TDCor algorithm for gene regulatory network inference

Description

TDCor (Time-Delay Correlation) is an algorithm designed to infer the topology of a gene regulatory network (GRN) from time-series transcriptomic data. The algorithm is described in details in Lavenus et al., Plant Cell, 2015. It was initially developped to infer the topology of the GRN controlling lateral root formation in Arabidopsis thaliana. The time-series transcriptomic dataset analysed in this study is included in the package.

Details

The reconstruction of a gene network using the TDCor package involves six steps.

1. Load the averaged non-log2 time series transcriptomic data into the R workspace.

2. Define the vector times containing the times (in hours) at which the samples were collected.

3. Define the vector containing the gene codes of the genes you want to reconstruct the network with (e.g. see l_genes), as well as the associated gene names (e.g. see l_names) and the associated prior (e.g. see l_prior).

4. Build or update the TPI database using the CalculateTPI or UpdateTPI functions.

5. Build or update the DPI database using the CalculateDPI or UpdateDPI functions.

6. Reconstruct the network using the TDCOR main function.

See examples below.

Besides the functions of the TDCor algorithm, the package also contains the lateral root transcriptomic dataset (LR_dataset), the times vector to use with this dataset (times), the vector of AGI gene codes used to reconstruct the network shown in the original paper (l_genes), the vector of the gene names (l_names) and the prior (l_prior). The associated TPI and DPI databases (TPI10 and DPI15) which were used to build the network shown in the original paper are not included. Hence to reconstruct the lateral root network, these first need to be generated. A database of about 1800 Arabidopsis transcription factors is also included (TF).

Three side functions, estimate.delay, shortest.path and draw.profile are also available to the user. These can be used to visualize the transcriptomic data, optimize some of the TDCOR parameters, and analyze the networks.

Author(s)

Author: Julien Lavenus jl.tdcor@gmail.com
Maintainer: Mikael Lucas mikael.lucas@ird.fr

References

Lavenus et al. (2015), Inference of the Arabidopsis lateral root gene regulatory network suggests a bifurcation mechanism that defines primordia flanking and central zones. The Plant Cell, in press.

See Also

See also CalculateDPI, CalculateTPI, UpdateDPI, UpdateTPI, TDCOR, estimate.delay.

Examples

## Not run: 
# Load the LR transcriptomic dataset
data(LR_dataset)

# Load the vectors of genes codes, gene names and prior
data(l_genes)
data(l_names)
data(l_prior)

# Load the vector of time points for the LR_dataset
data(times)

# Generate the TPI database (this may take several hours) 

TPI10=CalculateTPI(dataset=LR_dataset,l_genes=l_genes,l_prior=l_prior, 
times=times,time_step=1,N=10000,ks_int=c(0.5,3),kd_int=c(0.5,3), 
delta_int=c(0.5,3),noise=0.1,delay=3)

# Generate the DPI database (this may take several hours) 

DPI15=CalculateDPI(dataset=LR_dataset,l_genes=l_genes,l_prior=l_prior, 
times=times,time_step=1,N=10000,ks_int=c(0.5,3),kd_int=c(0.5,3), 
delta_int=c(0.5,3), noise=0.15, delay=3)

# Check/update if necessary the databases

TPI10=UpdateTPI(TPI10,LR_dataset,l_genes,l_prior)
DPI15=UpdateDPI(DPI15,LR_dataset,l_genes,l_prior)

# Choose your parameters 

ptime_step=1			
ptol=0.13			
pdelayspan=12			
pthr_cor=c(0.65,0.8)	
pdelaymax=c(2.5,3.5)		
pdelaymin=0			
pdelay=3			
pthrpTPI=c(0.55,0.8)		
pthrpDPI=c(0.65,0.8)		
pthr_overlap=c(0.4,0.6)		
pthr_ind1=0.65			
pthr_ind2=3.5			
pn0=1000			
pn1=10				
pregmax=5					
pthr_isr=c(4,6)			
pTPI=TPI10			
pDPI=DPI15			
pMinTarNumber=5			
pMinProp=0.6			
poutfile_name="TDCor_output.txt"	


# Reconstruct the network

tdcor_out= TDCOR(dataset=LR_dataset, l_genes=l_genes,l_names=l_names,n0=pn0,n1=pn1,
l_prior=l_prior, thr_ind1=pthr_ind1,thr_ind2=pthr_ind2,regmax=pregmax,thr_cor=pthr_cor,
delayspan=pdelayspan,delaymax=pdelaymax,delaymin=pdelaymin,delay=pdelay,thrpTPI=pthrpTPI,
thrpDPI=pthrpDPI,TPI=pTPI,DPI=pDPI,thr_isr=pthr_isr,time_step=ptime_step,thr_overlap=pthr_overlap,
tol=ptol,MinProp=pMinProp,MinTarNumber=pMinTarNumber,outfile_name=poutfile_name)


## End(Not run)

Generate the DPI database to be used by the TDCOR main function

Description

CalculateDPI builds a DPI database for the TDCOR main function to prune diamond motifs

Usage

CalculateDPI(dataset,l_genes, l_prior, times, time_step, N, ks_int, kd_int, 
delta_int, noise, delay)

Arguments

Details

CalculateDPI models two 4-genes networks showing slightly different topologies. Each network topology is modelled using a specific system of delay differential equations. For all genes listed in l_genes whose corresponding prior in l_prior is not null (i.e. the genes that are regarded as transcriptional regulators), the two systems of differential equations are solved N times with N different sets of random parameters. The Diamond Pruning Index (DPI) is calculated for all of these 2N networks. From these in silico data the conditional probability distribution of the DPI index given the regulator and the topology can be estimated. The probability distribution of the topology given DPI and the regulator is next calculated using Bayes' theorem and returned by the function. These shall be used when reconstructing the network to prune the "diamond" motifs.

CalculateDPI returns a list object which works as a database. It not only stores the conditional probability distributions but also all the necessary information for TDCOR to access the data, and the input parameters. The latter are read by the UpdateDPI function to update the database.

Value

CalculateDPI returns a list object.

Note

The computation of the TPI and DPI databases is time-consuming as it requires many systems of differential equations to be solved. It may take several hours to build a database for a hundred genes.

Author(s)

Julien Lavenus jl.tdcor@gmail.com

See Also

See also UpdateDPI, TDCor-package.

Examples

## Not run: 
# Load the LR transcriptomic dataset
data(LR_dataset)

# Load the vector of gene codes, gene names and prior
data(l_genes)
data(l_names)
data(l_prior)

# Load the vector of time points for the LR_dataset
data(times)

# Generate a small DPI database (3 genes)
DPI_example=CalculateDPI(dataset=LR_dataset,l_genes=l_genes[4:6],l_prior=l_prior[4:6],
times=times,time_step=1,N=5000,ks_int=c(0.5,3),kd_int=c(0.5,3),delta_int=c(0.5,3),
noise=0.15,delay=3)


## End(Not run)

Generate the TPI database to be used by the TDCOR main function

Description

CalculateTPI builds a TPI database for the TDCOR main function to prune triangle motifs

Usage

CalculateTPI(dataset,l_genes, l_prior, times, time_step, N, ks_int, kd_int, 
delta_int, noise, delay)

Arguments

Details

CalculateTPI models three 3-genes networks showing slightly different topologies. Each network topology is modelled using a specific system of delay differential equations. For all genes listed in l_genes whose corresponding prior in l_prior is not null (i.e. the genes that are regarded as transcriptional regulators), the three systems of differential equations are solved N times with N different sets of random parameters. The Triangle Pruning Index (TPI) is calculated for all of these 3N networks. From these in silico data the conditional probability distribution of the TPI index given the regulator and the topology can be estimated. The probability distribution of the topology given TPI and the regulator is next calculated using Bayes' theorem and returned by the function. These shall be used when reconstructing the network to prune the "triangle" motifs.

CalculateTPI returns a list object which works as a database. It not only stores the calculated probability distributions but also information on how to access the data, and the input parameters. The latter are read by the UpdateTPI function to update the database.

Value

CalculateTPI returns a list object.

Note

The computation of the TPI and DPI databases is time-consuming as it requires many systems of differential equations to be solved. It may take several hours to build a database for a hundred genes.

Author(s)

Julien Lavenus jl.tdcor@gmail.com

See Also

See also UpdateTPI, TDCor-package.

Examples

## Not run: 
# Load the lateral root transcriptomic dataset
data(LR_dataset)

# Load the vectors of gene codes, gene names and prior
data(l_genes)
data(l_names)
data(l_prior)

# Load the vector of time points for the the lateral root dataset
data(times)

# Generate a small TPI database (3 genes)

TPI_example=CalculateTPI(dataset=LR_dataset,l_genes=l_genes[4:6],
l_prior=l_prior[4:6],times=times,time_step=1,N=5000,ks_int=c(0.5,3),
kd_int=c(0.5,3),delta_int=c(0.5,3),noise=0.1,delay=3)

## End(Not run)

Lateral root transcriptomic dataset

Description

LR_dataset is a matrix of dimension 15240 lines x 18 columns. It stores a time-series transcriptomic dataset following the changes occuring in a young Arabidopsis root during the formation of a lateral root. To generate this dataset, lateral root formation was locally induced by a gravistimulus at t=0 and the stimulated part of the roots was collected every 3 hours from 6 hours to 54 hours. The transcriptomes were analyzed using the ATH1 affymetrix chip. For time point 0, unstimulated young primary root was taken as a control. Importantly, the transcript accumulation levels stored in this dataset are non-log2 values.

Usage

data("LR_dataset")

Details

The experiment spanned 54 hours in order to cover all aspects of lateral root development. Using this method, lateral root initiation (the first pericycle divisions) occurs synchroneously in all stimulated roots around 12 hours after stimulation and the fully formed lateral root emerges from the parental root around 45 hours. The dataset contains data for all significantly differentially expressed genes.

Each column is the average of 4 independent replicates. The columns are organized in the following order: 0, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51 and 54 hours. Each line of the matrix is labbelled with an AGI gene code (Arabidopsis Genome Initiative gene code).

Source

Voss et al., Lateral root organ initiation re-phases the circadian clock in Arabidopsis thaliana. Nature communication, in revision.

Examples

# Load the dataset
data(LR_dataset)

# Have a look at the first rows
head(LR_dataset)

The TDCOR main function

Description

This is the main function to run the TDCOR algorithm and reconstruct the gene network topology.

Usage

TDCOR(dataset,l_genes, TPI, DPI, ...)

Arguments

Details

The default values are certainly not the best values to work with. The TDCOR parameters have to be optimized by the user based on its own knowledge of the network, the quality of the data etc... Because TDCOR works by pruning interactions, it is probably easier (as a first go) to optimize the parameter values following the order of the filters.

Before starting inactivate all the filters using the less stringent parameter values possible or for the MRST filter by setting search.EP to FALSE. You should as well set the bootstrap parameters to a relatively low value (e.g. n0=100 and n1=1). Hence the runs will be quick and you will be able to rapidly assess whether the changes you made in the parameter values were a good thing.

Start by optimizing the parameters involved in time shifts estimation. That is to say, essentially delayspan, time_step, tol and delaymax. The latter (together with delaymin) is a biological parameters and the range of possible values is argueably limited. Though they ought to be adapted to the organism (e.g. in prokaryotes, the delays are extremely short since polysomes couple transcription and translation). Note that the estimate.delay function can be very helpful to optimize these various parameters thanks to the visual output. Use it with pairs of genes that have been shown to interact directly or indirectly in your system and for which the relationship in the dataset in clearly linear. For network reconstruction with TDCor, good time shift estimation is absolutely crucial. Once this is done, proceed with optimizing the threshold for correlation thr_cor and the thresholds on the index of directness (thr_ind1, thr_ind2). Then optimize the parameters of the triangle and diamond pruning filters (thrpTPI and thrpDPI). You may have to try a couple of different TPI and DPI databases (i.e. databases built with different input parameters). In particular increasing the noise level when generating these database enables one to decrease the stringency of the triangle and diamond filters, when increasing the thrpTPI and thrpDPI value is not sufficient. Subsequently fine-tune the parameters of the MRST filter (thr_bool_EP, MinTarNumber, MinProp, MaxEPNumber) if you want it on. Remember to set search.EP back to TRUE first. Next optimize thr_isr (self-regulation). Finally, restrict the number of maximum regulators if necessary (regmax).

Value

The TDCOR main function returns a list containing 7 elements

The table of predictions (without header) and the input parameters are printed at the end of the run in two separate text files located in the current R working directory (If you are not sure which directory this is, use the command getwd()).

Note

For a parameter to be involved in the bootstrapping process, one must feed the function a vector containing two values as input. These two values are respectively the lower and upper boundaries of the bootstrapping interval. If one chooses not to use a parameter for bootstrapping, one can either feed the function an input vector containing twice the same value, or only one value.

Author(s)

Julien Lavenus jl.tdcor@gmail.com

References

Lavenus et al., 2015, The Plant Cell

See Also

See also CalculateDPI, CalculateTPI, UpdateDPI, UpdateTPI, TDCor-package.

Examples

## Not run: 
# Load the lateral root transcriptomic dataset
data(LR_dataset)

# Load the vectors of gene codes, gene names and prior
data(l_genes)
data(l_names)
data(l_prior)

# Load the vector of time points for the LR_dataset
data(times)

# Generate the DPI databases

DPI15=CalculateDPI(dataset=LR_dataset,l_genes=l_genes,l_prior=l_prior,
times=times,time_step=1,N=10000,ks_int=c(0.5,3),kd_int=c(0.5,3),delta_int=c(0.5,3),
noise=0.15,delay=3)

# Generate the TPI databases

TPI10=CalculateTPI(dataset=LR_dataset,l_genes=l_genes,
l_prior=l_prior,times=times,time_step=1,N=10000,ks_int=c(0.5,3),
kd_int=c(0.5,3),delta_int=c(0.5,3),noise=0.1,delay=3)

# Check/update if necessary the databases (Not necessary here though.
# This is just to illustrate how it would work.)

TPI10=UpdateTPI(TPI10,LR_dataset,l_genes,l_prior)
DPI15=UpdateDPI(DPI15,LR_dataset,l_genes,l_prior)


### Choose your TDCOR parameters ###
 
# Parameters for time shift estimatation 
# and filter on time shift value
ptime_step=1			
ptol=0.13			 
pdelayspan=12
pdelaymax=c(2.5,3.5)
pdelaymin=0

# Parameter of the correlation filter
pthr_cor=c(0.65,0.8)

# Parameters of the ID filter
pdelay=3		
pthr_ind1=0.65			
pthr_ind2=3.5

# Parameter of the overlap filter
pthr_overlap=c(0.4,0.6)

# Parameters of the triangle and diamond filters
pthrpTPI=c(0.55,0.8)
pthrpDPI=c(0.65,0.8)	
pTPI=TPI10			
pDPI=DPI15

# Parameter for identification of self-regulations				
pthr_isr=c(4,6)

# Parameters for MRST identification			
pMinTarNumber=5			
pMinProp=0.6

# Max number of regulators		
pregmax=5

# Bootstrap parameters
pn0=1000			
pn1=10

# Name of the file to print network in
poutfile_name="TDCor_output.txt"	

### Reconstruct the network ###

tdcor_out= TDCOR(dataset=LR_dataset,l_genes=l_genes,l_names=l_names,n0=pn0,n1=pn1,
l_prior=l_prior,thr_ind1=pthr_ind1,thr_ind2=pthr_ind2,regmax=pregmax,thr_cor=pthr_cor,
delayspan=pdelayspan,delaymax=pdelaymax,delaymin=pdelaymin,delay=pdelay,thrpTPI=pthrpTPI,
thrpDPI=pthrpDPI,TPI=pTPI,DPI=pDPI,thr_isr=pthr_isr,time_step=ptime_step,
thr_overlap=pthr_overlap,tol=ptol,MinProp=pMinProp,MinTarNumber=pMinTarNumber,
outfile_name=poutfile_name)


## End(Not run)

Table of 1834 Arabidopsis Transcription factors

Description

TF is a dataframe with two columns. The first column contains the AGI gene code of 1834 genes encoding Arabidopsis transcription factors. The second column contains the associated gene names.

Usage

data("TF")

Source

Data published on the Agris database website (http://arabidopsis.med.ohio-state.edu/AtTFDB/).

References

Davuluri et al. (2003), AGRIS: Arabidopsis Gene Regulatory Information Server, an information resource of Arabidopsis cis-regulatory elements and transcription factors, BMC Bioinformatics, 4:25

Examples

# Load the database
data(TF)

# Obtain the transcription factors for which data is available in the LR dataset
# i.e. present on ATH1 chip and differentially expressed.
data(LR_dataset)
clean.at(LR_dataset,TF[,1])

Update or check the DPI database

Description

UpdateDPI analyzes the DPI database and add new entries into it if it does not contain all the necessary data for reconstructing the network with the genes listed in the vector l_genes.

Usage

UpdateDPI(DPI,dataset,l_genes, l_prior)

Arguments

Value

UpdateDPI returns an updated DPI database containing data for at least all the genes in l_genes whose associated prior is not null.

Author(s)

Julien Lavenus jl.tdcor@gmail.com

See Also

See also CalculateDPI.

Examples

## Not run: 
# Load the Lateral root transcriptomic dataset
data(LR_dataset)

# Load the vector of gene codes, gene names and prior
data(l_genes)
data(l_names)
data(l_prior)

# Load the vector of time points for the LR_dataset
data(times)

# Build a very small DPI database (3 genes)
DPI_example=CalculateDPI(dataset=LR_dataset,l_genes=l_genes[4:6],l_prior=l_prior[4:6],
times=times,time_step=1,N=5000,ks_int=c(0.5,3),kd_int=c(0.5,3),delta_int=c(0.5,3),
noise=0.15,delay=3)

# Add one gene in the database
DPI_example=UpdateDPI(DPI_example,dataset=LR_dataset,l_genes[4:7],l_prior[4:7])

## End(Not run)

Update or check the TPI database

Description

UpdateTPI analyzes the TPI database and add new entries into it if it does not contain all the necessary data for reconstructing the network with the genes listed in the vector l_genes.

Usage

UpdateTPI(TPI, dataset, l_genes, l_prior)

Arguments

Value

UpdateTPI returns an updated TPI database containing data for at least all the genes in l_genes whose associated prior is not null.

Author(s)

Julien Lavenus jl.tdcor@gmail.com

See Also

See also CalculateTPI.

Examples

## Not run: 
# Load the Lateral root transcriptomic dataset
data(LR_dataset)

# Load the vector of gene codes, gene names and prior
data(l_genes)
data(l_names)
data(l_prior)

# Load the vector of time points for the LR_dataset
data(times)

# Build a very small TPI database (3 genes)
TPI_example=CalculateTPI(dataset=LR_dataset,l_genes=l_genes[4:6],
l_prior=l_prior[4:6],times=times,time_step=1,N=5000,ks_int=c(0.5,3),
kd_int=c(0.5,3),delta_int=c(0.5,3),noise=0.1,delay=3)

# Add one gene in the database
TPI_example=UpdateTPI(TPI_example,dataset=LR_dataset,l_genes[4:7],l_prior[4:7])

## End(Not run)

Elimininate from a vector of gene codes the genes for which no data is available.

Description

clean.at removes from a vector of gene codes l_genes all the elements for which no data is present in the matrix dataset.

Usage

clean.at(dataset,l_genes)

Arguments

Examples

## Load lateral root transcriptomic dataset and the l_genes vector
data(LR_dataset)
data(l_genes)

# Clean the l_gene vector 
clean.at(LR_dataset,l_genes)

Plot the expression profile of a gene in dataset

Description

draw.profile plots the expression profile of gene in dataset with respect to times.

Usage

draw.profile(dataset, gene, ...)

Arguments

Author(s)

Julien Lavenus (jl.tdcor@gmail.com)

Examples

# draw the profile of GATA23 in the LR dataset

data(LR_dataset)
data(times)
draw.profile(LR_dataset,"AT5G26930",col="blue",main="GATA23")

Estimate the time shift between two gene profiles and make a plot

Description

estimate.delay computes the delay/time shift between two gene expression profiles contained in dataset. It returns a list with one or two estimated time shifts and their associated correlation. By default the function also returns a plot composed of four panels which show in more details how these estimate were obtained. This can help the user finding the appropriate parameter values to be used with the TDCOR main function. For more details see below.

Usage

estimate.delay(dataset, tar, reg, times, time_step, thr_cor, tol, 
delaymax, delayspan, ...)

Arguments

Details

Negative time shifts occur when the gene which the user set as being the regulator could actually be the target. When two time shifts are returned, one is necessarily positive and the other is negative. When the only time shift estimate is zero, the function does not return any estimate.

The function automatically guess the sign of the potential interaction (stimulatory or inhibitory) and adapt the analysis based on it. The sign of the potential interaction is indicated in the main title of the graph by (+) or (-). When both types of interaction are possible, the function generates two graphs (one for each sign).

The function returns by default a graph composed of four panels. The top panel shows the spline functions of the two normalised expression profiles with respect to time. The second panel consists of the plots of the F1 and F2 functions with respect to the time shift (mu). The third one is for the F3 and F4 functions. All of these four functions aim at estimating the time shift between the two expression profiles by minimizing a distance-like measurement. But they each do it in a slightly different manner. F1 and F3 use Pearson's correlation as a measure of distance while F2 and F4 use the sum of squares. Moreover F1 and F2 measure the distances directly between the spline functions while F3 and F4 do it between the first derivatives of these functions. The vertical red and purple lines in the second and third panel indicate the position of the respective maximum or minimum of the functions. In the fourth and last panel, the final score function is plotted. This score is computed for each possible time shift analysed by combining the four above-mentionned functions. The green horizontal line indicate the position of the tolerance threshold (tol) above which time shift estimates are rejected. The vertical dark grey line(s) represent(s) the position of the final estimated time shift(s). All these lines necessarily fall into regions where the score function is below the threshold (painted in light green). Other vertical light grey line(s) may indicate other time shift estimate(s) that have a score above the tolerance threshold and were therefore rejected.

Value

The function returns a list. The first element (delay) is a numerical vector containing the time-shift estimate(s). The second element (correlation) is another numerical vector containing the associated correlation. The function also returns a graph as explained above.

Author(s)

Julien Lavenus jl.tdcor@gmail.com

Examples

# Load the data

data(LR_dataset)
data(l_genes)
data(l_names)
data(times)

# Estimate the time shift between LBD16 and PUCHI (one time shift estimate returned)

estimate.delay(dataset=LR_dataset, tar=l_genes[which(l_names=="PUCHI")], 
reg=l_genes[which(l_names=="LBD16")], times=times, time_step=1, thr_cor=0.7, 
tol=0.15, delaymax=3, delayspan=12, reg.name="LBD16",tar.name="PUCHI")

# Estimate the time shift between ARF8 and PLT1 (two time shift estimates returned)

estimate.delay(dataset=LR_dataset, tar=l_genes[which(l_names=="PLT1")], 
reg=l_genes[which(l_names=="ARF8")], times=times, time_step=1, thr_cor=0.7, 
tol=0.15, delaymax=3, delayspan=12, reg.name="ARF8",tar.name="PLT1")

l_genes

Description

Character vector containing the AGI gene codes of the genes used to reconstruct the network in Lavenus et al. 2015, Plant Cell.

Usage

data("l_genes")

Examples

# Load the vector
data(l_genes)

# Have a look at it
l_genes

l_names

Description

Character vector containing the 'everyday names' of the genes used to reconstruct the network in Lavenus et al. 2015, Plant Cell.

Usage

data("l_names")

Examples

# Load the vector
data(l_names)

# Have a look at it
l_names

l_prior

Description

Vector containing the prior associated with the genes included in the network reconstruction in Lavenus et al. 2015, Plant Cell.

By defining the l_prior vector, the user defines which genes should be regarded as positive regulators, which others as negative regulators and which can only be targets. The prior code is defined as follow: -1 for negative regulator; 0 for non-regulator (target only); 1 for positive regulator; 2 for both positive and negative regulator. The i-th element of the vector is the prior to associate to the i-th gene in l_genes.

Usage

data("l_prior")

Examples

# Load the vector
data(l_prior)

# Have a look at it
l_prior

Calculate the shortest path linking every pairs of nodes in the network

Description

shortest.path computes the shortest influence path (in number of edges) linking every possible regulator/target pairs in the network.

Usage

shortest.path(bootstrap, BS_thr)

Arguments

Details

The paths are signed in order to keep track of the type of influence that the genes have on each other. If a path leads to the inhibition of a gene by another, shortest.path will return a negative number for this "pair" (Note that the (i,j) pair is not regarded as being the same than the (j,i) pair). Because the network is directed, edges can only be followed in one direction: from the regulator to the target. Hence if the network contains an edge from gene i to gene j, the length of the shortest path from i to j is 1 edge and therefore the function returns either 1 or -1 (depending on the sign of the interaction) for the length of i to j path. In absence of feedback loops between i and j, the network does not contain any path from gene j to gene i. In this case shortest.path shall return 0 for the length of the j to i path. Otherwise it will return the minimum number of edges to follow to go from j to i.

Value

shortest.path returns a list containing two matrices.

Author(s)

Julien Lavenus jl.tdcor@gmail.com

Examples

## Example with a 3-genes network where gene A upregulates B which upregulates A; and C represses B.
## the three edges have different bootstrap values (100, 60 and 55)

network=data.frame(matrix(c(0,100,0,0,60,0,0,-55,0),3,3))
names(network)=c("gene A","gene B","gene C")
rownames(network)=c("gene A","gene B","gene C")

shortest.path(as.matrix(network),1)

The times vector to use with the lateral root dataset

Description

Contains the times (in hours) at which the samples were collected to generate the Lateral Root transcriptomic dataset (data(LR_dataset))

Usage

data("times")

Examples

# Load the vector associated with the LR dataset
data(times)

# Have a look at it
times