Bioorganic chemistry — IUPAC Division III organic chemistry at the biomolecule / enzyme-mechanism grain. Foundations: Michaelis-Menten saturation kinetics (Michaelis & Menten 1913, Briggs-Haldane 1925): for E + S ⇌ ES → E + P under…
bioorganic-chemistry
Michaelis-Menten v = V·S/(Km+S): steady-state ES kinetics
Michaelis-Menten saturation kinetics (Michaelis & Menten 1913; Briggs-Haldane 1925 steady-state generalisation). For the single-substrate…
Hill v = V·Sⁿ/(Kⁿ+Sⁿ): n is the log-log slope at S = K
Hill cooperativity (A. V. Hill 1910). Multi-site substrate binding where n > 1 indicates positive cooperativity (one binding event raises…
pH = pKa + log₁₀([A⁻]/[HA]); pI = ½(pKa1 + pKa2) for amino acid
Henderson-Hasselbalch equation (Henderson 1908, Hasselbalch 1917): logarithmic rearrangement of the weak-acid equilibrium K_a =…
v = V·S/(Km+S) at S = Km ⇒ v = V/2 (half-saturation anchor)
Sympy-exact witness of the K_m = S = half-V_max defining identity. Setup: v(S) = V·S/(K_m + S). Substituting S = K_m gives v = V·K_m/(2…
1/v = Km/(V·S) + 1/V; y-intercept 1/V, x-intercept −1/Km
Sympy-exact witness of the Lineweaver-Burk double-reciprocal linearisation. Taking 1/v of the Michaelis-Menten equation and expanding as a…
pI = ½(pKa1 + pKa2); glycine (2.34, 9.60) ⇒ pI = 5.97
Sympy-exact witness of the amino-acid isoelectric-point formula on glycine. Setup: pK_a1 (carboxylic acid) = 2.34, pK_a2 (ammonium) =…