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.

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.

We propose a new approach to the model reduction of biochemical reaction networks governed by various types of enzyme kinetics rate laws with non-autocatalytic reactions, each of which can be reversible or irreversible. This method extends the approach for model reduction previously proposed by Rao et al. which proceeds by the step-wise reduction in the number of complexes by Kron reduction of the weighted Laplacian corresponding to the complex graph of the network. The main idea in the current manuscript is based on rewriting the mathematical model of a reaction network as a model of a network consisting of linkage classes that contain more than one reaction. It is done by joining certain distinct linkage classes into a single linkage class by using the conservation laws of the network. We show that this adjustment improves the extent of applicability of the method proposed by Rao et al. We automate the entire reduction procedure using Matlab. We test our automated model reduction to two real-life reaction networks, namely, a model of neural stem cell regulation and a model of hedgehog signaling pathway. We apply our reduction approach to meaningfully reduce the number of complexes in the complex graph corresponding to these networks. When the number of species’ concentrations in the model of neural stem cell regulation is reduced by 33.33%, the difference between the dynamics of the original model and the reduced model, quantified by an error integral, is only 4.85%. Likewise, when the number of species’ concentrations is reduced by 33.33% in the model of hedgehog signaling pathway, the difference between the dynamics of the original model and the reduced model is only 6.59%.

Mathematical models of chemical reaction networks are typically nonlinear ordinary differential equations that represent the dynamical behavior of the species participating in the corresponding reactions. For the purpose of precise mathematical modelling of chemical reaction networks, useful techniques for estimating their parameters from experimental data are necessary. In this manuscript, we propose a new parameter estimation method for enzymatic chemical reaction networks from time-series experimental data of reaction rates. The main idea is based on retrieving time-series data of the species' concentrations from the available experimental data of reaction rates by making use of parametric Bézier curves. The least squares method is applied to these retrieved data in order to determine the best-fitting values of the parameters in the corresponding mathematical model. Subsequently, we demonstrate the applicability of our parameter estimation method on three examples of enzymatic chemical reaction networks including a model of ryanodine receptor adaptation and a model of protein kinase cascades. We also address the issue of identifiability of chemical reaction network models from reaction rates.