Difference between revisions of "BE 150/Bi 250b Winter 2012"
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+   <center>'''WARNING: This page is for a previous year.'''<br> See [[BE 150/Bi 250bcurrent course homepage]] to find most recent page available.</center>  
+  }  
+  
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* Michael Elowitz (Bi/BE/APh)  * Michael Elowitz (Bi/BE/APh)  
* Richard Murray (CDS/BE)  * Richard Murray (CDS/BE)  
−  * Lectures:  +  * Lectures: MW 1011, 101 Kerckhoff 
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'''Teaching Assistants'''  '''Teaching Assistants'''  
* Emzo de los Santos  * Emzo de los Santos  
* Vanessa Jonsson  * Vanessa Jonsson  
+  * Recitation: F 1011, 111 Keck (BE 150), 3 BBB (Bi 250)  
}  }  
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=== Lecture Schedule ===  === Lecture Schedule ===  
Line 91:  Line 46:  
BE 150:  BE 150:  
* {{be150 pdfwi12caltech/bfsclassintro_01Jan12.pdfBFS, Ch 1}}: Introductory Concepts  * {{be150 pdfwi12caltech/bfsclassintro_01Jan12.pdfBFS, Ch 1}}: Introductory Concepts  
−  * {{be150 pdfwi12caltech/bfsclass  +  * {{be150 pdfwi12caltech/bfsclasscoreproc_18Jan12.pdfBFS, Ch 2}}: Modeling of Core Processes 
** Section 2.1: Modeling Techniques  ** Section 2.1: Modeling Techniques  
    
Line 108:  Line 63:  
BE 150:  BE 150:  
−  * {{be150 pdfwi12caltech/bfsclass  +  * {{be150 pdfwi12caltech/bfsclasscoreproc_18Jan12.pdfBFS, Ch 2}}: Modeling of Core Processes 
** Sections 2.22.3: transcription and translation, transcriptional regulation  ** Sections 2.22.3: transcription and translation, transcriptional regulation  
+  
+  Papers discussed in lecture:  
+  * [http://www.nature.com/nature/journal/v403/n6767/abs/403339a0.html Construction of a genetic toggle switch in <i>Escherichia coli </i>], Gardner TS, Cantor CR, Collins JJ. ''Nature'', <b>403</b>:339342, 2000.  
+  * [http://www.nature.com/nature/journal/v426/n6965/abs/nature02089.html A positivefeedbackbased bistable 'memory module' that governs a cell fate decision], Xiong and Ferrell. ''Nature'', <b>426</b>:460465, 2003.  
[https://www.cds.caltech.edu/~murray/wiki/images/c/c6/Hw1.pdf BEHW1] [https://www.cds.caltech.edu/~murray/wiki/images/e/e1/Hw1bio.pdf BIOHW1]  [https://www.cds.caltech.edu/~murray/wiki/images/c/c6/Hw1.pdf BEHW1] [https://www.cds.caltech.edu/~murray/wiki/images/e/e1/Hw1bio.pdf BIOHW1]  
* [http://www.cds.caltech.edu/~murray/courses/be150/wi12/lacIOpenMain.m lacIOpenMain.m]  * [http://www.cds.caltech.edu/~murray/courses/be150/wi12/lacIOpenMain.m lacIOpenMain.m]  
Line 131:  Line 90:  
    
Bi 250b:  Bi 250b:  
−  *  +  * Alon, Ch 4: The feedforward loop network motif 
−  +  * Alon, Ch 6: Network motifs in developmental, signal transduction, and neuronal networks  
BE 150:  BE 150:  
−  +  * {{be250c pdfwi12caltech/bfsclasscoreproc_18Jan21.pdfBFS, Ch 2}}: Modeling of Core Processes  
−  * {{be250c pdfwi12caltech/bfsclass  
** Section 2.4: posttranscriptoinal regulation  ** Section 2.4: posttranscriptoinal regulation  
** Section 2.5: cellular subsystems  ** Section 2.5: cellular subsystems  
−    +  
+  Papers discussed in lecture:  
+  * [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC349147/?tool=pmcentrez An amplified sensitivity arising from covalent modification in biological systems], Goldbeter A, Koshland DE. ''Proc. Natl. Acad. Sci. U.S.A.'', 78 (11): 6840–4, 1981.  
+  * [http://www.nature.com/msb/journal/v5/n1/full/msb200930.html Protein sequestration generates a flexible ultrasensitive response in a genetic network], N. E. Buchler and F. R. Cross. ''Molecular Systems Biology'', 5:272, 2009.  
+   [https://www.cds.caltech.edu/~murray/wiki/images/7/74/Hw2.pdf BEHW2] [https://www.cds.caltech.edu/~murray/wiki/images/5/51/Hw2_bio.pdf BIOHW2]  
+  * [http://www.cds.caltech.edu/~murray/courses/be150/wi12/prob1.m prob1.m]  
+  * [http://www.cds.caltech.edu/~murray/courses/be150/wi12/plot1.m plot1.m]  
+  * [http://www.cds.caltech.edu/~murray/courses/be150/wi12/phosphoMainIO.m phosphoMainIO.m]  
 valign=top   valign=top  
    
Line 146:  Line 111:  
 23 Jan <br> 25 Jan <br><br> MBE   23 Jan <br> 25 Jan <br><br> MBE  
 Biological clocks: how to produce oscillations in cells   Biological clocks: how to produce oscillations in cells  
+  * Plant clocks/circadian rhythm  
* Synthetic oscillators (repressilator, dualfeedback oscillator)  * Synthetic oscillators (repressilator, dualfeedback oscillator)  
* Circadian clocks in cyanobacteria  * Circadian clocks in cyanobacteria  
−  
−  
−  
−  
    
* [http://www.nature.com/nature/journal/v403/n6767/full/403335a0.html A synthetic oscillatory network of transcriptional regulators], Elowitz and Leibler. ''Nature'', 403:335338, 2000.  * [http://www.nature.com/nature/journal/v403/n6767/full/403335a0.html A synthetic oscillatory network of transcriptional regulators], Elowitz and Leibler. ''Nature'', 403:335338, 2000.  
* [http://www.nature.com/nature/journal/v456/n7221/full/nature07389.html A fast, robust and tunable synthetic gene oscillator], Stricker, ''et al.''. ''Nature'', 456:516519, 2008.  * [http://www.nature.com/nature/journal/v456/n7221/full/nature07389.html A fast, robust and tunable synthetic gene oscillator], Stricker, ''et al.''. ''Nature'', 456:516519, 2008.  
* [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1855407/ Cyanobacterial clock, a stable phase oscillator with negligible intercellular coupling], M. Amdaoud, M. Vallade, C. WeissSchaber, and I. Mihalcescu. ''Proc Natl Acad Sci'', 104(17):7051–7056, 2007.  * [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1855407/ Cyanobacterial clock, a stable phase oscillator with negligible intercellular coupling], M. Amdaoud, M. Vallade, C. WeissSchaber, and I. Mihalcescu. ''Proc Natl Acad Sci'', 104(17):7051–7056, 2007.  
−    +  BE 150: 
+  * {{be150 pdfwi12caltech/bfsclassdynamics_18Jan12.pdfBFS, Ch 3}}: Analysis of Dynamic Behavior  
+  ** Sections 3.5: Oscillatory Behavior  
+  [https://www.cds.caltech.edu/~murray/wiki/images/4/4b/Hw3.pdf BEHW3] [https://www.cds.caltech.edu/~murray/wiki/images/e/e1/Hw3bio.pdf BIOHW3]  
+  * [http://www.cds.caltech.edu/~murray/courses/be150/wi12/ddeoscillate.m ddeoscillate.m]  
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−    +   
+  
===== 5 =====  ===== 5 =====  
 30 Jan <br> 1 Feb <br><br> RMM   30 Jan <br> 1 Feb <br><br> RMM  
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* Alon, Ch 7: Robustness of protein circuits : the example of bacterial chemotaxis  * Alon, Ch 7: Robustness of protein circuits : the example of bacterial chemotaxis  
−  *  +  * H. Kitano, [http://www.ncbi.nlm.nih.gov/pubmed/15520792 Biological robustness], Nat Rev Genet, vol. 5, no. 11, pp. 826–837, Nov. 2004. 
−  * [http://www.  +  * N. Barkai and S. Leibler, [http://www.ncbi.nlm.nih.gov/pubmed/9202124 Robustness in simple biochemical networks], Nature, vol. 387, no. 6636, pp. 913–917, Jun. 1997. 
−   HW #4  +  * (optional) C. V. Rao, J. R. Kirby, and A. P. Arkin, [http://www.ncbi.nlm.nih.gov/pubmed/14966542 Design and diversity in bacterial chemotaxis: a comparative study in Escherichia coli and Bacillus subtilis], PLoS Biol, vol. 2, no. 2, p. E49, Feb. 2004. 
+  BE 150:  
+  * {{be150 pdfwi12caltech/bfsclassdynamics_29Jan12.pdfBFS, Ch 3}}: Sec 3.3 (Robustness) and Sec 3.6 (Bifurcations)  
+  * {{be150 pdfwi12caltech/bfsclasschemotaxis_29Jan12.pdfBFS, Sec 5.2}}: Bacterial chemotaxis  
+  * (optional) O. Shoval, L. Goentoro, Y. Hart, A. Mayo, E. Sontag, and U. Alon, [http://www.pnas.org/content/107/36/15995.long Foldchange detection and scalar symmetry of sensory input fields], Proceedings of the National Academy of Sciences, vol. 107, no. 36, pp. 15995–16000, Sep. 2010.  
+   [https://www.cds.caltech.edu/~murray/wiki/images/d/d3/Be150hw4.pdf BE150 HW #4] [https://www.cds.caltech.edu/~murray/wiki/images/8/88/Bi250bHw4.pdf Bi250b HW#4]  
+  *[http://www.cds.caltech.edu/~murray/courses/be150/wi12/problem1.nb problem1.nb]  
+  *[http://www.cds.caltech.edu/~murray/courses/be150/wi12/chemotaxis.m chemotaxis.m]  
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−    +   
+  
===== 6 =====  ===== 6 =====  
 6 Feb* <br> 8 Feb <br><br> RMM   6 Feb* <br> 8 Feb <br><br> RMM  
Line 182:  Line 157:  
* [http://www.sciencemag.org/content/297/5584/1183 Stochastic Gene Expression in a Single Cell], Michael B. Elowitz, Arnold J. Levine, Eric D. Siggia and Peter S. Swain. ''Science'', 297(5584):11831186, 2002.  * [http://www.sciencemag.org/content/297/5584/1183 Stochastic Gene Expression in a Single Cell], Michael B. Elowitz, Arnold J. Levine, Eric D. Siggia and Peter S. Swain. ''Science'', 297(5584):11831186, 2002.  
* [http://www.nature.com/nature/journal/v440/n7082/full/nature04599.html Stochastic protein expression in individual cells at the single molecule level], Long Cai, Nir Friedman and X. Sunney Xie. ''Nature'', 440:358362, 2006.  * [http://www.nature.com/nature/journal/v440/n7082/full/nature04599.html Stochastic protein expression in individual cells at the single molecule level], Long Cai, Nir Friedman and X. Sunney Xie. ''Nature'', 440:358362, 2006.  
−    +  BE 150: 
+  * {{be150 pdfwi12caltech/bfsclassstochastic_29Jan12.pdfBFS, Ch 4}}: Stochastic behavior  
+  * {{be150 pdfwi12caltech/bfsclassrandom_29Jan12.pdfBFS, App C}}: Probability and random processes (optional)  
+  
+    
+  [https://www.cds.caltech.edu/~murray/wiki/images/6/68/Hw5be.pdf BEHW5] [https://www.cds.caltech.edu/~murray/wiki/images/a/a7/Hw5bio.pdf BIOHW5]  
+  * [http://www.cds.caltech.edu/~murray/courses/be150/wi12/runner.m runner.m]  
+  * [http://www.cds.caltech.edu/~murray/courses/be150/wi12/hw5.sbproj hw5.sbproj]  
 valign=top   valign=top  
−    +   
+  
===== 7 =====  ===== 7 =====  
 13 Feb+ <br> 15 Feb <br><br> MBE   13 Feb+ <br> 15 Feb <br><br> MBE  
Line 193:  Line 176:  
* [http://www.nature.com/nature/journal/v455/n7212/full/nature07292.html Frequencymodulated nuclear localization bursts coordinate gene regulation], Long Cai, Chiraj K. Dalal and Michael B. Elowitz. Nature 455:485490, 2008.  * [http://www.nature.com/nature/journal/v455/n7212/full/nature07292.html Frequencymodulated nuclear localization bursts coordinate gene regulation], Long Cai, Chiraj K. Dalal and Michael B. Elowitz. Nature 455:485490, 2008.  
* [http://www.nature.com/nature/journal/v466/n7303/full/nature09145.html Singlecell NFkB dynamics reveal digital activation and analogue information processing], S. Tay ''et al''. ''Nature'', 466(7303):267271, 2010  * [http://www.nature.com/nature/journal/v466/n7303/full/nature09145.html Singlecell NFkB dynamics reveal digital activation and analogue information processing], S. Tay ''et al''. ''Nature'', 466(7303):267271, 2010  
−    +   [https://www.cds.caltech.edu/~murray/wiki/images/7/75/Hw6be.pdf BEHW6] [https://www.cds.caltech.edu/~murray/wiki/images/f/fe/Hw6bio.pdf BIOHW6] 
 valign=top   valign=top  
    
+  
===== 8 =====  ===== 8 =====  
 <s>20 Feb</s> <br> 22 Feb <br> 24 Feb <br><br> RMM   <s>20 Feb</s> <br> 22 Feb <br> 24 Feb <br><br> RMM  
Line 206:  Line 190:  
* [http://linkinghub.elsevier.com/retrieve/pii/S0959437X04000887 Elucidating mechanisms underlying robustness of morphogen gradients], Avigdor Eldar, BenZion Shilo and Naama Barkai. ''Curr Opin Genet Dev.'', 14(4):435439, 2004.  * [http://linkinghub.elsevier.com/retrieve/pii/S0959437X04000887 Elucidating mechanisms underlying robustness of morphogen gradients], Avigdor Eldar, BenZion Shilo and Naama Barkai. ''Curr Opin Genet Dev.'', 14(4):435439, 2004.  
* [http://www.pnas.org/content/107/15/6924.short Scaling of morphogen gradients by an expansionrepression integral feedback control], Danny BenZvia and Naama Barkai. ''PNAS'', 107(15):69246929, 2010.  * [http://www.pnas.org/content/107/15/6924.short Scaling of morphogen gradients by an expansionrepression integral feedback control], Danny BenZvia and Naama Barkai. ''PNAS'', 107(15):69246929, 2010.  
−    +   [https://www.cds.caltech.edu/~murray/wiki/images/d/df/Hw7be.pdf BEHW7] [https://www.cds.caltech.edu/~murray/wiki/images/d/d5/Hw7bio.pdf BioHW7] 
 valign=top   valign=top  
−    +   
+  
===== 9 =====  ===== 9 =====  
 27 Feb <br> 29 Feb*+ <br><br> MBK   27 Feb <br> 29 Feb*+ <br><br> MBK  
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===== 10 =====  ===== 10 =====  
−   5 Mar <br> 7 Mar <br> MBE  +   5 Mar <br> 7 Mar+ <br> MBE 
 Fine grain patterns   Fine grain patterns  
* Lateral inhibition  * Lateral inhibition  
Line 228:  Line 213:  
* [http://www.ncbi.nlm.nih.gov/pubmed/9015458 Pattern formation by lateral inhibition with feedback: a mathematical model of deltanotch intercellular signalling], Collier et al. Journal of theoretical biology (1996) vol. 183 (4) pp. 42946.  * [http://www.ncbi.nlm.nih.gov/pubmed/9015458 Pattern formation by lateral inhibition with feedback: a mathematical model of deltanotch intercellular signalling], Collier et al. Journal of theoretical biology (1996) vol. 183 (4) pp. 42946.  
* [http://www.ncbi.nlm.nih.gov/pubmed/20418862 Cisinteractions between Notch and Delta generate mutually exclusive signalling states], Sprinzak et al. Nature (2010) vol. 465 (7294) pp. 8690  * [http://www.ncbi.nlm.nih.gov/pubmed/20418862 Cisinteractions between Notch and Delta generate mutually exclusive signalling states], Sprinzak et al. Nature (2010) vol. 465 (7294) pp. 8690  
−    +   [https://www.cds.caltech.edu/~murray/wiki/images/d/d6/Hw8be.pdf BEHW8] [https://www.cds.caltech.edu/~murray/wiki/images/e/ef/Hw8bio.pdf BioHW8] 
+  * [http://www.cds.caltech.edu/~murray/courses/be150/wi12/NotchDeltaGui.m NotchDeltaGui.m]  
+  }  
+  <br>  
+  
+  === Course Description ===  
+  BE 150/Bi 250b is a jointly taught class that shares lectures but has different reading material and homework assignments. Students in BE 150 are expected to have a more quantitative background and the course material includes a combination of analytical and conceptual tools. Students in Bi 250b are expected to have more knowledge of basic biological processes and the course material focuses on the principles and tools for understanding biological processes and systems.  
+  
+  '''BE 150''': Quantitative studies of cellular and developmental systems in biology, including the architecture of specific genetic circuits controlling microbial behaviors and multicellular development in model organisms. Specific topics include chemotaxis, multistability and differentiation, biological oscillations, stochastic effects in circuit operation, as well as higherlevel circuit properties such as robustness. Organization of transcriptional and proteinprotein interaction networks at the genomic scale. Topics are approached from experimental, theoretical and computational perspectives.  
+  
+  '''Bi 250b''': The class will focus on quantitative studies of cellular and developmental systems in biology. It will examine the architecture of specific genetic circuits controlling microbial behaviors and multicellular development in model organisms. The course will approach most topics from both experimental and theoretical/computational perspectives. Specific topics include chemotaxis, multistability and differentiation, biological oscillations, stochastic effects in circuit operation, as well as higherlevel circuit properties such as robustness. The course will also consider the organization of transcriptional and proteinprotein interaction networks at the genomic scale.  
+  
+  === Textbook ===  
+  The primary text for the BE 150 and Bi 250b is  
+  {  
+   valign=top  
+   align=right  [Alon]  
+   U. Alon, ''An Introduction to Systems Biology: Design Principles of Biological Circuits'', CRC Press, 2006.  
}  }  
+  Students in BE 150 should also obtain the following notes (freely downloadable from the web):  
+  {  
+   valign=top  
+   align=right  [BFS]  
+   D. Del Vecchio and R. M. Murray, ''Biomolecular Feedback Systems''. Available online at http://www.cds.caltech.edu/~murray/amwiki/BFS.  
+  * Note: these notes are being written and will be updated during the course  
+  * Class version (Caltech access only, 29 Jan 2012): {{be150 pdfwi12caltech/bfsclassfrontmatter_01Jan12.pdfTOC}}, {{be150 pdfwi12caltech/bfsclassintro_01Jan12.pdfCh 1}}, {{be150 pdfwi12caltech/bfsclasscoreproc_18Jan12.pdfCh 2}}, {{be150 pdfwi12caltech/bfsclassdynamics_29Jan12.pdfCh 3}}, {{be150 pdfwi12caltech/bfsclassstochastic_29Jan12.pdfCh 4}}, {{be150 pdfwi12caltech/bfsclasschemotaxis_29Jan12.pdfSec 5.2}}, {{be150 pdfwi12caltech/bfsclassrandom_29Jan12.pdfApp C}}, {{be150 pdfwi12caltech/bfsclassbackmatter_01Jan12.pdfRefs}}  
+  }  
+  
+  The following additional texts and notes may be useful for some students:  
+  {  
+   valign=top  
+   align=right  [FBS]  
+   K. J. Astrom and R. M. Murray, ''Feedback Systems''. Available online at http://www.cds.caltech.edu/~murray/amwiki.  
+   valign=top  
+   align=right  [Klipp]  
+   Edda Klipp, Wolfram Liebermeister, Christoph Wierling, Axel Kowald, Hans Lehrach, Ralf Herwig, ''Systems biology: A textbook''. Wiley, 2009.  
+   valign=top  
+   align=right  [Strogatz]  
+   Steven Strogatz, ''Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering''. Westview Press, 2001.  
+  }  
+  
+  === Grading ===  
+  The ﬁnal grade will be based on biweekly homework sets. The homework will be due in class one week after they are assigned. Late homework will not be accepted without prior permission from the instructor. The lowest homework score you receive will be dropped in computing your homework average.  
+  
+  === Collaboration Policy ===  
+  Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course is not allowed. All solutions that are handed in should reﬂect your understanding of the subject matter at the time of writing.  
+  
−  
[[Category:Courses]]  [[Category:Courses]] 
Latest revision as of 06:17, 31 January 2013
See current course homepage to find most recent page available. 
Systems Biology  
Instructors

Teaching Assistants

Lecture Schedule
There will be two 1hour lectures each week, as well as a 1hour recitation section.
Week  Date  Topic  Reading  Homework 
1 
4 Jan 6 Jan+ MBE/RMM 
Course overview
Recitation section:

Bi 250b:
BE 150: 

2 
9 Jan 11 Jan+ MBE 
Gene circuit dynamics

Bi 250b:
BE 150:
Papers discussed in lecture:

BEHW1 BIOHW1 
3 
18 Jan* 20 Jan* RMM 
Circuit motifs

Bi 250b:
BE 150:
Papers discussed in lecture:

BEHW2 BIOHW2 
4 
23 Jan 25 Jan MBE 
Biological clocks: how to produce oscillations in cells

BE 150:

BEHW3 BIOHW3 
5 
30 Jan 1 Feb RMM 
Robustness

BE 150:

BE150 HW #4 Bi250b HW#4 
6 
6 Feb* 8 Feb RMM 
Noise

BE 150:


7 
13 Feb+ 15 Feb MBE 
Burstiness in gene expression and signalling


BEHW6 BIOHW6 
8 
22 Feb 24 Feb RMM 
Patterning


BEHW7 BioHW7 
9 
27 Feb 29 Feb*+ MBK 
Modeling of complex biological networks (Mary Kennedy) 


10 
5 Mar 7 Mar+ MBE 
Fine grain patterns


BEHW8 BioHW8 
Course Description
BE 150/Bi 250b is a jointly taught class that shares lectures but has different reading material and homework assignments. Students in BE 150 are expected to have a more quantitative background and the course material includes a combination of analytical and conceptual tools. Students in Bi 250b are expected to have more knowledge of basic biological processes and the course material focuses on the principles and tools for understanding biological processes and systems.
BE 150: Quantitative studies of cellular and developmental systems in biology, including the architecture of specific genetic circuits controlling microbial behaviors and multicellular development in model organisms. Specific topics include chemotaxis, multistability and differentiation, biological oscillations, stochastic effects in circuit operation, as well as higherlevel circuit properties such as robustness. Organization of transcriptional and proteinprotein interaction networks at the genomic scale. Topics are approached from experimental, theoretical and computational perspectives.
Bi 250b: The class will focus on quantitative studies of cellular and developmental systems in biology. It will examine the architecture of specific genetic circuits controlling microbial behaviors and multicellular development in model organisms. The course will approach most topics from both experimental and theoretical/computational perspectives. Specific topics include chemotaxis, multistability and differentiation, biological oscillations, stochastic effects in circuit operation, as well as higherlevel circuit properties such as robustness. The course will also consider the organization of transcriptional and proteinprotein interaction networks at the genomic scale.
Textbook
The primary text for the BE 150 and Bi 250b is
[Alon]  U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits, CRC Press, 2006. 
Students in BE 150 should also obtain the following notes (freely downloadable from the web):
[BFS]  D. Del Vecchio and R. M. Murray, Biomolecular Feedback Systems. Available online at http://www.cds.caltech.edu/~murray/amwiki/BFS. 
The following additional texts and notes may be useful for some students:
[FBS]  K. J. Astrom and R. M. Murray, Feedback Systems. Available online at http://www.cds.caltech.edu/~murray/amwiki. 
[Klipp]  Edda Klipp, Wolfram Liebermeister, Christoph Wierling, Axel Kowald, Hans Lehrach, Ralf Herwig, Systems biology: A textbook. Wiley, 2009. 
[Strogatz]  Steven Strogatz, Nonlinear Dynamics And Chaos: With Applications To Physics, Biology, Chemistry, And Engineering. Westview Press, 2001. 
Grading
The ﬁnal grade will be based on biweekly homework sets. The homework will be due in class one week after they are assigned. Late homework will not be accepted without prior permission from the instructor. The lowest homework score you receive will be dropped in computing your homework average.
Collaboration Policy
Collaboration on homework assignments is encouraged. You may consult outside reference materials, other students, the TA, or the instructor. Use of solutions from previous years in the course is not allowed. All solutions that are handed in should reﬂect your understanding of the subject matter at the time of writing.