Biophysics

The physics of the cell, one kT at a time

About this course

Physical reasoning applied to living matter — cell-scale numbers, diffusion and low Reynolds number, free energy and binding, motors, membranes and polymers, forces and rates, molecular noise, light, and pattern and mechanics.

What you will be able to do

  • Estimate the numbers, sizes and timescales of a cell
  • Model diffusion as a random walk and explain life at low Reynolds number
  • Apply free energy and binding models to molecular interactions
  • Model DNA as a worm-like chain and analyse forces on single molecules
  • Compute reaction rates with Arrhenius and Kramers theory and analyse molecular noise

What this course covers

  • Wolfenden's Uncatalyzed Rate Measurement
  • Arrhenius Rate Law and the Barrier Ladder
  • Kramers Prefactor: Diffusion Over a Barrier
  • Enzyme Catalysis as Barrier Lowering
  • Q10 and the Temperature Range of Life
  • Rate as the Tenth Clause of the Course Spine
  • Worked Example: Reading Barriers from Enzyme Rates
  • The cell as a molecular count
  • kT as the cell's energy currency
  • Protein fold stability and marginal design
  • Boltzmann's factor and two-state switching
  • Boltzmann equilibrium within a non-equilibrium cell
  • The ribosome factory and ATP budget
  • Fermi estimate: glucose consumption and metabolic power
  • Membrane as a parallel-plate capacitor
  • Debye screening and Bjerrum length
  • Electric double layer at a charged membrane
  • Membrane potential confined to the oil layer
  • Born energy barrier for ions crossing a bilayer
  • Single-channel conductance and ions per second
  • Integrated worked example: spike energetics
  • Photon energy in cellular currency
  • Rod photoreceptor amplification cascade
  • Thermal noise floor and vision threshold
  • Förster resonance energy transfer (FRET) as a nanoscale ruler
  • FRET in antenna complexes and photosynthetic energy transfer
  • Photosynthesis efficiency: sunlight to sugar
  • Worked example: Hecht's threshold unified across three lectures
  • Delta G equals minus kT log K: the ladder
  • ATP's value: standard state versus the cell
  • Coupling: buying irreversibility with surplus free energy
  • Concentration as electrochemical potential and osmotic pressure
  • ATP turnover: Fermi estimates for cell and body
  • Course spine: four habits and five things to keep
  • Worked Fermi: E. coli economy end-to-end
  • The Random Coil: Polymer as Random Walk
  • Entropic Spring and Worm-Like Chain Force Law
  • Unifying Rule: One Persistence Length Governs Coil, Spring, and Curve
  • Persistence Length and Bending Rigidity
  • Genome Compaction: Fermi Estimate of Nuclear Packing
  • Poisson counting noise: root N law
  • Transcriptional bursts and the Fano factor
  • Extrinsic noise and cellular noise floor
  • Berg–Purcell limit on concentration sensing
  • Chemotaxis Fermi: temporal vs. spatial gradient sensing
  • Synthesis: one square root across four scales
  • Morphogen gradient: diffusion with decay
  • Turing instability: local activation, long-range inhibition
  • Synthesis: every pattern is a length from D and a lifetime
  • Cell stiffness and the tissue stiffness ladder
  • Cell division force: the contractile ring Fermi estimate
  • Worked example: fly embryo segmentation hierarchy
  • Course spine clause 13 and closing synthesis
  • Random walk: root-N distance and Gaussian distribution
  • Diffusion coefficient: Stokes-Einstein relation
  • Directed vs. diffusive transport in cells
  • Diffusion time scales as distance squared
  • Smoluchowski encounter rate: diffusion-limited reactions
  • Motors vs. diffusion: crossover at ~10 microns
  • Dissociation constant: three readings
  • Single binding site as a soft switch
  • Hill equation and cooperative sharpening
  • MWC two-state mechanism for cooperativity
  • MWC as mechanism vs. Hill as description
  • Fermi estimate: ten repressors shutting a gene
  • Oxygen delivery: whole-lecture synthesis
  • Reynolds Number and the Low-Inertia Regime
  • Flow Reversibility and the Scallop Theorem
  • Stokes Drag, Swimming Power, and Coasting Distance
  • Why Bacteria Need a Motor Despite Tiny Drag
  • The Flagellar Motor: Torque, Power, and Proton Cost
  • Sedimentation and When Swimming Beats Diffusion
  • Capstone Worked Example and Lecture Synthesis
  • Human power budget: watts and ATP turnover
  • Cell-level power: picowatts and watts per kilogram
  • Kleiber's Law: metabolic scaling as M^(3/4)
  • Biosphere power budget vs. solar input
  • Course synthesis: fourteen numbers on one axis
  • The piconewton force ladder
  • Single-molecule instruments as springs and noise floors
  • Bell's law: force shortens bond lifetimes
  • Dynamic force spectroscopy and the loading-rate dependence of rupture force
  • Lecture summary and four analytical habits
  • Worked example: cargo tether under motor load
  • The cell's force strategy: tuning to the piconewton
  • Kinesin step: size, rate, and ATP coupling
  • Force–velocity curve and power peak
  • Feynman's ratchet and the need for an energy input
  • Motor efficiency and power density vs. a car engine
  • Central result: motor as step against load paid in ATP

Syllabus

  1. Scales and Motion

    1. L1 · The Numbers of the Cell
    2. L2 · Diffusion: the Random Walk
    3. L3 · Life at Low Reynolds Number

  2. Energy and Binding

    1. L4 · Free Energy at One kT
    2. L5 · Binding and Cooperativity
    3. L6 · Molecular Motors

  3. Membranes, Polymers and Forces

    1. L7 · Membranes and Electrostatics
    2. L8 · Polymers: DNA as a Worm-Like Chain
    3. L9 · Forces on Molecules

  4. Rates and Noise

    1. L10 · Rates: Arrhenius and Kramers
    2. L11 · Noise: Counting Molecules

  5. Light, Pattern and Energy

    1. L12 · Light and Biology
    2. L13 · Pattern and Mechanics
    3. L14 · The Energy Budget of Life, and the Close