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, https://user2014.r-project.org/abstracts/posters/181_Jung.pdf.
This website and these examples were created by F. Bertrand and M. Maumy-Bertrand.
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")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")}
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)
#> 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
plot of chunk plotmicroarrayclass
plot of chunk plotmicroarrayclass
There are several functions to carry out gene selection before the inference. They are detailed in the two vignettes of the package.
Let’s simulate some cascade data and then do some reverse engineering.
We first design the F matrix
T<-4
F<-array(0,c(T-1,T-1,T*(T-1)/2))
for(i in 1:(T*(T-1)/2)){diag(F[,,i])<-1}
F[,,2]<-F[,,2]*0.2
F[2,1,2]<-1
F[3,2,2]<-1
F[,,4]<-F[,,2]*0.3
F[3,1,4]<-1
F[,,5]<-F[,,2]We set the seed to make the results reproducible and draw a scale free random network.
set.seed(1)
Net<-Cascade::network_random(
nb=100,
time_label=rep(1:4,each=25),
exp=1,
init=1,
regul=round(rexp(100,1))+1,
min_expr=0.1,
max_expr=2,
casc.level=0.4
)
Net@F<-FWe simulate gene expression according to the network that was previously drawn
M <- Cascade::gene_expr_simulation(
network=Net,
time_label=rep(1:4,each=25),
subject=5,
level_peak=200)Get a summay and plots of the simulated data:
summary(M)
#> log(S/US) : P1T1 log(S/US) : P1T2 log(S/US) : P1T3
#> Min. :-887.428 Min. :-2060.695 Min. :-837.5811
#> 1st Qu.: -53.644 1st Qu.: -70.993 1st Qu.: -85.2176
#> Median : 6.122 Median : 2.206 Median : -6.6303
#> Mean : 3.928 Mean : -3.800 Mean : 0.5563
#> 3rd Qu.: 74.894 3rd Qu.: 79.999 3rd Qu.: 71.9501
#> Max. : 747.779 Max. : 1461.163 Max. :1279.6850
#> log(S/US) : P1T4 log(S/US) : P2T1 log(S/US) : P2T2 log(S/US) : P2T3
#> Min. :-2189.33 Min. :-431.905 Min. :-845.072 Min. :-557.840
#> 1st Qu.: -115.23 1st Qu.: -50.282 1st Qu.: -21.668 1st Qu.: -42.958
#> Median : -10.49 Median : -3.782 Median : 2.059 Median : -2.448
#> Mean : -75.60 Mean : 8.264 Mean : 18.235 Mean : 25.290
#> 3rd Qu.: 43.85 3rd Qu.: 40.975 3rd Qu.: 40.323 3rd Qu.: 46.573
#> Max. : 492.80 Max. :1287.819 Max. : 699.912 Max. :1754.081
#> log(S/US) : P2T4 log(S/US) : P3T1 log(S/US) : P3T2 log(S/US) : P3T3
#> Min. :-660.17 Min. :-868.834 Min. :-953.894 Min. :-1182.316
#> 1st Qu.: -63.34 1st Qu.: -44.656 1st Qu.: -59.964 1st Qu.: -87.170
#> Median : -10.97 Median : 1.839 Median : -1.306 Median : -2.614
#> Mean : 18.10 Mean : -2.150 Mean : 24.123 Mean : 10.224
#> 3rd Qu.: 42.56 3rd Qu.: 55.072 3rd Qu.: 78.430 3rd Qu.: 79.246
#> Max. :1418.99 Max. : 597.562 Max. :1808.233 Max. : 2761.291
#> log(S/US) : P3T4 log(S/US) : P4T1 log(S/US) : P4T2 log(S/US) : P4T3
#> Min. :-1027.24 Min. :-1012.76 Min. :-1569.32 Min. :-577.799
#> 1st Qu.: -61.31 1st Qu.: -33.79 1st Qu.: -118.83 1st Qu.: -62.623
#> Median : 16.27 Median : 11.57 Median : -13.84 Median : -8.788
#> Mean : 27.52 Mean : 10.98 Mean : -63.39 Mean : -14.803
#> 3rd Qu.: 60.93 3rd Qu.: 74.09 3rd Qu.: 40.22 3rd Qu.: 37.779
#> Max. : 1926.45 Max. : 891.60 Max. : 678.27 Max. : 430.737
#> log(S/US) : P4T4 log(S/US) : P5T1 log(S/US) : P5T2 log(S/US) : P5T3
#> Min. :-661.083 Min. :-555.708 Min. :-1467.268 Min. :-911.18
#> 1st Qu.: -41.705 1st Qu.: -64.469 1st Qu.: -68.769 1st Qu.: -71.66
#> Median : -1.468 Median : 2.697 Median : -1.565 Median : 1.54
#> Mean : 10.111 Mean : 9.403 Mean : 8.180 Mean : 13.03
#> 3rd Qu.: 67.888 3rd Qu.: 57.251 3rd Qu.: 62.256 3rd Qu.: 86.29
#> Max. : 492.723 Max. : 654.771 Max. : 990.550 Max. :1386.11
#> log(S/US) : P5T4
#> Min. :-621.705
#> 1st Qu.: -62.466
#> Median : -5.789
#> Mean : 7.083
#> 3rd Qu.: 62.041
#> Max. : 689.323
plot of chunk summarysimuldata
plot of chunk summarysimuldata
plot of chunk summarysimuldata
plot(M)
plot of chunk plotsimuldata
plot of chunk plotsimuldata
plot of chunk plotsimuldata
plot of chunk plotsimuldata
plot of chunk plotsimuldata
plot of chunk plotsimuldata
plot of chunk plotsimuldata
We infer the new network using subjectwise leave one out cross-validation (all measurement from the same subject are removed from the dataset)
Net_inf_C <- Cascade::inference(M, cv.subjects=TRUE)
#> We are at step : 1
#> The convergence of the network is (L1 norm) : 0.0072
#> We are at step : 2
#> The convergence of the network is (L1 norm) : 0.00139
#> We are at step : 3
#> The convergence of the network is (L1 norm) : 0.00106
#> We are at step : 4
#> The convergence of the network is (L1 norm) : 0.00095
plot of chunk netinf
plot of chunk netinf
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)
plot of chunk heatresults
###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.
data("network")
set.seed(1)
cutoff(network)
#> [1] "This calculation may be long"
#> [1] "1/10"
#> [1] "2/10"
#> [1] "3/10"
#> [1] "4/10"
#> [1] "5/10"
#> [1] "6/10"
#> [1] "7/10"
#> [1] "8/10"
#> [1] "9/10"
#> [1] "10/10"
#> [1] 0.000 0.001 0.126 0.112 0.091 0.584 0.885 0.677 0.604 0.363
#> $p.value
#> [1] 0.000 0.001 0.126 0.112 0.091 0.584 0.885 0.677 0.604 0.363
#>
#> $p.value.inter
#> [1] 0.0003073808 0.0222769859 0.0521597921 0.0819131661
#> [5] 0.1859011443 0.5539131661 0.8106723719 0.7795175496
#> [9] 0.6267996116 0.3396322205
#>
#> $sequence
#> [1] 0.00000000 0.04444444 0.08888889 0.13333333 0.17777778
#> [6] 0.22222222 0.26666667 0.31111111 0.35555556 0.40000000Analyze the network with a cutoff set to the previouly found 0.14 optimal value.
analyze_network(network,nv=0.14)
#> node betweenness degree output closeness
#> 1 1 0 3 0.8133348 16.4471148
#> 2 2 0 3 0.8884602 7.9547696
#> 3 3 0 1 0.1749376 10.0055952
#> 4 4 0 3 0.5159878 11.4854812
#> 5 5 0 0 0.0000000 0.0000000
#> 6 6 0 13 3.5794097 25.6388630
#> 7 7 0 4 0.9685114 7.0356510
#> 8 8 0 0 0.0000000 0.0000000
#> 9 9 0 0 0.0000000 0.0000000
#> 10 10 3 2 0.6047036 3.0439695
#> 11 11 31 10 1.9146802 8.2263869
#> 12 12 1 1 0.2056836 0.8489352
#> 13 13 97 19 3.7578360 18.6066356
#> 14 14 0 0 0.0000000 0.0000000
#> 15 15 0 0 0.0000000 0.0000000
#> 16 16 0 0 0.0000000 0.0000000
#> 17 17 2 2 0.3985715 1.6450577
#> 18 18 9 1 0.1408025 0.5811461
#> 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 0 0.0000000 0.0000000
#> 28 28 9 2 0.3786198 1.5627095
#> 29 29 0 0 0.0000000 0.0000000
#> 30 30 28 6 1.1216028 4.6292854
#> 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 3 1 0.1988608 0.8207750
#> 35 35 0 0 0.0000000 0.0000000
#> 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 0 0 0.0000000 0.0000000
#> 49 49 0 0 0.0000000 0.0000000
#> 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 10 3.2277268 22.2234874
#> 56 56 13 3 0.7360000 3.5063367
#> 57 57 0 0 0.0000000 0.0000000
#> 58 58 1 1 0.2291004 0.9455855
#> 59 59 0 0 0.0000000 0.0000000
#> 60 60 0 2 0.3955933 7.4313822
#> 61 61 0 3 1.2813639 7.0435303
#> 62 62 0 0 0.0000000 0.0000000
#> 63 63 0 0 0.0000000 0.0000000
#> 64 64 2 2 0.3878745 1.6009071
#> 65 65 0 2 1.2169141 10.8093303
#> 66 66 5 1 0.3016614 1.2450723
#> 67 67 3 3 0.5958934 2.4594808
#> 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 26 8 1.6479964 6.8019142
#> 72 72 0 0 0.0000000 0.0000000
#> 73 73 0 0 0.0000000 0.0000000
#> 74 74 0 0 0.0000000 0.0000000