Null Hypotheses and the Great Probability Distributions
Quantitative Biology Bootcamp
Fall 2025
The Great Probability Distributions as Null Hypotheses in Biology
We All Make Hypotheses
These Hypotheses Are Likely to Be Wrong, and That’s a Good Thing
Being Wrong About Specific Heat Led to the Quantum Theory of Solids
Null Hypotheses for the Motion of Molecules in Cells
Null Hypotheses for Segregation of Macromolecular Assemblies
Null Hypotheses for Cell Size Control
We Will Test the Constitutive Promoter Null Hypothesis
Going Back to Stuff(t)�The Rate Equation Protocol
Three Protocols for Solving Biological Dynamics
Cells Make Decisions About Their Diet
The Central Dogma of Molecular Biology Links Information and Action in Cells
Cartoon Model: Cellular Decisions by Turning Genes On and Off
Activators and Repressors�Regulate Access to the Promoter
Repressors and Activators In Action
The lac Operon
Jacques Monod
Francois Jacob
Labeling RNA Molecules using MS2
Dynamics of mRNA Production
Ido Golding et al., Cell (2005)
A Cartoon Model:�Balancing Production and Degradation
Phase diagram of the constitutive promoter
Dynamics of the Mean mRNA Number�What Sets the Time Scale to Reach Steady State?
How Do Model Parameters Determine the mRNA Dynamics?
Phase portraits are a quantitative tool to dissect dx/dt=f(x) without doing a lot of math!
mRNA life times
Cell Biology by the Numbers
Estimating the Production and Degradation Rates
Ido Golding et al., Cell (2005)
The Model Doesn’t Quite Agree With the Data
The MS2 Reporter Made the mRNA Immortal!�“Degradation” Is Given by Cell Division
A Simplified View of Protein Production Dynamics
The Constitutive Promoter Model Can Explain Protein Dynamics
Marbach and Bettenbroc, 2012
The Rate Equation Protocol
The Great Probability Distributions as Null Hypotheses in Biology
Today, We Will Test the Constitutive Promoter Null Hypothesis
Characterizing the mRNA and Protein Distributions
Taniguchi et al. (2010)
Cell Biology by the Numbers
What Does the mRNA Distribution Tell Us About How Transcription Happens?
Zenklusen et al. (2008)
What Is the Predicted mRNA Distribution for Our Simple Model?
Three Protocols for Solving Biological Dynamics
The Chemical Master Equation Protocol
Characterizing the mRNA Distribution
How the mRNA Distribution Changes
mRNA distributions are the result of production and degradation
Trajectories and Probabilities of the Constitutive Promoter
The Master Equation Dictates The Probability Flow
The Beauty of the Taylor Expansion
Calculating Functions Without Calculators: A Reminder of Our Privilege
We Have Always Had Big Data!�“Big” Means We Have to Tame It
(Berman et al.)
Taming Brahe’s Data for Mars
The mRNA Distribution in Space and Time
The Poisson Distribution Is Fully Determined by One Parameter
Testing the Null Hypothesis�Deviations from Poisson Reveal Molecular Mechanism
Zenklusen et al. (2008)
An Alternative Null Hypothesis: The Two-State Model of Transcription
Transcriptional Bursting is Widespread in Biology
Trajectories and Probabilities of the Two-State Promoter
Testing the Null Hypothesis�Deviations from Poisson Reveal Molecular Mechanism
Zenklusen et al. (2008)
A Closer Look at the Bacterial Data Reveals that mRNA is Produced in Bursts
Bursting Dynamics Dictates Gene Expression Variability
Testing the Two-State Model
Theory With a Capital T:�Turning Physics Into Biology’s Next Microscope
The Poisson Distribution is Everywhere
Bombs Dropped Over London
Where Bombs Targeted or Falling at Random?�The Poisson Distribution Is Everywhere!
An area was selected comprising 14 square kilometres of south London (…). The selected area was divided into 576 squares of 1/4 square kilometre each, and a count was made of the numbers of squares containing 0, 1, 2, 3 ...,etc. flying bombs. Over the period considered the total number of bombs within the area involved was 537.
Imagining Clarke’s Data
The Poisson Distribution is Everywhere
Sequencing coverage
Sequencing coverage
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