Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells
Traction force microscopy with optimized regularization and automated Bayesian parameter selection for comparing cells
复制标题
DOI：
10.1038/s41598-018-36896-x
复制
发表时间：
2019-01-24
影响因子：
4.6
通讯作者：
Sabass, Benedikt
中科院分区：
文献类型：
--
作者：
Huang, Yunfei;Schell, Christoph;Sabass, Benedikt
贴壁细胞对它们的环境施加牵引力，使它们能够迁移，保持组织完整性，并在发育形态发生期间形成复杂的多细胞结构。牵引力显微镜（TFM）能够测量弹性基底上的牵引力，从而以无扰动的方式提供细胞力学的定量信息。在TFM中，牵引力通常通过线性系统的解来计算，对于某些方法，该线性系统由于欠采样输入数据、采集噪声和大的条件数而变得复杂。因此，标准的TFM算法采用数据过滤或正则化。然而，这些方法需要手动选择滤波器或正则化参数，因此表现出很大程度的主观性。当要比较不同条件下的小区时，这个缺点尤其严重，因为需要针对每种情况调整最佳噪声抑制，这总是导致系统误差。在这里，我们系统地测试了计算机视觉和贝叶斯推理的新方法在TFM中解决逆问题的性能。我们比较了两个经典的计划，L1-和L2-正则化，与三个以前未经测试的计划，即弹性网络正则化，近端梯度套索，近端梯度弹性网络。总的来说，我们发现结合L1和L2正则化的弹性网络正则化在牵引重建的准确性方面优于所有其他方法。接下来，我们开发了两种方法，贝叶斯L2正则化和高级贝叶斯L2正则化，用于自动优化L2正则化。使用人工数据和实验数据，我们表明，这些方法使强大的重建牵引力，而不需要一个困难的选择正则化参数，专门为每个数据集。因此，贝叶斯方法可以减轻在不同条件下比较细胞牵引力所固有的相当大的不确定性。
Adherent cells exert traction forces on to their environment which allows them to migrate, to maintain tissue integrity, and to form complex multicellular structures during developmental morphogenesis. Traction force microscopy (TFM) enables the measurement of traction forces on an elastic substrate and thereby provides quantitative information on cellular mechanics in a perturbation-free fashion. In TFM, traction is usually calculated via the solution of a linear system, which is complicated by undersampled input data, acquisition noise, and large condition numbers for some methods. Therefore, standard TFM algorithms either employ data filtering or regularization. However, these approaches require a manual selection of filter-or regularization parameters and consequently exhibit a substantial degree of subjectiveness. This shortcoming is particularly serious when cells in different conditions are to be compared because optimal noise suppression needs to be adapted for every situation, which invariably results in systematic errors. Here, we systematically test the performance of new methods from computer vision and Bayesian inference for solving the inverse problem in TFM. We compare two classical schemes, L1- and L2-regularization, with three previously untested schemes, namely Elastic Net regularization, Proximal Gradient Lasso, and Proximal Gradient Elastic Net. Overall, we find that Elastic Net regularization, which combines L1 and L2 regularization, outperforms all other methods with regard to accuracy of traction reconstruction. Next, we develop two methods, Bayesian L2 regularization and Advanced Bayesian L2 regularization, for automatic, optimal L2 regularization. Using artificial data and experimental data, we show that these methods enable robust reconstruction of traction without requiring a difficult selection of regularization parameters specifically for each data set. Thus, Bayesian methods can mitigate the considerable uncertainty inherent in comparing cellular tractions in different conditions.