Applied Probability and Stochastic Processes for Biology

MATH 319 / BIOL 319-419 / PHOL 419 / EBME 419 / EECS 319


Books available at the Kelvin Smith Library Course Reserves include:


Date Assigned Type Assignment Date Due
8/25 Reading
  1. Read NCM Chapter 1 (skip 1.5), from course packet. See NCMChap1guide.txt. Bring questions about Matlab to class.
  2. Read for discussion:
    Statistical Fluctuations in Autocatalytic Reactions
    M. Delbruck
    Journal of Chemical Physics 1940 Volume 8 pp 120-124 (search for volume 8, page 120)
    Or try this link.
  3. Start Ecoli world contest in matlab -- see matlab file ecoliworld2b.m. Simulations due 9/1 but please bring questions about writing your matlab code to class on 8/27. The challenge is to write an improved "rule" for survival. The contest is to see who lives the longest, on average, over 50 trials.
  4. For those without a prior course in probability, please begin reading Stochastic Modeling for Systems Biology (SMSB) Chapter 3. We'll go over basic probability in detail in the third week.
8/27 Reading
  1. Stochastic Modelling for Systems Biology Chapter 1 (Introduction) & Chapter 2 (Petri net formalism).
  2. Review article: Modeling and Simulating Chemical Reactions, Desmond J. Higham, SIAM Review 2008 (Society for Industrial and Applied Mathematics Vol. 50, No. 2, pp. 347Ð368)
  3. As an example of a signal transduction system, please read: Spiro PA, Parkinson JS, Othmer HG. A model of excitation and adaptation in bacterial chemotaxis. Proc Natl Acad Sci U S A. 1997 Jul 8;94(14):7263-8.
9/3 Reading
  1. Spiro et al (above)
  2. Higham review article (above)
  3. Keep working on Wilkinson chapter 3.
9/3 Exercises Problem set 1 9/10 due in class
9/8-9/15 Reading Finish Wilkinson Chapter 3 (probability review) 9/8-9/15
9/11 Exercises Problem set 2 9/17 due in class
9/15 Reading
  1. Background, not required reading: Neher E, Sakmann B. Single-channel currents recorded from membrane of denervated frog muscle fibres. Nature. 1976 Apr 29;260(5554):799-802. Unfortunately, this is not available except by paying heavy roylaties to Nature Magazine.
  2. Single-Channel Recording, Chapter 9.1-9.3 (course packet)
9/17 First Project Proposal Project proposal (one page) due. As a guide to what I expect for the projects, here is a rubric I will use for grading the projects. 9/24
9/17 Reading
  1. Moler, Numerical Computing with Matlab Chapter 1.7, Floating Point Arithmetic (course packet).
  2. Moler, Numerical Computing with Matlab Chapter 9, Random Numbers (course packet).
9/17 Reading
  1. Wilkinson, Chapter 4, Stochastic Simulation. Read sections 4.1-4.7 on numerical generation of pseudorandom samples from different distributions. Also read section 4.8 (optional) if you would like an introduction to the R programming language.
9/25 Exercises Problem set 3 FRIDAY 10/3
9/29-10/8 Readings on Markov Chains and Time Series Analysis
  1. Wilkinson Chapter 5 "Markov Processes" (required)
  2. Colquhoun & Hawkes (Stochastic Interpretation of Ion-Channel Mechanisms, course packet) sections 4-10 (required)
  3. Taylor & Karlin, An Introduction to Stochastic Modeling, Chapters III-IV (optional: supplementary material on Markov Chains).
  4. Chatfield, The analysis of time series: an introduction, Chapters 3 & 6 (spectral analysis of stochastic time series) (required)
  5. Chatfield, The analysis of time series: an introduction, Chapters 7 & 8 (more on spectral analysis of stochastic time series) (optional)
  6. Austin et al, Nature 2006 Vol 439 No 2, Gene network shaping of inherent noise spectra. (for discussion)
  7. Pedraza et al, Science 2005 Vol 307, Noise Propagation in Gene Networks. (for discussion)
10/6 Exercises Problem set 4 10/20
10/8 Reading
  • Wilkinson Chapter 6 "Chemical and Biochemical Kinetics"
  • Review Higham article
  • 10/13
    10/27 Readings on Diffusion & Brownian Motion
    1. Berg, Random Walks in Biology, Chapters 1-5. This is a treatment of random walks and diffusion from a biologist's point of view.
    2. Taylor & Karlin Chapter VIII (Brownian Motion) -- on reserve at KSL. This is an introductory treatment of diffusion processes from a mathematical point of view. Read after finishing the chapters in Berg's book.
    11/2 Readings on diffusion models
    1. Berg & Purcell, Biophysical Journal 1977, Physics of Chemoreception
    2. Gerstein & Mandelbrot, Biophysical Journal 1964, RANDOM WALK MODELS FOR THE SPIKE ACTIVITY OF A SINGLE NEURON
    optional for 11/2-4
    1. Terman & Ermentrout draft chapter
    11/19 Exercises Problem set 5 12/3
    11/19 Reading
    • Wilkinson Chapter 7, "Case Studies"
    • Finish/review Higham review article.
    • optional: further case studies in C. Fall et al, Computational Cell Biology Chapters 12-13. See in particular 13.1 on the bacterial flagellar motor.
    11/19 Reading Wilkinson Chapter 8, "Beyond the Gillespie Algorithm" 11/26
    11/19 Reading
    1. Vellela & Qian (2007). A Quasistationary Analysis of a Stochastic Chemical Reaction: Keizer's Paradox, Bull Math Biol. 2007 Jul;69(5):1727-46. Epub 2007 Feb 23
    2. Kurtz, T.G. (1972). The relationship between stochastic and deterministic models for chemical reactions. J. Chem. Phys. 57, 2976–2978.

    Matlab References

    For more information, please contact Dr. Thomas.

    Updated: January 21, 2008