Binding Constants K1 Research Articles

Sulfate encapsulation by hydrogen bonding in organic clefts based on biphenyl-bridged oligourea ligands

Sulfate encapsulation faces great challenges due to the large hydration energy. Herein, a sulfate co-crystal [1, TBA4L(SO4)2, C104H174N16O20S2],was synthesized and characterized by 1H NMR, elemental analysis and Fourier transform infrared spectroscopy (FTIR). The X-ray single-crystal diffraction analysis showed that the sulfate anion was encapsulated by multiple hydrogen bonds in organic clefts containing biphenyl-bridged oligourea ligands. In the extended structure, a macrocycle including four ligands L and eight SO42- anions was constructed by N-H···O and C-H···O hydrogen bonds, which was further extended to two-dimensional hydrogen bonding network. DFT calculations showed that two sulfate anions were encapsulated by two clefts constructed by biphenyl bridged oligourea ligand, respectively, with the four corresponding tetrabutylammonium cations locating on both sides of the sulfate anions. This encapsulation mode is consistent with that of the crystal structure of the sulfate anion co-crystal 1. X-ray powder diffraction was used to study the phase purity of the bulk sample of co-crystal 1. In addition, the thermal stability of co-crystal 1 was explored by TG-DTG method, and the apparent activation energy Ea of co-crystal 1 was calculated during the main thermal decomposition process. Furthermore, the sulfate binding properties of L was investigated using UV/Vis spectroscopy method in CH3CN/DMSO solution. The binding ratio of ligand L to sulfate anion was derived as 1:2 by Job’s plot, with the binding constants K1 = 2.45 × 105 M−1 and K2 = 2.46 × 105 M−1, obtained by sulfate titration experiments. The study provides a new method for sulfate encapsulation and relative application.

Redox-Responsive Host–Guest Association between γ-Cyclodextrin and Mixed-Metal Keggin-Type Polyoxometalates

The complexation of Keggin-type polyoxometalates (POMs) with γ-cyclodextrin (γ-CD) leads to supramolecular inclusion assemblies in aqueous solution driven by a chaotropic effect. The strength of the interaction between γ-CD and oxidized or one-electron reduced POMs in a series of molybdenum and vanadium monosubstituted phospho- and silico-tungstates, [XW11MO40]n- Keggin-type anions where X = P or Si and M = MoV/VI or VIV/V, has been evaluated by isothermal titration calorimetry (ITC), NMR spectroscopy, and cyclic voltammetry. Such a study reveals that the host-guest binding constant K1:1 increases strongly with the decrease of the global ionic charge of the POM unit. There is an almost one magnitude order of variation in K1:1 per charge unit, where K1:1 falls down from about 105 M-1 to values close to zero as ionic charge varies from 3- to 6-. Such POMs with molybdenum and vanadium addenda offer the possibility of tuning the host-guest association strength by the simple addition/removal of one electron to POMs, opening a new avenue for the design of smart materials through redox stimuli.

Evaluation of the binding properties of drugs to albumin from DSC thermograms.

There is a demand in rapid and robust methods to determine the affinity of drugs to receptors, enzymes, and transport proteins. Differential scanning calorimetry (DSC) is a common method to prove the existence of ligand-protein binding from the shift of denaturation peak, but it is rarely used to obtain the binding constant values. The work is aimed to prove that the DSC experiments can be a source of reliable values of the binding constants and information on the stoichiometry of drug-albumin binding. DSC thermograms of bovine serum albumin denaturation in the presence of several drugs with different affinity and stoichiometry of binding to albumin: naproxen, warfarin, ibuprofen, and isoniazid were recorded. The dependences of the denaturation peak maximum temperature and area on the molar drug/protein ratio, which varied from 0 to 100, were considered. With the help of numerical modeling of the DSC curves, these dependences were predicted using the binding parameters determined in independent experiments and a simple two-state model of denaturation. The DSC data at relatively small concentrations of ligands are in good agreement with the calculation results. The deviations from the model predictions at high ligand concentrations in the cases of naproxen and ibuprofen indicate that albumin is able to bind several additional molecules of these drugs with its low-affinity sites. The fit was improved by using a sequential binding model with two binding constants K1=1.0×107 and K2=1.0×104 for naproxen and a cooperative binding model for ibuprofen. The stoichiometry of drug-albumin complexes fully saturated with drug ligand was calculated from the dependence of the denaturation temperature on the drug concentration. In the case of isoniazid, DSC thermograms indicated very weak binding to albumin.

Photophysical and thermodynamic evaluation on the in vitro and in silico binding profile of Camptothecin with DNA

Camptothecin (CMT) is an anti-tumour alkaloid drug exhibiting selective topoisomerase-I inhibitory activity by eventually hindering dynamic functions of DNA duplex via initiating apoptosis. Unravelling the binding mechanism of CMT with bio macromolecular systems can offer fundamental information regarding the mechanism of actions which can lead to the design of rational proactive drugs. This study endeavoured the binding interactions of CMT with calf thymus DNA (ct-DNA) along with the structural alterations attained by the DNA duplex owing to CMT interactions through multi-spectroscopic, calorimetric and molecular docking studies. The UV–visible absorbance and fluorescence quenching studies revealed the binding strength of CMT with ct-DNA, evident from the binding constants K1 = 3.79 × 103 M−1 and Kq = 2 × 103 M−1. The time-resolved lifetime measurements inferred that the quenching was static due to the non-fluorescent ground state complex formation. The dye displacement study, temperature melting and viscosity measurements established a typical non-intercalative binding mode of CMT with ct-DNA. The binding isotherm deduced from ITC was found to be spontaneous and exothermic exerting a promising ΔG value of −6.2 kcal mol−1. The thermal kinetic parameters implied that the forces primarily involved in the CMT-ct-DNA complexation are hydrogen bonding and van der Waals interactions. Moreover, the structural alterations of DNA duplex reflected in the CD and FTIR spectra could undeniably confirm the groove binding manner of CMT. The in silico extra precision docking study explored more accurate molecular illustrations of sequence specific minor groove binding mechanism evolved between CMT and DNA corroborating well with the experimental results. These innovative findings may shorten the path towards the development of novel and more effective CMT drug derivatives.

Investigation of bovine serum albumin/tropicamide interaction using a quartz crystal microbalance sensor

This study describes the kinetics and evaluation of thermodynamic parameters of bovine serum albumin (BSA) and tropicamide (TPA) interactions, by using quartz crystal microbalance (QCM) technique, under similar physiological status. BSA was immobilized on the gold electrode surface of a QCM by using cystamine and glutaraldehyde as crosslinking agent. The immobilizing steps were followed by cyclic voltammetry technique. A flow injection analysis set-up was applied for injection of the drug solutions into the fluid system. Kinetics of the interaction was interpreted by zero- and pseudo-first-order kinetic models, depending on TPA concentration and temperature. The binding constants (k1 = 9.12, 6.55 and 6.8 mol−1 L s−1), dissociation rate constants (k−1 = 0.0028, 0.0049 and 0.0102 s−1), the binding equilibrium constant (K = 3257, 1337 and 635 mol−1 L) and the thermodynamic parameters of the interaction were estimated at different temperatures (293, 303 and 310 K, respectively). The results revealed that hydrogen bonding and van der Waals forces are the major types of interactions of between BSA and TPA.

Host-guest assembly for highly sensitive probing of a chiral mono-alcohol with a zinc trisporphyrinate

A zinc trisporphyrinate has been developed as a chirality sensor for chiral mono-alcohols. In its structure, there are two “spaces” surrounded by three porphyrin moieties, which allow guests to fill in. It has shown extremely high CD sensitivity for a chiral mono-alcohol with a naphthyl substituent, 1-(1-naphthyl)ethanol, at μM level, which is at least three orders of magnitude lower concentration than previous reports. A crystallographic study of the host-guest complex reveals the binding of 1-(1-naphthyl)ethanol to the zinc trisporphyrinate is greatly enhanced by multipoint interactions, such as coordination interactions, hydrogen bonding, π-π and CH···π interactions etc. Spectroscopic studies suggest the corresponding binding constant K1 is over 105 M−1, which is two or three orders of magnitude larger than other mono-alcohols. Among porphyrin systems, this trisporphyrin have the strongest binding affinity for 1-(1-naphthyl)ethanol, which leads to the highest CD sensitivity.

In vitro Bioequivalence Studies in Tablet Formulation Containing 625 mg of Colesevelam Hydrochlorides

Colesevelam hydrochloride is a second generation bile acid sequestrant that is used principally for treatment of elevated LDL cholesterol. Additionally, it is indicated to improve glycemic control in adults with type 2 diabetes mellitus. Colesevelam hydrochloride is an insoluble, non-absorbed polymer that binds bile acids in the intestine, impeding their reabsorption. Because the drug is not absorbed into the systemic circulation, pharmacokinetic information is not available. The present abstract focuses on the study of in vitro BE in tablet formulation containing 625 mg of Colesevelam hydrochloride. Bile acid salts of Glycocholic Acid (GC), Glycochenodeoxycholic Acid (GCDC) and Taurodeoxycholic Acid (TDC) were used in vitro BE studies. The binding capacity HPLC method was developed and validated for these bile acid salts. The equilibrium binding study that is the pivotal BE study and in vitro kinetic binding study that is the support the pivotal equilibrium binding study was repeated twelve times. In the in vitro equilibrium binding studies, the Langmuir binding constants k1 (affinity) and k2 (capacity) were calculated for the three salts, individually and combined (GC+GCDC+TDC) using both nonlinear Langmuir equation and linear Langmuir equation for the test and reference products. The calculated capacity constant (k2), the more important parameter, were obtained very similar between test and reference products in the 90% confidence interval and acceptance criteria of 80% to 120%. The test/reference ratio for capacity constant, k2, was obtained 0.918 and 0.922 using equation 1 and 2 for total bile acid salts from the without acid pre-treatment equilibrium binding study and 0.948, 0.953 using equation 1 and 2 for total bile acid salts from the with acid pre-treatment equilibrium binding study.

Spectral studies of the interactions of protein CopC with gold ions

Protein CopC from a pathogenic bacterium Pseudomonas syringae pv. tomato (CopC) is one of four proteins (CopA, B, C and D) coded on the copper resistance operon (cop). Using fluorescence measurements, differential optical spectra, methods of cyclic voltammetry and studing the kinetics of oxidation of ascorbic acid, we investigated the possibility of protein CopC binding with AuIII ion. The results showed that the AuIII ion can be bound with CopC in the ratio of 2: 1. The apparent binding constants k1 and k2 are 3.68·103 and 3.92·104 L mol−1, respectively. Binding with AuIII ions does not result in considerable conformational changes of protein CopC.

Comparative evaluation of in vitro efficacy of colesevelam hydrochloride tablets

Context: Colesevelam hydrochloride is used as an adjunct to diet and exercise to reduce elevated low-density lipoprotein (LDL) cholesterol in patients with primary hyperlipidemia as well as to improve glycemic control in patients with type 2 diabetes. This is likely to result in submission of abbreviated new drug applications (ANDA).Objective: This study was conducted to compare the efficacy of two tablet products of colesevelam hydrochloride based on the in vitro binding of bile acid sodium salts of glycocholic acid (GC), glycochenodeoxycholic acid (GCDA) and taurodeoxycholic acid (TDCA).Methods: Kinetic binding study was carried out with constant initial bile salt concentrations as a function of time. Equilibrium binding studies were conducted under conditions of constant incubation time and varying initial concentrations of bile acid sodium salts. The unbound concentration of bile salts was determined in the samples of these studies. Langmuir equation was utilized to calculate the binding constants k1 and k2.Results: The amount of the three bile salts bound to both the products reached equilibrium at 3 h. The similarity factor (f2) was 99.5 based on the binding profile of total bile salts to the test and reference colesevelam tablets as a function of time. The 90% confidence interval for the test to reference ratio of k2 values were 96.06–112.07 which is within the acceptance criteria of 80–120%.Conclusion: It is concluded from the results that the test and reference tablets of colesevelam hydrochloride showed a similar in vitro binding profile and capacity to bile salts.

Comparative Evaluation of the In Vitro Efficacy of Lanthanum Carbonate Chewable Tablets

The aims of this study were to systematically evaluate the effects of pH levels, phosphate concentrations, and tablet integrity on the phosphate binding profiles of lanthanum carbonate chewable tablets, and to compare the in vitro phosphate binding efficacy of one reference and two test products of lanthanum carbonate chewable tablets. Langmuir equation was utilized to calculate the binding constants k1 and k2 . The phosphate binding to the tablets of lanthanum carbonate product was pH dependent, with a faster binding rate at low pH. The crushed tablets bind phosphate more rapid. Compared with the whole tablets, the kinetic binding profiles from the crushed tablets were less variable under all conditions for both test and reference products. The phosphate level has a significant impact on the phosphate binding for both whole and crushed tablets under all pH conditions, with more binding at higher phosphate concentration. The phosphate binding profiles displayed significant difference among the products. For a crushed tablet, the phosphate binding to lanthanum reached equilibrium within 8 h under all conditions. The 90% confidence interval for the k2 ratio (test/reference) was well within the 80%-125% under all pH conditions. However, the k1 ratio varies from 54% to 144%. © 2013 Wiley Periodicals, Inc. and the American Pharmacists Association J Pharm Sci 102:1370-1381, 2013.

Enhancing photostability of cyanine dye by cucurbituril encapsulation

A linear cyanine dye (LDP) guest comprising two binding sites, one 4-[2-[4-(dimethylamino)phenyl]ethenyl]pyridinium group and one p-aminophenoxy ethylene group, was synthesized and proved could form inclusion complexes with cucurbit[7]uril (CB[7]) in aqueous solution. A partially encapsulated ([2]pseudorotaxane) state in which one CB[7] ring moved fast between the two binding sites was originally detected and was then transferred into a full encapsulated ([3]pseudorotaxane) state where two CB[7] macrocycles resided on both binding sites with the continuously adding of CB[7] to LDP. The two binding constants K1 and K2 were determined as (6.29±0.88)×104M−1 and (1.58±0.17)×104M−1, respectively. Compared with the free LDP, the photostability of the [3]pseudorotaxane is found been distinctively promoted, while that of the [2]pseudorotaxane state is hardly improved.

Electrostatic interactions effect in the aminolysis of some β‐lactams in the presence of poly(ethyleneimine):structure‐reactivity

AbstractThe aminolysis reaction of a series of β‐lactams in the presence of poly(ethyleneimine) (PEI) at 30°C and pH = 8.40 has been studied. The substrates investigated follow a pseudo first order rate, except two β‐lactams which show a two step consecutive reaction. Increasing the polyelectrolyte concentration, Michaelis–Menten type kinetics are been observed and for four substrates a more complex rate behaviour was verified owing to the polyelectrolyte inhibition effect. Both the binding constant K1 between polyelelectrolyte and β‐lactam and the first order rate constant of the reactive complex decomposition kcat were calculated. The substituent effect at C‐6′ or C‐7′ position of β‐lactam on the aminolysis rate does not correlate with the σI value (Taft plot). Most probably, steric and electronic effects are important, but the electrostatic ones are determining factors for the relevant acceleration attributable to both the binding phenomena and the increased reactivity of the substrate–polyelectrolyte complex. The comparison between poly(ethyleneimine) and Human Serum Albumin (HSA) is also discussed. Copyright © 2007 John Wiley & Sons, Ltd.

Axial Coordination of Porphyrinatocobalt(II) Complexes with Bis(pyridinolato)silicon(IV) Phthalocyanines

AbstractTreatment of dichlorosilicon(IV) phthalocyanine with 3‐ or 4‐hydroxypyridine in the presence of pyridine in toluene gave the corresponding bis(pyridinolato)silicon(IV) phthalocyanine complexes SiPc(3‐OPy)2 (1) or SiPc(4‐OPy)2 (2), respectively, which were spectroscopically and structurally characterized. As shown by electronic absorption spectroscopy, these compounds axially bind to meso‐tetraphenylporphyrinatocobalt(II) [Co(TPP) (3)] and meso‐tetrakis(3,5‐di‐tert‐butylphenyl)porphyrinatocobalt(II) [Co(TBPP) (4)] with the two pyridyl ligands forming the corresponding mixed phthalocyanine–porphyrin triads. The binding constants K1 between the 4‐pyridyl phthalocyanine 2 and the porphyrinatocobalt(II) complexes (1.1–1.2 × 104 M–1) are about threefold higher than those for the 3‐pyridyl counterpart 1. The heterodyads 2·3 and 2·4 were isolated by column chromatography and characterized by mass and absorption spectroscopy. (© Wiley‐VCH Verlag GmbH & Co. KGaA, 69451 Weinheim, Germany, 2007)

Flexibility of Na,K-ATPase secondary structure upon drug-protein interaction

The enzyme Na+, K+-ATPase is an integral membrane protein which transports sodium and potassium cations against an electrochemical gradient. The transport of Na+ and K+ ions is connected to an oscillation of the enzyme between the two conformational states, the E1 (Na+) and the E2 (K+) conformations. The enzymatic activity of ATPase is largley affected by different ligands complexation. This review reports the effects of several drugs such as AZT (anti-AIDS), cis-Pt (antitumor), aspirin (anti-inflammatory) and vitamin C (antioxidant) on the stability and secondary structure of Na,K-ATPase in vitro. Drug-enzyme binding is mainly through H-bonding to the polypeptide C=O and C-N groups with two binding constants K1(AZT) = 5.30 × 105 M−1 and K2(AZT) = 9.80 × 103 M−1 for AZT and one binding constant for Kcis-Pt = 1.93 × 104 M−1, Kaspirin = 6.45 × 103 M−1 and Kascorbate = 1.04 × 104 M−1 for cis-Pt, aspirin and ascorbic acid. The enzyme secondary structure was altered from that of α-helix 19.8% (free protein) to almost 22–26% and the β-sheet from 25.6% to 18–22%, upon drug complexation with the order of induced stability AZT > cis-Pt > ascorbate > aspirin.

Monitoring and Estimation of the Kinetics Parameters in the Binding Process of Tannic Acid to Bovine Serum Albumin with Electrochemical Quartz Crystal Impedance System

Combined measurements of piezoelectric quartz crystal impedance (PQCI) and electrochemical impedance (EI) were utilized in situ to monitor the adsorption of bovine serum albumin (BSA) onto the newly prepared Au colloid-modified electrode and study the binding process of tannic acid (TA) to BSA on the BSA-modified electrode surface. The time courses of the resonant frequency and the equivalent parameters of the sensor were simultaneously obtained during BSA adsorption and TA-BSA binding. Compared with the bare gold electrode, the Au colloid-modified gold electrode showed better biocompatibility, and the absorption capacity for BSA was increased by approximately 2.4 times. The observed frequency decrease was ascribed to the mass increase of the sensor surface resulting from the TA-BSA binding, which is believed to result mainly from the hydrogen bonding from FT-IR characterization. The maximal molar binding ratio of TA binding to immobilized BSA obtained from the frequency shift of the adsorbed BSA and TA was estimated to be 10.3:1. On the basis of the frequency decrease with time, the kinetics of the binding was quantitatively studied. By way of fitting the experimental data, the kinetics parameters, that is, binding and dissociation constant (k1, k(-1)), and the binding equilibrium constant (ka) were determined, giving values of 9.51 x 10(4) M(-1) s(-1), 3.15 s(-1), and 3.1 x 10(4) M(-1), respectively.

Development of a Fitting Model Suitable for the Isothermal Titration Calorimetric Curve of DNA with Cationic Ligands

A novel curve fitting model was developed for the isothermal titration calorimetry (ITC) of a cationic ligand binding to DNA. The ligand binding often generates a DNA conformational change from an elongated random coil into a compact collapsed form that is referred to as "DNA condensation". The ligand binding can be classified into two regimes having different binding constants Ki, i.e., the binding to an elongated DNA chain with a binding constant K1 and with K2 that occurred during the conformational transition. The two-variable curve fitting models are usually bound by a strict regulation on the difference in the values of the binding constants K1 > K2. For the DNA condensation, however, the relationships for K1 and K2 are still unclear. The novel curve fitting model developed in this study takes into account this uncertainty on the relationship of the binding constants and is highly flexible for the two-variable binding constant system.

Visible-light sensitisation of near-infrared luminescence from Yb(iii), Nd(iii) and Er(iii) complexes of 3,6-bis(2-pyridyl)tetrazine

Reaction of the potentially bis-bidentate bridging ligand 3,6-bis(2-pyridyl)tetrazine (BPTZ) with various lanthanide complexes [Ln(tta)3(H2O)2] [Htta = thenoyl(trifluoro)acetone; Ln = La, Nd, Gd, Er, Yb] in aqueous ethanol afforded the mononuclear complexes [Ln(tta)3(BPTZ)] (Ln = La, Nd) or the dinuclear complexes [{Ln(tta)3}2(μ-BPTZ)] (Ln = Gd, Er, Yb) in which one or two, respectively, lanthanide tris-diketonate {Ln(tta)3} units are bound to the N,N-bidentate compartments of BPTZ. Crystal structures of the dinuclear complexes [{Yb(tta)3}2(μ-BPTZ)]·CH2Cl2 and [{Gd(tta)3}2(μ-BPTZ)]·2CH2Cl2 show that the metal centres have an approximately square-antiprismatic eight-coordinate geometry; there are close contacts above and below the plane of the BPTZ bridging ligand between peripheral trifluoromethyl groups from a tta ligand associated with each metal centre. It is not apparent why the larger lanthanides La and Nd only give a mononuclear complex whereas the smaller lanthanides Gd, Er and Yb give the dinuclear complex in each case. UV/Vis spectroscopic titrations of a solution of BPTZ in CH2Cl2 with increasing amounts of [Ln(tta)3(H2O)2] (Ln = La and Yb) show very similar behaviour, with stepwise binding constants K1 and K2 for association of the two {Ln(tta)3} units of ca. 106 M−1 and 105 M−1; allowing for the expected statistical factor of 4 there is an additional reduction in the value of K2 compared to K1 which may be associated with a steric interaction between the two {Ln(tta)3} units when the dinuclear complex forms. Steady-state and time-resolved luminescence studies on the complexes with Yb, Nd and Er, both in the solid state and CH2Cl2 solution, show that near-IR luminescence on the microsecond timescale can be sensitised by irradiation either at 337 nm into the tta-based transition, or at 520 nm into the low-energy BPTZ-centred transition.

Preferential Binding of Quinolones to DNA With Alternating G, C/A, T Sequences: A Spectroscopic Study

The binding of quinolones, nalidixic acid (Nal), oxolinic acid (Oxo) with double stranded polynucleotides was undertaken by using UV-melting, UV-Vis absorption, fluorescence and CD spectroscopic techniques. The binding of Nal or Oxo to the polynucleotides under low- salt buffer conditions were determined for poly (dA)·(dT), poly [d(A-T)], poly (dG)·(dC), poly [d(G-C)] and E. coli DNA. The fluorescence data were analyzed using a previously established two step mechanism with two different DNA-Drug complexes [Rajeswari et al, Biochemistry 26, 6825–31 (1987)]. The first complex [DN]1 with a binding constant K1, is formed where the interactions are ‘nonspecific’ and complex [DN]2 with a binding constant K2, is formed where the interactions are “specific” which involve (additional) hydrophobic type of interactions like ‘stacking’ of the drug and the overall association constant is represented as K(=K1K2). The order of binding for Nal and Oxo is: poly [d(G-C)] > poly [d(A- T)] > E. coli > poly (dG)·(dC) > poly (dA)·(dT). Interaction of quinolones seems to be preferential in the alternating G, C or A, T stretches of DNA than those of non-alternating. Within any alternating or non-alternating in DNA sequences the G, C rich sequences have distinctly greater binding than A, T sequences. The overall association constant data (K) reveal higher binding of Oxo to DNA compared to Nal to any given polynucleotide investigated; which also explains the higher antibacterial potency of Oxo. Changes in the absorption difference spectra and in circular dichroic spectra also manifest these results. As the melting temperatures of the polynucleotides were only marginally raised in presence of the quinolone, we rule out the possibility of ‘classical intercalation’ of the drug. Amino group of guanine facilitates the binding of quinolones and therefore has the greater binding with the DNA. However, poly (dG)·(dC) is known to exist in ‘A’ conformation which is not adopted by quinolones as in the case of poly (dA)·(dT). Present results suggest that Nal or Oxo bind to DNA in a non-classical fashion which is partially stacking in nature.

Monitoring and Kinetic Parameter Estimation for the Binding Process of Berberine Hydrochloride to Bovine Serum Albumin with Piezoelectric Quartz Crystal Impedance Analysis

A new method for monitoring, in real time, the drug-binding process to protein with piezoelectric quartz crystal impedance (PQCI) is proposed. The method was used to monitor the binding process of berberine hydrochloride to bovine serum albumin (BSA). BSA was immobilized on the silver electrode surface of a piezoelectric quartz crystal and the optimized experimental conditions were established. The BSA-coated piezoelectric sensor was in contact with berberine solution. The time courses of the resonant frequency and equivalent circuit parameters of the sensor during the protein–drug binding were simultaneously obtained. On the basis of the analysis of the multidimensional information provided by PQCI, it was concluded that the observed frequency decrease was mainly ascribed to the mass increase of the sensor surface resulting from the binding. According to the frequency decrease with time, the kinetics of the binding process were quantitatively studied. A piezoelectric response model for the binding was theoretically derived. Fitting the experimental data to the model, the kinetic parameters, such as the binding and dissociation rate constants (k1 and k−1) and the binding equilibrium constant (Ka), were determined. The k1, k−1, and Ka values obtained at 25°C were 67.5 (±0.1) (mol liter−1)−1 s−1, 1.7 (± 0.1) × 10−3 s−1, and 3.97 (± 0.06) ×104 (mol liter−1)−1, respectively.

Sulfite Stabilization and Reduction of the Aqueous Mercuric Ion: Kinetic Determination of Sequential Formation Constants

The aqueous sulfite ion reacts with Hg2+(aq) to form 1:1 and 2:1 coordination complexes. The Hg(SO3)22- complex is redox stable. However, dissociation of a sulfite ligand forms redox-unstable HgSO3. Under conditions where Hg(SO3)22- predominates, the rate of reduction of the mercuric ion to Hg0 by coordinated sulfite depends inversely on the concentration of uncoordinated sulfite, while it is unaffected by the amount of sulfite liberated by dissociation. Analysis of the kinetics yields the sequential sulfite binding constants K1 = 2.1 × 1013 and K2 = 1.0 × 1010 at μ = 0.10 M. These values lead to the prediction that HgSO3 is more abundant in clouds than is Hg(SO3)22- under virtually all atmospheric conditions. The product of the redox reaction appears to be a strongly bound Hg0·SO2 complex, which is at least 3 orders of magnitude more soluble than uncomplexed Hg0(aq). This finding may have important implications for the partitioning of atmospheric mercury from the gas phase into atmospheric water droplets...