Diffusion as Biology's Null�Hypothesis for Dynamics

MCB137L/237L

UC Berkeley

Spring 2025

Physical Approaches Allow Us to Formalize Our Null Hypotheses

The Constitutive Promoter Null Hypothesis

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?
• Today, we’re going to do “physics meets biology”

Droz and Leblond (1962)

Passive vs Active Transport in the Neuron

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

Our Second Key Equation�The Diffusion Equation

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 of 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

The Continuum Theory Protocol and Diffusion

Another Use of The Continuum Theory Protocol for Fluid Dynamics

Calculating the Temporal Evolution of the Concentration Profile

Three Different Ways of Solving the Diffusion Equation

The Great Probability Distributions�One of the Main Threads Throughout This Course

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!

Our Second Key Equation�The Diffusion Equation

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!

Three Different Ways of Solving the Diffusion Equation

Can we calculate the whole distribution?

A Probabilistic View of Concentration Profiles

Dynamics of the Probability Distribution

Dynamics of the Probability Distribution

Calculating the temporal evolution of the probability distributions by spreading the butter!

Solving Boundary Value Problems

FRAP: Fluorescence Recovery After Photobleaching

Ellenberg et al., J. Bacteriol. 188:3442 (2006)

FRAP: Fluorescence Recovery After Photobleaching

Mulliineaux et al., J. Bacteriol. 188:3442 (2006)

Simulating Bacterial FRAP

FRAP by spreading the butter

Three Different Ways of Solving the Diffusion Equation

The Powerful Continuum Theory Protocol

Defining the Field Variables

Mass Conservation in a Volume Element

A Constitutive Model for Diffusive Transport

The Diffusion Equation

The Powerful Continuum Theory Protocol

A universal speed limit for enzymatic reactions?

E. coli Signaling and Diffusion Limited Rates

Concentration of Ligands Around our Cell

The diffusion speed limit constrains enzymatic reactions

Homework: Does Diffusion Also Dictate the Maximum Translation Rate?

• Translation rate: 20 aa/s

Klump et al., PNAS 110:16754 (2013)

Diffusion-Limited Arrival of tRNAs to the Ribosome

Counting tRNA Molecules

Dong, Nilsson and Kurland, JMB (1996)