catalyzedRate
plain-language theorem explainer
The definition assigns to each enzyme the Boltzmann factor of its catalyzed barrier height. Researchers deriving enzymatic rate enhancements from J-cost cancellation would reference this when computing the dimensionless rate multiplier. It is a one-line wrapper that composes boltzmannFactor with catalyzedBarrier.
Claim. For an enzyme $E$ with transition-state coordinate $x^*$, the catalyzed rate factor is $e^{-(A(x^*) + J_E(x^*))}$, where $A(x^*)$ denotes the uncatalyzed activation barrier and $J_E(x^*)$ is the enzyme's J-cost contribution at $x^*$.
background
In the Recognition Science treatment of enzyme catalysis, an enzyme is a structure supplying a J-cost profile that complements the reaction's transition-state saddle. The Enzyme type records a function jcost_contribution : ℝ → ℝ together with the transition-state coordinate. The catalyzed barrier is defined as the sum of the bare activation barrier and this contribution, implementing the complementary cancellation J_total(x*) = 0 for ideal enzymes.
proof idea
The definition is a one-line wrapper that applies the boltzmannFactor to the result of catalyzedBarrier applied to the enzyme's transition state coordinate and the enzyme itself.
why it matters
This definition supplies the rate factor used by the theorems ideal_enzyme_unit_rate and rate_enhancement. It fills the catalytic rate enhancement step in the Q19 claim that enzymes achieve zero J-cost at the transition state via complementary cancellation. In the broader framework it connects the phi-scaled barriers to observable rate ratios.
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