Advanced process modelling with multivariate curve resolution

1
Advanced process modelling with multivariate
curve resolution

• Anna de Juan1,() and Romà Tauler2.
• Chemometrics group. Universitat de Barcelona.
  Diagonal, 647. 08028 Barcelona.
  anna.dejuan_at_ub.edu
• Dept. of Environmental Chemistry. IIQAB-CSIC.
  Barcelona.

2
Process. Definition and underlying model.

• Evolving chemical system monitored by a
  multivariate signal.
• Reaction system with a known mechanism (kinetic
  process)
• Evolving system with inexistent mechanism
  (chromatographic elution)

3
Process. Definition and underlying model.
4
Process. Definition and underlying model.

• Known mechanism
• Hard-modeling (HM)

No mechanism Soft-modeling (SM)
Ordered evolving concentration pattern
5
Process soft-modeling(Multivariate Curve
Resolution, MCR)
6
MCR in process analysis
Process raw data
7
Multivariate Curve Resolution Alternating Least
Squares (MCR-ALS)
D CST E

• Determination of the number of components (PCA).
• Building of initial estimates (C or ST) (EFA,
  SIMPLISMA, prior knowledge...)

Data exploration
Input of external information

• Iterative least squares calculation of C and ST
  subject to constraints.
• Check for satisfactory CST data reproduction.

Optimal and chemically meaningful process
description
R. Tauler. Chemom. Intell. Lab. Sys. 30 (1995)
133. A. de Juan and R. Tauler. Anal. Chim. Acta
500 (2003) 195. J. Jaumot et al. Chemom. Intell.
Lab. Sys. 76 (2005) 101.
8
Constraints

• Definition
• Any property systematically present in the
  profiles of the compounds in our data set.
• Chemical origin
• Mathematical properties.
• Application
• C and S can be constrained differently.
• The profiles within C and ST can be constrained
  differently.

Reflect the inherent order in a process
9
Process constraints
Non-negativity (C, S)
Selectivity!!
10
MCR in process modelling

• Advantages (low requirements)
• Bilinear data structure
• No process model required.
• No previous identification of process compounds
  needed.

• Limitations
• We model what we measure (non-absorbing species)
• Each compound should have a distinct
  concentration profile and spectrum
  (rank-deficiency).

11
MCR in process modelling

• Limitations
• We model what we measure (non-absorbing species)
• Each compound should have a distinct
  concentration profile and spectrum
  (rank-deficiency).

12
Advanced process modelingMultiset analysis
13
Processes and multiset models
14
Multiset arrangements. Advantages.

• The chemometric reasons
• Rotational ambiguity decreases/is suppressed.
• Rank-deficiency problems are solved.
• Noise effect is minimized
• The chemical reasons
• More information introduced in the process
  modelling.
• More robustness in the process description.
• Better characterization of process compounds
  (multitechnique analysis).
• More global description of process evolution and
  of effect of inducing agents. (multiexperiment
  analysis).

15
Rank-deficient systems(the concept)
Detectable rank lt nr. of process contributions
Rank(D) min(rank C, rank ST)

• Rank-deficiency can be linked to C or to ST

16
Rank-deficient systems(the concept)
Equally shaped concentration profiles A B ?
C Rank 2
17
Rank-deficient systems(the concept)
18
Breaking rank-deficiency(multiset data)
sA ksB
sA ? ksB
sA
sA
sB
sB

SUVT
SCDT
C
19
Multitechnique process analysis
20
Multitechnique data analysis

• Only the concentration direction is shared by all
  experiments.
• Completely different techniques can be treated
  together
• Higher spectral discrimination power among
  compounds.
• The augmented response contains complementary
  information of all techniques (superspectrum).
• The single matrix of process profiles provides
  cleaner process profiles and a more robust
  description of the process.
• Process profiles are not affected by specific
  noise patterns of particular techniques.
• Process description should be valid for all
  measurements collected.

Multiset ? multi-way
21
pH-induced transitions in hemoglobin

• Evolution of protein conformations
• Global process many events at different
  structural levels.
• No mechanism defined.

• Spectroscopic monitoring between pH 1.5 and 10.5
• Changes in secondary structure
• UV (350-650 nm), far-UV CD (200-250 nm)
• Changes in tertiary structure
• UV, near-UV CD (250-350 nm), fluorescence
  (300-450 nm)
• Binding of heme group
• UV, Soret CD (380-430 nm)

Muñoz, G. de Juan, A. Anal. Chim. Acta 2007,
595, 198.
22
pH-induced transitions in hemoglobin

• (single technique resolution)

3ary structure
2ary structure
Heme binding
Global
Near-UV CD
Soret CD
UV
Far-UV CD
Fluorescence
10
D3
8
6
4
2
0
-2
-4
250
275
300
325
350
Wavelengths (nm)
Wavelengths (nm)
Wavelengths (nm)
Wavelengths (nm)
Wavelengths (nm)
pH
pH
pH
pH
pH
23
pH-induced transitions in hemoglobin
(single technique resolution)
Technique Chemical event Nr. of process contributions pH transition values Explained variance ()
Far-UV CD Changes 2ary structure 2 4.0 99.75
Near-UV CD Changes 3ary structure 2 4.5 93.83
Fluorescence Changes 3ary structure 3 4.2 / 8.7 99.96
Soret CD Heme binding 2 7.8 99.77
UV-visible Global process 4 2.8 / 3.9 / 8.5 99.75

• Some chemical events are simpler than the global
  process.
• Non absorbing species are not modelled.
• Too similar spectral contributions may not be
  distinguished.
• Multitechnique analysis is needed to complete
  the puzzle.

24
pH-induced transitions in hemoglobin

• Global process resolution (multitechnique
  analysis)

25
pH-induced transitions in hemoglobin

• Global process resolution

OxyHb
D2
Native Hb
D1
C
S3T (2)
S4T (3)
S5T (4)
S1T (2)
S2T (2)
Figures in parentheses are number of resolved
species in single technique analysis.

• Non-absorbing species are modelled (Soret CD).
• Similar spectral contributions are distinguished
  (near-UV CD).

26
Multiexperiment process analysis
27
Multiexperiment data analysis

• Only the spectral direction is shared by all
  experiments.
• No batch synchronisation is needed.
• Process induced by different agents and performed
  in different conditions can be treated together
• The single matrix ST provides cleaner pure
  spectra and a more robust structural
  characterisation of process compounds.
• Easier modelling of minor process contributions
  by using experiments with complementary
  information.
• Good experimental design may provide experiments
  with presence/absence of different species.

Multiset ? multi-way
28
Protein-drug interaction
Protein TSPP
TSPPaggregate
Protein-TSPPcomplex

• Dominant at low ligandprotein ratio and low
  ligand.

Dominant at high ligandprotein ratio and high
ligand.
Multiexperiment analysis of experiments enhancing
low and high proteinligand ratios help in the
definition of all species involved.
29
Protein-drug interaction
D1 protein-ligand complex dominates. D2
aggregate dominates
30
Protein-drug interaction
31
Advanced process modeling(Incorporating hard
models)
32
Process modelling

• Hard-modeling. The variation of a process is
  fully described by fitting a specific
  mathematical model (physicochemical or empirical)
  to the experimental measurements.
• Soft-modeling. The variation of a process is
  described by the bilinear model of the
  measurements, optimised under chemical and/or
  mathematical constraints. No explicit
  mathematical model is used.

33
Process hard-modeling

• Output C, S and model parameters.
• Unique solutions
• The model must describe all the experimental
  variation.

34
Process Hard modeling (multibatch/multiexperiment)
Link among batches ? model

• Need of one global model
• or
• Knowledge of the link expression among different
  batch models

35
Soft- modeling (one experiment)
ST
C
D
,
Constrained ALS optimisation LS (D,C) ? S LS
(D,S) ? C min (D CS)

• Output C and S.
• Solutions might be ambiguous.
• All absorbing contributions in and out of
  the process are modelled.

36
Soft-modeling (multibatch/multiexperiment)
Link among batches ? pure spectra
Different experiments can be analysed
together Experimental conditions, link among
batches may be unknown.
37
Incorporating hard-modeling in MCR

• All or some of the concentration profiles can be
  constrained.
• All or some of the batches can be constrained.

38
Hybrid hard- and soft-modeling MCR (HS-MCR)

• Output C, S and model parameters.
• Hard models and soft-modeling constraints act
  simultaneously.
• Off-process contributions can be modelled
  separately.
• Process model can be recovered in the presence
  of absorbing interferences.

39
HS-MCR (multibatch/multiexperiment)
Link among batches (pure spectra)

• Global or individual models can be used.
• Link among different models can be unknown or
  inexistent.
• Model-free and model-based experiments can be
  analysed together.

40
Myoglobin denaturation
Mechanism
Steady-state process Native (N) ?
Intermediate (Is) ? Denatured (D) Kinetic
transient (It) Kinetic process
Steady-state process UV spectra, pH range
7.0-2.0 N ? Is ? ? D Unknown model
Kinetic process UV spectra, pH-jump
stopped-flow First-order consecutive reactions
P. Culberg, P.J. Gemperline, A. de Juan.
(submitted)
41
Myoglobin denaturation
Hard-modelling (kinetic unfolding, 1st order
reactions) Soft-modelling constraints
Model-free and model-based experiments can be
analyzed together.
42
Myoglobin denaturation
Steady-state process Native (N) ?
Denatured (D) Kinetic transient (It) Kinetic
process
time
pH

• Formation of a kinetic transient was detected and
  hard-modelled.
• k1 4.05 s.1 k2 0.62 s-1
• Steady-state unfolding was modelled with soft
  constraints.

Wavelengths
43
Photodegradation of decabromodiphenil ether
BDE-209 (flame retardant)

• UV kinetic monitoring in several THF/ water
  mixtures
• (10 water, 20 water, 30 water, 40
  water)
• Three replicates per solvent composition.

S. Mas, A. de Juan, S. Lacorte, R. Tauler
(submitted)
44
Data arrangement
45
Photodegradation of BDE-209
40 water
10 water
20 water
30 water
2
1
2
1
3
1
2
1
2
3
3
ST
C
Off-process contribution
Rate constants
Composition k1 (x 10-4) k2 (x 10-4) k3 (x 10-4)
9010 THF-water 2.76 (1) 2.60 (2) 1.38 (6)
8020 THF-water 2.448 (8) 1.613 (5) 1.362 (4)
7030 THF-water 2.41 (1) 0.99 (4) 0.77 (4)
6040 THF-water 1.933 (6) 1.092 (3) 0.68 (2)
46
MCR in process modelling. Conclusions

• Low requirements
• Bilinear data structure
• No process model required.
• No previous identification of process compounds
  needed.

• High flexibility
• In data arrangements
• Multitechnique analysis
• Multiexperiment analysis.
• Multitechnique and multiexperiment analysis.
• In input information
• Soft-modeling constraints.
• Hard models.
• Adaptable to individual compounds and/or
  experiments.

47
Acknowledgements

• Glòria Muñoz (pH-dependent hemoglobin example)
• Susana Navea (Protein-drug interaction).
• Sílvia Mas (UB and IIQAB-CSIC) (BDE-209 example)
• Pat Culberg, East Carolina University (myoglobin
  example).
• Lionel Blanchet, UB and Université des Sciences
  et Technologies de Lille (photochemical example)
• Financial support by Spanish Government
• Group Web page www.ub.es/gesq/mcr/mcr.htm

48
Process. Definition and underlying model.

• Evolving chemical system monitored by a
  multivariate signal.
• Reaction system with a known mechanism (kinetic
  process)
• Evolving system with inexistent mechanism
  (chromatographic elution)

Measurement channel
Process variable
49
Protein photochemical reaction
Photosynthetic reaction center Rhodobacter
Spheroides
Measurement IR rapid-scan spectroscopy (differenc
e spectra) (1200-1800 cm-1)
Blanchet, L. Ruckebusch, C. Huvenne, J. P. de
Juan, A. Chemom. Intell. Lab. Sys. 2007, 89, 26.
50
Protein photochemical reaction
?
?Q2
?
?P2

time
ST
D
C
Hard-modeling (ubiquinol formation and decay
contribution) Soft-modeling constraints
Kinetics of ubiquinol are modelled in the
presence of an interference (protein absorption).
51
Protein photochemical reaction
On
Off

• Kinetics of ubiquinol formation and decay are
  modelled (hard-modeling constraint).
• k1 7 10-4 s-1
• k-1 10-4 s-1
• Photoinduced protein conformational change
  (model-free) is modelled.

60
Time (s)
Amide II
Amide I
?Q2
1800
1200
-?Q1
Wavenumber (cm-1)
52
Rotational ambiguity and noise minimization
Single set of process profiles for all techniques
C,ST possible combinations with optimal fit are
less (rotational ambiguity decreases)
Noise is technique- and data set-dependent. C
encloses common information for all techniques
(noise effect is minimized)
53
Breaking rank-deficiency(multiset data)
sA
Equally shaped spectra D ? L (enantiomers) Spectra
D Spectra L Rank 1
sA ksB (rank 1)
sB
DUV

SUVT
C
D
54
D CST D CT inv(T)ST