MCB137/237 - Physical Biology of the Cell

Biology is being revolutionized by new experimental techniques that have made it possible to quantitatively query the inner workings of molecules, cells and multicellular organisms in ways that were previously unimaginable. The objective of this course is to respond to this deluge of quantitative data through quantitative models and the use of biological numeracy. The course will explore the description of a broad array of topics from modern biology using the language of physics and mathematics. One style of thinking we will emphasize imagines the kinds of simple calculations that one can do with a stick in the sand.

We will draw examples from broad swaths of modern biology from our department and beyond including cell biology (signaling and regulation, cell motility), physiology (metabolism, swimming), developmental biology (patterning of body plans, how size and number of organelles and tissues are controlled), neuroscience (action potentials and ion channel gating) and evolution (population genetics) in order to develop theoretical models that make precise predictions about biological phenomena. These predictions will be tested through the hands-on analysis of experimental data and by performing numerical simulations using Python. Physical biology will be introduced as an exciting new tool to complement other approaches within biology such as genetics, genomics and structural biology. The course will introduce students to the enabling power of biological numeracy in scientific discovery and make it possible for them to use these tools in their own future research.

Course instructor: Hernan Garcia ( Office hours: Wednesdays 3pm to 4pm @ 501C LSA. Please, see announcement on Piazza for updated office hours.

Course GSI: Yang Joon Kim (, Office hours: Tuesdays 5pm to 6pm @ 447 LSA) & Jiaxi( Jake) Zhao (, Office hours: Wednesday 11am to 12pm @ 349 LSA). 

NOTE: For transparency, rather than emailing Hernan, Yang Joon or Jake, we encourage you to message us through the course's Piazza website about any questions regarding homeworks and class logistics.


Course structure

The class as a whole will meet twice a week for one hour and a half. This time will be devoted to lectures, discussions and hands-on activities including Python exercises. Further, the class will be split into weekly one-hour lab sessions. During these lab sessions, students will work closely with the GSIs to implement the concepts they learned in class in the context of different biological problems. Homework assignment will be given every week and will represent 75% of the final grade. Twice during the semester, students will prepare a project. The first project will be a written assignment, while the second project will be presented in class. These projects will represent 25% of the final grade.

For undergraduate students (MCB137L), the projects will consist on carrying out an estimate on a biological phenomenon of interest followin the style presented in class. These presentations will be five minutes long.

For graduate students (MCB237L) the project will consist on presenting a theoretical model developed in a recent paper of their choosing to the class. These presentations will be ten minutes long.


Class materials:


Lecture : Tuesday and Thursday, 3:30pm -- 5:00pm, 20 Barrows

Discussion section I : Friday, 12:00pm -- 1:00pm, 70 Evans

Discussion section II : Friday, 1:00pm -- 2:00pm, 9 Evans



Date Topics Materials




A feeling for the numbers in biology, Part I

  • Street-Fighting Mathematics: Order-of-magnitude estimates as a tool for discovery in the living world.
  • What sets the scale of things?

A feeling for the numbers: Powerpoint Presentation

Papers: Mathematics Is Biology’s Next Microscope, Only Better; Biology Is Mathematics’ Next Physics, Only Better (Cohen2004); Theory in Biology: Figure 1 or Figure7? (Phillips2015b); Distribution of biomass on Earth (Bar-ON2018 and SI); Number of genes in human genome; The Tragic Matter (Schatz2003); Polymerases and the Replisome (Baker1998); Re-examination of the relationship between marine virus and microbial cell abundances (Wigington2016)

Extra reading material: PBoC chapters 1 through 3




A feeling for the numbers in biology, Part II

Homework 1 out, due 1/30 at 3:30pmNumber of cells in human body (Sender2016)

Homework 1 Solution

Introduction to GradeScope and Python CoLab

Simple estimates



Lectures Biological time scales

An obsession with dN/dt - Bacterial growth, Part I

  • Solving the exponential growth equation

E. coli by the numbers - Limits to bacterial growth: Powerpoint Presentation

Papers: An obsession with dN/dt (Neidhardt1999)

Simulating bacterial growth: (Python codeplease open with Google Colab)

Python Basics: (Python codeplease open with Google Colab)

Extra reading material: PBoC chapters 2 and 3; Kinder & Nelson's Python book Chapter 1, 2 and 3




An obsession with dN/dt - Bacterial growth, Part II

  • Solving the exponential growth equation

Homework 1 due at 3:30pm 

Homework 2 out, due 2/6 at 3:30pm: Schmidt2016Mass spec data on ATP synthaseCai2006

Papers: Stouthamer1973VanOijen2006, Scott2010 

Measuring bacterial growth using image analysis, Part I: (Data, Python code)



An obsession with dN/dt - Bacterial growth, Part III

  • The physical limits to bacterial growth





Diffusion, the null hypothesis of biological dynamics, Part I

  • Diffusion and axonal transport

Homework 2 due at 3:30pm

Homework 3 out, due 2/13 at 3:30pm

Diffusion: Powerpoint Presentation

Papers: Lipps2011Hochbaum2014Droz1962Cui2007Morfini2011Yildiz2003

Extra reading material: PBoC chapter 13

Measuring bacterial growth using image analysis, Part II



Diffusion, the null hypothesis of biological dynamics, Part II

  • Diffusion using continuum theory
  • Diffusion by coin flips 

Diffusion by coin flips: Python code 




Diffusion, the null hypothesis of biological dynamics, Part III

  • Diffusion by coin flips 
  • Diffusion using continuum theory

Homework 3 and estimate paragraph due at 3:30pm

Homework 4 out, due 2/20 at 3:30pm

Raw data for HW4-Question 5 (Figure 2B in Helenius2006)

Papers : Helenius2006

chi-square minimization to measure the growth rate: (Python code)



Diffusion, the null hypothesis of biological dynamics, Part IV

  • Diffusion using master equations
  • FRAP: Measuring diffusion using photobleaching






Diffusion, the null hypothesis of biological dynamics, Part V

  • A universal diffusion speed limit for enzyme catalysis and other reactions

Homework 4 due at 3:30pm: 1D diffusion along microtubules (Helenius2006)

1st estimate due on 2/27 at 3:30pm


Diffusion by master equations: Python code



Study Hall to prepare your first estimate





Biological dynamics, Part I

Regulatory biology: The constitutive promoter

1st estimate due at 3:30pm

Homework 5 out, due 3/5 at 3:30pm

Biological Dynamics: PowerPoint Slides

Papers: Golding2005




Lecture 10: Biological numeracy

– Order of magnitude estimates.

– Astronomical numbers in biology.

– Dimensionless numbers in biology.

– Dimensional analysis.







Probability as the quantitative language of biology

–  The binomial distribution: Coin flips, carboxysome partitioning and calibrating fluorescent protein counts.

–  The Poisson distribution: Bombs over London and sequencing the human genome.

– The exponential distribution: Waiting times for photobleaching and ion channel dynamics. The Boltzmann distribution and statistical mechanics


Homework 5 due at 3:30pm

Homework 6 out, due 3/12 at 3:30pm




Biological length control

– Mechanics of biological polymers.

– Cytoskeletal filament length distributions.




Regulatory biology

– Ion channels and two-state systems.

– The constitutive promoter.


Homework 6 due at 3:30pm   



Lecture 17 :     



Lecture 18 – 20: A life-or-death decision: The Lambda switch

– Cooperativity and the generation of biological sharpness.

– A dynamical systems view of the Lambda switch.




Lecture 19 : 




Lecture 20 :




Lectures 21 – 24: Phase transitions in biology.




Lectures 22 :





Lectrue 23 : 




Lecture 24 : 



4/21 Lectures 25 – 26: Biological specificity: Kinetic proofreading.    


4/23 Lecture 26 :     



Lectures 27 – 28: Second project presentations.    


4/30 Lecture 28 :     

Python tutorials: We will assume no previous Python experience. You will find the tutorial book by Kinder & Nelson (A student's guide to PYTHON for physical modeling, Updated edition) very helpful for the Python basics and programming.


Course policy and suggestions

Attending class and office hours

If you miss classes, it is your responsibility to get notes from one of your classmates. You cannot expect the instructor or GSI to redo the lecture during office hours.

Being able to attend office hours are a key to success. If you cannot attend any of the three offered office hours, you might want to reconsider taking this course.


Homework assignments

Homeworks are due at the beginning of class one week after they are posted.

Homeworks should be submitted through GradeScope (link) to the GSIs in PDF form. Any other form of homework submission will not be accepted.

No late homeworks. Time management is key. Start to work on your homework assignments early and make use of office hours and our availability over Piazza.

It is important to describe your reasoning. Just writing an equation or drawing a plot does not constitute a satisfactory answer to a homework problem.

All plots in the homeworks need to have labeled axes.

All code used needs to be submitted through GraceScope by the homework due date.

You can work in groups, but the answers should be your own. This includes the code!



Regrading is done only until a week after the homework solutions are posted.

If you ask us to regrade an answer in a homework assignment, we reserve the right to regrade all the answers it that homework assignment.

Your two worst scoring homeworks will not be considered for the final grade.

We do not grade on a curve(distribution) or anything like that. The grading scale we will used is shown below.



Jesse M.Kinder, Philip Nelson. A studnet's guide to PYTHON for physical modeling, Updated edition. Princeton University Press.

Phillips, R., et al. (2013). Physical Biology of the Cell, 2nd Edition. New York, Garland Science. (PBoC)

Alberts, B. (2015). Molecular Biology of the Cell. New York, NY, Garland Science. (MBoC)

Milo, R. and Phillips, R. (2016, can be downloaded from Cell Biology by the Numbers. New York, NY, Garland Science.

Mahajan, S. (2010). Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving. MIT Press (2010).

Weinstein, L. and Adam, J.A. (2008). Guesstimation: Solving the World's Problems on the Back of a Cocktail Napkin. Princeton University Press.

Spring 2020
Tuesday, January 21, 2020