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A new computational approach to graphically highlight regulatory relationships in polymorphic metabolic systems from chromatographic data University of Tunis El Manar Tunis, Tunisia Metabolic network analysis Highlighting regulation laws Understanding Polymorphism origins Simplex computational approach International Conference in Integrative Biology, Valencia, 2015 Nabil SEMMAR

Regulation levels (How much?) Scales (where?) Time-dependent systems (when?) Directions (How?) Biosystems (why?)

Growth Polymorphism Time-dependent system Acceleration Slow-down Cyclic, rythmic processes Multi-scale system Individual Family Pair Society Feedbacks Ressources Regulation & distribution Binary system Multidirectional system (50%) (10%) (40%) interactive

Computational approach to graphically highlight metabolic regulations in polymorphic chromatographic system Polymorphism chromatographic data Polymorphic Background Highlighted relationships Governing processes of polymorphism Input data Output graphics Combinatorial computations Population backbone Metabolic Regulatory Central

Illustrative case of the computational approach

Analysis of metabolic variations of dopamine derivatives in Parkinson-suffering population Administrated L-dopa ( mg) Dynamic analysis Metabolomics analysis 2) 1)

Highlighting metabolic polymorphism by correspondance analysis (CA) and hierarchical cluster analysis (HCA) CA Identify metabolic trends showing relatively high regulations for some metabolites Metabotypes CA

Metabolomics Analysis Variability analysis of the 248 metabolic profiles Relative levels

Highlighting metabolic polymorphism by correspondance analysis (CA) and hierarchical cluster analysis (HCA) CA Identify metabolic trends showing relatively high regulations for some metabolites Metabotypes Classification of the 248 profiles into appropriate metabotypes Cluster analysis CA

clusters  4 Metabolic trends  4 metabotypes MbTp 1 MbTp 2 MbTp 3 MbTp 4

Population Metabolic Backbone Polymorphic Background Metabolite x Metabolite y Metabolite z Metabolite x

Schéffé’s mixture design M=286 mixtures of n=10 metabolic profiles belonging to 4 metabotypes 1 2 M=286 : : : : : Population stratification into q metabotypes a priori mixture q=4 components Metabotype 1 Metabotype 2 Metabotype 3 Metabotype 4 n 1 + n 2 + n 3 + n 4 = n = 10 individuals

Geometrical representation of M mixtures of Schéffé’s design: (10,0,0,0) (0,0,10,0) (0,0,0,10) (9,1,0,0) (8,2,0,0) (7,3,0,0) (6,4,0,0) (5,5,0,0) (4,6,0,0) (3,7,0,0) (2,8,0,0) (1,9,0,0) (0,10,0,0) (9,0,1,0) (8,0,2,0) (7,0,3,0) (6,0,4,0) (5,0,5,0) (4,0,6,0) (3,0,7,0) (2,0,8,0) (1,0,9,0) M = 286 mixture points 286 ways to carry out mixtures of 10 individuals from 4 groups (4,5,1,0) q = 4 components to be combined & n = 10 individuals per mixture Simplex space with (q-1)=3 dimensions

Scheffé’s mixture design Response matrix 10 M=286 mixtures of 10 individuals belonging to 4 metabotypes 286 average profiles Average profile (3, 4, 2, 1) Average of 10 individual profiles Metabotypes’ weights Mixtures s

... k = iterations of Scheffé’s design 50 iterations of response matrix Final matrix of 286 smoothed average profiles (a) (b) (c) Metabotypes’ weights Mixtures s (d) Graphical analysis of smoothed results

Scatter plots Experimental data Smoothed data Spearman Correlations

Projections of metabotypes’ weights in the differents (286) mixture points Each point has 4 coordinates   each point results from weighted contributions of the 4 metabotypes

Multidirectional relationship between HVA and L-Dopa

1 248 : : : : : : :

Anti-clockwise Hysteretic relationship between HVA (derivative) and Dopac (precursor) 3-dimensions plot 2-dimensions plot HVA vs Dopac vs Time HVA vs Dopac (implicit time) Anti-clockwise hysteresis

… … … … … Lagged regulation Enzyme competitions

CONCLUSION

3 groups 4 groups Etc. Extraction of multidirectional and multiscale phenotype- dependent relationships Highly noised data treatment Polymorphic system time dependent processes Simplex analysis Highlighting deep regulatory dynamical lows through a serial of static relationships analyzed along time axis Combination, Iteration, Smoothing Multiscale processes Nonlinear Dynamics

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