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RETENTION PREDICTION AND SEPARATION OPTIMIZATION UNDER MULTILINEAR GRADIENT ELUTION IN HPLC WITH MICROSOFT EXCEL MACROS Aristotle University of Thessaloniki A Department of Chemistry, Aristotle University of Thessaloniki B Department of Chemical Engineering, Aristotle University of Thessaloniki S.Fasoula A,*, H. Gika B, A. Pappa-Louisi A, P. Nikitas A

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The aim Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 2 The exploration of Excel 2010 or 2013 capabilities in the whole procedure of separation optimizations under multilinear gradient elution in HPLC Microsoft Excel : friendly computational environment application of systematic optimization strategies much easier for the majority of chromatographers The Excel versions up to 2007 did not equip with the proper optimization tool. In the new versions, 2010 and 2013, the Solver add-in provides optimization capabilities when the cost function is not differential, like those adopted in liquid chromatography.

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The steps… Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 3 of a computer-assisted separation optimization under multilinear organic modifier gradient elution based on gradient retention data Fitting initial gradient data of each solute to a retention model Test the capability of the above by prediction under different conditions Determination of the optimal gradient conditions 1 2 3

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The retention models examined Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 4 k solute retention factor, k=(t R -t 0 )/t 0 t R solute retention time t 0 column dead time φ is the organic modifier volume fraction c 0, c 1, c 2 are the adjustable parameters 1. 5. 6. 4. 3. 2.

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Determination of retention model Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 5 Retention models 1-5 P.Nikitas, A. Pappa-Louisi, A. Papageorgiou, J. Chromatogr. A 1157(2007)178-186 has an analytical solution only in case of multilinear organic modifier gradient occurs Retention model 6 -Nikitas-Pappa's (NP) approach was adopted for the solution of the fundamental equation. by initial gradient data … The optimization procedure demands the solution of the fundamental gradient elution equation AND The solute retention is described by

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Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 6 Our approach… The multilinear gradient profile is divided into subsections, so that at each φ range the dependence of ln k vs. φ to be linear, although the total retention model is not linear 6 5 4 3 2 1 in 0 t 1 t 2 t 3 t 4 t 5 t 6 t 2 1

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Example of the whole optimization procedure Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 7 Fitting procedure 12 solutes (purines, pyrimidines, nucleosides) Under 5 different gradient conditions Retention data Step 1

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Results… Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 8 Nomodelmethod fitting aver % error 1 lnk=c0-c1φ A-M12.4 NP-M12.6 2lnk=c0-c1φ+c2φ^2 A-M21.5 NP-M21.5 3 lnk=c0-c1*lnφ A-M3 1.6 NP-M3 1.6 4 lnk=c0-c1*ln(1+c2*φ) A-M42.4 5 lnk=c0+2ln(1+c1*φ)-c2*ln(1+c1*φ) A-M51.4 NP-M51.4 6 lnk=c0-c2*φ/(1+c1*φ) NP-M6 1.4 o Our approach is a very satisfactory method to solve the fundamental gradient elution equation, especially in case there is no analytical solution. o Even in case an analytical solution exists, sometimes the solver is trapped in local minima and gives unreliable adjustable parameters, and then our approach to solve the fundamental gradient elution equation is a good alternative method. o M5 and M6 exhibit the best fitting performance among the 4 models with three adjustable parameters. o M3 exhibits the best fitting performance between the 2 models with two adjustable parameters

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Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 9 Prediction procedure The prediction ability of the retention models derived in the fitting procedure is detected on the prediction spreadsheets using the experimental retention data obtained under 7 mono-linear and 4 bilinear gradient profiles Step 2

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Results… Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 10 Nomodelmethod fittingprediction aver % error 1 lnk=c0-c1φ A-M12.45.2 NP-M12.65.3 2lnk=c0-c1φ+c2φ^2 A-M21.53.7 NP-M21.53.7 3 lnk=c0-c1*lnφ A-M3 1.63.6 NP-M3 1.63.6 4 lnk=c0-c1*ln(1+c2*φ) A-M42.45.2 5 lnk=c0+2ln(1+c1*φ)-c2*ln(1+c1*φ) A-M51.43.3 NP-M51.43.3 6 lnk=c0-c2*φ/(1+c1*φ) NP-M6 1.43.1 the M6 model seems to be the proper choice to be used in the optimization procedure.

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Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 11 Once the proper retention model is adopted the optimal gradient profile is determined on the proper optimization spreadsheet using the corresponding adjustable parameters Optimization procedure Step 3

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Conclusions Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 12 We created Excel spreadsheets that can be adopted both for a computer-assisted optimization of chromatographic separations and for metabolite identification by the majority of chromatographers without some experience or knowledge of programming Microsoft Excel is a user-friendly environment due to its unique features in organizing, storing and manipulating data using basic and complex mathematical operations, graphing tools, and programming.

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The project is implemented under the Operational Program “Education and Lifelong learning" and is co- funded by the European Union (European Social Fund) and National Resources (Excellence II: Metabostandards 5204) Fasoula Stella, Aegean Analytical Chemistry Days 2014, Chios 13 Acknowledgement

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© 2007 Pearson Education Chapter 14: Solving and Analyzing Optimization Models.

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