Kinetics analysis of microarray Modelling and clustering of gene expression profiles

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Kinetics analysis of microarray Modelling and
clustering of gene expression profiles
Robert-Granié C. INRA-Station dAmélioration
Génétique des Animaux San Cristobal M., Liaubet
L. INRA-Laboratoire de Génétique
Cellulaire Martin PGP. INRA-Laboratoire de
Pharmacologie et Toxicologie Déjean
S. Institut de Mathématiques, Université Paul
Sabatier
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Skeletal muscle gene expression after local injury

• 10 male piglets (ranging from 23 to 32 Kg body
  weight)
• 4 IM injection of propylene glycol in
  Longissimus dorsi (LD) muscle
• 5 random sites in the left and right LD muscles
  at different time-intervals

Control
Acclimatization period
- 21 days
- 7 days
- 48h
- 6h
Euthanasia
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cDNA microarrays
2.5 cm

• 50 muscle samples for RNA isolation
• 3456 pig cDNA clones
• spotted in duplicate on two separate fields in
  the same membrane
• Nylon cDNA microarrays

7.5 cm
Muscle Lesion 1
Muscle Lesion 2
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Mean profiles of the normalized intensities

• 10 pigs x 5 time points
• x 2 replicats
• 100 observations/clone
• 3456 clones

Sample of 50 gene profiles
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Hepatic gene expression profiles

• Temporal gene expression profiles during a
  fasting period for mouse
• 88 mice
• - 2 genotypes (wild-type and knockout PPAR?-/-)
• - 11 time points between 0 and 72 hours
• (0h-3h-6h-9h-12h-18h-24h-36h-48h-60h-72h)
• - 4 mice / time point / genotype
• - RNA from liver
• 200 genes (dedicated cDNA chip) on nylon
  membranes

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Means of the observed values by genotype
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Biological questions
- To fit the kinetics of gene expression - To
identify the differentially expressed genes along
times (pig) / both along times and between
genotype (mice) - To identify homogeneous
clusters of gene with similar profiles
whatever the level of expression
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The simplest semi parametric model
Each gene is fitted by a penalized linear spline
model (Ruppert, Wand, Caroll, 2003)
smooth function of time
The penalized spline smoother exactly corresponds
to the optimal predictor in a mixed model
framework - easy implementation in standard
statistical software - estimation and inference
about parameters are available
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Semi parametric mixed model using penalized
splines
To take account the differences between
individuals
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How do we select the best model ?

• Choice of the degree of the polynomial (linear,
  quadratic, cubic)
• Choice of the number of knots and knots
  locations
• - Selection of differentially expressed genes
  along times / both along times and between
  genotype

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The best model (mice data)
A linear penalized spline for each genotype
with 5 knots (12, 24, 36, 48, 60 hours)
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Selection of genes based on the significant times
x genotype interaction 23 genes are declared
differentially expressed both along times and
between genotype
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Selection of differentially expressed genes
along times (pig data)

• Locations of knots at time points 6h, 2, 7 and
  21 days
• Comparison models (RLT) to detect groups of gene
  
• with no, a low and an high individual
  variability
• Selection of genes varying during time
• 37 genes are declared differentially expressed
  along times in the group with a low individual
  variability

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Raw and fitted gene expression profiles

• Raw data Fitted individual
  profiles Mean profile

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Clustering of gene expression profiles

• On the fitted curves of 37 genes
• The curves are summarized by the values of the
  derivative of fitted expression profiles in some
  discretization points (20 points equally spaced
  between 0 and 21 days)
• 37 individual-genes in rows x 20
  variables-dates in columns
• - Hierarchical clustering (euclidian distance,
  Ward criterion)
  
  partitioning method (k-means)

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Profile clustering
Inflammation process Cellular movement Cellular
growth and proliferation
Cellular metabolism Cytoskeleton
Signal transduction Protein interaction
Protein synthesis
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Conclusion

• A flexible and simple method of fitting curves
  in kinetic studies of microarray data
• Computations are easily performed, thanks to the
  existing mixed model packages in many standard
  statistical software
• Results are in accordance with our current
  knowledge of the biological processes underlying
  muscular repair (pig data) / modulated during
  fasting (mice data)
• The models can be easily extended to more
  general models - polynomials of degree pgt1,
  - correlation among errors, -
  heterogeneity of variances

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Thank You For Your Attention
Questions !!!