The properties that have been used in the literature are the connectivity of the network and the length of pathways found.
While users can choose the direction or even the length of their pathway trip, an easy to follow visual overview of pathways, connected or otherwise related within a larger network, is provided by the pathway suites.
A single pathway was chosen from this pool on the basis of minimizing the length of the pathway, minimizing the number of unknown enzymatic steps, and predicting the thermodynamic likelihood of each reaction.
Estimated gains and losses of compounds in relation to length of metabolic pathway (Fig. 3a) and the role of dietary redundancy in sustaining elongation of metabolic pathways (Fig. 3b) both predict much more frequently occupied dietary nodes and limited diversification around these nodes.
From a network perspective, approaching perfection in atom mapping is important because if the probability of an incorrectly mapped atom is (pin (0,1)) but the length of a pathway involving that atom is k then the probabilty of an incorrectly mapped atom at the end of the pathway is ({mathcal {O}}(p^{k})), e.g., (0.91^{10}cong 0.91^{10}cong
The length of total pathway was measured over seven different temporal length scales (step lengths), ranging from one day to one week, and a seasonal mean was calculated.
As exponent α increases from 1.001 to 6, the dominant sub-network becomes denser, and the length of the pathway becomes longer.
The intensity of long-range connections among nodes was found to be negatively related to the simulated length of signaling pathway.
The difference in robustness can range from a few percent to fifty percent or more, depending on the length of the pathway and on the metabolite one considers.
The simulated length of signaling pathway became linear with internode distance when the grid distance between the two nodes was greater than m.
We fix the length of the pathway at n = 5genes.
