the kinase activity of Lck. Phosphorylation of Y505 allows an intramolecular interaction between pY505 and the SH2 domain of Lck, which downregulates Lck kinase activity through the resulting conformational change of the protein. A depiction of Lck and its above men tioned components in the graphical formalism of BNGL would only show that there are three domains and three tyrosine residues in Lck. There would be no indication that Y192 is part of the SH2 domain or that Y394 is part of the PTK domain. Below, we will show that these rela tionships are clear from a hierarchical graph representa tion of Lck. The hierarchical graphs that will be formally introduced later include directed edges to indicate struc tural relationships.

An edge directed from a component to a subcomponent can be interpreted to mean that the sub component is part of the component. Figure 1B depicts the TCR complex, a multimeric pro tein expressed on the surface of T lymphocytes. The TCR complex AV-951 has a subunit responsible for recognition of peptide antigens, which is composed of disulfide linked a and b chains. It also has a number of subunits responsible for interacting with cytoplasmic signaling proteins. Two subunits are composed of the CD3g, and chains, which each contain an ITAM and which form two disulfide linked heterodimers, a g heterodi mer and a heterodimer. Finally, there is a homodimer of disulfide linked �� chains, which each contain three ITAMs. Each ITAM in the TCR complex contains two tyrosine residues, which are dynamically phosphorylated and dephosphorylated during TCR signaling.

A tyrosine residue in the ITAM of CD3, Y188, is also part of a PRS that contains the motif PxxDY. It is important to recognize the structural overlap between the PRS and ITAM of CD3, because phosphorylation of Y188 inhibits interaction of the Y188 containing PRS with SH3 domains and SH3 domain binding at the PRS inhibits phosphorylation of Y188. The structural relationships discussed above cannot be explicitly repre sented using the regular graphs of BNGL. Below, we will show that these relationships are clear from a hier archical graph representation of the TCR complex. Graph isomorphism Graphs that are essentially the same are called iso morphic. As described elsewhere, to generate a reaction network from a set of rules, BioNetGen must determine, upon generation of a chemical species graph, if the graph has already been generated, i.

e. if it is already part of the reaction network. If the graph does not already exist in the network, it is added to the reaction network. Specifically, upon generation of a chemical species graph, the newly generated graph must be checked for isomorphism with every other existing che mical species graph in the reaction network. To reduce the time necessary for this procedure, BioNetGen assigns to each chemical species graph a canonical label, or for com putational efficiency, a pseudo canonical label, which is not guaranteed to be unique but often is