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) =…
Eyring enzyme framework: k_cat = (k_B T / h)·exp(-ΔG‡/RT) (transition-state rate)
The Eyring (1935) absolute-rate-theory expression specialised to enzyme turnover — k_cat is written as a universal frequency prefactor…
Hill full framework: θ(L) = Lⁿ/(Kⁿ + Lⁿ); half-saturation at L = K; Hill slope n/4 at L = K
The Hill (1910) cooperative-binding equation in its fractional-occupancy form, θ(L) = Lⁿ/(Kⁿ + Lⁿ), where L is the free-ligand…
Competitive inhibition framework: K_m^app = K_m·(1 + I/K_i); V_max unchanged
The competitive-inhibition equation — the canonical modification of the Michaelis-Menten constant in the presence of a competitive…
Eyring: k = T·k_B/h·exp(-ΔG/(RT)); zero-barrier k = T·k_B/h; ln k = log T − log h + log k_B − ΔG/(RT)
Sympy-exact witness of the Eyring enzyme-rate expression and its two canonical limits. Setup: k_B, h, R, T, DG (ΔG‡) all declared…
Hill: θ = Lⁿ/(Kⁿ+Lⁿ); θ(L=K) = 1/2; slope dθ/d(log L)|_K = n/4
Sympy-exact witness of the Hill cooperative-binding θ(L) and its two canonical anchors. Setup: L, K positive symbols; n positive; θ(L) =…
Competitive inhibition: K_m^app = K_m·(1+I/K_i); at I=K_i ⇒ K_m^app=2K_m; at I=0 ⇒ K_m^app=K_m
Sympy-exact witness of the competitive-inhibition K_m apparent formula and its two diagnostic anchors. Setup: K_m, K_i, I all positive…
Briggs-Haldane 1925 quasi-steady-state derivation
Briggs-Haldane 1925: rederived Michaelis-Menten kinetics under quasi-steady-state assumption d[ES]/dt = 0 (instead of equilibrium…
Induced fit (Koshland 1958)
D Koshland 1958 induced-fit: enzyme conformation changes upon substrate binding; updates Fischer 1894 lock-and-key; basis of allosteric +…
Ribozyme (Cech-Altman 1989)
T Cech 1989 + S Altman 1989 (Nobel 1989) catalytic RNA: Tetrahymena intron self-splicing + RNase P; basis of RNA-world hypothesis +…
DNA photolyase (Sancar 2015)
A Sancar 1990s+ DNA photolyase: FAD + 8-HDF antenna; CPD/6-4PP repair via ET; Nobel 2015 with Lindahl + Modrich; conserved in non-placental…
Ribosome structure (Nobel 2009)
Yonath + Ramakrishnan + Steitz Nobel 2009 atomic-resolution ribosome structures; 50S peptidyl-transferase ribozyme center;…
Ubiquitin (Nobel 2004)
Hershko-Ciechanover-Rose Nobel 2004 ubiquitin-proteasome: E1-E2-E3 cascade marks K48-poly-Ub for 26S proteasome degradation; basis of…
CRISPR-Cas9 (Charpentier-Doudna 2012)
Jinek-Charpentier-Doudna 2012 (Nobel 2020) RNA-guided endonuclease Cas9; modular DNA targeting; revolutionized genome editing; therapeutic…
Induced-fit (Koshland 1958)
D Koshland 1958 induced-fit; modern conformational-selection vs induced-fit debate Boehr-Wright 2009 + cryo-EM ensemble.
Self-splicing ribozyme (Cech 1981)
T Cech 1981 (Nobel 1989) Tetrahymena ribozyme; modern RNA-world hypothesis + group-I intron + therapeutic-RNA enzymes.
RNA world (Gilbert 1986)
W Gilbert 1986 'origin of life: RNA world'; modern abiotic-RNA + Sutherland 2009 prebiotic ribonucleotide synthesis.
Click chemistry (Sharpless 2001)
K B Sharpless 2001 + Meldal 2002 (Nobel 2022) CuAAC click-chemistry; modern bioorthogonal + drug-conjugates + ADCs.
Fab fragment (Porter 1959)
R Porter 1959 (Nobel 1972) papain digestion of antibody; modern Fab/scFv/nanobody therapeutic-formats.
DNA polymerase (Kornberg 1957)
A Kornberg 1957 (Nobel 1959) DNA polymerase I; modern Taq + Pfu + Phusion engineered polymerases for PCR / NGS.