1 of 89

Regulatory Biology and�The Unreasonable Effectiveness of Statistical Mechanics

MCB137/237 – Spring 2025

2 of 89

Neidhardt and his lifelong love for dN/dt

3 of 89

The insight from Monod and Jacob: Genes that control other genes

Monod (1949)

(also called shadow)

(also called shadow)

4 of 89

Cells Make Decisions About Their Diet

5 of 89

Can the input-output function of regulatory decisions be modeled?

  • Can model and experiment agree on the input-output relations of genetic circuits?

6 of 89

The Central Dogma of Molecular Biology Links Information and Action in Cells

7 of 89

Cartoon Model: Cellular Decisions by Turning Genes On and Off

8 of 89

Activators and Repressors�Regulate Access to the Promoter

9 of 89

Repressors and Activators In Action

10 of 89

The lac operon

Jacques Monod

Francois Jacob

11 of 89

“What is true for E. coli is true for the elephant”, Jacques Monod

12 of 89

A Simple Model of a Constitutive Promoter

13 of 89

Measuring gene expression

14 of 89

What does the mRNA distribution tell us about how transcription happens?

Zenklusen et al. (2008)

15 of 89

mRNA production is not continuous

Ido Golding

16 of 89

The Trajectory of the Constitutive Promoter

  • What’s the fraction of time (probability) that RNA polymerase spends bound on the promoter?

17 of 89

Calculating probabilities of different molecular states

18 of 89

The Entropy of the Whole System is Maximized, But the Free Energy of Our System is Minimized

19 of 89

How do we distribute a given amount of money among ourselves?

20 of 89

Distributing money or energy leads to the same probability distribution

Boltzmann Weight

21 of 89

The fundamental law of statistical mechanics

22 of 89

The Unreasonable Effectiveness of Mathematics in the Natural Sciences

23 of 89

The Unreasonable Effectiveness of Statistical Mechanics in Biology

24 of 89

The Boltzmann Distribution

25 of 89

Why statistical mechanics?

  • Can we use statistical mechanics to predictively understand cellular decision making?

26 of 89

Botlzmann’s Most Famous Equation

27 of 89

Sodium Channels and Action Potentials

28 of 89

Single Ion Channel Recordings

29 of 89

What Are the Probabilities of Each Ion Channel State?

30 of 89

A voltage-gated sodium channel

31 of 89

Ions and Membrane Potential

32 of 89

The Statistical Mechanics Protocol for an Ion Channel

33 of 89

Mathematizing Our Cartoons: mRNA Production Rate Is Proportional to Promoter Occupancy

34 of 89

Using Statistical Mechanics to Calculate the Fraction of Time RNAP Is Bound to the Promoter

35 of 89

RNA Polymerase Can Be Bound Specifically or Non-Specifically

36 of 89

The Statistical Mechanics Protocol

37 of 89

The Occupancy Hypothesis

38 of 89

How many ways can we seat P spectators in a stadium with NNS seats?

39 of 89

Seating P Distinguishable Spectators on NNS Seats

40 of 89

The Spectators Are Indistinguishable

41 of 89

Statistical Mechanics Determines the Probability of RNA Polymerase Binding to the Promoter Sequence

Bintu, et al., Curr Op Gen Dev (2005)

42 of 89

pbound for the Constitutive Promoter

43 of 89

The lac operon

Jacques Monod

Francois Jacob

44 of 89

A Simple Model of a Constitutive Promoter

45 of 89

Statistical Mechanics Determines the Probability of RNA Polymerase Binding to the Promoter Sequence

Bintu, et al., Curr Op Gen Dev (2005)

46 of 89

pbound for the Constitutive Promoter

47 of 89

Simple Repression States and Weights

48 of 89

A Theoretical Model of Repressor Action

49 of 89

Committing to a Mathematical Description of Simple Repression

50 of 89

Connecting Theory and Experiment Through the Fold-Change

  • We were the only ones that cared enough about these experiments to actually do them!
  • Problem: We had never done experiments in biology.

​

51 of 89

Bending the lac Operon to Make it Simpler

52 of 89

Classic Experiments Simplifying the lac Operon

You either want to be six months ahead of

everybody or 30 years behind

Sydney Brenner

​

Müller-Hill lab

53 of 89

Classical Enzymatic Approach to Measuring Gene Expression

54 of 89

Measuring repressor copy number using immunoblots

55 of 89

Testing our model’s predictions using bulk measurements

56 of 89

Measuring the Fold-Change in Gene Expression Using Fluorescent Proteins

57 of 89

Testing our model’s predictions in single cells

58 of 89

Measuring gene expression in single cells

59 of 89

Identifying the knobs that can be tuned theoretically and experimentally

  • We have performed a systematic dissection of each one of these knobs.

60 of 89

Our model predicts regulatory input-output functions analogous to electronic circuits

HGG et al., PNAS (2011)

61 of 89

Simple repression can be measured in multiple ways

62 of 89

A New Knob: The Number of Competing Binding Sites

63 of 89

Only One More Parameter to Describe�Binding Site Competition

64 of 89

We Make Parameter-Free Predictions About this More Complex Regulatory Scenario

65 of 89

Climbing the Simple Repression Pyramid

66 of 89

Statistical mechanics generates polarizing predictions about the input-output function of several regulatory architectures

Bintu, HGG, et al., Curr Op Gen Dev (2005)

​

67 of 89

The lac Operon Is Both About Repression and Activation

Jacques Monod

Francois Jacob

68 of 89

Your Turn: Derive the Statistical Weights of Simple Activation

69 of 89

States and Weights for Simple Activation

70 of 89

The Simple Activation Input-Output Function�Linear-Log vs. Log-Log

71 of 89

Statistical mechanics generates polarizing predictions about the input-output function of several regulatory architectures

Bintu, HGG, et al., Curr Op Gen Dev (2005)

​

72 of 89

Two Activators Working Cooperatively

73 of 89

Cooperativity Sharpens Input-Output Functions

74 of 89

The Effect of Cooperativity on the Different States

75 of 89

Binding From the Viewpoint of Statistical Mechanics Vs. Biochemistry

76 of 89

Different Measures of Sharpness

77 of 89

Sharpness of the Dual Activation Motif

78 of 89

Dissecting Sharpness In the lac Operon

79 of 89

Ligand-receptor binding

80 of 89

Hemoglobin and oxygen binding

81 of 89

Oxygen binding to hemoglobin

82 of 89

Cooperativity leads to sharper binding curves

83 of 89

Dimoglobin: A toy model for Oxygen binding

84 of 89

Protein allostery and the MWC model

85 of 89

Statistical Mechanics Generates Polarizing Predictions About the Input-Output Function of Several Regulatory Architectures

Bintu, HGG, et al., Curr Op Gen Dev (2005)

​

86 of 89

Building Logic Gates

87 of 89

Building Logic Gates

88 of 89

Building an AND Gate

Buchler et al., 2003

89 of 89

Building an OR Gate