Dinh Vu, Rundell Ann E, Buzzard Gregery T
Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907, USA,
Bull Math Biol. 2014 Mar;76(3):597-626. doi: 10.1007/s11538-014-9935-9. Epub 2014 Feb 13.
We address the problem of using nonlinear models to design experiments to characterize the dynamics of cellular processes by using the approach of the Maximally Informative Next Experiment (MINE), which was introduced in W. Dong et al. (PLoS ONE 3(8):e3105, 2008) and independently in M.M. Donahue et al. (IET Syst. Biol. 4:249-262, 2010). In this approach, existing data is used to define a probability distribution on the parameters; the next measurement point is the one that yields the largest model output variance with this distribution. Building upon this approach, we introduce the Expected Dynamics Estimator (EDE), which is the expected value using this distribution of the output as a function of time. We prove the consistency of this estimator (uniform convergence to true dynamics) even when the chosen experiments cluster in a finite set of points. We extend this proof of consistency to various practical assumptions on noisy data and moderate levels of model mismatch. Through the derivation and proof, we develop a relaxed version of MINE that is more computationally tractable and robust than the original formulation. The results are illustrated with numerical examples on two nonlinear ordinary differential equation models of biomolecular and cellular processes.
我们通过使用最大信息下一个实验（MINE）方法来解决利用非线性模型设计实验以表征细胞过程动力学的问题，该方法由W. Dong等人（《公共科学图书馆·综合》3(8):e3105，2008年）以及M.M. Donahue等人（《IET系统生物学》4:249 - 262，2010年）分别独立提出。在这种方法中，现有数据用于定义参数上的概率分布；下一个测量点是在此分布下产生最大模型输出方差的点。基于此方法，我们引入了期望动力学估计器（EDE），它是使用该分布将输出作为时间函数的期望值。我们证明了即使所选实验聚集在有限的一组点上，该估计器也是一致的（一致收敛到真实动力学）。我们将这种一致性证明扩展到关于噪声数据和适度模型失配水平下的各种实际假设。通过推导和证明，我们开发了一个比原始公式在计算上更易于处理且更稳健的MINE松弛版本。结果通过关于生物分子和细胞过程的两个非线性常微分方程模型的数值示例进行说明。
