本論文提出研究由配體黏著於生物膜上所引發的細胞攝入作用 (ligand induced endocytosis)的理論。 我們考慮一分隔內外溶液的生物膜，且只有外溶液中含有可黏著於生物膜上之粒子，這些粒子黏著於生物膜上後，會聚集形成區塊 (domains)；在生物膜上，夠大的區塊會形成囊泡而離開生物膜進入內溶液。我們的研究顯示，當系統達到穩定態 (steady state) 時 (1) 在合理的粒子吸收率 jon，解吸附率 joff，以及一個囊泡可以擁有的粒子數n*之下，區塊均是獨立成長的。(2) 當粒子的解吸附率夠大，而吸收率與一個囊泡可以擁有的粒子數夠小的時候，大部分的粒子在未加入區塊之前都離開生物膜數次。在這個情況下，每單位時間產生的囊泡數目與 (jon/joff)2 成正比。(3) 當粒子的吸收率夠大的時候，大部分的粒子在離開生物膜之前就已經加入區塊，且每單位時間產生的囊泡數目與粒子的吸收率成正比。 This thesis presents a theoretical analysis for ligand-induced endocytosis. We consider a flat membrane that separates the inner and outer fluids, the outer fluid contains particles that can be absorbed on the membrane and aggregate to form domains and the inner fluid does not, domains with sufficiently large size depart from the membrane and enter the inner fluid by vesicle fission. Assuming domain growth to be an irreversible diffusion-limited process, our study reveals that in the steady state: (i) At reasonable absorption rate jon, desorption rate joff and n*, number of particles in a vesicle, domains grow independently. (ii) When joff is sufficiently large, jon and n* are sufficiently small, particles leave the membrane many times before finally joining domains and number of vesicles produced per unit time scales as (jon/joff)2. (iii) When jon is sufficiently large, most particles absorbed on the membrane join domains before leaving the membrane and number of vesicles produced per unit time is proportional to number of particles absorbed on the membrane per unit time.
