雙物種成長與轉換模型與其生物應用

The Two-Species Logistic Growth-Transition model and the Discussion of Its Biological Application: A Mathematical Model of Heterogeneous Cancer Growth with Autocrine Signaling Pathway

李致遠(Chih-Yuan Lee)

指導教授 ： 陳義裕

共同指導教授 ： 龐寧寧(Ning-Ning Pan)

國立臺灣大學/理學院/物理研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.00341

摘要

在這篇論文中，我和學長胡耿銘一起發展了一個生物數學模型。這個模型數學結構的概念是從“Transcriptome-wide noise controls lineage choice in mammalian progenitor cells.”這篇文章延伸出來的。一開始我們探究這個模型的數學特性，想找到一些有趣的數學特性。接下來我們做了許多相關的生物數學模型的文獻回顧，發現我們的模型在生物和數學的詮釋上其實可能比其他的模型都還要好。尤其是我們的模型可以很好的對應到”癌症幹細胞假說”並與實驗數據有很好的對應。於是我們便由此發展出我們自己的模型並賦予它新的生物意涵。我們也藉由對應”癌症幹細胞假說”和實驗數據時做了許多有趣的討論。我們部分的成果已經寫成文章“A Mathematical Model of Heterogeneous Cancer Growth with Autocrine Signaling Pathway.”發表在期刊 Cell Proliferations。

關鍵字

非線性動力學 ； 生物數學模型 ； 癌症幹細胞 ； 系統生物學 ； 動態系統

並列摘要

In this thesis, I and my senior colleague, Dr. Geng-Ming Hu, develop a biological mathematical model in which the mathematical essence is derived from the paper “Transcriptome-wide noise controls lineage choice in mammalian progenitor cells”. At first, we want to find out some interesting mathematical characteristics such as limiting cycle, but we find that it’s almost impossible to do so. Then when we research associated biological model, we find that our model may have better biological and mathematical interpretation than other models and that our model could fit well with cancer stem cell hypothesis and associated experimental data. Thus we develop our own model with its new biological essence and use it to make excellent fit with associated experimental data. Part of our research is being published in Cell Proliferations under the title “A Mathematical Model of Heterogeneous Cancer Growth with Autocrine Signaling Pathway.”

並列關鍵字

nonlinear dynamics ； biological mathematical model ； cancer stem cells ； system biology ； dynamic system

參考文獻

[1] Chang, H. H., Hemberg, M., Barahona, M., Ingber, D. E., Huang, S.(2008) Transcriptome-wide noise controls lineage choice in mammalian progenitor cells. Nature,

453 , 544-548.

[2] Strogatz, S. H. (2000). Nonlinear dynamics and Chaos : with applications to physics, biology, chemistry, and engineering. Reading, Mass.: Addison-Wesley Pub.

[3] Ganguly, R. and Puri, I. K.(2006) Mathematical model for the cancer stem cell hypothesis. Cell Prolif., 39, 3-14.

[4] Ganguly, R. and Puri, I. K.(2006) Mathematical model for chemotherapeutic drug efficacy in arresting tumour growth based on the cancer stem cell hypothesis Cell Prolif., 40, 338-354.