New magnetic nano-absorbent for the determination of n-octanol/water partition coefficients

A novel and generic miniaturization methodology for the determination of partition coefficient values of organic compounds in noctanol/water by using magnetic nanoparticles is, for the first time, described. We have successfully designed, synthesised and characterised new colloidal stable porous silica-encapsulated magnetic nanoparticles of controlled dimensions. These nanoparticles absorbing a tiny amount of n-octanol in their porous silica over-layer are homogeneously dispersed into a bulk aqueous phase (pH 7.40) containing an organic compound prior to magnetic separation. The small size of the particles and the efficient mixing allow a rapid establishment of the partition equilibrium of the organic compound between the solid supported n-octanol nano-droplets and the bulk aqueous phase. UV-vis spectrophotometry is then applied as a quantitative method to determine the concentration of the organic compound in the aqueous phase both before and after partitioning (after magnetic separation). log D values of organic compounds of pharmaceutical interest (0.65-3.50), determined by this novel methodology, were found to be in excellent agreement with the values measured by the shake-flask method in two independent laboratories, which are also consistent with the literature data. It was also found that this new technique gives a number of advantages such as providing an accurate measurement of log D value, a much shorter experimental time and a smaller sample size required. With this approach, the formation of a problematic emulsion, commonly encountered in shake-flask experiments, is eliminated. It is envisaged that this method could be applicable to the high throughput log D screening of drug candidates. (c) 2005 Elsevier B.V. All rights reserved.

Preparation of nanomagnetic absorbent for partition coefficient measurement

In this paper, we report a new method based on supercritical carbon dioxide (scCO(2)) to fill and distribute the porous magnetic nanoparticles with n-octanol in a homogeneous manner. The high solubility of n-octanol in scCO(2) and high diffusivity and permeability of the fluid allow efficient delivery of n-octanol into the porous magnetic nanoparticles. Thus, the n-octanol-loaded magnetic nanoparticles can be readily dispersed into aqueous buffer (pH 7.40) to form a homogenous suspension consisting of nano-sized n-octanol droplets. We refer this suspension as the n-octanol stock solution. The n-octanol stock solution is then mixed with bulk aqueous phase (pH 7.40) containing an organic compound prior to magnetic separation. The small-size of the particles and the efficient mixing enable a rapid establishment of the partition equilibrium of the organic compound between the solid supported n-octanol nano-droplets and the bulk aqueous phase. UV-vis spectrophotometry is then applied to determine the concentration of the organic compound in the aqueous phase both before and after partitioning (after magnetic separation). As a result, log D values of organic compounds of pharmaceutical interest determined by this modified method are found to be in excellent agreement with the literature data. (c) 2006 Elsevier B.V. All rights reserved.

Quantitative affinity chromatography

The objective of this review is to summarize developments in the use of quantitative affinity chromatography to determine equilibrium constants for solute interactions of biological interest. Affinity chromatography is an extremely versatile method for characterizing interactions between dissimilar reactants because the biospecificity incorporated into the design of the affinity matrix ensures applicability of the method regardless of the relative sizes of the two reacting solutes. Adoption of different experimental strategies, such as column chromatography, simple partition equilibrium experiments, solid-phase immunoassay, and biosensor technology, has led to a situation whereby affinity chromatography affords a means of characterizing interactions governed by an extremely broad range of binding affinities-relatively weak interactions (binding constants below 10(3) M-1) through to interactions with binding constants in excess of 10(9) M-1. In addition to its important role in solute separation and purification, affinity chromatography thus also possesses considerable potential for investigating the functional roles of the reactants thereby purified. (C) 2001 Elsevier Science B.V. All rights reserved.

Determination of binding constants by affinity chromatography

This review summarizes developments in the use of affinity chromatography to characterize biospecific interactions in terms of reaction stoichiometry and equilibrium constant. In that regard, the biospecificity incorporated into the design of the experiment ensures applicability of the method regardless of the sizes of the reacting solutes. By the adoption of different experimental strategies (column chromatography, simple partition equilibrium, solid-phase immunoassay and biosensor technology protocols) quantitatiative affinity chromatography can be used to characterize interactions governed by an extremely broad range of binding affinities. In addition, the link between ligand-binding studies and quantitative affinity chromatography is illustrated by means of partition equilibrium studies of glycolytic enzyme interactions with muscle myofibrils. an exercise which emphasizes that the same theoretical expressions apply to naturally occurring examples of affinity chromatography in the cellular environment. (C) 2004 Elsevier B.V. All rights reserved.

Polyethylene glycol 8000+ citrate salts aqueous two-phase systems: Relative hydrophobicity of the equilibrium phases

The Gibbs free energy of transfer of a methylene group, G*(CH2), is reported as a measure of the relative hydrophobicity of the equilibrium phases. Furthermore, G*(CH2) is a characteristic parameter of each tie-line, and for that reason can be used for comparing different tie-lines of a given aqueous two-phase system (ATPS) or even to establish comparisons among different ATPSs. In this work, the partition coefficients of a series of four dinitrophenylated-amino acids were experimentally determined, at 23 °C, in five different tie-lines of PEG8000(sodium or potassium) citrate ATPSs. G*(CH2) values were calculated from the partition coefficients and used to evaluate the relative hydrophobicity of the equilibrium phases. PEG8000potassium citrate ATPSs presented larger relative hydrophobicity than PEG8000sodium citrate ATPSs. Furthermore, the results obtained indicated that the PEG-rich phase (top phase) has higher affinity to participate in hydrophobic hydration interactions than the salt-rich phase (bottom phase).

A Strategic-Equilibrium Based

The strategic equilibrium of an N-person cooperative game with transferable utility is a system composed of a cover collection of subsets of N and a set of extended imputations attainable through such equilibrium cover. The system describes a state of coalitional bargaining stability where every player has a bargaining alternative against any other player to support his corresponding equilibrium claim. Any coalition in the sable system may form and divide the characteristic value function of the coalition as prescribed by the equilibrium payoffs. If syndicates are allowed to form, a formed coalition may become a syndicate using the equilibrium payoffs as disagreement values in bargaining for a part of the complementary coalition incremental value to the grand coalition when formed. The emergent well known-constant sum derived game in partition function is described in terms of parameters that result from incumbent binding agreements. The strategic-equilibrium corresponding to the derived game gives an equal value claim to all players.  This surprising result is alternatively explained in terms of strategic-equilibrium based possible outcomes by a sequence of bargaining stages that when the binding agreements are in the right sequential order, von Neumann and Morgenstern (vN-M) non-discriminatory solutions emerge. In these solutions a preferred branch by a sufficient number of players is identified: the weaker players syndicate against the stronger player. This condition is referred to as the stronger player paradox.  A strategic alternative available to the stronger players to overcome the anticipated not desirable results is to voluntarily lower his bargaining equilibrium claim. In doing the original strategic equilibrium is modified and vN-M discriminatory solutions may occur, but also a different stronger player may emerge that has eventually will have to lower his equilibrium claim. A sequence of such measures converges to the equal opportunity for all vN-M solution anticipated by the strategic equilibrium of partition function derived game.    [298-words]

Liquid-Liquid Equilibrium Data for the System Lard plus Oleic Acid plus Ethanol + Water at 318.2 K: Cholesterol Distribution Coefficients

This research reports liquid liquid equilibrium data for the system lard (swine fat), cis-9-octadecenoic acid (oleic acid), ethanol, and water at 318.2 K, as well as their correlation with the nonrandom two-liquid (NRTL) and universal quasichemical activity coefficient (UNIQUAC) thermodynamic equations, which have provided global deviations of 0.41 % and 0.53 %, respectively. Additional equilibrium experiments were also performed to obtain cholesterol partition (or distribution) coefficients to verify the availability of the use of ethanol plus water to reduce the cholesterol content in lard. The partition experiments were performed with concentrations of free fatty acids (commercial oleic acid) that varied from (0 to 20) mass % and of water in the solvent that varied from (0 to 18) mass %. The percentage of free fatty acids initially present in lard had a slight effect on the distribution of cholesterol between the phases. Furthermore, the distribution coefficients decreased by adding water in the ethanol; specifically, it resulted in a diminution of the capability of the solvent to remove the cholesterol.

Topics in equilibrium and nonequilibrium thermodynamics: computing crystalline free energies and engineering Maxwell’s demon.

This dissertation covers two separate topics in statistical physics. The first part of the dissertation focuses on computational methods of obtaining the free energies (or partition functions) of crystalline solids. We describe a method to compute the Helmholtz free energy of a crystalline solid by direct evaluation of the partition function. In the many-dimensional conformation space of all possible arrangements of N particles inside a periodic box, the energy landscape consists of localized islands corresponding to different solid phases. Calculating the partition function for a specific phase involves integrating over the corresponding island. Introducing a natural order parameter that quantifies the net displacement of particles from lattices sites, we write the partition function in terms of a one-dimensional integral along the order parameter, and evaluate this integral using umbrella sampling. We validate the method by computing free energies of both face-centered cubic (FCC) and hexagonal close-packed (HCP) hard sphere crystals with a precision of $10^{-5}k_BT$ per particle. In developing the numerical method, we find several scaling properties of crystalline solids in the thermodynamic limit. Using these scaling properties, we derive an explicit asymptotic formula for the free energy per particle in the thermodynamic limit. In addition, we describe several changes of coordinates that can be used to separate internal degrees of freedom from external, translational degrees of freedom. The second part of the dissertation focuses on engineering idealized physical devices that work as Maxwell's demon. We describe two autonomous mechanical devices that extract energy from a single heat bath and convert it into work, while writing information onto memory registers. Additionally, both devices can operate as Landauer's eraser, namely they can erase information from a memory register, while energy is dissipated into the heat bath. The phase diagrams and the efficiencies of the two models are solved and analyzed. These two models provide concrete physical illustrations of the thermodynamic consequences of information processing.

Adsorption of amyloglucosidase from Aspergillus niger NRRL 3122 using ion exchange resin

Amyloglucosidase enzyme was produced by Aspergillus niger NRRL 3122 from solid-state fermentation, using deffated rice bran as substrate. The effects of process parameters (pH, temperature) in the equilibrium partition coefficient for the system amyloglucosidase - resin DEAE-cellulose were investigated, aiming at obtaining the optimum conditions for a subsequent purification process. The highest partition coefficients were obtained using 0.025M Tris-HCl buffer, pH 8.0 and 25ºC. The conditions that supplied the highest partition coefficient were specified, the isotherm that better described the amyloglucosidase process of adsorption obtained. It was observed that the adsorption could be well described by Langmuir equation and the values of Qm and Kd estimated at 133.0 U mL-1 and 15.4 U mL-1, respectively. From the adjustment of the kinetic curves using the fourth-order Runge-Kutta algorithm, the adsorption (k1) and desorption (k2) constants were obtained through optimization by the least square procedure, and the values calculated were 2.4x10-3 mL U-1 min-1 for k1 and 0.037 min-1 for k2 .

Rumor Propagation Model: An Equilibrium Study

Compartmental epidemiological models have been developed since the 1920s and successfully applied to study the propagation of infectious diseases. Besides, due to their structure, in the 1960s an interesting version of these models was developed to clarify some aspects of rumor propagation, considering that spreading an infectious disease or disseminating information is analogous phenomena. Here, in an analogy with the SIR (Susceptible-Infected-Removed) epidemiological model, the ISS (Ignorant-Spreader-Stifler) rumor spreading model is studied. By using concepts from the Dynamical Systems Theory, stability of equilibrium points is established, according to propagation parameters and initial conditions. Some numerical experiments are conducted in order to validate the model.

The non-equilibrium nature of culinary evolution

Food is an essential part of civilization, with a scope that ranges from the biological to the economic and cultural levels. Here, we study the statistics of ingredients and recipes taken from Brazilian, British, French and Medieval cookery books. We find universal distributions with scale invariant behaviour. We propose a copy-mutate process to model culinary evolution that fits our empirical data very well. We find a cultural 'founder effect' produced by the non-equilibrium dynamics of the model. Both the invariant and idiosyncratic aspects of culture are accounted for by our model, which may have applications in other kinds of evolutionary processes.

Phase Equilibrium and Optimization Tools: Application for Enhanced Structured Lipids for Foods

Solid-liquid phase equilibrium modeling of triacylglycerol mixtures is essential for lipids design. Considering the alpha polymorphism and liquid phase as ideal, the Margules 2-suffix excess Gibbs energy model with predictive binary parameter correlations describes the non ideal beta and beta` solid polymorphs. Solving by direct optimization of the Gibbs free energy enables one to predict from a bulk mixture composition the phases composition at a given temperature and thus the SFC curve, the melting profile and the Differential Scanning Calorimetry (DSC) curve that are related to end-user lipid properties. Phase diagram, SFC and DSC curve experimental data are qualitatively and quantitatively well predicted for the binary mixture 1,3-dipalmitoyl-2-oleoyl-sn-glycerol (POP) and 1,2,3-tripalmitoyl-sn-glycerol (PPP), the ternary mixture 1,3-dimyristoyl-2-palmitoyl-sn-glycerol (MPM), 1,2-distearoyl-3-oleoyl-sn-glycerol (SSO) and 1,2,3-trioleoyl-sn-glycerol (OOO), for palm oil and cocoa butter. Then, addition to palm oil of Medium-Long-Medium type structured lipids is evaluated, using caprylic acid as medium chain and long chain fatty acids (EPA-eicosapentaenoic acid, DHA-docosahexaenoic acid, gamma-linolenic-octadecatrienoic acid and AA-arachidonic acid), as sn-2 substitutes. EPA, DHA and AA increase the melting range on both the fusion and crystallization side. gamma-linolenic shifts the melting range upwards. This predictive tool is useful for the pre-screening of lipids matching desired properties set a priori.

Liquid-Liquid Equilibrium of Aqueous Two-Phase Systems Containing Some Synthetic Polyelectrolytes and Polyethylene Glycol

Experimental results are presented for the liquid-liquid equilibrium of aqueous two-phase systems containing a synthetic polyelectrolyte (polysodium acrylate, polysodium methacrylate, and polysodium ethylene sulfonate) and polyethylene glycol at (298.2 and 323.2) K. A total of 40 phase diagrams were obtained, comprising data both of the binodal curve (obtained through cloud-point measurements) and of equilibrium compositions. The influences of temperature, the nature of the polyelectrolyte monomer unit, and the chain length of both types of polymers are analyzed and discussed.

The Equilibrium Flux Method for the calculation of flows with non-equilbrium chemical reactions

The Equilibrium Flux Method [1] is a kinetic theory based finite volume method for calculating the flow of a compressible ideal gas. It is shown here that, in effect, the method solves the Euler equations with added pseudo-dissipative terms and that it is a natural upwinding scheme. The method can be easily modified so that the flow of a chemically reacting gas mixture can be calculated. Results from the method for a one-dimensional non-equilibrium reacting flow are shown to agree well with a conventional continuum solution. Results are also presented for the calculation of a plane two-dimensional flow, at hypersonic speed, of a dissociating gas around a blunt-nosed body.

Non-Equilibrium Reaction Rates in the Macroscopic Chemistry Method for DSMC Calculations

The Direct Simulation Monte Carlo (DSMC) method is used to simulate the flow of rarefied gases. In the Macroscopic Chemistry Method (MCM) for DSMC, chemical reaction rates calculated from local macroscopic flow properties are enforced in each cell. Unlike the standard total collision energy (TCE) chemistry model for DSMC, the new method is not restricted to an Arrhenius form of the reaction rate coefficient, nor is it restricted to a collision cross-section which yields a simple power-law viscosity. For reaction rates of interest in aerospace applications, chemically reacting collisions are generally infrequent events and, as such, local equilibrium conditions are established before a significant number of chemical reactions occur. Hence, the reaction rates which have been used in MCM have been calculated from the reaction rate data which are expected to be correct only for conditions of thermal equilibrium. Here we consider artificially high reaction rates so that the fraction of reacting collisions is not small and propose a simple method of estimating the rates of chemical reactions which can be used in the Macroscopic Chemistry Method in both equilibrium and non-equilibrium conditions. Two tests are presented: (1) The dissociation rates under conditions of thermal non-equilibrium are determined from a zero-dimensional Monte-Carlo sampling procedure which simulates ‘intra-modal’ non-equilibrium; that is, equilibrium distributions in each of the translational, rotational and vibrational modes but with different temperatures for each mode; (2) The 2-D hypersonic flow of molecular oxygen over a vertical plate at Mach 30 is calculated. In both cases the new method produces results in close agreement with those given by the standard TCE model in the same highly nonequilibrium conditions. We conclude that the general method of estimating the non-equilibrium reaction rate is a simple means by which information contained within non-equilibrium distribution functions predicted by the DSMC method can be included in the Macroscopic Chemistry Method.