An advanced Gibbs-Duhem integration method: theory and applications

The conventional Gibbs-Duhem integration method is very convenient for the prediction of phase equilibria of both pure components and mixtures. However, it turns out to be inefficient. The method requires a number of lengthy simulations to predict the state conditions at which phase coexistence occurs. This number is not known from the outset of the numerical integration process. Furthermore, the molecular configurations generated during the simulations are merely used to predict the coexistence condition and not the liquid- and vapor-phase densities and mole fractions at coexistence. In this publication, an advanced Gibbs-Duhem integration method is presented that overcomes above-mentioned disadvantage and inefficiency. The advanced method is a combination of Gibbs-Duhem integration and multiple-histogram reweighting. Application of multiple-histogram reweighting enables the substitution of the unknown number of simulations by a fixed and predetermined number. The advanced method has a retroactive nature; a current simulation improves the predictions of previously computed coexistence points as well. The advanced Gibbs-Duhem integration method has been applied for the prediction of vapor-liquid equilibria of a number of binary mixtures. The method turned out to be very convenient, much faster than the conventional method, and provided smooth simulation results. As the employed force fields perfectly predict pure-component vapor-liquid equilibria, the binary simulations were very well suitable for testing the performance of different sets of combining rules. Employing Lorentz-Hudson-McCoubrey combining rules for interactions between unlike molecules, as opposed to Lorentz-Berthelot combining rules for all interactions, considerably improved the agreement between experimental and simulated data.     

Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: "Umbrella integration"

We present a method to analyze biased molecular-dynamics and Monte Carlo simulations, also known as umbrella sampling. In the limiting case of a strong bias, this method is equivalent to thermodynamic integration. It employs only quantities with easily controllable equilibration and greatly reduces the statistical errors compared to the standard weighted histogram analysis method. We show the success of our approach for two examples, one analytic function, and one biological system.     

An analysis of the complex molecular orbitals method

Numerical results for the ground state of the HN ₂ ⁺ and HCO⁺ molecular ions at their near equilibrium geometry, obtained by the complex molecular orbitals (CMO) method in the extended basis set, are reported. The CMO wavefunction of the HN ₂ ⁺ ion is compared with the CI wavefunction obtained in the same basis set. This reveals the nature of approximations inherent in the CMO method. A peculiar feature of the occupation numbers of the CMO natural orbitals is also explained.Alexander von Humboldt Fellow. On leave from the Institute Rudjer Bokovi, Zagreb, Croatia, Yugoslavia.     

An integration strategy to measure enzyme activities for detecting irreversible inhibitors with dimethoate on butyrylcholinesterase as a model

An integration strategy was investigated to measure initial rates of horse butyrylcholinesterase (BChE) at 50.0?µmol?L^?1 butyrylthiocholine (BTCh) for detecting irreversible inhibitors as pollutants in environment and foods with dimethoate as a model. In this integration strategy: (a) if BTCh consumption within 5.0?min was >60%, BChE initial rates were derived from maximal reaction rates, estimated by an improved integrated method, according to Michaelies-Menten kinetics at 47.0?µmol?L^?1 BTCh and Michaelis-Menten constant at 94.0?µmol?L^?1; (b) or else initial rates were determined by the classical initial rate method. Thus, the differences in BChE initial rates without and after dimethoate treatment indexed final dimethoate contents in reaction mixtures to treat BChE. Results supported that this integration strategy determined BChE activities with a linear range about two magnitudes and an upper limit about twice that by the classical initial rate method alone at 2.0?mmol?L^?1 BTCh. The coefficient of variation with this integration strategy was below 5%. The difference in BChE initial rates before and after dimethoate treatment was proportional to final dimethoate contents in reaction mixtures. By enzymatic analyses, the molar contents of dimethoate extracted from polluted cabbages were consistent with the summed molar contents of dimethoate and dimethoxon by gas-chromatography. Therefore, this integration strategy was effective to detect irreversible inhibitors as pollutants in environment and foods.     

An automatic back titration method for microchemical analysis

An automatic back titration method for microchemical analysis is introduced, which is based on conventional volumetric analysis's principle and the use of flow injection analysis apparatus for the automation and microminiaturization of the process. The sample and a known, but excess amount of a calibrated reagent solution are injected and propelled into a titration cell, where their reaction takes place. The excess of the reagent is then titrated with a titrant containing an indicator and the end point is monitored photometrically. Since homogeneous mixing in the titration cell is obtained magnetically in the whole process, there is a linear relationship between the analyte's concentration and the volume of the titrant consumed. Nickel in the range of 10-70 g 1(-1) is determined by the above method, in which 30 microl of sample and 500 microl of EDTA are injected and the excess of EDTA is titrated with a standard zinc salt solution containing xylenol orange which could be blocked by nickel ion in a direct titration. This method is characteristic of low sample and reagent consumption, high sampling rate as high as 45 samples h(-1), negligible effect of sample's viscosity, small carry-over effect (lower than 0.14%), and very good precision, whose relative standard deviations are as small as 0.24%.     

基于核酸适配体的微流控芯片酶反应器用于蛋白质的分析

将核酸适配体作为胰蛋白酶固定化介质,制备了一种新型的微流控芯片酶反应器,并与高效液相色谱-串联质谱联用,搭建了在线分析平台;分别使用标准蛋白及混合蛋白样品对芯片的酶解效率及联用平台的分析能力进行了初步评价。结果表明,5 ng肌红蛋白经该平台分析后肽段覆盖率可达到37%;对500 ng混合蛋白进行3次平行分析,肽段覆盖率及相对标准偏差分别为44.3%、6.5%(牛血清白蛋白), 65.0%、2.7%(肌红蛋白)和62.0%、5.6%(细胞色素c);初步实验表明,该在线分析平台具有检测灵敏度高、重现性好、酶解效率高的特点,有望在蛋白质组学分析中发挥重要作用。     

An improved method for quantitative sugar analysis of glycoproteins

Although there are numerous methods available to hydrolyze glycans utilizing strong acids, it all requires lengthy steps to obtain quantitative yield. We have developed a new simple one-step method for analysis of amino and neutral monosaccharides of glycoproteins quantitatively. Free monosaccharides were found to be stable during hydrolysis of glycans with 6 N HCI at 80 degrees C up to 2 h. Using this condition, analysis of free monosaccharides hydrolyzed from the bovine fetuin showed sugar composition of Gal: Man: GlcN: GaIN = 13.2: 11.0: 15.5: 2.6, which is closely matched with the reported value of 12.4: 9.6: 17.2: 2.7 (Townsend et al., ABRF News 8: 14, 1997). This method was shown to be applicable to varieties of well-characterized glycoproteins, erythropoietin, fibrinogen and soybean agglutinin. The amounts of sugars released under the condition were very close to the experimental values by other procedures or to the theoretical ones. This condition was found to be suitable for direct sugar analysis of fetuin, which have been immobilized onto polyvinylidene difluoride membrane. Based on these results, it support that the 6 N HCl/80 degrees C/2 h is the simplest method for quantitative analysis of monosaccharide composition of glycoproteins.     

An integration strategy to estimate the initial rates of enzyme reactions with much expanded linear ranges using uricases as models

A new strategy was proposed to estimate the initial rates of reactions catalyzed by Michaelis-Menten enzymes via integrating the classical initial rate method for low activities with an improved integrated method for high activities. Between these two individual methods, this integration strategy required: (a) the consistent linear response slopes, acquired with an optimized preset substrate concentration (PSC) to derive the initial rates from the maximal reaction rates estimated by the improved integrated method; (b) an overlapped region of the initial rates measurable with consistent results, realized with an optimized reaction duration to record reaction curves for analyses by the improved integrated method; (c) a switch cutoff, preset as the instantaneous substrate concentration slightly above that after a given lag time when the enzyme activity was just below the upper limit for the linear response of the classical initial rates. By simulation with uricases at a given initial substrate concentration (S₀), the optimized PSC was 93% S₀, the optimized reaction duration at S₀ from 0.35-fold to 11.0-fold Michaelis-Menten constant (K_m) was within 6.0 min and the switch cutoff was available at the given S₀ after 30-s lag time, all of which were combined to produce 300-fold linear ranges. By experimentation with one uricase of K_m at 6.6 μM and the other uricase of K_m at 220 μM under optimized conditions, this integration strategy with S₀ at 75 μM produced 100-fold linear ranges. Thus, this integration strategy exhibited much expanded linear ranges and practical efficiency over wide ratios between S₀ and K_m.     

An improved method to measure all rate constants in the simplest enzyme kinetics model

Since Adrian Brown and Victor Henri’s work, the simplest enzyme kinetics model, which contains only three rate constants k ₁, k ₂ and k ₋₁ in 1902, has been thoroughly explored in many directions. By using the Michaelis–Menten equation, K _M and k ₂ can be measured quickly. All the three rate constants can be derived by temperature jump method or transient state kinetics, but both methods need more complicated techniques and equipments. In our previous paper (Li et al. in J Math Chem 46:290–301, 2009), we gave a method to measure all the rate constants which does not require any additional equipment other than those needed for measuring K _M and k ₂. Here, we propose a new one which needs no additional equipment either. This method is based on a study of inflection points of integral curves. Numerical results show that the new one is much better than the previous one in two aspects: near the end of the reaction, the new one gives more accurate estimation; during the quasi-steady state of the reaction, it also gives good estimations while the previous one can not. Hence, this method not only advances the estimation accuracy, but also has more choices for measuring.     

Determination of DNA by sub- and super-equivalence method of isotope dilution analysis using enzyme reaction

Sub- and super-equivalence method of isotope dilution analysis (SSE-IDA) using enzyme reaction was first applied for the determination of biological substance, DNA. Radioactive DNA (pUC18) to be analysed was prepared by incorporating 3H-thymidine in growing E. coli. A part of DNA was cut into the linear form (L-form) DNA under definite conditions using a restriction enzyme HindIII, following the separation of each by gel electrophoresis. Radioactivites of separated L-form DNA of two series were measured. The quantity of DNA was obtained by a graph method of SSE-IDA. As preliminary experiments, it was examined under what conditions the enzyme reaction proceeds as zeroth or first order reaction. We used the enzyme and substrate concentrations near zeroth order, where ordinary subst-IDA seems not to give a satisfactory results. As the results, 0.25 microgram of DNA was determined the error of about 10%.     

The self-referential method combined with thermodynamic integration

The self-referential method [M. B. Sweatman, Phys. Rev. E 72, 016711 (2005)] for calculating the free energy of crystalline solids via molecular simulation is combined with thermodynamic integration to produce a technique that is convenient and efficient. Results are presented for the chemical potential of hard sphere and Lennard-Jones face centered cubic crystals that agree well with this previous work. For the small system sizes studied, this technique is about 100 times more efficient than the parameter hopping technique used previously.     

An enzyme immunosensor for IgG

An enzyme immunosensor has been developed for assaying human immunoglobulin G (IgG). The sensor is composed of an oxygen sensoring system and an antibody-binding membrane. The assay procedure involves the competitive immunochemical reaction of the membrane-bound antibody with nonlabeled and catalase-labeled IgG and the electrochemical determination of membrane-bound catalase activity. The analytical result is directly displayed by the output current of the sensor. The sensor exhibited an excellent performance in monitoring specifically human IgG.     

On-chip integration of enzyme and immunoassays: simultaneous measurements of insulin and glucose

A microfluidic device coupling immunological and enzymatic assays within a single microchannel has been developed for simultaneous measurements of insulin and glucose. Such a dual-mode (enzyme/immuno) protocol involves precolumn reactions of insulin and glucose with the enzyme-labeled anti-human insulin and glucose-dehydrogenase/NAD+, respectively, followed by the electrophoretic separation of the free antibody, antibody-antigen complex, and the NADH product of the enzymatic reaction. The separation is followed by a postcolumn reaction of the alkaline-phosphatase tracer with the p-NPP substrate and a downstream amperometric detection of the p-nitrophenol and NADH products. Despite the huge concentration difference [millimolar (glucose) and nanomolar (insulin)] and the use of different assay principles, the new biochip responds independently to the corresponding target analytes, with linear dynamic ranges over their clinically relevant ranges. Complete assays, carried out within less than 4 min, lead to good precision (RSD 0.36%) for the insulin/glucose ratio. The resulting biochip allows simultaneous testing for insulin and glucose to be performed more rapidly, easily, and economically, and hence it holds great promise for improved management of diabetes.     

A novel method for enzyme design

Rational design of enzymes is a stringent test of our understanding of protein structure and function relationship, which also has numerous potential applications. We present a novel method for enzyme design that can find good candidate protein scaffolds in a protein-ligand database based on vector matching of key residues. Residues in the vicinity of the active site were also compared according to a similarity score between the scaffold protein and the target enzyme. Suitable scaffold proteins were selected, and the side chains of residues around the active sites were rebuilt using a previously developed side-chain packing program. Triose phosphate isomerase (TIM) was used as a validation test for enzyme design. Selected scaffold proteins were found to accommodate the enzyme active sites and successfully form a good transition state complex. This method overcomes the limitations of the current enzyme design methods that use limited number of protein scaffold and based on the position of ligands. As there are a large number of protein scaffolds available in the Protein Data Band, this method should be widely applicable for various types of enzyme design.