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First q-bio Summer School: Stochasticity in Biochemistry and Systems Biology

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In this theme, we will explore stoasticity in biochemical and systems biology modeling. As the subject is immense in its scope, we will be limited necessarily to exploring just a small section of the related topics. Specifically, we will review experimental manifestations of stochastic effects in biology, the methods used to treat them analytically and numerically, and effects of the stochasticity on behavior of certain systems.

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


Lecture 1

Scope
Stochastic effects in systems biology: experiments and standard computational treatments, Part I
Lecturer
Ilya Nemenman
Materials
Covered topics: Master equation, Fokker-Planck equation, Importance of noise, intrinsic/extrinsic noise, filtering
Relevant websites: Tools and approximations for stochastic analysis, Stochastic biochemistry
References
  1. W Bialek. Stability and noise in biochemical switches. In Todd K. Leen, Thomas G. Dietterich, and Volker Tresp, editors, Advances in Neural Information Processing Systems 13, pages 103-109. MIT Press, 2001. PDF
  2. P Detwiler, S Ramanathan, A Sengupta, and B Shraiman. Engineering aspects of enzymatic signal transduction: Photoreceptors in the retina. Biophys. J., 79:2801-2817, 2000. PDF.
  3. M Elowitz, A Levine, E Siggia & P Swain. Stochastic gene expression in a single cell. Science 207, 1183, 2002. PDF.
  4. C Gardiner. Handbook of Stochastic Methods: for Physics, Chemistry and the Natural Sciences (Springer Series in Synergetics, Springer; 3rd ed., 2004.
  5. E Schneidman, B Freedman, and I Segev. Ion channel stochasticity may be critical in determining the reliability and precision of spike timing. Neural Comp. 10, p.1679-1704, 1998. PDF.
  6. N.G. Van Kampen. Stochastic Processes in Physics and Chemistry. North Holland, 3rd edition, 2001.
  7. J Paulsson. Summing up the noise in gene networks. Nature 427, 415, 2004. PDF, Supplement.
Additional references
  1. W Blake, M Kaern, C Cantor, and J Collins. Noise in eukaryotic gene expression. Nature 422, 633-637, 2003. PDF.
  2. P Cluzel, M Surette, and S Leibler. An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells. Science, 287:1652-1655, 2000. PDF.
  3. T Kepler and T Elston. Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations. Biophys J. 81, 3116-3136, 2001. PDF.
  4. J Pedraza and A van Oudenaarden. Noise propagation in gene networks, Science 307, 1965-1969, 2005. PDF.
  5. J Raser and E O’Shea. Control of stochasticity in eukaryotic gene expression. Science 304, 1811-1814, 2004. PDF.
  6. N Rosenfeld, J Young, U Alon, P Swain, M Elowitz. Gene Regulation at the Single-Cell Level. Science 307, 1962, 2005. PDF.
  7. A Eldar, D Rosin, B-Z Shilo, and N Barkai. Self-Enhanced Ligand Degradation Underlies Robustness of Morphogen Gradients. Developmental Cell, Vol. 5, 635–646, 2003. PDF.

Lecture 2

Scope
Stochastic effects in systems biology: experiments and standard computational treatments, Part II
Lecturer
Ilya Nemenman
Materials
Lecture notes
Relevant websites: Tools and approximations for stochastic analysis, Stochastic biochemistry, E. coli chemoreceptor: mesoscopic model
References
  1. E Aurell and K Sneppen. Epigenetics as a first exit problem. Phys Rev Lett 88, 048101, 2002. PDF.
  2. J Cardy. Field theory and nonequilibrium statistical mechanics. In Troisieme Cycle de la Suisse Romande. 1999. PDF.
  3. D Gillespie. Stochastic Simulation of Chemical Kinetics. "Ann Rev Phys Chem" 58, 35-55, 2007. PDF.
  4. T Doan, A Mendez, P Detwiler, J Chen, F Rieke. Multiple phosphorylation sites confer reproducibility of the Rod's single-photon responses. Science 313, 530-3, 2006. PDF.
  5. V Elgart and A Kamenev. Rare event statistics in reaction-diffusion systems. Phys. Rev. E 70, 041106, 2004. PDF.
  6. M Gibson and J Bruck. Efficient Exact Stochastic Simulation of Chemical Systems with Many Species and Many Channels. J Phys Chem A, Vol. 104, No. 9, pages 1876-1889, 2000. PDF.
  7. F Rieke and D Baylor. Single photon detection by rod cells of the retina. Rev Mod Phys 70, 1027-1036, 1998. PDF.
  8. D Roma, R O’Flanagan, A Ruckenstein, A Sengupta, and R Mukhopadhyay. Optimal path to epigenetic switching. Phys Rev E 71, 011902, 2005. PDF.
  9. A Walczak, J Onuchic and P Wolynes. Absolute rate theories of epigenetic stability. PNAS 102, 18926, 2005. PDF.
  10. A Walczak, M Sasai, and P Wolynes. Self-consistent proteomic field theory of stochastic gene switches. Biophys J. 88, 828-850, 2005. PDF.
Additional references
  1. E Aurell, S Brown, J Johanson, and K Sneppen. Stability puzzles in phage lambda. Phys. Rev. E 65, 051914 (2002). PDF.
  2. E Korobkova, T Emonet, JMG Vilar, TS Shimizu, and P Cluzel. From molecular noise to behavioural variability in a single bacterium. Nature, 438:574-578, 2004. PDF.
  3. Y Tu and G Grinstein. How white noise generates power-law switching in bacterial flagellar motors. Phys. Rev. Lett., 2005. PDF.
  4. M Sasai and P Wolynes. Stochastic gene expression as a many body problem. PNAS 100, 2374-2379, 2003. PDF.
  5. J Zinn-Justin. Quantum Field Theory and Critical Phenomena. (Oxford University Press, Oxford, 1989)

Lecture 3

Title
Identification of Aggregated Markov Processes for Single Molecule Kinetics
Lecturer
John Pearson
Materials
Lecture notes -- These notes are the latest version as of Sunday evening 6:35 PM 7/29 http://cnls.lanl.gov/q-bio/wiki/images/0/0c/Notes_new.pdf
Relevant websites

Lecture 4

Scope
The method of the probability generating functional in stochastic kinetics
Lecturer
Nikolai Sinitsyn
Abstract
This lecture is an introduction to theoretical approaches to quantify stochastic effects in biochemical processes. In the first part I review the theory of stochastic reaction-diffusion processes and introduce the method of the probability generating functional to characterize the stochastic effects. On the way, I will discuss applications in single molecule experiments and simulations of complicated biochemical networks and then work out examples of processes that allow simple analytical solutions. In the second part I will review in more details the basic biochemical processes such as the Michaelis-Menten reaction and discuss recent and more advanced theoretical techniques to evaluate the generating functions of chemical fluxes.
Relevant websites: Michaelis-Menten reaction, The Berry phase in stochastic kinetics
References
  1. English B. P., et al. Nature. Chem. Biol. 2 (2006) 87. PDF.
  2. Gopich I.V. and Szabo A. J. Chem. Phys. 124, (2006) 154712. PDF.
  3. N. A. Sinitsyn, and I. Nemenman. EPL 77 (2007) 58001. Abstract.

Lecture 5

Scope
Selectivity of transport through the nuclear pore and other biological channels
Lecturer
Anton Zilman
Abstract
Biological transport devices, and channels and pores in particular, transport hundreds of molecules per second, while maintaining high selectivity. Namely, they must selectively transport only specific molecules, over the background of vast numbers of all others. I will briefly review different mechanisms of selectivity and will focus on a class of devices where selective transport is achieved without input of metabolic energy, but rather is based on the inherent properties of stochastic dynamics of transport. Despite the large variation of spatial scales and molecular structures, such devices possess rather general properties: I will present the general theory of selectivity transport through narrow channels, based on the theory of stochastic processes. In the second part of the lecture I will discuss in detail the applications of the theory to two particular systems: transport between the cell nucleus and the cytoplasm in eukaryotes, and transport through bacterial porins.
Materials
Lecture plan
References
  1. Berezhkovskii, Pustovoit, Bezrukov, J. Chem. Phys., 22, 116, (2002). PDF.
  2. Lu, Grayson, Schulten, Biophys. J, 85, 2977–2987 (2003). PDF.
  3. Zilman, Di Talia, Chait, Rout, Magnasco, PLoS Comp. Biol., July (2007). PDF.

Lecture 6

Scope
Information-processing properties of noisy biochemical networks
Lecturer
Chris Wiggins and Ilya Nemenman
Materials
Lecture notes
Relevant websites
References
1. Y. Lazebnik. Can a biologist fix a radio? - or, what i learned while studying apoptosis. Biochemistry (Moscow), 69(12):1403-1406, 2004. PDF.
2. A Arkin. Signal processing by biochemical reaction networks. In J Walleczek, editor. Self-Organized biological dynamics and nonlinear control. Cambridge UP, 2000. PDF.
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