Exploring metabolomic data from

designed experiments using

ANOVA Multiblock Orthogonal

Partial Least Squares

Julien Boccard

School of Pharmaceutical Sciences

University of Geneva, University of Lausanne

Experimental design in metabolomics

Several factors can be evaluated simultaneously

e.g. dose, time, genotype

Many experimental setups generate multivariate data

e.g. spectra, omics, multi-components response

Each factor has different levels

e.g. quantitative, qualitative, ordinal

Full factorial designs allow the systematic evaluation of

- main effects

- interactions between factors

• MANOVA is not able to handle underdetermined systems (k>n)

• PCA mixes the different sources of variation

ANOVA and multivariate data analysis

How to account for the study design and covariances between variables?

Between group

variation

Total variation

Within group

variation

ASCA

ANOVA-PCA

ANOVA-PLS

ANOVA-TP

AComDim

Resαββαμ X XXXXX

Existing strategies associate ANOVA decomposition of the

experimental matrix with projection methods

ANOVA Multiblock OPLS workflow

Experimental matrix

(n x k) X

ANOVA

decomposition

(n x k) + + + XRes X A X B X AB

SVD SVD SVD

For each main effect and interaction term:

Extraction of levels barycentres from pure effect

submatrices by Singular Value Decomposition

ASCA

ANOVA Multiblock OPLS workflow

Experimental matrix

(n x k) X

ANOVA

decomposition

(n x k) + + + XRes X A X B X AB

XRes X A+XRes X B+XRes X AB+XRes

For each main effect and interaction term:

Computation of experimental submatrices

Pure effect submatrices + Residuals

Hypothesis:

The structure of a significant effect will emerge from noise

ANOVA-PCA ANOVA-TP AComDim

ANOVA Multiblock OPLS workflow

Experimental matrix

(n x k) X

ANOVA

decomposition

(n x k) + + + XRes X A X B X AB

XRes X A+XRes X B+XRes X AB+XRes

X = tpαppαT + tpβppβ

T + tpαβppαβT + topo

T + E

Y = tpαqpαT + tpβqpβ

T + tpαβqpαβT + F

Joint analysis of

the submatrices

Prediction of level barycentres based on experimental submatrices

multiblock OPLS

Y

AMOPLS model outputs

Supervised multiblock OPLS model

Joint decomposition based on predictive/orthogonal component(s)

Balance between block saliences

Assign each latent structure to a factor

Assess statistical relevance by comparison with ANOVA residuals

Permutation tests (effect-to-residuals ratio)

λp2 λo1 λp1

Observations scores

Check for sample groupings tp2

tp1

tp4

tp3

to2

to1

Variables loadings

Highlight relevant biomarkers pp2

pp1

pp4

pp3

Dataset

UHPLC-TOF/MS metabolic profiles of 3D aggregating rat brain cells

36 observations x 1’397 variables (m/z @ RetTime)

Paraquat Neurotoxicity - Dataset

2 Factors design

(i) Maturation (2 levels): Immature / Mature

(ii) Paraquat (3 levels): Control / Paraquat 0.5 µM / Paraquat 1 µM

Imm

atu

re

Ma

ture

Control Paraquat 0.5 µM Paraquat 1 µM

Paraquat Neurotoxicity - PCA

-40

-30

-20

-10

0

10

20

30

-50 -40 -30 -20 -10 0 10 20 30 40 50

tp2 (Genotype*Time) vs. toScores

t1 32.5%

t2 10.3%

Immature

Ctrl

Immature

0.5 µM

Immature

1 µM

Mature

1 µM

Mature

0.5 µM

Mature

Ctrl

The principal components are not easily interpretable

?The factors under study affect the metabolic profiles

The groups are not well-separated

The effects of Maturation and Paraquat are mixed up

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Maturation Paraquat Interaction Residuals

to

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Maturation Paraquat Interaction Residuals

tp3

Paraquat Neurotoxicity - AMOPLS

4 terms ANOVA decomposition:

6 components AMOPLS model

5 predictive (2 main effects + 1 interaction) + 1 orthogonal

Goodness of fit

R2 0.903

Maturation 25.8%

Paraquat 10.6%

Interaction 4.5%

Residuals 59.1%

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Maturation Paraquat Interaction Residuals

tp1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Maturation Paraquat Interaction Residuals

tp2

0

0.1

0.2

0.3

0.4

0.5

0.6

Maturation Paraquat Interaction Residuals

tp4

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Maturation Paraquat Interaction Residuals

tp5

tp1: Maturation tp2: Paraquat

tp3: Interaction tp4: Interaction

tp5: Paraquat to1: Residuals

Maturation (p<1%)

Interaction (p>5%)

Permutation tests

Global model (p<5%)

Effect-to-residuals ratio

Paraquat (p<1%)

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

tp1

Paraquat Neurotoxicity - Maturation effect

tp1: Scores related to Maturation

tp1

Immature

Mature

-8

-6

-4

-2

0

2

4

6

8

pp1

Maturation has a strong

impact on metabolic profiles

Immature Mature

Acylcarnitines Tyrosine dipeptides

Neurotensin Hydroxyvitamin D

Mature cells exhibit more

elaborated phenotypes

Shift from tissue growth

to neuronal cells differentiation

Mature Immature

Gangliosides (GA1, GM2) Arachidonic acid metabolism Glutamate dipeptides Precursors of serotonin Sphingomyelin

-8

-6

-4

-2

0

2

4

6

8

Paraquat Neurotoxicity - Treatment effect

tp2: Scores related to Paraquat

Paraquat Control

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

-0.25 -0.15 -0.05 0.05 0.15 0.25

tp2 (Paraquat) vs. to

Control 0.5 µM

1 µM

tp2

pp2 Dihydroquinone QH2

Peroxydation Ubiquinone-1

Prostaglandin metabolites

Cathecholamine precursors Glutamate pathway Prostamides

Intoxicated cells show altered

metabolic profiles

Shift from neurotransmission

to oxidative stress

tp5

Paraquat treatment induces

a dose-related response

Conclusions

Supervised analysis of ANOVA submatrices

Joint analysis of the effects

Easy interpretation

Contribution of each ANOVA submatrix

Objective evaluation of the effects

AMOPLS combines ANOVA decomposition of the sources of

variation, OPLS interpretability and multiblock modelling

Broad field of application

(biomarker discovery, method development, etc.)

Prof. Serge Rudaz

Dr. Fabienne Jeanneret

Dr. David Tonoli

Acknowledgements

Prof. Florianne Tschudi-Monnet

Dr. Jenny Sandström von Tobel