Average the product of the outgoing and incoming degrees of nodes

Description

This is the average of the outgoing/incoming nodes, described by Barabasi in his paper 'Universal resilience patterns in complex networks'.

Usage

Barabasi.B_eff(M)

Arguments

Value

A numeric value describing the Beta_eff described by Barabasi.

Examples

   node_file <- system.file("extdata", "IL17.nodes.csv", package = "Rato")
   edge_file <- system.file("extdata", "IL17.edges.csv", package = "Rato")
   g <- Rato::graph.from.csv(node_file, edge_file, sep=",", header=TRUE)
 
   initial_parameters <- function(M){
     initial_params <- list('f' = 1, 'h' = 2, 'B' = 0.1, 'Beta' = Rato::Barabasi.B_eff(M))
     return(initial_params)
   }
   
   update_parameters <- function(params){
     M <- params$M
     params$Beta <- Rato::Barabasi.B_eff(M)
     return(params)
   }
 
   Rato::node.removal.thread( system = Rato::Michaelis.Menten.Fast
                            , M = g$M
                            , x0 = Rato::Barabasi.X_eff(g$M, g$initial_values)
                            , initial_params = initial_parameters
                            , update_params = update_parameters
                            , to.numeric = TRUE)

Average Nearest-Neighbor Activity

Description

This is the average nearest-neight activity described by Barabasi in his paper 'Universal resilience patterns in complex networks'. It can be used to characterize the effective state of the system.

Usage

Barabasi.X_eff(M, x)

Arguments

Value

A numeric value describing the effective state by the system by using the nearest-neighbour activity.

Examples

   node_file <- system.file("extdata", "IL17.nodes.csv", package = "Rato")
   edge_file <- system.file("extdata", "IL17.edges.csv", package = "Rato")
   g <- Rato::graph.from.csv(node_file, edge_file, sep=",", header=TRUE)
 
   initial_parameters <- function(M){
     initial_params <- list('f' = 1, 'h' = 2, 'B' = 0.1, 'Beta' = Rato::Barabasi.B_eff(M))
     return(initial_params)
   }
   
   update_parameters <- function(params){
     M <- params$M
     params$Beta <- Rato::Barabasi.B_eff(M)
     return(params)
   }
 
   Rato::node.removal.thread( system = Rato::Michaelis.Menten.Fast
                            , M = g$M
                            , x0 = Rato::Barabasi.X_eff(g$M, g$initial_values)
                            , initial_params = initial_parameters
                            , update_params = update_parameters
                            , to.numeric = TRUE)

Michaelis-Menten equations

Description

The standard Michaelis-Menten equations

Usage

Michaelis.Menten(t, x, params)

Arguments

Value

A list with 'dx'

Examples

   node_file <- system.file("extdata", "IL17.nodes.csv", package = "Rato")
   edge_file <- system.file("extdata", "IL17.edges.csv", package = "Rato")
   g <- Rato::graph.from.csv(node_file, edge_file, sep=",", header=TRUE)
 
   Rato::node.removal.thread(  Rato::Michaelis.Menten
                             , g$M
                             , g$initial_values
                             , initial_params = list('f' = 1, 'h'=2, 'B'=0.1))

Optimized Michaelis-Menten equations

Description

The optimized Michaelis-Menten equations described by Barabasi in his paper 'Universal resilience patterns in complex networks'.

Usage

Michaelis.Menten.Fast(t, x, params)

Arguments

Value

A list with 'dx'

Examples

   node_file <- system.file("extdata", "IL17.nodes.csv", package = "Rato")
   edge_file <- system.file("extdata", "IL17.edges.csv", package = "Rato")
   g <- Rato::graph.from.csv(node_file, edge_file, sep=",", header=TRUE)
 
   initial_parameters <- function(M){
     initial_params <- list('f' = 1, 'h' = 2, 'B' = 0.1, 'Beta' = Rato::Barabasi.B_eff(M))
     return(initial_params)
   }
   
   update_parameters <- function(params){
     M <- params$M
     params$Beta <- Rato::Barabasi.B_eff(M)
     return(params)
   }
 
   Rato::node.removal.thread( system = Rato::Michaelis.Menten.Fast
                            , M = g$M
                            , x0 = Rato::Barabasi.X_eff(g$M, g$initial_values)
                            , initial_params = initial_parameters
                            , update_params = update_parameters
                            , to.numeric = TRUE)

Loads a graph from Node / Edge CSV files

Description

This function takes the file paths to two CSV files: one containing the node information of a network and the other containing the edge information of the network. It returns a list containing several useful data related to the network.

Usage

graph.from.csv(nodeinfo_path, edgeinfo_path, ...)

Arguments

Value

A list 'L' with the following entries:

Examples

   node_file <- system.file("extdata", "IL17.nodes.csv", package = "Rato")
   edge_file <- system.file("extdata", "IL17.edges.csv", package = "Rato")
   M <- graph.from.csv(node_file, edge_file)

Node score in network dynamics

Description

This function evaluates the significance of one or more nodes in a network given a system. It initially tests the dynamics of the network under a healthy state (i.e., without any perturbation). Then, it removes the specified nodes and runs the ODE again. The function compares the final state of the network under the perturbation to that of the healthy network to assess the importance of the nodes for network health.

Usage

node.raw.score(
  system,
  M,
  x0,
  nodes,
  initial_params = list(),
  times = seq(0, 100, 1),
  reduction = mean
)

Arguments

Value

A list 'L' with the following entries:

- L$score: The score of the nodes.

- L$normalized.score: The normalized score of the nodes.

Examples

   node_file <- system.file("extdata", "IL17.nodes.csv", package = "Rato")
   edge_file <- system.file("extdata", "IL17.edges.csv", package = "Rato")

   g <- Rato::graph.from.csv(node_file, edge_file, sep=",", header=TRUE)
   
   
   # Get the raw score of a node in the network
   score <- Rato::node.raw.score(
       Rato::Michaelis.Menten  # Use the Michaelis-Menten equation
     , g$M               # The GRN as an adjacency matrix
     , g$initial_values  # The initial values of the genes
     , g$node_index("ko:K03171") # The gene of interest
     , initial_params = list('f' = 1, 'h'=2, 'B'=0.01) # Parameters of the Michaelis-Menten equation
   )

Simulates Network Dynamics under Random Node Removal Perturbations.

Description

This function simulates the behavior of a network undergoing multiple uniform removal of nodes. Starting with an initial healthy network, it calculates the network's trajectory by solving the system of ordinary differential equations (ODEs) after each perturbation. Nodes are removed randomly and uniformly, followed by dimension reduction using the specified reduction function.

Usage

node.removal.thread(
  system,
  M,
  x0,
  initial_params = list(),
  update_params = identity,
  reduction = identity,
  removal_order = NULL,
  ...
)

Arguments

Value

Depending on ‘to.numeric', returns either a list or a numeric matrix, representing the system’s state across multiple perturbations. If 'to.numeric' is 'FALSE', the function returns a list 'L', where 'L[[i]]' represents the final state of the system after the 'i'-th perturbation. If 'TRUE', the list is converted to a numeric matrix before being returned.#'

Examples

   node_file <- system.file("extdata", "IL17.nodes.csv", package = "Rato")
   edge_file <- system.file("extdata", "IL17.edges.csv", package = "Rato")
   g <- Rato::graph.from.csv(node_file, edge_file, sep=",", header=TRUE)
 
   Rato::node.removal.thread( Rato::Michaelis.Menten
                             , g$M
                             , g$initial_values
                             , initial_params = list('f' = 1, 'h'=2, 'B'=0.1))

Node score in network dynamics with significance test

Description

This function evaluates the significance of one or more nodes in a network given a system. It initially tests the dynamics of the network under a healthy state (i.e., without any perturbation). Then, it removes the specified nodes and runs the ODE again. The function compares the final state of the network under the perturbation to that of the healthy network to assess the importance of the nodes for network health. Additionally, it uses bootstrap methods to estimate a p-value associated with this score.

Usage

node.score(
  system,
  M,
  x0,
  nodes,
  initial_params = list(),
  times = seq(0, 100, 1),
  reduction = mean,
  bootstrap_iterations = 100,
  skip_equal_nodes = TRUE
)

Arguments

Value

A list 'L' with the following entries:

- L$score: The score of the nodes.

- L$normalized.score: The normalized score of the nodes.

- L$p.value: A p-value associated with the significance of the score.

- L$normalized.p.value: A normalized p-value associated with the significance of the score.

Examples

   node_file <- system.file("extdata", "IL17.nodes.csv", package = "Rato")
   edge_file <- system.file("extdata", "IL17.edges.csv", package = "Rato")

   g <- Rato::graph.from.csv(node_file, edge_file, sep=",", header=TRUE)
   
   
   # Get the raw score of a node in the network
   score <- Rato::node.score(
       Rato::Michaelis.Menten  # Use the Michaelis-Menten equation
     , g$M               # The GRN as an adjacency matrix
     , g$initial_values  # The initial values of the genes
     , g$node_index("ko:K03171") # The gene of interest
     , initial_params = list('f' = 1, 'h'=2, 'B'=0.01) # Parameters of the Michaelis-Menten equation
   )

Simulates Network Dynamics under Iterative Perturbations

Description

This function simulates the behavior of a network undergoing multiple iterations of custom perturbations. Starting with an initial healthy network, it calculates the network's trajectory by solving the system of ordinary differential equations (ODEs) after each perturbation. Perturbations are applied iteratively, followed by dimension reduction using the specified reduction function.

Usage

perturbation.thread(
  system,
  M,
  x0,
  perturbation_function,
  initial_parameter_function,
  times = seq(0, 100, 1),
  reduction = identity,
  to.numeric = FALSE,
  only.final.state = TRUE
)

Arguments

Value

Depending on ‘to.numeric', returns either a list or a numeric matrix, representing the system’s state across multiple perturbations. If 'to.numeric' is 'FALSE', the function returns a list 'L', where 'L[[i]]' represents the final state of the system after the 'i'-th perturbation. If 'TRUE', the list is converted to a numeric matrix before being returned.

Examples

   node_file <- system.file("extdata", "IL17.nodes.csv", package = "Rato")
   edge_file <- system.file("extdata", "IL17.edges.csv", package = "Rato")
   g <- Rato::graph.from.csv(node_file, edge_file, sep=",", header=TRUE)
 
   initial_params = list('f' = 1, 'h'=2, 'B'=0.01)
   removal_order = NULL
   update_params = identity
   reduction = identity
   initial_parameter_function <- function(M) {

     if (is.list(initial_params)) {
       params <- initial_params
     }
     else if (is.function(initial_params)) {
       params <- initial_params(M)
     }
     n <- nrow(M) # The number of nodes of the graph

     if(is.null(removal_order)){
         removal_order <- sample(1:n, n) 
     }

     if(is.null(params$M)){
       params$M = M
     } 
     params$removal_order = removal_order
     return(params)
   }
   perturbation <- function(params, iter) {
     removal_order <- params$removal_order
     M <- params$M
 
     if(length(removal_order) > 0 ) {
       index <- removal_order[1] 
       removal_order <- removal_order[-1] 
       M[index, ] <- 0 # Remove entries
       M[, index] <- 0 # Remove entries
 
       params$M = M
       params$removal_order = removal_order
 
       # Add the list of removed indices to the parameter list.
       if(is.null(params$removed_indices)){
         params$removed_indices <- c(index)
       } else {
         removed_indices <- c(params$removed_indices, index)
         params$removed_indices <- removed_indices
       }
 
       output <- update_params(params)
       return(output) # Return updated parameters
     }
 
     # If we removed every single entry, just STOP.
     return(NULL)
   }
 
   Rato::perturbation.thread( Rato::Michaelis.Menten
                             , g$M
                             , g$initial_values
                             , initial_parameter_function = initial_parameter_function
                             , perturbation_function = perturbation)