Biomedical Engineering 580.429

Systems Bioengineering 3

Fall 2016

(4 credits, EN)


Systems bioengineering 3 (580.429 SB3) is an upper-level course required of all BME majors. Progress in biomedicine requires understanding how individual cellular components function together. Cell and tissue engineers can exploit this knowledge for regenerative medicine. Basic researchers need to understand how failures of individual components, for example due to mutation, lead to disease. This course provides the fundamental tools that you will need to develop and apply quantitative models of cellular systems, including protein signal transduction, gene regulation, metabolism, and large-scale network science.


Prof. Joel S. Bader, joel.bader at,

Office: Clark 201C; Miller Research Building 319

Office hours: Tue/Thurs in Shaffer 3 immediately following lecture, 11:45 AM until the last question is answered, possibly walking back to Clark 201C, or by arrangement.

Teaching Assistants

  • Lydia Carroll (1st half)
  • Collin Tokheim (1st half)
  • Isac Lee (2nd half)
  • YiFan Zhang (2nd half)

Office hours: To be announced.


Lectures: Tuesday and Thursday, 10:30 – 11:45 AM, Shaffer 3


  1. Friday, 11:00 AM – 11:50 AM, Latrobe 120, Lydia
  2. Friday, 1:30 PM – 2:20 PM, Hackerman 320, Collin
  3. Friday, 12:00 PM – 12:50 PM, Latrobe 120, Lydia
  4. Friday, 3:00 PM – 3:50 PM, Maryland 217, Collin

TA Office Hours

  • Wednesdays, 4-5 PM
  • Wednesdays, 7-8 PM

Key Dates

Lecture, HW, Quiz, and Exam Dates

Lecture numbers in the course notes.


Collected lecture notes, 2013 edition

Revised lecture notes

Recommended: Uri Alon, Introduction to Systems Biology


Homework 1, Laplace transform review. sb3-hw1key

Homework 2, Deriving the Laplace transform and its normalization. sb3-hw2key

Homework 3, Contour integrals and the inverse Laplace transform. sb3-hw3key

Homework 4, MAPK signaling cascades. sb3-hw4key

Homework 5, Gain, activation time, and signaling duration. HW5 key

Homework 6, Linear cascades with serial connections, parallel connections, and feedback. sb3-hw6-key

Homework 7, Shannon entropy, motif widths, information content, and coding length. HW7 key

Homework 8, Transcription factor binding with cooperative, independent, and sequential models. HW8 key.

Homework 9, Signal transduction coupled to gene regulation, analytical and numerical solutions. HW9 key.

Homework 10, Gene regulatory motifs. HW10 key.

Homework 11, Combinatorial regulation, activators and repressors together. HW11 key.

Homework 12, Stochastic dynamics. HW12 key. Key improved to contain answers to 2c, 2d: HW12 key, new and improved.

Homework 13, Stability analysis, stochastic systems, fluctuation-dissipation.
Kent Wilson obituary written by Nobel Laureate Dudley Herschbach.
HW13 key.

Homework 14, Diffusion and spatial patterning.
HW14 key.

Homework 15, Networks. Questions 4 and 5 were not covered in lecture in 2016 and will not be on the 2016 final exam. All other questions were covered and could be on the final exam.
HW15 key.



On-line material

Signal processing by the HOG MAP kinase pathway, Hersen et al. 2008 PNAS. PNAS-2008-Hersen-7165-70.

Square wave (SM2):


Caffeine Signaling Involvement of DARPP-32 phosphorylation in the stimulant action of caffeine. Maria Lindskog et al. 2002 Nature

Caffeine News and Views commentary Vaugeois 2002 Nature

Structural basis of DNA recognition: Glucocorticoid receptor zinc finger, Fos-Jun leucine zipper heterodimer with NFAT1, NFKB p50/p65 beta sheet immunoglobulin fold

Eric Davidson’s gene regulatory network model for sea urchin embryonic development Isabelle S. Peter, Emmanuel Faure, Eric H. Davidson. Predictive computation of genomic logic processing functions in embryonic development. PNAS 2012.

Toggle switch. Nature 403, 339-342 (20 January 2000) | doi:10.1038/35002131; Construction of a genetic toggle switch in Escherichia coli. Timothy S. Gardner (then helped found Amyris), Charles R. Cantor & James J. Collins

A synthetic oscillatory network of transcriptional regulators Michael B. Elowitz & Stanislas Leibler. Nature 403, 335-338 (20 January 2000)
Video from the Elowitz website.

Youtube repressilator

Edge detector. Jeffrey J. Tabor, Howard M. Salis, Zachary Booth Simpson, Aaron A. Chevalier, Anselm Levskaya, Edward M. Marcotte, Christopher A. Voigt, Andrew D. Ellington, A Synthetic Genetic Edge Detection Program, Cell, Volume 137, Issue 7, 26 June 2009, Pages 1272-1281, ISSN 0092-8674,

A fast, robust and tunable synthetic gene oscillator. Stricker J, Cookson S, Bennett MR, Mather WH, Tsimring LS, Hasty J. Nature. 2008 Nov 27;456(7221):516-9. doi: 10.1038/nature07389. Epub 2008 Oct 29. PubMed PMID: 18971928.

Synchronized clocks. A synchronized quorum of genetic clocks. Nature 463, 326-330 (21 January 2010). Tal Danino, Octavio Mondragón-Palomino, Lev Tsimring & Jeff Hasty

Li GW, Xie XS. Central dogma at the single-molecule level in living cells. Nature. 2011 Jul 20;475(7356):308-15. doi: 10.1038/nature10315. Review. PubMed PMID: 21776076; PubMed Central PMCID: PMC3600414.

Taniguchi Y, Choi PJ, Li GW, Chen H, Babu M, Hearn J, Emili A, Xie XS. Quantifying E. coli proteome and transcriptome with single-molecule sensitivity in single cells. Science. 2010 Jul 30;329(5991):533-8. doi: 10.1126/science.1188308. Erratum in: Science. 2011 Oct 28;334(6055):453. PubMed PMID: 20671182; PubMed Central PMCID: PMC2922915.

Eldar A, Elowitz MB. Functional roles for noise in genetic circuits. Nature. 2010 Sep 9;467(7312):167-73. doi: 10.1038/nature09326. Review. PubMed PMID: 20829787.


Calculus 1/2 (AS.101.106/AS.101.107)

Linear Algebra and Differential Equations (AS.101.201/AS.101.302 or EN.550.291)

Introduction to Probability and Statistics (EN.550.310)

Introduction to Programming (facility with numerical programming, simulation, and exploratory data analysis in a language of your choice)

Cellular and Molecular Biology (EN.580.221)

Signals, Systems, and Control (EN.580.222)

All prerequisites may be satisfied by an equivalent course or by the instructor’s permission.

Online Resources

… are on this page. Please login to Blackboard for additional materials and grade center.

Course Objectives

  1. Understand the mathematics behind linear systems theory, including spectral transforms and linear operators. Apply linear systems theory to predict cellular behavior close to equilibrium.
  2. Understand what constraints cause cells to behave non-linearly, and how non-linearity affects cellular response, including cooperativity.
  3. Understand why non-deterministic behavior is important in biology. Develop and apply mathematical models to describe equilibrium fluctuations. Understand how equilibrium fluctuations and correlations predict non-equilibrium response. Understand quantitatively how stochastic phenomena are essential for patterning specific tissues.
  4. Understand tempero-spatial dynamics that are driven by diffusion. Understand the mathematics behind the diffusion equation. Develop a physical understanding of the relationship between time and distance in diffusive motion. Understand different methods by which diffusive processes create tissue-scale spatial patterns in development.
  5. Use networks as a model to unify studies of complex systems of genes, cells, and organisms. Understand concepts of network percolation and giant component and their relevance to disease and information spread. Understand how diffusion creates a distance metric for networks. Understand the relationship between graph diffusion and graph clustering. Understand the meaning of small-world and scale-free when applied to networks. Understand the representation of metabolism as a reaction network. Apply optimization methods to predict how cells optimize their internal state for the environment.

Course Topics

  1. Cells as linear systems. Linear systems theory. Spectral transforms. Reverse engineering linear systems. Protein signal transduction.
  2. Cells as non-linear systems. Thresholds and ultra-sensitivity. Analog-digital converters. Information theory and gene transcription. Coupled dynamics of transcription and translation. Amplifiers, logic gates, feedback control, oscillators.
  3. Cells as stochastic systems. Non-deterministic behavior. Noise in transcription and translation. Delta-Notch patterning.
  4. Cells as spatial systems. Spatial patterning of tissues. Morphogen diffusion. Diffusion kernels.
  5. Networks of genes, cells, and organisms. Disease propagation on a network. Small-world and scale-free networks. Motifs. Clustering. Metabolic networks and metabolic optimization.

Course Expectations & Grading

Each homework and quiz is generally worth 1 grading unit. Two in-class exams are generally worth 6 grading units each. The final exam is worth 12 grading units. Each grading unit is scored out of 10 total points. The course grade will be calculated by dropping the lowest grading unit and averaging the remaining grading units, with letter grades assigned at standard breakpoints with no curve other than the dropped unit. Note that if your lowest grading unit is a quiz, for example if you were away for a med school interview or BMES, that grade will be dropped in its entirety. But if your lowest grade is an exam, you will keep 5 of the 6 grading units.

Homework assignments are generally due Fridays at 5 PM in Clark 318. If you are traveling, for example for a medical school interview, homework may be submitted by email to the instructor, PDF attachments preferred. Late homework is not accepted.

Quizzes will be announced at least one main lecture in advance and will be given during the main lecture at the end of the period.

If you must be absent for an academic or professional reason, including BMES or other conferences, medical school or graduate school interviews, or other on-site interviews, please speak to me ahead of time. You must speak to me ahead of time if an absence conflicts with a quiz or exam date.

If you are absent for a non-academic reason, primarily health-related, please have the Dean of Students email me on your behalf.


The strength of the university depends on academic and personal integrity. In this course, you must be honest and truthful. Ethical violations include cheating on quizzes and exams, plagiarism, reuse of assignments, improper use of the Internet and electronic devices, unauthorized collaboration, alteration of graded assignments, forgery and falsification, lying, facilitating academic dishonesty, and unfair competition.

In addition, the specific ethics guidelines for this course are:

  • Homework: students are permitted to work in groups, collaborate to any extent, and to use any external resources, including previous years’ assignments, in preparing homework assignments for this course. Each student must turn in a separate physical or electronic copy of each homework, however, to assist with study and record keeping.
  • Study materials: all study materials are generally permitted, including course materials from previous years. Advance copies of current-year questions are not permitted, however. Students taking exams at different times, particularly for make-up exams, may not share information.
  • Quizzes, exams, and the final: only blank paper, pens, and pencils are permitted. Electronic devices, including calculators, phones, and computers, are strictly forbidden. Equation sheets, if necessary, will be provided in the exam itself.

Report any violations you witness to the instructor.

You can find more information about university misconduct policies on
the web at these sites:

Students with Disabilities

Any student with a disability who may need accommodations in this class must obtain an accommodation letter from Student Disability Services, 385 Garland, (410)

ABET Outcomes

  • Ability to apply mathematics, science and engineering principles (a).
  • Ability to design and conduct experiments, analyze and interpret data (b).
  • Ability to design a system, component, or process to meet desired needs (c).
  • Ability to function on multidisciplinary teams (d).
  • Ability to identify, formulate and solve engineering problems (e).
  • Understanding of professional and ethical responsibility (f).
  • Ability to communicate effectively (g).
  • The broad education necessary to understand the impact of
    engineering solutions in a global and societal context (h).
  • Recognition of the need for and an ability to engage in life-long learning (i).
  • Knowledge of contemporary issues (j).
  • Ability to use the techniques, skills and modern engineering
    tools necessary for engineering practice (k).
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