Determination Of Equilibrium Constants Research Articles

Measurement of large ribosomal subunit size in cytoplasm and nucleus of living human cells.

Ribosomes are the most essential macromolecules in cells, as they serve as production lines for every single protein. Here, we address the demand to study ribosomes in living human cells by applying time-resolved microscopy. We show that oxazole yellow iodide (YO-PRO-1 dye) intercalates tRNA and rRNA with a determined equilibrium constant of 3.01 ± 1.43 × 105 M-1. Fluorescence correlation spectroscopy (FCS) is used to measure both the rotational (∼14 ms-1) and translational (∼4 μm2 s-1) diffusion coefficients of the 60S ribosomes directly within living human cells. Furthermore, we apply the empirical length-scale dependent viscosity model to calculate the hydrodynamic radius of 60S ribosomes, equal to ∼15 nm, for the first time determined inside living cells. The FCS in YO-PRO-1 stained cells is used to assess ribosome abundance changes, exemplified in rapamycin-treated HeLa cells, highlighting its potential for dynamic ribosome characterization within the cellular environment.

Process Understanding of Transamination Reaction in Chiral Pharmaceutical Intermediate Production Catalyzed by an Engineered Amine Transaminase

AbstractChiral amines are key building blocks for the synthesis of many active pharmaceutical ingredients (APIs). Biocatalytic routes offer significant advantages to provide sustainable access to such motifs on commercial scale, with sacubitril valsartan sodium hydrate as a recent example. In this study a deeper mechanistic and kinetic understanding of the central biocatalytic step in the synthesis of sacubitril valsartan sodium hydrate, applying the evolved transaminase CDX‐043, was gained. The equilibrium of the transamination reaction was investigated in detail, and two kinetic models (ping‐pong two‐substrate kinetics and Michaelis–Menten double substrate kinetics) were established, considering substrate and product inhibition. The determined equilibrium constant indicates that the equilibrium lies strongly on the product side. The results of the kinetic studies demonstrate that the transaminase reaction is in conformity with the Michaelis–Menten double substrate kinetic model. Product inhibition was found to be more severe than substrate inhibition. The application of a plug flow reactor (PFR) was shown to be the preferred reactor setup to reduce the occurring inhibition.

Quantitative Analysis of Protein-Protein Equilibrium Constants in Cellular Environments Using Single-Molecule Localization Microscopy.

Current methods for determining equilibrium constants often operate in three-dimensional environments, which may not accurately reflect interactions with membrane-bound proteins. With our technique, based on single-molecule localization microscopy (SMLM), we directly determine protein-protein association (Ka) and dissociation (Kd) constants in cellular environments by quantifying associated and isolated molecules and their interaction area. We introduce Kernel Surface Density (ks-density,) a novel method for determining the accessible area for interacting molecules, eliminating the need for user-defined parameters. Simulation studies validate our method's accuracy across various density and affinity conditions. Applying this technique to T cell signaling proteins, we determine the 2D association constant of T cell receptors (TCRs) in resting cells and the pseudo-3D dissociation constant of pZAP70 molecules from phosphorylated intracellular tyrosine-based activation motifs on the TCR-CD3 complex. We address challenges of multiple detection and molecular labeling efficiency. This method enhances our understanding of protein interactions in cellular environments, advancing our knowledge of complex biological processes.

Structure-Reactivity Relationships in a Small Library of Imine-Type Dynamic Covalent Materials: Determination of Rate and Equilibrium Constants Enables Model Prediction and Validation of a Unique Mechanical Softening in Dynamic Hydrogels.

The development of next generation soft and recyclable materials prominently features dynamic (reversible) chemistries such as host-guest, supramolecular, and dynamic covalent. Dynamic systems enable injectability, reprocessability, and time-dependent mechanical properties. These properties arise from the inherent relationship between the rate and equilibrium constants (RECs) of molecular junctions (cross-links) and the resulting macroscopic behavior of dynamic networks. However, few examples explicitly measure RECs while exploring this connection between molecular and material properties, particularly for polymeric hydrogel systems. Here we use dynamic covalent imine formation to study how single-point compositional changes in NH2-terminated nucleophiles affect binding constants and resulting hydrogel mechanical properties. We explored both model small molecule studies and model polymeric macromers, and found >3-decade change in RECs. Leveraging established relationships in the literature, we then developed a simple model to describe the cross-linking equilibrium and predict changes in hydrogel mechanical properties. Interestingly, we observed that a narrow ≈2-decade range of Keq's determine the bound fraction of imines. Our model allowed us to uncover a regime where adding cross-linker before saturation can decrease the cross-link density of a hydrogel. We then demonstrated the veracity of this predicted behavior experimentally. Notably this emergent behavior is not accounted for in covalent hydrogel theory. This study expands upon structure-reactivity relationships for imine formation, highlighting how quantitative determination of RECs facilitates predicting macroscopic behavior. Furthermore, while the present study focuses on dynamic covalent imine formation, the underlying principles of this work are applicable to the general bottom-up design of soft and recyclable dynamic materials.

Moment Analysis Method for Measurement of Reaction Equilibrium and Rate Constants by Using High-Performance Liquid Chromatography.

The moment analysis method was developed for the determination of association equilibrium constant (KA) and association (ka) and dissociation (kd) rate constants of intermolecular interactions between solute and ligand molecules. They are accurately determined by using moment equations from elution peak profiles because they are measured by using high-performance liquid chromatography (HPLC) under preferable conditions that neither immobilization nor chemical modification (i.e., fluorescence labeling) of solute and ligand molecules is required. To demonstrate the effectiveness of the method, it was applied to the inclusion complex formation system between dibenzo-18-crown-6 (DB18C6) and alkaline earth metal cations, i.e., Mg2+, Ca2+, and Sr2+, as a concrete example. Because the diameter of the three metal cations is smaller than that of the inner cavity of DB18C6, the values of KA, ka, and kd were analytically determined by assuming the stoichiometry of 1:1 between DB18C6 and the metal cation. They reflected the influence of the difference in the size between the inner cavity of DB18C6 and the metal cations on the inclusion complex formation. It seems that the moment analysis method based on HPLC separation is effective for the multifaceted analysis of chemical reactions because some characteristics of the method are different from those of other conventional methods. It must contribute to the dissemination of an opportunity for the study of chemical reactions to many researchers because of the versatility of HPLC.

Modeling Henry's law and phase separations of water-NaCl-organic mixtures with solvation and ion-pairing.

Empirical measurements of solution vapor pressure of ternary acetonitrile (MeCN) H2O-NaCl-MeCN mixtures were recorded, with NaCl concentrations ranging from zero to the saturation limit, and MeCN concentrations ranging from zero to an absolute mole fraction of 0.64. After accounting for speciation, the variability of the Henry's law coefficient at vapor-liquid equilibrium (VLE) of MeCN ternary mixtures decreased from 107% to 5.1%. Solute speciation was modeled using a mass action solution model that incorporates solute solvation and ion-pairing phenomena. Two empirically determined equilibrium constants corresponding to solute dissociation and ion pairing were utilized for each solute. When speciation effects were considered, the solid-liquid equilibrium of H2O-NaCl-MeCN mixtures appear to be governed by a simple saturation equilibrium constant that is consistent with the binary H2O-NaCl saturation coefficient. Further, our results indicate that the precipitation of NaCl in the MeCN ternary mixtures was not governed by changes in the dielectric constant. Our model indicates that the compositions of the salt-induced liquid-liquid equilibrium (LLE) boundary of the H2O-NaCl-MeCN mixture correspond to the binary plateau activity of MeCN, a range of concentrations over which the activity remains largely invariant in the binary water-MeCN system. Broader comparisons with other ternary miscible organic solvent (MOS) mixtures suggest that salt-induced liquid-liquid equilibrium exists if: (1) the solution displays a positive deviation from the ideal limits governed by Raoult's law; and (2) the minimum of the mixing free energy profile for the binary water-MOS system is organic-rich. This work is one of the first applications of speciation-based solution models to a ternary system, and the first that includes an organic solute.

Fundamental Determinants of the Accuracy of Equilibrium Constants for Affinity Complexes.

The equilibrium constant of a chemical reaction is arguably the key thermodynamic parameter in chemistry; we naturally expect that equilibrium constants are determined accurately. The majority of equilibrium constants determined today are those of binding reactions that form affinity complexes, such as protein-protein, protein-DNA, and protein-small molecule. There is growing awareness that the determination of equilibrium constants for highly stable affinity complexes may be very inaccurate. However, fundamental (i.e., method-independent) determinants of accuracy are poorly understood. Here, we present a study that explicitly shows what the accuracy of equilibrium constants of affinity complexes depends on. This study reveals the critical importance of the choice of concentration of interacting components and creates a theoretical foundation for improving the accuracy of the equilibrium constants. The predicted influence of concentrations on accuracy was confirmed experimentally. The results of this fundamental study provide instructive guidance for experimentalists independently on the method they use.

Understanding fluoride adsorption from groundwater by alumina modified with alum using PHREEQC surface complexation model

Fluoride is recognized as a vital ion for human and animal growth because of the critical role it plays in preventing skeletal and dental problems. However, when it is ingested at a higher concentration it can cause demineralization of teeth and bones resulting in fluorosis, therefore, the production of high-adsorptive capacity material which is also cost-effective is necessary for the treatment of fluorides. In this study, aluminium foil is valorised into alumina nanoparticles. The as-prepared alumina was modified with alum in two different ratios of 1:0.5 and 1:1 (alumina to alum w/w%) and later used as adsorbents for the removal of fluoride from groundwater. The adsorbents were characterized by Fourier transform infrared spectroscopy, point of zero charge and X-ray diffraction. Different factors that influence the removal efficiency of fluorides such as pH, initial concentrations, contact time and adsorbent dosage were studied and optimized using a simulated fluoride solution. The optimum conditions obtained were used to test real groundwater. The static experiment conditions were used to calibrate a PHREEQC geochemical model which was later used to simulate the fluoride sorption onto the modified alumina at different conditions. PHREEQC was also coupled with parameter estimation software to determine equilibrium constants for the surface reactions between the fluoride species and the adsorbent in a way that the simulations accurately reflect the outcomes of laboratory experiments. Isotherm studies were carried out on the adsorbents. Both Langmuir and Freundlich's non-linear models fitted well for the equilibrium data. However, with a higher coefficient of regression and low chi-square test values, the adsorption process was more of chemisorption on a monolayer surface. Kinetic studies were also carried out by using the non-linear equations from the pseudo-first-order and pseudo-second-order models. The pseudo-second-order model fitted well for the equilibrium data. The mechanism for the fluoride ion adsorption was also studied by the intraparticle (IP) diffusion model and was found that IP was not the rate-determining factor, and therefore the most plausible mechanism for the sorption process was ion exchange or attraction of fluoride ions to the sorbent surface. The findings obtained from this research show that readily available aluminium waste could be valorised into a useful product that could be employed in the removal of fluoride from water samples, including groundwater, that may contain too much fluoride and pose a risk to the general public's health.

Separation of Mixtures of Rutin and Quercetin: Evaluating the Productivity of Preparative Chromatography

AbstractThe flavonoid rutin is present in significant amounts in the flower buds of Sophora japonica L. It offers numerous desired pharmacological effects. Under certain extraction conditions quercetin is found as a hydrolysis product which needs to be separated from rutin. This paper describes the application of liquid chromatography to solve this task. Based on the determination of adsorption equilibrium constants and column efficiencies, the productivity of the separation process is estimated, and scale‐up considerations are presented. A comparison with alternatively directly crystallizing rutin from raw extracts is also reported.

Microwave Inhibition of the Hydrogenation of CO2 for Methane Formation

The complex equilibria associated with the hydrogenation of CO2 to form valuable products are of considerable interest for the remediation of CO2. Due to the potential usefulness of these reactions, alternative methods of driving them more favorably using alternative energy sources, such as microwave radiation, are also of interest. We report here a study of the methanation reaction that yields CH4, which was studied under microwave and conventional convective heating conditions. An essential part of the science that arises from such studies is characterizing the microwave-specific effects on the reaction. From the determined equilibrium constants, we found that microwave radiation strongly inhibited the formation of CH4. The effective thermodynamic parameters obtained from a van’t Hoff plot reflect this inhibition. The enthalpy under microwave conditions is −38.63 kJ/mol, compared to −180.02 kJ/mol under conventional heating methods. Similarly, the free energy across the temperature range is less negative, suggesting a decrease in spontaneity under microwave conditions. We also observed a significant difference in the entropy, with entropy of −52 J/mol under microwave conditions and −206 J/mol under conventional conditions. This is consistent with prior observations that microwaves do not accelerate exothermic reactions. As discussed, this difference may arise from the microwave-driven dissociation of the reactant before CH4 bonds are made. Analysis of this system is of interest in understanding how the microwave inhibits the formation of the products of exothermic reactions. These results are of significance for understanding the broad area of microwave driven heterogeneous catalysis.

Effect of equilibrium constant for carbon dioxide recombination in hypersonic flow analysis

An equilibrium constant is an important parameter in regard to determining the backward reaction rate constant in chemical kinetics modeling for a hypersonic flow. Three common approaches for the equilibrium constant determination are based on the partition function, Gibbs free energy, and the experimental reaction rate measurement. The present study conducted a computational fluid dynamics (CFD) analysis with different equilibrium constant formulations in a thermochemical nonequilibrium hypersonic flow in order to study the influence of the equilibrium constant in carbon dioxide flow during the Martian entry. The equilibrium constant for the carbon dioxide molecule dissociation differs from one method to another among the reactions that are considered in the carbon dioxide flow. Three different flow conditions, which are based on the experimental data that is provided in the literature, are considered in the detailed comparison analysis using CFD. The variation of the flow properties in terms of pressure, temperature, and mass fraction along the stagnation line is compared for different cases of the equilibrium constant computation. The results that are obtained from the present study confirm that the equilibrium constant influences the numerical computation in the thermochemical nonequilibrium flow especially for the non-catalytic wall boundary condition.

Synthesis and determination of dissociation equilibrium constants of novel metal chelating agent against Alzheimer's disease

In this paper, we have synthesized a new metal chelating agent HPM and characterized it by NMR, IR and LC-MS/MS measurements. The HPM obtained three pKa values: pKa1=3.1988, pKa2=4.4157 and pKa3=9.0091. The pKa1 is due to the carboxyl group on the C11 position, the pKa2 is due to the hydroxyl group on the C6 position and the pKa3 is due to the NH2+ on the N8 position.

Mathematical modeling of the equilibrium and kinetics of sulfamethoxazole adsorption from aqueous solution

The determination of kinetic and equilibrium constants of the adsorption process is an important step to evaluate the efficiency of the industrial process. In this work, the analysis was carried out innovatively, by proposing analytical solutions for the partial differential equations that describe the adsorption of sulfamethoxazole on Pirangi clay. The equations proposed here provide a global description of the process and a software with a simplified visual environment was created to facilitate the determination of kinetic constants.

Moment theory of affinity capillary electrophoresis for analysis of reaction kinetics of intermolecular interactions

A theoretical basis for affinity capillary electrophoresis (ACE) was systematically developed by applying the moment theory to the study on intermolecular interactions between solute (S) and ligand (L) molecules to form complex (X). Moment equations were developed for both complete filling and partial filling ACE systems, in which SLm or SnL forms as X. They are effective for the determination of equilibrium and kinetic constants of association between S and L and dissociation of X from the first absolute and second central moments of elution peaks measured by ACE. In order to demonstrate their effectiveness, simulative calculations of partial filling ACE behavior was conducted by assuming the stoichiometry of 1:1 between S and L. Because partial filling ACE systems are classified into five categories based on experimental conditions, calculation results for all the five cases are explained. The combination of ACE and moment theory is effective because there are some advantages concerning the accurate analysis of intermolecular interactions. The results of this study provide an opportunity for the study on intermolecular interactions to many researchers because CE is already versatile.

Reactive extraction of gallic acid using tri-n-octylamine in a biocompatible mixture of diluents

The present study is an approach to develop a biocompatible extraction system using tri-n-octylamine (TOA), with a modifier, 1-decanol and inert diluent, n-dodecane for the recovery of gallic acid (GA) from aqueous solution. The effects of GA concentration, modifier volume ratio, solvent polarity and pH of aqueous solution on reactive extraction of GA, are examined. With optimized extraction system of 20% TOA with 40% 1-decanol and 40% n-dodecane, further investigations are carried out for the determination of reaction stoichiometry ( m = 1.53 – 2.02), equilibrium constants (K E = 20.30 – 83.23) and thermodynamics (∆H o = -94,385.86 J.mol –1 , ∆S o = -267.51 J.mol –1 .K –1 and ∆G o = -14,627.83 to -6602.54 J.mol –1 .K –1 ) in the range of GA concentrations (0.00294 kmol.m –3 – 0.04703 kmol.m –3 ) at different temperature (298.15 K – 328.15 K) using a bio-inspired, population based genetic algorithm, differential evolution (DE). At the temperature 298.15 K, maximum distribution of GA in organic phase is found as 81%.

The AuSc, AuTi, and AuFe molecules: Determination of the bond energies by Knudsen effusion mass spectrometry experiments combined with ab initio calculations.

The AuTi gaseous molecule was for the first time identified in vapors produced at high temperature from a gold-titanium alloy. The homogeneous equilibria AuTi(g) = Au(g) + Ti(g) (direct dissociation) and AuTi(g) + Au(g) = Au2(g) + Ti(g) (isomolecular exchange) were studied by Knudsen effusion mass spectrometry in the temperature range 2111-2229K. The so determined equilibrium constants were treated by the "third-law method" of thermodynamic analysis, integrated with theoretical calculations, and the dissociation energy at 0K was derived as D0K ° (AuTi) = 241.0 ± 5.2 kJ/mol. A similar investigation was carried out for the AuSc and AuFe species, whose dissociation energies were previously reported with large uncertainties. The direct dissociation and the isomolecular exchange with the Au2 dimer were studied in the 1969-2274 and 1842-2092K ranges for AuSc and AuFe, respectively, and the dissociation energies derived as D0K ° (AuSc) = 240.4 ± 6.0 and D0K ° (AuFe) = 186.2 ± 4.2 kJ/mol. The experimental bond energies are compared with those calculated here by coupled cluster with single, double, and perturbative triple excitations with the correlation-consistent basis sets cc-pVXZ(-PP) and cc-pwCVXZ(-PP) (with X = T, Q, 5), also in the limit of complete basis set, and with those from complete active space self-consistent field-multi-reference configuration interaction calculations, recently available in the literature. The stronger bond of AuTi compared to AuFe parallels the trend observed in monochlorides. This analogy is shown to be more generally observed in the AuM and MCl diatomic series (with M = first row transition metal), in accordance with a picture of "pseudo-halogen" bonding behavior of gold.

Determination of association equilibrium constant from single molecule fluorescence localization microscopy.

Single molecule fluorescence localization microscopy provides molecular localization with a precision in the tens of nanometer range in the plane perpendicular to the light propagation. This opens the possibility to count molecules and correlate their locations, starting from a map of the actual positions in a single molecule super resolution image. Considering molecular pair correlation as an indication of interaction, and a way to discern them from free molecules, we describe a method to calculate thermodynamic equilibrium constants. In this work, we use as a test system two complementary homo-oligonucleotides, one strand marked with Cyanine 3.5 and the other with Alexa Fluor 647. Hybridization is controlled by the amount of each strand, temperature, and the ionic force, and measured in steady state emission. The same samples are examined in Stochastic Optical Reconstruction Microscopy (STORM) experiments with split-field simultaneous two-colour detection. The effect of multiblinking, labelling-detection efficiency, and determination of the critical distance for association are discussed. We consistently determine values in STORM coincident with those of the bulk experiment.

Electrochemical Modeling of Iodide Oxidation in Metal-Halide Molten Salts

The oxidation of iodide in NaI-AlBr3, NaI-AlCl3, and NaI-GaCl3 molten salts was analyzed using simulation software to extract relevant kinetic parameters. The experimental oxidation potentials were ordered AlCl3 < AlBr3 < GaCl3, with higher oxidation potentials correlating with softer Lewis acidity of the metal halide. An iodide oxidation and metal halide speciation model was developed and simulated to fit the electrochemical response, enabling determination of electrochemical charge transfer parameters and chemical equilibrium constants. NaI-AlBr3 displayed the fastest electron transfer rates yet showed the lowest current densities. All salts revealed smaller than expected current densities, explained by equilibrium between various species, where some are not electrochemically active at the studied potentials. These equilibrium reactions are due to the various metal halide species, controlling the reactant concentration of iodide and the resultant current. We hypothesize the electrochemically active iodide species, present as a metal halide monomer (MX3I−), is decreased dramatically from the expected concentration, sequestered as a more stable metal halide dimer species (M2X6I−) with a higher oxidation potential. Traditional Tafel analysis of the experimental data supports the validity of the simulations. These results increase understanding of iodide oxidation in low-temperature Lewis acidic molten salts and inform task-specific molten salt design.

Quantification of the Lewis Basicities and Nucleophilicities of 1,3,5‐Tris(dialkylamino)benzenes

AbstractEquilibrium constants for the formation of Wheland complexes from 1,3,5‐tris(dialkylamino)benzenes and benzhydrylium ions (Ar2CH+) have been determined photometrically in dichloromethane solution at 20 °C. The Lewis basicity of the ring carbons increases in the series trimorpholinobenzene&lt;tripiperidinobenzene&lt;tripyrrolidinobenzene. Wheland complexes, which are formed with equilibrium constants 102&lt;K/M−1&lt;106 in the reactions of triaminobenzenes with carbenium ions, show temperature‐dependent dynamic 1H NMR spectra, due to rapid reverse reactions and recombination at different positions of the triaminobenzenes. Since the rates of the formation of the Wheland complexes are too high to be measured directly, they were calculated as the product of photometrically determined equilibrium constants and the rate constants for the reverse reactions, which were derived from the dynamic 1H NMR spectra. The experimentally determined equilibrium and rate constants were in good agreement with the results of DFT calculations using the SMD solvent model. The calculations show that in all cases the Wheland complexes are thermodynamically more stable than the ammonium ions formed by attack of the benzhydrylium ions at the amino group of the title compounds, which explains the exclusive formation of Wheland complexes in thermodynamically controlled reactions. With nucleophilicity parameters in the range 10&lt;N&lt;15 the triaminobenzenes have comparable nucleophilic reactivities as enamines, silyl ketene acetals as well as stabilized phosphonium and sulfonium ylides.

Exploring the thermodynamics of the bromine electrode in concentrated solutions for improved parametrisation of hydrogen–bromine flow battery models

Thermodynamic properties of the bromine electrode in an exemplary hydrogen–bromine flow battery (HBFB) are investigated in detail. Open-circuit potential (OCP) measurements of HBRB electrolytes in a liquid junction-free setup and electrolyte Raman spectra are employed to estimate polybromides speciation. An improved mathematical description of the bromine electrode OCP versus state of charge is provided. This paper addresses the phenomenon of polybromides formation at concentrations up to 7.7 mol L -1 HBr and 3.85 mol L -1 Br 2 and their significant impact on the OCP. The model takes into account tri-, penta- and heptabromides formation, precisely modelled electrolyte activity coefficients (up to 11-molal HBr), electrolyte density, and temperature. It is elucidated that the polybromide formation constants found in literature treating dilute electrolytes are substantially too low. Newly determined equilibrium constants, applicable over a wider concentration range are provided for 25 and 43 °C together with their standard enthalpy changes. The model is successfully validated in an independent experiment using a real, pilot-scale HBFB. It is concluded that the usage of a simple Nernst-like equation to calculate the OCP of flow battery electrodes containing concentrated electrolytes leads to erroneous results. • A novel thermodynamic bromine electrode model is described and validated. • It is applied to describe the open-circuit voltage of a pilot-scale flow battery. • Polybromide formation constants are re-evaluated at high electrolyte concentrations. • Mean activity coefficient of aqueous HBr up to 11 m between 0 and 70 °C is modelled.