Physics of biological matter — membrane elasticity, single-molecule force-spectroscopy, polymer statistics of biopolymers, low-Reynolds swimming, ion channel electrochemistry, optical/fluorescence methods. L1 because the underlying laws…
biophysics
Membrane physics
Mechanics of fluid bilayer membranes. Helfrich free energy F = ∫ [½κ(2H − c₀)² + κ̄ K] dA drives shape — bending modulus κ ≈ 10–20 k_BT for…
Lipid bilayer mechanics
Fluid 2D layer ~5 nm thick. Area-stretch modulus K_A ≈ 0.2 J/m² (lyses at ~3 % strain), bending modulus κ from Helfrich, in-plane viscosity…
Single-molecule biophysics
Force-spectroscopy and fluorescence techniques on individual biomolecules — optical/magnetic tweezers, AFM pulling, FRET. Resolves…
Polymer statistical mechanics
Statistical-mechanical treatment of polymer chains — ideal-chain Gaussian statistics ⟨R²⟩ = N b², excluded-volume Flory exponent ν=3/5 in…
Worm-like chain model
Continuous semiflexible-polymer model with persistence length ℓ_p; force-extension F = (k_BT/ℓ_p)[¼(1−x/L)⁻² − ¼ + x/L]. Quantitatively…
Molecular motors (physics)
Stochastic mechanochemistry: kinesin, myosin, dynein convert ATP hydrolysis (~20 k_BT per cycle) into directed motion against load (~5–7 pN…
Low-Reynolds-number biological flow
At cellular scales (Re ~ 10⁻⁴–10⁻²) viscous forces dominate inertia. Time-reversibility of Stokes flow imposes Purcell's scallop theorem:…
Ion channel physics
Selective ion permeation through membrane proteins. Single-channel currents (1–100 pA) follow Goldman–Hodgkin–Katz electrodiffusion; gating…
Fluorescence correlation spectroscopy (FCS)
Statistical analysis of fluorescence intensity fluctuations in a femtolitre confocal volume. Autocorrelation G(τ) yields diffusion…
Förster resonance energy transfer (FRET)
Non-radiative dipole-dipole energy transfer between donor and acceptor fluorophores, with efficiency E = 1/[1 + (r/R₀)⁶]. The r⁻⁶ steepness…
Langevin equation (biophysical use)
Stochastic ODE for a degree of freedom in a heat bath: m ẍ = −γ ẋ − ∂_x U + √(2γk_BT) η(t). Underlies Brownian-dynamics simulation of…
Kramers' rate theory
Escape rate over an energy barrier ΔE in a viscous medium: k ≈ (ω_0 ω_b/2πγ) exp(−ΔE/k_BT) (high friction). Sets the temperature- and…
Single-molecule fluorescence (Betzig)
Moerner 1989 / Betzig 1995 first single-fluorophore detection; Nobel 2014 super-resolution PALM/STORM imaging beats diffraction limit ~10…
Optical tweezers (Ashkin)
Ashkin 1986 / Nobel 2018: focused laser-beam exerts pN force on micron-scale dielectric particles; manipulates DNA / RNA / motors; basis of…
Cryo-EM revolution (Kuhlbrandt)
Kuhlbrandt 2014 'resolution revolution': direct-electron-detector + Bayesian-classification (Scheres RELION) brought cryo-EM to ~2 A;…
Molecular dynamics simulation (MD)
Alder-Wainwright 1957 first MD; modern AMBER/CHARMM/GROMACS sim 100M-atom systems for microseconds; AlphaFold + MD coupling provides…
Brownian motor (Vale-Kinesin)
Vale 1985 + Howard 1989: kinesin-1 walks 8 nm steps along microtubule consuming 1 ATP per step; Brownian-ratchet mechanism converts thermal…
DNA mechanics (Bustamante stretching)
Bustamante-Smith 1996 single-molecule DNA stretching: force-extension curve fit by worm-like-chain (Marko-Siggia 1995); B->S overstretch…
Hodgkin-Huxley (1952)
Hodgkin-Huxley 1952 (Nobel 1963) action-potential; foundational biophysics; modern stochastic-channel + neural-mass extensions.
Optical trap (Ashkin 1986)
A Ashkin 1986 (Nobel 2018) optical tweezers; modern single-molecule biophysics + cell-mechanics + DNA-stretching.
Cryo-EM (Frank 2017)
Frank-Dubochet-Henderson Nobel 2017 cryo-EM; modern resolution-revolution + sub-2A apoferritin record.
Magnetic tweezers (Strick 1996)
Strick 1996 magnetic-tweezers + DNA-supercoiling; modern Charvin 2002 + protein-folding force-spectroscopy.
smFRET (Ha 1996)
T Ha 1996 single-pair-FRET; modern PIE + ALEX + 3-color smFRET; conformational-dynamics standard.
MD (McCammon 1977)
J A McCammon 1977 first protein MD; modern AMBER + GROMACS + Anton2 special-purpose; ms-scale millisecond MD.