Midterm 2 Answers - 2007 - UC Berkeley, Chem C130/MCB 100A,...

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Unformatted text preview: UC Berkeley, Chem C130/MCB 100A, Fall 2007, Mid-term Exam 2. Your Name UNIVERSITY OF CALIFORNIA, BERKELEY CHEM Cl30/MCB ClOOA MIDTERM EXAMINATION #2. October 18, 2007 INSTRUCTORS: John Kuriyan and Bryan Krantz THE TIME LIMIT FOR THIS EXAMINATION IS I HOUR AND 20 MINUTES SIGNATURE: Maw [3 K57 Please SIGN your name (in indelible ink) on the line above. YOUR NAME: Please PRINT your name (in indelible ink) on the line above (& on the top right hand corner of every page). Also, please write all of your answers as Iegibly as possible. PLEASE CIRCLE THE NAME OF THE GSI FROM WHOM YOU WILL PICK UP YOUR GRADED MID-TERM EXAM: Rachel Bernstein Padma Gunda Katie Thoren James Fraser This exam consists of 5 questions, each worth 20 points total, as indicated below, for a total of 100 points. Question Part A Pan B Part C Part D Your Maximfi‘ Total Score 1 | (7) (7) (6) ............. -- 20 | 2 (12) (8) I ------------ -- | ————————————— -— 20 3. (10) (10) | ............ -- | ............ -- | | 20 | 4. (14) (6) ‘ ----------- -- | ——————————— —— | | 20 5 | 20 TOTAL -------- —- ——————— —— l ———————— —- i --------- —— i l 100 Page I of12 UC Berkeley, Chem C130/MCB 100A, Fall 2007, Mid-term Exam 2. Your Name Question 1 20 points total. (A) (7 points) Consider the two systems shown below, labeled A and B. Each consists of identical molecules, indicated by black circles. Each system is divided into 16 equal-sized gridboxes. (i) (2 points) Which has higher entropy, A or B? (ii) (5 points) What is the difference in entropy between in A and B (assume that kg: 1 to simplify calculations). Provide the details of how you work out the answer. {14$ NM W2; 2': WELL l2! #4 6/ my r”. 10/ W a ’ , :- >4, ~--- 52%» - .. a 22 :7 W3 /2/ 44 /L,X// M “a” (2)," g A m Afifigfiw [Mk/L», at? iv a}: l, {tafiwfth/,(::‘;r. A fin / a.» — M We ' Page 2 of 12 UC Berkeley, Chem C130/MCB 100A, Fall 2007, Mid-term Exam 2. Your Name Question 1, continued. (B) (7 points). The state C of a System consists of six molecule, indicated by black circles. Three of these molecules undergo a conformational change, and the new state of the system is shown on the right. There is no change in energy. _— ,—~——-— A—».--———- —-—-‘~—7 —A—A-~4 Will State C convert spontaneously to State D? Explain your answer fully. ,. i , i; n :4 I Lfl‘lf‘, w! 153/ 3/ l0! (sup $5 igl' g, .7 (C) (6 points) A bag contains two each of the 26 letters of the alphabet (A, B, C....; two copies each). You repeatedly put your hand in the bag, pull out a letter, then take another letter without putting the previous letter back. What is the probability of pulling out the 26 letters A, B, C in alphabetical order? . l . ~ . . / I! ' ' l _. / , 4 ,l i I I a ‘ 2 ‘1 v . . V, ‘ , , w“ '_ ' I w \ i v . ‘ , n u ,, w 4’: . l‘ g ,- “v .53 _ L' , r .7 ' g - I: l i ’r v 3'/\. .',A {q V i.) - ,w _. 1 i L {Wu — a 1 .A ‘ , g a’ r I) A f w L4 9-“ 7""?5 C. ‘V; . A a , '2' . M. u- r", .w M 3 I. :7 V > w Page 3 0f12 X“ 36 x A9 UC Berkeley, Chem ClSO/MCB 100A, Fall 2007, Mid-term Exam 2. Your Name Question 2 20 points total. (A) (12 points) This question concerns the amino acid codon table and the BLOSUM substitution matrix, which are given below. (i) (4 points) Assume that all single base mutations occur with the same frequency. Based on the codon table, calculate the relative probability of a histidine residue being replaced by Leucine (L) versus Asparagine (N) by a single base mutation. That is, calculate the following ratio: probability ofa His codon being converted to a Leu codon probability of at His codon being converted to an Asn codon . i y/ x M; (Ads? Cod -w» ' . V ,.«(.A g! ~. .- f3» a... 9 ' ,2" v, ‘ (N v, fig“, l- : .l ‘_ ‘ ‘ L1 - V" v , i H J c AK” > g x . g I y - t u J! . F: "7 I ‘i a ‘ 5 .a" {5175 /“ if? n ’9 / fl L If r / l 1‘) ‘: .« ,i'i “ .. I A , x xi ( ,r J) fi/H " V f ’ 5" c (ii) (4 points) Based on the BLOSUM matrix, what is the relative probability of a H—>L mutation versus a H-—>N mutation? 5;) “"3 r? f R ‘4 K “ “T: ,1 " . .. u ‘ a. ’ ‘0‘); r 4...; ,5 fly) “I i ! K l ,1 .0“ to] a" cf ‘ ” i" 0 3 . .A _ I 5’3 ' L . I... , ,c. " , I i) . i/' a)” :2: :7 *3 [n 2» Z ‘“ OH All RN ’1 ‘ a H v. A .1 i if 1 t in r” i" M“ V; "J “a. t) l a \ ‘1 w~~“"‘ ’ :1"! l PM: Page 4 of 12 UC Berkeley, Chem CtSO/MCB 100A, Fall 2007. Mid-term Exam 2. Your Name Question 2, continued. (iii) (4 points) Are your answers to (i) and (ii) similar or different? Justify the outcome clearly. . _ ,. 7 , ‘ s ‘ é a " v i , - . ( e » s. it v .. . x Q ' I, . 11!! -! i“ "3 L A" ‘ "i V. a - i a 3 fl ' .. A H! ’ r [J I , ,Jt‘ , , . A ' a {i f {x}, L ’4 . C I _A / fi > I / . .A ‘ y l. . , \ ’4 A; I K h. If“ ' x ’ f,’ “3-4.” H a L" 4’ ’ ' f ’ 9' ‘ M r { d (I ‘ L M ‘t a , ‘ . A a 1. 2 “.1 “» -5524/‘3114712. xiii“) ) \ H” ‘ ( ‘ 3 ‘le 6 C ‘. BLOSUM MATRIX: C 9 S '1 4 T '1 l 5 P '3 '1 '1 7 A 0 1 0 '1 4 G '3 0 '2 '2 0 6 N '3 l 0 '2 '2 O 6 D '3 0 '1 'l '2 '1 l 6 E '4 0 '1 '1 '1 '2 0 2 5 a 0 2 H l 0 R O 0 K M 5 I 1 4 L '1 '2 '1 '3 '1 '4 '3 '4 '3 ' '2 '2 2 2 4 V '1 '2 0 '2 0 '3 '3 '3 '2 ' '3 '2 l 3 l 4 F '2 '2 '2 '4 '2 '3 '3 '3 '3 ' '3 '3 0 0 U '1 6 Y '2 '2 '2 '3 '2 '3 '2 '3 '2 ' '2 '2 '1 '1 '1 '1 3 7 W '2 '3 '2 '4 '3 '2 '4 '4 '3 ' '3 '3 '1 '3 '2 '3 l 2 11 H R K M I L V F Y W first posmon (5' end) thwdposMoni3'enm Page 5 of 12 UC Berkeley, Chem C130/MCB 100A, Fall 2007, Mid—term Exam 2. Your Name Question 2, continued. (8) (8 points) (i) (3 points) What is meant by the heat capacity of a system? Write down the units of the heat capacity. I' ’ P ’ A J I I ’ , ~“ j g ~‘ '\ 1 . , _. . I , x , “a A f A; " ‘ r" 17 I 1Z1 (in: l a x .5 )m e l x r N a“ , I .9; l-L-~*-~- w 2" * . t. 7' / I . - l I I § X ' ‘ 4 I: . 1 ,, .“ A I '14 ,: ’l ! _ 2/0 92a» at [i z" r = ‘ ~ ‘ " ” “‘~ ‘ " ’ ’9 " ‘ " L . I i v _‘ t . . o N , M \ \ 3 J (ii) (5 points) Shown below are four diagrams showing the variation in heat capacity of a system with increasing temperature. Which one best represents the behavior of DNA molecules, which convert from double-helical to single stranded forms with increasing temperature? Clearly explain your answer. / I \\ ,/ s 3' a a l a m m m m e e a l a 8 o o f 8 m ‘03 ‘6 i E a: I a re / e Temperature Temperature Temperature I ‘ , I f ! " 4 / l. v y y, 1 5 ' . , ‘ a, I " f .44 ‘7. I 3 g: If" {a ’ I i a g, $5: 1:) “at V. ,4. x) J {7,3 .I‘ n W) w «to. - > I .I , V I I, i . I [A l , ,- ‘ J k 1 r , K .7 2 - MW “in”, tr’i‘ (Alt-WU KM" “NW " “ “A”, I h V ’ " ‘ ‘r L I l l‘ K v, £ a 3 ,1: t. J A I V 7 ,—3 ~ "g ,5 ? I > " w‘ 1" (- 11“?ij I ilk/"Liv? ." Viki/‘1 "i' ’l/ 0 Smfi’u" « “W ’. l p ‘~ / _ E ,l A? 1;} - ‘ . l r (\r// r‘ 0‘ ‘ ‘ .I i, /x Ira/4 ’4“ I. ~ r". ’L’ 4 f I) ,5 l4 J n- 1 5 1 “w, ‘F t L l 1" ~ 1“ “OWL TM‘ /«_ Q ‘J’ Q l l‘ A g l I I J I / .‘ r’ w ,1 y '0 I"? I _m R e , ' e A , a 1! 1 fax? ‘ A wfi‘ilac ( ' 1.5.x '5 “*1 l: I /\ rm", i ‘ A: r J u « . t l i‘ ‘ ' ' A , ,1 I ‘5 m‘ i g v k Am .9 w? V ff! .2, Page 6 of 12 ' [it UC Berkeley, Chem ClBO/MCB 100A, Fall 2007. Mid-term Exam 2. Your Name Question 3 (20 points) (A) (10 points). The potential energy of a covalent bond can be approximated by the following function: U (r) = D [Le—(HO) T (i) (2 points) If U(r) is expressed in kJ mol ‘1, what are the units of D? ’\ x w fl ,.‘ - | my. a“; fi 1 46 :1 n M (ii) (4 points) What is the physical significance of D? What is a reasonable value of D for a carbon - carbon covalent bond? D 4/;- £252 figure? din/42,4». a 51,11: En We l/W W /00 ’ /O)OC30 £3— mafl (iii) (4 points) A covalent bond is stretched by 1 A from its equilibrium value (r0). Given the value of D you specified in (ii), what is the magnitude of the force on one of the atoms, in units of kJ mol “1 A"? (r I, > __ (F’Vo> - > 3 + z Page 7 of 12 UC Berkeley, Chem C130/MCB 100A, Fall 2007, Mid-term Exam 2. Your Name Question 3, continued. (B) (10 points) A protein molecule has two conformations, which differ only by the breakage of a single non-covalent interaction. The difference in energy between the two conformations is 50 kJ mol '1. (i) (5 points )Conformation A has the non-covalent bond formed, and conformation B has the bond broken. At 300K, what is the population of a conformation A relative to the population of B? Show all the steps of how you work out the answer. population ofA _ A U {population of B — ‘ 1, ‘ ’50 i , 20 3 (ii) (5 points) The strength of the non-covalent interaction is weakened so that the populations of A and B are equal at 300K. What is the new value of the difference in energy between the two conformation? Show all the steps of how you work out the answer. All/2‘5— és H r; Page 8 of 12 UC Berkeley, Chem CfSO/MCB 100A, Fall 2007, Mid-term Exam 2. Your Name Question 4 (20 points total) (A) (14 points) A piston contains 1 mole of an ideal gas. The gas expands isothermally and in a near—equilibrium (reversible) process at 300K. The volume increases from 1 liter to 2 liters during the expansion. (i) (2 points) What is the change in energy of the ideal gas? fem (ii) (3 points) Would the energy change be the same if the gas were carbon dioxide? Clearly explain your answer. i No. 716 C O; dwéwjg 5/63 “.174? / 713 {EA/~15: W: I m 3,4,1; a 0w - 2367“ c: F (iii) (3 points) What is the change in entropy of the gas? What are the units of the entropy change? 45: “9%[l/2/>=83/w&2 :57; -1 “l T rm»? /< (iv) (3 points) How much heat is transferred to the system during this process? \ r ! flu»)! /WD(£’r’)/3 M g :2 ~l z 5'7éX300 J’mM" = /'728 ATM or; (1': “W = +nRTqu‘1 = + '(lmol)(8.3\‘4$ Tmal"L“>(300K> in (3}) v (v) (3 points) What is the final value of the enthalpy of the gas? Specify the units _ you use. — [7078 T PL): U%/9V pl/: 12/— HI’ 3éP7—7" Pr = [5 .7’:Q.5X2.5 kin/w? Page 9 of 12 UC Berkeley, Chem C130/MCB 100A, Fall 2007, Mid-term Exam 2. Your Name Question 4, continued. (B) (6 points) A moveable piston separates a chamber into two sides, as shown schematically in the diagram below. The chamber on the left contains 1 mol of molecules and that on the right contains 2 moles. Two states of the system (A and B) are shown in the diagram. State A State B Volume = V Volume = V Volume Volume = 1.5V = 0.5v n = 1 mole n = 2 moles n = 2 moles n:1 mole What is the change in entropy on going from State A to State B? That is, calculate S(B) — S(A). 4 ,A A e a 5A : \SLEpr 7L DIQXGHT’ 335 : JZEVT 7L “IR/6,417— ‘g,:fl : A51“? +- 45pm”? " a / L: 92 R /67/ 1:5 A :LETT ’ 2 A 7 J Vflg’é/fi V’ Page 10 of12 UC Berkeley, Chem C130/MCB 100A, Fall 2007, Mid-term Exam 2. Your Name Question 5. 20 points total. Multiple choice and True/False questions. Circle the best option (or circle either TRUE or FALSE). +2 points for each correct answer, -2 points for each wrong answer. To get the maximum score you do not need to answer all the questions, so be careful not to answer questions incorrectly. Maximum points: 20. Minimum points: 0. (i) Fold recognition algorithms test the compatibility of amino acids in a protein sequence for the hree dimensional environments at each position in a known structure. FALSE) (ii) A protein sequence can lways be matched to a protein of known structure. (TRUEI@ (iii) The size of a typical protein domain is: (a) 30 — (b) 100 — 300 residues (0) — resrdues (d) greater than 400 residues (iv) Decrease in energy always indicates the direction of spontaneous change in molecular systems. (TRUE AFALSE‘) (v) In an ide kinetic energy and potential energy can interconverflt I. (TRUE FALS ( 2M w w )99 Add WW ) /' (vi) The force required to break a non-covalent interaction in a protein is in the range of: 10 — 100 iconewtons (a) (b) .10 — 100 nanonewtons, (c) 10 — 100 micronewtons (d) 10 — 100 millinewtons (vii) A valid unit for force is calories per micrometer. FALSE) (viii) Water reduces the effective strengths of hydrogen bonds in proteins. Choose the best explanation: (a) Water weakens electrostatic interactions (b) Water com etes with polar groups for hydrogen bonds ( Both (a) and (b) I (d) e IS false. Water has no effect on hydrogen bonds. Page 11 0f12 (ix) (Xi) (xii) (xiii) UC Berkeley, Chem C130/MCB 100A, Fall 2007, Mid-term Exam 2‘ Your Name There is no specific energy function describing the hydrophobic interaction because i ' e net result of many electrostatic interactions and entropic effects. / FALSE) An interaction between two atoms results in an energetic stabilization of —100 kJ’mol ‘1. This interaction will be easily broken at room temperature. (TRUE FALSE Electrostatic interaction within water are reduced about eighty fold with respect to vacuum. / FALSE) The following represents the outcomes of two series of coin tosses: (a) HTTHHTTHTH (b) TTTTTTTTTT The specific order of heads and/or tails (b) is much less likely than outcome (a) because th ' t outcome has an equal number of heads (H) and tails (T). (TRUE / ALS ) Entropy is an additive fun tion because the multiplicities of independent events are multiplied FALSE) Page 12 of12 ...
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This note was uploaded on 02/23/2011 for the course MCB 100A taught by Professor Kuryian during the Spring '09 term at University of California, Berkeley.

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Midterm 2 Answers - 2007 - UC Berkeley, Chem C130/MCB 100A,...

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