Enzymatic Degradation of Polyester Urethanes Studied by Multi-Angle

Chapter 23

Enzymatic Degradation of Polyester Urethanes Studied by Multi-Angle Laser Light Scattering 1

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Downloaded by GEORGETOWN UNIV on August 24, 2015 | http://pubs.acs.org Publication Date: December 10, 2002 | doi: 10.1021/bk-2003-0840.ch023

D. Himel , D. P. Norwood , and W. F. Reed 1

Department of Chemistry and Physics, Southeastern Louisiana University, Hammond, LA 70402-0878 Department of Physics, Tulane University, New Orleans, LA 70118 2

We report an investigation of the degradation of polyester urethanes using enzymes purified from members of the genus Pseudomonas. Using multi-angle laser light scattering [MALLS], we observe the decrease in substrate weight-average molecular weight as enzymes purified from Comomonas acidovirans attack and degrade polyurethanes suspended in unsalted water. We obtain an enzymatic degradation rate of (8.50±1.56).10 min . Using a typical model of enzyme catalysis, we conclude that KM

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sin (Thêta / 2) - 6333 * c RMS Radius : 39.7 +/- 1.9 ma Molecular Weight : (6.45 +/- 0.1)e4 g/mol 2nd V i r i a l Coef. : 0.00e+00 mol ml/g**2 Figure 2 - Zimm plot results for the purified enzyme. Molecular weight results are in excellent agreement with SDS-PAGE measurements. Radius of gyration suggests the molecule is expanded in its structure.

In Biocatalysis in Polymer Science; Gross, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2002.

291 enzyme separately (shown in Figs. 1 and 2) were acquired and analyzed using the DAWN for Windows software, ver. 3.31 (Wyatt Technology Corporation). Time resolved data for the enzymatic degradation experiments was acquired and analyzed using the ASTRA for Windows software, ver. 4.73 (Wyatt Technology Corp.).

Results and Discussion Figure 1 shows a Zimm plot of light scattering data taken for the polyurethane substrate. Parametersfromafitto equation (1) are: molecular weight of 39 · 10 g/mol, radius of gyration of 43 nm, and a virial coefficient of 4 · 10" mol-mL/g. Using this molecular weight and radius of gyration, we can investigate the geometry of the polyurethane substrate molecule. We estimate the molecular weight and length of the repeat unit as m=150 g/mole and 1=1.5 nm (precise details of this proprietary material are not known). From this, we can estimate the persistence length, Lr, of the polyurethane substrate, assuming a linear, random coil. Using Lr = 3 Rg /L, with the measured radius of gyration and the contour length estimated as L = (M / m) 1 = 390,000 nm, we estimate L = 0.01 nm. This clearly unlikely result suggests strongly that the polyurethane substrate is NOT linear, but is in fact a very compact molecule; either highly branched or perhaps in the form of extremely small, heavily cross-linked pellets. This is not surprising, as isolated polyurethane chains would not be expected to be water soluble, as this proprietary material is. We can also compute a straightforward density (mass/volume = m/v = (M /N )/(4/3 π Rg ) Ξ 0.3 g/mL) for the substrate and use it to predict the intrinsic viscosity, whose relationship to the density is as predicted by Einstein's expression for spherical particles: [η] = 2.5 v /m = 2.5 N (4/3 π R / M ) = 7.7 mL/g. This is in good agreement with our measured intrinsic viscosity for this material of [η] = 3.8 mL/g. Differences here are probably due to our assumption that the radius of gyration is the precisely the same as the hydrodynamic radius - these data suggest they differ by about 25%. The close agreement reinforces the idea that the substrate material consists of tightly packed molecules. The enzyme light scattering data, shown in Figure 2, gives a molecular weight of 64.5· 10 g/mole and a radius of gyration of 40 nm. This agrees well with other results, obtained by other methods (primarily SDS-PAGE) which give 65 10 g/mole (these other methods give no information on size of the molecule). A calculation similar to that above gives a persistence length of L = 10 nm. Although the enzyme in question is almost certainly NOT a random coil, this calculation still suggests that the molecule is quite expanded (as opposed to compact) in its structure. Finally, the relative dimensions of the enzyme and the


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292 substrate suggest that degradation occurs when one enzyme attaches to one substrate molecule. That is, since the radii of gyration of the two molecule are comparable, it is unlikely that more than one enzyme can attach to a given substrate molecule. Finally, Figure 3 shows the inverse of the molecular weight as measured by M A L L S plotted as a function of time. The slope of this graph gives the enzymatic degradation rate (enzyme cuts per unit time) divided by the initial molecular weight, and the intercept gives the inverse of the initial molecular weight. Thus, the degradation rate is obtained directlyfromthe ratio of the slope to the intercept. Using the parameters obtainedfromthe fitted straight line, we calculate a degradation rate of (8.503±1.558)-10" min" . The very small value for the enzymatic degradation rate constant is not unexpected considering the very small concentration of both substrate and enzyme used in this particular experiment. We now consider the effect of diffusion on the rate we extract. The substrate molecules are approximately 10" cm apart (obtained by setting the reciprocal of the number density of the substrate molecules equal to 4/37CR). Using a diffusion coefficient typical of macromolecules (D~10~ cm /s), enzyme molecules will diffuse near a substrate molecule on a time scale of τ = L /D ~ 1 sec. That the observed time for enzyme action is so much longer (~10 sec) suggests that either the bond between enzyme and substrate is extremely weak (requiring many encounters to form the complex) or that the enzyme scission itself is extremely slow. With only one degradation experiment, we cannot determine MichaelisMenten parameters. However, since we are in a regime for which [E] » [S], we can make some statements. We assume a reaction of the typical form:


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We assume, given the condition |£Jo » [S]o, that entropy will drive the first reaction to the right. That is, we assume that [E] = [E] + [ES] = [Ε] and that [S] = [S] + [ES] = [ES]. Also, the large disparity in enzyme versus substrate molecules suggests that (1/[E]) d [E]/dt = d In [E]/dt = 0. Then (k.i+k )[ES] = [E] (k. [P] + kt [S]), and making the standard assumption that k. [P] is small, we have the typical result that [ES] = k [E][S] / (k_! + k ) = [E][S] / K . With the above assumptions, this can be put in the form [S]/[S] = KM/[E] . Now, assuming that the majority of substrate is bound to enzyme (i.e., that [S]/[S] « 1), we conclude that K « [E] = 6· 10" M. 0

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In Biocatalysis in Polymer Science; Gross, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 2002. 1

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Figure 3 - Light scattering measurements of the molecular weight of the polyurethane substrate while under attack by polyurethanase enzyme. The ratio of the slope to the initial molecular weight gives the degradation rate of the enzyme (enzyme cuts per unit time).

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Conclusions We have used multi-angle laser light scattering [MALLS] to measure the degradation of polyesterurethanes by an enzyme purified from Comomonas acidovirans, and to characterize the substrate and the enzyme. Light scattering results for the substrate and enzyme separately show that, while the enzyme and substrate differ in molecular weight by a factor of 1000, they are comparable in spatial extent. This suggests that enzyme action occurs when a single protein attaches to a single substrate molecule. The time dependence of the measured molecular weight allows us to calculate an enzyme degradation rate of (8.503±1.558) 10* min" . This rate is much slower than is suggested by a simple diffusive encounter model, implying that the affinity of enzyme for the substrate is very small or that the scission process itself is very slow.


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Acknowledgements The researchers gratefully acknowledge the support of the SLU College of Arts and Sciences OSCAR Program, the Louisiana Board of Regents grant # LEQSF (1999-02) - RD - A - 33, and the SLU Department of Chemistry and Physics.

References 1

Kaplan, Arthur M., Richard T. Darby, Marvin Greenberger, and Morris R. Rogers, Microbial Deterioration of Polyurethane Systems, Developments in Industrial Microbiology, Vol 9 (Society for Industrial Microbiology, 1968) 2

Phua, Β. Κ., E. Castillo, J. M. Anderson and A Hiltner, Journal of Biomedical Materials Research,21,231-246 (1987) 3

Santerre, J. P., R. S. Labow, D. G. Duguay, D. Erfle, and G. A. Adams, Journal of Biomedical Materials Research,28,1187-1199 (1994) 4

Ruiz, C., T. Main, N . Hilliard, and G.T. Howard. International Biodeterioration and Biodegradation.43,43-47 (1999) 5

Arakawa, T., Cell Technology,15(5) 679-688 (1996).

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Benmouna, M., and Reed, W.F.; "Theoretical developments in static light scatteringfrompolymers," in Light Scattering, Principles and Development Ch. 1, (Clarendon Press, Oxford, England 1996).


295 7

Kamide, K., M. Saito, and Y. Miyazaki, "Molecular weight determination", in Polymer Characterization Ch. 5, (Blackie Academic and Professional Press, London 1993). 8

Norwood, D. P.; Benmouna, M.; and Reed, W. F.; "Static Light Scattering from Mixtures of Polyelectrolytes in Low Ionic Strength Solution", Macromolecules, 29, 4293-4304 (1996) 9

Zimm, Bruno H., "The Scattering of Light and the Radial Distribution Function of High Polymer Solutions", J. Chem. Phys., 16, 1093-1116 (1948)


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Norwood, D. P.; and Reed, W. F.; "Determination of Polymer Solution Structure by Time Resolved Static Light Scattering", Polymer Preprints, 37(1), 752 (1996)

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Ghosh, S., and W. F. Reed, "New characteristic signatures from time¬ dependent static light scattering during polymer depolymerization, with application to proteoglycan subunit degradation," Biopolymers, 35, 435-450 (1995).

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Reed, W. F.; Reed, C. E.; and Byers, L. D.; "Random Coil Scission Rates Determined by Time-Dependent Total Intensity Light Scattering: Hyaluronate Depolymerization by Hyaluronidase", Biopolymers, 30, 1073-1082 (1990)

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Ghosh, S., I. Kobal, D. Zanette, and W. F. Reed, "Conformational contraction and hydrolysis of hyaluronate in sodium hydroxide solutions," Macromolecules, 26, 4685-93 (1993).

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Singh, S.K., S.P. Jacobssen, "Kinetics of acid hydrolysis of k-carrageenan as determined by molecular weight (SEC-MALLS-RI), gel breaking strength, and viscosity measurements," Carbohydrate Polymers, 23 89-103 (1994).

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Catalani L.H.; Rabello, A.M.; Florenzano, F.H.; Politi,M.J.; and Reed,W.F.; "Real-time Determination of Ultraviolet Degradation Kinetics of Polymers in Solution", Int'l. J. of Polymer Characterization and Analysis, 3 (2), 231-247 (1997)

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Reed,W.F.; "Time dependent light scattering from single and multiply stranded polymers undergoing random and endwise scission", J. Chem. Phys., 103, 7576-7584(1995)

17

Jackson, C., L.M. Nilsson and P.J. Wyatt, "Characterization of biopolymers using a multi-angle light scattering detector with size exclusion chromatography," J. Appl. Polym.Sci.43 99 (1989).


296 Jackson, C.; and Barth, Howard G.; "Size Exclusion Chromatography with Multiple Detectors: Inherent Problems in Data Analysis", Trends in Polymer Science, 2, 203-207 (1994)

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Reed, W.F., "Data evaluation for unified multi-detector size exclusion chromatography-molar mass, viscosity and radius of gyration distributions", Macromol. Chem. Phys.,196,1539-1575 (1995).


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Enzymatic Degradation of Polyester Urethanes Studied by Multi-Angle

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