View source for Physics 434, 2012: Information Processing in Biology

{{PHYS434-2012}}

==News==
*Please choose papers for presentations now.
*No office hours between October 12 and October 16. [[User:Ilya|Ilya]] 12:03, 6 October 2012 (PDT)
*'''Next week (Sep 24)''', I will be available for questions on Monday 3-3:30, and Thursday 5:30-7. (No session on Friday). [[User:Ilya|Ilya]] 11:34, 21 September 2012 (PDT)
*Please see the '''new schedule''' for the office hours/study sessions in the Logistics section of this document. [[User:Ilya|Ilya]] 11:34, 21 September 2012 (PDT)
*From now on, '''homework''' will be announced on Tuesdays or Wednesdays, and they will be due on a Monday of the following week. [[User:Ilya|Ilya]] 19:31, 19 September 2012 (PDT)
*Welcome to the class!

==Logistics==
*[[Physics 434, 2012: Syllabus|Syllabus]] -- we will deviate from it in the course of the class
*[[Installing Octave on your PC and Mac]].
*Weekly study sessions/office hours: Mon 3-4 (MSC N240), Thu 5:30-7 (MSC E116), Fri 1:45-2:45 (MSC N240).

==Lecture Notes==
*Introduction: [[Physics 434, 2012: Lecture 1 | Lecture 1]]
*[[Physics 434, 2012: Block one: Biological information processing is probabilistic|Block one: Biological information processing is probabilistic]]
**Basic probability theory: neural stochasticity, fluctuations in population genetics, and molecular motion: [[Physics 434, 2012: Lectures 2-3 | Lectures 2-3]], [[Physics 434, 2012: Lecture 4 | Lecture 4]]
**Central Limit Theorem and random walks and diffusion in molecular and cellular systems: [[Physics 434, 2012: Lecture 5 | Lecture 5]], [[Physics 434, 2012: Lecture 6 | Lecture 6]], [[Physics 434, 2012: Lecture 7 | Lecture 7]], [[Physics 434, 2012: Lectures 8, 9 | Lecture 8]], [[Physics 434, 2012: Lectures 8, 9 | Lecture 9]], [[Physics 434, 2012: Lecture 10 | Lecture 10]].
**Does noise matter for larger systems? -- Cells searching for food: [[Physics 434, 2012: Lecture 10 | Lecture 10]].
*[[Physics 434, 2012: Block two: Information theory in biological signaling|Block two: Information theory in biological signaling]]
**Basic Information theory: [[Physics 434, 2012: Lectures 10-11 | Lectures 10-11]]
**Are biological systems good information transducers? [[Physics 434, 2012: Lectures 12-13 | Lectures 12-13]]
**Information, gambling, and population biology: nongenetic antibiotic resistance: [[Physics 434, 2012: Lecture 14 | Lecture 14]].
**Information loss as a measure of distortion: Which gene controls which other gene? [[Physics 434, 2012: Lecture 14 | Lecture 14]].
*[[Physics 434, 2012: Block three: Dynamical Information Processing|Block three: Dynamical Information Processing]]
**Biochemical kinetics: [[Physics 434, 2012: Lecture 15 | Lecture 15]].
**Signal transduction in the vertebrate retina:  [[Physics 434, 2012: Lecture 16| Lecture 16]], [[Physics 434, 2012: Lecture 17| Lecture 17]], [[Physics 434, 2012: Lecture 18|Lecture 18]], [[Physics 434, 2012: Lecture 19|Lecture 19]]
**Qualitative analysis of dynamical systems:  [[Physics 434, 2012: Lecture 20|Lecture 20]],  [[Physics 434, 2012: Lecture 21|Lecture 21]]
**Means of suppressing noise: waiting for a long time, or taking a vote in a population of neurons: [[Physics 434, 2012: Lecture 20|Lecture 20]]
*[[Physics 434, 2012: Block four: Adaptation |Block four: Adaptation]]
**Extracting relevant information, and adaptation as extracting relevant information: [[Physics 434, 2012: Lecture 23|Lecture 23]]
**Three types of adaptation and robust perfect adaptation:  [[Physics 434, 2012: Lecture 24|Lecture 24]]
**Animal learning in a changing world and Student presentations: [[Physics 434, 2012: Lecture 25|Lecture 25]]
**Student presentations: [[Physics 434, 2012: Lecture 26|Lecture 26]]
*Summary: [[Physics 434, 2012: Lecture 27|Lecture 27]]

==Homework assignments==
*[[Physics 434, 2012: Homework 1| HW 1]], due Sep 10.
*[[Physics 434, 2012: Homework 2| HW 2]], due Sep 17.
*[[Physics 434, 2012: Homework 3| HW 3]], due Sep 24.
*[[Physics 434, 2012: Homework 4| HW 4]], due Oct 1.
*[[Physics 434, 2012: Homework 5| HW 5]], due Oct 17.
*[[Physics 434, 2012: Homework 6| HW 6]], due Oct 29.
*[[Physics 434, 2012: Homework 7| HW 7]], due Nov 5.
*[[Physics 434, 2012: Homework 8| HW 8]], due Nov 16.
*[[Physics 434, 2012: Homework 9| HW 9]], due Dec 3.
*[[Physics 434, 2012: Homework 10| HW 10]], due Dec 10.

==Original Literature for Presentation in Class==
A large part of the class grade will be determined by your in-class presentation of a recent research paper. Papers will be divided into four blocks, just like the whole class: Noise,  information, dynamics, and adaptation/learning. In your presentations, aim for half an hour talk. Try to structure your presentations the following way:
#What is the question being asked?
#What are the findings of the authors?
#Which experimental or computational tools (whichever applicable) they use in their work?
#What in this findings is unique to the studied biological system, and what should be general?
Working individually, please select one paper from this list and be ready to present it during the identified week. Selections are on First Come - First Served basis. 

*Stochastic effects and their propagation. I need two people will present during the weeks of Nov 5. One person should select one of the first three papers, and the other should select one of the last two.
# Elowitz et al., 2002 -- this paper measures the effect of molecule noise on the single cell level
# Blake et al., 2003 -- noise in eukaryotic transcription is investigated
# Raser and O'Shea, 2004 -- measuring noise in yeast transcription, '''Xi Jiang, Nov 8'''
# Pedraza and van Oudenaarden, 2005 -- a study in noise propagation in transcriptional networks, '''Zhijia Liang, Nov 6'''
# Cagatay et al., 2009 -- this papers analyses the phenomenon of competence in ''B. subtilis'' to conclude that large noise if functionally important
*Information theoretic characterization of biological signaling. I need three people will present during the week of Nov 12 and Nov 19. One person should select from the first two papers, and the second from the second pair, and the third should take the last paper
#Strong et al., 1998 --  the authors calculate the amount of information transmitted by the fly motion sensitive neuron to the rest of the fly brain, '''Claire Tang, Nov 12'''
#Cheong et al., 2011 -- it took thirteen years to do a similar calculation for a molecular signaling pathway
#Andrews and Iglesias, 2007 -- in this paper, the authors study chemotaxis by a slime mold cell from the information-theoretic perspective
#Vergassola et al, 2007 -- one can find the source of smell by choosing steps that maximize the information about its location, '''David Trac, Nov 20'''
#Margolin et al, 2006 -- using mutual information to reconstruct transcriptional networks, '''Rebecca Butterfield, Nov 15'''
*Dynamical information processing and dealing with noise. One of the first three papers, and the last one will need to be presented the week of Nov 27.
# Gardner et al., 2000 -- a bistable toggle switch has been constructed inside the ''E. coli'', '''Hamin Jeon, Nov 27'''
# Cagatay et al., 2009 -- this papers builds a (noisy) dynamical systems model of ''B. subtilis'' competence
# Sprinzak et al., 2010 -- development, such as patterning an eye, also involves multistability
# Averbeck et al., 2006 -- analyzing population codes in neural systems, '''Sara List, Nov 29'''
*Adaptation and learning. I am only giving three papers here. Each of the remaining three presenters should choose one. Presentations are during the week of Dec 3.
# Gallistlel et al., 2001 -- this paper argues that a foraging rat learns (i.e., adapts to) optimally from its environment, '''Yan Yan, Dec 6'''
# Brenner et al., 2000 -- this neural system is capable of changing its gain: '''Shengming Zhang, Dec 4'''
# Fairhall et al., 2001 -- this same neural system, as it turns out, is capable of adjusting its response time: '''Skanda Vivek, Dec 4'''

==References==
The list is far from being complete now. Stay tuned.

===Textbooks===
#R Phillips, J Kondev, J Theriot. ''Physical Biology of the Cell'' (Garland Science, 2008)
#*''Sizing up E. coli''. [[media:sizing-up-e-coli.pdf |PDF]]
#CM Grinstead and JL Snell, [http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/pdf.html Introduction to Probability].
#W Bialek, [http://www.princeton.edu/~wbialek/PHY562.html Biophysics: Searching for Principles] (2011). 
#*Information theory overview is in [http://www.princeton.edu/~wbialek/PHY562/4.pdf Chapter 4].
#For information about Wiener processes and diffusion, a good source is: [http://en.wikipedia.org/wiki/Wiener_process Wiener Process article in Wikipedia].
#The most standard textbook on information theory is: T Cover and J Thomas, ''Elements of Information Theory'', 2nd ed (Wiley Interscience, 2006).

===Sensory Ecology and Corresponding Evolutionary Adaptations===
#T Cronin, N Shashar, R Caldwell. Polarization vision and its role in biological signaling. ''Integrative and Comparative Biology'' 43(4):549-558, 2003. [[media:cronin-etal-03.pdf|PDF]].
#D Stavenga,  Visual acuity of fly photoreceptors in natural conditions--dependence on UV sensitizing pigment and light-controlling pupil. ''J Exp Biol'' 207 (Pt 10) pp. 1703-13, 2004. [[media:stavenga-2004.pdf|PDF]].

===Transcriptional regulation===
#O Berg and P von Hippel. Selection of DNA binding sites by regulatory proteins. Statistical-mechanical theory and application to operators and promoters. ''J Mol Biol.'' 193(4):723-50, 1987. [[media:berg-von-hippel-87.pdf |PDF]].
#O Berg et al. Diffusion-driven mechanisms of protein translocation on nucleic acids. 1. Models and theory. ''Biochemistry'' 20(24):6929-48, 1981. [[media:berg-etal-81.pdf|PDF]].
#C Guet, M Elowitz, W Hsing, S Leibler. Combinatorial synthesis of genetic networks. ''Science'' 296:1466, 2002. [[media:guet-etal-02.pdf|PDF]].
#M Slutsky and L Mirny. Kinetics of protein-DNA interaction: facilitated target location in sequence-dependent potential. ''Biophysical J'' 87(6):4021-35, 2004. [[media:slutsky-mirny-04.pdf|PDF]].
#E Ozbudak, M Thattai, H Lim, B Shraiman, A van Oudenaarden. Multistability in the lactose utilization network of Escherichia coli. ''Nature'' 427: 737, 2004. [[media:ozbudak-etal-04.pdf|PDF]].
#D Dreisigmeyer, J Stajic, I Nemenman, W Hlavacek, and M Wall. Determinants of bistability in induction of the Escherichia coli lac operon. ''IET Syst Biol'' 2:293-303, 2008. [[media:dreisigmeyer-etal.08.pdf|PDF]].

===Signal Processing in Vision===
# P Detwiler et al. Engineering aspects of enzymatic signal transduction: Photoreceptors in the retina. ''Biophys. J.'', 79:2801-2817, 2000. [[media:detwiler-etal-00.pdf | PDF]].
# A Pumir et al. Systems analysis of the single photon response in invertebrate photoreceptors. ''Proc Natl Acad Sci USA'' 105 (30) pp. 10354-9, 2008. [[media:pumir-etal-00.pdf|PDF]].
# F Rieke and D Baylor. Single photon detection by rod cells of the retina.  ''Rev Mod Phys'' 70, 1027-1036, 1998. [[media:rieke-baylor-98.pdf | PDF]].
# T Doan, A Mendez, P Detwiler, J Chen, F Rieke. Multiple phosphorylation sites confer reproducibility of the rod's single-photon responses. ''Science'' 313, 530-533, 2006. [[media:doan-etal-06.pdf|PDF]].

===Bacterial chemotaxis===
#J  Adler. Chemotaxis in bacteria. ''Annu Rev Biochem'' 44 pp. 341-56, 1975. [[media:adler-75.pdf | PDF]]
#H Berg and D Brown. Chemotaxis in Escherichia coli analysed by three-dimensional tracking. ''Nature'' 239 (5374) pp. 500-4, 1972. [[media:berg-brown-1972.pdf|PDF]].
#E Budrene and H Berg. Dynamics of formation of symmetrical patterns by chemotactic bacteria. ''Nature'' 376 (6535) pp. 49-53, 1995. [[media:budrene-berg-1995.pdf|PDF]]
#E Budrene and H Berg. Complex patterns formed by motile cells of Escherichia coli. ''Nature'' 349 (6310) pp. 630-3, 1991.  [[media:budrene-berg-1991.pdf|PDF]]
#E Purcell. Life at low Reynolds number. ''Am J Phys'' 45 (1) pp. 3-11, 1977. [[media:purcell-77.pdf |PDF]]
#H Berg. Motile behavior of bacteria. ''Phys Today'' 53 (1) pp. 24-29, 2000. [[media:berg-00.pdf |PDF]]
#C Rao and A Arkin. Design and diversity in bacterial chemotaxis: a comparative study in Escherichia coli and Bacillus subtilis. ''PLoS Biol'' 2 (2) pp. E49, 2004. [[media:rao-arkin-04.pdf |PDF]]
#C Rao et al. The three adaptation systems of Bacillus subtilis chemotaxis. ''Trends Microbio'' l16 (10) pp. 480-7, 2008. [[media:rao-etal-08.pdf |PDF]].
#A Celani and M Vergassola. Bacterial strategies for chemotaxis response. ''Proc Natl Acad Sci USA''107, 1391-6, 2010. [[media:celani-vergassola-10.pdf|PDF]].

===Eukaryotic chemotaxis===
#J Franca-Koh et al. Navigating signaling networks: chemotaxis in Dictyostelium discoideum. ''Curr Opin Genet Dev'' 16 (4) pp. 333-8, 2006. [[media:franca-koh-etal-06.pdf|PDF]].
#W-J Rappel et al. Establishing direction during chemotaxis in eukaryotic cells. ''Biophysical Journal'' 83 (3) pp. 1361-7, 2002. [[media:rappel-etal-02.pdf |PDF]].

===Random walks===
#G Bel, B Munsky, and I Nemenman. The simplicity of completion time distributions for common complex biochemical processes. ''Physical Biology'' '''7''' 016003, 2010. [[media:bel-et-al-10.pdf | PDF]].

===Information theory===
#J Ziv and A Lempel. A Universal Algorithm for Sequential Data Compression. ''IEEE Trans. Inf. Thy'' '''3''' (23) 337, 1977. [[media:ziv-lempel-77.pdf |PDF]].
#N Tishby, F Pereira, and W Bialek. The information bottleneck method. arXiv:physics/0004057v1, 2000. [[media:tishby-etal-00.pdf |PDF]].
#E Ziv, I Nemenman, and C Wiggins. Optimal signal processing in small stochastic biochemical networks. ''PLoS ONE'' '''2''': e1077, 2007. [[media:ziv-etal-07.pdf | PDF]].
#S Strong, R Koberle, R de Ruyter van Steveninck, and W Bialek. Entropy and information in neural spike trains. ''Phys Rev Lett'' '''80''':197–200, 1998. [[media:strong-etal-98.pdf | PDF]].
#R Cheong, A Rhee, CJ Wang, I Nemenman, and A Levchenko. Information Transduction Capacity of Noisy Biochemical Signaling Networks.  ''Science'' doi:10.1126/science.1204553, 2011. [[media:cheong-etal-11.pdf |PDF]].
#A Margolin, I Nemenman, K Basso, U Klein, C Wiggins, G Stolovitzky, Riccardo D Favera, and A Califano. ARACNE: An algorithm for reconstruction of genetic networks in a mammalian cellular context. ''BMC Bioinformatics'', '''7 (Suppl. 1)''':S7, 2006. [[media:margolin-etal-06a.pdf | PDF]]

===Noise in biochemistry, population biology, and neuroscience===
# S Luria and M Delbruck. Mutations of bacteria from virus sensitivity to virus resistance. ''Genetics'' 28, 491-511, 1943. [[media:luria-delbruck-43.pdf|PDF]].
# 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. [[media:schneidman-etal-98.pdf | PDF]].
# T Kepler and T Elston. Stochasticity in transcriptional regulation: Origins, consequences, and mathematical representations. ''Biophys J.''  81, 3116-3136, 2001. [[media:kepler-elston-01.pdf | PDF]].
# M Elowitz, A Levine, E Siggia & P Swain. Stochastic gene expression in a single cell.  ''Science''  207, 1183, 2002. [[media:elowitz-etal-02.pdf |PDF]].
# W Blake, M Kaern, C Cantor, and J Collins. Noise in eukaryotic gene expression. ''Nature'' 422, 633-637, 2003. [[media:blake-etal-03.pdf | PDF]].
# J Raser and E O’Shea. Control of stochasticity in eukaryotic gene expression. ''Science'' 304, 1811-1814, 2004. [[media:raser-oshea-04.pdf | PDF]].
# G Lahav. et al. Dynamics of the p53-Mdm2 feedback loop in individual cells. ''Nat Genet'' 36, 147–150, 2004. [[media:lahav-etal-04.pdf|PDF]].
# J Paulsson. Summing up the noise in gene networks. ''Nature'' 427, 415, 2004. [[media:paulsson-04.pdf |PDF]], [[media:paulsson-04-supplement.pdf | Supplement]].
# J Pedraza and A van Oudenaarden. Noise propagation in gene networks, ''Science'' 307, 1965-1969, 2005. [[media:pedraza-oudenaarden-05.pdf | PDF]].
# N Rosenfeld, J Young, U Alon, P Swain, M Elowitz. Gene Regulation at the Single-Cell Level. ''Science'' 307, 1962, 2005. [[media:rosenfeld-etal.pdf |PDF]].
# B Averbeck et al. Neural correlations, population coding and computation. ''Nat Rev Neurosci'' 7, 358-66, 2006. [[media:averbeck-etal-06.pdf|PDF]].
# D Gillespie. Stochastic Simulation of Chemical Kinetics. ''Ann Rev Phys Chem'' 58, 35-55, 2007. [[media:gillespie-07.pdf | PDF]].
# T Cağatay et al. Architecture-dependent noise discriminates functionally analogous differentiation circuits. ''Cell'' 139:512-22, 2009. [[media:cagatay-etal-2009.pdf|PDF]], [[media:cagatay-etal-2009-suppl.pdf|supplement]].
# A Walczak, G Tkacik, and W Bialek. Optimizing information flow in small genetic networks. II. Feed-forward interactions. ''Phys Rev E'' 81, 041905, 2010. [[media:walczak-etal-2010.pdf|PDF]].

===Memory in noisy environments===
#T Gardner et al.  Construction of a genetic toggle switch in ''Escherichia coli''. ''Nature'' 403: 339-42, 2000. [[media:gardner-etal-00.pdf|PDF]]
# 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. [[media:bialek-01.pdf | PDF]]
# E Aurell and K Sneppen. Epigenetics as a first exit problem. ''Phys Rev Lett'' 88, 048101, 2002. [[media:aurell-sneppen-02.pdf | PDF]].
# 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. [[media:korobkova-etal-04.pdf | PDF]].
#N Balaban, J Merrin, R Chait, L Kowalik, S Leibler. Bacterial persistence as a phenotypic switch. ''Science'' 305:1622, 2004. [[media:balaban-etal-04.pdf | PDF]].
# Y Tu and G Grinstein. How white noise generates power-law switching in bacterial flagellar motors. ''Phys Rev Lett'', 2005. [[media:tu-grinstein-05.pdf | PDF]].
# E Kussell and S Leibler. Phenotypic diversity, population growth, and information in fluctuating environments. ''Science'' 309:2075–2078. 2005. [[media:kussell-leibler-05.pdf |PDF]].
# D Sprinzak et al. Cis-interactions between Notch and Delta generate mutually exclusive signalling states. ''Nature'' 465, 86–90, 2010. [[media:sprinzak-etal-10.pdf|PDF]].

===Adaptation===
# N Barkai and S Leibler. Robustness in simple biochemical networks. ''Nature'' 387, 913–917, 1997. [[media:barkai-etal-97.pdf|PDF]].
# U Alon, M Surette, N Barkai, and S Leibler. Robustness in bacterial chemotaxis. ''Nature'' 397, 168–171, 1999. [[media:alon-etal-99.pdf|PDF]].
# N Brenner et al. Adaptive rescaling maximizes information transmission. ''Neuron'' 26, 695-702. [[media:brenner-etal-00.pdf|PDF]].
# P Cluzel, M Surette, and S Leibler. An ultrasensitive bacterial motor revealed by monitoring signaling proteins in single cells. ''Science'', 287:1652-1655, 2000. [[media:cluzel-etal-00.pdf |PDF]].
# B Andrews et al. Optimal noise filtering in the chemotactic response of Escherichia coli. ''PLoS Comput Biol'' 2, e154, 2006. [[media:andrews-etal-06.pdf|PDF]].
# T Sharpee et al. Adaptive filtering enhances information transmission in visual cortex. ''Nature'' 439, 936-42, 2006. [[media:sharpee-etal-06.pdf|PDF]].
# A Fairhall et al. Efficiency and ambiguity in an adaptive neural code. ''Nature'' 412, 787-92, 2001. [[media:fairhall-etal-00.pdf|PDF]].
# I Nemenman et al. Neural coding of natural stimuli: information at sub-millisecond resolution. ''PLoS Comput Biol'' 4, e1000025, 2008. [[media:nemenman-etal-08.pdf|PDF]].
#T Friedlander and N Brenner. Adaptive response by state-dependent inactivation. ''Proc Natl Acad Sci USA'' 106, 22558-63, 2009. [[media:friedlander-brenner-09.pdf |PDF]].
#W Ma et al. Defining network topologies that can achieve biochemical adaptation. ''Cell'' 138, 760-73, 2009. [[media:ma-etal-09.pdf|PDF]].

===Robustness===
# 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. [[media:eldar-etal-03.pdf |PDF]].
# T Gregor, W Bialek, R de Ruyter van Steveninc, D Tank, and E Wieschaus. Diffusion and scaling during early embryonic pattern formation. ''PNAS'' 102:18403, 2005. [[media:gregor-etal-05.pdf|PDF]].
# 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. [[media:doan-etal-06.pdf | PDF]].
#A Lander et al. The measure of success: constraints, objectives, and tradeoffs in morphogen-mediated patterning. ''Cold Spring Harb Perspect Biol'' 1, a002022, 2009. [[media:lander-etal-09.pdf|PDF]]

===Learning===
#CR  Gallistel et al. The rat approximates an ideal detector of changes in rates of reward: implications for the law of effect. ''J Exp Psychol Anim Behav Process'' 27, 354-72, 2001. [[media:gallistel-etal-01.pdf|PDF]].
#CR Gallistel et al. The learning curve: implications of a quantitative analysis. ''Proc Natl Acad Sci USA'' 101, 13124-31, 2004. [[media:gallistel-etal-04.pdf|PDF]].
#B Andrews and P Iglesias. An information-theoretic characterization of the optimal gradient sensing response of cells. ''PLoS Comput Biol'' 3, e153, 2007. [[media:andrews-iglesias-07.pdf|PDF]].
#M Vergassola et al. 'Infotaxis' as a strategy for searching without gradients. ''Nature'' 445, 406-9, 2007. [[media:vergassola-etal-07.pdf|PDF]].

===Eukaryotic signaling===
#C-Y Huang and J Ferrell. Ultrasensitivity in the mitogen-activated protein kinase cascade. ''Proc Natl Acad Sci USA'' 93:10078, 1996. [[media:huang-ferrell-96.pdf|PDF]].
#N Markevich et al. Signaling switches and bistability arising from multisite phosphorylation in protein kinase cascades. ''J Cell Biol'' 164:353-9, 2004. [[media:markevich-etal-04.pdf|PDF]].
#C Gomez-Uribe, G Verghese, and L Mirny. Operating regimes of signaling cycles: statics, dynamics, and noise filtering. ''PLoS Comput Biol'' 3:e246, 2007. [[media:gomez-uribe-etal-07.pdf|PDF]].



[[Category:Ilya's Science]]