Multiscale Modeling &Simulation, Volume 19, Issue 1, Page 87-112, January 2021.
Investigation of dynamic processes in cell biology very often relies on the observation in two dimensions of three-dimensional (3D) biological processes. Consequently, the data are partial and statistical methods and models are required to recover the parameters describing the dynamical processes. In the case of molecules moving over the 3D surface, such as proteins on walls of bacteria cell, a large portion of the 3D surface is not observed in two-dimensional (2D)-time microscopy. It follows that biomolecules may disappear for a period of time in a region of interest, and then reappear later. Assuming Brownian motion with drift, we address the mathematical problem of the reconstruction of biomolecules trajectories on a cylindrical surface. A subregion of the cylinder is typically recorded during the observation period, and biomolecules may appear or disappear in any place of the 3D surface. The performance of the method is demonstrated on simulated particle trajectories that mimic MreB protein dynamics observed in 2D time-lapse fluorescence microscopy in rod-shaped bacteria.

中文翻译：

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封闭表面截断粒子轨迹的概率重建

多尺度建模与仿真，第 19 卷，第 1 期，第 87-112 页，2021 年 1 月。
细胞生物学中动态过程的研究通常依赖于对三维 (3D) 生物过程的二维观察。因此，数据是部分的，需要统计方法和模型来恢复描述动态过程的参数。在分子在 3D 表面上移动的情况下，例如细菌细胞壁上的蛋白质，在二维 (2D) 时间显微镜中无法观察到大部分 3D 表面。因此，生物分子可能会在感兴趣的区域内消失一段时间，然后再出现。假设有漂移的布朗运动，我们解决了在圆柱表面上重建生物分子轨迹的数学问题。通常在观察期间记录圆柱体的一个子区域，生物分子可能会出现或消失在 3D 表面的任何地方。该方法的性能在模拟粒子轨迹上得到证明，该轨迹模拟在杆状细菌的 2D 延时荧光显微镜中观察到的 MreB 蛋白动力学。