S
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-LouisiA, P. NikitasA
The aim
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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.
The steps…
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
4
The retention models examined
10)(ln cck lnc)(ln 10 ck
)1ln()(ln 210 ccck
1
210 1)1ln(2)(ln
c
ccck
1
20 1
)(lnc
cck
k solute retention factor, k=(tR-t0)/t0
tR solute retention timet0 column dead time
φ is the organic modifier volume fractionc0, c1, c2 are the adjustable parameters
2210)(ln ccck
1.
5.
6.
4.
3.
2.
Determination of retention model
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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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 t1 t2 t3 t4 t5 t6 t
2
1
1
20 1
)(lnc
cck
Example of the whole optimization procedure
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Fitting procedure
12 solutes (purines, pyrimidines, nucleosides)
Under 5 different gradient conditions
Retention data
Step 1
Results…
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No model methodfitting
aver % error
1 lnk=c0-c1φA-M1 2.4
NP-M1 2.6
2 lnk=c0-c1φ+c2φ^2A-M2 1.5
NP-M2 1.5
3 lnk=c0-c1*lnφA-M3 1.6
NP-M3 1.6
4 lnk=c0-c1*ln(1+c2*φ)A-M4 2.4
5 lnk=c0+2ln(1+c1*φ)-c2*ln(1+c1*φ)A-M5 1.4
NP-M5 1.4
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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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
Results…
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No model methodfitting prediction
aver % error aver % error
1 lnk=c0-c1φA-M1 2.4 5.2
NP-M1 2.6 5.3
2 lnk=c0-c1φ+c2φ^2A-M2 1.5 3.7
NP-M2 1.5 3.7
3 lnk=c0-c1*lnφA-M3 1.6 3.6
NP-M3 1.6 3.6
4 lnk=c0-c1*ln(1+c2*φ)A-M4 2.4 5.2
5 lnk=c0+2ln(1+c1*φ)-c2*ln(1+c1*φ)A-M5 1.4 3.3
NP-M5 1.4 3.3
6 lnk=c0-c2*φ/(1+c1*φ)
NP-M6 1.4 3.1
the M6 model seems to be the proper choice to be used in the optimization procedure.
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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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ConclusionsWe 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)
Acknowledgement
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THANK YOU FOR YOUR ATTENTION!
Fasoula StellaPhD student
Department of ChemistryAristotle University of
Thessaloniki