examples of mcr-als applications (from r.tauler et al.) - cid… · rank-deficient matrices a data...

Examples of MCR-ALS applications (from R.Tauler et al.)

•Chromatographic coelution•Spectrometric titrations of multiequilibriasystems•Process analysis• continuous flow methods FIA•melting conformations of polynucleotides•protein folding•voltamperometric data (Me-peptide interactions)•environmental data

R.Tauler, A.Izquierdo-Ridorsa and E.CasassasChemometrics and Intelligent Laboratory Systems, 18 (1993, 293-300

Spectrometric titrations: An easy way for the generation of two- and three-way data in the study of chemical reactions and interactions

T=37oC

Spectrophotometer

Peristalticpump

0.050 ml

-125.3

pHmeter

Autoburette

Computer

PrinterStirrer

Thermostatic bath

400 450 500 550 600 650 700 750 800 850 9000

0.1

0.2

0.3

0.4

400 450 500 550 600 650 700 750 800 850 9000

0.1

0.2

0.3

0.4

0.5

400 450 500 550 600 650 700 750 800 850 9000

0.1

0.2

0.3

0.4

0.5

n

Three spectrometric titrations of a multiequilibria system:Cu(II)-salicylate

3 4 5 6 7 8 90

10

20

30

40

50

60

70

80

90

100

pH

.- individual anal., +- simoult. anal., --co

ncen

tratio

n in

%

3 4 5 6 7 8 90

10

20

30

40

50

60

70

80

90

100

pH

conc

entra

tion

in %

.- individual anal., +- simoult. anal., --

400 500 600 700 800 9000

5

10

15

20

25

30

35

40

45ab

sorb

ance

s

n

.- individual anal., +- simoult. anal., --

R.Tauler, B.Kowalski and S.FlemingAnal. Chem., 65 (1993) 2040-47

0 10 20 30 40 50 60 700.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

spectra channel

IR a

bsor

banc

e

IR raw process data: one run

0 10 20 30 40 50 60 70-10

-8

-6

-4

-2

0

2

4x 10

-4

spectra channel

sign

al s

econ

d de

rivat

ive

2nd derivative raw process data

0 10 20 30 40 50 60 70-10

-8

-6

-4

-2

0

2

4x 10

-4

spectra channel

sign

al s

econ

d de

rivat

ive

PCA filtered (3 comp.) 2nd derivative raw process data

0 20 40 60 80 100 120 1400

0.05

0.1

0.15

0.2

0.25

0.3

0.35

time

conc

entra

tion,

a.u

.

EFA of 2nd derivative data: initial estimation of process profiles

for 3 components

0 10 20 30 40 50 60 700

1

2

3

4

5

6

7

spectra channel

abso

rban

ce, a

.u.

1

2

3

ALS resolved pure IR spectra profiles

0 100 200 300 400 500 600 700 8000

0.05

0.1

0.15

0.2

0.25

time

conc

entra

tion,

a.u

.

1 1

1

1

11

1

3

13

1

2

2

33 2

3

2222

ALS resolved pure concetration profilesin the simultaneous analysis of eigth

runs of the process

J.Saurina, S.Hernandez-Cassou, R.Tauler, A.Izquierdo-Ridorsa

Anal.Chem.,1998

Mixture analysis of nucleic acid constituents bymeans of continuous flow methods

Acid-base properties of the compounds analyzed

Compound pKa Working conditionscytosine 4.56 (N(3)) 37oC; I=0.15 M

11.7 (N(1)) 25oC; I=0.1 Mcytidine 4.13 (N(3)) 37oC; I=0.15 Madenosine 3.6 (N(1)) 25oC; I=0.1 Muridine 8.855 (N(3)) 37oC; I=0.15 Minosine 8.50 (N(1)) 37oC; I=0.15 Minosine-5’-monophosphate 6.00 (phosphate) 34oC; 0.5 M

9.27 (N(1)) 34oC; 0.5 M

Absorption spectra for the protonated and deprotonatedforms of the nucleosides adenosine, cytidine, inosine anduridine

200 250 300 3500

0.05

0.1

0.15

0.2

0.25

Wavelength (nm)

Abs

orba

nce

HA

HC

HI HU

200 250 300 3500

0.05

0.1

0.15

0.2

0.25

Wavelength (nm)

Abs

orba

nce

C

A

I

U

CONTINUOUS-FLOW SYSTEM

D

Sample

H3PO4 WT

MCP

PO43-SV

Flow

H3PO4PO43- Sample +Sample +

250300

350 0

50

1000

0.2

0.4

0.6

0.8

1

Wavelength (nm)Time (s)

Abs

orba

nce

SINGLE INJECTION FLOW-INJECTION SYSTEM

V

PMC

D WRC

H3PO4

PO43-

Sample

Flow

H3PO4 H3PO4PO43-Sample +

250

300

350 0 50100 150 200

0

0.01

0.02

0.03

0.04

0.05

0.06

Wavelength (nm) Time (s)

Abs

orba

nce

RESOLUTION OF THE EXPERIMENTAL DATA WITH

THE MCR-ALS METHOD

. Compliance of the linear Beer’s law:

Daug = Caug ST + E

Spectra

t1

tm

=

NC

NC

�n �n��

t1

t1

t1

tm

tm

tm

Sample

Standard

Csam.

Cstd.

Species correspondence between matrices

Continuous-flow system

1 1 1 1 1 1 Sample matrix

1 1 1 0 0 0 Standard matrix

Single injection flow-injection system

1 1 1 1 Sample matrix

1 1 0 0 Standard matrix

Initial estimation of the Caug data matrix

Spectra

t1

tm

NC

NC

�n �n��

t1

t1

t1

tm

tm

tm

Sample

Standard

xxxxxxxxxx

xxxxxxxxxx

xxxxx00000

xxxxx00000

ALS optimization

1st step: ST = (Caug)+ D*aug

2nd step: Caug = D*aug (ST)+

These steps are repeated until convergence is achieved.

Constraints applied:

(a) unimodal concentration profiles (not applicable to single injection

flow-injection system)

(b) non-negative concentration profiles and pure spectra

(c) the pure spectrum of each species is the same in all runs

(d) concentration profiles of common species present in different runs

have equal shapes.

RESULTS: CONTINUOUS-FLOW SYSTEM

250 300 3500

0.2

0.4

0.6

0.8

1

Wavelenght (nm)

Abs

orba

nce

interf.

interf.

interf.

HC

C

DC

0 50 1000

0.5

1

1.5

Time (seconds)

Arb

itrar

y co

ncen

tratio

n

DC

CHC

standard [C]

0 50 1000

0.5

1

1.5

Time (seconds)

Arb

itrar

y co

ncen

tratio

n

HCC DC

interf.

interf.interf.

mixture [CIAU]

Data matrix %Prediction error %fitting error

Acidic Basic Decomposition product

[CIAU;C] 9.2 51.6 7.8 1.45

[CU;C] 1.9 14.9 1.4 1.07

[CIA;C] 3.6 1.7 0.2 1.31

[drug;S] 2.4 8.6 1.1 1.74

RESULTS: SINGLE INJECTION FLOW-INJECTION

250 300 3500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

Wavelength (nm)

Abs

orba

nce

interf

interf

C

HC

0 100 2000

0.5

1

1.5

2

Time (s)

Arb

itrar

y co

ncen

tratio

n

HC

C

interf

interf

mixture [CIAU]

0 100 2000

0.5

1

1.5

2

Time (s)

Arb

itrar

y co

ncen

tratio

n

C

HC

standard [C]

Data matrix Prediction error %fitting error

Acidic Basic

[CIAU;C] 1.1 1.3 2.61

[CU;C] 2.8 0.3 6.68

[CIA;C] 17.4 0.5 4.78

[drug;S] 3.4 3.7 5.31

RANK-DEFICIENT MATRICES

A data matrix is rank-deficient when the number of significant contributions to the datavariance is lower than the number of chemical components.

In closed reacting systems in which the different concentration profiles are linearlydependent due to the governing equilibrium reactions:

Rank (D) � min (R+1, S)

R = number of independent reactions; S = number of species

Acid-base processes:

System R S Rank

1 analyte 1 2 2 Full-rank

2 analytes 2 4 3 Rank-deficient

3 analytes 3 6 4 Rank-deficient

RANK-AUGMENTATION BY MATRIX-AUGMENTATION

The inclusion of the matrix of the standard in a rank-deficient system

increases the rank of the system by one:Sample Rank of the matrices

Individual Augmented

Single analyte 2 2 Full-rank

Binary mixture 3 4 Full-rank

Ternary mixture 4 5 Rank-deficient

Quaternary mixture 5 6 Rank-deficient

For quantitative purposes only partial resolution involving those species to

be quantified is required.

This partial resolution is already achieved when the analysis is performed o

the augmented matrix which contains the data matrix of the sample and tha

of the standard.

n

t

For quantitative purposes only partial resolution involving those

species to be quantified is required.

This partial resolution is already achieved when the analysis is

performed on the augmented matrix which contains the data

matrix of the sample and that of the standard.

R.Tauler, R.Gargallo, M.Vives and A.Izquierdo-Ridorsa

Chemometrics and Intelligent Lab Systems, 1998

poly(adenylic)-poly(uridylic) acid systemMelting data

10 20 30 40 50 60 70 80 900.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

Temperature (oC)

Abs

orba

nce

Melting data recorded at 260 nm(univariate data analysis)

20 30 40 50 60 70 80 900.23

0.235

0.24

0.245

0.25

0.255

0.26

0.265

Temperature (oC)

Abso

rban

ce

Melting recorded at 280 nm

Melting 1Melting 2

20 30 40 50 60 70 80 900

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Temperature

Rel

ativ

e co

ncen

tratio

n

poly(A)-poly(U) ds

poly(U) rc

poly(A)-poly(U)-poly(U) tspoly(A) cs

poly(A) rc

poly(A)-poly(U) system. Two different melting experiments

ALS recovered concentrationprofiles

ALS recovered pure spectra

240 260 280 3000

0.05

0.1

0.15

0.2poly(A)-poly(U)-poly(U) ts

240 260 280 3000

0.05

0.1

0.15

0.2poly(A)-poly(U) ds

240 260 280 3000

0.05

0.1

0.15

0.2poly(U)

240 260 280 3000

0.05

0.1

0.15

0.2

poly(A)

rc

ss

Example: Two-phase induction of the non-native �-helical form of the �-

lactoglobulin in the presence of trifluoroethanol (Biophys. J.)

-40-30-20-10

0

10

20

30

40

50

0

10

20

30

40

210220

230240

250

[��]

x103

(deg

·cm

2 ·dm

ol-1

)

% TFE

/H 2O (v

/v)� (nm) nr. of components

1 2 3 4 5 6 7 8

Sing

ular

Val

ues

0

50

1001000

1100

nr. of components1 3 5 7

ln (S

.V.)

0

2

4

6

8a)b)

Mendieta J, Folque H. and Tauler R., Biophys. J., in pressMendieta J, Folque H. and Tauler R., Biophys. J., in press

��(nm)

200 210 220 230 240 250

��x

103 (d

eg·c

m2 ·d

mol

-1)

-40-30-20-10

01020304050

I

IIIII

a)

% TFE/H2O (v/v)

0 5 10 15 20 25 30 35 40

rela

tive

conc

.

0.0

0.2

0.4

0.6

0.8

1.0IIII II

b)

Table 1: Secondary structure of the spectra recovery after ALS optimizationnative like form Intermediate form non-native helical form

�-helix 21.14 56.11 79.61�-sheet 53.81 2.14 0.00random coil 25.05 41.75 20.39

* The content of secondary structure was evaluated by least squares deconvolution using as basis spectracorresponding to �-helix, �-sheet and random coil, those described by Chen et al. (ref 36)


% TFE/H2O (v/v)0 10 20 30 40 50 60

rela

tive

conc

.

0.0

0.2

0.4

0.6

0.8

1.0

�-sheet

random coil

�-helix


Example: Cadmium binding properties of the C-terminal

hexapeptide from mouse methylthionein (submited for

publication)

0

2

4

6

8

10

12

14

0.0

0.5

1.01.5

2.0

-0.8-0.7

-0.6

Current (nA

)

[Cd]/[FT]Potential (V)

Number of Components0 1 2 3 4 5 6 7 8 9 10

Nor

mal

ized

Sin

gula

r Val

ues

0.0

0.1

0.2

0.8

0.9

1.0

Mendieta J, Diaz-Cruz M.S., Monjonell A., Tauler R., Esteban M., submittedMendieta J, Diaz-Cruz M.S., Monjonell A., Tauler R., Esteban M., submitted

Potential (V)-0.5 -0.6 -0.7 -0.8 -0.9 -1.0

0.00

0.25

0.50

0.75

1.00 V I IV III IIa

[Cd]/[FT]0.0 0.5 1.0 1.5 2.0

Curr

ent (

nA)

0

5

10

15

20

pH3 4 5 6 7 8 9 10 11 12

Pote

ntia

l (V)

-1.2

-1.1

-1.0

-0.9

-0.8

-0.7

-0.6

-0.5

II

III

IV

V

Mendieta J, Diaz-Cruz M.S., Monjonell A., Tauler R., Esteban M., submitted

-16

-12

-8

-4

0

4

0.00.2

0.40.60.81.01.2

200 220 240 260 280

��

[Cd]

/[FT]

wavelength�(nm)

wavelength (nm)200 220 240 260 280

��

-18

-14

-10

-6

-2

2

220 240 260 280

-2

-1

0

1

Mendieta J, Diaz-Cruz M.S., Monjonell A., Tauler R., Esteban M., submitted

J.S.Salou, R.Tauler*,J.M.Bayona and I.Tolosa, Environ.Sci.Technol., 31,

(1997) 3482-90

0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6

chemical compounds

stan

dard

ized

con

cent

ratio

ns

concentration of 96 organic compounds in 22 sampling sites of Northwestern Mediterranean Sea

0 5 10 15 20 250

10

20ALS resolved contribution profiles

0 5 10 15 20 250

10

20

30

0 5 10 15 20 250

10

20

Data site stations

examples of mcr-als applications (from r.tauler et al.) - cid… · rank-deficient matrices a data...

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