Cascade, Selection, Reverse-Engineering and Prediction in Cascade Networks
Frédéric Bertrand and Myriam Maumy-Bertrand
https://doi.org/10.32614/CRAN.package.Cascade
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.
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")} #> Loading required 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) #> Loading required package: cluster #> N1_US_T60 N1_US_T90 N1_US_T210 N1_US_T390 N2_US_T60 #> Min. : 1.0 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 1st Qu.: 18.5 #> Median : 38.0 Median : 37.2 Median : 34.9 Median : 40.2 Median : 36.9 #> Mean : 107.5 Mean : 106.9 Mean : 109.6 Mean : 105.7 Mean : 110.6 #> 3rd Qu.: 80.6 3rd Qu.: 82.1 3rd Qu.: 82.8 3rd Qu.: 84.8 3rd Qu.: 85.3 #> Max. :8587.9 Max. :8311.7 Max. :7930.3 Max. :7841.8 Max. :7750.3 #> N2_US_T90 N2_US_T210 N2_US_T390 N3_US_T60 N3_US_T90 #> Min. : 1.0 Min. : 1.0 Min. : 1.0 Min. : 1.0 Min. : 1.0 #> 1st Qu.: 17.1 1st Qu.: 15.8 1st Qu.: 17.7 1st Qu.: 17.3 1st Qu.: 19.5 #> Median : 36.7 Median : 36.0 Median : 37.4 Median : 34.4 Median : 38.2 #> Mean : 102.1 Mean : 106.8 Mean : 111.3 Mean : 101.6 Mean : 107.1 #> 3rd Qu.: 78.2 3rd Qu.: 83.5 3rd Qu.: 86.4 3rd Qu.: 75.4 3rd Qu.: 82.3 #> Max. :8014.3 Max. :8028.6 Max. :7498.4 Max. :8072.2 Max. :7889.2 #> N3_US_T210 N3_US_T390 N4_US_T60 N4_US_T90 N4_US_T210 #> Min. : 1.0 Min. : 1.0 Min. : 1.0 Min. : 1.0 Min. : 1.0 #> 1st Qu.: 16.4 1st Qu.: 20.9 1st Qu.: 20.4 1st Qu.: 19.5 1st Qu.: 20.5 #> Median : 34.7 Median : 41.0 Median : 38.9 Median : 38.5 Median : 39.9 #> Mean : 100.3 Mean : 113.9 Mean : 113.6 Mean : 114.8 Mean : 110.1 #> 3rd Qu.: 76.3 3rd Qu.: 89.2 3rd Qu.: 84.6 3rd Qu.: 86.1 3rd Qu.: 86.8 #> Max. :8278.2 Max. :6856.2 Max. :9502.3 Max. :9193.4 Max. :9436.0 #> N4_US_T390 N5_US_T60 N5_US_T90 N5_US_T210 N5_US_T390 #> Min. : 1.0 Min. : 1.0 Min. : 1.0 Min. : 1.0 Min. : 1.0 #> 1st Qu.: 19.9 1st Qu.: 16.8 1st Qu.: 18.8 1st Qu.: 19.5 1st Qu.: 19.9 #> Median : 38.8 Median : 34.5 Median : 36.9 Median : 38.2 Median : 39.0 #> Mean : 111.7 Mean : 111.3 Mean : 108.0 Mean : 107.4 Mean : 109.8 #> 3rd Qu.: 85.4 3rd Qu.: 82.0 3rd Qu.: 81.4 3rd Qu.: 82.4 3rd Qu.: 84.9 #> Max. :8771.0 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
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Gene selection
There are several functions to carry out gene selection before the inference. They are detailed in the package vignette and in the website-only E-MTAB-1475 re-analysis PDF.
Data simulation
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<-F
We 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) #> Loading required package: VGAM #> Loading required package: stats4 #> Loading required package: splines
Get a summay and plots of the simulated data:
summary(M) #> log(S/US) : P1T1 log(S/US) : P1T2 log(S/US) : P1T3 log(S/US) : P1T4 #> Min. :-887.428 Min. :-2060.695 Min. :-837.5811 Min. :-2189.33 #> 1st Qu.: -53.644 1st Qu.: -70.993 1st Qu.: -85.2176 1st Qu.: -115.23 #> Median : 6.122 Median : 2.206 Median : -6.6303 Median : -10.49 #> Mean : 3.928 Mean : -3.800 Mean : 0.5563 Mean : -75.60 #> 3rd Qu.: 74.894 3rd Qu.: 79.999 3rd Qu.: 71.9501 3rd Qu.: 43.85 #> Max. : 747.779 Max. : 1461.163 Max. :1279.6850 Max. : 492.80 #> log(S/US) : P2T1 log(S/US) : P2T2 log(S/US) : P2T3 log(S/US) : P2T4 log(S/US) : P3T1 #> Min. :-431.905 Min. :-845.072 Min. :-557.840 Min. :-660.17 Min. :-868.834 #> 1st Qu.: -50.282 1st Qu.: -21.668 1st Qu.: -42.958 1st Qu.: -63.34 1st Qu.: -44.656 #> Median : -3.782 Median : 2.059 Median : -2.448 Median : -10.97 Median : 1.839 #> Mean : 8.264 Mean : 18.235 Mean : 25.290 Mean : 18.10 Mean : -2.150 #> 3rd Qu.: 40.975 3rd Qu.: 40.323 3rd Qu.: 46.573 3rd Qu.: 42.56 3rd Qu.: 55.072 #> Max. :1287.819 Max. : 699.912 Max. :1754.081 Max. :1418.99 Max. : 597.562 #> log(S/US) : P3T2 log(S/US) : P3T3 log(S/US) : P3T4 log(S/US) : P4T1 #> Min. :-953.894 Min. :-1182.316 Min. :-1027.24 Min. :-1012.76 #> 1st Qu.: -59.964 1st Qu.: -87.170 1st Qu.: -61.31 1st Qu.: -33.79 #> Median : -1.306 Median : -2.614 Median : 16.27 Median : 11.57 #> Mean : 24.123 Mean : 10.224 Mean : 27.52 Mean : 10.98 #> 3rd Qu.: 78.430 3rd Qu.: 79.246 3rd Qu.: 60.93 3rd Qu.: 74.09 #> Max. :1808.233 Max. : 2761.291 Max. : 1926.45 Max. : 891.60 #> log(S/US) : P4T2 log(S/US) : P4T3 log(S/US) : P4T4 log(S/US) : P5T1 #> Min. :-1569.32 Min. :-577.799 Min. :-661.083 Min. :-555.708 #> 1st Qu.: -118.83 1st Qu.: -62.623 1st Qu.: -41.705 1st Qu.: -64.469 #> Median : -13.84 Median : -8.788 Median : -1.468 Median : 2.697 #> Mean : -63.39 Mean : -14.803 Mean : 10.111 Mean : 9.403 #> 3rd Qu.: 40.22 3rd Qu.: 37.779 3rd Qu.: 67.888 3rd Qu.: 57.251 #> Max. : 678.27 Max. : 430.737 Max. : 492.723 Max. : 654.771 #> log(S/US) : P5T2 log(S/US) : P5T3 log(S/US) : P5T4 #> Min. :-1467.268 Min. :-911.18 Min. :-621.705 #> 1st Qu.: -68.769 1st Qu.: -71.66 1st Qu.: -62.466 #> Median : -1.565 Median : 1.54 Median : -5.789 #> Mean : 8.180 Mean : 13.03 Mean : 7.083 #> 3rd Qu.: 62.256 3rd Qu.: 86.29 3rd Qu.: 62.041 #> Max. : 990.550 Max. :1386.11 Max. : 689.323
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plot(M)
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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)
Net_inf_C <- Cascade::inference(M, cv.subjects=TRUE) #> Loading required package: nnls #> 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
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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 0.40000000
Analyze 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