Biophysics

A rigorous course on biophysics — from molecular forces and polymer physics through membrane dynamics, ion channels, and molecular motors — to single-molecule experiments, fluorescence techniques, and structural biology methods — with full derivations and MathJax equations.

Course Overview

Biophysics applies the principles and quantitative tools of physics to understand biological systems at every scale — from the forces between individual atoms in a protein to the mechanics of entire cells. This course develops the theoretical foundations rigorously, deriving key equations from statistical mechanics, thermodynamics, and continuum mechanics, following the tradition of Nelson, Phillips, Howard, and Boal.

What You Will Learn

  • ● Molecular forces: electrostatics, van der Waals, hydrogen bonding, hydrophobic effect
  • ● Statistical mechanics of biomolecules: free energy landscapes, Boltzmann distributions
  • ● Polymer physics: worm-like chain model, DNA elasticity, entropic springs
  • ● Protein folding: energy landscapes, misfolding, aggregation, and amyloid formation
  • ● Membrane biophysics: lipid bilayers, bending elasticity, vesicle shapes
  • ● Ion channels, Nernst & Goldman equations, action potentials
  • ● Molecular motors: kinesin, myosin, ATP synthase, stochastic stepping
  • ● Experimental methods: optical traps, AFM, FRET, cryo-EM, X-ray crystallography

Key Equations

Langevin Equation: $m\ddot{x} = -\gamma \dot{x} + F(x) + \xi(t)$

Kramers' Rate: $k = \frac{\omega_0 \omega_b}{2\pi \gamma} e^{-\Delta G^\ddagger / k_B T}$

Worm-Like Chain: $F(x) = \frac{k_B T}{l_p}\left[\frac{1}{4}\left(1-\frac{x}{L}\right)^{-2} - \frac{1}{4} + \frac{x}{L}\right]$

Nernst-Planck: $J = -D\left(\frac{\partial c}{\partial x} + \frac{zec}{k_BT}\frac{\partial \phi}{\partial x}\right)$

Helfrich Bending: $f_b = \frac{\kappa}{2}(c_1 + c_2 - c_0)^2 + \bar{\kappa}\, c_1 c_2$

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Part I: Molecular Biophysics

Molecular forces & interactions, statistical mechanics of biomolecules, polymer physics & DNA, protein folding & misfolding.

4 chapters →
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Part II: Cellular Biophysics

Membrane biophysics, ion channels & electrophysiology, molecular motors, cellular mechanics.

4 chapters →
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Part III: Experimental Methods

Single-molecule techniques, fluorescence & FRET, X-ray crystallography & cryo-EM.

3 chapters →

Prerequisites & References

Prerequisites

  • • Classical mechanics and thermodynamics
  • • Statistical mechanics (introductory level)
  • • Introductory molecular biology or biochemistry
  • • Multivariable calculus and differential equations
  • • Basic probability and statistics

Recommended Texts

  • • Nelson, Biological Physics: Energy, Information, Life
  • • Phillips, Kondev, Theriot & Garcia, Physical Biology of the Cell
  • • Howard, Mechanics of Motor Proteins and the Cytoskeleton
  • • Boal, Mechanics of the Cell