MOGAMUN is a Multi Objective Genetic Algorithm to find active modules (i.e., highly connected subnetworks with an overall deregulation) in MUltiplex biological Networks. For a detailed description of MOGAMUN check out the preprint https://www.biorxiv.org/content/10.1101/2020.05.25.114215v1. All the expression datasets and networks that we used to obtain the results reported in our preprint are available in the GitHub repository https://github.com/elvanov/MOGAMUN-data.
IMPORTANT. Please note that there was a bug in the non-domination sorting process. All the runs executed between October 15th, 2020 and February 12th, 2021 must be re-executed. We apologize for the inconveniences.

Workflow

The workflow of MOGAMUN is composed of 3 main steps: initialization of parameters, providing input data and running the algorithm.

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 $log_2(fold_change)$, 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. Please note that these files do not contain full networks and they are only provided to test the algorithm.
• 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 = '.')

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.

Postprocessing of the results

In our preprint (https://www.biorxiv.org/content/10.1101/2020.05.25.114215v1), we ran MOGAMUN 30 times for each experiment. This increases the chances to find the global maxima. Given that the result of every run is the set of subnetworks with rank = 1, if you execute MOGAMUN multiple times the final result is the union of the results of all the individual runs. But considering that in such set there might be subnetworks that are better than others (according to the Pareto dominance), to obtain the final result we calculate the accumulated Pareto front. To this goal, we re-rank the set composed by the union of all the results, and leave only those subnetworks with rank = 1. In addition, we propose to merge the subnetworks that are very similar, in order to avoid having two different networks if they only differ for one node, for instance (see JaccardSimilarityThreshold).

Depending on the number of runs you execute, there are other plots that might be generated during the postprocessing, such as scatter plots (always) and boxplots (only if NumberOfRunsToExecute in mogamun_run > 1).

Finally, it is possible to visualize the subnetworks from the accumulated Pareto front in Cytoscape. Please note that the network you used to build the multiplex will be filtered to leave only those interactions among the genes that are included in the result. The nodes will be colored according to their logFC value, where green stands for downregulated, red means upregulated, and white means no deregulation. Nodes corresponding to significantly differentially expressed genes will have black border, and the color of the edges will be different for each layer of the multiplex network. To check the layer an edge corresponds to, click on the edge and check the value of the TypeOfInteraction, in the edge table.

The postprocessing is done with the function mogamun_postprocess, which has 4 parameters:

• ExperimentDir is a string with the full path to the directory where the results are stored. It must coincide with the ResultsDir folder from mogamun_run.
• LoadedData is the list returned by mogamun_load_data.
• JaccardSimilarityThreshold is an integer that determines the minimum Jaccard similarity coefficient that a pair of subnetworks must have to be merged in a single subnetwork (default = 70).
• VisualizeInCytoscape is a boolean value (TRUE/FALSE) that determines whether the accumulated Pareto front is to be displayed in Cytoscape or not. NOTE. When VisualizeInCytoscape is TRUE, Cytoscape needs to be up and running in the computer (default = TRUE).

Please note that you can make use of mogamun_postprocess with any number of runs. If the experiment to be postprocessed contains a single run, the result will be the set of subnetworks in the first Pareto front. Otherwise, the result will be the accumulated Pareto front, as we already explained.

mogamun_postprocess(
    LoadedData = loadedData, 
    ExperimentDir = '.', 
    VisualizeInCytoscape = FALSE
)