Mayawala Kapil, Vlachos Dionisios G, Edwards Jeremy S
Department of Chemical Engineering, 150 Academy Street, University of Delaware, Newark, DE 19716, USA.
Biophys Chem. 2006 Jun 1;121(3):194-208. doi: 10.1016/j.bpc.2006.01.008. Epub 2006 Feb 28.
Bimolecular reactions in the plasma membrane, such as receptor dimerization, are a key signaling step for many signaling systems. For receptors to dimerize, they must first diffuse until a collision happens, upon which a dimerization reaction may occur. Therefore, study of the dynamics of cell signaling on the membrane may require the use of a spatial modeling framework. Despite the availability of spatial simulation methods, e.g., stochastic spatial Monte Carlo (MC) simulation and partial differential equation (PDE) based approaches, many biological models invoke well-mixed assumptions without completely evaluating the importance of spatial organization. Whether one is to utilize a spatial or non-spatial simulation framework is therefore an important decision. In order to evaluate the importance of spatial effects a priori, i.e., without performing simulations, we have assessed the applicability of a dimensionless number, known as second Damköhler number (Da), defined here as the ratio of time scales of collision and reaction, for 2-dimensional bimolecular reactions. Our study shows that dimerization reactions in the plasma membrane with Da approximately >0.1 (tested in the receptor density range of 10(2)-10(5)/microm(2)) require spatial modeling. We also evaluated the effective reaction rate constants of MC and simple deterministic PDEs. Our simulations show that the effective reaction rate constant decreases with time due to time dependent changes in the spatial distribution of receptors. As a result, the effective reaction rate constant of simple PDEs can differ from that of MC by up to two orders of magnitude. Furthermore, we show that the fluctuations in the number of copies of signaling proteins (noise) may also depend on the diffusion properties of the system. Finally, we used the spatial MC model to explore the effect of plasma membrane heterogeneities, such as receptor localization and reduced diffusivity, on the dimerization rate. Interestingly, our simulations show that localization of epidermal growth factor receptor (EGFR) can cause the diffusion limited dimerization rate to be up to two orders of magnitude higher at higher average receptor densities reported for cancer cells, as compared to a normal cell.
质膜中的双分子反应，如受体二聚化，是许多信号系统的关键信号步骤。受体要发生二聚化，必须先扩散，直到发生碰撞，此时才可能发生二聚化反应。因此，研究膜上细胞信号传导的动力学可能需要使用空间建模框架。尽管有空间模拟方法，例如随机空间蒙特卡罗（MC）模拟和基于偏微分方程（PDE）的方法，但许多生物学模型仍采用均相假设，而没有完全评估空间组织的重要性。因此，选择使用空间还是非空间模拟框架是一个重要的决定。为了先验地评估空间效应的重要性，即在不进行模拟的情况下，我们评估了一个无量纲数（称为第二达姆科勒数（Da））对于二维双分子反应的适用性，这里将其定义为碰撞和反应时间尺度的比值。我们的研究表明，质膜中的二聚化反应，当Da约大于0.1时（在受体密度范围为10² - 10⁵/μm²内进行测试），需要进行空间建模。我们还评估了MC和简单确定性PDE的有效反应速率常数。我们的模拟表明，由于受体空间分布随时间的变化，有效反应速率常数会随时间降低。结果，简单PDE的有效反应速率常数与MC的有效反应速率常数可能相差高达两个数量级。此外，我们表明信号蛋白拷贝数的波动（噪声）也可能取决于系统的扩散特性。最后，我们使用空间MC模型来探索质膜异质性，如受体定位和扩散率降低，对二聚化速率的影响。有趣的是，我们的模拟表明，与正常细胞相比，在癌细胞报道的较高平均受体密度下，表皮生长因子受体（EGFR）的定位可使扩散限制的二聚化速率提高高达两个数量级。
