The GEBIK and GEBIF equations describe the dynamics of the following state variables
:; S : substrate concentration
:; P : product concentration
:; E : enzyme concentration
:; C : complex concentration
:; B : biomass concentration
Both S and P contain at least one isotopic expression of a tracer atom. For instance, if the carbon element is used as a tracer, both S and P contain at least one C atom, which may appear as  and . The isotopic expression within a molecule is
where  is the number of tracer atoms within S, while  is the number of isotopic substitutions in the same molecule. The condition  must be satisfied. For example, the  product in which 1 isotopic substitution occurs (e.g., ) will be described by .
Substrates and products appear in a chemical reaction with specific stoichiometric coefficients. When chemical reactions comprise combinations of reactants and products with various isotopic expressions, the stoichiometric coefficients are functions of the isotope substitution number. If  and  are the stoichiometric coefficient for  substrate and  product, a reaction takes the form
For example, in the reaction , the notation is  with  for both isotopologue reactants of the same substrate with substitution number  and , and with  for  and  because the reaction does not comprise production of  and .
For isotopomers, the substitution location is taken into account as  and , where  and  indicate a different expressions of the same isotopologue . Isotopomers only exist when  and . The substitution location has to be specifically defined depending on the number of tracer atoms , number of substitutions , and molecule structure. For multiatomic molecules that are symmetric with respect to tracer position, there is no need to specify the substitution position when . For example, one substitution of deuterium  in the symmetric methane molecule  does not require the use of the right superscript. In the case that , the substitution location has to be specified, while for  and  it is not required. For example, two D substitutions in  can occur in adjacent or non-adjacent locations. Using this notation, the reaction  can be written as
where  in  defines only one of the two methane forms (either with adjacent or non-adjacent D atoms). The location of D in the two isotopologue water molecules produced on the right-hand side of the reaction has not been indicated because D is present in only one water molecule at saturation, and because the water molecule is symmetric. For asymmetric and multiatomic molecules with  and , definition of the substitution location is always required. For instance, the isotopomers of the (asymmetric) nitrous oxide molecule  are  and .
Reactions of asymmetric isotopomers can be written using the partitioning coefficient  as
where . For example, using N isotope tracers, the isotopomer reactions
can be written as one reaction in which each isotopomer product is multiplied by its partition coefficient as
with . More generally, the tracer element does not necessarily occur in only one substrate and one product. If  substrates react releasing  products, each having an isotopic expression of the tracer element, then the generalized reaction notation is
For instance, consider the  and  tracers in the reaction
In this case the reaction can be written as
with two substrates and two products without indication of the substitution location because all molecules are symmetric.
Biochemical kinetic reactions of type () are often catalytic reactions in which one or more substrates, , bind to an enzyme, E, to form a reversible activated complex, C, which releases one or more
products, , and free, unchanged enzyme. These reactions belong to the type of reactions that can be described by Michaelis–Menten kinetics. Using this approach for substrate and product isotopologue and isotopomer expressions, and under the prescribed stoichiometric relationships among them, leads to the general reactions of the Michaelis–Menten type
with the index , where  depends on the number of possible atomic combinations among all isotopologues and isotopomers. Here, , , and  are the rate constants indexed for each of the m reactions.