Exact model reduction of combinatorial reaction networks

Conzelmann, Holger; Fey, Dirk; Gilles, Ernst D

doi:10.1186/1752-0509-2-78

BMC Systems Biology

Table 6 Hierarchical transformation for the example system.

From: Exact model reduction of combinatorial reaction networks

[R(, ).*]	=	[R(0, 0)] + [R(EGF, 0)] + [R(0, P)] + [R(EGF, P)] + 2 [R(0, 0).R(0, 0)]
		+ 2 [R(EGF, 0).R(0, 0)] + 2 [R(0, P).R(0, 0)] + 2 [R(EGF, 0).R(EGF, 0)]
		+ 2 [R(EGF, P).R(0, 0)] + 2 [R(EGF, 0).R(0, P)] + 2 [R(0, P).R(0, P)]
		+ 2 [R(EGF, P).R(EGF, 0)] + 2 [R(EGF, P).R(0, P)] + 2 [R(EGF, P).R(EGF, P)]
[R(EGF, ).]	=	[R(EGF, 0)] + [R(EGF, P)] + [R(EGF, 0).R(0, 0)] + 2 [R(EGF, 0).R(EGF, 0)]
		+ [R(EGF, P).R(0, 0)] + [R(EGF, 0).R(0, P)] + 2 [R(EGF, P).R(EGF, 0)]
		+ [R(EGF, P).R(0, P)] + 2 [R(EGF, P).R(EGF, P)]
[R(, ).R(, )]	=	[R(0, 0).R(0, 0)] + [R(EGF, 0).R(0, 0)] + [R(0, P).R(0, 0)] + [R(EGF, 0).R(EGF, 0)]
		+ [R(EGF, P).R(0, 0)] + [R(EGF, 0).R(0, P)] + [R(0, P).R(0, P)]
		+ [R(EGF, P).R(EGF, 0)] + [R(EGF, P).R(0, P)] + [R(EGF, P).R(EGF, P)]
[R(, P).]	=	[R(0, P)] + [R(EGF, P)] + [R(0, P).R(0, 0)] + [R(EGF, P).R(0, 0)] + [R(EGF, 0).R(0, P)]
		+ 2 [R(0, P).R(0, P)] + [R(EGF, P).R(EGF, 0)] + 2 [R(EGF, P).R(0, P)]
		+ 2 [R(EGF, P).R(EGF, P)]
[R(EGF, P).*]	=	[R(EGF, P)] + [R(EGF, P).R(0, 0)] + [R(EGF, P).R(EGF, 0)] + [R(EGF, P).R(0, P)]
		+ 2 [R(EGF, P).R(EGF, P)]
[R(EGF, ).R(, *)]	=	[R(EGF, 0).R(0, 0)] + 2 [R(EGF, 0).R(EGF, 0)] + [R(EGF, P).R(0, 0)]
		+ [R(EGF, 0).R(0, P)] + 2 [R(EGF, P).R(EGF, 0)] + [R(EGF, P).R(0, P)]
		+ 2 [R(EGF, P).R(EGF, P)]
[R(, P).R(.*)]	=	[R(0, P).R(0, 0)] + [R(EGF, P).R(0, 0)] + [R(EGF, 0).R(0, P)] + 2 [R(0, P).R(0, P)]
		+ [R(EGF, P).R(EGF, 0)] + 2 [R(EGF, P).R(0, P)] + 2 [R(EGF, P).R(EGF, P)]
[R(EGF, ).R(EGF, )]	=	[R(EGF, 0).R(EGF, 0)] + [R(EGF, P).R(EGF, 0)] + [R(EGF, P).R(EGF, P)]
[R(, P).R(, P)]	=	[R(0, P).R(0, P)] + [R(EGF, P).R(0, P)] + [R(EGF, P).R(EGF, P)]
[R(EGF, P).R(, )]	=	[R(EGF, P).R(0, 0)] + [R(EGF, P).R(EGF, 0)] + [R(EGF, P).R(0, P)]
		+ 2 [R(EGF, P).R(EGF, P)]
[R(EGF, ).R(, P)]	=	[R(EGF, 0).R(0, P)] + [R(EGF, P).R(EGF, 0)] + [R(EGF, P).R(0, P)]
		+ 2 [R(EGF, P).R(EGF, P)]
[R(EGF, P).R(EGF. *)]	=	[R(EGF, P).R(EGF, 0)] + 2 [R(EGF, P).R(EGF, P)]
[R(EGF, P).R(*, P)]	=	[R(EGF, P).R(0, P)] + 2 [R(EGF, P).R(EGF, P)]
[R(EGF, P).R(EGF, P)]	=	[R(EGF, P).R(EGF, P)]

The new states also correspond to the occurrence levels of different subcomplexes. Due to the symmetric structure of the recptor dimers some species have to be counted twice. For instance the macroscopic state [R(EGF, *).*] is an aggregation of all species that comprise a subcomplex consisting of one receptor and one EGF molecule. The two micro-states [R(EGF, 0).R(0, 0)] and [R(EGF, 0).R(EGF, 0)] obviously fit into this pattern. However, the state [R(EGF, 0).R(EGF, 0)] has to be counted twice since the regarded subcomplex also occurs twice in this species. Furthermore, the transformation can be structured in six different tiers.

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ISSN: 1752-0509

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