課程資訊
課程名稱
 動態系統生物學
DYNAMICS IN SYSTEMS BIOLOGY 
開課學期
 97-1 
授課對象
 理學院  化學系  
授課教師
 許昭萍 
課號
 Chem5057 
課程識別碼
 223EU2640 
班次
  
學分
 3 
全/半年
 半年 
必/選修
 選修 
上課時間
 星期三7,8,9(14:20~17:20) 
上課地點
 新405 
備註
 本課程以英語授課。詳選課須知。外系所學生選修需經授課教師同意。
限學士班三年級以上 且 限本系所學生(含輔系、雙修生)
總人數上限：60人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/971dsb 
課程簡介影片
 
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課程概述

The vast advancement in technology and accumulation of information nowadays has enabled us to study biology with great details in the molecular level. Understanding of biology at the systems level has become possible in many cases. The dynamical aspect of these studies can often be included in a model to describe and to predict the behavior of a complex biological system. The construction, evolution and prediction of these biological models are closely related to a branch in mathematics – nonlinear dynamics.  

課程目標
 1. In this course, we will learn the fundamental mathematics of nonlinear dynamics by following “Nonlinear dynamics and chaos” written by Strogatz, which is a very readable book with the simplest possible mathematical ingredients. In particular, the following subjects will be covered:

1. Solving ordinary differential equations both numerically and analytically. We will use simple online solver to numerically solve ODE’s. For analytical solutions, only the basic aspects and commonly used skills will be covered.
2. Stability analysis of linear and nonlinear dynamics. Students will learn to search for fixed points, sketch flows in phase space and to judge for the stability of these fixed points.
3. Bifurcations in one-dimension and higher dimensions. Bifurcations lead to changes of systems behavior with a change of a system parameter (condition). Important bifurcations including the saddle-node, transcritical, pitchfork and Hopf bifurcations will be introduced with examples and exercises.
4. Elementary nonlinear analysis for limit cycles that govern oscillatory behavior of a system, and periodic oscillation is seen in many important biological systems.
5. Applications/examples in the area of ecology and molecular biology.

2. We will study several interesting papers published in recent years, which involves quantitative observation in biological systems and a model description or even prediction with nonlinear dynamics. Alon’s book contains a good number of examples in a well-organized layout.

1. Feed-forward loops and their biological implications.
2. Positively feedback loops and their roles in biology. Examples include the MAPK protein regulatory network, regulation of the Gal gene expressions in yeast, and the Lac genes in E. coli.
3. Negatively feedback loops and their roles in biology. Examples include the regulation of NF-κB activity via the expression of its inhibitors and the circadian clock gene network.
4. The sources and characters of noises in biological systems. Numerical methods for simulation involving noises. Recent observations in single-cell experiments and their implications.
5. Reaction-diffusion systems and their application in the study of animal skin patterns.
 
課程要求
Prerequisite: Elementary calculus

 
預期每週課後學習時數
  
Office Hours
 每週三 13:30~15:00 備註： 地點在新生大樓４０４（須事先約定） 
指定閱讀
  
參考書目
 1. (required) An introduction to systems biology by U. Alon, Published by
Chapman &
Hall/CRC.
2. (optional) Nonlinear dynamics and chaos by S. H. Strogatz, Published by
Perseus Book,
Cambridge, USA in 1994.
3. (optional) Chemical Biophysics by D. A. Beard and H. Qian, Published by
Cambridge University Press, UK, 2008.

 
評量方式
(僅供參考)
  
No.
項目
百分比
說明
1. 
 problem sets 
40% 
 Up to 10 problemsets will be given. 1. Homeworks are due one week after they are assigned, before the class starts. Late homeworks are not accepted. 2. Discussion when working on homeworks is allowed. However, students are expected to write up their own solutions independently. Problem sets that are identical in any fraction will not be graded, and will not receive any credit.  
2. 
 midterm 
30% 
 written test 
3. 
 final report 
30% 
 either oral or written reports required, depends on the number of students and number of slots available. The list of papers for reading will be available after mid-term examination. In this report, a compresive introduction to the paper required, and personal opinions, ideas or plausibile proposal related to the research described in that paper are encouraged. Grading will be based on both the presentation and the new ideas and/or proposals. 
 
課程進度
週次
日期
單元主題
Week 1
 2008/09/17  Class setup.<br>Introductory information.<br>Central dogma in molecular biology.<br>Survey on mathematical backgrounds. 
Week 2
 2008/09/24  Michaelis-Menten kinetics: <br> <a href=http://www.biochemj.org/bj/019/bj0190338.htm> Briggs and Sanderson Haldane, Biochem. J. (1925) 19 338</a> <br>Gene input functions (Alon Appendices A and B) <br>Supplementary mathematics: Taylor Expansions, special functions. <br>
<font COLOR="#FF0000">NOTE PS1 updated, with the 3rd problem deleted.</font> 
Week 3
 2008/10/01  One-dimensional flow <br>Stability analysis <br>(Strogatz, Chapter 2) <br>
<font COLOR="#FF0000">NOTE we will do Exercise 2.1.4 instead of 2.5.6. </font> <br> Supplementary mathematics: ordinary differential equations<br><a href=http://en.wikibooks.org/wiki/Calculus/Ordinary_differential_equations> Wikibook link</a> 
Week 4
 2008/10/08  Bifurcations on a one-dimensional systems <br>(Strogatz, Chapter 3) <br>Supplementary mathematics: Linear Algebra<br>
<font COLOR="#FF0000">NOTE PS-S3 will be due on Oct 22 instead.</font><br>
<a href=http://webwork.math.rochester.edu/webwork_system_html/applets/phaseplane/launchXfunctions.html> xFunctions plotter</a> <br>
<a href=http://www.math.psu.edu/melvin/phase/newphase.html> ODE phase portraits 1</a> <br>
<a href=http://www.math.uu.nl/people/beukers/phase/newphase.html> ODE phase portraits 2</a> <br> 
Week 5
 2008/10/15  More example on bifurcation <br> (Strogatz, Chapter 3)<br>Supplementary mathematics (Eigenvalues and eigenvectors)<br> 
Week 6
 2008/10/22  <font COLOR="#FF0000">
NOTE we will move this class to Yang-Ming university for <a href=http://incob.binfo.org.tw/?q=node/4#p1>Terry Gaasterland's talk</a>, in the <a href=http://incob.binfo.org.tw/?q=node/3#d3> 7th InCoB
</a> conference.<br>
Problem sets due today will be collected next week October 29.</font><br>
 
Week 7
 2008/10/29  Fireflies: synchronization in oscillations. (Strogatz,
Chapter 4)
Two-dimensional systems: linear analysis
(Strogatz, Chapters 5) <br>
<font COLOR="#FF0000">No more supplementary math classes </font> 
Week 8
 2008/11/05  Classification of 2-d linear systems (Strogatz, Chap 5) <br>
Transcriptional network and network motifs (Alon, Chapter 2)
<br>
Autoregulation (Alon, Chapter 3) <br>
 
Week 9
 2008/11/12  Feed-forward loops (Alon, Chapter 4) <br>

Review for Midterm <br> 
Week 10
 2008/11/19  Midterm exam 
Week 11
 2008/11/26  Network motif-Feedforward Loop (selected from Alon, Chapters 4) <br>
 
Week 12
 2008/12/03  Single-input module and temperal programs (Alon, Chap 5)
<br>
Network motifs in signal transduction (Alon, Chap 6)
 
Week 13
 2008/12/10  Network motifs in signal transduction (Alon, Chap 6) <br>
Hopf bifurcation and limit cycles (Selected from Strogatz, Chapters 7-8)<br>
 
Week 14
 2008/12/17  Hopf bifurcation and limit cycles (Selected from Strogatz, Chapters 7-8)<br>
Special topics: noises in a cell (materials will be given) <br> 
Week 15
 2008/12/24  Term project report <br>
吳家宜 and Surendhar <br>
cell cycle oscillator-Ferrell <br>
林呈祥 and 謝明偉 <br>
Single molecular study on Lac operon 
Week 16
 2008/12/31  Term project report<br>
陳淑慧 and 徐健翔 <br>
Small-amplitude cycles emerge from stagestructured interactions. (population dynamics) <br>
林俊揚 and 莊凱能 <br>
(TBA) <br> 
Week 17
 2009/01/07  Term project report <br>
陳奕丞 <br>
Oscillatory perturbation-van Oudenaarden 2 <br>

Special Topics: <br>
Bacterial cell fate determination: the competence state of Bacillus subtilis
 
Week 18
 2009/01/14  Final exam week. No more classes.