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Aristotle University of Thessaloniki RETENTION PREDICTION AND SEPARATION OPTIMIZATION UNDER MULTILINEAR GRADIENT ELUTION IN HPLC WITH MICROSOFT EXCEL MACROS S.Fasoula A,*, H. Gika B, A. Pappa-LouisiA, P. NikitasA S Department of Chemistry, Aristotle University of Thessaloniki B Department of Chemical Engineering, Aristotle University of Thessaloniki A The aim 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. 2 The steps… 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 1 2 3 Test the capability of the above by prediction under different conditions Determination of the optimal gradient conditions 3 The retention models examined 1. ln k ( ) c0 c1 3. ln k ( ) c0 c1 ln 2. ln k ( ) c0 c1 c2 2 k solute retention factor, k=(tR-t0)/t0 tR solute retention time t0 column dead time φ is the organic modifier volume fraction c0, c1, c2 are the adjustable parameters 4. ln k ( ) c0 c1 ln( 1 c2 ) 6. ln k ( ) c0 5. ln k ( ) c0 2 ln( 1 c1 ) c2 1 c1 4 c2 1 c1 Determination of retention by initial gradient data … model The optimization procedure demands the solution of the fundamental gradient elution equation has an analytical solution only in case of multilinear organic modifier gradient occurs AND P.Nikitas, A. Pappa-Louisi, A. Papageorgiou, J. Chromatogr. A 1157(2007)178-186 The solute retention is described by Retention models 1-5 Retention model 6 -Nikitas-Pappa's (NP) approach was adopted for the solution of the fundamental equation. 5 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 c2 ln k ( ) c0 1 c1 6 5 4 2 3 2 1 in 1 0 t1 t2 t3 t4 t5 t6 6 t Example of the whole optimization procedure Step 1 Fitting procedure Retention data 12 solutes (purines, pyrimidines, nucleosides) Under 5 different gradient conditions 7 Results… No model 1 lnk=c0-c1φ 2 lnk=c0-c1φ+c2φ^2 3 lnk=c0-c1*lnφ 4 lnk=c0-c1*ln(1+c2*φ) 5 lnk=c0+2ln(1+c1*φ)-c2*ln(1+c1*φ) 6 lnk=c0-c2*φ/(1+c1*φ) method A-M1 NP-M1 A-M2 NP-M2 fitting aver % error 2.4 2.6 1.5 1.5 NP-M3 1.6 1.6 A-M4 2.4 A-M5 NP-M5 1.4 1.4 NP-M6 1.4 A-M3 o Even in case an analytical solution exists, sometimes the solver is trapped M5 Our andapproach M6 the exhibit istheabest very fitting satisfactory performance method among the to 4solve models the with oo oM3 exhibits best between the 2 models withthen two in local minima andfitting gives performance unreliable adjustable parameters, and our three fundamental adjustable gradient parameters. elution equation, especially in case there is no adjustable approach parameters to solve the fundamental gradient elution equation is a good analytical solution. alternative method. 8 Step 2 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 Prediction procedure 9 Results… No model 1 lnk=c0-c1φ 2 lnk=c0-c1φ+c2φ^2 3 lnk=c0-c1*lnφ 4 lnk=c0-c1*ln(1+c2*φ) 5 lnk=c0+2ln(1+c1*φ)-c2*ln(1+c1*φ) 6 lnk=c0-c2*φ/(1+c1*φ) fitting aver % error 2.4 2.6 1.5 1.5 prediction aver % error 5.2 5.3 3.7 3.7 NP-M3 1.6 1.6 3.6 3.6 A-M4 2.4 5.2 A-M5 NP-M5 1.4 1.4 3.3 3.3 NP-M6 1.4 3.1 method A-M1 NP-M1 A-M2 NP-M2 A-M3 the M6 model seems to be the proper choice to be used in the optimization procedure. 10 Step 3 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 11 Conclusions 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. 12 Acknowledgement 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) 13 14