Branched pathways

This is where an intermediate species is chemically made or transformed by multiple enzymatic processes.

linear pathways only have one enzymatic reaction producing a species and one enzymatic reaction consuming the species.

Branched pathways are present in numerous metabolic reactions, including glycolysis, the synthesis of lysine, glutamine, and penicillin,[1] and in the production of the aromatic amino acids.

the consumption and production rates must be equal: Biochemical pathways can be investigated by computer simulation or by looking at the sensitivities, i.e. control coefficients for flux and species concentrations using metabolic control analysis.

A simple branched pathway has one key property related to the conservation of mass.

In general, the rate of change of the branch species based on the above figure is given by: At steady-state the rate of change of

This gives rise to a steady-state constraint among the branch reaction rates: Such constraints are key to computational methods such as flux balance analysis.

Branched pathways have unique control properties compared to simple linear chain or cyclic pathways.

These properties can be investigated using metabolic control analysis.

The fluxes can be controlled by enzyme concentrations

is the fraction of flux going through the upper arm,

will be the observed variable in response to changes in enzyme concentrations.

The former, depicted in panel a), is the least interesting as it converts the branch in to a simple linear pathway.

(condition (b) in the figure), the flux control coefficients for

acquires proportional influence over its own flux,

only carries a very small amount of flux, any changes in

, it means that the remaining two coefficients must be equal and opposite in value.

This also means that in this situation, there can be more than one Rate-limiting step (biochemistry) in a pathway.

Depending on the values of the elasticities, it is possible for the control coefficients in a branched system to greatly exceed one.

[3] This has been termed the branchpoint effect by some in the literature.

[4] The following branch pathway model (in antimony format) illustrates the case

When combined with the connectivity theorems and the summation theorem, it is possible to derive the control equations shown in the previous section.

Following these assumptions two sets of equations can be derived: the flux branch point theorems and the concentration branch point theorems.

and, assuming that the flux rates are directly related to the enzyme concentration thus, the elasticities,

, equal one, the local equations are: Substituting

in the system equation results in: Conservation of mass dictates

term from the system equation: Dividing out

results in: Rearrangement yields the final form of the first flux branch point theorem:[6] Similar derivations result in two more flux branch point theorems and the three concentration branch point theorems.

Following the flux summation theorem[7] and the connectivity theorem[8] the following system of equations can be produced for the simple pathway.

Using these theorems plus flux summation and connectivity theorems values for the concentration and flux control coefficients can be determined using linear algebra.

Simple Branch Pathway. and are the reaction rates for each arm of the branch.
Changes in flux control depending on whether the flux goes through the upper or lower branches. The system output is J2. If most of the flux goes through J2(a) then the pathway behaves like a simple linear change, where flux control on J3 is negligible and control is shared between J1 and J2. The other extreme is when most of the flux goes through J3 (b). This makes J2 highly sensitive to changes in J1 and J3 resulting is very high flux control, often greater than 1.0. Under these conditions the flux control at J3 is also negative since J3 can siphon off flux from J2.
Flux control coefficients in a branched pathway where most flux goes through . Note that step 2 has almost proportional control over while steps 1 and 3 show greater than proportional control over .