Introduction to Quantitative Biology


Course Description

This course provides an introduction to key concepts in systems biology, with an emphasis on the modeling of genetic networks and evolutionary processes. We will describe our current understanding on how the vast network of biochemical interactions in a cell works together to perform cellular functions. The aim of the mathematical models studied in this class is not to precisely reproduce experimental data, but rather to allow intuitive understanding of general principles.

We will start by studying the regulation of gene expression, and how transcription networks in the cell are organized using recurring motifs. We will analyze the function and stability of these network motifs, and show how they can be used to build different synthetic circuits. We will then study the evolution of optimized network designs. We will see how cells tune their gene expression levels in response to new selective pressures; we will analyze how beneficial mutations are fixed in a cell population; and we will determine the possible paths of adaptation of an organism towards a new optimum.



We aim to introduce the students to the mathematical formulation necessary to understand the biological problems we will discuss. Some background in calculus and programming is helpful, but not required. Part of our goal is to expose those with little quantitative background to some of the interesting theories that have shaped the field of systems biology. Given the wide range of backgrounds among students in this class we will try to avoid unnecessary jargon.


Suggested Reading

- Alon, Uri. An Introduction to Systems Biology: Design Principles of Biological Circuits.

- Nowak, Martin A. Evolutionary Dynamics: Exploring the Equations of Life.

- Ptashne, Mark. A Genetic Switch.

- Strogatz, Steven H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.



The course will have two problem sets, at the end of each week. Each of these problem sets will count as half of the final grade.



Instructor: Daniel Schultz

Office: Vail Bldg, 206








Intro: Basic concepts of genetic networks.


Gene expression and gene regulation.


Stability, bistability and oscillations.


Synthetic genetic circuits.

Gardner TS, et al. Construction of a Genetic Toggle Switch in Escherichia ColiNature (2000)

Elowitz MB, and Leibler S. A Synthetic Oscillatory Network of Transcriptional Regulators. Nature (2000)


Optimal genetic circuit design.

Dekel E, and Alon U. Optimality and Evolutionary Tuning in the Expression Level of a Protein. Nature (2005)


Fitness landscapes and sequence spaces.


Evolutionary games.


Evolution in finite populations.


Microbial evolution experiments.

Blount ZD, et al. Historical contingency and the evolution of a key innovation in an experimental population of E. coli. PNAS (2008)

Toprak E, et al. Evolutionary paths to antibiotic resistance under dynamically sustained drug selection. Nature Genetics (2012)

Baym M, et al. Spatiotemporal microbial evolution on antibiotic landscapes. Science (2016)