生物馬達的動力特性

Abstract

在1983年Tsong(鄭天佑)指出可在實驗上運用交流電場來驅動鈉鉀離子幫浦(Na+,k+ ATPase)的方法，並根據實驗結果建立了電構型耦合理論(Theory of electroconformational coupling，TEC)，之後便有許多針對這個系統的相關實驗和理論方面的研究，如簡化的二階動力模型，四階動力模型，外加直流、交流電場以及有不同類型噪聲環境下系統的傳輸效率問題等等。 本文主要研究的系統為鈉鉀離子幫浦四階動力系統模型，第一章是鈉鉀離子幫浦原理的簡介，第二章探討TEC理論的四階模型建構過程，並比較系統狀態與點源項的動力行為，最後將分析的結果推廣至類似情形的高階環狀動力系統。第三章考慮兩種特殊且易於求解的狀況──去除速率係數的指數項，以及速率係數受電場影響相同的情形，並討論在系統中離子能夠產生傳輸的成因。第四章討論在外加交流電場振幅不大的情形，利用傅立葉級數展開的方法來求出該模型的系統狀態解以及系統離子傳輸的平均流量和外加電場頻率之間的關係。第五章是總結以及展望，我們得出了點源解逼近點源項的動力行為以及系統可以存在淨流量的條件，也得出了外加電場頻率跟淨流量之間的關係，未來的研究則可以探討外加噪聲項和系統傳輸之間的關係。

In 1983,Tsong , T. Y. indicated that we could perform an experiment which Na+ K+ ATPase pump cations could be caused by an applied alternating electric field. Then people establish the theory of electroconformational coupling(TEC) according to experimental data. Afterward many theoretical and experimental research results were arose,e.g., the dynamical behavior of the two-states kinetic model and the four-states kinetic model,the optimum efficiency problems of the transport of cations activated by different applied field like constant electric filed ,oscillating electric field and eletric noise, etc. In the thesis we focus on the four-states kinetic model.We introduce the physiological representation of Na+Ka+ ion pumps and use the point source terms of the kinetic equations to approach the dynamical behavior of the system, and the relation between the average flux of the transmission of cations and the frequecy of applied oscillating electric field can be derived by Fourier series expansion method as well.