Laboratory of Systems Biology, National Institute of Allergy and Infectious Diseases, National Institutes of Health, Bethesda, Maryland 20892, USA.
J Chem Phys. 2012 Aug 7;137(5):054104. doi: 10.1063/1.4737662.
We derive an exact Green's function of the diffusion equation for a pair of disk-shaped interacting particles in two dimensions subject to a backreaction boundary condition. Furthermore, we use the obtained function to calculate exact expressions for the survival probability and the time-dependent rate coefficient for the initially unbound pair and the survival probability of the bound state. The derived expressions will be of particular utility for the description of reversible membrane-bound reactions in cell biology.
我们推导出了一个在二维空间中，受到反作用边界条件约束的一对相互作用的圆盘状粒子的扩散方程的精确格林函数。此外，我们还使用所得到的函数来计算初始未结合对的生存概率和时变速率系数以及结合态的生存概率的精确表达式。所推导的表达式对于描述细胞生物学中可逆的膜结合反应将特别有用。
