020213gkmdch-general multidimensional chromatography jiří ŠevČÍk prague, the czech republic
TRANSCRIPT
020213GK MDCH-GENERAL
PROBLEMS of measurements
residual error of a complex response model
n
iii XbaY1
)(
020213GK MDCH-GENERAL
PROBLEMS of measurements
extremly high number of isomers
low concentration levels
missing - standards - generally valid QSPR models
limited hardware possibilities
020213GK MDCH-GENERAL
DESCRIPTORS of measurement
residua l error o f response m odel
sta nda rds
Q SPR m odels
ha rdw a re
L I M I T E D B Y
reproducib ility
identif ica tion
inform a tion ba sed instrum enta tion
inform a tion content
a dditivity o f proba bility
ultim a te uncerta inty
Q U A N T I F I E D B Y
MEASUREMENT
020213GK MDCH-GENERAL
what is ULTIMATE UNCERTAINTY
causality
ultimate uncertainty
complementarity
probability
020213GK MDCH-GENERAL
EXPRESSING UU
for one-dimensional system
NZPUU nn /11
nr
rR
ij
ijij
1
4
1
ijij
ijn Rr
rZUU
11
4
1
020213GK MDCH-GENERAL
EXPRESSING UU
UU is determined by system efficiency (for one-dimensional system)
ttt ij // nttw ij /14 /
ntt
ttZUU
i
in 12
2 /
/
020213GK MDCH-GENERAL
PROBABILITY of the retention position
x position mean component density
xexP
x
020213GK MDCH-GENERAL
PROBABILITY of the difference in the retention position
x0 difference
saturation factor of sep space X
eedxexxP xx
x 11 00
00
x0
t1 t2
020213GK MDCH-GENERAL
PEAK CAPACITY
nc peak capacity
saturation factor of sep space X
x0
t1 t2
mn
mX
xx
c
100
020213GK MDCH-GENERAL
PEAK CAPACITYin isothermal mode
peak width = (a+btx)
x0
t1 t2
1
2ln1
11
41
2
1tba
tba
RbdttR
nn
t
tc
020213GK MDCH-GENERAL
PEAK CAPACITYin a linear temperature program mode
peak width = (a)
x0
t1 t2
121
111
12
1
ttRw
dtwR
nt
tc
020213GK MDCH-GENERAL
PEAK CAPACITYcomparison of operation modes
The effect of the chromatografic conditions on the peak capacity in a one-dimensional system
(for R=1 and k<1;10>)
0
500
1 000
0 80 000 160 000
plate number
peak
cap
acity
isothermal temp.program
020213GK MDCH-GENERAL
PROBABILITY of peak clusters overlapping
pn number of clusters with the same number of compounds
x0
t1 t2
nn Pmp
emeempn
n 1
2 1
020213GK MDCH-GENERAL
CLUSTERS (n-tets) in one-dimensional chromatography
10
00
0
20
00
0
30
00
0
40
00
0
50
00
0
60
00
0
70
00
0
80
00
0
90
00
0
10
00
00
10
9
8
7
6
5
43
21
0
5
10
15
20
25
30
35
Po
če
t s
ing
letů
v n
-te
tec
h
Počet teoretických pater
n-tet
020213GK MDCH-GENERAL
WHAT isthe chromatographic
dimension
chromatography (a constant value of KD)
switching (a straight inlet-separation-detector)
020213GK MDCH-GENERAL
WHAT ismultidimensional
chromatography (within one run
changes of KD for the same analyte)
switching (within one run
multiplication of any part of trajectory inlet-separation-detector)
020213GK MDCH-GENERAL
WHAT ishyphenation
can be multi-d-chromatography (HPLC-GC)
can be multi-d-switching (FID-MS)
interface of different techniques
020213GK MDCH-GENERAL
PEAK CLUSTERS in multidimesional chromatography
pn number of clusters with the same number of compounds
KD1
122 1
nd
nd
dd
d
een
mp
d
d
dd
e
emp d
dd
2
2
12
KD2
KD3
020213GK MDCH-GENERAL
PEAK CAPACITY in multidimesional chromatography
nc(d) maximum number of separated peaks
KD1
KD2
KD3
d
icd
dd
c in
dn
12
12
2
020213GK MDCH-GENERAL
RELATIVE PEAK DENSITY in multidimensional chromatography
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 1 2 3 4 5 6 7
log(m)
p/m
1-D 2-D 3-D 4-D
_
_
020213GK MDCH-GENERAL
WHAT isthe information content
uncertainty (entropy) prior to an experiment
and after it
probability that some input and output events will happen
020213GK MDCH-GENERAL
WHAT isthe information content
input P(Ii)prior to an experiment - there is an analyte i
output P(Ok)
after the experiment – there will be a measurable signal (larger than LOD)
conditional probability
020213GK MDCH-GENERAL
CONDITIONAL PROBABILITIES
P(Ok/Ii)there will be the output - measurable signal larger than LOD
when there will be the analyte i as the input
P(Ii/Ok)there will be the analyte i as the input when there will be
the output - measurable signal larger than LOD
i
kikm
kkik
kikik IP
OIPOP
OIPOP
OIPOPIOP
/
/
//
1
020213GK MDCH-GENERAL
PROBABILITIES in chromatography
output/input relation
P(Ok/Ii)
P(Ii/Ok)
P(Ok)
m k 1
aposteriory probability
m k 1
1 i n
1 i n1
1
output prob
P(Ii)
apriori probability
020213GK MDCH-GENERAL
UNCERTAINTY (ENTROPY) of
a priori status H(I)prior to an analysis
a posteriori status H(I/Ok)after the signal Ok has been measured
a posteriori status H(I/O)after the analysis has been performed
020213GK MDCH-GENERAL
UNCERTAINTY (ENTROPY) of
a priori status H(I)prior to an analysis
in
ii IPldIPIH
1
020213GK MDCH-GENERAL
UNCERTAINTY (ENTROPY) of
a posteriori status H(I/Ok)after the signal Ok has been measured
ki
n
ikik OIPldOIPOIH ///
1
020213GK MDCH-GENERAL
UNCERTAINTY (ENTROPY) of
a posteriori status H(I/O)after the analysis has been performed
km
kk OIHOPOIH //
1
020213GK MDCH-GENERAL
INFORMATION CONTENT
the difference between uncertaintiesbefore and after the analysis has been carried out
dIOIIIId
dd
//
1
OIHIHOII //
multidimensional
020213GK MDCH-GENERAL
INFORMATION CONTENTways of quantification
integration assumption of the normal distribution of the data and of the measuring error a histogram an approach based on maximum peak capacity an approach based on real peak capacity
020213GK MDCH-GENERAL
QUANTIFICATIONusing peak capacity
separation system configuration (efficiency, selectivity, operational modes)
sample composition (number of compounds, chromatographic similiarities and overlap)
n
Rtt
ldnldI1log
logmin
max
max
020213GK MDCH-GENERAL
INFORMATION CONTENTin multidimensional chromatography
mode expression [bit]
IXFR 3 to 8
IMON 5 to 11
2
122
2
22
2
1
11 100
11
4
1 RI
A
An
A
Anld
XFRIA
Anld
1
11
1
4
1
020213GK MDCH-GENERAL
INFORMATION based GC INSTRUMENTATION
multidimensional column systems IF (RIA)i= a THEN (RIA)k= c AND (RIA)k= d
hyphenated techniques P(SA)k <<>> P(SB)k
expert systems lim Σ(ε)i= 0
020213GK MDCH-GENERAL
SWITCHING MODESin multidimensional chromatography
SFL solvent-flush
XFR transfer
MON monitoring
BFL back-flush
TRP trapping
RJN re-injecton
020213GK MDCH-GENERAL
PROCESS OF IDENTIFICATION
matching actual found pattern with true one
- peak identification (noise reduction, integration, deconvolution)
- peak correlation (similarity link)
- analyte identification (match with standards)
redundant information content
ii
m
ii SAPSPAP
1
1
req
obtSI
SI
020213GK MDCH-GENERAL
FUTURE INSTRUMENTATION
principle of additivity of partial probabilities
1lim1
iiP
),,( 2iji rPifUU
020213GK MDCH-GENERAL
FUTURE INSTRUMENTATION
HW miniaturization
SW deconvolution routines multidimensional statistics