Parameter Ka Research Articles

Measurement of O2 Binding by Sensory Hemeproteins.

The discovery of an increasing number of proteins that function in the detoxification and sensing of gaseous ligands has renewed interest in hemeproteins. It is critical to measure the affinities of these proteins for ligands like O2, CO, and NO, know with confidence when a protein is fully saturated with a specific ligand, and be able to estimate how well a ligand will compete against other ligands for a specific protein. Below we describe how to obtain an intact O2-binding hemeprotein with a full complement of heme, how to evaluate the factors that can impact its affinity for O2, and how to determine accurately the equilibrium and kinetic parameters Kd, kon, and koff for O2 binding.

A parameterized perspective on protecting elections

We study the parameterized complexity of the Optimal Defense and Optimal Attack problems in voting. In both the problems, the input is a set of voter groups (every voter group is a district consisting of a set of votes) and two integers ka and kd corresponding to respectively the number of voter groups the attacker can attack and the number of voter groups the defender can defend. A voter group gets removed from the election if it is attacked but not defended. In the Optimal Defense problem, we want to know if it is possible for the defender to commit to a strategy of defending at most kd voter groups such that, no matter which ka voter groups the attacker attacks, the outcome of the election does not change. In the Optimal Attack problem, we want to know if it is possible for the attacker to commit to a strategy of attacking ka voter groups such that, no matter which kd voter groups the defender defends, the outcome of the election is always different from the original one (without any attack). We show that both the Optimal Defense problem and the Optimal Attack problem are computationally intractable for every scoring rule and the Condorcet voting rule even when we have only 3 candidates. We also show that the Optimal Defense problem for every scoring rule and the Condorcet voting rule is W[2]-hard for both the parameters ka and kd, while it admits a fixed parameter tractable algorithm parameterized by the combined parameter (ka,kd). The Optimal Attack problem for every scoring rule and the Condorcet voting rule turns out to be much harder – it is W[1]-hard even for the combined parameter (ka,kd). We propose two greedy algorithms for the Optimal Defense problem and empirically show that they perform effectively on many voting profiles.

Application of the SPR Biosensor for the Analysis of Protein–Protein Interactions in Aqueous Environment and Bilayer Lipid Membrane As Exemplified by P450scc (CYP11A1)

Protein–protein interactions (PPIs) are crucial for the successful realization of many metabolic and signaling pathways. Of particular interest are PPIs of membrane proteins, which form stable and/or transient complexes for the signal transduction, ion transport, and electron transfer within electron transfer chains. The Surface Plasmon Resonance (SPR) allows analyzing the thermodynamic and kinetic parameters (kon and koff) and equilibrium constants (Kd) of PPI, as well as the assessment of the effects of low molecular weight compounds. The aim of the present study was the adaptation of the SPR protocols for PPIs involving mitochondrial cytochrome P450 CYP11A1, mitochondrial cytochrome b5 (CYB5B), and adrenodoxin (Adx). We found that the Adx–CYP11A1 and CYB5B–CYP11A interactions depend on the method of protein immobilization and on the microenvironment. For example, the koff values for complexes Adx–CYP11A1 and CYB5B–CYP11A1 in the aqueous environment were similar (1.5 ± 0.2) × 10–3 s–1, while the values of kon for these complexes differed from each other by almost one order of magnitude ((6.5 ± 0.5) × 104 and (0.30 ± 0.03) × 104 M–1 s–1, respectively). This is in good agreement with the known high affinity of CYP11A1 to its cognate redox partner Adx. In the lipid environment, the rate of complex dissociation was higher than that in the aqueous environment with koff value equal to (9.1 ± 0.3) × 10–3 s–1. For the CYP11A1–CYB5B complex, the parameters of interaction in the lipid phase were not determined due to unspecific binding of the proteins used as analytes to the lipids immobilized on the L1 chip. We show for the first time that SPR method could be used for the detection and quantitative analysis of PPI involving mitochondrial cytochromes (CYP) with their redox partners in both aqueous and lipid environment. Experimental protocols developed and validated in our previous work and in this one can serve as valuable tools for studies of interactions of CYP proteins and could also be applied for other membrane proteins.

Mechanism and optimization of supramolecular complexation-enhanced fluorescence spectroscopy for the determination of SN-38 in plasma and cells.

Quantitative detection of two different forms of SN-38 in biological samples is, currently, cumbersome and difficult. A revisit to the mechanism of supramolecular complexation-enhanced fluorescence spectroscopy helps to optimize the determination of SN-38 in plasma and the cellular pharmacokinetics in A549 cells based on the supramolecular complexation. Firstly, the inclusion mechanism dominated by thermodynamic constants was determined by measuring kinetic/thermodynamic parameters (kon , koff , ΔG, ΔH, ΔS). On this basis, the best effect of fluorescence sensitization was optimized through screening the interaction conditions (cyclodextrin species and concentrations, drug levels, temperature, pH of the buffer, and reaction time). Furthermore, the proportional relationship between the concentration of the inclusion complex and the fluorescence intensity was confirmed. Finally, a highly sensitive, selective spectrofluorimetric method was established and validated for quantitative analysis of the lactone and carboxylate molecular states of SN-38 plasma levels in rats and cell membrane transfer kinetics in A549 cell lines. The limits of detection for the lactone and carboxylate forms in plasma were found to be 0.44 ng·ml-1 and 0.28 ng·ml-1 , respectively. Precision and accuracy met the requirements of biological samples analysis. The proposed detection method provided a reference for elucidating the biodistribution of SN-38.

Conductametric studies of some organotellurium(IV) trihalides

The electrical conductance of a series of aryl tellurium trihalides (i.e. pRC6H4TeX3: R=H, OCH3, Cl; X=Cl, Br, I) has been measured in dimethylsulphoxide(DMSO) and dimethylformamide(DMF) at 298K. The results indicated that their behavior was as weak electrolytes. The conductance data were analyzed by a minimization technique using complete and modified equations of Pitt (P) and Fuoss - Hsia (F/H) equations. The variation in the three parameters KA, Ʌo and a was fully investigated.

Determination of glass transition temperature and surface properties of novel chalcone modified poly (styrene) based polymer

The novel chalcone modified poly (styrene) based polymer (PVBC-DMAC) has been prepared and characterized. By using the inverse gas chromatography method, we determined glass transition temperature and surface properties of PVBC-DMAC. The obtained glass transition temperature, Tg, is a good agree with the one obtained by differential scanning calorimetry. Also considering some isomeric alcohol and acetate solvents in the temperature range from 303.2 K to 353.2 K, we investigated the polymer selectivity. The parameters KA(acidic) and KD(basic) of the PVBC-DMAC surface were calculated. The obtained KA, KD values reflected that PVBC-DMAC surface has a basic character.

General Pharmacokinetic Features of Small-Molecule Compounds Exhibiting Target-Mediated Drug Disposition (TMDD): A Simulation-Based Study.

Although target-mediated drug disposition (TMDD) can occur in both large- and small-molecule compounds, TMDD in small-molecule compounds has received much less attention due to its lower prevalence. To facilitate the identification of nonlinear pharmacokinetics of small-molecule compounds caused by TMDD, a comprehensive simulation was conducted in the current study to provide the general pharmacokinetic features of small-molecule compounds exhibiting TMDD. Various conditions, including single escalating intravenous bolus doses, multiple escalating intravenous bolus doses, and intravenous infusion, were simulated for small-molecule compounds with saturable binding to (1) targets located in tissues and (2) targets located in plasma. Sobol global sensitivity analysis was performed to evaluate the impact of key parameters (Rmax , kon and koff ) in a small-molecule TMDD model on the apparent volume of distribution and apparent clearance. Our simulation data indicated that small-molecule compounds with saturable binding to targets in plasma demonstrate distinctly different TMDD behavior compared with those with binding to targets in tissue. Sobol global sensitivity analysis results showed that, in general, koff is much more influential than kon and Rmax on apparent clearance and apparent volume of distribution. The TMDD features predicted in various situations in the current work could serve as a valuable reference to help quickly recognize TMDD when it does happen in a small-molecule compound. The TMDD principals summarized based on our simulation could be used to aid pharmacokinetic data interpretation, dose regimen optimization, and clinical trial design of small-molecule drugs exhibiting TMDD.

The optimisation of chromatographic conditions for the determination of acceptor-donor properties of graphene oxide and reduced graphene oxide

The oxidised and reduced graphene samples (having different surface functionalities) were studied by inverse gas chromatography to characterise their acceptor-donor properties. The DN values denoting the donor number in the Gutmann scale and the AN* values denoting the acceptor number in the Riddle-Fowkes scale have been chosen in the estimation of the electron-acceptor parameter KA and electron-donor parameter KD values

Pharmacokinetics of sildenafil in children with pulmonary arterial hypertension.

Recently, sildenafil was introduced to treat pulmonary arterial hypertension (PAH); however, there are currently few studies on the pharmacokinetics of sildenalfil in children. Therefore, we aimed to carry out a pharmacokinetic study of sildenafil in children with PAH using a single dose. Twelve children diagnosed with PAH, consisting of with ten males and two females, were recruited for the study after obtaining written consent from their parents or guardians. Blood samples were obtained predose and at 0.25, 0.5, 1, 2, 4, 8 and 12 hours after the oral administration of 1 mg/kg of sildenafil using an extemporal pediatric formulation developed in our laboratory. The samples were analyzed using a previously validated high performance liquid chromatography method. A pharmacokinetic analysis using the WinNonlin 3.1 program that considered the Akaike information criterion (AIC) for selecting a more adjustable model was performed. The following pharmacokinetic parameters were obtained: maximal concentration (Cmax): 366±179 ng/mL, time to maximal concentration: 0.92±0.30 hours, elimination half-life (t1/2): 2.41±1.18 hours, total clearance (CLtot/F): 5.85±2.81 L/hour, volume of distribution (Vd/F): 20.13±14.5 L, absorption rate constants (Ka): 0.343 hour-1, elimination rate (Ke): 0.35 hour-1, area under curve from zero to infinity: 2061±618 ng/mL/hour. The data of all patients adjusted to the model of one compartment were corroborated using AIC. The parameters Ka, Ke and t1/2 were found to be similar to those reported in adults; however, the values of Cmax and Vd/F were significantly higher. Based on these findings, we propose that treatment regimen of sildenafil be adjusted in children with PAH.

Discovery and Kinetic Profiling of 7-Aryl-1,2,4-triazolo[4,3-a]pyridines: Positive Allosteric Modulators of the Metabotropic Glutamate Receptor 2.

We report the synthesis and biological evaluation of a series of 7-aryl-1,2,4-triazolo[4,3-a]pyridines with mGlu2 positive allosteric modulator (PAM) activity and affinity. Besides traditional in vitro parameters of potency and affinity, kinetic parameters kon, koff and residence time (RT) were determined. The PAMs showed various kinetic profiles; kon values ranged over 2 orders of magnitude, whereas RT values were within a 10-fold range. Association rate constant kon was linearly correlated to affinity. Evaluation of a short, medium, and long RT compound in a label-free assay indicated a correlation between RT and functional effect. The effects of long RT compound 9 on sleep-wake states indicated long RT was translated into sustained inhibition of rapid eye movement (REM) in vivo. These results show that affinity-only driven selection would have resulted in mGlu2 PAMs with high values for kon but not necessarily optimized RT, which is key to predicting optimal efficacy in vivo.

Analyses of Morphological Properties of a Generalized Miura Origami Structure

In this paper, we generalize Miura origami and propose a method for analyzing a generalized Miura origami structure. Morphological properties of the generalized Miura origami element during the deploy motion are analyzed using the proposed method, which mainly utilizes the principle of spherical trigonometry and is verified in the folding limit state. The longitudinal length, horizontal length, and height of the generalized Miura origami element are defined and obtained using the proposed method. Results show the relationship between the range of deployment and the element parameters as well as the changes of the folding plane angles in the deployment process. During the deploy motion, both the longitudinal and horizontal length increased while the height decreased. However, the change speed of horizontal length decreased, whereas those of longitudinal length and height initially increased and then decreased. The increment of the folding element angle difference Δα reduced folding range and put off the severe change time of longitudinal length and height. The length parameters Ka, Kb, and Kab had slight effects on the results, but their changes did not alter the change trends. These results are useful to the design of fold structure and analysis of errors in standard Miura-ori structures.

Extending ITC to Kinetics with kinITC.

Isothermal titration calorimetry (ITC) has long been used for kinetic studies in chemistry, but this remained confined to enzymatic studies in the biological field. In fact, the biological community has long had the tendency of ignoring the kinetic possibilities of ITC considering it solely as a thermodynamic technique, whereas surface plasmon resonance is seen as the kinetic technique par excellence. However, the primary signal recorded by ITC is a heat power which is directly related to the kinetics of the reaction. Here, it is shown how this kinetic signal can be recovered by using kinITC, the kinetic extension of ITC. The theoretical basis of kinITC is detailed for the most common situation of a second-order reaction A+B Ω C characterized by kinetic parameters kon, koff. A simplified kinITC-ETC method based upon the determination of an "Equilibration Time Curve" (ETC) is presented. The ETC is obtained by automatic determination of the "effective end" of each injection. The method is illustrated with experimental results with a comparison to Surface Plasmon Resonance (SPR) data. kon values were obtained in a wide range, from 10(3) to 0.5×10(6) M(-1) s(-1). All procedures were implemented in the program AFFINImeter (https://www.affinimeter.com/).

Abstract 1362: Distinct binding mode of lenvatinib to VEGFR2 revealed by biochemical characterization

Abstract Background: Lenvatinib mesilate (lenvatinib) selectively inhibits vascular endothelial growth factor receptors (VEGFR1-3), and other proangiogenic and oncogenic pathway-related RTKs including fibroblast growth factor receptors (FGFR1-4), the platelet-derived growth factor receptor (PDGFR) α, KIT, and RET. Lenvatinib is currently evaluated in several clinical trials, including two phase 3 clinical trials in patients with thyroid cancers and hepatocellular carcinoma. Recently, lenvatinib achieved the primary endpoint in a phase 3 clinical trial in patients with differentiated thyroid cancer. To gain insight into the origin of the potency of lenvatinib in VEGFR2 inhibition, crystal structure analysis of VEGFR2 complexed with lenvatinib and kinetics interaction analysis of lenvatinib against VEGFR2 were conducted in comparison with other VEGFR2 inhibitors. Experimental procedures: Recombinant human VEGFR2 was crystalized with lenvatinib or sorafenib, respectively. The resulting crystals of kinase-inhibitor complexes were subjected to x-ray structural analysis and the three dimensional structures were solved. The reporter displacement assay was conducted by using recombinant human VEGFR2 and a synthetic reporter probe. Reporter displacement was measured after addition of compounds and the kinetic parameters were determined. Results: In crystal structure analysis, both lenvatinib and sorafenib bind to the ATP-binding site and the neighboring allosteric region. However there was a notable difference in the conformation of the DFG motif in the activation loop. While DFG motif assumed a DFG-out conformation in the complex with sorafenib as reported, it was maintained in a DFG-in conformation in the complex with lenvatinib. In the reporter displacement assay, lenvatinib showed intermediate binding kinetics of those of sorafenib and sunitinib. Its association rate constant (kon) and dissociation rate constant (koff) values were 4.8 × 105 s−1 × M−1 (61 times of sorafenib, a representative type 2 inhibitor) and 9.9 × 10−4 s−1 (3.8 times), respectively. Sunitinib, a representative type 1 VEGFR2 inhibitor had a much faster binding kinetics and we could not determine kinetics parameters (kon>1.9 × 105, koff >57 × 10−4). Conclusions: Lenvatinib was suggested to have interaction with not only ATP region but also the neighboring allosteric region of VEGFR2, which is a typical feature of type 2 inhibitors. However, VEGFR2 adopted DFG-in conformation in complex with lenvatinib, which is a characteristic of type 1 inhibitors. Kinetics analysis revealed that lenvatinib had intermediate characteristics among these three types of VEGFR2 inhibitors. These results suggest lenvatinib is very distinct in its ability in binding with VEGFR2. Citation Format: Kiyoshi Okamoto, Megumi Ikemori Kawada, Anja Jestel, Konstanze von König, Yasuhiro Funahashi, Tomohiro Matsushima, Akihiko Tsuruoka, Atsushi Inoue, Junji Matsui. Distinct binding mode of lenvatinib to VEGFR2 revealed by biochemical characterization. [abstract]. In: Proceedings of the 106th Annual Meeting of the American Association for Cancer Research; 2015 Apr 18-22; Philadelphia, PA. Philadelphia (PA): AACR; Cancer Res 2015;75(15 Suppl):Abstract nr 1362. doi:10.1158/1538-7445.AM2015-1362

Characterization of surface properties of 1-allyl-3-methylimidazolium chloride ionic liquid by inverse gas chromatography

The determination of the dispersive component of surface free energies (gamma(s)d) at different temperatures and Lewis acid-base parameters of 1-allyl-3-methylimidazolium chloride ionic liquid ([AMIM]Cl) were investigated by means of inverse gas chromatography (IGC). Four n-alkanes, including n-hexane (C6), n-heptane (C7), n-octane (C8) and n-nonane (C9), were chosen as the apolar probes to characterize the dispersive component of the surface free energies at 343.15, 353.15, 363.15 and 373.15 K, respectively; and dichloromethane (DCM), trichloromethane (TCM), tetrahydrofuran (THF), ethyl acetate (EtAc), acetone (Acet) as the polar probes to estimate the Lewis acid-base parameters to judge the interactions between [AMIM] Cl and the solvents. The IGC characterizations encompassed the adsorption thermodynamic parameters to acid-base surface interactions, including the standard enthalpy (deltaHa(s)) and the free energy change of adsorption (deltaGa(s)) at different temperatures. The results showed that the Lewis acid parameter Ka of [AMIM] Cl was 0.34, and the base parameter Kb was 1.68, which indicated it was Lewis amphoteric with predominantly basic character. Furthermore, the free energy of adsorption deltaGa(s) was also figured out. It was found that the gamma(s)d of the [AMIM] Cl were 52.26, 50.82, 46.08 and 42.05 mJ/m2 at 343.15, 353.15, 363.15 and 373.15 K, respectively. The results are of great importance to the study of the surface properties and the application of ionic liquid.

Furin-cleaved Proprotein Convertase Subtilisin/Kexin Type 9 (PCSK9) Is Active and Modulates Low Density Lipoprotein Receptor and Serum Cholesterol Levels

Proprotein convertase subtilisin/kexin 9 (PCSK9) regulates plasma LDL cholesterol levels by regulating the degradation of LDL receptors. Another proprotein convertase, furin, cleaves PCSK9 at Arg(218)-Gln(219) in the surface-exposed "218 loop." This cleaved form circulates in blood along with the intact form, albeit at lower concentrations. To gain a better understanding of how cleavage affects PCSK9 function, we produced recombinant furin-cleaved PCSK9 using antibody Ab-3D5, which binds the intact but not the cleaved 218 loop. Using Ab-3D5, we also produced highly purified hepsin-cleaved PCSK9. Hepsin cleaves PCSK9 at Arg(218)-Gln(219) more efficiently than furin but also cleaves at Arg(215)-Phe(216). Further analysis by size exclusion chromatography and mass spectrometry indicated that furin and hepsin produced an internal cleavage in the 218 loop without the loss of the N-terminal segment (Ser(153)-Arg(218)), which remained attached to the catalytic domain. Both furin- and hepsin-cleaved PCSK9 bound to LDL receptor with only 2-fold reduced affinity compared with intact PCSK9. Moreover, they reduced LDL receptor levels in HepG2 cells and in mouse liver with only moderately lower activity than intact PCSK9, consistent with the binding data. Single injection into mice of furin-cleaved PCSK9 resulted in significantly increased serum cholesterol levels, approaching the increase by intact PCSK9. These findings indicate that circulating furin-cleaved PCSK9 is able to regulate LDL receptor and serum cholesterol levels, although somewhat less efficiently than intact PCSK9. Therapeutic anti-PCSK9 approaches that neutralize both forms should be the most effective in preserving LDL receptors and in lowering plasma LDL cholesterol.

Similarity and grouping of perlite and zeolite abrasive fillers: A replacement test

AbstractInverse gas chromatography was used to estimate surface activity expressed by the dispersive component of the surface free energy, γ, as well as parameters KA and KD describing surface ability to act as electron acceptor and donor, respectively. These parameters characterize the ability of the surface to specific interactions. The method was also applied to describe the magnitude of filler‐phenolic resin interaction by Flory‐Huggins parameter, χ′23. Granulation, surface area and porosity were also determined. The minimum number of parameters required to complete characterization of filler properties has been selected by principal component analysis. The usefulness of the selection for the abrasive industry has been proven. Moreover, the similarities and deviations from “an average” filler was determined by chemometric methods. Principal component analysis (PCA) and a novel procedure based on sum of ranking differences (SRD) were successfully applied for selection of the best fillers, and of advantageous parameters for characterization of the fillers. Similar and diverse fillers have been chosen based on clustering pattern by PCA and SRD. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2013

Measurement of 5-HT1A Receptor Density and in-vivo Binding Parameters of [18F]mefway in the Nonhuman Primate

The goal of this work was to characterize the in-vivo behavior of [(18)F]mefway as a suitable positron emission tomography (PET) radiotracer for the assay of 5-hydroxytryptamine(1A) (5-HT(1A)) receptor density (B(max)). Six rhesus monkeys were studied using a multiple-injection (M-I) protocol consisting of three sequential bolus injections of [(18)F]mefway. Injection times and amounts of unlabeled mefway were optimized for the precise measurement of B(max) and specific binding parameters k(off) and k(on) for estimation of apparent K(D). The PET time series were acquired for 180 minutes with arterial sampling performed throughout. Compartmental analysis using the arterial input function was performed to obtain estimates for K(1), k(2), k(off), B(max), and K(Dapp) in the cerebral cortex and raphe nuclei (RN) using a model that accounted for nontracer doses of mefway. Averaged over subjects, highest binding was seen in the mesial temporal and dorsal anterior cingulate cortices with B(max) values of 42±8 and 36±8 pmol/mL, respectively, and lower values in the superior temporal cortex, RN, and parietal cortex of 24±4, 19±4, and 13±2 pmol/mL, respectively. The K(Dapp) of mefway for the 5-HT(1A) receptor sites was 4.3±1.3 nmol/L. In conclusion, these results show that M-I [(18)F]mefway PET experiments can be used for the in-vivo measurement of 5-HT(1A) receptor density.

Evidence of Direct Binding of G-Actin and Calmodulin to PMCA by Surface Plasmon Resonance

Previous studies of our laboratory suggest that the main isoform of the plasma membrane calcium ATPase (PMCA) from erythrocytes, PMCAh4b, associates with the actin cytoskeleton and its catalytic activity can be regulated through this interaction. Apparently, G-actin and/or short oligomers enhance the catalytic activity of the pump, while F-actin seems to inhibit it. To further explore the interaction between PMCA and G-actin, we performed binding experiments based on Surface Plasmon Resonance technology (SPR) using purified PMCAh4b from erythrocytes and purified rabbit muscle G-actin on a BIAcore T100 system. Our strategy consisted in immobilizing G-actin to the sensor chip surface while PMCA constituted the analyte (125 nM to 2 μM). The sensorgrams obtained showed an increase in the response as a function of PMCA concentration with a saturable binding. The unspecific binding values were subtracted from the response obtained in the control flow cell (without immobilized G-actin). The apparent KD (1.25 μM) was determined by kinetic analysis with parameters kon (1.33±0.07) 104 M-1s-1 and koff (1.66±0.03) 10-2 s-1.Conversely, we immobilized PMCAh4b to the sensor chip surface. The analytes were (i) G-actin (0.6 to 5 μM) or (ii) Calmodulin, a known activator of PMCAh4b (1.8 to 15 nM). Results show that G-actin binds to the activated sensor with KD=3μM, kon (2.98±0.45) 104 M-1s-1 and koff (8.98±0.67) 10-2 s-1 and calmodulin binds with an apparent KD of (1.14±0.6) 10-8 M. This last value agrees with the known value of calmodulin binding affinity determined by other methods.These results show a specific and high apparent affinity binding between PMCA and G-actin and reveal the usefulness of SPR technology to determine binding constants between small molecules and a large membrane protein like the plasmatic calcium pump. With grants of ANPCYT/CONICET/UBACYT.

Investigation into the froth flotation and selection of reagents on the basis of the mechanism of their action report 2. A comparison of flotation properties of millimeter, micrometer, and nanometer bubbles based on equations of capillary physics (Part Two)

The influence of the capillary pressure Pca of gas in microbubbles on bubble spread over a substrate (particle) after adhesion is considered (for bubbles ranging in size from 2 mm to 20 nm). The dimensionless parameter Ka characterizes the microbubble spread with decrease in the bubble form factor β by no more than 0.000001 of its initial value. There is a clear symbatic relation between Pca and Ka. The microbubble begins to spread when it measures 200 μm; its motion increases markedly as it becomes smaller. With decrease in bubble size, the rock and slurry particles adhering to its surface are removed. Of course, this enhances the foam quality.

High frequency dispersion model for the water-saturated granular medium

Dispersion relation for the p-wave sound speed and attenuation has been described by several models based on continuum or scattering theory. As an alternative approach, this study proposes a model describing the dispersion relation for the p-wave in case of grain scatterers existing in background porous medium. Dispersion relations are shown as a function of different grain size distribution and Rayleigh parameter ka. For quantitative analysis of the proposed model, experiments are performed using water-saturated glass beads. Two sets of experiments employing unimodal and bimodal grain size distributions are performed and are used for comparison with the current proposed model.