Mathematical analysis of microbial depolymerization processes of xenobiotic polymers

Abstract

Biodegradation of polyethylene glycol is studied mathematically. A mathematical model for depolymerization process of exogenous type is described, and numerical techniques based on the model are illustrated. A comparison between a numerical result and an experimental result shows that the mathematical method is appropriate for practical applications. References

• F. Kawai, M. Watanabe, M. Shibata, S. Yokoyama, and Y. Sudate, Experimental analysis and numerical simulation for biodegradability of polyethylene, Polymer Degradation and Stability 76 (2002) 129--135. doi:10.1016/S0141-3910(02)00006-X
• M. Watanabe, F. Kawai, M. Shibata, S. Yokoyama, and Y. Sudate, Computational method for analysis of polyethylene biodegradation, Journal of Computational and Applied Mathematics, Volume 161, Issue 1, 1 December 2003, 133--144. doi:10.1016/S0377-0427(03)0051-X
• F. Kawai, Biodegradability and chemical structure of polyethers, Kobunshi Ronbunshu, 50(10), 775--780 (1993) (in Japanese).
• F. Kawai, Breakdown of plastics and polymers by microorganisms, Advances in Biochemical Engineering/Biotechnology, Vol. 52, 151--194 (1995).
• F. Kawai, Microbial degradation of polyethers, Applied Microbiology and Biotechnology (2002) 58:30--38. doi:10.1007/s00253-001-0850-2
• F. Kawai, M. Watanabe, M. Shibata, S. Yokoyama, Y. Sudate, and S. Hayashi, Comparative study on biodegradability of polyethylene wax by bacteria and fungi, Polymer Degradation and Stability 86 (2004), 105--114. doi:10.1016/j.polymdegradstab.2004.03.015
• J. D. Murray, Mathematical Biology, Springer--Verlag, 1989.
• M. Watanabe, F. Kawai, Masaru Shibata, Shigeo Yokoyama, Yasuhiro Sudate, and Shizue Hayashi, Analytical and computational techniques for exogenous depolymerization of xenobiotic polymers, Mathematical Biosciences 192 (2004) 19--37. doi:10.1016/j.mbs.2004.06.006
• M. Watanabe and F. Kawai, Analysis of biodegradability for polyethylene glycol via numerical simulation, Environmental Research and Control 26 (2004), 17--22 (in Japanese).
• F. Kawai, Xenobiotic polymers, in: T. Imanaka, ed., Great Development of Microorganisms, (NTS. Inc., Tokyo, 2002) 865--870 (in Japanese).
• M. Watanabe and F. Kawai, Numerical simulation of microbial depolymerization process of exogenous type, Proc. of 12th Computational Techniques and Applications Conference, CTAC-2004, Melbourne, Australia in September 2004, Editors: Rob May and A. J. Roberts, ANZIAM J. 46(E) pp.C1188--C1204, 2005. http://anziamj.austms.org.au/V46/CTAC2004/Wata
• M. Watanabe and F. Kawai, Mathematical study of the biodegradation of xenobiotic polymers with experimental data introduced into analysis, Proceedings of the 7th Biennial Engineering Mathematics and Applications Conference, EMAC-2005, Melbourne, Editors: Andrew Stacey and Bill Blyth and John Shepherd and A. J. Roberts, ANZIAM J. 47 pp.C665--C681, 2007. http://anziamj.austms.org.au/V47EMAC2005/Watanabe
• M. Watanabe and F. Kawai, Numerical study of biodegradation of xenobiotic polymers based on exogenous depolymerization model with time dependent degradation rate, Journal of the Faculty of Environmental Science and Technology, Okayama University, Vol. 12, No. 1, pp.1--6, March 2007.
• M. Watanabe and F. Kawai, Modeling and simulation of biodegradation of xenobiotic polymers based on experimental results, BIOSIGNALS 2009, Second International Conference on Bio-inspired Systems and Signal Processing, Proceedings, Porto, Portugal, 14--17 January, 2009, 25--34, 2009.
• G. Madras and B. J. McCoy, Numerical and similarity solutions for reversible population balance equations with size-dependent rates, Journal of Colloid and Interface Science 246 (2002) 356--365. doi:10.1006/jcis.2001.8073
• B. J. McCoy and G. Madras, Evolution to similarity solutions for fragmentation and aggregation, Journal of Colloid and Interface Science 201 (1998) 200--209. doi:10.1006/jcis.1998.5434
• B. J. McCoy, Distribution Kinetics for Temperature-Programmed Pyrolysis, Industrial and Engineering Chemistry Research 38 (1999) 4531--4537.
• B. J. McCoy and G. Madras, Discrete and continuous models for polymerization and depolymerization, Chemical Engineering Science 56 (2001) 2831--2836. doi:10.1016/S0009-2509(00)00516-9
• J. E. J. Staggs, A continuous model for vaporization of linear polymers by random scission and recombination, Fire Safety Journal 40 (2005) 610--627. doi:10.1016/j.firesaf.2005.05.004
• M. Watanabe and F. Kawai, Numerical simulation for enzymatic degradation of poly(vinyl alcohol), Polymer Degradation and Stability 81 (2003), 393--399. doi:10.1016/S0141-3910(03)00122-8
• M. Watanabe and F. Kawai, Mathematical modelling and computational analysis for enzymatic degradation of xenobiotic polymers, Applied Mathematical Modelling 30 (2006) 1497--1514.
• M. Watanabe, F. Kawai, S. Tsuboi, S Nakatsu, and H. Ohara, Study on enzymatic hydrolysis of polylactic acid by endogenous depolymerizaion model, Macromolecular Theory and Simulations 16 (2007) 619--626. doi:10.1002/mats.200700015
• M. Watanabe and F. Kawai, Modeling and analysis of biodegradation of xenobiotic polymers based on experimental results, Proceedings of the 8th Biennial Engineering Mathematics and Applications Conference, EMAC-2007, Editors: Geoffry N. Mercer and A. J. Roberts, ANZIAM J. 49 (EMAC-2007) pp.C457--C474, 2008. http://anziamj.austms.org.au/ojs/index.php/ANZIAM/article/view/361
• M. Watanabe and F. Kawai, Mathematical Modeling and Numerical Study of Biodegradation of Xenobiotic Polymers with Experimental Data, Ecological Modeling for Sustainable Development, 2nd Regional Conference on Ecological and Environmental Modelling, August 28--30, 2007, Penang, Malaysia, Editors: Koh Hock Lye, ShahrulAnuar Mohd Sah, Anita Talib, Zary Shariman Yahaya, pp.80--87 (2009).