Identify important states in probabilistic Boolean networks

Description

Identifies important states in probabilistic Boolean networks (PBN) using a Markov chain simulation

Usage

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markovSimulation(network, 
                 numIterations = 1000, 
                 startStates = list(), 
                 cutoff = 0.001, 
                 returnTable = TRUE)

Arguments

network

An object of class ProbabilisticBooleanNetwork or BooleanNetwork whose transitions are simulated

numIterations

The number of iterations for the matrix multiplication, which corresponds to the number of state transitions to simulate

startStates

An optional list of start states. Each entry of the list must be a vector with a 0/1 value for each gene. If specified, the simulation is restricted to the states reachable from the supplied start states. Otherwise, all states are considered.

cutoff

The cutoff value used to determine if a probability is 0. All output probabilities less than or equal to this value are set to 0.

returnTable

If set to true, a transition table annotated with the probabilities for the transitions is included in the results. This is required by plotPBNTransitions and getTransitionProbabilities.

Details

The algorithm identifies important states by performing the following steps: First, a Markov matrix is calculated from the set of transition functions, where each entry of the matrix specifies the probability of a state transition from the state belonging to the corresponding row to the state belonging to the corresponding column. A vector is initialized with uniform probability for all states (or – if specified – uniform probability for all start states) and repeatedly multiplied with the Markov matrix. The method returns all states with non-zero probability in this vector. See the references for more details.

Value

An object of class MarkovSimulation with the following components:

reachedStates

A data frame with one state in each row. The first columns specify the gene values of the state, and the last column holds the probability that the corresponding state is reached after numIterations transitions. Only states with a probability greater than cutoff are included in this table.

genes

A vector of gene names of the input network

table

If returnTable=TRUE, this structure holds a table of transitions with the corresponding probabilities that transitions are chosen. This is a list with the following components:

initialStates

A matrix of encoded start states of the transitions

nextStates

The encoded successor states of the transitions

probabilities

The probabilities that the transitions are chosen in a single step

References

I. Shmulevich, E. R. Dougherty, S. Kim, W. Zhang (2002), Probabilistic Boolean networks: a rule-based uncertainty model for gene regulatory networks. Bioinformatics 18(2):261–274.

See Also

reconstructNetwork, plotPBNTransitions, getTransitionProbabilities

Examples

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# load example network
data(examplePBN)

# perform a Markov chain simulation
sim <- markovSimulation(examplePBN)

# print the relevant states and transition probabilities
print(sim)

# plot the transitions and their probabilities
plotPBNTransitions(sim)

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