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2015-11-13T15:02:33Z

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{{PHYS434-2015}}

==News==
*Schedule for the rest of the semester available. [[User:Ilya|Ilya]] 10:02, 13 November 2015 (EST)
*Midterm on '''November 2'''.
*Homework due date rescheduled. [[User:Ilya|Ilya]] 11:26, 13 October 2015 (EDT)
*Office hours rescheduled: Monday 4-5pm, Friday 3-4pm, MSC N240
*HW 2 posted. [[User:Ilya|Ilya]] 03:57, 9 September 2015 (EDT)
*HW 1 posted -- make it a habit of checking the class web page. [[User:Ilya|Ilya]] 10:11, 2 September 2015 (EDT)
*Welcome to the class!

==About the class==
This class is aimed to teach you to think physically about biological systems. Thinking physically means, in the context of this class, creating ''simple'' predictive mathematical models of biological processes that provide ''insight''. If you are still confused, we will talk a lot more during the lectures what it means to think physically. The class relies a lot on computer simulations as a tool to verify our understanding -- and you will learn Matlab during this class (no prior programming experience necessary). The main ideas that we will explore are the ideas of dynamics, randomness, control, inference, and information -- all applied to biology in two different ways: first, how we model and learn biology, and, second, how biological organisms model and learn the world around them. These ideas will be explored in a variety of biological systems, from viruses and bacteria, to neural systems, and to entire populations.

==Logistics==
*[[Physics 434, 2015: Syllabus|Syllabus]] -- we will deviate from it in the course of the class
*[[Installing Octave on your PC and Mac]].
*Weekly office hours: Monday, 2:00-3:30, subject to change
*'''Main Textbook''': P Nelson, [http://www.physics.upenn.edu/biophys/PMLS/index.html Physical Modeling of Living Systems], WH Freeman, Dec 2014.
:: See also [http://www.physics.upenn.edu/biophys/PMLS/Student/index.html student resources] for the book.
:: Make sure to download the [https://github.com/NelsonUpenn/PMLS-MATLAB-Guide Matlab guide].

==Lecture Notes and Detailed Schedule==
Detailed schedule and Lecture notes will be provided as needed (the latter only when we deviate substantially from the Nelson's textbook). This is the first time I am teaching largely based on Nelson's book, and so it is hard for me to gauge how quickly the class would proceed. Therefore, I am not providing a detailed schedule for the full semester, but will be updating it as the course progresses.

; Aug 26, Week 1
:Chapters 0, 1 from Nelson.
:[[Physics 434, Lecture 1 additional notes| Lecture 1 additional notes]]
;Aug 31, Week 2
:Chapter 1 and 2, Appendix B -- briefly mentioned in class; you are responsible for this on your own
;Sep 2, Week 2
:Chapters 3
:*[[Physics 434, 2014: Discrete randomness | Discrete randomness]]: additional lecture notes, partially overlapping with the textbook (last edited on 10/21/2014).
:*[[Physics 434, 2014: Law of large numbers| Law of large numbers]]: additional lecture notes complementing the textbook (last edited on 10/16/2014).
;Sep 7 -- Labor Day, no classes, Week 3
;Sep 9, Week 3
:Chapter 4
:*See also [[Physics 434, 2014: Law of large numbers| Law of large numbers]]: additional lecture notes complementing the textbook (last edited on 10/16/2014).
;Sep 14, Week 4
:Chapter 4
:*Discrete probability distributions
:*Luria-Delbruck experiment, See also [[Physics 434, 2014: Luria-Delbruck experiment | additional notes on LD experiment]] (last edited on 10/16/2014).
;Sep 16, Week 4
:Chapter 5
:*Continuous random variables, see also [[Physics 434, 2014: Continuous randomness| additional notes]] (last edited 10/21/2014).
:*Central limit theorem, see also [[Physics 434, 2014: Central limit theorem| additional notes]] (last edited 10/27/2014).
;Sep 21, Week 5
:No book chapter
:*Continuing Central limit theorem, see also [[Physics 434, 2014: Central limit theorem| additional notes]] (last edited 10/27/2014).
;Sep 23, Week 5
:No book chapter
:*Random walks and diffusion, [[Physics 434, 2014: Random walks and diffusion| Lecture notes]] (last edited 11/05/2014).
:*Search and first passage time , [[Physics 434, 2014: Search and first passage times|Lecture notes]] (last edited 11/06/2014).
;Sep 28, Week 6
:No book chapter
:*Random walks and diffusion, [[Physics 434, 2014: Random walks and diffusion| Lecture notes]] (last edited 11/05/2014).
:*Search and first passage time , [[Physics 434, 2014: Search and first passage times|Lecture notes]] (last edited 11/06/2014).
;Sep 30, Week 6
:No book chapter
:*The diffusion equation, and problems in development, [[Physics 434, 2014: Random walks and diffusion| Lecture notes]] (last edited 11/05/2014).
;Oct 5, Week 7
:Chapter 6
:*Maximum likelihood, inference, and model selection.
;Oct 7, Week 7
:Chapter 7
:*Poisson processes.
;Oct 12, Week 8 -- No classes
:Fall break
;Oct 14, Week 8
:Chapter 8
:*Randomness in cells
:*See also [[Physics 434, 2014: Stochastic chemical kinetics| these notes]]
;Oct 19, Week 9
:Chapter 8
:*Randomness in cells
:*See also [[Physics 434, 2014: Stochastic chemical kinetics| these notes]]
;Oct 21, Week 9
:*Randomness in cells
:*See also [[Physics 434, 2014: Stochastic chemical kinetics| these notes]]
;Oct 26, Week 10
:Chapter 9
:*Negative Feedback
;Oct 28, Week 10
:Chapter 9
:*Negative Feedback
:Chapter 10, Genetic Switches
;Nov 2, Week 11 -- Exam
;Nov 4, Week 11
:Chapter 10
:*Genetic Switches
:*Exam solution
;Nov 9, Week 12
:Chapter 11
:*Cellular Oscillations,
:[[Physics 434, 2015: Introduction to Information theory|Intro to information theory]]
;Nov 11, Week 12
:[[Physics 434, 2015: Introduction to Information theory|Intro to information theory]]
;Nov 16, Week 13
:[[Physics 434, 2015: Introduction to Information theory|Intro to information theory]]
;Nov 18, Week 13
:Does biology care about bits?
;Nov 23, Week 14
:Examples of information transmission in various systems. What can we learn?
;Nov 25, Week 14 -- Thanksgiving
;*No class
;Nov 30, Week 15
:Examples of information transmission in various systems. What can we learn?
;Dec 2, Week 15
:Information for reverse-engineering of cellular networks.
;Dec 7, Week 16
:In-class project presentations.

==Homework assignments==
*[[Physics 434, 2015: Homework 1| HW 1]], Due Sep 9.
*[[Physics 434, 2015: Homework 2| HW 2]], Due Sep 16.
*[[Physics 434, 2015: Homework 3| HW 3]], Due Sep 23.
*[[Physics 434, 2015: Homework 4| HW 4]], Due Sep 30.
*[[Physics 434, 2015: Homework 5| HW 5]], Due Oct 7.
*[[Physics 434, 2015: Homework 6| HW 6]], Due Oct 21.
*[[Physics 434, 2015: Homework 7| HW 7]], Due Oct 28.
*[[Physics 434, 2015: Homework 8| HW 8]], Due Nov 18.
*[[Physics 434, 2015: Homework 9| HW 9]], Due Nov 25.
*[[Physics 434, 2015: Homework 10| HW 10]], Due Dec 2.

==Projects==
# [[Physics 434, 2015: Project 1 | Project 1]].
# [[Physics 434, 2015: Project 2 | Project 2]].
# [[Physics 434, 2015: Project 3 | Project 3]].
# [[Physics 434, 2015: Project 4 | Project 4]].
# [[Physics 434, 2015: Project 5 | Project 5]].

==References==
Below are some of the papers we will be mentioning in class. Projects will be based on some of them. Enjoy the reading.

===Additional 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]]
#I Nemenman, Information theory and adaptation. In ''Quantitative biology: From molecules to Cellular Systems'', ME Wall, ed. (Taylor and Francis, 2012). [[media:nemenman-2011.pdf|PDF]].
#A Levchenko and I Nemenman. Cellular noise and information transmission. ''Current Opinion Biotech'' '''28''', 156, 2014. [[media:levchenko-nemenman-14.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]].

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