Modeling chain-end scission using the fixed pivot technique - Ho, Yong Kuen; Doshi, Pankaj; Yeoh, Hak Koon; Ngoh, Gek Cheng (Chemical Engineering Science, 2014)
Chain-end scission of polymer molecules is the breakage of a fixed-size oligomer or monomer from either end of the macromolecule. A common example is the generation of the glucose monomer from the hydrolysis of starch by glucoamylase. Modeling the dynamics of chain-end scission from first principles by considering each molecular size is challenging due to the large number of differential equations to be solved. The Population Balance Modeling (PBM) is a helpful framework as it could be formulated to lump a few molecular sizes together. However, it is then not obvious how to accurately account for the temporal evolution of the low molecular weight species, which is often of the greatest industrial interest. Here, the Fixed Pivot (FP) technique - one of the methods to solve PBM equations was appropriately modified to address this difficulty. By treating the lower molecular size range as a discrete domain in conjunction with a continuous domain in the upper ranges, the modified FP technique not only retains its original strengths, but also captures accurately the distribution of oligomers including the monomer. The results, which were obtained at a fraction of computational expense, benchmarked very well against the exact solutions for a polymer with a broad size distribution at different Degrees of Polymerization up to similar to O(10(5)). To facilitate wider adoption, guidelines on choice of pivots and observations of the performance of the modified FP technique are also deliberated. (C) 2014 Elsevier Ltd. All rights reserved.
Keywords: Chain-end scission; Fixed Pivot; Polymers; Population balance

Interlinked population balance and cybernetic models for the simultaneous saccharification and fermentation of natural polymers - Ho, Yong Kuen; Doshi, Pankaj; Yeoh, Hak Koon; Ngoh, Gek Cheng (Biotechnology and Bioengineering, 2015)
Simultaneous Saccharification and Fermentation (SSF) is a process where microbes have to first excrete extracellular enzymes to break polymeric substrates such as starch or cellulose into edible nutrients, followed by in situ conversion of those nutrients into more valuable metabolites via fermentation. As such, SSF is very attractive as a one-pot synthesis method of biological products. However, due to the co-existence of multiple biochemical steps, modeling SSF faces two major challenges. The first is to capture the successive chain-end and/or random scission of the polymeric substrates over time, which determines the rate of generation of various fermentable substrates. The second is to incorporate the response of microbes, including their preferential substrate utilization, to such a complex broth. Each of the above-mentioned challenges has manifested itself in many related areas, and has been competently but separately attacked with two diametrically different tools, i.e., the Population Balance Modeling (PBM) and the Cybernetic Modeling (CM), respectively. To date, they have yet to be applied in unison on SSF resulting in a general inadequacy or haphazard approaches to examine the dynamics and interactions of depolymerization and fermentation. To overcome this unsatisfactory state of affairs, here, the general linkage between PBM and CM is established to model SSF. A notable feature is the flexible linkage, which allows the individual PBM and CM models to be independently modified to the desired levels of detail. A more general treatment of the secretion of extracellular enzyme is also proposed in the CM model. Through a case study on the growth of a recombinant Saccharomyces cerevisiae capable of excreting a chain-end scission enzyme (glucoamylase) on starch, the interlinked model calibrated using data from the literature (Nakamura et al., Biotechnol. Bioeng. 53:21-25, 1997), captured features not attainable by existing approaches. In particular, the effect of various enzymatic actions on the temporal evolution of the polymer distribution and how the microbes respond to the diverse polymeric environment can be studied through this framework. Biotechnol. Bioeng. 2015;112: 2084-2105. (c) 2015 Wiley Periodicals, Inc.
Keywords: cybernetic modeling; population balance modeling; simultaneous saccharification and fermentation