catalyzedBarrier
plain-language theorem explainer
The catalyzed barrier definition adds an enzyme's J-cost contribution to the bare activation barrier to obtain the net transition-state cost. Kinetic modelers using Recognition Science to explain enzymatic rate enhancements would cite this when computing catalyzed rates from J-cost cancellation. It is realized as a direct algebraic sum of the upstream activation barrier and the enzyme profile.
Claim. For transition coordinate $x^*$ and enzyme $E$, the catalyzed barrier equals $J(x^*) - J(1) + E. jcost_contribution(x^*)$, with $J$ the recognition cost function.
background
The Enzyme structure associates to each reaction coordinate a J-cost contribution function that encodes the enzyme's effect on the cost landscape. Activation barrier is the excess J-cost at the transition state relative to the reactant at coordinate 1. The module frames enzymes as J-cost lenses whose topology cancels the saddle at the active site, per the documentation: 'an enzyme acts as a J-cost lens: its folded topology focuses the ambient σ-field to cancel the J-cost saddle point at the active site'.
proof idea
One-line definition summing the activation barrier at the given coordinate with the enzyme's J-cost contribution at that point.
why it matters
This supplies the net barrier input to the catalyzed rate definition and to theorems establishing zero barrier for ideal enzymes and nonzero barriers for off-target substrates. It fills the module's claim of complementary cancellation for rate enhancement. In the framework it links to phi-ladder scaling of barriers and the requirement that enzyme active sites match the transition state's rung for exact cancellation.
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