calc_node_activities {pastboon}

Calculate activity rate for each node

Description

Calculates the activity rate of the nodes (i.e., the number of times a node is active, i.e., ON, divided by the number of repeats) for a specified number of time-steps.

Usage

calc_node_activities(net, method = c("BNp", "SDDS", "PEW"), params, steps,
                     repeats = 1000, initial_prob = NULL, last_step = FALSE,
                     asynchronous = TRUE, update_prob = NULL)

Arguments

net

A network structure of the class BooleanNetwork from the BoolNet package.

method

The parameterization method to be used. Options are:

• "BNp": Boolean network with perturbations.

• "SDDS": Stochastic discrete dynamical systems.

• "PEW": Boolean network with probabilistic edge weights.

Each method requires a different format for the params argument.

params

The parameter values depending on method:

• For method = "BNp", a single vector of probabilities, equal in length to the number of network nodes.

• For method = "SDDS", a list of four equal-length vectors of probabilities: p00, p01, p10, and p11, each equal in length to the number of network nodes.

• For method = "PEW", a list of two equal-length vectors of probabilities: p_on and p_off, each as long as the number of network edges, ordered according to extract_edges.

steps

The number of time-steps (non-negative integer) to simulate the network.

repeats

The number of repeats (positive integer).

initial_prob

The probability that each of the nodes is ON (1) in the initial state (time-step 0). If NULL (default), 0.5 is used as the probability for all nodes, meaning the initial state is randomly chosen based on a uniform distribution.

last_step

If TRUE, only the node activity rates for the last time-step are returned. Otherwise, the entire activity rate trajectory of the nodes is returned.

asynchronous

If TRUE, the asynchronous update scheme is used, where a single node is updated at each time-step. In this case, update_prob indicates update probabilities. If FALSE, the synchronous update scheme is utilized.

update_prob

The probability of updating each variable (node) in each time-step when asynchronous = TRUE. If NULL (default), nodes are updated randomly based on a uniform distribution. If asynchronous = FALSE, this argument is ignored.

Details

By incorporating stochasticity into the update rule of a Boolean network and repeating the simulation several times, the average value of each node across repeats can be considered as a continuous variable. This approach transforms discrete binary variables into continuous ones, enabling continuous analysis methods applicable for studying the dynamic behavior of the Boolean network. This function calculates the average value (i.e., node activity) of each network node at each time-step.

Value

If last_step = TRUE, a vector with a length equal to the number of network nodes, representing the activity rate of each node at the last time-step, is returned. If last_step = FALSE, a matrix with steps + 1 rows (where the first row corresponds to time-step 0) and length(net$genes) columns (representing node activities at each time-step) is returned. The order of the nodes in the vector or columns (depending on last_step) is the same as net$genes.

References

Golinelli, O., & Derrida, B. (1989). Barrier heights in the Kauffman model. Journal De Physique, 50(13), 1587-1601. Shmulevich, I., Dougherty, E. R., & Zhang, W. (2002). Gene perturbation and intervention in probabilistic Boolean networks. Bioinformatics, 18(10), 1319-1331.

Shmulevich, I., Dougherty, E. R., & Zhang, W. (2002). Gene perturbation and intervention in probabilistic Boolean networks. Bioinformatics, 18(10), 1319-1331.

Trairatphisan, P., Mizera, A., Pang, J., Tantar, A. A., Schneider, J., & Sauter, T. (2013). Recent development and biomedical applications of probabilistic Boolean networks. Cell communication and signaling, 11, 1-25.

Murrugarra, D., Veliz-Cuba, A., Aguilar, B., Arat, S., & Laubenbacher, R. (2012). Modeling stochasticity and variability in gene regulatory networks. EURASIP Journal on Bioinformatics and Systems Biology, 2012, 1-11.

Deritei, D., Kunšič, N., & Csermely, P. (2022). Probabilistic edge weights fine-tune Boolean network dynamics. PLoS Computational Biology, 18(10), e1010536.

Examples

# >>>>>>>>>>>>>>>>  Load network and generate random initial states  <<<<<<<<<<<<<<<<<

# Load the example network
data(lac_operon_net)

# Define plot function
plot_node_activities <- function(node_activities) {
  old_par <- par(no.readonly = TRUE)
  layout(matrix(c(1, 2), nrow = 1), width = c(4, 1))
  par(mar = c(5, 4, 4, 0))
  matplot(1:nrow(node_activities), node_activities, type = "l", frame = TRUE, lwd = 2,
      lty = 1, xlab = "Time-step", ylab = "Node activity")
  par(mar = c(5, 0, 4, 2))
  plot(c(0, 1), type = "n", axes = FALSE, xlab = "")
  legend("center", colnames(node_activities), col = seq_len(ncol(node_activities)),
      cex = 0.5, fill = seq_len(ncol(node_activities)))
  layout(1)
  par(old_par)
}

# >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>  Method: BNp  <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

# Define the parameters for the BNp method
params <- rep(0.05, length(lac_operon_net$genes))

# Get node activities after simulation using the BNp method
node_act <- calc_node_activities(lac_operon_net, method = "BNp", params = params,
    steps = 100, repeats = 10000)

# Plot node activities
plot_node_activities(node_act)

# >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>  Method: SDDS  <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

# Define the parameters for the SDDS method
props <- rep(0.95, length(lac_operon_net$genes))
params <- list(p00 = props, p01 = props, p10 = props, p11 = props)

# Get node activities after simulation using the SDDS method
node_act <- calc_node_activities(lac_operon_net, method = "SDDS", params = params,
    steps = 100, repeats = 10000)

# Plot node activities
plot_node_activities(node_act)

# >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>  Method: PEW  <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<

# Extract edges from the network
edges <- extract_edges(lac_operon_net)

# Define the parameters for the PEW method
p_on <- runif(nrow(edges))
p_off <- runif(nrow(edges))
params <- list(p_on = p_on, p_off = p_off)

# Get node activities after simulation using the PEW method
node_act <- calc_node_activities(lac_operon_net, method = "PEW", params = params,
    steps = 100, repeats = 10000)

# Plot node activities
plot_node_activities(node_act)