Meinecke Lina
Department of Information Technology, Uppsala University, Uppsala, Sweden.
University of California at Irvine, Irvine, CA, USA.
Bull Math Biol. 2017 Nov;79(11):2672-2695. doi: 10.1007/s11538-017-0346-6. Epub 2017 Sep 18.
We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space-dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size, and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.
我们提出了一种多尺度方法来模拟拥挤环境中的扩散及其对反应速率的影响。生物系统中的扩散通常通过离散空间跳跃过程进行建模，以便捕捉生物系统固有的噪声，这在低拷贝数情况下变得很重要。为了有效地模拟拥挤细胞环境中的扩散，我们根据局部首次退出时间计算这个介观模型中的跳跃速率，该时间考虑了拥挤分子的微观位置，而扩散分子则在更粗的笛卡尔网格上跳跃。然后，我们从所得的跳跃速率中提取宏观描述，其中排除体积效应由具有空间依赖性扩散系数的扩散方程建模。拥挤分子可以具有任意形状和大小，数值实验表明，这些因素与扩散分子的大小一起，对扩散运动减小的幅度起着关键作用。当校正反应速率以适应改变后的扩散时，我们可以表明，分子拥挤根据障碍物密度的局部波动增强或抑制化学反应。
