are many empirical ways to compute the potential energy of a conformation. Functions such as CHARMM are very involved for the purpose of this assignment. Therefore, let us notworry about all the energetic terms to be considered from the atomic interactions. Consider only unfavorable interactions due to collisionsbetween atoms, also referred to as steric clashes. Think about a simple energy function that checks for steric clashes. Yourfunction should report high energies for conformations with collisions and low energies for collision-free conformations. You can model each atom asa sphere with a certain radius known as the Van der Waals (VDW) radius. Even though different atoms have different VDW radii, you can assume thatall atoms have the same radius of 1.7 A. To assist you in devising a function that checks for collisions over all pairs of atoms, consider the following:

## Evaluating rotations by energy

• Now think about the effect of the dihedral rotation of the last bond the energetic stability of the new conformation. Please answer Q2 .
• When you rotated a dihedral bond in the middle of the backbone until you reached a conformation that had collisions, you verified the presence ofsteric clashes by visualizing the conformation. You can quantify the presence of steric clashes now through your energy function. Please answer Q5 .

Again, as in dihedral rotations, you are encouraged to use Matlab. After you have the cartesian coordinates of the manipulated conformation, you caniterate over the atoms and check whether they are in collision with one another. You can do this with a double loop. Assume that the radius of everyatom is the same, 1.7 A. In order to avoid reporting collisions for bonded atoms, you can consider only pairs of atoms that are 4 positions apart. Thatis, check atom i with atom i+4 for a possible steric clash.

## For submission

NOTE: remember that in order to open a .crd file in VMD (to attach it to a loaded structure) it has to contain a dummy first line. If your implementation writes out ASCII coordinates, remember to add an empty/dummy line at the beginning before opening with VMD. Please follow this list of deliverables closely:

• ## Q1

Superimpose the conformation resulting from rotating the dihedral bond between the N and CA of the last aminoacid by 30 degrees over the native backbone conformation. Prepare an image that clearly shows which atoms' locations have changed. Submit this image.
• ## Q2

Now you need to quantify the energetic cost of rotating this dihedral bond by 30 degrees by reporting whether this rotation causes any steric clashes. Please test your energy function on the conformation you obtained from rotating the last dihedral bond by 30 degrees. Please report the answer of your energy function. It should be compatible with what you can visualize from the image you prepared above.
• ## Q3

Provide the index of the dihedral bond you need to rotate to generate a large scale motion that results on collisions between atoms. Report on the amount of rotation that you need to perform in order to obtain a conformation that contains steric clashes. Plot this conformation superimposed on the native backbone conformation so as to show that it is very different from the native. Render this image and submit it.
• ## Q4

Zoom in on that part of your conformation that contains collisions. Make sure that this image clearly shows steric clashes and submit this image.
• ## Q5

Compute the energy of the above conformation with your energy function. Report the answer that your energy function returns. Make sure that this answer reflects the fact that there are steric clashes. Please provide the atomic distances for the atom pairs that your function reports in collision.
• ## Bonus

Upon a situation when the energy of the conformation resulting from a dihedral rotation is high, how would you minimize the energy of this conformation? Provide a discussion and pseudo-code on how you would perform the minimization.
Note: While you are welcome to use any programming language, please typeset your deliverables and make sure that the quality of your images is good. You can use any visualization software to produce your images. You are welcome to perform the asked rotations either through the Denavit-Hartenberg derivation provided in our [PDF] document , or through simple rotations around arbitrary vectors. If you choose the latter, please note that there is a typo in the formula for therotation matrix Ri in Zhang-Kavraki, 2002 [PDF] on page 2: The second column, first row entry of this matrix is given as ${u}_{x}{v}_{y}\mathrm{1-cos\left(theta\right)}+{v}_{z}\mathrm{sin\left(theta\right)}$ , but it should be ${v}_{x}{v}_{y}\mathrm{1-cos\left(theta\right)}-{v}_{z}\mathrm{sin\left(theta\right)}$ .

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research.net
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