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Gene network inference




Alberto de la Fuente
    alf@crs4.it
CRS4 Bioinformatica
“Systems Genetics”
                                 (ALF lab)

              Andrea Pinna



             Nicola Soranzo



             Vincenzo de Leo



 GENOTYPE
     +                          PHENOTYPE
ENVIROMENT
ALF lab activities


• Gene network inference



• Systems Genetics simulator



• Differential networking in disease
Overview of the
                                    presentation

• Introduction to Gene networks

• Gene network inference

• Differential networking in disease
Overview of the
                                   presentation

• Introduction to Gene networks

• Gene network inference

• Differential networking in disease
Molecular genetics 101
GCCACATGTAGATAATTGAAACTGGATCCTCATCCCTCGCCTTGTACAAAAATCAACTCCAGATGGATCTAAG
ATTTAAATCTAACACCTGAAACCATAAAAATTCTAGGAGATAACACTGGCAAAGCTATTCTAGACATTGGCTT
AGGCAAAGAGTTCGTGACCAAGAACCCAAAAGCAAATGCAACAAAAACAAAAATAAATAGGTGGGACCTGATT
AAACTGAAAAGCCTCTGCACAGCAAAAGAAATAATCAGCAGAGTAAACAGACAACCCACAGAATGAGAGAAAA
TATTTGCAAACCATGCATCTGATGACAAAGGACTAATATCCAGAATCTACAAGGAACTCAAACAAATCAGCAA
GAAAAAAATAACCCCATCAAAAAGTGGGCAAAGGAATGAATAGACAATTCTCAAAATATACAAATGGCCAATA
AACATACGAAAAACTGTTCAACATCACTAATTATCAGGGAAATGCAAATTAAAACCACAATGAGATGCCACCT
TACTCCTGCAAGAATGGCCATAATAAAAAAAAATCAAAAAAGAATAAATGTTGGTGTGAATGTGGTGAAAAGA
GAACACTTTGACACTGCTGGTGGGAATGGAAACTAGTACAACCACTGTGGAAAACAGTACCGAGATTTCTTAA
AGAACTACAAGTAGAACTACCATTTGATCCAGCAATCCCACTACTGGGTATCTACCCAGAGGAAAAGAAGTCA
TTATTTGAAAAAGACACTTGTACATACATGTTTATAGCAGCACAATTTGCAATTGCAAAGATATGGAACCAGT
CTAAATGCCCATCAACCAACAAATGGATAAAGAAAATATGGTATATATACACCATGGAACACTACTCAGCCAT
AAAAAGGAACAAAATAATGGCAACTCACAGATGGAGTTGGAGACCACTATTCTAAGTGAAATAACTCAGGAAT
GGAAAACCAAATATTGTATGTTCTCACTTATAAGTGGGAGCTAAGCTATGAGGACAAAAGGCATAAGAATTAT
ACTATGGACTTTGGGGACTCGGGGGAAAGGGTGGGAGGGGGATGAGGGACAAAAGACTACACATTGGGTGCAG
TGTACACTGCTGAGGTGATGGGTGCACCAAAATCTCAGAAATTACCACTAAAGAACTTATCCATGTAACTAAA
AACCACCTCTACCCAAATAATTTTGAAATAAAAAATAAAAATATTTTAAAAAGAACTCTTTAAAATAAATAAT
GAAAAGCACCAACAGACTTATGAACAGGCAATAGAAAAAATGAGAAATAGAAAGGAATACAAATAAAAGTACA
GAAAAAAAATATGGCAAGTTATTCAACCAAACTGGTAATTTGAAATCCAGATTGAAATAATGCAAAAAAAAGG
CAATTTCTGGCACCATGGCAGACCAGGTACCTGGATGATCTGTTGCTGAAAACAACTGAAAATGCTGGTTAAA
ATATATTAACACATTCTTGAATACAGTCATGGCCAAAGGAAGTCACATGACTAAGCCCACAGTCAAGGAGTGA
GAAAGTATTCTCTACCTACCATGAGGCCAGGGCAAGGGTGTGCACTTTTTTTTTTCTTCTGTTCATTGAATAC
AGTCACTGTGTATTTTACATACTTTCATTTAGTCTTATGACAATCCTATGAAACAAGTACTTTTAAAAAAATT
GAGATAACAGTTGCATACCGTGAAATTCATCCATTTAAAGTGAGCAATTCACAGGTGCAGCTAGCTCAGTCAG
CAGAGCATAAGACTCTTAAAGTGAACAATTCAGTGCTTTTTAGTATATTCACAGAGTTGTGCAACCATCACCA
CTATCTAATTGGTCTTAGTCTGTTTGGGCTGCCATAACAAAATACCACAAACTGGATAGCTCATAAACAACAG
GCATTTATTGCTCACAGTTCTAGAGGCTGGAAGTGCAAGATTAAGATGCCAGCAGATTCTGTGTCTGCTGAGG
GCCTGTTCCTCATAGAAGGTGCCCTCTTGCTGAATTCTCACATGGTGGAAGGGGGAAAACAAGCTTGCATTGC
What are Gene networks?
ACTIVATOR 1   ACTIVATOR 2   REPRESSOR 1


       A1           A2          R1




                    T1



                TARGET 1
What are Gene networks?

                           Metabolic space

            Metabolite 1                 Metabolite 2




                        Protein space
            Protein 2

                  Complex 3:4
                                   Protein 4

Protein 1                   Protein 3




              Gene 2

                                Gene 3
Gene 1
               Gene space                      Gene 4
What are Gene networks?

                                    1      0    01  0
                                                  
                                    1      1    00  0
                                A = 0      1    10  0
X1        X2        X3                            
                                    0      0    10  1
                                    0      1 0 0 1
                                                  

     X5        X4
                                 a11 0         0         0   a15 
                                                                 
                                 a21 a22       0         0    0 
                           AW =  0 a32         a33    0       0 
                                                                 
                                 0    0        a43   a44      0 
                                                                 
                                 0 a52          0     0      a55 
Gene expression data




Matrix representation
of data:
          X p×n
 (p = #genes, n = #observations)
Overview of the
                                    presentation

• Introduction to Gene networks


• Gene network inference

• Differential networking in disease
Inferring Gene Networks
                                                = inverse problem
                                           = system identification
“~omics” data




                    algorithms


                                                          = f (x, k )
                  Correlation, partial                 dx
                correlation, regression,               dt
                    linear Ordinary
                Differential Equations,
                  graphical Gaussian
                 models, perturbation
                       analysis…
Where are the non-zeros?

                                    1      0    01  0
                                                  
                                    1      1    00  0
                                A = 0      1    10  0
X1        X2        X3                            
                                    0      0    10  1
                                    0      1 0 0 1
                                                  

     X5        X4
                                 a11 0         0         0   a15 
                                                                 
                                 a21 a22       0         0    0 
                           AW =  0 a32         a33    0       0 
                                                                 
                                 0    0        a43   a44      0 
                                                                 
                                 0 a52          0     0      a55 
Experimental strategies

‘Observational data’
  Repeated measurements of a given tissue/cell type
    without experimental intervention
     ALLOWS ONLY FOR INFERRING UNDIRECTED NETWORKS


‘Perturbation data’
  Creating targeted perturbations and measuring
    systems dynamic responses (steady states or
    time-series)
     ALLOWS FOR INFERRING DIRECTED NETWORKS
Observational data




                                                Gene C activity level
Gene B activity level




                        Gene A activity level                               Gene A activity level
Correlation ≠ Causation




    A       B
                                   C
A       B       A       B      A       B
Perturbation data


     Wild type
Over-expression Gene 1
Over-expression Gene 2
Over-expression Gene 3

Over-expression Gene n




                 Stress
Perturbation analysis
Perturbation analysis
Measure gene-expression in unperturbed (WT) state
Perturb each gene and measure gene-expression responses


                                               Perturb X2


                   Perturb X1
                   (over-express,
                   knock-down)




                                                            All perturbed
Perturbation analysis
Distinguish direct from indirect edges:
   Algebraic relation between the deviation matrix X (perturbed levels –
      wild type levels) and the network matrix (encoding the network A of
      direct interactions)




                                                                         −1
      a11 0      0    0     a15   ∆x11   0      0      0     ∆x15 
                                                                  
      a21 a22    0    0      0   ∆x21 ∆x22      0      0     ∆x25 
      0 a       a33   0      0  =  ∆x31 ∆x32   ∆x33    0     ∆x35 
           32
                                                                   
      0    0    a43   a44   a54   ∆x41 ∆x42    ∆x43   ∆x44   ∆x45 
      0    0     0     0    a55   0      0      0      0     ∆x55 
                                                                  
Linear modeling approach

                   d∆xi   n
                        = ∑ aij ∆x j + ∆u i
                    dt    j


        n                                n
   0 = ∑ aij ∆x j + ∆ui                 ∑ a ∆xij   j   = − ∆ui
        j                                j

                          JX = −U

 J = {aij } Effect of gene j on rate of change of gene i
 U = {u kk } Diagonal perturbation matrix
X = {xik } Change in gene i expression after perturbation k


              J = − UX −1
             R = U −1 J = − X −1
Further reading




                                                        Trends Genet. 2002 Aug;18(8):395-8




Scheinine, A., Mentzen, W., Pieroni E., Fotia, G., Maggio, F., Mancosu, G. and de la
Fuente, A. (2009) Inferring Gene Networks: Dream or nightmare? Part 2: Challenges 4
and 5. Annals of the New York Academy of Sciences 1158: 287301
Perturbation analysis
Perturbation analysis

Weight estimation for edge i→j: change in the
mRNA level xi,j of gene j after knockout of gene i
Z-score:

                    xi , j = x⋅, j
         Wi , j =
                        s⋅, j
Transitive reduction

The edge weight measures the total causal effect of
a gene on another gene: direct or mediated?
                     G1      G2    G3


                              X
The initial network can have many feed-forward
loops
  Not essential for reachability
  We want to remain with only “essential” edges
Further reading




Pinna, A., Soranzo, N. and de la Fuente, A. (2010) From Knockouts to Networks:
Establishing Direct Cause-Effect Relationships through Graph Analysis, PLoS ONE 5(10),
e12912 (DREAM4 Special Collection)
Figure 7 from: GeneNetWeaver: In silico benchmark generation and performance profiling of
network inference methods. Schaffter T, Marbach D, Floreano D. Bioinformatics (2011) 27 (16):
2263-2270.
Overview of the
                                    presentation

• Introduction to Gene networks

• Gene network inference


• Differential networking in disease
Disease studies




                           ?
Group 1 (healthy tissue,        Group 2 (tumor tissue,
treated with medicine,         not treated with medicine,
  tumor stage X, etc.)            tumor stage Y, etc.)
‘Differential expression’


 ?
‘Differential networking’


                        = f (x, k)
                 s   dx
        ri   thm     dt
    o
alg




                      ?
 algorit
        hms
                           = f (x, k)
                        dx
                        dt
‘Differential networking’
Differential co-expression



Healthy




 Sick




                                     (                 )
                              p     p
                     1
                           × ∑ ∑ rijhealty − rijsick
                                                       2
          D=
               p ( p − 1) 2 i =1 j =i +1
GenExpReg database

                          NCBI RefSeq
                        (32735 mRNAs)


  NCBI Gene                                          mirBase 18
(43448 genes)                                   (1921 mature miRNAs)

                        GenExpReg



 FANTOM4 EdgeExpressDB                 TargetScanHuman 6.1
       + Transmir 1.2               (669760 miRNA regulations)
   (46602 TF regulations)
In silico evaluation
Lung cancer miRNAs?
     Bhattacharjee,A. et al. (2001) Classification of human lung carcinomas by
     mRNA expression profiling reveals distinct adenocarcinoma subclasses. Proc.
     Natl Acad. Sci., 98, 13790-13795.
Family name        Seed    N. of target genestarget P-value for Notes on LungCancer3, 10000 permutations
                                        N. of in TargetScan with at least one conserved site
                                                    genes also GSCA
                                                                in LungCancer3 dataset
miR-1293           GGGUGGU           73          23     0.0022
miR-28/28-3p       ACUAGAU           77          19     0.0024 upregulated in serum copy number of lung cancer patients w.r.t. healthy [1]
miR-1244           AGUAGUU          147          53     0.0027
miR-1269           UGGACUG           77          21     0.0048
miR-1224/1224-5p   UGAGGAC           88          34     0.0050
miR-578            UUCUUGU          229          65     0.0052
miR-1305           UUUCAAC          414        106      0.0060
miR-433            UCAUGAU          207          63     0.0061
                                                                highly specific marker for squamous cell lung carcinoma [2] and non-small cell
                                                                lung cancer [3]; located in a region amplified in lung cancer; upregulated in
miR-205            CCUUCAU          288          92     0.0063 lung cancer tissues w.r.t. noncancerous lung tissues [4]
miR-1237           CCUUCUG          177          42     0.0082
miR-520a-5p/525-5p UCCAGAG          296          79     0.0085
miR-582-3p         AACUGGU           97          46     0.0086
miR-568            UGUAUAA          308          85     0.0087
miR-432            CUUGGAG          133          37     0.0090 member of miR-127 cluster, which is downregulated in tumors [5]
miR-524-3p/525-3p AAGGCGC            38          10     0.0091
miR-513c           UCUCAAG          223          64     0.0094
miR-370            CCUGCUG          239          52     0.0096 downregulated after lung development [6]

[1] Chen, X., et al. - Cell Res. 18(10) pp. 997–1006 – 2008
[2] Lebanony, D., et al. - J. Clinical Oncology 27(12) – pp. 2030-2037 – 2009
[3] Markou, A., et al. – Clin. Chem. 54(10) – pp. 1696-1704 – 2008
[4] Yanaihara, N., et al. - Cancer Cell 9(3) – pp. 189-198 – 2006
[5] Saito, Y., et al. - Cancer Cell 9(6) – pp. 435-443 – 2006
[6] Williams, A. E., et al. - Dev. Dyn. 236(2) – pp. 572-580 – 2007
IMPROVER
IMPROVER
Thank you for your
        attention

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