Neu John C, Krassowska Wanda
Department of Mathematics, University of California at Berkeley, Berkeley, California 94720, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Feb;67(2 Pt 1):021915. doi: 10.1103/PhysRevE.67.021915. Epub 2003 Feb 27.
The Smoluchowski equation (SE), which describes the evolution of pores created by electric shocks, cannot be applied to modeling large and long-lived pores for two reasons: (1) it does not predict pores of radius above 20 nm without also predicting membrane rupture; (2) it does not predict postshock growth of pores. This study proposes a model in which pores are coupled by membrane tension, resulting in a nonlinear generalization of SE. The predictions of the model are explored using examples of homogeneous (all pore radii r are equal) and heterogeneous (0<or=r<or=r(max)) distributions of pores. Pores in a homogeneous population either shrink to zero or assume a stable radius corresponding to the minimum of the bilayer energy. For a heterogeneous population, such a stable radius does not exist. All pores, except r(max), shrink to zero and r(max) grows to infinity. However, the unbounded growth of r(max) is not physical because the number of pores per cell decreases in time and the continuum model loses validity. When the continuum formulation is replaced by the discrete one, the model predicts the coarsening process: all pores, except r(max), shrink to zero and r(max) assumes a stable radius. Thus, the model with tension-coupled pores does not predict membrane rupture and the predicted postshock growth of pores is consistent with experimental evidence.
描述电激产生的孔演变的斯莫卢霍夫斯基方程（SE），由于两个原因不能应用于对大尺寸且寿命长的孔进行建模：（1）它在不预测膜破裂的情况下，无法预测半径超过20纳米的孔；（2）它无法预测电击后孔的生长。本研究提出了一个模型，其中孔通过膜张力相互耦合，从而得到SE的非线性推广。使用孔的均匀分布（所有孔半径r相等）和非均匀分布（0≤r≤r(max)）的例子来探究该模型的预测结果。均匀群体中的孔要么收缩至零，要么呈现对应双层膜能量最小值的稳定半径。对于非均匀群体，不存在这样的稳定半径。除r(max)外的所有孔都收缩至零，而r(max)则增长至无穷大。然而，r(max)的无界增长不符合实际情况，因为每个细胞中的孔数量会随时间减少，连续体模型会失效。当用离散形式取代连续体公式时，该模型预测了粗化过程：除r(max)外的所有孔都收缩至零，而r(max)呈现稳定半径。因此，具有张力耦合孔的模型不会预测膜破裂，且预测的电击后孔的生长与实验证据一致。
