Diffusion as Biology's Null�Hypothesis for Dynamics

Quantitative Biology Bootcamp

Fall 2026

Adventure Map

a physical view

of biological phenomena

(for your rotations

and your PhD project)

physical

models

order-of-magnitude

estimates

pen-and-paper

calculations

numerical

simulations

in Python

theory —

experiment

dialogue

Math and

computation

as biology’s

next microscope

the power

of abstraction

biological

numeracy

statistical

analysis

Physical Approaches Allow Us to Formalize Our Null Hypotheses

We Will Examine Diffusion as Biology’s Null Hypothesis for Molecular Dynamics

Time Scales in Biology and�Usain Bolt

False Starts and Olympic Runners

Lipps et al. (2011)

But This Might Not Be That Fair!

Time Scales of Information Transfer in Neurons

• What are the time scales of these processes?

Electrical Impulse Propagation in Unmyelinated Neurons

Hochbaum et al. (2014)

Electrical Impulse Propagation in Unmyelinated Neurons

• Note that propagation in myelinated neurons is ~100 m/s

Hochbaum et al. (2014)

Cell Biology by the Numbers

Axonal transport of cellular components

• Is this fast or slow?

Droz and Leblond (1962)

Passive vs Active Transport in the Neuron

Fourier Takes Stuff(t) Beyond Mechanics - New Concepts Everywhere

Look at the Ambition

Look at the Ambition

Look at the Ambition

We Will Examine Diffusion as Biology’s Null Hypothesis for Molecular Dynamics

Robert Brown and the Discovery of Brownian Motion

Jean Perrin

How Long Does it Take for a Molecule to Diffuse a Distance x?

Thermal Fluctuations Drive Diffusion

The Concept of the Field Revolutionized Physics

The Field Concept�Concentration Field

A Constitutive Model for Diffusive Transport

Fick’s Law and the Units of the Diffusion Coefficient

Using Dimensional Analysis to Estimate the Time Scale for Diffusion

Diffusion times

• Diffusion time for a protein in water (100 μm²/s)

Stroboscopic Illumination to Track Diffusing Molecules in E. coli

English et al. (2011)

Your Turn: Estimate the Diffusion Coefficient of GFP in E. coli

English et al. (2011)

Diffusion constants vary greatly in biology

Diffusion constants depend on the molecular size and environment

Axonal transport of cellular components

• Is this fast or slow?
• Could this be diffusion?

Droz and Leblond (1962)

Watching axonal transport in real time

• What’s the speed of protein movement?

Cui et al., J. PNAS 104:13666 (2007)

Active or Passive?�Vastly Different Time Scales in Axonal Transport

Morfini et al. (2011)

Beating the Diffusion Speed Limit

• Impossibly long time scales associated with diffusion over large distances
• Nature’s solution: active transport

Time Scales of Information Transfer in Neurons

• What are the time scales of these processes?

Diffusion at the Synapse

Your Turn: Estimate the Current Flowing Through a Potassium (Ion) Channel

Single Ion-Channel Current Measurements

Calculating the Temporal Evolution of the Concentration Profile

Three Different Ways of Solving the Diffusion Equation

Jean Perrin Measurements�Early 20^th Century

Measuring One-Dimensional Diffusion of a Molecular Motor on a Microtubule

Joe Howard

Diffusion and the Random Walk

Stochastic and Probabilistic Views of Diffusion

Diffusion and the Random Walk

Diffusion by Coin Flips

A Random Walk in 2D

• We can simulate this in Python!

Three Different Ways of Solving the Diffusion Equation

Our Second Key Equation�The Diffusion Equation

Adventure Map

a physical view

of biological phenomena

(for your rotations

and your PhD project)

physical

models

order-of-magnitude

estimates

pen-and-paper

calculations

numerical

simulations

in Python

theory —

experiment

dialogue

Math and

computation

as biology’s

next microscope

the power

of abstraction

biological

numeracy

statistical

analysis

The Power of Abstraction�The Map Is Not the Territory

One Person’s Mechanism Is Another Persons’s Coarse Grained Model

to understand a phenomenon you don’t need to know where the molecules are!

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