Mathematical modeling of the myosin light chain kinase activation

The mathematical model presented here describes the interactions among Ca2+, calmodulin (CaM), and myosin light chain kinase (MLCK) and consists of a kinetic scheme taking into account 7 reactions instead of 12 as proposed previously. We derive a system of 5 nonlinear ordinary differential equations. Solving it yields the prediction of active MLCK as a function of [Ca2+] whereby the active MLCK is defined to be proportional to the Ca4CaM.MLCK complex concentration. The model predictions are compared with other theoretical and experimental predictions of active MLCK as well as with the results of our previously proposed complex model.     

Mathematical modeling of the graft reaction between polystyrene and polyethylene

Polystyrene (PS) and polyethylene (PE) are two major components of household plastic waste whose blends are immiscible. Recycling them together is an attractive option that requires a compatibilization process to improve the blend mechanical properties. If a PE/PS copolymer is added or formed in situ, it may act as compatibilizer. The structure and molecular properties of this copolymer are key factors to assure its effectivity as a compatibilizer. In this work, we study the graft copolymerization reaction between polystyrene and polyethylene using the catalytic system composed of AlCl₃ and styrene. We develop a model of this process which considers that PE/PS grafting and PS degradation occur simultaneously. We propose a kinetic mechanism for the whole process and apply the method of moments to solve the mass balance equations. The model is able to calculate average molecular weights as well as the amount of grafted PS. It accurately describes the available experimental data, constituting a valuable tool for simulation and optimization purposes.     

Mathematical modeling of biosensor action in the region between diffusion and kinetic modes

We describe the action of electrochemical enzyme-based biosensor by applying mathematical modeling. We consider two types of biosensors: a biosensor containing a single heterogeneous enzyme layer and biosensor containing an additional protecting polymer-based layer. The initial parameters of the biosensor were selected on the basis of typical immobilized glucose oxidase-based electrochemical biosensor. A phenomenon of the accumulation of the electrochemically active product inside the biocatalytic layer was evaluated. It was shown that accumulation of the product can increase sensitivity of the biosensor no more than 2.6 times. Due to the asymmetric distribution of the electrochemically active product inside the enzyme-containing membrane and asymmetric diffusion of the substrate, it was shown that the thickness of the membrane possesses an optimal value. For the selected set of initial parameters, the optimal thickness of the enzyme-containing layer was 2.9–4.5  $\upmu $ m. Real profiles of the impact of the thickness of the membranes were evaluated. A method for the evaluation of acceptable fluctuations of the membrane diffusion parameters on biosensor response was created, and the profiles of the dependence were calculated. These dependencies can be used for development of the software for biosensor monitoring.     

Mathematical modeling of electrical conductivity in electrolyte solution between two gas-evolving electrodes

This paper studies how the electrolyte conductivity has effects on the performance of an alkaline water electrolyzer. A mathematical model of the electrolyte conductivity between two electrodes has been developed based on a combination of electrolyte conductivity, void fraction and velocity of bubble rising in a liquid. The Design of Experiment technique along with statistical method is used to develop the empirical model to investigate the correlation between void fraction, current and solution temperature. The mathematical results show that the drop of the electrical conductivity is caused by an increase of solution temperature and the height of electrode. On the other hand, an increase of bubble diameter results in an increase of conductivity. Subsequently, the mathematical results are compared with the experimental results where the void fraction obtained from the model agrees well with those obtained from the experimental results.     

Mathematical modeling of the co-decontamination process in PUREX

Journal of Radioanalytical and Nuclear Chemistry - A mathematical model of co-decontamination process (1A) containing U(VI), Pu(IV), Zr(IV), and Ru(III) was developed with a high-performance...     

Mathematical modeling in the development of indicator tubes for determining chromium(VI) in natural waters

The adsorption dynamics of the chromium(VI) complex of 1,5-diphenylcarbazide on the KU-2-8 strongly acidic cation exchanger was studied. A mathematical model was developed that adequately describes the processes in the system and provides recommendations on the procedure for determining chromium(VI) in natural water using an indicator tube. The experimental data were evaluated by processing model solutions of the composition of natural surface waters.     

Mathematical modeling of hysteresis in porous electrodes

We study the mathematical model of the Li+ ions’ intercalation from the electrolyte into the porous graphite surface of the negatively charged electrode and further Li diffusion inside the electrode particle. For proper approximation of experimental data we use the cubic polynomial. We prove the multiplicity of the steady state solutions in a certain range of the electrode potential values. This multiplicity may be explained by the simultaneous existence of several phases at the graphite electrode surface. Numerical investigation allows us to demonstrate the experimentally observed hysteresis. After including the diffusion of Li into the model we compare the charging time for various electrode structures.     

Mathematical modeling and simulation of the reaction environment in electrochemical reactors

An electrochemical reactor, enabling controlled flow and capable of including a varied range of forms of electrodes, is important in the studies of electrochemical processes, such as energy production and storage, electrosynthesis of chemicals, electrowinning of metals, purification of water, wastewater treatment, remediation of soils, and so on, before the process development and scale-up. Here, we reviewed recent advances in modeling and simulation of the reaction environment in many electrochemical reactors used in multiple applications. The importance of computational fluid dynamics simulations to study existing reactors and to design novel reactor geometries and some components of existing cells is discussed. Aspects include the effect of electrolyte velocity on the flow dispersion, mass transport rates, and current distribution.     

Mathematical modeling of heterogeneous catalytic reactions and processes

The problems of heterogeneous catalysis are considered using mathematical modeling of catalytic reactions beginning from the atomic and molecular level. Some problems of the nonlinear dynamics of heterogeneous catalytic reactions are discussed. Mathematical models of these systems were designed using a combination of laboratory and computer experiments. The results of simulation of the nonlinear phenomena involved in the reactions NO+CO, NO+H₂, and CO+O₂, which are important for environmental catalysis, are discussed. Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 1895–1904, October, 1998.     

Dietary genistein enhances phosphorylation of regulatory myosin light chain in the myocardium of ovariectomized mice

There is evidence that isoflavones, such as genistein, can directly or indirectly improve lipid profile and lower blood pressure and hence exert cardiovascular protection. It is further believed, that genistein attenuates vascular contraction and thus vascular tone and blood pressure through altering the phosphorylation of the regulatory myosin light chain (MLC) probably via the myosin light chain kinase (MLCK) or the RhoA pathway. However, the direct role of genistein in the myocardium is poorly reviewed. In this study, we investigated the impact of genistein on the cardiac proteome in ovariectomized female mice using a 2DE-MS approach. Dietary genistein intake considerably changed the abundance of several cytoskeletal and contractile proteins and enhanced the phosphorylation of MLC. The MLC phosphorylation was mediated through increased abundance of MLCK and inhibition of myosin light chain phosphatase latest known to be inversely regulated by RhoA. Contrary to others, in our model genistein did neither inhibit the cardiac MLCK, nor the cardiac RhoA pathway in vivo.     

Mathematical modeling of dispersion in single interface flow analysis

This work describes the optimization of the recently proposed fluid management methodology single interface flow analysis (SIFA) using chemometrics modelling. The influence of the most important physical and hydrodynamic flow parameters of SIFA systems on the axial dispersion coefficients estimated with the axially dispersed plug-flow model, was evaluated with chemometrics linear (multivariate linear regression) and non-linear (simple multiplicative and feed-forward neural networks) models. A D-optimal experimental design built with three reaction coil properties (length, configuration and internal diameter), flow-cell volume and flow rate, was adopted to generate the experimental data. Bromocresol green was used as the dye solution and the analytical signals were monitored by spectrophotometric detection at 614 nm. Results demonstrate that, independent of the model type, the statistically relevant parameters were the reactor coil length and internal diameter and the flow rate. The linear and non-linear multiplicative models were able to estimate the axial dispersion coefficient with validation r² = 0.86. Artificial neural networks estimated the same parameter with an increased accuracy (r² = 0.93), demonstrating that relations between the physical parameters and the dispersion phenomena are highly non-linear. The analysis of the response surface control charts simulated with the developed models allowed the interpretation of the relationships between the physical parameters and the dispersion processes.     

Thermodynamic and structural basis of phosphorylation-induced disorder-to-order transition in the regulatory light chain of smooth muscle myosin

We have performed molecular dynamics simulations of the phosphorylation domain (PD) of the regulatory light chain (RLC) of smooth muscle myosin, to gain insight into the thermodynamic principles governing the phosphorylation-induced disorder-to-order transition. Simulations were performed in explicit water under near-physiological conditions, starting with an ideal alpha-helix. In the absence of phosphorylation, the helical periodicity of the peptide was disrupted at residues T9-K11, while phosphorylation significantly favored the helical periodicity, in agreement with experimental data. Using the MM/PBSA approach, we calculated a relative free energy of -7.1 kcal/mol for the disorder-to-order transition. A large enthalpic decrease was compensated by a large loss of conformational entropy, despite the small helical increase (no more than three residues) upon phosphorylation. Phosphorylation decreased the conformational dynamics of K and R side chains, especially R16, which forms a salt bridge with pS19. Mutation of R16 to A or E prevented this phosphorylation-dependent ordering. We propose that phosphorylation balances the enthalpy-entropy compensation of the disorder-to-order transition of RLC via short and long-range electrostatic interactions with positively charged residues of the phosphorylation domain. We suggest that this balance is necessary to induce a disorder-to-order conformational change through a subtle energy switching.     

Mathematical modeling of self-oscillations in ethane oxidation over nickel

The methodology of constructing a phenomenological model for complex heterogeneous catalytic reactions is described in detail. The proposed approach is applicable to development of mathematical models describing the onset of self-oscillations in hydrocarbon oxidation on the transition metal surface. The approach is based on construction of a microkinetic scheme taking into account the formation of main reaction products and intermediates, on estimation of the heat of reaction, activation energy, and preexponential factor for elementary steps and includes development and a subsequent analysis of the corresponding mathematical model. Catalytic reactions are considered in the ideal adsorption layer approximation without taking into account the relationship between coverages and spatial coordinates. Accordingly, the mathematical model is an independent system of ordinary differential equations. This methodology is used to develop a point (lumped) model for ethane oxidation over nickel, which is based on a 36-step microkinetic scheme taking into account the oxidation and reduction of nickel and the formation of total (CO₂ and H₂O) or partial (CO and H₂) ethane oxidation products, as well as the dehydrogenation of ethane into ethylene. The proposed model predicts the onset of self-oscillations in this reaction at atmospheric pressure in the temperature range from 850 to 1400 K. The kinetic oscillations are caused by the cyclic oxidation and reduction of nickel. The self-oscillations of the reaction rate are accompanied by oscillations of the catalyst temperature. The results of modeling are compared with experimental data.     

Mathematical modeling and numerical simulation of metal nanoparticles electrooxidation

A mathematical model is proposed that describes the processes of electrooxidation of metal nanoparticles localized on the surface of an indifferent macroelectrode. In contrast to previously proposed models based on geometric factors (shapes of particles and diffusion zones), the proposed model has introduced thermodynamic considerations which take into account the energy differences between the nanoparticle ensembles from microparticles and macroparticles. A series of voltammograms was obtained as a result of calculations and characteristic relationships between the different parameters were found. An analysis of the findings, on the one hand, predicts the shape and characteristic features of the experimental voltammograms and, on the other hand, provides information regarding energetic properties of the nanoparticles.     

Mathematical homogenization and stochastic modeling of energy storage systems

Mathematical homogenization theory as a multiscale modeling strategy for deriving macroscopic models is gaining relevance in modeling electrochemical energy storage systems (ESSs) for its ability to capture the detailed microstructural properties of a material. Stochastic modeling, on the other hand, captures molecular fluctuations and uncertainties associated with ESSs. In this short review, modeling ESSs using both tools is presented. Integrating mathematical homogenization theory and stochastic modeling provides an effective tool for deriving macroscopic models that accurately predict various macroscopic behavior and electrochemical properties of ESSs to enable optimization and manufacturing of high performance ESSs.     

Mathematical modeling and simulation of inulinase adsorption in expanded bed column

A mathematical model for an expanded bed column was developed to predict breakthrough curves for inulinase adsorption on Streamline SP ion-exchange adsorbent, using a crude fermentative broth with cells as the feedstock. The kinetics and mass transfer parameters were estimated using the PSO (particle swarm optimization) heuristic algorithm. The parameters were estimated for each expansion degree (ED) using three breakthrough curves at initial inulinase concentrations of 65.6 U mL⁻¹. In sequence, the model parameters for an ED of 2.5 were validated using the breakthrough curve at an initial concentration of 114.4 U mL⁻¹. The applicability of the validated model in process optimization was investigated, using the model as a process simulator and experimental design methodology to optimize the column and process efficiencies. The results demonstrated the usefulness of this methodology for expanded bed adsorption processes.