Describing the movement of molecules in reduced-dimension models.
Describing the movement of molecules in reduced-dimension models.
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DOI：
10.1038/s42003-021-02200-3
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发表时间：
2021-06-07
影响因子：
5.9
通讯作者：
Savage NS
中科院分区：
文献类型：
--
作者：
Savage NS
当使用数学模型解决空间生物学问题时，系统内的对称性通常被用来通过减少其物理维度来简化问题。在降维模型中，分子运动被限制在降维范围内，从而改变了分子运动的性质。分子运动的这种变化可以导致完全和简化系统中定量甚至定性的不同结果。在这份手稿中，我们讨论的条件下，限制分子运动的降维模型准确地近似分子运动在整个系统。对于那些不满足条件的体系，我们提出了一种在降维模型中近似无限制分子运动的一般方法。我们将推导出一个数学上鲁棒的有限差分方法，用于求解一维降维模型中的二维扩散方程。这里描述的方法可以用来提高许多降维模型的精度，同时保留系统简化的好处。Natasha Savage开发了一种通用的有限差分方法，用于使用1D简化模型对2D扩散进行建模。该方法可以有效地提高许多降维模型的精度，同时保留系统简化的优点。
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. Natasha Savage develops a general finite difference method for modeling 2D diffusion using a 1D reduced model. This method can be useful to improve the accuracy of many reduced-dimension models while retaining benefits of system simplification.
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DOI：
10.1098/rstb.1952.0012
发表时间：
1952-01-01
期刊：
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES B-BIOLOGICAL SCIENCES
影响因子：
--
作者：
TURING, AM
通讯作者：
TURING, AM
中性粒细胞梯度传感和极化的数学模型。
影响因子：
4.3
作者：
Onsum M;Rao CV
通讯作者：
Rao CV
影响因子：
2.1
作者：
Brena-Medina, V.;Champneys, A. R.;Ward, M. J.
通讯作者：
Ward, M. J.
影响因子：
4.3
作者：
Chiou, Jian-Geng;Ramirez, Samuel A.;Lew, Daniel J.
通讯作者：
Lew, Daniel J.
DOI：
10.1111/tra.12008
发表时间：
2012-12
期刊：
Traffic (Copenhagen, Denmark)
影响因子：
--
作者：
Kang M;Day CA;Kenworthy AK;DiBenedetto E
通讯作者：
DiBenedetto E