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

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.

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

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 t1 t2 t3 t4 t5 t6 t

2

1

1

20 1

)(lnc

cck

Example of the whole optimization procedure

7

Fitting procedure

12 solutes (purines, pyrimidines, nucleosides)

Under 5 different gradient conditions

Retention data

Step 1

Results…

8

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

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

Results…

10

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.

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

12

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.

13

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

14

THANK YOU FOR YOUR ATTENTION!

Fasoula StellaPhD student

Department of ChemistryAristotle University of

Thessaloniki