ABSTRACT
The current manuscript addresses the problem of parameter estimation for kinetic models of chemical reaction networks from observed time series partial experimental data of species concentrations. It is demonstrated how the Kron reduction method of kinetic models, in conjunction with the (weighted) least squares optimization technique, can be used as a tool to solve the above-mentioned ill-posed parameter estimation problem. First, a new trajectory-independent measure is introduced to quantify the dynamical difference between the original mathematical model and the corresponding Kron-reduced model. This measure is then crucially used to estimate the parameters contained in the kinetic model so that the corresponding values of the species' concentrations predicted by the model fit the available experimental data. The new parameter estimation method is tested on two real-life examples of chemical reaction networks: nicotinic acetylcholine receptors and Trypanosoma brucei trypanothione synthetase. Both weighted and unweighted least squares techniques, combined with Kron reduction, are used to find the best-fitting parameter values. The method of leave-one-out cross-validation is utilized to determine the preferred technique. For nicotinic receptors, the training errors due to the application of unweighted and weighted least squares are 3.22 and 3.61 respectively, while for Trypanosoma synthetase, the application of unweighted and weighted least squares result in training errors of 0.82 and 0.70 respectively. Furthermore, the problem of identifiability of dynamical systems, i.e., the possibility of uniquely determining the parameters from certain types of output, has also been addressed.
ABSTRACT
Human ingestion of microplastics (MPs) is common and inevitable due to the widespread contamination of food items, but implications on the gastric digestion of food proteins are still unknown. In this study, the interactions between pepsin and polystyrene (PS) MPs were evaluated by investigating enzyme activity and conformation in a simulated human gastric environment in the presence or absence of PS MPs. The impact on food digestion was also assessed by monitoring the kinetics of protein hydrolysis through static in vitro gastric digestion of cow's milk contaminated with PS. The binding of pepsin to PS showed that the surface chemistry of MPs dictates binding affinity. The key contributor to pepsin adsorption seems to be π-π interactions between the aromatic residues and the PS phenyl rings. During quick exposure (10 min) of pepsin to increasing concentrations (222, 2219, 22188 particles/mL) of 10 µm PS (PS10) and 100 µm PS (PS100), total enzymatic activities were not affected remarkably. However, upon prolonged exposure at 1 and 2 h, preferential binding of pepsin to the small, low zeta-potential PS caused structural changes in the protein which led to a significant reduction of its activity. Digestion of cow's milk mixed with PS10 resulted in transient accumulation of larger peptides (10-35 kDa) and reduced bioavailability of short peptides (2-9 kDa) in the gastric phase. This, however, was only observed at extremely high PS10 concentration (0.3 mg/mL or 5.46E+05 particles/mL). The digestion of milk peptides, bound preferentially over pepsin within the hard corona on the PS10 surface, was delayed up to 15 min in comparison to bulk protein digestion. Intact caseins, otherwise rapidly digested, remained bound to PS10 in the hard corona for up to 15 min. This work presents valuable insights regarding the interaction of MPs, food proteins, and pepsin, and their dynamics during gastric digestion.
