SOLUTION/EXAMPLES. Contact during the exam: phone: , EXAM TBT4135 BIOPOLYMERS. 14 December Time:

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1 1 NRWEGIN UNIVERSITY F SCIENCE ND TECHNLGY DEPRTMENT F BITECHNLGY Professor Bjørn E. Chrstensen, Department of Botechnology Contact durng the exam: phone: , EXM TBT4135 BIPLYMERS 14 December 2007 Tme: des: B1 pproved calculator wth empty memory, accordng to lst provded by NTNU, s permtted. No prnted or wrtten documents may be used durng exam. Please use pen not pencl! SLUTIN/EXMPLES

2 2 Queston 1 ppendx 1 (last page) shows fragments of 7 dfferent polysacchardes. Identfy each polysaccharde (name), name of monosacchardes (marked or B) found n the polysaccharde, conformaton of the monosacchardes (most stable conformaton), and state whether or not the polysaccharde s a polyelectrolyte at ph 2 and 8, respectvely. Fll drectly nto table or use separate sheet Structure (ppendx 1) Name of polysaccharde Monosacchardes (name, D/L, α/β) Conformaton of monosacchardes Polyelectrolyte at ph 2 (Yes/no) Polyelectrolyte at ph 8 (Yes/no) a lgnate β-d-mannuronc acd 4 C 1 No Yes B α-l-guluronc acd B 1 C 4 b Pectn α-d-galacturonc acd 4 C 1 No Yes B α-l-rhamnose B 1 C 4 c Cellulose β-d-glucose 4 C 1 No No d mylose α-d-glucose 4 C 1 No No e Chtosan β-d-glucosamne 4 C 1 Yes No B N-acetyl-D-glucosamne B 4 C 1 f garose g Hyaluronc acd 1 Student number: (In case you fll drectly nto the table above) 1 Error n structure: should be CH at C6 of the unt, and the equatoral H at C4 of the B unt s mssng

3 3 Queston 2 a) Calculate the ntrnsc vscosty of a bopolymer n soluton (solvent: 0.1 M NaCl, shear rate: 100 s -1 ) gven the followng vscosty measurements (flow-troughtmes n the vscometer): c (g/ml) t (sec) nswer: b) Gven that the bopolymer s a lnear (unbranched) and randomly coled polyelectrolyte, would the ntrnsc vscosty ncrease, decrease, or reman unchanged f the solvent was changed to 0.01 M NaCl? Gve a bref explanaton.

4 4 nswer: Reducng the onc strength from 0.1 M to 0.01 M ncreases the electrostatc repulson between charged monomers => The molecule expands => The ntrnsc vscosty ncreases (see fg n textbook) c) What s Newtonan and non-newtonan behavor of polymer solutons? nswer: Newtonan flow: The vscosty s ndependent of the shear rate. Non- Newtonan flow: The vscosty depends on the shear rate. For most polymers n soluton the vscosty decreases wth ncreasng shear rate ( shear thnnng or pseudoplastcty) due to chan deformaton and algnment wth the flow See chapter n textbook

5 5 Queston 3 a) Determne the shape of a polysaccharde based on the followng data for fractons wth dfferent molecular weghts (measurements n 0.1 M NaCl, 20 C): M (g/mol) R G (nm) Soluton: R g = const. x M b. Fnd b by takng logs. Plot log Rg vs log M and fnd slope = b. log RG log M Result: b = 0.95, whch s close to 1.0, the value of a stff rod. The polysaccharde s essentally rod-lke. b) Defne the radus of gyraton (R G ) (mathematcal formula)

6 6 nswer: c) Show (prove) that the molecular weght of a polydsperse sample determned by osmometry s M n nswer: t c 0 2 c 0 =>! " 1 % = RT c # $ M & ' for each speces " (! = RT # $! s addtve: c M! = )! = RT % & ' ) " # $ c M % & ' Multply and dvde by c = ) c :! = )! = RTc ) " c % # $ M & ' ) c =RTc ) 1c ) " # $ c M % & ' = RTc 1 M n

7 7 Queston 4 a) Calculate M n and M w for the followng mxture of polysacchardes: : 0.1 grams, M = B: 0.3 grams, M = C: 0.1 grams, M = nswer: c = n M M (g/mol) n = c /M n M = c n M 2 =c M , E E E+03 M n 60, , E E E+04 M w 164, , E E E E E E+04 b) If t takes 10 mn to degrade algnate from M w = to M w = , how long tme does t take to degrade to M w = ? nswer: 1 M w (t) = 1 M w (t = 0) + kt 2M 0 Frst, fnd k/2m 0 : k " 1 = 2M 0 M w (t = 10 mn)! 1 % # $ M w (t = 0) & ' /10 mn Insert for t = 10 mn: k " 1 = 2M ! 1 % # $ & ' /10 mn = mn!1 Then, solve the equaton for M w (t) = : 1 M w (t) = 1 M w (t = 0) + kt 2M = ( mn!1 )t t = 30 mn

8 8 Queston 5 The fgure shows a polypeptde wth 7 amno acds. HN C 2 C H CH 2 CH 3 H SH a) Identfy the amno acds 1-7 Note: Error n fgure: No N at ntrogen on amno acd 4 (Prolne) 1 = la (alanne) 2 = Glu (glutamc acd) 3 = sp (aspartc acd) 4 = Pro (prolne) 5 = Lys (lysne) 6 = rg (argnne) 7 = Cys (cystene) b) Is t lkely that ths peptde can be part of an α-helx at ph 7? Explan brefly

9 9 No, because t contans a central Prolne, whch break α-helxes (tectbook fg text). lso proxmty of equally charged R-groups (Glu, sp and Lys, rg) destablze helx c) Estmate roughly (+/- 1) the net charge of the peptde at ph 7 (Snce part of a larger proten termnal 2 and CH should not be ncluded) mno acd pka Charge at ph 7 la - Glu Ca 4 (CH) -1 sp Ca 4 (CH) -1 Pro - Lys Ca rg Ca Cys Ca TTL 0 The peptde has essentally zero net charge at ph 7. d) Whch amno acds n the peptde have a hydrophobc (non-polar) sde chan? la, Pro Queston 6 a) Explan brefly the concept of Donnan equbrum

10 10 The Donnan equlbrum refers to a stuaton (at equlbrum) where a dssolved, charged polymer (polyelectrolyte) s separated from the solvent (contanng dssolved salt) by means of a sempermeable membrane. The membrane s permeable to both solvent (water) and dssolved salts, but not to the polymer. The equlbrum also ncludes mathematcal expressons for e.g. chemcal potental or the osmotc pressure. b) Whch thermodynamc crtera must be fulflled n order to determne equlbrum propertes such as osmotc pressure? ) Electroneutralty ([+] = [-]) at both sdes of the membrane ) The chemcal potental of all components whch can pass through the membrane (water and salts) must be the same on both sdes of the membrane

11 11 ) PPENDIX 1 Structures for Queston 1 C H 1a H H CH H H B H CH 3 1b C H H H B H CH2 H CH2 H 1c H H H () H H C H 2 H 1d H H H () H 1e HH 2 C H 2 HH 2 C H B H 3 C 1f H H B H H 1g HH 2C H H HH 2C B H 3 C Error n 1g: : -CH at C6 nstead of H B: -H (equatoral) mssng at C4

12 12 Crtera for censorng: Queston Max ponts 1 44 Name polysaccharde: 2p, otherwse 1 p per answer 2a 4 2b 2 2c 2 3a 5 3b 2 3c 3 4a 4 4b 5 5a 7 5b 4 5c 5 5d 3 6a 4 6b 6 Total 100