KIF1A是一種單頭馬達蛋白（single-headed motor protein），沿著微管（microtubule）朝正端方向運動。KIF1A和其他分子馬達相同，皆利用水解ATP及水解後產物的釋放而產生機械運動。
文中提出KIF1A的運動模型，此模型乃基於ATP水解循環及KIF1A的運動行為所建立，此運動過程可分成四個步驟：起動、分離、隨機晃動及再結合等。
在模型中，我們利用酵素動力學及隨機過程分析，計算出KIF1A之平均位移與位移變異數。並推導出平均位移與負載的關係式，發現當外力負載增加，KIF1A的平均位移呈下降趨勢。
最後，本文採用Langevin equation描述布朗運動的效應，以及利用Fokker-Planck equation推導KIF1A在步進運動的機率密度。分析結果顯示，不同位移變異數大小，KIF1A則呈現不同的機率分佈。而反應時間則是影響位移變異數的主要因素。

KIF1A is a one-head motor protein that moves along microtubule toward plus end. Like the other molecular motors, KIF1A use ATP hydrolysis and product release to produce movement.

In this paper, we construct a model to analyze KIF1A movement, that was built up ATP hydrolyze cycle and motion behavior of KIF1A. The process is including four steps: start, detach, oscillate stochastic, and re-bind.

In this model, we use the enzyme kinetics and stochastic processes analysis for computing the mean displacement and standard deviation displacement. Then, we calculate the mean displacement with external force formula. When the external force raise, the mean displacement is decreased.

Finally, we adopt Langevin equation to describe the Brownian motion effect and use Forkker-planck equation to calculate probability density for stepping motion. The analysis reveals the variation of probability distribution with standard deviation displacement. The main factor in influencing standard deviation displacement is reaction time.

1.Y. Okada, N. Hirokawa (1999). A Processive Single-Headed Motor: Kinesin Superfamily Protein KIF1A. SCIENCE 283,1152-1157.

2.R. D. Vale, E. Sabin, R. Case, C. Hart, and R. Fletterick (2000). Searching for kinesin’s mechanical amplifier. Phil. Trans. R. Soc. Lond. B. 355, 449-457.

3.Y. Okada, N. Hirokawa (2000). Mechanism of the single-headed processivity: Diffusional anchoring between the K-loop of kinesin and the C terminus of tubulin. PNAS 97,640-645.

4.R. D. Vale and R. A. Milligan (2000). The way things move: looking under the hood of molecular motor proteins. Science 288, 88-95.

5.M. Kikkawa, E. P. Sablin, Y. Okada, H. Yajima, R. J. Fletterick, and N. Hirokawa (2001). Switch-based mechanism of kinesin motors. Nature 411, 439-445.

6.D. H. Seog, D. H. Lee, and S. K. Lee (2004). Molecular Motor Proteins of the Kinesin Superfamily Proteins (KIFs): Structure. Cargo and Disease. J Korean Med Sci 19, 1-7.

7.簡清富 (2003).運動素於外加負載下之運動分析,國立成功大學工程科學系碩士論文.

8.林信成 (2004).運動素於微管之步進分析,國立成功大學工程科學系碩士論文.

9.簡嘉佑 (2004).運動素結構之模擬分析,國立成功大學工程科學系碩士論文.

10.郭光輝 (2003).生物分子馬達專利地圖及分析生物分子馬達地圖, 行政院國家科學委員會技術資料中心,64-89.

11.李盛,黃偉達 (2002).構築生命：蛋白質、核酸與酶, 世潮出版有限公司.

12.葉東柏 (2002).生物化學精要, 藝軒出版有限公司.

13.R. Nitta, M. Kikkawa, Y. Okada, and N. Hirokawa (2004). KIF1A Alternately Uses Two Loops to Bind Microtubules. Science 305, 678-683.

14.Y. Okada, H. Higuchi, and N. Hirokawa (2003). Processivity of the single-headed kinesin KIF1A through biased binding to tubulin. Nature 424, 574-577.

15.A. B. Kolomeisky and M. E. Fisher (2001). Force-velocity relation for growing microtubules. Biol. J. 80, 149-154.

16.E. Nelson (1967). Dynamic Theories of Brownian motion. Princeton Univ. 5-17.

17.http://www.dls.ym.edu.tw/neuroscience/cells_c.html

18.M. Kikkawa, Y. Okada, and N. Hirokawa (2000). 15 angstrom Resolution Model of the Monomeric Kinesin Motor, KIF1A. Cell, 100, 241-252.

19.H. Risken (1989). The Fokker-Planck equation: methods of solution and applications. New York: Springer-Verlag.

20.D. Keller and C. Bustamante (2000). The Mechanochemistry of Molecular Motors. Biophysical Journal 78, 541-566.

21.A. Mogilner, H. Wang, T. Elston, and G. Oster (2002). Molecular motors: theory and experiment. In: Computational Cell Biology. New York: Springer-Verlag.

22.N. Hirokawa and R. Takemura (2004). Kinesin superfamily proteins and their various functions and dynamics. Experimental Cell Research 301,50-59.