IndisputableMonolith.Chemistry.EnzymeCatalysis
This module models enzyme catalysis by characterizing an enzyme as a J-cost profile added along the reaction coordinate. It defines the Enzyme type together with uncatalyzed and catalyzed barriers, Boltzmann factors, and rate enhancements. The module builds directly on the J-cost landscape from ActivationEnergy and the tick time unit from Constants. It consists entirely of definitions and simple lemmas with no non-trivial proofs.
claimAn enzyme is characterized by the J-cost profile $J_E(x)$ it adds at each point $x$ on the reaction coordinate. This yields an uncatalyzed barrier $J_0$ and a catalyzed barrier $J_E$, with rates given by the Boltzmann factor $e^{-J/kT}$ and enhancement factor derived from their difference.
background
Recognition Science derives chemical activation barriers from the J-cost landscape, where the transition state is the point of maximum J-cost along the reaction coordinate (ActivationEnergy module). The Constants module supplies the native time quantum as the tick with value 1. The present module introduces the Enzyme object as an additive J-cost profile that modifies this landscape, together with derived quantities such as uncatalyzedBarrier, catalyzedBarrier, boltzmannFactor, and rate_enhancement.
proof idea
This is a definition module, no proofs. It introduces the Enzyme type as a J-cost profile, then defines barrier and rate functions by direct application of the J-cost addition to the upstream activation-energy construction.
why it matters in Recognition Science
The module extends the J-cost framework (T5 J-uniqueness) into enzymatic catalysis, supplying the catalyzedRate and rate_enhancement terms needed for RS-native kinetic models. It fills the chemistry-module step that links barrier reduction to observable rate changes while remaining within the phi-ladder scaling conventions. No downstream uses are recorded yet.
scope and limits
- Does not derive any specific molecular structure for an enzyme.
- Does not compute absolute numerical rates without external parameters.
- Does not treat non-ideal enzymes, inhibition, or multi-step mechanisms.
- Does not connect the J-cost profile to the phi-ladder mass formula.
depends on (2)
declarations in this module (16)
-
structure
Enzyme -
def
uncatalyzedBarrier -
def
catalyzedBarrier -
def
IsIdealEnzyme -
theorem
ideal_enzyme_zero_barrier -
theorem
ideal_enzyme_exists -
def
boltzmannFactor -
def
uncatalyzedRate -
def
catalyzedRate -
theorem
ideal_enzyme_unit_rate -
theorem
rate_enhancement -
def
rungBarrier -
theorem
enzyme_rung_matching -
theorem
different_rungs_different_barriers -
theorem
off_target_not_ideal -
theorem
enzyme_jcost_lens_summary