count_pairwise_trans {pastboon}

Count pairwise transitions between a given set of states

Description

Counts the frequencies of transitions between each pair of states from a given set of states.

Usage

count_pairwise_trans(net, method = c("BNp", "SDDS", "PEW"), params, states,
                     steps = 1, repeats = 1000, 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.

states

The network states among which pairwise transitions are to be counted. This should be a matrix (where the rows represent the binary form of the states) or a vector (for the binary form of a single state). The number of matrix columns (or the length of the vector) should match the number of network nodes.

steps

The number of time-steps, which should be a non-negative integer.

repeats

The number of repeats, which should be a positive integer.

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

Counting the number of transitions between each pair of states reveals the reachability of one state from another. This function performs simulations by starting from each state in states for steps time-steps and repeats iterations, and counts the number of transitions to other states in states.

Value

A matrix where each element (i, j) represents the number of transitions from the ith state to the jth state across steps time-steps and repeats iterations.

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.

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)

# Generate some random states
states <- matrix(sample(c(0, 1), 10 * length(lac_operon_net$genes),
    replace = TRUE), nrow = 10, ncol = length(lac_operon_net$genes))

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

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

# Obtain frequency of pairwise transitions
pairwise_trans <- count_pairwise_trans(lac_operon_net, states = states,
    method = "BNp", params = params, steps = 100, repeats = 10)

# >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>  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)

# Obtain frequency of pairwise transitions
pairwise_trans <- count_pairwise_trans(lac_operon_net, states = states,
    method = "SDDS", params = params, steps = 100, repeats = 10)

# >>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>>  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)

# Obtain frequency of pairwise transitions
pairwise_trans <- count_pairwise_trans(lac_operon_net, states = states,
    method = "PEW", params = params, steps = 100, repeats = 10)