Simplex optimisation of conditions for the determination of antimony in environmental samples by using electrothermal atomic absorption spectrometry

Analysis of the total antimony in plant material was unsuccessful using the electrothermal atomic absorption spectrometry (ETAAS) conditions recommended by the instrument manufacturer. For this reason, an optimisation procedure utilising the Plackett-Burman method, simplex optimisation and visualisation of the generated response surface via principal components analysis, was carried out. The Plackett-Burman method was used to eliminate four of the initial variables chosen. Four variables (atomisation temperature, atomisation time, ash temperature and modifier concentration) were subsequently optimised using the composite modified simplex method and the results were visualised as a contour diagram, after reduction to two principal components. The optimised conditions were used for the analysis of both an acid digested pine needle standard reference material (NIST 1575) and a pond weed sample, collected from a contaminated site at Yellowknife Bay, Yellowknife, NWT, Canada. The total concentration of antimony present in the pine needles was statistically indistinguishable from the non-certified value, as was the value for the pond weed sample, compared with a value determined by neutron activation analysis (NAA). The results for the analysis of the pond weed sample by ETAAS agreed with those obtained from a subsequent analysis by inductively coupled plasma-mass spectrometry.     

Simplex optimisation of conditions for the determination of antimony in environmental samples by using electrothermal atomic absorption spectrometry

Analysis of the total antimony in plant material was unsuccessful using the electrothermal atomic absorption spectrometry (ETAAS) conditions recommended by the instrument manufacturer. For this reason, an optimisation procedure utilising the Plackett-Burman method, simplex optimisation and visualisation of the generated response surface via principal components analysis, was carried out. The Plackett-Burman method was used to eliminate four of the initial variables chosen. Four variables (atomisation temperature, atomisation time, ash temperature and modifier concentration) were subsequently optimised using the composite modified simplex method and the results were visualised as a contour diagram, after reduction to two principal components. The optimised conditions were used for the analysis of both an acid digested pine needle standard reference material (NIST 1575) and a pond weed sample, collected from a contaminated site at Yellowknife Bay, Yellowknife, NWT, Canada. The total concentration of antimony present in the pine needles was statistically indistinguishable from the non-certified value, as was the value for the pond weed sample, compared with a value determined by neutron activation analysis (NAA). The results for the analysis of the pond weed sample by ETAAS agreed with those obtained from a subsequent analysis by inductively coupled plasma-mass spectrometry.     

Automated exploration and exploitation of flow-injection response surfaces

Three-dimensional plots of instrumental responses vs. chemical concentrations or flow parameters have been 1 obtained in an automated manner on a computer-controlled flow-injection methods development system. Consideration of several alternative responses for flow-injection systems is shown to help characterize a chemistry more thoroughly and reveal the best experimental conditions. One may see the effects of individual experimental variables (reagent concentrations, pH, flow-rates, etc.), the interactions of these variables, instrumental factors and limitations of the surface exploration procedure employed. Chemical systems studied were the photometric determination of phosphate, palladium(II), iron(II) and persulfate. The propriety of automated response surface mapping is demonstrated and the efficacies of simplex and grid search approaches to response surface exploration are contrasted. Responses obtained include absorbance at peak maximum, relative standard deviation of maximum absorbance, time from injection to peak maximum and wavelength of maximum absorbance. Higher dimensional response surface representations of peak shape and absorbance spectra are also presented. The results show that the response chosen governs the general shape of the surface and the height at any point. This approach to automated characterization of chemical reactions in flow analysis is critically assessed.     

Comparison of the simplex and Powell methods with a weighted response function for the optimization of FIA systems

An experimental comparison between the relative performances of the Powell and simplex methods for the optimization of a Flow Injection Analysis (FIA) system for the determination of nitrite in water is reported. An evaluation of the advantages of using a weighted linear combination of two variables (related to sensitivity and sample throughput rate) as the response function in the guidance of the optimization procedures towards different practical requirements is also included. Both methods proved to be effective for the optimization, none having shown definite advantages over the other. The use of a weighted response function in these optimization methods proved to be useful for assessing the versatility of FIA systems.     

Optimized spectrophotometric determination of trace cobalt and manganese by their catalysis of the tiron—hydrogen peroxide reaction

A kinetic—spectrophotometric method for the detemination of traces of cobalt(II) and manganese(II) based on their catalytic effect on the tiron—hydrogen peroxide indicator reaction is proposed. Optimal conditions for determination of Co(II) are deduced from response surface studies, considering the sensitivity and the blank absorbance as responses. The detection limit is 0.05 ng Co ml^?1. The Mn(II)-catalyzed reaction was optimized for 1,10-phenanthroline as the activator by the simplex method and for 2,2′-bipyridine as the activator by response surface methodology on the basis of a previously described mechanistic model of the catalytic reaction. In the presence of 2,2′-bipyridine, the detection limit is 0.2 ng Mn ml^?1. The influence of foreign metal ions on both determinations is discussed and is related in the case of the 2,2′-bipyridine—activated Mn(II)-catalyzed reaction with model generated effects of these metal ions.     

Application of a modified simplex method to the multivariable optimization of a new FIA system for the determination of osmium

A methodology based on the coupling of experimental design and a modified simplex method is proposed for the optimization of a new flow injection-kinetic system for the spectrophotometric determination of Os (IV) with m-acetylchlorophosphonazo, which has for the first time been used as chromogenic reagent in the quantitative analysis of this element. An orthogonal array design is utilized to design the experimental protocol, in which six variables are varied simultaneously, and obtain the initial simplex using 25 experiments. A modified simplex method is applied to continuously optimize the data of the orthogonal array design; the search for optimum conditions of ¶6 variables using the modified simplex method required only 25 experiments. The efficiency and simplicity of the coupling of the experimental design and the modified simplex method are attractive for the development of new analytical methods. The method has been applied to the determination of Os (IV) in a refined ore as well as in a secondary alloy and provided satisfactory results.     

Application of a modified simplex method to the multivariable optimization of a new FIA system for the determination of osmium

A methodology based on the coupling of experimental design and a modified simplex method is proposed for the optimization of a new flow injection-kinetic system for the spectrophotometric determination of Os (IV) with m-acetylchlorophosphonazo, which has for the first time been used as chromogenic reagent in the quantitative analysis of this element. An orthogonal array design is utilized to design the experimental protocol, in which six variables are varied simultaneously, and obtain the initial simplex using 25 experiments. A modified simplex method is applied to continuously optimize the data of the orthogonal array design; the search for optimum conditions of 6 variables using the modified simplex method required only 25 experiments. The efficiency and simplicity of the coupling of the experimental design and the modified simplex method are attractive for the development of new analytical methods. The method has been applied to the determination of Os (IV) in a refined ore as well as in a secondary alloy and provided satisfactory results.     

Simplex Optimization for the Simultaneous HPLC Assay of the Activities of Purine-Nucleoside Phosphorylase and Hypoxanthine-Guanine Phosphoribosyl Transferase

Abstract

The modified sequential simplex procedure is shown to be effective for maximizing a complex enzyme assay. The optlmum levels for two factors, pH and substrate concentration, for a coupled enzyme assay of hypoxanthine-quanlne phosphor Ibosy I-transferase (HGPRTase) and purine nucleoside phosphorylase (PNPase) were found by searching a factor space made up of these variables. The performance Index or response to be optimized was a function of the product of the two single activities. The maximum activity for this function was found at a pH of 7.9 and a concentration of Inosine in the reaction mix of 0.84 mM.     

Optimization of high-performance liquid chromatographic parameters for the determination of capsaicinoid compounds using the simplex method.

A high-performance liquid chromatographic method was developed for the analysis of capsaicinoid compounds, the pungent principles of capsicum fruits. A sequential simplex method was applied to optimize the chromatographic response function used to assess the quality of separation by varying the chromatographic parameters. The separation was achieved in 11 min using a C-8 column of 15-cm length and 4.6 mm diameter using a UV detector. A flow rate of 1.15 ml min(-1) at a column temperature of 43.5 degrees C using 63.7% methanol in water gave the most efficient separation. The method was found to be suitable for the determination of the major capsaicinoid compounds in the capsicum samples.     

Pattern recognition strategies for molecular surfaces. II. Surface complementarity

Fuzzy logic based algorithms for the quantitative treatment of complementarity of molecular surfaces are presented. Therein, the overlapping surface patches defined in article I1 of this series are used. The identification of complementary surface patches can be considered as a first step for the solution of molecular docking problems. Standard technologies can then be used for further optimization of the resulting complex structures. The algorithms are applied to 33 biomolecular complexes. After the optimization with a downhill simplex method, for all these complexes one structure was found, which is in very good agreement with the experimental results.     

Evaluation of the super-modified simplex for use in chemical pattern recognition

A simplex optimization technique, the super-modified simplex (SMS), is evaluated for use in the pattern recognition analysis of low-resolution mass spectra. For the recognition of eleven functional group categories, the performances of SMS-derived weight vectors are shown to be comparable to those obtained by a previously developed modified simplex method. Data are presented which indicate that the SMS procedure requires fewer simplices and decreased computational time to converge to an optimized solution for the structural analysis problems investigated.     

Rotation in simplex optimization

A modification of the modified simplex method of optimization was tested. This modification involves rotation of the simplex when the standard simplex motion by reflection, expansion and contraction, fails to lead to continued progress of the simplex. Two other methods and several kinds of rotation are compared for four response surfaces. Certain rotations are shown to be superior to others and to two previously reported operations that do not involve rotation.     

Semiglobal simplex optimization and its application to determining the preferred solvation sites of proteins

The classical simplex method is extended into the Semiglobal Simplex (SGS) algorithm. Although SGS does not guarantee finding the global minimum, it affords a much more thorough exploration of the local minima than any traditional minimization method. The basic idea of SGS is to perform a local minimization in each step of the simplex algorithm, and thus, similarly to the Convex Global Underestimator (CGU) method, the search is carried out on a surface spanned by local minima. The SGS and CGU methods are compared by minimizing a set of test functions of increasing complexity, each with a known global minimum and many local minima. Although CGU delivers substantially better success rates in simple problems, the two methods become comparable as the complexity of the problems increases. Because SGS is generally faster than CGU, it is the method of choice for solving optimization problems in which function evaluation is computationally inexpensive and the search region is large. The extreme simplicity of the method is also a factor. The SGS method is applied here to the problem of finding the most preferred (i.e., minimum free energy) solvation sites on a streptavidin monomer. It is shown that the SGS method locates the same lowest free energy positions as an exhaustive multistart Simplex search of the protein surface, with less than one-tenth the number of minizations. The combination of the two methods, i.e.. multistart simplex and SGS, provides a reliable procedure for predicting all potential solvation sites of a protein.     

The hybrid experimental simplex algorithm – An alternative method for ‘sweet spot’ identification in early bioprocess development: Case studies in ion exchange chromatography

The capacity to locate efficiently a subset of experimental conditions necessary for the identification of an operating envelope is a key objective in many studies. We have shown previously how this can be performed by using the simplex algorithm and this paper now extends the approach by augmenting the established simplex method to form a novel hybrid experimental simplex algorithm (HESA) for identifying ‘sweet spots’ during scouting development studies. The paper describes the new algorithm and illustrates its use in two bioprocessing case studies conducted in a 96-well filter plate format. The first investigates the effect of pH and salt concentration on the binding of green fluorescent protein, isolated from Escherichia coli homogenate, to a weak anion exchange resin and the second examines the impact of salt concentration, pH and initial feed concentration upon the binding capacities of a FAb′, isolated from E. coli lysate, to a strong cation exchange resin. Compared with the established algorithm, HESA was better at delivering valuable information regarding the size, shape and location of operating ‘sweet spots’ that could then be further investigated and optimized with follow up studies. To test how favorably these features of HESA compared with conventional DoE (design of experiments) methods, HESA results were also compared with approaches including response surface modeling experimental designs. The results show that HESA can return ‘sweet spots’ that are equivalently or better defined than those obtained from DoE approaches. At the same time the deployment of HESA to identify bioprocess-relevant operating boundaries was accompanied by comparable experimental costs to those of DoE methods. HESA is therefore a viable and valuable alternative route for identifying ‘sweet spots’ during scouting studies in bioprocess development.     

Difficulties in the Application of Simplex Optimization to Analytical Chemistry

Abstract

The propagation of mistakes and misunderstandings in the application of simplex optimization to analytical chemical problems is delineated. Proper selection of factors and response is discussed.     

High performance liquid chromatographic method for the separation and quantification of some psychotherapeutic benzodiazepines optimized by the modified simplex procedure

An accurate high performance liquid chromatography method for the separation and quantification of a solution mixture of nitrazepam, diazepam and medazepam and medazepam was developed. The modified simplex program has been utilized for the optimization of the chemical and chromatographic parameters using the chromatographic response function as the quality criterion and a photodiode array as a detector. The separation was achieved in 2 min using a 20 cm long, 4.6 mm diameter Lichrosorb C18 reverse phase column. A 5 mul solution mixture containing 10 ppm of each drug was injected into a mobile phase containing 89:11 v/v acetonitrile: acetate buffer and a flow rate of 3.44 ml min(-1) was found to be optimal. The method was found to be suitable for the determination of these compounds in proprietary drugs without suffering interferences.     

Reassessment of the calibration constant for the IAsys biosensor.

A magnitude of 50 are s ng-1 mm2 has been determined for the calibration constant relating biosensor response to the amount of protein bound to the sensor surface of an IAsys cuvette. These studies entailed enzymatic assessment of the extent of lactate dehydrogenase depletion in the liquid phase arising from enzyme binding to a carboxymethyldextran-coated sensor surface, and also estimation of a maximum biosensor response for the electrostatic interaction of ovalbumin with an aminosilane-coated sensor surface. The latter results required correction for contributions to biosensor response resulting from changes in the refractive index of the liquid phase effected by high protein concentrations.     

A modified simplex method for multifactor optimization of selectivity in gas chromatography

A computer-assisted advanced simplex method is presented for the simultaneous optimization of multifactor ( stationary phase loading, carrier gas flow rate and column temperature ) for separation of ten compounds in gas chromatography. A three factors factorial design was used. The method was based on a special polynomial established from fifteen preliminary runs, using resolution as the selection criterion, with connection to a general simplex method. Excellent agreement is found between the predicted data and the experimental results, and most of experiments required in the general simplex method can be omitted.     

Optimisation of sensitivity in the multi-elemental determination of 83 isotopes by ICP-MS as a function of 21 instrumental operative conditions by modified simplex, principal component analysis and partial least squares

The optimisation of the sensitivity in the ICP-MS determination of 83 isotopes, as a function of 21 operative parameters was performed by generating an initial experimental design that was used to define, by principal component analysis, the multi-criteria target function. The first PC, which contained an overall evaluation of the signal intensity of all isotopes, was used to rank the experiments. The modified simplex optimisation technique was then applied on the ranked experiments. The increase in signal intensity was, on the average, 3.9 times for the isotopes considered for the simplex procedure. When finally convergence was achieved, a PLS regression model calculated on the available experiments allowed to investigate the effect played by each factor on the experimental response. Simplex and PCA proved to be extremely effective to obtain the optimisation and to generate the multi-criteria target function: they can be suggested as an automatic method to perform the optimisation of the instrumental operative conditions.