Cascade
Selection, Reverse-Engineering and Prediction in Cascade Networks
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) <doi:10.1093/bioinformatics/btt705>.
README
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# Cascade <img src="man/figures/logo.png" align="right" width="200"/>
# Cascade, Selection, Reverse-Engineering and Prediction in Cascade Networks
## Frédéric Bertrand and Myriam Maumy-Bertrand
<https://doi.org/10.32614/CRAN.package.bigalgebra>
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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!](https://user2014.r-project.org/) 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](https://CRAN.R-project.org) with:
``` r
install.packages("Cascade")
```
You can install the development version of Cascade from [github](https://github.com) with:
``` r
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.
``` r
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:
``` r
summary(micro_US)
#> 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
```
<div class="figure">
<img src="man/figures/README-plotmicroarrayclass-1.png" alt="plot of chunk plotmicroarrayclass" width="100%" />
<p class="caption">plot of chunk plotmicroarrayclass</p>
</div><div class="figure">
<img src="man/figures/README-plotmicroarrayclass-2.png" alt="plot of chunk plotmicroarrayclass" width="100%" />
<p class="caption">plot of chunk plotmicroarrayclass</p>
</div>
### 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
``` r
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.
``` r
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
``` r
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:
``` r
summary(M)
#> log(S/US) : P1T1 log(S/US) : P1T2 log(S/US) : P1T3 log(S/US) : P1T4 log(S/US) : P2T1
#> Min. :-887.428 Min. :-2060.695 Min. :-837.5811 Min. :-2189.33 Min. :-431.905
#> 1st Qu.: -53.644 1st Qu.: -70.993 1st Qu.: -85.2176 1st Qu.: -115.23 1st Qu.: -50.282
#> Median : 6.122 Median : 2.206 Median : -6.6303 Median : -10.49 Median : -3.782
#> Mean : 3.928 Mean : -3.800 Mean : 0.5563 Mean : -75.60 Mean : 8.264
#> 3rd Qu.: 74.894 3rd Qu.: 79.999 3rd Qu.: 71.9501 3rd Qu.: 43.85 3rd Qu.: 40.975
#> Max. : 747.779 Max. : 1461.163 Max. :1279.6850 Max. : 492.80 Max. :1287.819
#> log(S/US) : P2T2 log(S/US) : P2T3 log(S/US) : P2T4 log(S/US) : P3T1 log(S/US) : P3T2
#> Min. :-845.072 Min. :-557.840 Min. :-660.17 Min. :-868.834 Min. :-953.894
#> 1st Qu.: -21.668 1st Qu.: -42.958 1st Qu.: -63.34 1st Qu.: -44.656 1st Qu.: -59.964
#> Median : 2.059 Median : -2.448 Median : -10.97 Median : 1.839 Median : -1.306
#> Mean : 18.235 Mean : 25.290 Mean : 18.10 Mean : -2.150 Mean : 24.123
#> 3rd Qu.: 40.323 3rd Qu.: 46.573 3rd Qu.: 42.56 3rd Qu.: 55.072 3rd Qu.: 78.430
#> Max. : 699.912 Max. :1754.081 Max. :1418.99 Max. : 597.562 Max. :1808.233
#> log(S/US) : P3T3 log(S/US) : P3T4 log(S/US) : P4T1 log(S/US) : P4T2 log(S/US) : P4T3
#> Min. :-1182.316 Min. :-1027.24 Min. :-1012.76 Min. :-1569.32 Min. :-577.799
#> 1st Qu.: -87.170 1st Qu.: -61.31 1st Qu.: -33.79 1st Qu.: -118.83 1st Qu.: -62.623
#> Median : -2.614 Median : 16.27 Median : 11.57 Median : -13.84 Median : -8.788
#> Mean : 10.224 Mean : 27.52 Mean : 10.98 Mean : -63.39 Mean : -14.803
#> 3rd Qu.: 79.246 3rd Qu.: 60.93 3rd Qu.: 74.09 3rd Qu.: 40.22 3rd Qu.: 37.779
#> Max. : 2761.291 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 log(S/US) : P5T4
#> Min. :-661.083 Min. :-555.708 Min. :-1467.268 Min. :-911.18 Min. :-621.705
#> 1st Qu.: -41.705 1st Qu.: -64.469 1st Qu.: -68.769 1st Qu.: -71.66 1st Qu.: -62.466
#> Median : -1.468 Median : 2.697 Median : -1.565 Median : 1.54 Median : -5.789
#> Mean : 10.111 Mean : 9.403 Mean : 8.180 Mean : 13.03 Mean : 7.083
#> 3rd Qu.: 67.888 3rd Qu.: 57.251 3rd Qu.: 62.256 3rd Qu.: 86.29 3rd Qu.: 62.041
#> Max. : 492.723 Max. : 654.771 Max. : 990.550 Max. :1386.11 Max. : 689.323
```
<div class="figure">
<img src="man/figures/README-summarysimuldata-1.png" alt="plot of chunk summarysimuldata" width="100%" />
<p class="caption">plot of chunk summarysimuldata</p>
</div><div class="figure">
<img src="man/figures/README-summarysimuldata-2.png" alt="plot of chunk summarysimuldata" width="100%" />
<p class="caption">plot of chunk summarysimuldata</p>
</div><div class="figure">
<img src="man/figures/README-summarysimuldata-3.png" alt="plot of chunk summarysimuldata" width="100%" />
<p class="caption">plot of chunk summarysimuldata</p>
</div>
``` r
plot(M)
```
<div class="figure">
<img src="man/figures/README-plotsimuldata-1.png" alt="plot of chunk plotsimuldata" width="100%" />
<p class="caption">plot of chunk plotsimuldata</p>
</div><div class="figure">
<img src="man/figures/README-plotsimuldata-2.png" alt="plot of chunk plotsimuldata" width="100%" />
<p class="caption">plot of chunk plotsimuldata</p>
</div><div class="figure">
<img src="man/figures/README-plotsimuldata-3.png" alt="plot of chunk plotsimuldata" width="100%" />
<p class="caption">plot of chunk plotsimuldata</p>
</div><div class="figure">
<img src="man/figures/README-plotsimuldata-4.png" alt="plot of chunk plotsimuldata" width="100%" />
<p class="caption">plot of chunk plotsimuldata</p>
</div><div class="figure">
<img src="man/figures/README-plotsimuldata-5.png" alt="plot of chunk plotsimuldata" width="100%" />
<p class="caption">plot of chunk plotsimuldata</p>
</div><div class="figure">
<img src="man/figures/README-plotsimuldata-6.png" alt="plot of chunk plotsimuldata" width="100%" />
<p class="caption">plot of chunk plotsimuldata</p>
</div><div class="figure">
<img src="man/figures/README-plotsimuldata-7.png" alt="plot of chunk plotsimuldata" width="100%" />
<p class="caption">plot of chunk plotsimuldata</p>
</div>
### 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)
``` r
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
```
<div class="figure">
<img src="man/figures/README-netinf-1.png" alt="plot of chunk netinf" width="100%" />
<p class="caption">plot of chunk netinf</p>
</div><div class="figure">
<img src="man/figures/README-netinf-2.png" alt="plot of chunk netinf" width="100%" />
<p class="caption">plot of chunk netinf</p>
</div>
Heatmap of the coefficients of the Omega matrix of the network
``` r
stats::heatmap(Net_inf_C@network, Rowv=NA, Colv=NA, scale="none", revC=TRUE)
```
<div class="figure">
<img src="man/figures/README-heatresults-1.png" alt="plot of chunk heatresults" width="100%" />
<p class="caption">plot of chunk heatresults</p>
</div>
###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.
```r
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
```
<img src="man/figures/README-cutoff-1.png" title="plot of chunk cutoff" alt="plot of chunk cutoff" width="100%" />
```
#> $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.
``` r
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
```
Versions across snapshots
| Version | Repository | File | Size |
|---|---|---|---|
2.3 |
rolling linux/jammy R-4.5 | Cascade_2.3.tar.gz |
1.9 MiB |
2.3 |
rolling linux/noble R-4.5 | Cascade_2.3.tar.gz |
1.9 MiB |
2.3 |
rolling source/ R- | Cascade_2.3.tar.gz |
1.9 MiB |
2.3 |
latest linux/jammy R-4.5 | Cascade_2.3.tar.gz |
1.9 MiB |
2.3 |
latest linux/noble R-4.5 | Cascade_2.3.tar.gz |
1.9 MiB |
2.3 |
latest source/ R- | Cascade_2.3.tar.gz |
1.9 MiB |
2.3 |
2026-04-26 source/ R- | Cascade_2.3.tar.gz |
1.9 MiB |
2.3 |
2026-04-23 source/ R- | Cascade_2.3.tar.gz |
1.9 MiB |
2.1 |
2025-04-20 source/ R- | Cascade_2.1.tar.gz |
1.9 MiB |