This document provides instructions for representing chromatographic data using reciprocal symmetry (ReS) and reciprocal symmetry scaling (ReSS). It explains how to calculate partition coefficients (K) from chromatograms and plot the data in ReS or ReSS format. Guidelines are given for selecting the midline position and adjusting the x-axis to fit the data appropriately. Examples show how these techniques can be used to compare chromatographic methods and solvent systems.

1. How to ReS and ReSS
A
280nm
230nm
A
K
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.14 1.33 1.6 2 2.67 4 8 ∞
IIII II
IIIII I1/K
GUESSmix in Hexane / Ethyl acetate / Methanol / Water 4:6:4:6
Reverse Phase
Normal Phase
G
H
X
T
r
C
D
F
R
U
V
A
Q
M
N
Z
E O
I
Y
b

2. Traditional Chromatogram
HEMWat +2
0
0 25 50 75 100 125 150 175 200 225 250 275 300 325 350mL
A
280nm
230nm
120 mL HSCCC (CCC-1000)
1 mL/min, 1,200 rpm
fraction collection 3 mL/tube
Elution Extrusion Method

3. How to represent the partition
coefficient K on the
chromatograph?
0
0 50 100 150 200 250 300 350mL
A
0
10
20
30
40
50
60
70
80
90
100
280nm
230nm
K
0 ≥ K ≤ infinity K = (VR-VM)/VS

4. Reciprocal Symmetry
Chose a midline “M” .
To the left of “M” à 0 ≥ K ≤ M
To the right of “M” à M ≥ K ≤ infinity
To graph it: Chose “1” as midline
To the left of 1 à x = K
To the right of 1 à x = 2-(1/K)

5. Reciprocal Symmetry Plot
0
5
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
X = K
Kvalues
x = 2- 1/K
(0.25,0.25)
(1.75,4)
ReS Excel plot
Reciprocal Symmetry K’(1) adjusted values

6. ReS x-axis adjusted plot
Reciprocal Symmetry Plot
0
5
10
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.25 2 2.5 10
8
K
Kvalues
5
Reciprocal Symmetry K axis
K = 1/(2-x)

7. Reciprocal Symmetry
Chose a midline “M” .
To the left of “M” à 0 ≥ K ≤ M
To the right of “M” à M ≥ K ≤ infinity
To graph it: Chose “M” as midline
To the left of “M” à x = K
To the right of “M” à x = 2(M)-(M2/K)

8. ReSS Excel Plot
Reciprocal Symmetry Plot
0
10
20
30
0 1 2 3 4 5 6 7 8
X = K
Kvalues
x = 8 – (16/K)
(1,1)
(7,16)
Reciprocal Symmetry K’ adjusted values
M = 4

9. ReSS x-axis adjusted plot
K = 16/(8-x)
Reciprocal Symmetry Plot
0
10
20
30
0 1 2 3 4
8
K
Kvalues
(1,1)
(16,16)
5.33 8 16
Reciprocal Symmetry K axis

10. Chromatograms!
HEMWat +2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2K'(1)
A
280nm
230nm
0
0 0.25 0.5 0.75 1 1.33 2 4 ∞K'(1)
A

11. ReSS
HEMWat +2
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4K'(2)
A
280nm
230nm
0
0 0.5 1 1.5 2 2.67 4 8
∞K'(2)
A

12. HEMWat +2
0 25 50 75 100 125 150 175 200 225 250 275 300 325 350mL
A 280nm
230nm
0 0.25 0.5 0.75 1 1.33 2 4
∞K'(1)
A
0 0.5 1 1.5 2 2.67 4 8 ∞K'(2)
A
T
H
X
r
D
Y
b
I
OZ
M
E
N
A
V
U
F
R
G
Q
C

13. How to decide where to put “M”?
What looks nice.
HEMWat 0
-0.01
0 0.5 1 1.5 2 2.5 3 3.5 4K'(2)
A
280nm
230nm
HEMWat 0
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2K'(1)
A
280nm
230nm

14. M should represent volume midline:
Same number of data points on each side of the midline
0
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.125 1.25 1.375 1.5 1.625 1.75 1.875 2
A
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3 3.25 3.5 3.75 4KD
A
280nm
230nm
G Mix H/EtOAc/MeOH/Water 4:6:4:6
0
0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6K' (3)
A
280nm
230nm

15. How to ReS/ReSS
What you need:
• UV-vis trace for EECCC chromatogram
• Time trace for EECCC chromatogram
• Mobile phase volumeà VM = void volume
• The total time of run à Vrun
• Column Volume à VM

16. • Equations:
• K = (VR-VM)/(VC-VM) before Vee
• K = Vcm/(Vcm+VC-VR) after Vee
• ReS x = K’(1) 1 = midline
x = K for 0 < K < 1
x = 2-(1/K) for 1 < K < infinity
• ReSS x = K’(2) 2 = midline
x = K for 0 < K < 2
x = 4-(4/K) for 2 < K < infinity
• ReSS x = K’(<M) M = any number as a midline
x = K for 0 < K < M
x = 2M-(M2/K) for M < K < infinity

17. • Excel Sheet set up:
• A – “Elapsed time” in 20 second intervals A2 = date
• B – 280nm
• C – 230nm
• D – mL & min
• E – tube (3 mL/tube)
• F – VM F2
• Vcm F4 [F8-F10]
• Vee F6 [F8-F10+F2]
• ` Vrun F8
• VC F10
• G – K Vm < K < Vee [ROUND((D___-F$2)/(F$10-F$2),4)]
Vee < K < Vrun [ROUND(F$4/((F$4+F$10)-D___),4)]
• H – K’(1) 0 < K < 1 [ROUND((D___-F$2)/(F$10-F$2),4)]
1 < K < infinity [ROUND(2-1/G____,4)]
• I – K’(2) 0 < K < 2 [ROUND((D____-F$2)/(F$10-F$2),4)]
2 < K < infinity [ROUND(4-4/G____,4)]

18. Notes
With this set-up you can fool around with VM
and Vrun to fit the chromatogram nicely into
the plot.
• Columns G, H, and I require you to
manually put the two different equations in
for the proper intervals.
• Put K values into the plot, for x > midline,
once you have it in powerpoint.

19. Applications
Instrument comparison
Solvent system family mapping
Experiment time and separation
Reversed-phase / normal phase plot
Fractogram ReSS plot

20. GUESSmix in hexane / ethyl acetate / methanol / water 4:6:4:6
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.29 2.67 3.2 4 5.33 8 16 ¥K'(2)
A
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.29 2.67 3.2 4 5.33 8 16 ¥K'(2)
A
280nm
230nm
J-type centrifuge 120 mL
Fast Centrifugal Partition Chromatography (FCPC) 200 mL
220 mg
440 mg
G
H
X
T
r
C
D
F
R
U
V
A
Q
M
N
Z
E O
I
Y
b

21. HEMWat +3 VCM = 313 mL
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.29 2.67 3.2 4 5.33 8 16 ∞
KD
A 280nm
230nm
I II III
r C
F
U
V
M
Q
N
Z E
O
b
HEMWat +3 VCM = 254.5 mL
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.29 2.67 3.2 4 5.33 8 16 ∞KD
A
HEMWat +3 VCM = 228 mL
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.29 2.67 3.2 4 5.33 8 16 ∞
KD
A
HEMWat +3 VCM = 162 mL
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.29 2.67 3.2 4 5.33 8 16 ∞KD
A
I II III
I II III
I II III
a
b
c
d
MS

22. GUESSmix in hexane /ethyl acetate / methanol / water 4:6:4:6
0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425
mL
A
280nm
230nm
r
C
F
U
V
M
Q
N
Z
E
O
b
I II III
run time = 7.2 hours
0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425
mL
A
I II III
run time = 6.3 hours
Experiment time and separation behavior

23. 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425
mL
A
I II III
run time = 4.8 hours
0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425
mL
A
I II III
run time = 5.8 hours
Experiment time and separation behavior

24. A
280nm
230nm
A
K
0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1 1.14 1.33 1.6 2 2.67 4 8 ∞
IIII II
IIIII I1/K
Reversed Phase
Normal Phase
G
H
X
T
r
C
D
F
R
U
V
A
Q
M
N
Z
E O
I
Y
b

25. KD
intervals
0
≤ KD < 0.0625
0.0625
≤ KD <
0.125
0.125
≤ KD < 0.25
0.25
≤ KD < 0.5
0.5
≤ KD <
1
1
≤ KD <
2
2
≤ KD <
4
4
≤ KD <
8
8
≤ KD <
16
16
≤ KD <
32
32
≤ KD <
∞
HEMWat
0 rXHTG DR CF
QUA
V
N ME Z O I Yb
DEMWat
0 rXHT G D C
FUV
A
RQ
ZMN
E
OI Yb
GUESS Mix in DEMWat 5:5:5:5
0 0.25 0.5 0.75 1 1.33 2 4 ∞K'(1)
A
HEMWat 0
0 0.25 0.5 0.75 1 1.33 2 4
∞K'(1)
A
280nm
230nm
O
I
Yb
Z
E
M
NA
VU
F
DRX
H
T
G
r
C
Q
I
X
H
T
r
G
D
C
F
U
V
A
R
Q
ZMNE
OIYb

26. Alpinia combined fraction in hexane / tert-butylmethylether / methanol / water 5:5:5:5
0 0.25 0.5 0.75 1 1.33 2 4 ¥K'(1)
A
Alpinia DCM extract in hexane / ethyl acetate / methanol / water 5:5:5:5
0 0.25 0.5 0.75 1 1.33 2 4 ¥K'(1)
A
0
5
10
15
mg
280nm
230nm
mg
OH
O
OO
HO
OO
O
OH
O
O
OH
O

27. 0 0.5 1 1.5 2 2.5 3 3.5 4 4.57 5.33 6.4 8 10.67 16 32 ¥
Oplopanax crude extract in hexane / DCM / methanol / water 7:3:7:3
hexane / ethyl acetate 8:2 hexane / ethyl acetate 7:3
ReS
40
60
80
100
120
140
0 0.25 0.5 0.75 1.33 2 4 ¥K'(1)
40
60
80
100
120
140
0 0.5 1 1.5 2.67 4 8 ¥K'(2)
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3.6 4.5 6 9 18 ¥K'(3)
40
60
80
100
120
140
0 1 2 3 5.33 8 16 ¥K'(4)
tube tube
tubetube
ReSS

28. References
Reciprocal Symmetry Plots as a New Representation of
Countercurrent Chromatograms. G.F. Pauli, J.B. Friesen US
8175817 B2 awarded 05/08/2012.
http://www.google.com/patents/US8175817
Friesen, J. B.; Pauli, G. F., Reciprocal symmetry plots as a
representation of countercurrent chromatograms. Analytical
Chemistry 2007, 79, 2320-2324
Friesen, J. B.; Pauli, G. F., Rational development of solvent system
families in counter-current chromatography. Journal of
Chromatography A 2007, 1151, 51-59.
Friesen, J. B.; Pauli, G. F., Performance characteristics of countercurrent
separation in analysis of natural products of agricultural significance. Journal
of Agricultural and Food Chemistry 2008, 56, 19-28.
Friesen, J. B.; Pauli, G. F., GUESSmix-guided optimization of
elution-extrusion counter-current separations. Journal of
Chromatography A 2009, 1216, 4225-4231.