论文标题
随机切换扩散与部分反应性表面
Stochastically switching diffusion with partially reactive surfaces
论文作者
论文摘要
在本文中，我们开发了基于遭遇的方法的混合版本，用于在反应性表面上扩散介导的吸收，该方法考虑了扩散粒子构象状态的随机切换。为简单起见，我们考虑了一个两态模型，其中表面吸收的概率取决于当前的粒子状态以及粒子在每个状态的表面附近花费的时间。后者由一对本地时间$ \ ell_ {n，t} $，$ n = 0,1 $确定，这是布朗功能，可以在时间间隔$ [0，t] $中跟踪粒子表面相遇。我们通过为一对通用的繁殖器$ p_n（\ x，\ ell_0，\ ell_1，t）$构造一个差异Chapman-Kolmogorov方程来进行，其中$ p_n $是集合$（\ x_t，\ ell_ ell_ {0，t}，wery p__t}，p__t}，wery \ ell_ $， $ \ x_t $表示粒子位置，$ n_t $是相应的构象状态。相对于$ \ ell_0，\ ell_1 $，执行双拉拉斯变换会产生一个有效的方程系统，描述了在有界域$ω$中扩散的方程式，在$ \ \partialΩ$上，在两个robin边界条件之间正在切换。相应的常数反应性为$κ__j= d z_j $，$ j = 0,1 $，其中$ z_j $是对应于$ \ ell_j $和$ d $的laplace变量，是扩散性。给定对拉普拉斯空间中传播器的解决方案，我们为部分吸收构建了相应的概率模型，该模型需要相对于$ z_0，z_1 $找到逆拉普拉斯变换。我们通过考虑将粒子扩散在半线上的扩散，边界在$ x = 0 $之间有效切换在完全反射和部分吸收状态之间来说明理论。最后，我们指出了如何使用Dirichlet到Neumann运算符的光谱理论将分析扩展到更高的空间维度。
In this paper we develop a hybrid version of the encounter-based approach to diffusion-mediated absorption at a reactive surface, which takes into account stochastic switching of a diffusing particle's conformational state. For simplicity, we consider a two-state model in which the probability of surface absorption depends on the current particle state and the amount of time the particle has spent in a neighborhood of the surface in each state. The latter is determined by a pair of local times $\ell_{n,t}$, $n=0,1$, which are Brownian functionals that keep track of particle-surface encounters over the time interval $[0,t]$. We proceed by constructing a differential Chapman-Kolmogorov equation for a pair of generalized propagators $P_n(\x,\ell_0,\ell_1,t)$, where $P_n$ is the joint probability density for the set $(\X_t,\ell_{0,t},\ell_{1,t})$ when $N_t=n$, where $\X_t$ denotes the particle position and $N_t$ is the corresponding conformational state. Performing a double Laplace transform with respect to $\ell_0,\ell_1$ yields an effective system of equations describing diffusion in a bounded domain $Ω$, in which there is switching between two Robin boundary conditions on $\partial Ω$. The corresponding constant reactivities are $κ_j=D z_j$, $j=0,1$, where $z_j$ is the Laplace variable corresponding to $\ell_j$ and $D$ is the diffusivity. Given the solution for the propagators in Laplace space, we construct a corresponding probabilistic model for partial absorption, which requires finding the inverse Laplace transform with respect to $z_0,z_1$. We illustrate the theory by considering diffusion of a particle on the half-line with the boundary at $x=0$ effectively switching between a totally reflecting and a partially absorbing state. Finally, we indicate how to extend the analysis to higher spatial dimensions using the spectral theory of Dirichlet-to-Neumann operators.
