麻省理工大学：《生物材料的分子结构》教学讲义（英文版）Problem set 1 Solution

Problem set 1 Solution BE462J3.962J Biodegradable Solid Polymers Spring 2003 Issued Day 1 5 points/problem(20 points total) 1. The chemical structure of a new degradable polymer, poly(ethylene glycol)-b-polylysine-b- poly (D, L-lactide), is shown below a. Based on chemical structure alone, discuss your prediction of whether this material will degrade more quickly or more slowly than poly (L-lactide)in vivo This material will likely degrade much more quickly than PLLA for several reasons i. It contains two highly hydrophilic blocks in the PEG and polylysine components, and both of these blocks can hydrogen bond with water, aiding water uptake in this polymer and allowing access of water to the ester bonds ii. The amine side chain may provide self-destroying properties to the polymer by attacking the PLa block ester bond i. The polymer is likely non-crystalline unless the molecular weight of the individual blocks is quite large, which will make hydrolysis easier relative to semicrystalline PLLA iv. Polylysine maybe recognized by a peptidase or a protease and degraded in vivo. In general, it must be remembered that only L-amino acids and D-sugars are metabolized by the body. The non-physiological amino acids and sugars are recognized by some special enzymes but those enzymes are rare Generally, the physiological forms of amino acids and sugars are used for synthesizing biodegradable polymers Note: Polyethylene glycol(PEG)contains ether(R-O-R) bonds and is therefore not degradable. The only mechanism for clearing body of any residual PEG is elimination which is dependent on the size (and consequently on the molecular weight) of the polymer chain b. Cite 2 physical data you would want to know to make a better prediction in part (a) and explain why these would aid in this estimate i. Melting temperature(s)(if there are any )-account for possible crystallinity i. Glass transition temperature(s)of the copolymer: lower Tg, more mobility in chains and more rapid hydrolysis; higher Tg, less mobility, slower hydrolysis C. What will the end-point degradation products of this polymer be if it is degraded by incubation in vitro in phosphate buffered saline pH 7.4 at 37C? Would these products be different if the material were degraded in vivo? E4623962JPS1

Problem Set 1Solution BE.462J/3.962J Biodegradable Solid Polymers Spring 2003 Issued: Day 1 Due: Day 4 5 points/problem (20 points total) 1. The chemical structure of a new degradable polymer, poly(ethylene glycol)-b-polylysine-b￾poly(D,L-lactide), is shown below. a. Based on chemical structure alone, discuss your prediction of whether this material will degrade more quickly or more slowly than poly(L-lactide) in vivo. This material will likely degrade much more quickly than PLLA for several reasons: i. It contains two highly hydrophilic blocks in the PEG and polylysine components, and both of these blocks can hydrogen bond with water, aiding water uptake in this polymer and allowing access of water to the ester bonds. ii. The amine side chain may provide ‘self-destroying’ properties to the polymer by attacking the PLA block ester bonds. iii. The polymer is likely non-crystalline unless the molecular weight of the individual blocks is quite large, which will make hydrolysis easier relative to semicrystalline PLLA. iv. Polylysine maybe recognized by a peptidase or a protease and degraded in vivo. In general, it must be remembered that only L-amino acids and D-sugars are metabolized by the body. The ‘non-physiological’ amino acids and sugars are recognized by some special enzymes but those enzymes are rare. Generally, the physiological forms of amino acids and sugars are used for synthesizing biodegradable polymers. Note: Polyethylene glycol (PEG) contains ether (R-O-R’) bonds and is therefore not degradable. The only mechanism for clearing body of any residual PEG is elimination which is dependent on the size (and consequently on the molecular weight) of the polymer chain. b. Cite 2 physical data you would want to know to make a better prediction in part (a), and explain why these would aid in this estimate. i. Melting temperature(s) (if there are any)- account for possible crystallinity. ii. Glass transition temperature(s) of the copolymer: lower Tg, more mobility in chains and more rapid hydrolysis; higher Tg, less mobility, slower hydrolysis. c. What will the end-point degradation products of this polymer be if it is degraded by incubation in vitro in phosphate buffered saline, pH 7.4 at 37°C? Would these products be different if the material were degraded in vivo? BE.462J/3.962J PS 1 1 of 1

In vitro, the polymer will break down to poly(ethylene glycol), poly L-lysine)(attached to one molecule of lactic acid at end)and lactic acid, due to hydrolysis of ester bonds in the polymer. The amide bonds are relatively stable under these conditions. In vivo, polylysine will also be degraded to amino acids by the action of proteases and peptidases CH,0 CH2CH20 一NH 2. The generation of acidic or basic degradation products is a serious issue complicating the design of devices for in vivo application, even for well-established materials like poly (lactide Co-glycolide). Propose an approach to limit or eliminate the generation of a low pH within and near a PLGa device implant. Be creative! (limit -1/2 page explanation Many solutions are possible, a few examples Add an acid/base titrating compound(amine monomers) into the material ii. Co-encapsulating lactate dehydrogenase(LDH). LDH will convert lactate into pyruvate-the end product of glycolysis and starting component of Citric acid i. Using salts like Mg(OH)2. The salt being basic will take up all the free protons om lactic acid generation and therefore act as a buffering agent 3. Propose a route to synthesize the hydrolyzable polymer shown below. Show the structure of the monomers you would use and any initiators/catalysts CH3 CH3-c-0-F-CH2-CH2-0-(C-CH-0-C-CH-N)n-H H3 NH As discussed in class, this structure, exactly as drawn, is impossible to synthesize by any common chemical routes. Condensation polymerization of lactic acid and lysine can provide a random arrangement of lactic acid and lysine units in the polymer, but cannot provide a regular repeat-LA- LYS-LA-LYS-LA-LYS-etc. as shown, nor is it straightforward to cap one end of such polymers with a tert-butyl group as shown. The structure that was INTENDEd to be shown is: E4623962JPS1 20f2

In vitro, the polymer will break down to poly(ethylene glycol), poly(L-lysine) (attached to one molecule of lactic acid at end) and lactic acid, due to hydrolysis of ester bonds in the polymer. The amide bonds are relatively stable under these conditions. In vivo, polylysine will also be degraded to amino acids by the action of proteases and peptidases. 2. The generation of acidic or basic degradation products is a serious issue complicating the design of devices for in vivo application, even for well-established materials like poly(lactide￾co-glycolide). Propose an approach to limit or eliminate the generation of a low pH within and near a PLGA device implant. Be creative! (limit ~1/2 page explanation). Many solutions are possible, a few examples: i. Add an acid/base titrating compound (amine monomers) into the material ii. Co-encapsulating lactate dehydrogenase (LDH). LDH will convert lactate into pyruvate – the end product of glycolysis and starting component of Citric acid cycle. iii. Using salts like Mg(OH)2. The salt being basic will take up all the free protons from lactic acid generation and therefore act as a buffering agent. 3. Propose a route to synthesize the hydrolyzable polymer shown below. Show the structure of the monomers you would use and any initiators/catalysts. CH3 O O H CH3-C-O-C-CH2-CH2-O-(C-CH-O-C-CH-N)n-H CH3 O CH3 (CH2)4 NH2 As discussed in class, this structure, exactly as drawn, is impossible to synthesize by any common chemical routes. Condensation polymerization of lactic acid and lysine can provide a random arrangement of lactic acid and lysine units in the polymer, but cannot provide a regular repeat –LA￾LYS-LA-LYS-LA-LYS-etc. as shown, nor is it straightforward to cap one end of such polymers with a tert-butyl group as shown. The structure that was INTENDED to be shown is: BE.462J/3.962J PS 1 2 of 2

H3 CH3-F-O-F-CH2-CH2-O-( -CH-IN-C-CH-O)H CH O H CH3 THIS structure CAN be synthesized using a ring-opening catalyst and a 6-membered ring monomer formed by lactic acid and lysine following the mechanism of ring-opening polymerization discussed in THIs CAT ALYSTS LIKE STANNOUS OCTOAT OR AUMINUM EN CLEAVE To ExRSE SIDE-CHAIN AMINE GROJP THE INTIAToR Is: Hy-C-O-C-CHz- CH2-OH To prevent self-attack of the side chain amine of lysine on the backbone of the growing polymer chain, the side chain must be blocked by a protecting group of some type as shown above. Chain growth from the hydroxyl group of the initiator provides the endgroup structure followed by LA-LYs repeats 4. In order to carry out studies of polymer hydrolysis on reasonable experimental timescales, a number of researchers have used elevated temperature to speed up degradation. Using the data given below, determine the degradation mechanism(surface or bulk erosion) for a sample of polycaprolactone(p=1.146 g/cm")0.02m thick degraded in water at 37C and whether the mechanism is changed by degrading the sample at 85..( Hint: assume both the hydrolysis rate constant and the diffusivity of water in the polymer have an Arhennius form At37°C:k=97X10 10-8 cm2s At50°C:k=54x107s1 k= rate constant of PCL bond hydrolysis E4623962JPS1 3 of 3

CH3 O H O CH3-C-O-C-CH2-CH2-O-(C-CH-N-C-CH-O)n-H CH3 O (CH2) CH3 NH2 THIS structure CAN be synthesized using a ring-opening catalyst and a 6-membered ring monomer formed by lactic acid and lysine following the mechanism of ring-opening polymerization discussed in class: To prevent self-attack of the side chain amine of lysine on the backbone of the growing polymer chain, the side chain must be blocked by a protecting group of some type as shown above. Chain growth from the hydroxyl group of the initiator provides the endgroup structure followed by LA-LYS repeats. 4. In order to carry out studies of polymer hydrolysis on reasonable experimental timescales, a number of researchers have used elevated temperature to speed up degradation. Using the data given below, determine the degradation mechanism (surface or bulk erosion) for a sample of polycaprolactone (ρ = 1.146 g/cm3 ) 0.02m thick degraded in water at 37°C and whether the mechanism is changed by degrading the sample at 85°. (Hint: assume both the hydrolysis rate constant and the diffusivity of water in the polymer have an Arhennius form.) At 37°C: k = 9.7x10-8 s-1 DH2O = 10-8 cm2 s-1 At 50°C: k = 5.4x10-7 s-1 DH2O = 3.5x10-8 cm2 s-1 k = rate constant of PCL bond hydrolysis BE.462J/3.962J PS 1 3 of 3

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DH2O = diffusivity of water in PCL BE.462J/3.962J PS 1 4 of 4

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BE.462J/3.962J PS 1 6 of 6