The Sixth q-bio Summer School: Stochastic Gene Regulation

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In this theme, we will explore stochasticity and cell-to-cell variability in the measurement and modeling of biochemical systems. In particular, we will concentrate on the effects that small numbers of important molecules (i.e. genes, RNA, and protein) have on the dynamics of living cells. We will review experimental manifestations of stochastic effects in molecular biology, as can be measured using single-cell and single-molecule techniques. We will discuss the most recent analytical and numerical methods that are used to model these systems and show how these methods can improve interpretation of experimental data. We will study how different cellular mechanisms control and/or exploit randomness in order to survive in uncertain environments. Similarly, we will explore how single-cell measurements of cell-to-cell variability can reveal more information about underlying cellular mechanisms.

This section of the summer school will include a number of instructor-suggested group projects, in which students will apply various numerical techniques to formulate, identify and solve stochastic models for gene regulatory systems. Students will then apply these tools to model experimental flow cytometry or other single-cell data. Access and knowledge of Matlab will be helpful, but is not strictly necessary.

This section of the summer school is organized by Brian Munsky. Please address all questions about this section of the summer school to its organizer.




Project Mentors

Course Materials


  • Introduction to Stochasticity. The importance of stochasticity in gene regulatory networks. Key examples from the literature.
  • Discussion of the importance of stochasticity in small populations. Stochastic Phenomena: switching, focusing, resonance, filtering.
  • The effects of positive and negative feedback.
  • The physics behind stochastic chemical kinetics.
  • Connection between deterministic and stochastic reaction rates.
  • Derivation of the Master Equation for discrete stochastic processes.
  • Solving the Chemical Master Equation: exact solutions for linear propensity functions,
  • Kinetic Monte Carlo algorithms: Tau Leaping. Chemical Langevin equation. Time separation schemes. Hybrid methods.
  • Density Computation Approaches: Finite State projections techniques, Moment Generating Function Techniques, Moment Closure Techniques, Fokker Planck equation.
  • Simplification of complex biochemical processes.
  • Switch rate analyses, waiting/completion times.
  • Single cell measurement techniques: flow cytometry, fluorescence microscopy, time lapse microscopy.
  • Using fluctuations to infer system mechanisms and parameters.
  • Signal Processing in Biochemical networks.
  • Synthetic Biology
  • siRNA Effects in Host Pathogen Interactions

Lectures and slides


  • All homework problems are meant to be done in groups. Feel free to use Matlab, c++ fortran, python or whatever.
  • Students should write and test Stochastic Simulation Algorithm representations of the toggle switch model in Homework 2. These should be analyzed with three different approaches: First Reaction method, Direct Reaction Method, and Tau Leaping. Run many trajectories and collect statistics. Comment upon the similarities and differences between the various methods.
  • Homework 1: Media:QBIO HWK1.pdf
  • Homework 2: Stochastic Analysis of a toggle Switch: Media:Toggle HWK.pdf
  • Group projects will be announced in an afternoon session.


  • FSP_Tool_Kit 1.0 Please email me, and I will send the software to you.
  • Others.

Journal Club Readings

  • All students with an emphasis in this section should be prepared to read and discuss the following articles on the effects, importance, and analysis of single-cell variability. This list is by no means comprehensive. Additional materials will be sent to you directly, and other articles will be posted here as the course progresses. The citations in bold face are probably to the most useful and accessible for the course.
  • [1] McAdams, M., and A. Arkin. 1999. Its a noisy business! Tren. Gen. 15:65–69.
  • [2] Elowitz, M., A. Levine, E. Siggia, and P. Swain. 2002. Stochastic gene expression in a single cell. Science. 297:1183–1186.
  • [3] Thattai, M., and A. van Oudenaarden. 2001. Intrinsic noise in gene regulatory networks. Proc. Natl. Acad. Sci. 98:8614–8619.
  • [4] Arkin, A., J. Ross, and M. H. 1998. Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-infected escherichia coli cells. Genetics. 149:1633–1648.
  • [5] Becskei, A., and L. Serrano. 2000. Engineering stability in gene networks by autoregulation. Nature. 405:590–593.
  • [6] Cagatay, T., M. Turcotte, M. Elowitz, J. Garcia-Ojalvo, and G. Suel. 2009. Architecture- dependent noise discriminates functionally analogous differentiation circuits. Cell. 139:512–522.
  • [7] Kobayashi, H., M. Kaern, M. Araki, K. Chung, T. Gardner, C. Cantor, and J. Collins. 2004. Programmable cells: Interfacing natural and engineered gene networks. PNAS. 101:8414–8419.
  • [8] Raj, A., and A. van Oudenaarden. 2009. Single-molecule approaches to stochastic gene expression. Annual Review of Biophysics. 38:255–270
  • [9] Gillespie, D. T. 1992. A rigorous derivation of the chemical master equation. Physica A. 188:404–425.
  • [10] Gillespie, D. T. 1977. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81:2340–2360.
  • [11] Elf, J., and M. Ehrenberg. 2003. Fast evaluations of fluctuations in biochemical networks with the linear noise approximation. Genome Research. 13:2475–2484.
  • [12] Gmez-Uribe, C., and G. Verghese. 2007. Mass fluctuation kinetics: Capturing stochastic effects in systems of chemical reactions through coupled mean-variance computations. J. Chem. Phys. 126.
  • [13] Munsky, B., and M. Khammash. 2008. The finite state projection approach for the analysis of stochastic noise in gene networks. IEEE Trans. Automat. Contr./IEEE Trans. Circuits and Systems: Part 1. 52:201–214.
  • [14] Gillespie, D. T. 2000. The chemical Langevin equation. J. Chem. Phys. 113:297–306.
  • [15] Salis, H., and Y. Kaznessis. 2005. Accurate hybrid stochastic simulation of a system of coupled chemical or biological reactions. J. Chem. Phys. 112.
  • [16] Dunlop, M., R. Cox III, J. Levine, R. Murray, and M. Elowitz. 2008. Regulatory activity revealed by dynamic correlations in gene expression noise. Nature Genetics. 40:1493–1498.
  • [17] Munsky, B., B. Trinh, and M. Khammash. 2009. Listening to the noise: random fluctuations reveal gene network parameters. Molecular Systems Biology. 5.
  • [18] Bel, G., B. Munsky, and I. Nemenman. 2010. Simplicity of completion time distributions for common complex biochemical processes. Physical Biology. 7.
  • [19] Paulsson, J., O. Berg, and M. Ehrenberg. 2000. Stochastic focusing: Fluctuation-enhanced sensitivity of intracellular regulation. PNAS. 97:7148–7153.
  • [20] Munsky, B., Neuert, G., van Oudenaarden, A. Using Gene Expression Noise to Understand Gene Regulation, Science, 337:183-187.
  • [21] J. Raser, et al. (2004) Science, 304:1811-1814.
  • [22] Raj, et al. (2006) PLoS Biology, 4:1707-1719.
  • [23] Zenklusen, D. et al. Nature Struct. and Mol. Biol. 15, 1263–1271.
  • [24] So L-H. et al. (2011) Nature Genetics 6, 554–560.
  • [25] Gandhi, S. et al. (2011) Nature Struct. and Mol. Biol. 18, 27–34.
  • [26] Dunlop, M. et al. (2008) Nature Genetics 40, 1493.
  • [27] Taniguchi, et al. (2010) Science 329, 553.

Group Projects

  • A variety of group projects will be proposed and discussed in the first few days of class. Projects are expected to last beyond the dates of the school and may result in a scientific publications. Projects will consider open problems in the integration of experimental and computational investigations of stochastic gene regulation. General research projects will include: single cell image processing, computational analysis of single cell and single molecule measurements, computer aided experiment selection, among others.
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