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Theory of <strong>Gradient</strong> Separations:<br />

Load<br />

Example: Peptides<br />

Why do we use gradients?<br />

<strong>Gradient</strong> Wash Re-equilibration<br />

0 3 10 12.5<br />

<strong>Gradient</strong> Operation<br />

Data acquisition ‘Wasted’ cycle time<br />

Dr. Shulamit Levin 1<br />

20


Theory of <strong>Gradient</strong> Separations:<br />

Example: Peptides<br />

Why do we use gradients?<br />

Load<br />

<strong>Gradient</strong> Wash Re-equilibration<br />

0 3 10 12.5<br />

20<br />

Data acquisition ‘Wasted’ cycle time<br />

Why do we use gradients?<br />

The retention (k) of peptides have a steep dependence<br />

on the % organic in the mobile phase<br />

Neue<br />

ln (k)<br />

6<br />

4<br />

2<br />

0<br />

0<br />

Small Molecule<br />

- The steeper the slope of the line the shallower the<br />

gradient must be to achieve maximum resolution<br />

0.2<br />

Peptide<br />

0.4<br />

Protein<br />

0.6<br />

Volume Fraction Acetonitrile<br />

0.8<br />

1<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

Why do we use gradients?...<br />

...because...<br />

Properties of analytes<br />

Retention (k) of the solutes has a steep<br />

dependence on the % organic in the<br />

mobile phase<br />

Wide range of differing hydrophobicities<br />

of the analytes<br />

Introduction<br />

Outline<br />

Theory of <strong>Gradient</strong> Separations of Peptides<br />

Optimization of Separations to...<br />

achieve maximum resolution<br />

maximize throughput<br />

maximize reproducibility<br />

Assay Reproducibility<br />

Conclusion<br />

Dr. Shulamit Levin 1-4<br />

© 1998 Waters Corporation<br />

© 1998 Waters Corporation


Column dead<br />

time<br />

Calculation of Isocratic<br />

Mobile Phase<br />

k-Dependence on Mobile Phase Composition<br />

in Reversed-Phase HPLC:<br />

<strong>Gradient</strong> Retention Times:<br />

( )<br />

t = t + t + G 0 d 1<br />

b ×S ×ln b×S ×t ×k(Φ ) + 1<br />

0 0<br />

System delay<br />

time<br />

ln( k ) = ln( k ) - S . Φ<br />

0<br />

<strong>Gradient</strong> slope<br />

Resolution Equations<br />

Slope of lnk vs. organic<br />

-Factors Factors Influencing Resolution for an Isocratic<br />

Separation RR s<br />

t N a - 1 k<br />

~ × ×<br />

w 4 a k +1<br />

Rs =<br />

}<br />

}<br />

Efficiency Selectivity<br />

k at gradient starting<br />

composition<br />

s = Resolution<br />

t = Retention time<br />

w = Peak width<br />

N = Plate Count<br />

a = Selectivity Factor<br />

k = Retention Factor<br />

-Factors Influencing Resolution for a <strong>Gradient</strong> Separation<br />

Rs =<br />

}<br />

}<br />

Efficiency Selectivity<br />

-Factors are similar, however...<br />

}<br />

Retention<br />

t N 1<br />

~ × ln a ×<br />

w 4 Bct0 + 1<br />

}<br />

Retention<br />

B = Slope of of ln ln (k) (k) with<br />

solvent composition (an<br />

analyte dependent<br />

property)<br />

c = <strong>Gradient</strong> Slope<br />

t 0<br />

0=<br />

= Time of of elution for an an<br />

unretained peak<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

Basic Resolution Equation<br />

-Factors Factors Influencing Resolution for an<br />

Isocratic Separation<br />

t<br />

Rs =<br />

w<br />

N<br />

~ ×<br />

4<br />

}<br />

α − 1 k<br />

×<br />

α k +1<br />

}<br />

Rs= Resolution Efficiency Selectivity<br />

N = Plate Count<br />

t = Retention Time<br />

w = Average peak width<br />

α = Selectivity Factor<br />

k = Retention Factor<br />

{<br />

w1<br />

}<br />

t<br />

{<br />

Retention<br />

Analyte Retention as a Function of <strong>Gradient</strong><br />

Slope<br />

kk (retention) for each<br />

analyte changes<br />

independently as the<br />

gradient slope changes.<br />

Thus, the resolution<br />

between peaks<br />

changes.<br />

ln k<br />

peak 8<br />

peak 9<br />

w2<br />

peak 10<br />

peak 11<br />

% Acetonitrile<br />

Dr. Shulamit Levin 5-8<br />

Carmody<br />

© 1998 Waters Corporation<br />

© 1998 Waters Corporation


What Factors Influence <strong>Gradient</strong> RP-HPLC<br />

Separations...<br />

Part I - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c<br />

Column Length; L and N<br />

Flow Rate; F<br />

Part II II - Factors influencing selectivity<br />

Concentration and Type of Modifier<br />

Temperature<br />

Chemistry and Pore Size of the Packing Material<br />

Part III - Factors influencing reproducibility<br />

Column<br />

HPLC system<br />

© 1998 Waters Corporation<br />

What Factors Influence <strong>Gradient</strong> Slope?<br />

c = %B/minute =<br />

Two ways to change the slope<br />

change the percent organic (D ( %) of the mobile<br />

phase across a specified gradient run time.<br />

change the gradient run time (t (tg<br />

g ) while keeping<br />

the % organic of the mobile phase constant.<br />

%<br />

tg<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

Rs (Resolution)<br />

Factors Influencing Resolution in<br />

<strong>Gradient</strong> RP-HPLC Separations...<br />

Part I - Factors influencing efficiency and<br />

retention<br />

<strong>Gradient</strong> Slope; c (%B/min.) - increase in organic<br />

concentration per unit time<br />

t N 1<br />

Rs = ∼ × ln α ×<br />

w 4 Bct0 + 1<br />

}<br />

}<br />

}<br />

Efficiency Selectivity Retention<br />

Selectivity<br />

Retention<br />

Principle of <strong>Gradient</strong> Separations<br />

Neue<br />

approaching<br />

isocratic<br />

<strong>conditions</strong><br />

General slope of the gradient<br />

© 1998 Waters Corporation<br />

0 0.01 0.1 1 10<br />

Dr. Shulamit Levin 9-12<br />

© 1998 Waters Corporation


0.400<br />

0.300<br />

AU 0.200<br />

0.100<br />

0.000<br />

0.300<br />

0.200<br />

AU AU<br />

0.100<br />

0.000<br />

What Factors Influence <strong>Gradient</strong> RP-HPLC<br />

Separations...<br />

Part I - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c (%B/min.) - varied by changing the % organic across across<br />

a specified gradient run time . . All All other other variables are are kept constant.<br />

Rs =<br />

t N<br />

∼ × lnα<br />

w 4<br />

}<br />

Efficiency Selectivity<br />

×<br />

}<br />

1<br />

Bct0 + 1<br />

}<br />

Retention<br />

tg = gradient<br />

run time<br />

1<br />

%<br />

B. . t0 + 1<br />

Resolution as a Function of <strong>Gradient</strong> Slope<br />

30.00 35.00 40.00<br />

Minutes<br />

0.62%/min (0-28%)<br />

30.00 30.00 35.00 35.00<br />

Minutes Minutes<br />

40.00 40.00<br />

Alden<br />

9<br />

10<br />

8 11<br />

0.66%/min<br />

9<br />

10<br />

8 11<br />

Rs (btw. 8 and 9) = 2.0<br />

Rs (btw. 9 and 10) = 5.4<br />

Rs (btw. 10 and 11) = 6.9<br />

Rs (btw. 8 and 9) = 2.3<br />

Rs (btw. 9 and 10) = 6.0<br />

Rs (btw. 10 and 11) = 6.8<br />

0.600<br />

0.500<br />

0.400<br />

0.300<br />

AU<br />

0.200<br />

0.100<br />

tg<br />

Conditions<br />

9<br />

0.71%/min (0-35%)<br />

© 1998 Waters Corporation<br />

-Column: Symmetry300, C 18,<br />

5 µm, 3.9 x 150 mm<br />

- Sample: Tryptic digests of<br />

bovine cytochrome c<br />

- Injection: 20 µL<br />

- Mobile Phase:<br />

Solvent A: 0.1% TFA in water<br />

Solvent B: 0.1% TFA in acetonitrile<br />

- Detection: 214 nm<br />

- Flow rate: 0.75 mL/min.<br />

- Temperature: 35 ºC<br />

Rs (btw. 8 and 9) = 1.7<br />

10<br />

Rs (btw. 9 and 10) = 4.7<br />

Rs (btw. 10 and 11) = 6.8<br />

8 11<br />

0.000<br />

30.00 35.00<br />

Minutes<br />

40.00<br />

<strong>Gradient</strong> Operation<br />

Resolution as a Function of<br />

<strong>Gradient</strong> Slope<br />

-Slope of the gradient = 0.66%/min<br />

0.400<br />

0.300<br />

AU 0.200<br />

0.100<br />

0.000<br />

0.00 20.00 40.00<br />

Minutes<br />

Alden<br />

8<br />

9<br />

10<br />

11<br />

Conditions<br />

-Column: Symmetry300, C 18 ,<br />

5 µm, 3.9 x 150 mm<br />

- Sample: Tryptic digests of bovine<br />

cytochrome c<br />

- Injection: 20µL<br />

- Mobile Phase:<br />

Solvent A: 0.1% TFA in water<br />

Solvent B: 0.1% TFA in<br />

acetonitrile<br />

- <strong>Gradient</strong>: 0-45 min., 0-30%B<br />

- Flow rate: 0.75 mL/min.<br />

- Temperature: 35 ºC<br />

- Detection: 214 nm<br />

© 1998 Waters Corporation<br />

Analyte Retention as a Function of <strong>Gradient</strong><br />

Slope<br />

kk (retention) for each<br />

analyte changes<br />

independently as as the<br />

gradient slope changes.<br />

Thus, the the resolution<br />

between peaks changes.<br />

Carmody<br />

ln k<br />

peak 8<br />

peak 9<br />

peak 10<br />

peak 11<br />

% Acetonitrile<br />

Dr. Shulamit Levin 13-16<br />

© 1998 Waters Corporation


0.2000<br />

0.1500<br />

0.1000<br />

AU AU<br />

0.1000 0.1000<br />

AU AU<br />

0.2000 0.2000<br />

0.1500 0.1500<br />

0.0500 0.0500<br />

0.0000 0.0000<br />

-0.0500 -0.0500<br />

0.0500<br />

0.0000<br />

-0.0500 -0.0500<br />

What Factors Influence <strong>Gradient</strong> RP-HPLC<br />

Separations...<br />

Part I - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c (%B/min.) - - varied by by changing the the<br />

gradient run time. time.<br />

All other variables are kept constant.<br />

t N<br />

Rs = ∼ × lnα<br />

w 4<br />

}<br />

×<br />

}<br />

Efficiency Selectivity<br />

1<br />

%<br />

B. . t0 + 1<br />

tg<br />

}<br />

Retention<br />

<strong>Gradient</strong> Modifications:<br />

Initial ACN% in Peptide Separations<br />

0.00 0.00<br />

0-28% in 75 min.,<br />

(0.37%/min)<br />

20.00 20.00<br />

40.00 40.00<br />

Minutes Minutes<br />

6-28% in 60 min.,<br />

9<br />

(0.37%/min)<br />

1<br />

3<br />

5<br />

4<br />

2<br />

5<br />

1 4<br />

3<br />

2<br />

6<br />

7<br />

8<br />

60.00 60.00<br />

80.00 80.00<br />

0.00 0.00 20.00 20.00 40.00 40.00 60.00 60.00 80.00 80.00<br />

Minutes Minutes<br />

6<br />

7<br />

8<br />

9<br />

10<br />

11<br />

10<br />

11<br />

r.t. = 85 min.<br />

r.t. = 70 min.<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> SLOPE is<br />

more important if peaks<br />

elute during gradient (not<br />

in initial condition)<br />

-By changing the initial<br />

mobile phase <strong>conditions</strong>,<br />

but keeping the gradient<br />

slope the same, the run<br />

time can effectively be<br />

shortened without a loss<br />

in resolution.<br />

<strong>Gradient</strong> Operation<br />

Resolution as a Function of <strong>Gradient</strong> Duration<br />

0.1200<br />

0.1000<br />

0.0800<br />

AU 0.0600<br />

0.0400<br />

0.0200<br />

0.0000<br />

0.00 5.00 10.00 15.00<br />

Minutes<br />

0.0800 0.0800<br />

0.0600 0.0600<br />

0.0400 0.0400<br />

AU AU<br />

0.0200 0.0200<br />

0.0000 0.0000<br />

0.00 0.00 10.00 10.00 20.00<br />

Minutes Minutes<br />

0.0600<br />

0.0400<br />

AU<br />

0.0200<br />

0.0000<br />

0.0500 0.0500<br />

0.0400 0.0400<br />

0.0300 0.0300<br />

AU AU<br />

0.0200 0.0200<br />

0.0100 0.0100<br />

0.0000 0.0000<br />

0.0300 0.0300<br />

0.0200 0.0200<br />

AU AU<br />

0.0100 0.0100<br />

0.0000 0.0000<br />

0.00 20.00 40.00<br />

Minutes<br />

0.00 0.00 20.00 20.00 40.00 40.00<br />

Minutes Minutes<br />

60.00 60.00<br />

78 Peaks<br />

15 Minutes<br />

98 Peaks<br />

25 Minutes<br />

114 Peaks<br />

50 Minutes<br />

137 Peaks<br />

75 Minutes<br />

162 Peaks<br />

150 Minutes<br />

0.00 0.00 50.00 Minutes Minutes<br />

100.00 100.00 150.00 150.00<br />

Conditions<br />

-Column: Symmetry300, C 18, 5<br />

µm,<br />

4.6 x 150 mm<br />

- Sample: Tryptic digests of<br />

bovine serum albumin<br />

- Injection: 20 µL<br />

- Mobile Phase:<br />

Solvent A: 0.1% TFA in water<br />

Solvent B: 0.1% TFA in<br />

acetonitrile<br />

- <strong>Gradient</strong>: 0-45 min., 0-30%B<br />

- Detection: 214 nm<br />

- Flow rate: 0.75 mL/min.<br />

- Temperature: 35 ºC<br />

-Longer RT;<br />

Shallower the slope;<br />

Increases Rs<br />

-Rs~ 1/c where c =<br />

gradient slope. All<br />

other variables are<br />

kept constant<br />

Alden<br />

Summary of Part I - <strong>Gradient</strong> Slope<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Slope is one of the most powerful<br />

operational parameter you have at your<br />

disposal<br />

Resolution increases as gradient slope<br />

decreases.<br />

Change in the initial percent organic can<br />

decrease the run time, maintain the resolution<br />

of your separation and preserve your elution<br />

pattern.<br />

Alden © 1998 Waters Corporation<br />

© 1998 Waters Corporation<br />

Dr. Shulamit Levin 17-20


Volumes in an HPLC System<br />

A B C<br />

D<br />

Proportioning<br />

Valve<br />

System Volume<br />

Waters 2690


Column Volume to to <strong>Gradient</strong> Volume Relationship (Approach 1) 1)<br />

-- <strong>Gradient</strong> volume scaled to to column volume<br />

50 mm column<br />

Column volume = 0.5 mL Column volume = 2.5 mL<br />

5 minute gradient @ 1 mL/min<br />

gradient volume = tg x f.r. = 5<br />

Total volume = g.v./c.v. = 10 column vols.<br />

250 mm column<br />

25 minute gradient @ 1 mL/min<br />

gradient volume = tg x f.r. = 25<br />

Total volume = g.v./c.v. = 10 column vols.<br />

Variation in Column Lengths at Equal Ratio of<br />

<strong>Gradient</strong> Volumes to Column Volumes<br />

0.0600<br />

AU AU0.0400<br />

0.0400<br />

0.0200<br />

0.1500<br />

0.1000<br />

AU<br />

0.0500<br />

0.1500<br />

0.1000<br />

AU<br />

0.0500<br />

4.00 5.00 6.00<br />

Minutes<br />

10.00 12.00 14.00 16.00<br />

Minutes<br />

Alden<br />

Column Volume = 0.83 mL<br />

Total Volume = 4.5 c.v.<br />

Column Volume = 2.5 mL<br />

Total Volume = 4.5 c.v.<br />

Column Volume = 4.2 mL<br />

Total Volume = 4.5 c.v.<br />

20.00 25.00<br />

Minutes<br />

5 minutes<br />

4.6 X 50 mm<br />

© 1998 Waters Corporation<br />

Conditions<br />

- Column: Symmetry300, C 18 , 5 µm<br />

- Sample: Tryptic digests of bovine<br />

serum albumin<br />

- Injection: 20 µL<br />

- Mobile Phase:<br />

Solvent A: 0.1% TFA in water<br />

Solvent B: 0.1% TFA in acetonitrile<br />

- 0 - 30 %B in the time shown.<br />

- Flow rate: 0.75 mL/min.<br />

15 minutes<br />

4.6 X 150 mm, - Detection: 214 nm<br />

- Temperature: 35 ºC<br />

25 minutes<br />

4.6 X 250 mm,<br />

- Elution pattern<br />

stays the same.<br />

- Resolution inc. as<br />

the # of plates inc.<br />

- Run time inc. as<br />

column length inc.<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

What Factors Influence <strong>Gradient</strong> RP-HPLC<br />

Separations...<br />

Part I I - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c<br />

Column Length; L and N<br />

Rs =<br />

t<br />

w<br />

N<br />

∼<br />

4<br />

}<br />

× ln α ×<br />

}<br />

. % . εt . πr .L/F + 1<br />

tg<br />

2<br />

Efficiency Selectivity<br />

Retention<br />

L (column length) is is varied. <strong>Gradient</strong><br />

volume is is scaled in in proportion to to the<br />

column volume.<br />

B<br />

1<br />

}<br />

Column Volume to <strong>Gradient</strong> Volume<br />

Relationship (Approach 2)<br />

-- <strong>Gradient</strong> volume not scaled to column volume<br />

50 mm column<br />

Column volume = 0.5 mL Column volume = 2.5 mL<br />

5 minute gradient @ 1 mL/min<br />

gradient volume = tg x f.r. = 5<br />

Total volume = g.v./c.v. = 10 column vols.<br />

250 mm column<br />

5 minute gradient @ 1 mL/min<br />

Terms are<br />

constant<br />

© 1998 Waters Corporation<br />

gradient volume = t g x f.r. = 5<br />

Total volume = g.v./c.v. = 2 column vols.<br />

Dr. Shulamit Levin 25-28<br />

© 1998 Waters Corporation


What Factors Influence <strong>Gradient</strong> RP-HPLC<br />

Separations...<br />

Part I - Factors influencing efficiency and<br />

retention<br />

<strong>Gradient</strong> Slope; c<br />

Column Length; L and N<br />

Rs =<br />

t<br />

w<br />

N<br />

∼ × ln α ×<br />

4<br />

B<br />

}<br />

}<br />

Efficiency Selectivity<br />

1<br />

. % . . εt πr .L/F + 1<br />

tg<br />

2<br />

}<br />

Retention<br />

© 1998 Waters Corporation<br />

Column Length Effects on Resolution at a Constant<br />

<strong>Gradient</strong> Duration (cont'd)<br />

0.02000<br />

0.01500<br />

0.01000<br />

AU<br />

0.00500<br />

0.00000<br />

-0.00500<br />

0.00<br />

20.00<br />

Minutes<br />

130 Peaks<br />

Symmetry300 4.6 X 50 mm,<br />

C 18, 5 µm<br />

40.00<br />

0.1200<br />

0.1000<br />

0.0800<br />

AU 0.0600<br />

0.0400<br />

0.0200<br />

131 Peaks<br />

Symmetry300 4.6 X 150<br />

mm,<br />

C 5 µm<br />

18,<br />

0.0000<br />

0.00 20.00<br />

Minutes<br />

40.00<br />

Conditions<br />

- Sample: Tryptic digests of bovine serum<br />

albumin<br />

- Injection: 20 µL (7 µL for 4.6 X 50 mm)<br />

- Mobile Phase:<br />

Solvent A: 0.1% TFA in water<br />

Solvent B: 0.1% TFA in acetonitrile<br />

- <strong>Gradient</strong>: 0-45 min., 0-30%B<br />

- Temperature: 35 ºC<br />

- Flow rate: 0.75 mL/min.<br />

- Detection: 214 nm<br />

-50 mm column has a<br />

similar resolving power<br />

as 250 mm column if the<br />

gradient duration<br />

remains the same.<br />

<strong>Gradient</strong> Operation<br />

0.2500 0.2500<br />

0.2000 0.2000<br />

0.1500 0.1500<br />

AU AU0.1000 0.1000<br />

0.0500 0.0500<br />

1<br />

0.0000 0.0000<br />

-0.0500 -0.0500<br />

0.00 0.00<br />

0.500 0.500<br />

0.400 0.400<br />

0.300 0.300<br />

AU AU<br />

0.200 0.200<br />

0.100 0.100<br />

0.000 0.000<br />

0.800<br />

0.600<br />

AU 0.400<br />

0.200<br />

0.00 0.00<br />

Column Length Effects on Resolution at a<br />

Constant <strong>Gradient</strong> Duration<br />

Column Volume = 0.83 mL<br />

Total Volume =40.7 c.v..<br />

1<br />

2<br />

1<br />

3<br />

4<br />

5,6<br />

20.00 20.00<br />

Column Volume = 2.5 mL<br />

Total Volume =13.5 c.v.<br />

5,6<br />

2 4<br />

3<br />

20.00 20.00<br />

Column Volume = 4.2 mL<br />

Total Volume = 8.0 c.v.<br />

0.000<br />

0.00 20.00<br />

Minutes<br />

40.00<br />

Alden<br />

2<br />

3<br />

4<br />

7<br />

5 6<br />

9<br />

8<br />

Minutes Minutes<br />

Minutes Minutes<br />

7<br />

10<br />

11<br />

7<br />

9<br />

8<br />

Symmetry300 4.6 X 50 mm,<br />

C18, 5 µm<br />

Conditions<br />

13<br />

- Sample: Tryptic digests of bovine<br />

12<br />

cytochrome c<br />

- Injection: 20 µL<br />

- Mobile Phase:<br />

Solvent A: 0.1% TFA in water<br />

Solvent B: 0.1% TFA in acetonitrile<br />

- <strong>Gradient</strong>: 0-45 min., 0-30%B<br />

Symmetry300 4.6 X 150<br />

mm,<br />

- Flow rate: 0.75 mL/min.<br />

- Detection: 214 nm<br />

10<br />

C 5 µm<br />

18, 13<br />

- Temperature: 35 ºC<br />

40.00 40.00<br />

8<br />

11<br />

40.00 40.00<br />

9 10<br />

11<br />

12<br />

Symmetry300 4.6 X 250<br />

mm,<br />

C 5 µm<br />

18,<br />

13<br />

12<br />

-Will observe elution<br />

pattern changes.<br />

-Resolution changes<br />

-Run time remains<br />

the same.<br />

Summary Part I - Column Length<br />

If the gradient volume is scaled proportionally to the<br />

column volume<br />

elution pattern does not change<br />

resolution increases with column length.<br />

© 1998 Waters Corporation<br />

If the gradient volume is not scaled in proportion to the<br />

column volume<br />

0.1200<br />

0.1000<br />

0.0800<br />

AU 0.0600<br />

0.0400<br />

0.0200<br />

134 Peaks<br />

Symmetry300 4.6 X 250<br />

mm,<br />

C 5 µm<br />

18,<br />

elution pattern and resolution changes<br />

50 mm column exhibits similar resolving power to a 250<br />

mm column.<br />

0.0000<br />

0.00 20.00<br />

Minutes<br />

40.00<br />

Alden © 1998 Waters Corporation<br />

© 1998 Waters Corporation<br />

Dr. Shulamit Levin 29-32


Rs (Resolution)<br />

What Factors Influence <strong>Gradient</strong> RP-HPLC<br />

Separations...<br />

Neue<br />

Part I - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c<br />

Column Length; L and N<br />

Flow Rate; FF<br />

Part II II - Factors influencing selectivity<br />

Concentration and Type of Modifier<br />

Temperature<br />

Chemistry and Pore Size of the Packing Material<br />

Part III - Factors influencing reproducibility<br />

Column<br />

HPLC system<br />

© 1998 Waters Corporation<br />

Resolution as a Function of Flow Rate at a Constant<br />

<strong>Gradient</strong> Duration<br />

12<br />

10<br />

8<br />

6<br />

4<br />

2<br />

0<br />

(50 mm Column)<br />

0.33<br />

1 mL/min<br />

Flow Rate (mL/min)<br />

3.3<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

What Factors Influence <strong>Gradient</strong> RP-HPLC<br />

Separations...<br />

Part I I - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c<br />

Column Length; L and N<br />

Flow Rate; F<br />

Rs =<br />

t<br />

w<br />

N<br />

∼ × lnα<br />

×<br />

4<br />

B<br />

}<br />

}<br />

Efficiency Selectivity<br />

Flow Rate Effects on Resolution<br />

at a Constant <strong>Gradient</strong> Duration<br />

0.0500<br />

0.0400<br />

AU<br />

0.0300<br />

0.0200<br />

0.0100<br />

0.0000<br />

0.00<br />

0.0400<br />

0.0300<br />

20.00<br />

Minutes<br />

40.00<br />

75 Peaks<br />

0.3 mL/minute<br />

100 Peaks<br />

AU 0.0200<br />

0.0100<br />

0.0000<br />

0.00 20.00 Minutes 40.00<br />

0.5 mL/minute<br />

135 Peaks<br />

0.02500<br />

0.02000<br />

0.01500<br />

AU 0.01000<br />

0.00500<br />

0.00000<br />

-0.00500<br />

0.00 20.00 Minutes<br />

1.0 mL/minute<br />

40.00<br />

0.02000<br />

0.01500<br />

AU AU<br />

0.01000<br />

0.00500<br />

0.00000<br />

-0.00500 -0.00500<br />

0.00 0.00 20.00 20.00 Minutes Minutes 40.00<br />

Alden<br />

1<br />

. % . εt . πr .L/F + 1<br />

tg<br />

2<br />

}<br />

Retention<br />

F (flow rate) is is varied. All other<br />

variables are kept constant<br />

130 Peaks<br />

2.0 mL/minute<br />

Conditions<br />

© 1998 Waters Corporation<br />

- Column: Symmetry300, C 18,<br />

5 µm, 4.6x50mm<br />

- Sample: Tryptic digests of bovine<br />

serum albumin<br />

- Injection: 20 µL<br />

- Mobile Phase:<br />

Solvent A: 0.1% TFA in water<br />

Solvent B: 0.1% TFA in acetonitrile<br />

- <strong>Gradient</strong>: 0-45 min., 0-30%B<br />

- Temperature: 35 ºC<br />

- Detection: 214 nm<br />

-Best resolution<br />

occurred at a flow rate<br />

of 1.0 mL/min. for this<br />

peptide under these<br />

<strong>conditions</strong>.<br />

-Elution pattern<br />

changes.<br />

Dr. Shulamit Levin 33-36<br />

© 1998 Waters Corporation


Summary of Part I - Flow Rate<br />

Maximum resolution is achieved at an<br />

optimal flow rate:<br />

As flow rate changes N changes<br />

As flow rate changes the elution pattern<br />

changes.<br />

Type of Modifiers<br />

Solvation<br />

Ionization<br />

Ion-pairing<br />

Volatility (Collection)<br />

© 1998 Waters Corporation<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

What Factors Influence <strong>Gradient</strong> RP-HPLC<br />

Separations...<br />

Part I - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c<br />

Column Length; L and N<br />

Flow Rate; F<br />

Part II II - Factors influencing selectivity<br />

Concentration and Type of of Modifier<br />

Temperature<br />

Chemistry and Pore Size of the Packing Material<br />

Part III - Factors influencing reproducibility<br />

Column<br />

HPLC system<br />

Effects of TFA Concentration on Resolution<br />

- Typical gradient <strong>conditions</strong><br />

0.300<br />

0.200 0.200<br />

AU AU<br />

0.100 0.100<br />

0.000 0.000<br />

Alden<br />

0.1% TFA in<br />

solvents A and B<br />

0.00 0.00<br />

1<br />

5,6<br />

2 4<br />

3<br />

9<br />

7 8<br />

10<br />

11<br />

20.00 Minutes Minutes 40.00<br />

13<br />

12<br />

Conditions<br />

- Column: Symmetry300, C 18,<br />

5 µm, 3.9x150mm,<br />

© 1998 Waters Corporation<br />

- Sample: Tryptic digests of bovine<br />

cytochrome c<br />

- Injection: 20 µL<br />

- Mobile Phase:<br />

Solvent A: water<br />

Solvent B: acetonitrile<br />

- <strong>Gradient</strong>: 0-45 min., 0-30%B<br />

- Flow rate: 0.75 mL/min.<br />

- Temperature: 35 ºC<br />

- Detection: 214 nm<br />

Dr. Shulamit Levin 37-40<br />

© 1998 Waters Corporation


The Power of Different TFA Concentrations in<br />

Your Mobile Phase<br />

- 0.05% TFA in<br />

solvents A and B<br />

2<br />

1 3<br />

- 0.1% TFA in solvents<br />

A and B<br />

- 0.2% TFA in<br />

solvents A and B<br />

2<br />

1 3<br />

1<br />

4<br />

5 6<br />

2 4<br />

3<br />

5,6<br />

5,6<br />

4<br />

0.00 20.00 40.00<br />

Minutes<br />

Alden<br />

Absorbance (214 nm)<br />

Alternate Ion Pairing Reagents<br />

TFA and HFBA (Heptafluorobutyric Acid)<br />

0.40<br />

0.02<br />

0.00<br />

0.40<br />

0.20<br />

0.00<br />

TFA<br />

HFBA<br />

20 40 60 80<br />

Time (min)<br />

7<br />

7<br />

7<br />

8<br />

9<br />

8<br />

10<br />

9<br />

11<br />

10<br />

9<br />

8<br />

11<br />

10<br />

11<br />

12<br />

13<br />

12 13<br />

13<br />

12<br />

© 1998 Waters Corporation<br />

Sample: Rabbit cytochrome c<br />

tryptic digest, 500 pmol<br />

Column: Delta-Pak C 18, 5µm,<br />

300Å, 2.0 x 150 mm<br />

Eluents: A=water/ 0.1% TFA or<br />

HFBA<br />

B=acetonitrile/ 0.1%<br />

TFA or HFBA<br />

<strong>Gradient</strong>: O-60 % B 120 min<br />

Flow: 0.18 mL/min<br />

Temp: 35 ºC<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

0.200<br />

0.100 0.100<br />

0.000 0.000<br />

The Power of Different TFA<br />

Concentrations in Your Mobile Phase<br />

0.300 0.300<br />

AU AU<br />

0.3000<br />

0.2500<br />

0.2000<br />

AU 0.1500<br />

0.1000<br />

0.0500<br />

0.0000<br />

Alden<br />

0.00 0.00<br />

0.1% TFA in Solvent A<br />

0.1% TFA in Solvent B<br />

1<br />

1<br />

2<br />

3<br />

20.00 20.00<br />

2<br />

3 4<br />

5,6<br />

4<br />

Minutes Minutes<br />

0.05% TFA in Solvent A<br />

0.1% TFA in Solvent B<br />

7<br />

8<br />

9<br />

10<br />

11<br />

40.00 40.00<br />

0.00 20.00 40.00<br />

Minutes<br />

5 6<br />

7<br />

8<br />

9<br />

10<br />

11<br />

12<br />

13<br />

12 13<br />

Conditions<br />

- Column: Symmetry300, C 18, 5 µm,<br />

3.9x150mm<br />

- Sample: Tryptic Digests of Bovine<br />

Cytochrome c<br />

- Injection: 20 µL<br />

What Factors Influence <strong>Gradient</strong><br />

RP-HPLC Separations...<br />

- Mobile Phase:<br />

Solvent A: water<br />

Solvent B: acetonitrile<br />

- <strong>Gradient</strong>: 0-45 min., 0-30%B<br />

- Flow rate: 0.75 mL/min.<br />

- Temperature: 35 ºC<br />

- Detection: 214 nm<br />

Part I I - - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c<br />

Column Length; L and N<br />

Flow Rate; FF<br />

Part II II - - Factors influencing selectivity<br />

Concentration and Type of Modifier<br />

Temperature<br />

Chemistry and Pore Size of the Packing Material<br />

Part III III - - Factors influencing reproducibility<br />

Column<br />

HPLC system<br />

Dr. Shulamit Levin 41-44<br />

© 1998 Waters Corporation<br />

© 1998 Waters Corporation


Temperature Effects on Resolution<br />

Resolution is temperature dependent<br />

Temperature is a critical parameter to control<br />

in order to achieve reproducible separations.<br />

What Factors Influence <strong>Gradient</strong><br />

RP-HPLC Separations...<br />

Part I - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c<br />

Column Length; L and and N<br />

Flow Rate; F<br />

Part II - Factors influencing selectivity<br />

Concentration and Type of Modifier<br />

Temperature<br />

Pore Size and Chemistry of of the Packing Material<br />

Part III - Factors influencing reproducibility<br />

Column<br />

HPLC system<br />

© 1998 Waters Corporation<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

0.300<br />

0.200<br />

AU<br />

0.100<br />

0.000<br />

0.300<br />

0.200<br />

AU<br />

0.100<br />

0.000<br />

0.300<br />

0.200<br />

AU<br />

0.100<br />

0.000<br />

Temperature Effects on Resolution<br />

Alden<br />

0.300 0.300<br />

AU AU<br />

0.200 0.200<br />

5, 6<br />

7<br />

25.00 30.00 35.00 40.00<br />

Minutes<br />

5, 6<br />

7<br />

25.00 30.00 35.00 40.00<br />

Minutes<br />

5 6<br />

Rs (5,6) = 0<br />

Rs (8,9) = 2.39<br />

Rs (5,6)= 0<br />

Rs (8,9)= 2.07<br />

Rs (5,6)= 0.84<br />

Rs (8,9)= 1.63<br />

7<br />

25.00 30.00 35.00 40.00<br />

Minutes<br />

8<br />

8<br />

9<br />

9<br />

8<br />

9<br />

10<br />

10<br />

10<br />

11<br />

11<br />

11<br />

30 °C<br />

35 °C<br />

40 °C<br />

Conditions<br />

- Column: Symmetry300, C 18 ,<br />

5 µm, 3.9x150mm<br />

- Sample: Tryptic digests of bovine<br />

cytochrome c<br />

- Injection: 20 µL<br />

- Mobile Phase:<br />

Solvent A: 0.1% TFA in water<br />

Solvent B: 0.1% TFA in acetonitrile<br />

- <strong>Gradient</strong>: 0-45 min., 0-30%B<br />

- Flow rate: 0.75 mL/min.<br />

- Detection: 214 nm<br />

Pore Size Effects on Resolution<br />

0.30<br />

0.20<br />

AU<br />

0.10<br />

0.00<br />

0.500 0.500<br />

0.400 0.400<br />

0.100 0.100<br />

0.000 0.000<br />

0.00 0.00<br />

1<br />

1<br />

5 6<br />

2 4<br />

3<br />

-0.10<br />

0.00 20.00<br />

Minutes<br />

40.00<br />

Carmody<br />

2 4<br />

3<br />

20.00 20.00<br />

5,6<br />

7<br />

Minutes Minutes<br />

8<br />

7<br />

Symmetry300, C 18, 5 µm,<br />

4.6 X 150 mm, 300Å<br />

10<br />

13<br />

9<br />

Symmetry®, C18, 5µm,<br />

4.6 X 150 mm, 100Å<br />

9<br />

8<br />

11<br />

10<br />

11<br />

40.00 40.00<br />

12<br />

13<br />

12<br />

Conditions<br />

© 1998 Waters Corporation<br />

- Sample: Tryptic digests of<br />

cytochrome c (bovine)<br />

- Injection: 20 µL<br />

- Mobile Phase:<br />

Solvent A: 0.1% TFA in water<br />

Solvent B: 0.1% TFA in acetonitrile<br />

- <strong>Gradient</strong>: 0-50 min., 0-30%B<br />

- Temperature: 35 ºC<br />

- Flow Rate: 0.75 mL/min.<br />

- Detection: 214 nm<br />

-Different pore<br />

sizes change<br />

selectivity.<br />

Dr. Shulamit Levin 45-48<br />

© 1998 Waters Corporation


Selectivity Differences Between Packings<br />

Alberta Peptides on Symmetry® Reversed-Phase Columns<br />

0.10<br />

AUFS<br />

AUFS<br />

0.05<br />

0.00<br />

0.10<br />

0.05<br />

0.00<br />

SymmetryShield RP 8, 100Å<br />

1<br />

2<br />

3<br />

5.00 10.00 15.00<br />

Symmetry® C 8, 100Å<br />

1 2<br />

5.00 10.00 15.00<br />

Minutes<br />

3<br />

4<br />

4<br />

5<br />

5<br />

Ac-Arg-Gly-X-X-Gly-Gly-Leu-Gly-LysAmide<br />

-X-X-:<br />

1: Ala-Gly with free alpha amino group<br />

2: Gly-Gly 3: Ala-Gly<br />

4: Val-Gly 5: Val-Val<br />

Peptide Mapping Validation<br />

-Robustness Testing<br />

Choice and quality of enzyme<br />

Digestion <strong>conditions</strong><br />

HPLC <strong>conditions</strong><br />

Equipment<br />

System<br />

Column<br />

Conditions:<br />

Columns: 3.9 mm x 150 mm<br />

Flow Rates: 0.8 mL/min<br />

Mobile Phase: A. 0.1% TFA aqueous;<br />

B. acetonitrile with 0.1% TFA<br />

<strong>Gradient</strong>: 10% to 40% B in 30 minutes,<br />

step to 60% B for 5 min<br />

Sample: 9 µL Alberta Peptides, mix<br />

with 5 decapeptides<br />

Detector: 214 nm<br />

Temperature: 35°C<br />

© 1998 Waters Corporation<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

What Factors Influence <strong>Gradient</strong><br />

RP-HPLC Separations...<br />

Part I - Factors influencing efficiency and retention<br />

<strong>Gradient</strong> Slope; c<br />

Column Length; L and N<br />

Flow Rate; FF<br />

Part II II - Factors influencing selectivity<br />

Concentration and Type of Modifier<br />

Temperature<br />

Chemistry and Pore Size of the Packing Material<br />

Part III - Factors influencing reproducibility<br />

Column<br />

HPLC HPLC system system<br />

Effects of Irreproducible <strong>Gradient</strong> Delivery<br />

-- Traditional HPLC System<br />

Experience resolution<br />

differences and<br />

retention time shifts<br />

0.00 20.00 40.00<br />

Minutes<br />

Carmody<br />

Dr. Shulamit Levin 49-52<br />

© 1998 Waters Corporation<br />

© 1998 Waters Corporation


Waters 2690 Separations Module<br />

<strong>Gradient</strong> Accuracy & Precision<br />

0.08<br />

0.07<br />

0.06<br />

0.05<br />

AU 0.04<br />

0.03<br />

0.02<br />

0.01<br />

0.00<br />

10%B<br />

10.0 20.0 30.0 40.0 50.0 60.0<br />

Minutes<br />

Reproducible <strong>Gradient</strong> Delivery<br />

-Waters Alliance HPLC System<br />

-Overlay of 15 Consecutive Injections<br />

Conditions:<br />

Column: Symmetry300 C18, 5 µm, 3.9 x 150 nm<br />

Sample: 20 µL of bovine, cytochrome c (tryptic digest)<br />

Flow rate: 1 mL/min.<br />

Temperature: 35 ºC<br />

Linear gradient: 0 - 28%B in 45 min.<br />

Mobile phase: A: 0.05% TFA in water<br />

B: 0.1% TFA in Methanol<br />

Alden<br />

1% Step <strong>Gradient</strong> at 1.0 mL/min<br />

Accuracy


Complex <strong>Gradient</strong> Conditions:<br />

Column:<br />

Column:<br />

AccQ<br />

AccQ<br />

Tag<br />

Tag<br />

Column,<br />

Column,<br />

3.9<br />

3.9<br />

x<br />

x<br />

150<br />

150<br />

mm<br />

mm<br />

Eluent<br />

Eluent<br />

A:<br />

A:<br />

AccQ<br />

AccQ<br />

Tag<br />

Tag<br />

Eluent<br />

Eluent<br />

A<br />

Eluent<br />

Eluent<br />

B:<br />

B:<br />

Acetonitrile<br />

Acetonitrile<br />

Eluent C: C: Water<br />

Flow<br />

Flow<br />

Rate:<br />

Rate:<br />

1.0<br />

1.0<br />

mL/min.<br />

mL/min.<br />

Column<br />

Column<br />

Temp.:<br />

Temp.:<br />

37<br />

37<br />

°C<br />

°C<br />

Detection:<br />

Detection:<br />

Fluorescence,<br />

Fluorescence, kk ex =<br />

ex =<br />

250<br />

250<br />

nm,<br />

nm,<br />

kem k<br />

=<br />

em=<br />

395 nm nm<br />

Sample: 50 50 pmol Hydrolysate Standard<br />

Sample<br />

Sample<br />

Temp.:<br />

Temp.:<br />

5<br />

5<br />

°C<br />

°C<br />

<strong>Gradient</strong>:<br />

<strong>Gradient</strong>:<br />

Time Flow %A %B %C %D Curve<br />

0.00 1.00 100.0 0.0 0.0 0.0 *<br />

0.50 1.00 99.0 1.0 0.0 0.0 11<br />

18.0 1.00 95.0 5.0 0.0 0.0 6<br />

19.0 1.00 91.0 9.0 0.0 0.0 6<br />

29.5 1.00 83.0 17.0 0.0 0.0 6<br />

33.0 1.00 0.0 60.0 40.0 0.0 11<br />

36.0 1.00 100.0 0.0 0.0 0.0 11<br />

65.0 1.00 0.0 60.0 40.0 0.0 11<br />

100.0 0.00 100.0 0.0 0.0 0.0 6<br />

"Consideration must be given to<br />

column-to-column variation attributed to<br />

production differences from a recommended<br />

manufacturer. Column-to-column variability<br />

was recently bemoaned as the 'Achilles heel' in<br />

the HPLC of protein pharmaceuticals (20).<br />

Although this problem has been both ignored by<br />

many and overstated by others, peptide<br />

mapping does place very high demands on<br />

column performance. Thus, column-to-column<br />

variability is of special concern (21,22)."<br />

© 1998 Waters Corporation<br />

Garnick et al. Biologicals (1996) 24 , 255-275<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

Why is Column Reproducibility<br />

Important?<br />

Validated RP-HPLC assays require HPLC columns to<br />

be reproducible from column-to-column and<br />

batch-to-batch.<br />

Columns which perform reproducibly in terms of<br />

selectivity and separation characteristics from<br />

batch-to-batch ensures reliable, reproducible and<br />

robust assays over the life of of the product.<br />

© 1998 Waters Corporation<br />

Column-to-Column Reproducibility<br />

Employed 8 different Symmetry300, C 18, , 5 µm<br />

18<br />

columns from the same batch (#107)<br />

Conducted evaluation over a 3-week time period<br />

Different mobile phase preparations for each run<br />

Dr. Shulamit Levin 57-60<br />

© 1998 Waters Corporation


Symmetry300<br />

Batch-to-Batch Reproducibility<br />

Batch 107<br />

Batch 106<br />

Batch 104<br />

Batch 103<br />

10 30 50<br />

Minutes<br />

Costello<br />

Conclusions (continued)<br />

Conditions<br />

- Column: Symmetry300, C 18,<br />

5 µm, 3.9x150mm<br />

- Sample: Tryptic digests of<br />

cytochrome c (bovine)<br />

- Injection: 20 µL<br />

- Mobile Phase:<br />

Solvent A: 0.05% TFA in water<br />

Solvent B: 0.1% TFA in acetonitrile<br />

- <strong>Gradient</strong>: 0-45 min., 0-28%B<br />

- Flow rate: 1.0 mL/min.<br />

- Temperature: 35 °C<br />

- Detection: 220 nm<br />

For Rugged/Robust gradient method<br />

development consider...<br />

System performance<br />

reproducibility of gradient delivery<br />

system delay volume<br />

Column performance<br />

column-to-column reproducibility<br />

batch-to-batch reproducibility<br />

- Instrument:<br />

Waters Alliance<br />

HPLC system<br />

© 1998 Waters Corporation<br />

© 1998 Waters Corporation<br />

<strong>Gradient</strong> Operation<br />

Conclusion<br />

There are several factors to assess when<br />

developing/optimizing a gradient RP-HPLC<br />

method.<br />

Primary tools for gradient optimization are<br />

gradient slope, column length and modifier<br />

type.<br />

Secondary tools to be used for fine tuning<br />

your gradient are temperature, modifier<br />

concentration and flow rate.<br />

Acknowledgments:<br />

Bonnie Alden<br />

Ray Crowley<br />

Uwe Neue<br />

Tom Walter<br />

Ray Fisk<br />

Dave Costello<br />

Edouard Bouvier<br />

...and Waters' Symmetry® Team<br />

Dr. Shulamit Levin 61-64<br />

© 1998 Waters Corporation<br />

© 1998 Waters Corporation

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