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relationships that the node was implied into, whereas in the case of the arc, we
directly perturb only one relation (the one corresponding to the arc) so that the
entity of the damage is proportional to the number of elements related to that arc.
This is pretty intuitive if we think of the consequences on the traffic of the block
of a 'peripheral' highway connecting two cities and the consequences of a block
of a central road, which keeps many of alternative pathways open.
This last example allows us to comment another important biological feature
emerging from our purely topological analysis of metabolic network wiring
patterns: the lack of lethal 'purely kinetical' mutations.
We could imagine that cars and trucks could escape the block of the above
mentioned highway by using more narrow alternative roads (kinetically non
optimal solutions). Soon or later this solution will not be efficient at all, the
narrow roads cannot sustain the traffic load of the highway and the flux will be
again blocked due to the 'kinetic insufficiency' of the alternative paths. This
situation never happens in our data, if an alternative pathway does exist, this will
invariably sustain the yeast growth so pointing to a huge plasticity of the kinetic
constants governing the entire metabolism.
This effect was still more clear in another experiment in which, instead of
studying the location of essential mutations in the metabolic network, we
concentrated on the 'double essential mutations' i.e. those mutation couples (two
genes are knocked out simultaneously) whose each member is
per se
non lethal
but the knocked out couple becomes lethal. In this case the essential character is
emerging from the particular coupling and is not peculiar of the specific enzyme.
In this case too only double mutations for which the continuity of the network is
interrupted are lethal, whenever an alternative pathway, albeit non optimal in
kinetic terms is present, the double mutation is not essential.
In a quite schematic form the “upgraded” relationship between biological and
topological “missing alternative” property can be summarized by the following
points:
•
multiple genes synthesizing the same enzymatic function,
•
supplementary enzymes participating in the same metabolic reaction,
•
availability of other pathways in the graph connecting the separated nodes
after the knockouts.
A minimal model has been used in order to build metabolic network: every
gene involved in a reaction is considered as an arc; the network has 'multiple
edges' between nodes if more than one gene participates in the same reaction (or
reactions). A single knockout can disconnect two nodes in the network if the
deleted gene (arc) is the only responsible for the catalysis of a reaction, no
