The perturbation proof by Kacser and Burns is given as follows.
Given the simple linear pathway catalyzed by two enzymes  and :
where  is the fixed boundary species. Let us increase the concentration of enzyme  by an amount . This will cause the steady state flux and concentration of , and all downstream species
beyond  to increase. The concentration of  is now decreased such that the flux and steady-state concentration of  is restored back to their original values. These changes allow one to write down the following local and systems equations for the changes that occurred:
There is no  term in either equation because the concentration of is unchanged. Both right-hand sides of the equations are guaranteed to be zero by construction. The term  can be eliminated by combining both equations. If we also assume that the reaction rate for an enzyme-catalyzed reaction is proportional to the enzyme concentration, then , therefore:
Since 
this yields:
This proof can be generalized to the case where  may act at multiple sites.