Modelling simultaneous chain-end and random scissions using the fixed pivot technique

A reaction-diffusion framework for hydrolytic degradation of amorphous polymers based on a discrete chain scission model

Hydrolytic degradation of polymers involves the scission of long chain molecules, leading to molecular weight reduction and mass loss. The precise degradation response however depends on the scission probability of individual bonds along the polymer backbone. In particular, bonds near the chain ends are considered to be more susceptible to hydrolysis than inner bonds. In this paper, we incorporate a discrete chain scission model that can handle arbitrary bond scission probabilities within a continuum reaction-diffusion framework. Overall hydrolysis kinetics (including autocatalysis) is described independently of the chain scission model. By decoupling the description of the chain scission mechanism from kinetics, our framework enables the identification of the chain scission mechanism from molecular weight reduction and mass loss curves commonly reported in experimental degradation studies. We further propose a reduced continuum model which is better suited for large-scale simulations while retaining the predictive capability of the full discrete-continuum model. The model capability is illustrated in representative case studies based on experimental data from the literature for different materials and geometries. STATEMENT OF SIGNIFICANCE: Many models have been proposed to predict the evolution of molecular weight and mass loss in biodegradable polymers undergoing hydrolytic degradation. However, existing models remain limited in their ability to describe the degradation mechanism, autocatalytic kinetics and short chains diffusion simultaneously. Moreover, existing models often rely on empirical relations and a large number of fitting parameters. Here, we propose a conceptually simple discrete-continuum mathematical framework with a small number of parameters which all have a clear physical meaning. Model calibration against experimental data is simplified, and further provides insights into the degradation mechanisms at play, namely random scission, chain-end scission, or a combination of both. The framework can serve as a basis for future generalisations, including a description of evolving crystallinity, or other degradation mechanisms, such as thermal oxidation or photo-degradation.

Modeling coordinated enzymatic control of saccharification and fermentation by Clostridium thermocellum during consolidated bioprocessing of cellulose

Consolidated bioprocessing (CBP) of cellulose is a cost-effective route to produce valuable biochemicals by integrating saccharification, fermentation and cellulase synthesis in a single step. However, the lack of understanding of governing factors of interdependent saccharification and fermentation in CBP eludes reliable process optimization. Here, we propose a new framework that synergistically couples population balances (to simulate cellulose depolymerization) and cybernetic models (to model enzymatic regulation of fermentation) to enable improved understanding of CBP. The resulting framework, named the unified cybernetic-population balance model (UC-PBM), enables simulation of CBP driven by coordinated control of enzyme synthesis through closed-loop interactions. UC-PBM considers two key aspects in controlling CBP: (1) heterogeneity in cellulose properties and (2) cellular regulation of competing cell growth and cellulase secretion. In a case study on Clostridium thermocellum, UC-PBM not only provides a decent fit with various exometabolomic data, but also reveals that: (i) growth-decoupled cellulase-secreting pathways are only activated during famine conditions to promote the production of growth substrates, and (ii) starting cellulose concentration has a strong influence on the overall flux distribution. Equipped with mechanisms of cellulose degradation and fermentative regulations, UC-PBM is practical to explore phenotypic functions for primary evaluation of microorganisms' potential for metabolic engineering and optimal design of bioprocess.