摘要翻译：
本研究发展了一个描述三维膜转化的方程，该方程通过膜上形态发生密度分布调节其组成细胞的增殖。该方程是在映射到膜上的二维坐标系中展开的，称为膜坐标。当膜膨胀时，膜坐标以同样的方式膨胀，因此膜在坐标中是不变的。在膜坐标系中，膜的变换用度量张量的时间导数方程来描述。通过定义形态发生密度分布与细胞分裂方向和速率之间的关系，根据形态发生分布得到膜转化轨迹。用数值方法给出了膜变换的一个算例。
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英文标题：
《Metric dynamics for membrane transformation through regulated cell
  proliferation》
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作者：
Hiroshi C. Ito
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最新提交年份：
2016
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  This study develops an equation for describing three-dimensional membrane transformation through proliferation of its component cells regulated by morphogen density distributions on the membrane. The equation is developed in a two-dimensional coordinate system mapped on the membrane, referred to as the membrane coordinates. When the membrane expands, the membrane coordinates expand in the same manner so that the membrane is invariant in the coordinates. In the membrane coordinate system, the transformation of membrane is described with a time-derivative equation for metric tensors. By defining relationships between morphogen density distributions and the direction and rate of cell division, trajectories of membrane transformation are obtained in terms of the morphogen distributions. An example of the membrane transformation is shown numerically.
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PDF链接：
https://arxiv.org/pdf/1605.01893