Initialization of parameters

We set here the values for the evolution parameters and other general parameters, such as the minimum and maximum sizes of the subnetworks, via mogamun_init. Please note that we strongly recommend to run the algorithm with the default values. The only exception is for MinSize and MaxSize, which you can adapt to get bigger or smaller subnetworks, knowing that MOGAMUN tends to give as result subnetworks of sizes near or equal to MinSize. In total, there are 11 customizable parameters:

• PopSize is an integer that determines the size of the population (default = 100).
• MinSize and MaxSize are integers that determine the minimun and maximum number of nodes that are allowed in each subnetwork (i.e. individual), respectively (default min. = 15, max. = 50).
• Generations is an integer that determines the total number of generations of the evolution process (default = 500).
• TournamentSize is an integer that determines the size of the tournament, i.e. the number of individuals that will participate in the tournament for the selection of parents (default = 2).
• CrossoverRate is a real value in the [0-1] range that determines the crossover rate, where 0 means that crossover will never be performed and 1 means that crossover will always be performed (default = 0.8).
• MutationRate is a real value in the [0-1] range that determines the mutation rate, where 0 means that mutation will never be performed and 1 means that mutation will always be performed (default = 0.1).
• JaccardSimilarityThreshold is an integer that determines the maximum Jaccard similarity coefficient to consider two subnetworks as different (default = 30). Subnetworks with a Jaccard similarity coefficient higher than this value are considered as duplicates. Only one of them (the best one, according to the Pareto dominance criteria) will remain in the population, and the rest will be replaced by random subnetworks.
• MaxNumberOfAttempts is an integer that determines the maximum number of attempts allowed to try to find compatible parents for the crossover (default = 3).
• Measure is a string that can take any of two values: FDR or PValue. It determines which statistical value will be taken into account to obtain the list of significantly differentially expressed genes (default = FDR).
• ThresholdDEG is a real value that determines the maximum value of the Measure to consider a gene as significantly differentially expressed (default = 0.05).

If MOGAMUN is to be run with the default values, execute EvolutionParameters <- mogamun_init(). Otherwise, specify the parameters to change, separated by commas. Please be aware than although we recommend to let the evolution run for 500 generations, this process can be long. For instance, using a multiplex networks with the three layers that we provide in https://github.com/elvanov/MOGAMUN-data and the default values for all the parameters, the process took approximately 12 hours in a desktop computer with Intel processor i7 at 3.60GHz and 32GB of RAM.

parameters <- mogamun_init(Generations = 1, PopSize = 10)

Providing input data

MOGAMUN uses two sources of information: one or more biological networks, and the statistical values resulting from a differential expression analysis or any other test that gives as result p-values or False Discovery Rates (FDR) associated to genes. The second step of the workflow is to provide the input data using the mogamun_load_data function, which has 5 parameters:

• EvolutionParameters is the list returned by mogamun_init.
• DifferentialExpressionPath is a string with the full path to the comma separated file containing the results of the differential expression analysis. Please note that such file must be composed of at least two columns: “gene” and Measure. The column “gene” must contain gene names and the column Measure must be called either “FDR” or “PValue” (depending on which of the two was seleced in mogamun_init) and it should contain the results of the statistical test. We strongly recommend to have a third columm (“logFC”) with the log₂(fold_change), i.e. the ratio of difference of the expression between the two groups under study (e.g. patients vs control). There is a sample file in MOGAMUN/extdata/DE/Sample_DE.csv.
• NodesScoresPath is a string with the full path to the comma separated file containing the nodes scores for every node in the network. Please note that if this file does not exist, MOGAMUN will create it.
• NetworkLayersDir is a string with the path to the directory (i.e. folder) that contains the networks that will compose the multiplex network. Please note that each biological network must be in a separate file with 2-column tab separated format. The name of each file must start with a different character, which will be used in the Layers parameter. There are two example files in MOGAMUN/extdata/LayersMultiplex.
• Layers is a string composed of a chain of characters that determine which files from the NetworkLayersDir are to be used to build the multiplex network (e.g. “123” to use the networks which names start with “1”, “2”, and “3”).

dePath <- system.file("extdata/DE/Sample_DE.csv", package = "MOGAMUN")
scoresPath <-
    system.file("extdata/DE/Sample_NodesScore.csv", package = "MOGAMUN")
layersPath <-
    paste0(system.file("extdata/LayersMultiplex", package = "MOGAMUN"), "/")

loadedData <-
    mogamun_load_data(
        EvolutionParameters = parameters,
        DifferentialExpressionPath = dePath,
        NodesScoresPath = scoresPath,
        NetworkLayersDir = layersPath,
        Layers = "23"
    )

Running the algorithm

Once we have defined all the parameters and provided the input data, we are ready to run MOGAMUN using the mogamun_run function, which has 4 parameters:

• LoadedData is the list returned by mogamun_load_data
• Cores is an integer that determines the number of cores that will be used to run MOGAMUN. This number must be in line with the number of physical processor cores (default = 1). One core is needed per run. Please note that the execution in parallel is NOT allowed in Windows.
• NumberOfRunsToExecute is an integer that determines the number of runs to be performed (default = 1). If you have enough resources, we strongly recommend to run MOGAMUN 30 times. Please note that if you wish to run MOGAMUN a higher number of times than cores you have, the pending runs will be executed sequentially.
• ResultsDir is a string with the full path to the directory where the results must be stored (default = ‘.’, i.e. current working directory).

mogamun_run(LoadedData = loadedData, ResultsDir = '.')

## [1] "Run 1. Gen. 1 completed"
## [1] "FINISH TIME, RUN 1: 2024-10-30 08:20:35.064394"

## [[1]]
##           used (Mb) gc trigger  (Mb) max used  (Mb)
## Ncells 1540419 82.3    2319590 123.9  2319590 123.9
## Vcells 2691127 20.6    8388608  64.0  5183068  39.6

In the results directory (ResultsDir) you will find a subfolder which name contains the date when you executed the experiment. Inside, there will be two files per run (MOGAMUN_Results_StatisticsPerGeneration_RunN.csv and **MOGAMUN_Results__Run_N.txt). The file MOGAMUN_Results_StatisticsPerGeneration_RunN.csv** contains the best values for the two objectives (average nodes score and density) per generation, which you can use to check the convergence, for instance. The file **MOGAMUN_Results__Run_N.txt** contains the complete final population of size PopSize (i.e. all the subnetworks from the last generation), one per row. The number of elements in every row is variable because the size of each subnetwork can vary between MinSize and MaxSize. If X_n is the number of elements in the n-th row: the nodes of the subnetwork are the first X_n-4 elements. The last four elements correspond to the average nodes score, density, rank, and crowding distance, respectively. The best (non-dominated) subnetworks have are those with rank = 1.