Biophysical chemistry — the intersection of physical-chemistry methods with biological macromolecules (proteins, nucleic acids, lipid bilayers, multi-protein assemblies). Distinguished from biochemistry-bridge (compositional / structural…
biophysical-chemistry
WLC framework: Marko-Siggia F = (k_B·T/L_p)·[1/(4(1-x/L)²) - 1/4 + x/L]
The worm-like-chain (WLC) model — Kratky-Porod 1949 continuum limit of the freely-rotating-chain, parametrised by two length scales:…
ITC framework: Wiseman single-site isotherm; c = n·K·[M]_tot
Isothermal titration calorimetry — the gold-standard direct-enthalpy method for biomolecular binding. In an ITC experiment, aliquots of a…
DLVO framework: Π(D) = 64·k_B·T·c·γ²·exp(-D/λ_D); linearised-PB double-layer
DLVO theory — Derjaguin-Landau (1941) + Verwey-Overbeek (1948) framework for the net interaction between two charged surfaces in…
WLC: F(x=0) = 0 and dF/dx|_{x=0} = 3·k_B·T/(2·L·L_p) (Hookean entropic-elasticity)
Sympy-exact symbolic witness of the two physically meaningful low-extension anchors of the Marko-Siggia WLC force law. Setup: F(x) =…
ITC: lim_{K→∞} θ(r=1) = 1; Q_stoich = n·[M]_tot·V·ΔH (model-free endpoint)
Sympy-exact symbolic witness of the ITC stoichiometric-endpoint anchor in the Wiseman tight-binding regime. Setup: θ(r, K, M) = (1/2) · [1…
DLVO: Π(D=λ_D) = 64·k_B·T·c·γ²·exp(-1); ln[Π(D)/Π(2D)] = D/λ_D
Sympy-exact symbolic witness of the DLVO linearised-PB double-layer pressure at the Debye-length anchor plus the log-slope fingerprint. …
Förster resonance energy transfer framework: E = 1/(1 + (r/R_0)^6) (sixth-power dipole-dipole distance dependence)
Förster resonance energy transfer efficiency sixth-power distance dependence: E = 1/(1 + (r/R_0)^6), where R_0 is the Förster radius at…
Stokes drag framework: F = 6π·η·r·v (low-Re sphere in Newtonian fluid; Einstein-Stokes translational)
Stokes drag on a sphere in Newtonian fluid at low Reynolds number: F = 6π·η·r·v, where η is dynamic viscosity, r sphere radius, v…
Debye-Waller framework: I(q)/I_0 = exp(−⟨u²⟩·q²) (thermal-displacement Gaussian-in-q² attenuation)
Debye-Waller factor for thermal attenuation of X-ray / neutron diffraction intensity: I(q)/I_0 = exp(−⟨u²⟩·q²), where ⟨u²⟩ is the…
FRET distance dependence: E(R_0) = 1/2; E(0) = 1; E(∞) = 0 (three exact sixth-power witnesses)
FRET-efficiency evaluations: E(r = R_0) = 1/2 exactly (Förster-radius definition); E(r = 0) = 1 exactly (contact limit); E(r → ∞) = 0…
Stokes drag: F(η=r=v=1) = 6π; F(2v)/F(v) = 2; F(2r)/F(r) = 2 (triple linearity fingerprint)
Drag evaluations: F at (η,r,v) = (1,1,1) = 6π exactly (unit-argument reference); F(2v)/F(v) = 2 exactly (linearity in v); F(2r)/F(r) = 2…
Debye-Waller X-ray: I/I_0(q=0) = 1; I/I_0(q=sqrt(ln2/⟨u²⟩)) = 1/2; I/I_0(⟨u²⟩=0) = 1
Attenuation-factor evaluations: I/I_0(q = 0) = 1 exactly (no-attenuation at forward scattering); I/I_0(q = sqrt(ln(2)/⟨u²⟩)) = 1/2 exactly…
Flory polymer statistics (1953)
P Flory 1953 (Nobel 1974) random-walk chain: <R^2> = N b^2; Flory radius R_F = b N^nu with nu=3/5 in good solvent; basis of…
Worm-like chain (Marko-Siggia 1995)
Marko-Siggia 1995 force-extension: F(z) = (k_B T / l_p) [1/(4(1-z/L)^2) - 1/4 + z/L]; persistence-length l_p extracted from optical-tweezer…
Helfrich membrane bending (1973)
Helfrich 1973 elastic-membrane bending energy density (kappa/2)(c1+c2-c0)^2 + kappa_bar c1 c2; basis of vesicle shape + membrane-undulation…
Kramers rate (1940)
H Kramers 1940 escape rate over barrier: k = (omega_a / 2 pi) * exp(-Ea/kT) * (gamma-prefactor); turnover from energy-diffusion to…
DNA melting (Poland-Scheraga 1966)
Poland-Scheraga 1966 helix-coil transition: cooperative melting of dsDNA; sequence-dependent Tm = sum_dinuc deltaG/deltaS; basis of…
smFRET (Stryer-Haugland 1967)
Stryer-Haugland 1967 FRET as spectroscopic ruler 1-10 nm; Ha-Selvin 1996 single-molecule FRET; modern smFRET with sCMOS + ALEX + 3-color…
Anfinsen (1973)
C Anfinsen 1973 (Nobel 1972) thermodynamic-hypothesis ribonuclease-A refolding; foundation of structure-prediction.
FRET (Förster 1948)
T Förster 1948 dipole-dipole resonance R0^6/R^6; modern smFRET single-molecule + DNA-PAINT super-resolution dynamics.
Cryo-EM (Frank 2017)
J Frank-J Dubochet-R Henderson 2017 (Nobel 2017) cryo-electron-microscopy; modern 1.5Å direct-detector + AlphaFold-validation.
Optical tweezers (Ashkin 1986)
A Ashkin 1986 (Nobel 2018) optical-trap; modern single-molecule force-spectroscopy + RNA/DNA stretching + protein unfolding.
smFISH (Singer 1998)
R Singer 1998 single-molecule-FISH; modern MERFISH + 100k-gene spatial-transcriptomics tissue-atlas + cancer-heterogeneity.
ITC (Wiseman 1989)
T Wiseman 1989 ITC; modern thermodynamic-fingerprint binding-isotherm + entropy-enthalpy compensation + MicroCal benchmark.