mcbC100A-fa09-mt3-Wemmer-soln

mcbC100A-fa09-mt3-Wemmer-soln - UNIVERSITY OF CALIFORNIA...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA "this exam should have 8 pages CHEM C130 I MCB C100A" ' ' including the cover MIDTERM EXAMINATION #3 November 12, .2009 INSTRUCTORS: John Kuriyan and David Wemmer TIME LIMIT FOR THIS EXAM: 1 HOUR 20 MINUTES SIGNATURE: é _ Please SIGN you ame above in INDELIBLE INK YOUR NAME: Please PRINT your name clearly in INDELIBLE INK PLEASE CIRCLE the name of your GSI: Anna Asmundson Geoffrey Feld _ Zhijuan Gao Patrick Visperase PLEASE: Write answers as CLEARLY as possible, ILLEGIBLE answers will not be given points. SCORING - the number here are the number of points possible for'each part of each problem page 1 Problem 1. Movement of biological molecules can be roughly approximated as jumps between points on a grid. Although real molecules move in three dimensions we can learn about aspects of movement using simpler models, even steps on a one dimensional line starting at the origin. Suppose that a molecule takes a ‘step' 1000 times per second, and each step can randomly be to the left or to the right with equal probability and has unit size, is. one step goes from 0 to 1 or -1, etc. To think about the average movement of molecules during such a process we can look at the distribution of probabilities of different outcomes, for example ending up a specific number of steps from the origin. a) if a molecule moves for 1 second (1000 steps): What is the most probable location of the molecule: 0} ‘H/kfi 95%)“: C1 (lug-{GUM it Mgr-twill“ {ti fix 2' :3 n; “Misfit” {pd-t? b) if the distribution is examined after 1 second and again after 100 seconds, does the probability of being Exactly 10 steps away from the origin increase or decrease at 100 sec. relative to 1 see? (explain briefly) bottle. Ci is. let; titan lot“ :2 ’30 step? mixers) bi ill (EQQQQEQ (2w M St, vwfi-te {-3 isi‘t'i-t (gift disbllwiém {in i £13.}. miti- E‘j’i item “is. c) What is the relative width of the distribution of final locations at 100 sec. vs. 1 sec. times? (be quantitative) I _ ........ mt (alga-lit, m. Mfiifii a?“ at ling-{spit so in l-K. ago wt» was it) “trim-3" :1) Suppose that the cell taking the steps is sensing food in its environment, and biases its steps to move toward the food. if there is a food source to the right (positive numbers), and the probability of stepping toward food is 2'3 and the probability of stepping away from food is 113, what is the most probable location for a cell after 1 second? (think carefully about the distribution and its relation to final location in this case). (ME. mil: its. 7 re...‘ K M3 “3%”? fl «size it. is? with... W; “"4 ‘1 "M page 2 Problem 2. Thenucleobase adenosine is a weak acid, when protonated on the N1 atom of the Watson- Crick edge with a pKa = 3.5 observed in an unstructured RNA molecule. - - - a) a particular adenosine was thought to play an important role in the activity of a catalytically active RNA molecute. if its pKa were normal as in the unstructured RNA, what fraction of this adenosine would be protonated in a solution with a pH of 7.0 ? E3 5” RN ass} a e W amid K6. la : “films” at gift ‘7 almfit suit wilt be: A 59 Lfii'i’ttit‘xj’k UM H ‘ ; an“; i. Mi _,, tom“ "fig-11" “ is?“ “my;th b) in the actual structured RNA the pKa of the adenosine of interest was followed by NMR, and its pKa value was determined to be 6.5. Describe two interactions which could contribute substantially to this shift in pKa value (be brief but specific in your description) i’VxOfii' filmth it 5R,- fiefifi' it: {:- Oc‘itfi PQSEQWQ A‘i’vfivxfi Hob-oné “it; Cilia gm UREE} QM N rm a limit” {of unisex—1‘)- A, t—iwlrcmé i. +0 Ce... wet set. for ts? tilt-3th.. sit titties-titted c) Calculate the value of AG for the protonxatipn of a normai adenosine in an unstructured RNA if the RNA is present at 1 uM concentration and 'the'pr is 7.0. 25 c“G. AC7: eat t m as? er is. ml 2 PT In Kt AG : “lOLJ/ + H" + A refit» HA is pretty-vast"; wt I W e x [M mi: .... mvatae. at acid suede-9m g‘mklxgfio \016 ‘16 K91: VKQ tardy“; g; itk.€..._%gkfi : — 1‘ LFOILMSXWQ 1" ‘k‘rlbt‘gt’mii baa C “(Z-O kT/MOKQ aw t it" ' d d) Will the AG value for protonating the adenosine in the folded ribozyme structure be: a 1 more positive the same (more negative} (circie one)? pKQ 1g“ {in A63 if Wt"? Mattie-t2; more fiwflwflé’ “is; firm-e Watt? Beam .5153 f p “l sew wags at» it [i l f l t-' .«I page 3 Problem 3. DNA sequences have been studied in which a ‘core' duplex region is fixed, but bases are added to make either one or two loops which are unstructured, giving molecules such as: - - - (a) . (b) ' to) Consider the thermodynamic parameters below all referring to the ‘melting’ transition (dupiex to random coil transition) _ mm... Answer the following questions by circling a letter or letters (if more than one is correct) or no letter (if no answer is correct) corresponding to the appropriate structure(s): part A) Structure (a) ; (b) ; (c) ' will have the highest Tm value part B) Structure ; (b) ; (c) will have the most negative value of AG" at 25°C part C) Structure ; (b) ; (c) will have the largest AS" associated with melting part D) Structure ; (b) ; (c) will have a lower Tm if the sample is diluted 2 fold part E) Structure ; ; will have a AH°va|ue that is independent of concentration A) {mega-tic». fiat-M. teem}? new??? I B) Unite L31; alth am [met 1L AC1 “J t . it? aafitegt“ +0 mfiob}; —_ (a) 6) his at state- chase tide tug—tie est-t mtg-fit:de ' “it Git it.) 33) out tj Le) titer “ha—it? gt-etutttlt r:- tgwi'tt ‘t t . ) Wkai Put dear-u git... AGES net i“ «site-QR. behest at“ “’t‘krfi" tfifi {.ti‘t‘ttfi‘t' 2% at?" (JR, pagezt E Note. at: if kjW Emit» aged. KefifC'er Problem 4) The melting of the self-complementary DNA duplex hexamer CGATCG to two identical single strands was studied by calorimetry at a concentration of 0.10 mM of DNA strands, and it was found that AH“ = -177 lemol and the Tm was 38.3 c‘C. (reminder. for nucleic acids ACp=0) For this problem consider the reaction direction to be duplex going to single strands (i.e. the unfolding direction) part A) What is the value of the equilibrium constant for unfolding at Tm ? duvlgx #9 2 SW 3.3 out-"T... flama3=zfévpiefl iijq ’3’— K f. Lil a, a1 {lbrz‘k thmg'fir lLdthlex ] ":3. M part B) Calculate the A8" for the melting (unfolding) of this duplex. AGO: AW-«TAP : .. RT [MKQR a 33.1 r; = 3M K sl‘iiiia‘ywvjll A5" 3 U3 Vim/wt A39 2 éLtEjymut/l< part C) In analogy to the calculation done for protein folding, assume that each unconstrained single bond along the backbone has three equally iow energy conformers, and that bases have two allowed conformations relative to sugars both when in a single strand state, while there is one commtiqu for bonds between nucleotides or connecting to the base in the duplexgtate. Estimate the conformational entropy change (on a per mole of duplex DNA melted basis) for the melting precess. 0 We: “2. ‘Dfl‘f b» duptfix S Jamal/@338: betwam ngflxéq’ )3} Eye—tat Cmshaieefi , easy with “Wolff? S (matte. (met, + " as Z SW35 _ t : pigwfi _ W» ” WWW“! :1. 50 W3 a -:. O acid, set {if Q tater ye! 5pm.}, [fishnets x Z rower stat-er N"R NBSO- 2”) part D) Lifittifiher contributions to the AS” value that have been ignored in the calcuiation in‘part B), explain these very briefly. «w- CKMEC/S 1:“ {JQQé-W fe'lusxxf {pow} ‘ I f a t k“ mfztfiiih t 4mm M... 6913’ ex. is? thQ guaranties 923?. .c... 9K M My»: éufl... is W6“ pew tightened balm-tee u-S‘WS page 5 Problem 5) A DNA otigomer was observed to be a duplex with all 12 bases in Watson—Crick base pairs. However in low salt concentrations when temperature was increased each duplex converted-to two hairpins, and then at yet higher temperature to random coil single strands, as shown in the diagram below. F is the fraction of the DNA strands in the higher temperature form for each of the transitions, i.e. - for the left curve it is the fraction hairpin. The total strand concentration was 3.8 lel. part A) Estimate the free energy. AG“. for conversion of duplex to hairpin at 35 °C. . ._. l as; lead Same as 4A a h? “I act:- “laws 16% Sines Q 2&3” «this "it 0K WM {45$ Mtg” we RC3 in-S‘il’fi‘fl-é. HP part B) Use these data to estimate the value of AH” for the transition from the dupiex to single strands. at, =AR»”T"M f r s " i = " Abba; w (A R m K Afiif‘t‘fi Mt- wa WW» 5 .4 T Mi“ \ am 1 “it; {A 3 a "f" 1' ‘ "‘m‘” “t” 1 . l / ‘3.- ‘ Kt... _, “is. b w 3:339 { ’5- KESO "32% LN} cit”: Myth 3mm; 9 a),an MM. :51“ [DH 3: l ‘f 1‘“? éf‘iiufit a) a} 9 ,9 fix a; Wig", :, Eligible part C) The raterof conversion of the duplex to hairpin was measured as a function of temperature, and the rate constants were used to generate the plot at the right. From these data determine the activation energy for this reaction. A ~ & 9w numb L" {,9 "" «#3:? A >4 k {’4. _ a fl, 5M. was.“ t ht “ ca 53):; 5‘3 ‘2 m {:65 ’7." ’3 I','-M.H~NQ I. ' ‘fr {:03 part D) The estimated value of AH" between the duplex and random coil single strands was estimated to be 377 lemol. The most obvious mechanism for the transition from the DNA duplex to individual single strands is for the strands to dissociate to make two random coils, which then each folds up to make the hairpin. Do the available data support this mechanism? (explain briefly) $3 SCN dupe 1x as a: “a 9"? ‘1 ga- tfifimé W- ‘2 apr What? The EU f fibng M1332 < gm?" if? Ufgffillia‘; 5%} a; t Most ml:- afio 'W gum? “MS- g k -' " w“ -- 1- ','.L"':.’CL. .. r" thmhjiafi: Emirate Qatar as“? m S a? use? VWM its “the; “{“\mé'i+-:z a“ page 7 Problem 6. Some bacterial proteins are phosphorylated by a protein called a-histidine kinase, HK. The kinase reacts with ATP to make a phospho-intermediate HK-P. The HK-P reacts with a receiver domain, RD, transferring phosphate to give RD-P, which can hydrolyze to give RD plus phosphate. k1 ' HK + ATP -> HK-P + ADP k2 HK-P + RD —» HK + RD-P k3 RD—P + H20 -* RD + Pi Suppose the ATP concentration in the cell is held constant by other processes. Part A) Since RD is used in one step but then recovered in the next step, the concentrations of RD and RD-fiashould reachageadystate: Write a difiemmt‘di equation describing this steady state in terms of the reactions given, and give an equation for the ratio [RD-PIIIRD]. lib stat-a. re Ag? :1 cs 1-. -ltkteflUlK—fl + kfiRD-fltwfl Part B) Suppose that the reaction is done in vitro, starting with known concentrations of pure HK and _RD. and then adding ATP. Write the differential equation describing the change in concentration of HK as a function of time. ' - - . w 53"“; f, «Blotter? mot—tithe} ‘ Part C) Suppose the rate of the reaction RD-P + H20 also increases with increased [M92+]. Under what conditions would you expect the addition of Mg2+ to the solution to substantially affect the rate of disappearance of ATP ? (explain briefly) ' Hun-61.x. “to See. i.) Mi await; J.) “title. [4,3 feta-3:; must he: at} least- thidu‘m mi? 1M r m M. , m . ping. f‘t «a " _ E ‘ fig 3 Kb”? j @133} g kiwi-1K; i: REE} sate; kfldifiifi’fl'i j 2-5.: at? kt wed in “$9 Li; Lat-L oslu “$1: '- _ it is”... See cm, ed: page 8 ...
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mcbC100A-fa09-mt3-Wemmer-soln - UNIVERSITY OF CALIFORNIA...

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