Law Of Mass Action Research Articles

Statistical theory of individual activity coefficients of electrolytes including multiple ionic charges

In previous work we developed a new statistical method for calculating the individual activities of ions including the association of ions. Here we study multi-particle electrostatic interactions connected within higher cluster integrals and identify the ionization constants of the mass action law of associating ion clusters. In contrast to Bjerrum and Fuoss, our concept of association is not based on spatial criteria, but instead on the strength of interaction measured in powers of the Bjerrum parameter (e2/D0kBTa; a is contact) and defined by asymptotic properties of the cluster integrals. For ion pair formation our mass action constant is the classical counterpart of Planck's famous hydrogenic partition function. As a rule, the new association constants are smaller than traditional expressions, e.g., by Fuoss and Kraus, in the interesting regions of interaction parameters about fifty percent. Several examples including CaCl2, MgCl2, Na2SO4, K2SO4, LaCl3 and a model of seawater are studied. For several associating electrolytes and seawater, reasonable agreement with experiments and Monte Carlo results is achieved.

Detailed-balance limits for sunlight-to-protonic energy conversion from aqueous photoacids and photobases based on reversible mass-action kinetics

(Photo)chemical and photophysical detailed balance analyses are used to predict optimal properties and efficiency limits for sunlight-to-protonic energy conversion from aqueous photoacids or photobases.

On geometry of multiscale mass action law and its fluctuations

The classical mass action law in chemical kinetics is put into the context of geometric multiscale thermodynamics, which allows for description of chemical reactions with inertial effects. The kinetics is extended to an enlarged state space with reaction rates as new state variables, and it has the structure a Lie-algebroid dual. Subsequently, the dynamics is lifted to the Liouville description within kinetic theory of the enlarged state space, so that we can include also dynamics of fluctuations. The lifted kinematics has the geometric structure of a matched pair, which allows for reduction to moments by a Lie-algebra homomorphism, as in the Grad hierarchy. In particular, the first and second moments then lead to evolution equations for chemical kinetics with inertia and for correlations between composition and reaction rates. Finally, dissipation is added in the extended state space which leads to the classical mass action law when the moments relax to their respective quasi-equilibria. We demonstrate, for instance, the possibility of oscillating homogeneous chemical reactions, and how correlations between composition and reaction rates contribute to the chemical kinetics.

The history of chemical concepts and field studies of CO2 in seawater: A tribute to Kurt Buch (1881–1967)

This review of the research on the marine CO2 system spans the time between the mid-19th century and the first years after World War II. It covers the period from the first attempts to determine the amount of CO2 dissolved in seawater to the first complete physico-chemical characterization of the marine CO2 system. The development of the latter was significantly influenced by the theoretical and experimental work of the Finnish chemical oceanographer Kurt Buch (1881–1967) during the first half of the 20th century. To acknowledge his outstanding achievements in Chemical Oceanography, this review is dedicated to him.The first part of our discussion is organized along the characteristic variables of the marine CO2 system. The analytical procedures that led successively to the definition of total CO2, alkalinity (“neutral carbonate”), the CO2 partial pressure (“CO2 tension”) and pH are briefly described. We trace the attempts to connect these variables quantitatively through the mass action law. After several failed attempts, CO2 dissociation constants were finally determined with the support of the International Council for the Exploration of the Sea (1931). Their results constituted the basis of the marine CO2 studies conducted after World War II.The second focus of our review refers to the various field studies, including early measurements of total CO2 and alkalinity during Norwegian (1878) and Danish expeditions (1895/96) in the North Atlantic and Arctic Ocean and the first measurements of surface water pCO2 in the North Atlantic, in 1902. Furthermore, we acknowledge the achievements of the German Atlantic expedition (1925–1927) for the characterization of the vertical and horizontal distribution of pH, pCO2 and CaCO3 saturation in the Atlantic Ocean. Among Buch's field studies of the CO2 system, we consider the Finnish monitoring program, in which pH and alkalinity were measured at over 70 stations in the northern Baltic Sea.Whenever it is appropriate, we show the connection between past scientific ideas, concepts and knowledge with current efforts and developments concerning the understanding of the marine carbon cycle and its response to increasing atmospheric CO2.

Transmission dynamics and sensitivity analysis of pine wilt disease with asymptomatic carriers via fractal-fractional differential operator of Mittag-Leffler kernel

Pine wilt disease is caused by nematodes transmitted by pine sawyer beetles and is fatal for several pine species. The trees might be destroyed within a few months after being attacked, leads to major ecological and financial losses. In this article, we presented a model of pine wilt disease in the trees considering the interaction between nematodes, transmitting beetles with both asymptomatic and symptomatic pine trees. The disease dynamics is first displayed through a schematic diagram which is then transformed to non-linear coupled integer order ODEs through the law of mass action. The positivity, boundedness and equilibrium points has been analyzed and basic reproduction number is calculated through the next generation technique. Sensitivity analysis is also done for the most sensitive parameters which is also displayed through different figures and tables. The solution of the considered nonlinear fractal-fractal model has been obtained through numerical method via MATLAB software. Some numerical results have been obtained and it has been observed that the fractional model give us the more general results by considering different non-integer orders and the integer order results can be easily recovered. It is also noticed that reducing the interaction among the infected beetles and susceptible trees by killing the main source of the infection i.e., killing beetles can reduce the infection drastically, which are briefly discussed and conclusion has been drawn on the basis of the obtained results.

Experimental validation of computerised models of clustering of platelet glycoprotein receptors that signal via tandem SH2 domain proteins.

The clustering of platelet glycoprotein receptors with cytosolic YxxL and YxxM motifs, including GPVI, CLEC-2 and PEAR1, triggers activation via phosphorylation of the conserved tyrosine residues and recruitment of the tandem SH2 (Src homology 2) domain effector proteins, Syk and PI 3-kinase. We have modelled the clustering of these receptors with monovalent, divalent and tetravalent soluble ligands and with transmembrane ligands based on the law of mass action using ordinary differential equations and agent-based modelling. The models were experimentally evaluated in platelets and transfected cell lines using monovalent and multivalent ligands, including novel nanobody-based divalent and tetravalent ligands, by fluorescence correlation spectroscopy. Ligand valency, receptor number, receptor dimerisation, receptor phosphorylation and a cytosolic tandem SH2 domain protein act in synergy to drive receptor clustering. Threshold concentrations of a CLEC-2-blocking antibody and Syk inhibitor act in synergy to block platelet aggregation. This offers a strategy for countering the effect of avidity of multivalent ligands and in limiting off-target effects.

Assessing the impact of transport and kinetic mechanisms during the analysis of a LiFePO4 cathode: A different perspective during the operation and modeling of a battery cell

Although (de)lithiation in the anisotropic and nonconductive LiFePO4 solid phase has been broadly studied, yet there are some uncertainties about transport and kinetic mechanisms related to this active material, that have not been fully understood during the operation of a cell battery due to today's limitations on the development of in-depth experiments, and first principle calculations. Particularly, this work combines experimentation and theoretical foundations to elucidate the impact of these mechanisms on the performance of a LiFePO4/Csp:PVDF cathode. As part of the experimental strategy, the composition of the active material and additives in the solid phase, and the initial concentration of Li+ in the active material were intentionally manipulated to analyze their influences on transport and kinetic mechanisms during the cathode operation. The experimental evidence led to the proposal of a heterogeneous model that overcomeslimitations identified in conventional pseudo-continuous models by including in its conceptualization the effect of the solid-electrolyte interphase transport, the diffusion of Li+ over the surface of the solid phase and intra-solid phase transport on electrochemical kinetics. To minimize uncertainties related to the reaction model, a new kinetic approach, based on the mass action law, the transition state theory, the mean-field approximation and thermodynamics was also proposed and coupled to the heterogeneous model. The modelling approach showed its adequacy by describing observation trends properly. Based on the non-conventional experimental strategy and the modelling approach, transport resistances associated with the solid-electrolyte interphase and intra-solid phase are identified as the main processes limiting kinetics and, hence, the macroscopic performance of the cell. Although the experimental and modeling framework was only applied for a LiFePO4 cathode, it is still valid for any other active material involved in a battery cell.

Mathematical Modeling of Fluconazole Resistance in the Ergosterol Pathway of Candida albicans.

Candidiasis is reported to be the most common fungal infection in the critical care setting. The causative agent of this infection is a commensal pathogen belonging to the genus Candida, the most common species of which is Candida albicans. The ergosterol pathway in yeast is a common target by many antifungal agents, as ergosterol is an essential component of the cell membrane. The current antifungal agent of choice for the treatment of candidiasis is fluconazole, which is classified under the azole antifungals. In recent years, the significant increase of fluconazole-resistant C. albicans in clinical samples has revealed the need for a search for other possible drug targets. In this study, we constructed a mathematical model of the ergosterol pathway of C. albicans using ordinary differential equations with mass action kinetics. From the model simulations, we found the following results: (i) a partial inhibition of the sterol-methyltransferase enzyme yields a fair amount of fluconazole resistance; (ii) the overexpression of the ERG6 gene, which leads to an increased sterol-methyltransferase enzyme, is a good target of antifungals as an adjunct to fluconazole; (iii) a partial inhibition of lanosterol yields a fair amount of fluconazole resistance; (iv) the C5-desaturase enzyme is not a good target of antifungals as an adjunct to fluconazole; (v) the C14α-demethylase enzyme is confirmed to be a good target of fluconazole; and (vi) the dose-dependent effect of fluconazole is confirmed. This study hopes to aid experimenters in narrowing down possible drug targets prior to costly and time-consuming experiments and serve as a cross-validation tool for experimental data. IMPORTANCE Candidiasis is reported to be the most common fungal infection in the critical care setting, and it is caused by a commensal pathogen belonging to the genus Candida, the most common species of which is Candida albicans. The current antifungal agent of choice for the treatment of candidiasis is fluconazole, which is classified under the azole antifungals. There has been a significant increase in fluconazole-resistant C. albicans in recent years, which has revealed the need for a search for other possible drug targets. We constructed a mathematical model of the ergosterol pathway in C. albicans using ordinary differential equations with mass action kinetics. In our simulations, we found that by increasing the amount of the sterol-methyltransferase enzyme, C. albicans becomes more susceptible to fluconazole. This study hopes to aid experimenters in narrowing down the possible drug targets prior to costly and time-consuming experiments and to serve as a cross-validation tool for experimental data.

Study on the compounding of sodium N-lauroyl glutamate and cationic cellulose

Abstract In this work, sodium N-lauroyl glutamate (SLG) was mixed with cationic cellulose JR30 M. The rapidly occurring change in surface tension and the mass action law of the mixed (compound) system were investigated using dynamic and equilibrium surface tension methods. The behaviour of the system during phase separation was investigated by turbidimetry. The results showed that in the presence of JR30 M, the surface tension of SLG was reduced to a lower level in the given time interval due to the strong interaction compared to that of a solution with the same concentration of SLG but without JR30 M. The largest decrease was obtained with a JR30 M concentration of 0.2 g L−1, which reduced the equilibrium surface tension of SLG from 38.4 mN m−1 to 31.7 mN m−1. The rate of decrease in surface tension increased from 37.61 mN m−1 s−1 to 74.7 mN m−1 s−1. An association complex formed between SLG and JR30 M, and the equilibrium surface tension curve showed a double platform. As the concentration of JR30 M increased, the first platform broadened and the CMC value increased. The phase separation behaviour of the compound system disappeared with the increase of SLG concentration, and the area became narrower with the decrease of JR30 M concentration.

Experimental and numerical investigations on the heat production and thermal storage characteristics of rapid preparation amorphous powder activated coke

• Preparation of rapid preparation amorphous powder activated coke was showed. • The oxidation characteristics of RAC were studied through experimental method. • The Arrhenius equation was used to analyze the oxidation reaction rate of RAC. • The thermal storage characteristics of RAC were studied with CFD simulation. • The temperature fields and concentration fields of coke bin were analyzed. The heat production and thermal storage characteristics of rapid-preparation amorphous powder activated coke (RAC) were investigated. RAC was prepared by using a drop-tube reactor system. The natural oxidation characteristics of RAC were studied through combined TG–FTIR analysis and temperature-programmed experiment. Experimental results showed that CO and CO 2 were the main oxidation products of RAC in air, and that the oxidation reaction was in accordance with the Arrhenius equation and law of mass action. Thermal storage characteristics were studied through computational fluid dynamics simulation. The maximum excess temperature θ max increases linearly with the increase of the initial temperature. The concentration fields of the products show that CO 2 is mainly concentrated in the upper part of the coke bin, and the CO generated by CO 2 at high temperature is mainly concentrated in the central part of the coke bin.

Evaluating the power-law response for tin dioxide nanostructured sensors in the presence of oxygen and reducing gases

It is well known that the electrical conductance of gas sensors, based on polycrystalline metal-oxide semiconductors, obeys a power-law response with a gas pressure as p -γ . The value of the exponent γ, which determines the sensor sensitivity, is regularly derived resorting to the mass action law applied to proposed reactions at the surface of the semiconductor. Conversely, based on the experimentally observed values of γ for different gases, researchers also determine the possible species present at the surface and the reactions that can occur. In line with this approach, we present experimental results, for oxygen and a typical reducing gas, which confirm that oxygen is adsorbed/desorbed neutral, as predicted by the Wolkenstein theory of chemisorption, and ionosorbs doubly charged. • The power law exponent for the electrical resistance of tin oxide gas sensors is derived resorting to the mass action law. • Possible mechanisms compatible with the power law exponent for oxygen and a typical reducing gas are presented. • We found that the surface chemistry is correctly dictated by the Wolkenstein theory of chemisorption.

PolyODENet: Deriving mass-action rate equations from incomplete transient kinetics data.

Kinetics of a reaction network that follows mass-action rate laws can be described with a system of ordinary differential equations (ODEs) with polynomial right-hand side. However, it is challenging to derive such kinetic differential equations from transient kinetic data without knowing the reaction network, especially when the data are incomplete due to experimental limitations. We introduce a program, PolyODENet, toward this goal. Based on the machine-learning method Neural ODE, PolyODENet defines a generative model and predicts concentrations at arbitrary time. As such, it is possible to include unmeasurable intermediate species in the kinetic equations. Importantly, we have implemented various measures to apply physical constraints and chemical knowledge in the training to regularize the solution space. Using simple catalytic reaction models, we demonstrate that PolyODENet can predict reaction profiles of unknown species and doing so even reveal hidden parts of reaction mechanisms.

The effect of the immunoassay curve fitting routine on bias in troponin.

Unlike many dose-response curves used in clinical chemistry, the immunoassay curve used to quantitate measurands is often sigmoidal rather than linear. Consequently, a more complex curve fitting model is required. Various models are available, but they can introduce bias, and there can be little awareness of why this error can be introduced. These curve-fitting models include those based on the law of mass-action, empirical models such as splines or linearization models such as the log/logit function. All these models involve assumptions, which can introduce bias as the dose-response curve is 'forced' to fit or minimize the distance between the standard concentration points to the theoretical curve. The most common curve fitting model is the four or five parameter model, which uses four or five parameters to fit a sigmoidal curve to a set of standard points. Measurement of cardiac troponin is an important element in establishing a diagnosis of acute myocardial infarction. We use troponin, a cardiac biomarker, to demonstrate the potential effect of the bias that the curve fit could introduce. Troponin is used for both rule-in and rule-out decisions at different concentrations and at either end of the dose-response curve. The curve fitting process can cause lot-to-lot reagent (and calibrator) variation in immunoassay. However, laboratory staff need to be aware of this potential source of error and why it occurs. Understanding how the error occurs leads to a greater awareness of the importance of validating new reagent/calibrator assessment using patient samples with concentrations at crucial decision points.

Fractionalized mathematical models for drug diffusion

In this study, an effort is made to develop mathematical models that may be used to explain the distribution of drug administration in the human body after oral and intravenous administration of the drug. The diffusion process was utilized to create three models, applying Fick’s principle and the law of mass action. The Sumudu transform algorithm analyzes the rate of change of concentration in various compartments, such as blood and tissue medium. The general solution of drug concentration is demonstrated in the form of extended Mittag-Leffler function. The amount of drug that is contained in each compartment has been determined via the use of numerical parameters. The effect of the fractional parameter on the drug concentration is shown in graphical form. Using MAPLE software, graphs are created to highlight the change in drug concentration over time. The fractional model gives important and relevant inferences to infer new information about the medical field.

Chemical Kinetics and Mass Action in Coexisting Phases.

The kinetics of chemical reactions are determined by the law of mass action, which has been successfully applied to homogeneous, dilute mixtures. At nondilute conditions, interactions among the components can give rise to coexisting phases, which can significantly alter the kinetics of chemical reactions. Here, we derive a theory for chemical reactions in coexisting phases at phase equilibrium. We show that phase equilibrium couples the rates of chemical reactions of components with their diffusive exchanges between the phases. Strikingly, the chemical relaxation kinetics can be represented as a flow along the phase equilibrium line in the phase diagram. A key finding of our theory is that differences in reaction rates between coexisting phases stem solely from phase-dependent reaction rate coefficients. Our theory is key to interpreting how concentration levels of reactive components in condensed phases control chemical reaction rates in synthetic and biological systems.

Vertex results for the robust analysis of uncertain biochemical systems

We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator.

Electric double layer of spherical pH-responsive polyelectrolyte brushes in an electrolyte solution: A strong stretching theory accounting for excluded volume interaction and mass action law

In this paper, we study the electrostatics of pH-responsive polyelectrolyte-grafted spherical particles by using a strong stretching theory that takes into account the excluded volume interaction and the density of chargeable sites on the polyelectrolyte molecules. Based on free energy formalism, we obtain self-consistent field equations for determining the structure and electrostatics of spherical polyelectrolyte brushes. First, we find that the smaller the radius of the inner core, the longer the height of the polyelectrolyte brush. Then, we also prove that an increase in the excluded volume interaction yields a swelling of the polyelectrolyte brush height. In addition, we demonstrate how the effect of pH, bulk ionic concentration, and lateral separation between adjacent polyelectrolyte chains on the electrostatic properties of a spherical polyelectrolyte brush is affected by the radius of the inner core, the excluded volume interaction, and the chargeable site density.

Modelling the dynamic relationship between spread of infection and observed crowd movement patterns at large scale events

Understanding how contact patterns arise from crowd movement is crucial for assessing the spread of infection at mass gathering events. Here we study contact patterns from Wi-Fi mobility data of large sports and entertainment events in the Johan Cruijff ArenA stadium in Amsterdam. We show that crowd movement behaviour at mass gathering events is not homogeneous in time, but naturally consists of alternating periods of movement and rest. As a result, contact duration distributions are heavy-tailed, an observation which is not explained by models assuming that pedestrian contacts are analogous to collisions in the kinetic gas model. We investigate the effect of heavy-tailed contact duration patterns on the spread of infection using various random walk models. We show how different types of intermittent movement behaviour interact with a time-dependent infection probability. Our results point to the existence of a crossover point where increased contact duration presents a higher level of transmission risk than increasing the number of contacts. In addition, we show that different types of intermittent movement behaviour give rise to different mass-action kinetics, but also show that neither one of two mass-action mechanisms uniquely describes events.

Pharmacodynamic model of slow reversible binding and its applications in pharmacokinetic/pharmacodynamic modeling: review and tutorial.

Therapeutic responses of most drugs are initiated by the rate and degree of binding to their receptors or targets. The law of mass action describes the rate of drug-receptor complex association (kon) and dissociation (koff) where the ratio koff/kon is the equilibrium dissociation constant (Kd). Drugs with slow reversible binding (SRB) often demonstrate delayed onset and prolonged pharmacodynamic effects. This report reviews evidence for drugs with SRB features, describes previous pharmacokinetic/pharmacodynamic (PK/PD) modeling efforts of several such drugs, provides a tutorial on the mathematics and properties of SRB models, demonstrates applications of SRB models to additional compounds, and compares PK/PD fittings of SRB with other mechanistic models. We identified and summarized 52 drugs with in vitro-confirmed SRB from a PubMed literature search. Simulations with a SRB model and observed PK/PD profiles showed delayed and prolonged responses and that increasing doses/kon or decreasing koff led to greater expected maximum effects and a longer duration of effects. Recession slopes for return of responses to baseline after single doses were nearly linear with an inflection point that approaches a limiting value at larger doses. The SRB model newly captured literature data for the antihypertensive effects of candesartan and antiallergic effects of noberastine. Their PD profiles could also be fitted with indirect response and biophase models with minimal differences. The applicability of SRB models is probably commonplace, but underappreciated, owing to the need for in vitro confirmation of binding kinetics and the similarity of PK/PD profiles to models with other mechanistic determinants.

A condensate dynamic instability orchestrates actomyosin cortex activation

A key event at the onset of development is the activation of a contractile actomyosin cortex during the oocyte-to-embryo transition1–3. Here we report on the discovery that, in Caenorhabditis elegans oocytes, actomyosin cortex activation is supported by the emergence of thousands of short-lived protein condensates rich in F-actin, N-WASP and the ARP2/3 complex4–8 that form an active micro-emulsion. A phase portrait analysis of the dynamics of individual cortical condensates reveals that condensates initially grow and then transition to disassembly before dissolving completely. We find that, in contrast to condensate growth through diffusion9, the growth dynamics of cortical condensates are chemically driven. Notably, the associated chemical reactions obey mass action kinetics that govern both composition and size. We suggest that the resultant condensate dynamic instability10 suppresses coarsening of the active micro-emulsion11, ensures reaction kinetics that are independent of condensate size and prevents runaway F-actin nucleation during the formation of the first cortical actin meshwork.