Both sets of reactions have an identical input-output relationship : D + ADP —> H + ATP.

We identified three different mechanisms that contribute to the increase in vertices: (i) splitting can yield additional CoPE-FBA subnetworks that originate from rays or linealities with a input-output relationship different from zero.

In the constructed Ecoli subnetworks, the input-output relationship was the only constraint.

CoPE-FBA subnetworks are defined Within this flux space and have a fixed input-output relationship , Which we can write mathematically as:

Subsequently, N A and I A are the stoichiometric matrix and the flux vector of the subnetwork, and d is the fixed input-output relationship of the subnetwork.

Bow-tie can evolve for a nonlinear input-output relation too, if the input can be more compactly represented with no effect on the output.

Here we considered the input-output relation as the sole force guiding the evolution of the network, however there may be other constraints or processes affecting network structures.

In the linear model, the total input-output relationship of the network is given by the product of the matrices A1, A2,.

The composite model outperforms both the multiplicative and additive models, though less so when Ca2+ conductance is decreased by 75%, suggesting that the inability of the multiplicative and additive models to represent the input-output relationship depends on dendritic electrogenesis (Fig.

In other words, the dendritic, spike-dependent manner in which tuft input changes the input-output relationship between basal input and frequency output is explicitly accounted for in the form of the composite equation.

We create three abstract models to describe the input-output relationship from tuft and basal excitatory input to firing rate output.