Kuznetsov I A, Kuznetsov A V
Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA.
Department of Bioengineering, University of Pennsylvania, Philadelphia, PA 19104, USA.
Proc Math Phys Eng Sci. 2017 May;473(2201):20170045. doi: 10.1098/rspa.2017.0045. Epub 2017 May 3.
In this paper, we first develop a model of axonal transport of tubulin-associated unit (tau) protein. We determine the minimum number of parameters necessary to reproduce published experimental results, reducing the number of parameters from 18 in the full model to eight in the simplified model. We then address the following questions: Is it possible to estimate parameter values for this model using the very limited amount of published experimental data? Furthermore, is it possible to estimate confidence intervals for the determined parameters? The idea that is explored in this paper is based on using bootstrapping. Model parameters were estimated by minimizing the objective function that simulates the discrepancy between the model predictions and experimental data. Residuals were then identified by calculating the differences between the experimental data and model predictions. New, surrogate 'experimental' data were generated by randomly resampling residuals. By finding sets of best-fit parameters for a large number of surrogate data the histograms for the model parameters were produced. These histograms were then used to estimate confidence intervals for the model parameters, by using the percentile bootstrap. Once the model was calibrated, we applied it to analysing some features of tau transport that are not accessible to current experimental techniques.
在本文中，我们首先建立了一个微管相关蛋白（tau）的轴突运输模型。我们确定了重现已发表实验结果所需的最少参数数量，将完整模型中的参数数量从18个减少到简化模型中的8个。然后我们探讨以下问题：是否有可能利用非常有限的已发表实验数据来估计该模型的参数值？此外，是否有可能估计所确定参数的置信区间？本文所探讨的思路基于使用自助法。通过最小化模拟模型预测与实验数据之间差异的目标函数来估计模型参数。然后通过计算实验数据与模型预测之间的差异来确定残差。通过对残差进行随机重采样生成新的替代“实验”数据。通过为大量替代数据找到最佳拟合参数集，生成了模型参数的直方图。然后通过使用百分位数自助法，利用这些直方图来估计模型参数的置信区间。一旦模型校准完成，我们就将其应用于分析一些当前实验技术无法获取的tau运输特征。
