Cascade is a modeling tool allowing gene selection, reverse engineering, and prediction in cascade networks. Jung, N., Bertrand, F., Bahram, S., Vallat, L., and Maumy-Bertrand, M. (2014) https://doi.org/10.1093/bioinformatics/btt705.

The package was presented at the User2014! conference. Jung, N., Bertrand, F., Bahram, S., Vallat, L., and Maumy-Bertrand, M. (2014). “Cascade: a R-package to study, predict and simulate the diffusion of a signal through a temporal genenetwork”, book of abstracts, User2014!, Los Angeles, page 153, http://user2014.r-project.org/abstracts/posters/181_Jung.pdf.

Reverse-engineered network.

Reverse-engineered network.

Simulation of an intervention on a gene of the network.

Simulation of an intervention on a gene of the network.

This website and these examples were created by F. Bertrand and M. Maumy-Bertrand.

Installation

You can install the released version of Cascade from CRAN with:

install.packages("Cascade")

You can install the development version of Cascade from github with:

devtools::install_github("fbertran/Cascade")

Examples

Data management

Import Cascade Data (repeated measurements on several subjects) from the CascadeData package and turn them into a micro array object. The second line makes sure the CascadeData package is installed.

library(Cascade)
if(!require(CascadeData)){install.packages("CascadeData")}
#> Le chargement a nécessité le package : CascadeData
data(micro_US)
micro_US<-as.micro_array(micro_US,time=c(60,90,210,390),subject=6)

Get a summay and plots of the data:

summary(micro_US)
#> Le chargement a nécessité le package : cluster
#>    N1_US_T60        N1_US_T90        N1_US_T210       N1_US_T390    
#>  Min.   :   1.0   Min.   :   1.0   Min.   :   1.0   Min.   :   1.0  
#>  1st Qu.:  19.7   1st Qu.:  18.8   1st Qu.:  15.2   1st Qu.:  20.9  
#>  Median :  38.0   Median :  37.2   Median :  34.9   Median :  40.2  
#>  Mean   : 107.5   Mean   : 106.9   Mean   : 109.6   Mean   : 105.7  
#>  3rd Qu.:  80.6   3rd Qu.:  82.1   3rd Qu.:  82.8   3rd Qu.:  84.8  
#>  Max.   :8587.9   Max.   :8311.7   Max.   :7930.3   Max.   :7841.8  
#>    N2_US_T60        N2_US_T90        N2_US_T210       N2_US_T390    
#>  Min.   :   1.0   Min.   :   1.0   Min.   :   1.0   Min.   :   1.0  
#>  1st Qu.:  18.5   1st Qu.:  17.1   1st Qu.:  15.8   1st Qu.:  17.7  
#>  Median :  36.9   Median :  36.7   Median :  36.0   Median :  37.4  
#>  Mean   : 110.6   Mean   : 102.1   Mean   : 106.8   Mean   : 111.3  
#>  3rd Qu.:  85.3   3rd Qu.:  78.2   3rd Qu.:  83.5   3rd Qu.:  86.4  
#>  Max.   :7750.3   Max.   :8014.3   Max.   :8028.6   Max.   :7498.4  
#>    N3_US_T60        N3_US_T90        N3_US_T210       N3_US_T390    
#>  Min.   :   1.0   Min.   :   1.0   Min.   :   1.0   Min.   :   1.0  
#>  1st Qu.:  17.3   1st Qu.:  19.5   1st Qu.:  16.4   1st Qu.:  20.9  
#>  Median :  34.4   Median :  38.2   Median :  34.7   Median :  41.0  
#>  Mean   : 101.6   Mean   : 107.1   Mean   : 100.3   Mean   : 113.9  
#>  3rd Qu.:  75.4   3rd Qu.:  82.3   3rd Qu.:  76.3   3rd Qu.:  89.2  
#>  Max.   :8072.2   Max.   :7889.2   Max.   :8278.2   Max.   :6856.2  
#>    N4_US_T60        N4_US_T90        N4_US_T210       N4_US_T390    
#>  Min.   :   1.0   Min.   :   1.0   Min.   :   1.0   Min.   :   1.0  
#>  1st Qu.:  20.4   1st Qu.:  19.5   1st Qu.:  20.5   1st Qu.:  19.9  
#>  Median :  38.9   Median :  38.5   Median :  39.9   Median :  38.8  
#>  Mean   : 113.6   Mean   : 114.8   Mean   : 110.1   Mean   : 111.7  
#>  3rd Qu.:  84.6   3rd Qu.:  86.1   3rd Qu.:  86.8   3rd Qu.:  85.4  
#>  Max.   :9502.3   Max.   :9193.4   Max.   :9436.0   Max.   :8771.0  
#>    N5_US_T60        N5_US_T90        N5_US_T210       N5_US_T390    
#>  Min.   :   1.0   Min.   :   1.0   Min.   :   1.0   Min.   :   1.0  
#>  1st Qu.:  16.8   1st Qu.:  18.8   1st Qu.:  19.5   1st Qu.:  19.9  
#>  Median :  34.5   Median :  36.9   Median :  38.2   Median :  39.0  
#>  Mean   : 111.3   Mean   : 108.0   Mean   : 107.4   Mean   : 109.8  
#>  3rd Qu.:  82.0   3rd Qu.:  81.4   3rd Qu.:  82.4   3rd Qu.:  84.9  
#>  Max.   :8569.3   Max.   :7970.1   Max.   :8371.0   Max.   :7686.5  
#>    N6_US_T60        N6_US_T90        N6_US_T210       N6_US_T390    
#>  Min.   :   1.0   Min.   :   1.0   Min.   :   1.0   Min.   :   1.0  
#>  1st Qu.:  21.1   1st Qu.:  21.5   1st Qu.:  19.9   1st Qu.:  20.2  
#>  Median :  40.9   Median :  40.8   Median :  39.1   Median :  39.4  
#>  Mean   : 110.1   Mean   : 108.5   Mean   : 112.0   Mean   : 109.5  
#>  3rd Qu.:  86.3   3rd Qu.:  85.6   3rd Qu.:  86.3   3rd Qu.:  86.6  
#>  Max.   :8241.0   Max.   :8355.0   Max.   :8207.1   Max.   :9520.0

Gene selection

There are several functions to carry out gene selection before the inference. They are detailed in the two vignettes of the package.

Data simulation

Let’s simulate some cascade data and then do some reverse engineering.

We first design the F matrix

We set the seed to make the results reproducible and draw a scale free random network.

We simulate gene expression according to the network that was previously drawn

Get a summay and plots of the simulated data:

summary(M)
#>  log(S/US) : P1T1   log(S/US) : P1T2     log(S/US) : P1T3   
#>  Min.   :-759.882   Min.   :-2024.5979   Min.   :-1007.748  
#>  1st Qu.: -36.758   1st Qu.:  -22.5653   1st Qu.:  -68.054  
#>  Median :   6.265   Median :    0.5759   Median :   -4.192  
#>  Mean   :  10.613   Mean   :   -6.6230   Mean   :    3.085  
#>  3rd Qu.:  74.682   3rd Qu.:   78.2516   3rd Qu.:   74.866  
#>  Max.   : 647.643   Max.   :  870.7513   Max.   : 1155.413  
#>  log(S/US) : P1T4    log(S/US) : P2T1   log(S/US) : P2T2   
#>  Min.   :-1075.637   Min.   :-790.431   Min.   :-1505.543  
#>  1st Qu.:  -31.538   1st Qu.: -65.394   1st Qu.:  -59.833  
#>  Median :   -2.293   Median :   2.087   Median :   -1.262  
#>  Mean   :    9.055   Mean   :   7.791   Mean   :  -18.568  
#>  3rd Qu.:   75.316   3rd Qu.:  70.108   3rd Qu.:   76.908  
#>  Max.   :  556.449   Max.   : 669.203   Max.   : 1058.385  
#>  log(S/US) : P2T3   log(S/US) : P2T4   log(S/US) : P3T1    
#>  Min.   :-980.965   Min.   :-547.117   Min.   :-1278.6158  
#>  1st Qu.: -55.077   1st Qu.: -58.721   1st Qu.:  -42.1909  
#>  Median :  -7.144   Median :  -3.519   Median :    0.4064  
#>  Mean   : -35.647   Mean   : -24.277   Mean   :   -3.8860  
#>  3rd Qu.:  41.364   3rd Qu.:  37.621   3rd Qu.:   48.4275  
#>  Max.   :1114.897   Max.   : 270.423   Max.   :  527.3972  
#>  log(S/US) : P3T2   log(S/US) : P3T3    log(S/US) : P3T4   
#>  Min.   :-624.834   Min.   :-1018.897   Min.   :-2403.703  
#>  1st Qu.: -48.460   1st Qu.:  -52.456   1st Qu.:  -57.493  
#>  Median :  -2.505   Median :   -2.026   Median :   -4.529  
#>  Mean   : -11.950   Mean   :    5.893   Mean   :  -33.088  
#>  3rd Qu.:  33.781   3rd Qu.:   43.214   3rd Qu.:   51.808  
#>  Max.   : 576.141   Max.   : 1159.517   Max.   :  495.014  
#>  log(S/US) : P4T1   log(S/US) : P4T2     log(S/US) : P4T3  
#>  Min.   :-683.000   Min.   :-1957.3692   Min.   :-591.460  
#>  1st Qu.: -81.510   1st Qu.:  -39.3372   1st Qu.: -39.499  
#>  Median :   5.102   Median :   -0.0215   Median :   2.251  
#>  Mean   :  -2.034   Mean   :    2.9550   Mean   :  27.377  
#>  3rd Qu.:  74.738   3rd Qu.:   77.1869   3rd Qu.:  62.097  
#>  Max.   : 454.955   Max.   :  955.0680   Max.   :1341.859  
#>  log(S/US) : P4T4   log(S/US) : P5T1   log(S/US) : P5T2   
#>  Min.   :-577.069   Min.   :-436.986   Min.   :-647.1962  
#>  1st Qu.: -31.924   1st Qu.: -69.809   1st Qu.: -48.5156  
#>  Median :   2.456   Median :   2.156   Median :  -0.2949  
#>  Mean   :  29.675   Mean   :  -2.929   Mean   :   6.2300  
#>  3rd Qu.:  35.322   3rd Qu.:  47.462   3rd Qu.:  47.9558  
#>  Max.   :1577.042   Max.   : 651.596   Max.   :1359.9584  
#>  log(S/US) : P5T3   log(S/US) : P5T4  
#>  Min.   :-409.347   Min.   :-188.652  
#>  1st Qu.: -44.205   1st Qu.: -33.097  
#>  Median :  -1.056   Median :   1.873  
#>  Mean   :   6.190   Mean   :  26.740  
#>  3rd Qu.:  47.694   3rd Qu.:  67.879  
#>  Max.   : 434.178   Max.   : 743.820

plot(M)

Network inference

We infer the new network using subjectwise leave one out cross-validation (all measurement from the same subject are removed from the dataset)

Heatmap of the coefficients of the Omega matrix of the network

stats::heatmap(Net_inf_C@network, Rowv=NA, Colv=NA, scale="none", revC=TRUE)

###Post inferrence network analysis We switch to data that were derived from the inferrence of a real biological network and try to detect the optimal cutoff value: the best cutoff value for a network to fit a scale free network.

#> $p.value
#>  [1] 0.000 0.000 0.569 0.295 0.242 0.147 0.012 0.387 0.351 0.096
#> 
#> $p.value.inter
#>  [1] -0.0655747  0.2027477  0.3488525  0.3976355  0.2215038  0.1046155
#>  [7]  0.1257731  0.2560059  0.2561465  0.1560364
#> 
#> $sequence
#>  [1] 0.00000000 0.04444444 0.08888889 0.13333333 0.17777778 0.22222222
#>  [7] 0.26666667 0.31111111 0.35555556 0.40000000

Analyze the network with a cutoff set to the previouly found 0.14 optimal value.

analyze_network(network,nv=0.14)
#> Le chargement a nécessité le package : tnet
#> Le chargement a nécessité le package : igraph
#> 
#> Attachement du package : 'igraph'
#> The following object is masked from 'package:Cascade':
#> 
#>     compare
#> The following objects are masked from 'package:stats':
#> 
#>     decompose, spectrum
#> The following object is masked from 'package:base':
#> 
#>     union
#> Le chargement a nécessité le package : survival
#> tnet: Analysis of Weighted, Two-mode, and Longitudinal networks.
#> Type ?tnet for help.
#>     node betweenness degree    output  closeness
#> 1      1           0      2 0.8926116  3.4568936
#> 2      2           8      4 1.9743442  7.6462127
#> 3      3           0      7 1.8553824  7.9432707
#> 4      4           0      8 1.7486586 19.3833453
#> 5      5           0      2 0.6506125  2.5196830
#> 6      6           0      1 0.2574582  3.5710079
#> 7      7           0      0 0.0000000  0.0000000
#> 8      8           0      1 0.1473340  9.6745021
#> 9      9           4      3 0.6096656  3.1298983
#> 10    10          13      5 0.9515114  4.1040201
#> 11    11           0      3 0.6334876 14.4151521
#> 12    12           0      8 1.9464590  8.2961649
#> 13    13           0      0 0.0000000  0.0000000
#> 14    14           0      1 0.1887766  2.8205567
#> 15    15           0      6 1.8989053 14.1284848
#> 16    16          80     21 5.9550024 25.8561407
#> 17    17           0      9 1.8968626 10.3999011
#> 18    18           0      7 1.2824028  5.6754961
#> 19    19           0      0 0.0000000  0.0000000
#> 20    20           0      0 0.0000000  0.0000000
#> 21    21           0      0 0.0000000  0.0000000
#> 22    22           0      0 0.0000000  0.0000000
#> 23    23           0      0 0.0000000  0.0000000
#> 24    24           0      0 0.0000000  0.0000000
#> 25    25           0      0 0.0000000  0.0000000
#> 26    26           0      0 0.0000000  0.0000000
#> 27    27           0      6 2.1415518  8.7562239
#> 28    28           0      1 0.1541501  0.5969904
#> 29    29           0      0 0.0000000  0.0000000
#> 30    30           0      0 0.0000000  0.0000000
#> 31    31           0      0 0.0000000  0.0000000
#> 32    32           0      0 0.0000000  0.0000000
#> 33    33           0      0 0.0000000  0.0000000
#> 34    34           0      1 0.2454127  0.9504308
#> 35    35           0      5 1.1015903  4.6510336
#> 36    36           0      0 0.0000000  0.0000000
#> 37    37           0      0 0.0000000  0.0000000
#> 38    38           0      0 0.0000000  0.0000000
#> 39    39           0      0 0.0000000  0.0000000
#> 40    40           0      0 0.0000000  0.0000000
#> 41    41           0      0 0.0000000  0.0000000
#> 42    42           0      0 0.0000000  0.0000000
#> 43    43           0      0 0.0000000  0.0000000
#> 44    44           0      0 0.0000000  0.0000000
#> 45    45           0      0 0.0000000  0.0000000
#> 46    46           0      0 0.0000000  0.0000000
#> 47    47           0      0 0.0000000  0.0000000
#> 48    48           1      1 0.2637553  1.0214678
#> 49    49           0      1 0.1802868  0.6982120
#> 50    50           0      0 0.0000000  0.0000000
#> 51    51           0      0 0.0000000  0.0000000
#> 52    52           0      0 0.0000000  0.0000000
#> 53    53           0      0 0.0000000  0.0000000
#> 54    54           0      0 0.0000000  0.0000000
#> 55    55           0      0 0.0000000  0.0000000
#> 56    56           0      0 0.0000000  0.0000000
#> 57    57           5      1 0.4122623  1.5966037
#> 58    58           0      0 0.0000000  0.0000000
#> 59    59           0      0 0.0000000  0.0000000
#> 60    60           0      0 0.0000000  0.0000000
#> 61    61           0      0 0.0000000  0.0000000
#> 62    62           0      0 0.0000000  0.0000000
#> 63    63           4      1 0.1408429  0.5454544
#> 64    64           0      0 0.0000000  0.0000000
#> 65    65           0      0 0.0000000  0.0000000
#> 66    66           0      0 0.0000000  0.0000000
#> 67    67           0      0 0.0000000  0.0000000
#> 68    68           0      0 0.0000000  0.0000000
#> 69    69           0      0 0.0000000  0.0000000
#> 70    70           0      0 0.0000000  0.0000000
#> 71    71           0      0 0.0000000  0.0000000
#> 72    72           4      1 0.2259305  0.8749804
#> 73    73           0      0 0.0000000  0.0000000
#> 74    74           0      0 0.0000000  0.0000000
#> 75    75           3      1 0.2113341  0.8184518
#> 76    76           0      0 0.0000000  0.0000000
#> 77    77           0      0 0.0000000  0.0000000
#> 78    78           0      0 0.0000000  0.0000000
#> 79    79           2      1 0.1566707  0.6067519
#> 80    80           0      0 0.0000000  0.0000000
#> 81    81           0      0 0.0000000  0.0000000
#> 82    82           4      2 0.6126892  2.3728140
#> 83    83           7      1 0.2063532  0.7991616
#> 84    84           5      1 0.2370599  0.9180821
#> 85    85           4      1 0.1582045  0.6126923
#> 86    86           0      0 0.0000000  0.0000000
#> 87    87           0      0 0.0000000  0.0000000
#> 88    88           0      0 0.0000000  0.0000000
#> 89    89           0      0 0.0000000  0.0000000
#> 90    90           5      1 0.2023903  0.7838142
#> 91    91           0      0 0.0000000  0.0000000
#> 92    92           0      0 0.0000000  0.0000000
#> 93    93           0      1 0.1544264  0.5980606
#> 94    94           0      0 0.0000000  0.0000000
#> 95    95           0      0 0.0000000  0.0000000
#> 96    96           0      0 0.0000000  0.0000000
#> 97    97           0      0 0.0000000  0.0000000
#> 98    98           0      0 0.0000000  0.0000000
#> 99    99           0      0 0.0000000  0.0000000
#> 100  100           0      0 0.0000000  0.0000000
#> 101  101           0      0 0.0000000  0.0000000
#> 102  102           0      0 0.0000000  0.0000000