bioe10-fall07-mt-Kumar-soln - BioE 10 Introduc tion to Bio...

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BioE 10 Introduction to Biomedicine for Engineers Midterm Exam Fall 2007 Name SID Write your name and SID on the top of each page! If you need extra space, use the back of the sheet. No computers or electronic communications devices allowed. SCORE (for instructors only) Question 1: 25 Question 2: 30 Question 3: 20 Question 4: 20 Question 5: 25 Question 6: 10 TOTAL 130
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NAME: SID: 1. The following peptide sequence is found in the sidearm domain of the heavy subunit of the human neurofilament protein: Lysine-Alanine-Lysine-Serine-Proline-Alanine-Lysine-Glutamate-Glutamate-Alanine A. Write out this sequence using three-letter amino acid code. (5 pts) Lys-Ala-Lys-Ser-Pro-Ala-Lys-Glu-Glu-Ala B. Write out this sequence using one-letter amino acid code. (5 pts) KAKSPAKEEA C. Suppose that the pKa of Glutamate is 4.0 and the pKa of Lysine is 9.0. Use the Henderson-Hasselbalch equation to calculate the fraction of charged glutamate residues at pH. 5.0. (10 pts) HH Equation: pH = pKa + log ([A-]/[HA]) Rearrange to get [A-]/[HA] = 10 (pH-pKa) For Glu, 10 (pH-pKa) = 10 (5-4) = 10; i.e., 10x as many deprotonated (charged) residues than protonated (uncharged) residues. Therefore fraction charged is 10/(1+10) = 0.91 . D. Which residue(s) in this peptide sequence is (are) most likely to be modified in a cell by addition of a phosphate group? Draw the structure of this phosphorylated residue (you do not need to draw the structures of the other amino acids). (5 pts) The phosphorylated residue is likely to be serine :
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NAME: SID: 2. Suppose you are interested in predicting the structure of a 100-residue protein of known sequence. A. Suppose you come up with an energy function (U elec ) that describes the electrostatic interaction between each pair of atoms in the protein as a function of the distance between the two atoms (r 12 ): U elec (r 12 )= A/r 12 Where A is a constant. Derive an expression that describes the electrostatic force (F elec ) between any two atoms in the protein. (10 pts) Force is related to potential energy through the expression F(r) = –dU(r)/dr Thus, F elec (r) = –dU elec (r 12 )/dr 12 = –d/dr 12 (A/r 12 ) = –(–A/r 2 12 ) = A/r 2 12 B. Considering only electrostatic interactions, write a differential equation involving an effective mass (m) that you can solve to determine r 12 as a function of time. (5 pts) Use Newton’s equations of motion, F = ma = md 2 x/dt 2 Here F = A/r 2 12 , thus the differential equation to solve is md 2 x/dt 2 = A/r 2 12 C. Suppose you want to evaluate U elec for every conformation of the protein. Assuming that each amino acid can occupy 3 conformations and that you can perform 1 million energy
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This note was uploaded on 09/16/2009 for the course BIO ENG 10 taught by Professor Lar during the Spring '08 term at University of California, Berkeley.

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bioe10-fall07-mt-Kumar-soln - BioE 10 Introduc tion to Bio...

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