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課程名稱 |
動態系統生物學
Dynamics in Systems Biology |
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開課學期 |
101-2 |
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授課對象 |
生命科學院 基因體與系統生物學學位學程 |
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授課教師 |
許昭萍 |
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課號 |
GenSys5006 |
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課程識別碼 |
B48 U0210 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期一@,5,6(~14:10) |
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上課地點 |
生科4C |
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備註 |
本課程中文授課,使用英文教科書。本課程中文授課,使用英文教科書。外系所學生選修需經授課教師同意。
限學士班三年級以上
總人數上限：50人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1012DynSysBio2013 |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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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 time and space resolution, and in the molecular level. Understanding of biology at the systems level has become possible in many cases. The dynamical aspect of these studies often include a mathematical model to describe and to predict the behavior of the system. The construction, evolution and prediction of these biological models are closely related to a branch in mathematics – nonlinear dynamics. To help students better understand the literatures in this area, this course is divided into two parts:
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課程目標 |
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. For mathematics that is beyond the basic freshman Calculus, I plan to use the first few chapters in O'Neil's book. In particular, the following subjects will be covered:
Solving ordinary differential equations both numerically (for general cases) and analytically (for a limited number of cases).
Basic linear algebra. A brief review on vectors, matrices and determinants. The goal is to be able to find eigenvalues and eigenvectors for a given matrix, and to understand their meanings.
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.
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.
Elementary nonlinear analysis for limit cycles that govern oscillatory behavior of a system, and periodic oscillation is seen in many important biological systems.
Applications/examples in the area of ecology and molecular biology.
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.
Feed-forward loops and their biological implications.
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.
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.
The sources and characters of noises in biological systems. Numerical methods for simulation involving noises. Recent observations in single-cell experiments and their implications.
Reaction-diffusion systems and their application in the study of animal skin patterns. |
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課程要求 |
There will be 6-8 problem sets, a written midterm exam and a term project report.
Prerequisite: Elementary calculus
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
"Nonlinear dynamics and chaos" by S. H. Strogatz, Published by Perseus Book, Cambridge, USA in 1994.
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參考書目 |
"An introduction to systems biology" by U. Alon, Published by Chapman & Hall/CRC, London, UK in 2006.
"Advanced Engineering Mathematics" by Peter V. O'Neil, Published by Thomson Brooks/Cole.
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
problem sets |
40% |
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2. |
mid term exam |
30% |
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3. |
final report |
30% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/18 |
Class setup.
Introductory information.
Central dogma in molecular biology.
Survey on mathematical backgrounds. |
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第2週 |
2/25 |
Michaelis-Menten kinetics
Appendices A and B (Alon)
Basic functions, differential and integration.
Taylor expansion. |
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第3週 |
3/04 |
First-order Ordinary differential equations(O'Neil). |
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第4週 |
3/11 |
Second-order ordinary differential equations
Linear Algebra(O'Neil)
Linear transformation (Chapter 8 O'Neil)
Solving Linear ODEs with eigen values and eigen vectors. (Strogatz chapter 5) |
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第5週 |
3/18 |
Qing Nie's introductory lecture |
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第6週 |
3/25 |
Bifurcation analysis I (Chapters 2-4 Strogatz) |
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第7週 |
4/01 |
Bifurcation analysis I (Chapters 2-4 Strogatz) |
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第8週 |
4/08 |
Review for Midterm |
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第9週 |
4/15 |
Midterm |
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第10週 |
4/22 |
Bifurcation analysis II (Chapters 4 Strogatz)
Two-dimensional flows (Chapter 6 Strogatz) Two-dimensional flows (Chapter 6 Strogatz)
Limit Cycles (Chapter 7, Strogatz) |
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第11週 |
4/29 |
Two-dimensional flows (Chapter 6 Strogatz)
Limit Cycles (Chapter 7, Strogatz) |
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第12週 |
5/06 |
Lani Wu's Introductory Lectures 1 (PM 1:30-PM4:30)
How has mathematical modeling approaches helped us to understand cell polarity network? |
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第13週 |
5/13 |
Limit Cycles (Chapter 7, Strogatz)
Hopf bifurcation (Chapter 8) |
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第14週 |
5/20 |
Noises in biology-introduction
Where are noise from?
How noisy is it?
Noise propagation.
Consequences
A collection for feedback control papers.
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第15週 |
5/27 |
Noises in Biology
Chemical Lengevin equation
Generation and propagation theories |
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第16週 |
6/03 |
Term paper discussion |
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第17週 |
6/10 |
Final exam |
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