text: In the following reaction network, A is irreversibly converted to an intermediate B, which irreversibly reacts to form C.
  The pools of A, B, and C have delta values defined as δ, δ, and δ respectively. These values are related to the ratio of heavy to light isotopes in each pool, and are the conventional means by which scientists express the isotopic composition of materials. Importantly, δ is distinct from δ listed on the diagram, as δ is the isotopic composition of B produced from A before it mixes with the pool of B. The isotopic compositions of the pools and products are related through fractionation factors that reflect the kinetic isotope effects (KIEs) associated with each reaction. For A → B,
  Rearranging for δ gives  in which . In many cases,  and . This is consistent with a normal kinetic isotope effect in which the product is slightly depleted in a heavy isotope relative to the reactant. If the isotope effect is small, as is typical for C and N,  and . From this, we can see that the product produced from A will be depleted by roughly ‰ relative to the starting material.
  At steady state, the mass flux  of material entering pool B must equal the flux  leaving pool B. In other words, the amounts of heavy and light isotopes entering and exiting the pool must be identical, so . Since there is no flux of material out of pool C, its delta value is also equal to . This analysis shows that the end product of a linear, irreversible reaction network has an isotopic composition determined solely by the composition of the starting material and the KIE of the first reaction in the network.