For any finite Markov chain, the logarithmic sensitivity of the mean first-passage time to any single rate lies in [-1,1] and the sensitivities sum to -1, yielding a conserved control budget that caps kinetic-proofreading discrimination at the number of checkpoints.
Simple Proofs of the Summation and Connectivity Theorems in Metabolic Control Analysis
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In the early 1970s, the Kacser/Burns and the Heinrich/Rapoport groups independently discovered the important summation and connectivity theorems in metabolic control analysis. These theorems were derived originally by using thought experiments and proved mathematically later. The mathematical proofs are not easy for me to read and follow. But the proofs actually can be very simple and need only a couple of lines as I give here.
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A Universal Control Budget for First-Passage Kinetics
For any finite Markov chain, the logarithmic sensitivity of the mean first-passage time to any single rate lies in [-1,1] and the sensitivities sum to -1, yielding a conserved control budget that caps kinetic-proofreading discrimination at the number of checkpoints.