论文标题
描述分子在降低模型中的运动
Describing the movement of molecules in reduced-dimension models
论文作者
论文摘要
在使用数学模型解决空间生物学问题时，通常利用系统内的对称性来通过减少其物理维度来简化问题。在减少尺寸的模型中，分子运动仅限于降低的尺寸，改变了分子运动的性质。分子运动的这种变化可以在整体和减少的系统中导致定量甚至在质量上不同的结果。在此手稿中，我们讨论了在降低模型中限制分子运动的条件，可以准确地近似整个系统中的分子运动。对于那些不满足条件的系统，我们提出了一种近似降低模型中不受限制分子运动的通用方法。我们将得出一种在1D降低数模型中求解2D扩散方程的数学稳健，有限的差异方法。此处描述的方法可用于提高许多减少尺寸模型的准确性，同时保留系统简化的益处。
When addressing spatial biological questions using mathematical models, symmetries within the system are often exploited to simplify the problem by reducing its physical dimension. In a reduced-dimension model molecular movement is restricted to the reduced dimension, changing the nature of molecular movement. This change in molecular movement can lead to quantitatively and even qualitatively different results in the full and reduced systems. Within this manuscript we discuss the condition under which restricted molecular movement in reduced-dimension models accurately approximates molecular movement in the full system. For those systems which do not satisfy the condition, we present a general method for approximating unrestricted molecular movement in reduced-dimension models. We will derive a mathematically robust, finite difference method for solving the 2D diffusion equation within a 1D reduced-dimension model. The methods described here can be used to improve the accuracy of many reduced-dimension models while retaining benefits of system simplification.
