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…