Chemical Engineering 170 October 16, 2003 Midterm Exam Closed Book and Closed Notes One 8.5 x 11 in. page of notes allowed

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1 Cheical ngineering 70 Octber 6, 00 Mier xa Clsed B and Clsed Ntes One 8.5 x in. page f ntes allwed ectin. hrt Answers. Nae fur interactins invlved in aintaining the tertiary structure f prteins. Hydrgen bnd Hydrphbic Interactins Inic Interactins (electrstatic) Van der Waals Disulfide bnds. Define the Dahler nuber fr an ibilized enzye reactin and explain its physical eaning. Da V ax Maxiu Reactin Rate Da ; Maxiu Transprt Rate. xplain why, in physical ters, η I << when φ >>. What is the cntrlling resistance in such a case? R Vax φ D eff If φ >> then Vax>> D eff, hence the syste ust be transprt-liited. Reactant lecules are cnsued befre they diffuse very far, and the reactin is liited t a thin regin near the periphery f the particle. Thus, the bserved reactin rate is uch saller than the rate in the absence f an internal cncentratin gradient (η I <<). What are three f the ajr differences between RNA and DNA that we discussed in class? - RNA has a hydrxyl grup at the carbn f its sugar - RNA uses uracil as ne f its base, while DNA uses thyine as ne f its base - The extra hydrxyl grup f RNA prevents it fr fring a stable duble stranded structure, hence RNA exists as a single stranded lecule. - e regins f RNA can fr duble helix (hairpin lps) (i.e. secndary structure) - RNA can fr any different tertiary structures, r stable three-diensinal structures

2 5. In site-directed utagenesis, a neutral utatin has n effect n the prperties f the utated prtein. Indicate whether the fllwing wuld liely be neutral r nn-neutral utatins, and briefly explain why. (Ignre pssible effects n prtein secndary structure.) i. glutaate changed t aspartate Neutral siilar size and pa s. ii. leucine changed t valine Neutral bth branched-chain hydrphibics f siilar size. iii. valine changed t glycine Nt neutral G is very sall, allws significant free rtatin arund peptide bnds. iv. cysteine changed t alanine Nt neutral A is hydrphbic, C is plar and can even dissciate. v. serine changed t threnine Neutral bth cntain OH in side chains and siilar size. vi. tryptphan changed t phenylalanine Neutral bth are hydrphbic aratics f siilar size. vii. arginine changed t lysine Neutral bth are large and basic. viii. histidine changed t alanine Nt neutral H is plar and inizes with a pa arund neutrality, A is nn-plar. 6. What is the tw-stage del fr enzye inactivatin, and what is the crrespnding expressin fr bs, the bserved rate cnstant fr inactivatin? The tw-stage del f enzye inactivatin is: N D I The crrespnding expressin fr bs is: bs, where N D

3 7. a) What are the general reactin schees fr cpetitive and uncpetitive enzye inhibitin? Cpetitive Inhibitin: Inhibitr cpetes with substrate fr enzye active site?? P? I I Uncpetitive Inhibitin: Inhibitr binds t enzye-substrate cplex instead f enzye active site?? P? I I b) etch an adie-hfstee plt fr each type f inhibitin in part (a). On each plt, include lines fr results btained in the presence and in the absence f the inhibitr. Be sure t label each line and each axis. Cpetitive Inhibitin Uncpetitive Inhibitin (sae y-intercept, steeper slpe with I) (sae x-intercept, re shallw slpe with I) V N inhibitr V N inhibitr With inhibitr With inhibitr V/ V/ Cpetitive inhibitin: app V ax is unchanged, I I Uncpetitive inhibitin: app Vax Vax, I I ax app ax, I I

4 ectin. hrt Prbles. nzye that is ibilized n a nnprus supprt beys the fllwing reactin schee: Yu are als given the fllwing infratin: p 5 x 0 - c/sec P 0.5 M M η 0.0 v ' ax 00 µm c - in - a) Write an expressin that relates the flux f prduct fr the surface t the rate f substrate cnsuptin at the surface. Please define any paraeters in yur expressin that are nt given abve. p ' * * v ( ) ax * P P OR ( ) * p P P P* cncentratin f prduct at surface * cncentratin f substrate at surface ' ax? v b) Calculate the easured rate f appearance f prduct in the bul per unit area. ' *? vax µM M ( P P ) p 5. µm c - in - c in 0.5 M M

5 . A bicheical engineer, wh was attepting t enhance the rate f a particular enzye by anipulating its structure via site-directed utagenesis, prduced a utant that exhibited rather unusual behavir. The enzye-substrate cplex was fund t reversibly aggregate int an inactive dier, accrding t the fllwing reactin: Hwever, the utant enzye still fllws general enzye inetics: D P Use these definitins in answering the fllwing questins: - - ; a) Assuing the reactin ccurs in a clsed syste, begin by writing ass balances fr the enzye cplexes ( and D): d D d D D b) Using the pseud-steady-state-hypthesis fr each enzye cplex, derive an expressin fr in ters f (and ther paraeters, including cnstants, but n ther enzye cplexes): d D 0 D > D als, since : D d 0 D ( ) 5

6 6 D 0 This can be slved using the quadratic equatin: c) Use yur expressin fr part (b) and the general definitin f the reactin rate t btain an expressin fr the rate, v, that cntains and : P d v v

7 . Cnsider ur il-eating rganis discussed in class. In additin t hexadecane, the sae rganis can als grw n glucse accrding t the fllwing bilgical reactin: C 6 H O 6 a O b NH c (C. H 7. N 0.86 O. ) d H O e CO Assue that the cells can cnvert / (wt/wt) f the substrate carbn t biass. a) Calculate each f the stichietric cefficients, a, b, c, d, and e. Aunt f C per l f glucse: 7g; /*(7g) 8g cnverted t biass Biass balance: 8 g/l (.)(c)g/l c N balance: b (0.86)(0.909) b 0.78 H balance: (0.78) (0.909)(7.) d d.86 C balance: 6() 0.909()(.) e e O balance: 6(6) (6)a (0.909)(.)(6) (.86)(6).6e a.75 b) Calculate the yield cefficient Y X/ (g dw cell/g substrate). Y X/ (0.909)(MW biass)/(mw glucse) (0.909)(9.)/80 Y X/ 0.6 g biass/ g glucse c) Hw wuld yu expect this cefficient t cpare t Y X/ fr hexadecane (i.e., larger r saller)? Why? It shuld be lwer because hexadecane is re reduced than glucse (i.e. Y X/ Hex > Y X/ Glu ). In ther wrds, hexadecane has a greater degree f reductance, s it has re electrns/energy t fr biass. 7