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The finite state projection based Fisher information matrix approach to estimate information and optimize single-cell experiments

机译：基于有限状态投影的Fisher信息矩阵方法来估计信息并优化单细胞实验

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Modern optical imaging experiments not only measure single-cell and single-molecule dynamics with high precision, but they can also perturb the cellular environment in myriad controlled and novel settings. Techniques, such as single-molecule fluorescence in-situ hybridization, microfluidics, and optogenetics, have opened the door to a large number of potential experiments, which begs the question of how to choose the best possible experiment. The Fisher information matrix (FIM) estimates how well potential experiments will constrain model parameters and can be used to design optimal experiments. Here, we introduce the finite state projection (FSP) based FIM, which uses the formalism of the chemical master equation to derive and compute the FIM. The FSP-FIM makes no assumptions about the distribution shapes of single-cell data, and it does not require precise measurements of higher order moments of such distributions. We validate the FSP-FIM against well-known Fisher information results for the simple case of constitutive gene expression. We then use numerical simulations to demonstrate the use of the FSP-FIM to optimize the timing of single-cell experiments with more complex, non-Gaussian fluctuations. We validate optimal simulated experiments determined using the FSP-FIM with Monte-Carlo approaches and contrast these to experiment designs chosen by traditional analyses that assume Gaussian fluctuations or use the central limit theorem. By systematically designing experiments to use all of the measurable fluctuations, our method enables a key step to improve co-design of experiments and quantitative models.
机译：现代光学成像实验不仅可以高精度测量单细胞和单分子动力学，而且还可以在无数受控和新颖的环境中干扰细胞环境。单分子荧光原位杂交，微流体技术和光遗传学等技术为大量潜在的实验打开了大门，这引出了如何选择最佳实验的问题。 Fisher信息矩阵（FIM）估算了潜在实验对模型参数的约束程度，可用于设计最佳实验。在这里，我们介绍基于有限状态投影（FSP）的FIM，它使用化学主方程的形式来推导和计算FIM。 FSP-FIM不对单细胞数据的分布形状做任何假设，也不需要对此类分布的高阶矩进行精确测量。我们针对组成性基因表达的简单案例，针对著名的Fisher信息结果验证了FSP-FIM。然后，我们使用数值模拟来演示FSP-FIM的使用，以优化具有更复杂的非高斯起伏的单细胞实验的时序。我们验证了使用FSP-FIM和蒙特卡洛方法确定的最佳模拟实验，并将这些实验与采用高斯波动或使用中心极限定理的传统分析选择的实验设计进行了对比。通过系统地设计实验以使用所有可测量的波动，我们的方法使关键步骤得以改进实验和定量模型的协同设计。

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