Formal Definition
Given a set M of molecules, chemical reactions can be roughly defined as pairs r=(A, B) of subsets from M.
a1 + a2 + ... + an → b1 + b2 + ... + bmLet R be the set of allowable reactions. A pair (M, R) is a reaction system (RS).
A molecule m ∈ A ∩ B of a reaction r is a catalyst of this reaction.
A RS is autocatalytic, if all the catalysts for all its reactions are in M.
The above definition is not sufficient to describe dependency on external resources or nutrients. This can be formulated by a closure over a generating subset of M.
Formally, cl(S) denotes the smallest subset Y of M that contains S such that for each reaction (A, B)
A ⊆ S ∪ Y ⇒ B ⊆ YA RS is generated (over some resources S), if all reactants A in its reactions are in cl(S) and none of the resources is a catalyst.
A generated autocatalytic set is an RS that is both autocatalytic and generated.
Read more about this topic: Autocatalytic Set
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