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: $f_b = \frac{\kappa}{2}(c_1 + c_2 - c_0)^2 + \bar{\kappa}\, c_1 c_2$
Part I: Molecular Biophysics
Molecular forces & interactions, statistical mechanics of biomolecules, polymer physics & DNA, protein folding & misfolding.
Part II: Cellular Biophysics
Membrane biophysics, ion channels & electrophysiology, molecular motors, cellular mechanics.
Part III: Experimental Methods
Single-molecule techniques, fluorescence & FRET, X-ray crystallography & cryo-EM.
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
Classical Mechanics
Newtonian, Lagrangian, and Hamiltonian mechanics
Thermodynamics
Laws of thermodynamics, free energy, and equilibrium
Statistical Mechanics
Ensembles, partition functions, and Boltzmann distributions
Cell Physiology
Membrane biology, ion channels, and cellular processes
Quantum Mechanics
Wave functions, operators, and quantum statistical foundations
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
🎓 Course Completion Certificate
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