本論文提出一種可在非平衡生物膜上形成具有特徵大小的區塊的模型，並以蒙地卡羅模擬法來探討此模型與生物系統之關聯。本模型考慮由一種脂質分子與一種兩態活性分子組成之系統。兩種具有不同交互作用的特例被提出並討論之：(１)激發態活性分子傾向聚集﹔(２)基態活性分子傾向聚集。我們發現以下的結論：(i)藉由調整兩態活性分子的活性大小，可調控膜上區塊的大小。(ii)活性分子的密度與膜曲率的耦合可使區塊大小具有形成特徵大小的上限。(iii) 活性分子在膜上的擴散率亦與上述兩特性有關。

We propose a model that leads to the formation of non-equilibrium
finite-size domains in a biological membrane. Our model considers
the active conformational change of the inclusions and the coupling
between inclusion density and membrane curvature. Two special cases
with different interactions are studied by Monte Carlo simulations.
In case (i) exited state inclusions prefer to aggregate. In case
(ii) ground state inclusions prefer to aggregate. When the inclusion
density is not coupled to the local membrane curvature, in case (i)
the typical length scale ($sqrt{M}$) of the inclusion clusters
shows weak dependence on the excitation rate ($K_{on}$) of the
inclusions for a wide range of $K_{on}$ but increases fast when
$K_{on}$ becomes sufficiently large; in case (ii) $sqrt{M}sim
{K_{on}}^{-frac{1}{3}}$ for a wide range of $K_{on}$. When the
inclusion density is coupled to the local membrane curvature, the
curvature coupling provides the upper limit of the inclusion
clusters. In case (i) (case (ii)), the formation of the inclusions
is suppressed when $K_{off}$ ($K_{on}$) is sufficiently large such
that the ground state (excited state) inclusions do not have
sufficient time to aggregate. We also find that the mobility of an
inclusion in the membrane depends on inclusion-curvature coupling.
Our study suggests possible mechanisms that produce finite-size
domains in biological membranes.

[1] H. Lodish et al., Molecular cell biology, 3rd ed (W.H. Freeman, New York, 1995).
[2] G. Vereb et al, Proc. Natl. Acad. Sci. USA 100, 8053, (2003).
[3] S.L. Veatch, I.V. Polozov, K. Gawrisch, and S.L. Keller, Biophys. J. 86, 2910,
(2004).
[4] M.S. Turner, P. Sens, and N.D. Socci, Phys. Rev. Lett. 95, 168301, (2005).
[5] L. Forest, Europhys. Lett. 71, 508, (2005).
[6] K. Simons and E. Ikonon, Nature, 387, 569, (1997).
[7] E. Sparr, Langmuir 15, 6950, (1999).
[8] H.Y. Chen, Phys. Rev. Lett. 92, 16, (2004).
[9] T.R. Weikl, Phys. Rev. E 66, 061915, (2002).
[10] M.C. Sabra and O.G. Mouritsen, Biophys. J. 74, 745, (1998).
[11] H. Strey, M. Peterson, and E. Sackmann, Biophys. J. 69, 478, (1995).
[12] Needham. D. and R. M. Hochmuth, Biophys. J. 61, 1664, (1992).
48
[13] K. Binder and D.W. Heermann, Monte Carlo Simulation in Statistical Physics.
2nd corrected ed. (Springer-Verlag, Berlin, 1992).
[14] W.R. Gibbs, Computaion in Modern Physics. (World Scientific, Singapore,
1994).
[15] T.R. Weikl and R. Lipowsky, Biophys. J. 87, 3665, (2004).
[16] M. Seul, N. Y. Morgan, and C. Sire, Phys. Rev. Lett. 73, 2284, (1994).
[17] A. J. Bray, Adv. Phys. 43, 357, (1994).
[18] L. C. -L Lin and F. L. H. Brown, Biophys. J. 86, 764, (2004).
[19] M. Doi and S. F. Edwards, The Theory of Polymer Dynamics. (Clarendon Press,
Oxford, 1993).
[20] H-G D¨obereiner, E. Evanc, U. Seifert, and M. Wartis, Phys. Rev. Lett. 75, 3360,
(1995).