DynaFit Scripting Manual

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Restrictions on mechanism

Even more important than our inability to determine certain equilibrium constants is the fact that not all elementary equilibrium constants, which describe individual steps in a reaction mechanism, can even be considered as independent parameters. Some equilibrium constants necessarily must be expressed only as a combination of other equilibrium constants. This has important implications for the way equilibrium binding mechanisms are written in DynaFit script files (see section 3.1).

Branched pathways and equilibrium binding

Consider the following branched reaction mechanism:

$$\begin{array}{rclll} & \phantom{i_{M_{M}}} & & \quad \qu... ...ghtleftharpoons & ABC & \quad \quad k_7 & k_8 \\ \end{array}$$

It transpires that all eight rate constants in this mechanism can be uniquely determined from the experimental data only if we observe the evolution of the biochemical mixture over time. This statement applies even for the hypothetical case when the measurements are performed virtually with zero experimental error.

If the mixture is first allowed to come to equilibrium and then a measurement is performed on it, there is no possibility of determining the values of all individual equilibrium constants $K_{12} = k_1/k_2$, $K_{34} = k_3/k_4$, $K_{56} = k_5/k_6$, and $K_{78} = k_7/k_8$. The branched pathway in the reaction mechanism must be somehow eliminated, because one of the equilibrium constants is expressed in terms of the remaining three.

$$\begin{array}{rcll} & \phantom{i_{M_{M}}} & & \quad \qua... ...\rightleftharpoons & ABC & \quad \quad K_{78} \\ \end{array}$$

The only way to eliminate a branched pathway from the reaction mechanism, without arbitrarily deleting those reaction steps that we know for certain must be present, is to formulate the reaction mechanism in terms of the overall formation of complex species, even if it means using elementary reactions of higher order (molecularity). In this example, we will consider the overall formation constant of the ternary complex $ABC$.

$$\begin{array}{rcll} & \phantom{i_{M_{M}}} & & \quad \qua... ...rightleftharpoons & ABC & \quad \quad K_{abc} \\ \end{array}$$

The above reaction mechanism is the only one that should be used for the biochemical mixture consisting of the molecular species, $A$, $B$, $C$, $AB$, $AC$, and $ABC$, if we can measure only the composition of the mixture at equilibrium (as opposed to monitoring the formation or dissociation of the complexes over time). This follows from the general principle that at equilibrium the chemical system has lost the ``memory'' of how it arrived at the equilibrated state.

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Petr Kuzmic | Jul 12 2005