MIDIA Software (v1.1)

TUTORIAL EXAMPLES & QUICKSTART

Two reaction networks are included as examples in the MIDIA R workspace: a MAP Kinase Signalling cascade (BioModels Database model number 11); and the NF-kappaB signalling network analysed in Bowsher (2010b). The networks may be inputted to the MIDIA(.) function using the matrices mSMAPK,mRMAPK and mSNFkB2,mRNFkB2 respectively (all of which are supplied as objects in the MIDIA R workspace).

The MAPK network forms the basis of this quickstart tutorial section. The NF-kappaB network serves to illustrate the principles, theory and methods underlying MIDIA in Section 5. Code snippets relating to the NF-kappaB network are included there.

MAP Kinase Signalling

The MAPK network used is BioModels Database model number BIOMD0000000011. Full details of the reaction network and species are available from the BioModels Database official website here. The matrices mR and mS needed for analysis of the network using MIDIA are included as the objects mRMAPK and mSMAPK in the MIDIA R workspace.

The Kinetic Independence Graph (KIG) describes the local dynamic dependencies between species arising from the network's mass action kinetics. For each node (i.e. species), this directed cyclic graph displays those other nodes whose copy number influences the instantaneous kinetics of that species.
KIG_MAPK = MIDIA(mS=mSMAPK,uG=matrix(0,0,0),mR=mRMAPK,mP=(mSMAPK>0),MODE="COARSEGRAIN",OutputSelectn="KIG",Fraternise=FALSE,PLOT=c(TRUE,TRUE,"MIDIAOutput.pdf")) returns the MAPK KIG.

A modularisation based on mass action kinetics identifies important intermediaries, here the phosphorylated kinases RAFp and MEKpp. This is the exact network decomposition given by:
T_MI1 = MIDIA(mS=mSMAPK,uG=matrix(0,0,0),mR=mRMAPK,mP=(mSMAPK>0),MODE="COARSEGRAIN",OutputSelectn="T_MI",PLOT=c(TRUE,TRUE,"MIDIAOutput.pdf"),Granularity=c(2,3,4,5,6,8,9,10,11,12,14, 15,16),PlotJTree=c("Species","Cliques"))
Here Granularity is a vector of modules in the clique tree that are to be aggregated with their parents. A similar modularisation is obtained by instead setting Granularity to a minimum module residual size of 3:
T_MI2 = MIDIA(mS=mSMAPK,uG=matrix(0,0,0),mR=mRMAPK,mP=(mSMAPK>0),MODE="COARSEGRAIN",OutputSelectn="T_MI",PLOT=c(TRUE,TRUE,"MIDIAOutput.pdf"),Granularity=3,PlotJTree=c("Species","Cliques"))

Given any type of biomolecular network represented as a graph, MIDIA provides a generic approach for exact, computationally efficient decomposition into possibly overlapping modules. As an illustration, suppose we are given uG, the undirected version of the KIG for the MAPK network (uG = as(ugraph(KIG_MAPK),"matrix")). Notice that the undirected graph should be in the form of its adjacency matrix. Then the previous output is obtained alternatively from:
T_MI2 = MIDIA(mS=matrix(0,0,0),uG=uG,mR=matrix(0,0,0),mP=matrix(0,0,0),MODE="COARSEGRAIN",OutputSelectn="T_MI",PLOT=c(TRUE,TRUE,"MIDIAOutput.pdf"),Granularity=3,PlotJTree=c("Species","Cliques"))
The same approach applies to inputting the adjacency matrices of network graphs not derived from kinetic independence graphs.

The corresponding modularisation based on dynamic conditional independence of module trajectories is given, for example, by:
T_M1 = MIDIA(mS=mSMAPK,uG=matrix(0,0,0),mR=mRMAPK,mP=(mSMAPK>0),MODE="COARSEGRAIN",OutputSelectn="T_M",PLOT=c(TRUE,TRUE,"MIDIAOutput.pdf"),Granularity=c(2,3,4,5,6,8,9,10,11,12,14, 15,16),PlotJTree=c("Species","Cliques"))
Each module's time course (trajectory) is independent of the time course of the rest of the network given the time course of the edge(s) associated with that module.

The sequential propagation of information from the input (i.e., the driving process of RAF Kinase) to the time course of the output (MAPKpp) corresponds to the Input-Output path in the MIDIA tree and is visualised using the I-O path matrix. The call is:
T_M2 = MIDIA(mS=mSMAPK,uG=matrix(0,0,0),mR=mRMAPK,mP=(mSMAPK>0), MODE="INFOPROCESSING",OutputSelectn="T_M.IOmatrix",Fraternise=FALSE,PLOT=c(TRUE,TRUE,"MIDIAOutput.pdf"),InfoProc=list("IOSpecies",c("RAFK","RAFRAFK"),c("MAPKpp"),c("RAFK"), c("MAPKpp")),MaxIter=100,PlotJTree=c("Species","Cliques"))

Note that conservation relations can allow equivalent formulations of certain edges (groups of encoding species) in the MIDIA tree. The construction and interpretation of I-O path matrices are carefully described in Section 5.2.4 of this Supplementary Material.

Control over appearance of graphics is via the PlotJTree variable and, where required, via the inputs to the functions PlotJunctionTree() and PlotIOPathMatrix().