Structural Kinetic Model Research Articles

PERSPECTIVE: Analysis of thixotropic timescale

Thixotropy is characterized by a time-dependent rise in viscosity under no or weak flow conditions and a decrease in viscosity over time when subjected to strong flow conditions. The characteristic timescale associated with the thixotropic phenomenon, particularly how the viscosity increases with time, has been termed the thixotropic timescale. Several approaches have been suggested in the literature for estimating the thixotropic timescale. The most prominent approach, however, infers it from a specific form of a kinetic expression for structure parameter evolution. In this paper, we study the various kinds of structural kinetic models. By carefully analyzing the same, we propose a parameter for the thixotropic timescale associated with the most generic form of kinetic expression for structure parameter evolution. We observe that increasing the thixotropic timescale weakens the thixotropic character of a system when the viscosity of the structural kinetic model continuously increases over time and eventually diverges under quiescent conditions. We also propose a new phenomenological measure of the thixotropic timescale: τthix=(dlnη/dt)−1, where η is viscosity and t is time. The proposed definition allows a straightforward and unique way to determine the thixotropic timescale through experiments and agrees well with the conventional notion of thixotropy.

A Theoretical Investigation of the Polyaddition of an AB2+A2+B4 Monomer Mixture.

Hyperbranched polymers (HBPs) are widely applied nowadays as functional materials for biomedicine needs, nonlinear optics, organic semiconductors, etc. One of the effective and promising ways to synthesize HBPs is a polyaddition of AB2+A2+B4 monomers that is generated in the A2+CB2, AA'+B3, A2+B'B2, and A2+C2+B3 systems or using other approaches. It is clear that all the foundational features of HBPs that are manufactured by a polyaddition reaction are defined by the component composition of the monomer mixture. For this reason, we have designed a structural kinetic model of AB2+A2+B4 monomer mixture polyaddition which makes it possible to predict the impact of the monomer mixture's composition on the molecular weight characteristics of hyperbranched polymers (number average (DPn) and weight average (DPw) degree of polymerization), as well as the degree of branching (DB) and gel point (pg). The suggested model also considers the possibility of a positive or negative substitution effect during polyaddition. The change in the macromolecule parameters of HBPs formed by polyaddition of AB2+A2+B4 monomers is described as an infinite system of kinetic equations. The solution for the equation system was found using the method of generating functions. The impact of both the component's composition and the substitution effect during the polyaddition of AB2+A2+B4 monomers on structural and molecular weight HBP characteristics was investigated. The suggested model is fairly versatile; it makes it possible to describe every possible case of polyaddition with various monomer combinations, such as A2+AB2, AB2+B4, AB2, or A2+B4. The influence of each monomer type on the main characteristics of hyperbranched polymers that are obtained by the polyaddition of AB2+A2+B4 monomers has been investigated. Based on the results obtained, an empirical formula was proposed to estimate the pg = pA during the polyaddition of an AB2+A2+B4 monomer mixture: pg = pA = (-0.53([B]0/[A]0)1/2 + 0.78)υAB2 + (1/3)1/2([B]0/[A]0)1/2, where (1/3)1/2([B]0/[A]0)1/2 is the Flory equation for the A2+B4 polyaddition, [A]0 and [B]0 are the A and B group concentration from A2 and B4, respectively, and υAB2 is the mole fraction of the AB2 monomer in the mixture. The equation obtained allows us to accurately predict the pg value, with an AB2 monomer content of up to 80%.

An Accurate Algebraic Closed Form Solution for Drug Transport Kinetics through P-Glycoprotein Expressing Confluent Cell Monolayers by Fitting Our Experimentally Derived Empirical Fitting Function with the Elementary Rate Constants of 370 Virtual P-gp subs

The kinetics of transport by P-gp through confluent cell monolayers is typically modelled by a version of the Michaelis-Menten equations within PBPK mechanistic models1-5. The quasi-steady-state Michaelis-Menten equation was solved by the Lambert W-function, which is an infinite summation series that can only be evaluated in Matlab, Maple and a few other math programs6. Our Structural Mass Action Kinetic Model (SMAKM) for P-gp transport through confluent cell monolayers was built from a more accurate set of mass action kinetic equations. Its most significant departure from PBPK mechanistic models was that P-gp can only bind drug that has partitioned from the cytosol into the cytosolic monolayer, according to its molar partition coefficient KPC, since that is where P-gp’s substrate binding site resides. Our analysis of P-gp transport for many drugs using SMAKM has shown that most, if not all, commonly used P-gp expressing cells also express basolateral and apical uptake transporters for many, if not all, P-gp substrates. An algebraic Closed Form Solution for P-gp transport has been built by fitting the elementary rate constants of 370 Virtual P-gp substrates to an algebraic equation we started building in 2005 to fit our experimental drug transport kinetics through P-gp expressing confluent cell monolayers. The resultant algebraic Closed Form Solution clearly shows how each of P-gp’s elementary rate constants contributes to transport. It is currently used, within Excel, to predict the upper and lower bounds required to fit the elementary rate constants of new experimental drug transport data using Matlab’s Particle Swarm program.

Investigating the Rheological Properties of Silicon/Carbon (Si/C) Composite Supraparticles Used in Lithium-Ion Battery Anodes

Silicon-based active materials emerged as a very promising replacement for graphite in lithium-ion battery (LIB) anodes [1]. The unfavorable issue of particle pulverization due to inherent volume changes during lithiation / delithiation, which is still a problem hindering the full-scale implementation of silicon anodes in LIB, can be avoided by utilizing nanosized active materials. Our new approach of spray drying the nanometer-sized building blocks to micrometer-sized supraparticles enables additional improvement for Si-based anodes [2]. This approach, however, creates new hurdles for processing and quality control since a stable processing of the supraparticles to final electrodes is a key criterion for enhanced LIB performance.Figure 1: Schematic representation of the deagglomeration/breakage behavior of Si/C supraparticles in a slurry as a factor of particle motion/shear [3].In order to find indicators for supraparticle breakage early in the process chain of Si/C anode manufacturing, we conducted detailed rheological investigations on the slurry level. We parameterized structural kinetic models for slurries prepared with mixtures of supraparticles and nanosized building blocks particles to simulate supraparticle breakage (Fig. 1). With this approach, two indicators were found. First, the thixotropic response showed a strong dependence on the ratio between the spherical supraparticles and the nanosized building blocks. Second, the viscosity decreased with increasing percentage of the fractal-shaped nanosized particles. While further investigating this unexpected effect on viscosity, additional rheological characterizations of the components gave interesting insights into the overall rheological properties of hierarchically structured particle dispersions. The component carbon black and the nanosized/agglomerated active material were individually characterized in aqueous binder solutions to determine their individual contributions to the rheological properties of the full slurry. Here, the focus was laid on shear thinning and thixotropy and how the observed properties relate to the well-known rheology of hard spheres [4].In conclusion, a deeper understanding of anode slurry rheology enables tailored formulations and process conditions. Moreover, our methodology is applicable to other energy-related materials that are a key part of formulation science and particle technology. References Xiao, L.; Sehlleier, Y. H.; Dobrowolny, S.; Orthner, H.; Mahlendorf, F.; Heinzel, A.; Schulz, C.; Wiggers, H., Si-CNT/rGO Nanoheterostructures as High-Performance Lithium-Ion-Battery Anodes, ChemElectroChem 2, 1983-1990 (2015).Amin, A.; Loewenich, M.; Kilian, S. O.; Wassmer, T.; Bade, S.; Lyubina, J. et al, One-Step Non-Reactive Spray Drying Approach to Produce Silicon/Carbon Composite-Based Hierarchically Strucutured Supraparticles for Lithium-Ion Battery Anodes, J. Electrochem. Soc. 170,020523 (2023).Watermann, J.; Amin, A.; Wiggers, H.; Segets, D.; Özcan, F., Connecting structure and rheology of silicon/carbon supraparticle-based lithium-ion battery anode slurries, In Powder Technology, manuscript submitted.De Kruif, C.G.; van Lersel, E. M. F.;Vrij, A., Hard sphere colloidal dispersions: Viscosity as a function of shear rate and volume fraction, J. Chem. Phys. 83, 4717-4725 (1985). Figure 1

On the thixotropy of mature fine tailings

The rheological behavior of mature fine tailings (MFTs) is investigated using transient and steady shear flow fields. The structure breakdown of intact MFT samples is examined by a startup flow experiment at various shear rates. The yield stress of MFTs is estimated by the steady shear stress values at low shear rates. Oscillatory shear (strain amplitude sweep) is also used to verify the obtained yield stress value. MFT samples exhibit thixotropy and a positive hysteresis loop at short shearing time intervals in increasing and decreasing stepwise shear rate tests. The observed hysteresis loops and thixotropy disappear by increasing the shearing time intervals, as the system reaches its equilibrium steady-state structure. The time-dependent rheological behavior of MFTs is quantified by a structural kinetics model through the dimensionless structure parameter, λ. [Toorman, “Modelling the thixotropic behaviour of dense cohesive sediment suspensions,” Rheol. Acta 36, 56–65 (1997).] The kinetic parameters are estimated based on steady-state stresses, elucidating the relative effects of shear rate and Brownian motion on buildup and breakdown of the structure. The flow behavior of MFTs predicted by the structural kinetics model is in agreement with the experimental data.

Connecting structure and rheology of silicon/carbon supraparticle-based lithium-ion battery anode slurries

Due to the globally increasing demand for lithium-ion-batteries of high energy density, novel silicon-based materials of hierarchical structure are investigated as a potential replacement for conventional anode materials such as graphite. Since industrial process technologies cannot keep up with the development of new formulations, such approaches should be suited as ”drop-in” methods to the existing manufacturing processes. In this study, spray-dried silicon-based supraparticles of hierarchical structure are investigated regarding their suitability for industrial slurry processing under harsh mechanical conditions. The chosen strategy is to connect the structural integrity of the supraparticles with their time-dependent rheological behavior in anode slurries to provide methods for a mechanical characterization tailored to supraparticles. Apart from questions of battery processing, this study also provides general guidance on the rheology of supraparticle dispersions, which has been little studied so far. Structural kinetic models, experimentally determined thixotropic relaxation times, and a differential effective medium approach tailored for supraparticles are used herein. With this developed rheological toolset, a strong indicator of the mixing fraction of supraparticles and their primary particles inside full anode slurries is presented and the deagglomeration dynamics of the supraparticle structure in shear flow are resolved.

Improvement of Asterarcys quadricellulare biomass solubilization and subsequent biogas production via pretreatment approaches: structural changes and kinetic modeling evaluation.

This study investigated the effect of enzymatic and hydrothermal pretreatment approaches on the solubilization of organic matter, structure, and biogas yield from microalgal biomass. The soluble chemical oxygen demand (sCOD) concentration increased by 1.21-3.30- and 5.54-6.60-fold compared to control by enzymatic and hydrothermal pretreatments respectively. The hydrothermal pretreatment affected the structural changes in the microalgal biomass markedly; nonetheless, increased enzymatic concentration also had a definite effect on it as determined by qualitative approaches like scanning electron microscopy and Fourier transform infrared spectroscopy. Also, the hydrothermal pretreatment (100°C for 30min) resulted in the highest biogas production potential (P) of 765.37 mLg-1 VS at a maximum biogas production rate (Rm) of 22.66 mLg-1day-1 with a very short lag phase (λ) of 0.07days. The biogas production of pretreated microalgal biomass particularly at higher enzyme dose (20%, 24h) and higher hydrothermal pretreatment temperature (120°C, 30min) showed a significant but weak correlation (R = 0.53) with sCOD, thus demonstrating that the less organic matter was used up for the biogas production. The modified Gompertz model explained the anaerobic digestion of microalgal biomass more accurately and had a better fit to the experimental data comparatively because of the low root mean square error (3.259-16.728), residual sum of squares (78.887-177.025), and Akaike's Information Criterion (38.605-62.853).

On the nature of flow curve and categorization of thixotropic yield stress materials

Thixotropy is a phenomenon related to time dependent change in viscosity in the presence or absence of flow. The yield stress, on the other hand, represents the minimum value of stress above which steady flow can be sustained. In addition, the yield stress of a material may also change as a function of time. Both these characteristic features in a material strongly influence the steady state flow curve of the same. This study aims to understand the interrelation between thixotropy, yield stress, and their relation with the flow curve. In this regard, we study five thixotropic materials that show yield stress. The relaxation time of all the five systems shows power-law dependence on aging time with behaviors ranging from weaker than linear, linear to stronger than linear. Furthermore, the elastic modulus and yield stress have been observed to be constant for some systems while time dependent for the others. We also analyze the experimental behavior through a viscoelastic thixotropic structural kinetic model that predicts the observed experimental behavior of constant as well as time-dependent yield stress quite well. These findings indicate that a nonmonotonic steady-state flow curve in a structural kinetic formalism necessarily leads to time-dependent yield stress, while constant yield stress is predicted by a monotonic steady-state flow curve with stress plateau in the limit of low shear rates. The present work, therefore, shows that thixotropic materials may exhibit either monotonic or nonmonotonic flow curves. Consequently, thixotropic materials may show no yield stress, constant yield stress, or time-dependent yield stress.

Predicting the influence of combined oxygen and glucose gradients based on scale-down and modelling approaches for the scale-up of penicillin fermentations

In large scale fermentors the cultivated cells are exposed to dynamic changes in the nutrient concentrations due to imperfect mixing. Based on the characterization of these nutrient gradients in space and time, a rational scale down design can be obtained. This study focuses on the combined gradients of dissolved sugar and oxygen concentrations. Based on a recent computational fluid dynamics (CFD) study, firstly a scale-down design was developed. From intracellular metabolite measurements during these scale-down experiments, the metabolic behavior of the cells under highly dynamic conditions was revealed. Under the combined influence of oscillating glucose and oxygen concentrations, the penicillin production declined to 50 % of the value under steady state conditions. This decline was similar as observed during glucose oscillations alone. The influence of oxygen oscillations on the levels of the majority of the intracellular metabolites analyzed was negligible, although these metabolites were strongly affected by the varying oxygen levels under solely oxygen oscillations. Additionally, a metabolic structured kinetic model was developed and validated with data from glucose and oxygen oscillation experiments. This model can be coupled to CFD simulations to obtain an accurate prediction of the performance of industrial strains in space and time in large industrial scale bioreactors.

One-Pot Synthesis of Hyperbranched Polyurethane-Triazoles with Controlled Structural, Molecular Weight and Hydrodynamic Characteristics.

We report a simple and convenient approach to the one-pot synthesis of hyperbranched polyurethane-triazoles with desirable properties. This method is based on in situ generation of an AB2 + A2 + B4 azide-acetylene monomer mixture of known composition, due to quantitative reactions of urethane formation between isophorone diisocyanate (IPDI), 1,3-diazidopropanol-2 (DAPOL) (in the first stage) and propargyl alcohol (in the second stage). The obtained monomer mixture can be involved in step-growth polymerization by azide-alkyne cycloaddition without additional purification (in the third stage). The properties of the resulting polymers should depend on the composition of the monomer mixture. Therefore, first the model revealing the correlation between the monomer composition and the ratio and reactivity of the IPDI and DAPOL active groups is developed and proven. In addition, the newly developed structural kinetic model considering the substitution effect at polyaddition of the complex mixture of monomers allows the prediction of the degree of branching of the target polymer. Based on our calculations, the hyperbranched polyurethane-triazoles were synthesized under found conditions. All products were characterized by 1H NMR, FTIR, SEC, DLS, DSC, TGA and viscometry methods. It was shown that the degree of branching, molecular weight, intrinsic viscosity, and hydrodynamic radius of the final hyperbranched polymers can be specified at the first stage of one-pot synthesis. The obtained hyperbranched polyurethane-triazoles showed a degree of branching from 0.21 to 0.44 (calculated DB-0.25 and 0.45, respectively).

Fabrication, characterization and in vitro digestion of camellia oil body emulsion gels cross-linked by polyphenols

This study was designed to investigate the formation of camellia oil body (OB) emulsion gels covalently cross-linked by oxidized polyphenols: catechin (OCT), caffeic acid (OCF), chlorogenic acid (OCA), and tannic acid (OTA). The structural characteristics, thermal stabilities, antioxidant activities, rheological properties, and lipid digestion kinetics of the cross-linked OB-polyphenol emulsion gels were studied. The results of free sulfhydryl and amino group contents, FT-IR, fluorescence spectroscopy, surface hydrophobicity and thermal stability analyses confirmed the formation of covalent interactions between polyphenols and OB emulsions. Based on the second-order structural kinetic model, OB emulsion gel cross-linked by OTA had stronger intermolecular interactions and more developed 3-D network structures than those of OCA, OCF and OCT. Furthermore, lipid digestion kinetics showed that the cross-linking of polyphenols with the OBs slowed down the disintegration of protein matrix under gastric conditions, resulting in delay the release of free fatty acid, which was confirmed by CLSM observations.

Tryptophan Production Maximization in a Fed-Batch Bioreactor with Modified E. coli Cells, by Optimizing Its Operating Policy Based on an Extended Structured Cell Kinetic Model.

Hybrid kinetic models, linking structured cell metabolic processes to the dynamics of macroscopic variables of the bioreactor, are more and more used in engineering evaluations to derive more precise predictions of the process dynamics under variable operating conditions. Depending on the cell model complexity, such a math tool can be used to evaluate the metabolic fluxes in relation to the bioreactor operating conditions, thus suggesting ways to genetically modify the microorganism for certain purposes. Even if development of such an extended dynamic model requires more experimental and computational efforts, its use is advantageous. The approached probative example refers to a model simulating the dynamics of nanoscale variables from several pathways of the central carbon metabolism (CCM) of Escherichia coli cells, linked to the macroscopic state variables of a fed-batch bioreactor (FBR) used for the tryptophan (TRP) production. The used E. coli strain was modified to replace the PTS system for glucose (GLC) uptake with a more efficient one. The study presents multiple elements of novelty: (i) the experimentally validated modular model itself, and (ii) its efficiency in computationally deriving an optimal operation policy of the FBR.

Thixotropy, nonmonotonic stress relaxation, and the second law of thermodynamics

Many thixoviscoelastic materials have been reported to undergo enhancement in elastic modulus with time and decrease in the same under application of deformation field. Incorporation of this feature in a viscoelastic structural kinetic model has an apparent possibility of violating the second law of thermodynamics. Furthermore, in a related experimental observation, stress has been reported to undergo a nonmonotonic change as a function of time under the application of constant strain. We analyze both these scenarios through a structural kinetic model that shows viscoelastic aging but undergoes rejuvenation only due to the viscous rate of strain. We observe that such formalism does not violate the second law. Interestingly, the proposed simple formalism predicts the experimental observation of the nonmonotonic stress relaxation very well.

Structural Kinetics Model to Describe the Thixotropic Behavior of Cathode Slurry for Lithium-Ion Batteries

Structural Kinetics Model to Describe the Thixotropic Behavior of Cathode Slurry for Lithium-Ion Batteries

Study on dynamic and static structural build-up of fresh cement paste with limestone powder based on structural kinetics model

The structural build-up of fresh cement-based materials is of great significance to the early forming and later performance. A structural kinetics model (SKM) used to indicate the structural build-up was developed by combining a kinetic equation described by structural parameter (λ) and a relationship between yield stress (τy) and λ in the paper. SKM transforms the structuration rate (Athix) in linear Roussel model and the characteristic time (tc) in non-linear Perrot model into more specific indicators such as initial solid volume fraction (ϕ0), rate of hydration during induction period (α̇ind), and shear rate (γ.). The yield stress (τy) obtained by RHEOLAB QC rotary viscometer was explored the dynamic and static structural build-up of fresh cement paste. The yield stress of fresh cement paste (W/C = 0.4) exhibits a quasilinear pattern with rate of 0.42 Pa/s for 210 min of mixing, with rate of 0.88 Pa/s for 100 min of resting after 4 min of mixing. The static yield stress of fresh cement paste evolves from linear to non-linear patterns within 100 min of resting after beyond 30 min of mixing. The fitting results show that SKM can well fit the evolution of yield stress including linear and nonlinear phases. Comparing with the dynamic structural build-up, the effect of limestone powder on the static structural build-up of cement paste is more obvious. When the mixing process is longer than 60 min, the content of limestone powder less than 20 wt% is beneficial to the structural build-up of fresh paste. Additionally, a declined rate of cement hydration in the induction period with increasing mixing time indicates that the rising yield stress, in this case, cannot be attributed entirely to the contribution of hydration to structural build-up.

A CCM-based modular and hybrid kinetic model to simulate the tryptophan synthesis in a fed-batch bioreactor using modified E. coli cells

This paper presents a novel methodology to develop complex structured bi-level (hybrid) kinetic models of some important cell bioprocesses. The approached case study refers to the tryptophan (TRP) synthesis in E. coli cells. The required experimental data were collected from a fed-batch bioreactor (FBR). The developed structured kinetic model includes several inter-connected reaction pathway (modules) able to simulate the kinetics of glycolysis, TRP-operon expression, ATP-recovery system, all belonging to the central carbon metabolism (CCM). Experiments were carried out by using an E. coli strain modified to replace the PTS-system with a more efficient one to uptake the glucose (GLC) from the environment. By linking the FBR macroscopic state variables with the nano-scale variables describing the cell metabolic processes of interest, the resulted structured hybrid dynamic model presents a large number of advantages, such as: allows further in-silico (model-based) more accurate engineering developments; it can be used for bioinformatics purposes.

Rheological characterization of coconut cream emulsion using steady-state shear and time-dependent modeling

The rheological properties of raw coconut-cream emulsion (RCCE) were evaluated under various shear rates (0–500 s −1 ) and temperatures (10 °C–50 °C) through steady-state shear and time-dependent modeling. Thixotropic behavior of the samples was observed at all temperatures tested, and it decreased with increased temperature. The Power law model was found to better fit the obtained data. The effects of temperature on regression parameters, namely, the Arrhenius and Turian relations were explored by approaches. The modeling parameters were assessed under the combined impacts of shearing and temperature, resulting in two generalized state equations governing the RCCE steady-state flow behavior. The extent and rate of thixotropy were measured with the Weltmann model, and the structural kinetics model was found to best describe the time-dependent behavior of RCCE. In conclusion, the structural breakdown was found in stress-decay tests at a high shear rate of 250 s −1 and a relatively high temperature of 50 °C. • Raw coconut cream emulsion exhibits thixotropic behavior at all temperatures tested. • Thixotropicity reduces with increasing temperature from 10 to 50 °C. • Weltmann model and SKM approach best describe time-dependent behavior. • The structural breakdown is evident in the high shearing & high temperature.

Molecular Determinants of D and L-Sotalol Stereoselective Proarrhythmia Procilivties

Cardiac arrhythmias can be caused by drug induced blockade of cardiac potassium channel KV11.1 encoded by the human Ether-à-go-go-Related Gene (hERG), being a major obstacle for the development of new pharmaceuticals. Inhibition of this protein activity leads to an increased cardiac action potential duration manifesting as a prolonged QT interval on the surface ECG, which can cause potentially lethal arrhythmias. However, not all hERG channel blocking and QT prolonging drugs are arrhythmogenic leading to possible attrition of safe and effective pharmaceuticals. Previously we developed a multi-scale in silico pipeline to predict arrhythmogenicity of two hERG blocking drugs, dofetilide and moxifloxacin, from their chemical structures using a combination of atomistic structural and functional kinetic modeling approaches (Yang et al. Circ. Res. 2020, 126: 947). Here we applied such computational pipeline backed by an enantiomeric separation and electrophysiology recordings to predict the pro-arrhythmia risks of two enantiomers of sotalol, an anti-arrhythmic drug with known stereoselective beta-blocking properties. We determined similar hERG channel binding affinities of d and l-sotalol from both patch-clamp recordings and umbrella sampling all-atom molecular dynamics (MD) simulations. MD derived hERG channel - drug on and off rates were used as functional model parameters. In cardiac tissue simulations our model predicted substantially higher emergent arrhythmogenicity of d-sotalol compared to the l-stereoisomer due to a more potent beta adrenergic receptor blockade by the latter and also provided good agreement with clinical QT interval prolongation for the racemic mixture. Our study helped to elucidate molecular mechanisms of stereoselective arrhythmogenicity for dl-sotalol allowing to predict cardiac safe and dangerous drug formulations. This work has been made possible by NIH NHLBI and Common Fund as well as American Heart Association funding, usage of XSEDE, PSC Anton 2, TACC Frontera, and Oracle for Research computational resources.

Rheological determination of molecular weight of honey adulterated with high fructose corn syrup

Adulteration of honey represents an essential quality assurance concern in the utilisation of this natural product. Honey was serially diluted with high fructose corn syrup and analysed for its rheological profiles at 27 °C. Pure honey at ambient temperatures exhibits a peculiar non-Newtonian rheological behaviour while the behaviour of fructose syrup tends towards Newtonian. The adulteration of honey with this material drags its viscosity towards Newtonian flow behaviour. The results show that the Carreau-Yasuda model correlates the rheology of pure honey samples. Parameters of the Carreau-Yasuda model were observed to reflect the quality of the samples and thus aided their classification. Modified with the insertion of the Mark-Houwink’s relation, the Carreau-Yasuda model yielded average molecular weight data on the samples. The Structural Kinetic Model was utilised to give rheological structural information and a second independent assessment of average molecular weight from the rheograms. The average molecular weight of 202 g/mol was obtained using the Structural Kinetic model, while 205 g/mol was obtained using the amended Carreau-Yasuda model.

Case Study 8: Status of the Structural Mass Action Kinetic Model of P-gp-Mediated Transport Through Confluent Cell Monolayers.

In the first edition of this book, we presented the basics of explicitly incorporating the lipid biochemistry into a confluent cell monolayer transport model and the novel findings of this model up to 2013, including the use of global optimization to fit the elementary rate constants and the efflux active P-glycoprotein (P-gp) membrane concentrations for the transport of four P-gp substrates across MDCKII-hMDR1-NKI confluent cell monolayers. This chapter is an update on that model, which has been focused primarily on discovering how microvilli morphology regulates the efflux active P-gp and the existence of, as yet, unidentified uptake transporters of P-gp substrates in all of the commonly used P-gp expressing cell lines used in the pharmaceutical industry, thereby adding new players to DDI predictions and IVIVE. The structural mass action kinetic model uses the general mass action reactions for P-gp binding and efflux, with the membrane structural parameters for the confluent cell monolayer to predict drug transport over time. Binding of drug to P-gp occurs within the cytosolic monolayer of the apical membrane, according to (a) the molar partition coefficient of the drug to the cytosolic monolayer and (b) the association rate constant, k1 (M-1s-1), of the drug from the basolateral or apical outer monolayers into the P-gp binding site. Release of substrate from P-gp back into the cytosolic monolayer occurs with a dissociation rate constant kr (s-1) or, much less frequently, into the apical aqueous chamber with an efflux rate constant k2 (s-1). The model fits the efflux active P-gp concentration, T(0), i.e., the P-gp whose effluxed drug actuallyreaches the apical aqueous chamber, as opposed to the majority of P-gp whose effluxed drug is reabsorbed back into the same or neighboring microvilli prior to reaching the apical aqueous chamber. Efflux active P-gp largely resides near the tips of the microvilli. We have shown using kinetics and structured illumination microscopy that: (a) efflux active P-gp is controlled by microvilli morphology; (b) there are apical (AT) and basolateral (BT) uptake transporters for P-gp substrates in most, if not all, P-gp expressing cell lines used in the pharmaceutical industry, whichexist, but which remain unidentified; (c) the lab-to-lab variability in P-gp IC50 values observed in the P-gp IC50 initiative was due to the conflated inhibition of P-gp and the basolateral digoxin uptake transporters by all 15 P-gp substrates tested in that study; (d)even the IC50 values for P-gp inhibition alone do not obey the Cheng-Prusoff relationship; (e) the fitted elementary rate constants and the molecular dissociation constant Ki for this kinetic model are system independent; and (f) the time dependence of product formation for these confluent cell monolayers is correlated withthe P-gp Vmax/Km, whendefined by its fitted elementary rate constants and uptake transporter clearances, without any steady-state assumptions.