Differential methods for assessing sensitivity in biological models.
Differential methods for assessing sensitivity in biological models.
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DOI：
10.1371/journal.pcbi.1009598
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发表时间：
2022-06
影响因子：
4.3
通讯作者：
中科院分区：
文献类型：
--
作者：
微分灵敏度分析在拟合参数、理解不确定度和预测思想实验和实验室实验的结果方面都是不可或缺的。尽管目前有许多方法可用于执行生物模型的微分灵敏度分析，但很难确定哪种方法最适合特定的模型。在本文中，我们解释了各种微分灵敏度方法，并在一些典型的生物模型中评估了它们的价值。首先，我们解释了三种数值方法的数学基础：伴随灵敏度分析、复摄动灵敏度分析和正模灵敏度分析。然后，我们进行了四个具有启发性的案例研究。(A)用于肿瘤-免疫相互作用的CARRGO模型突出了微分敏感性分析提供的传统朴素敏感性方法之外的额外信息，(B)确定性SIR模型展示了使用二阶敏感性改进模型预测的价值，(C)随机SIR模型展示了如何在随机建模中攻击差异敏感性，以及(D)离散的出生-死亡-迁移模型说明了如何将复杂的微分敏感性摄动法推广到更广泛的生物模型中。最后，我们比较了这些方法的速度、准确性和易用性。结果表明，正向模式自动微分法的计算速度最快，而复扰动法是最容易实现的，也是最具通用性的。在过去的几十年里，数学建模已经成为生物学家工具箱中不可或缺的工具。从确定性模型到随机性模型再到统计模型，计算建模几乎无处不在地存在于生物学的各个领域。由于模型参数估计往往有噪声或依赖于了解较少的交互作用，因此研究定量和定性预测如何随着参数估计的变化而变化，特别是随着参数数量的增加而变化是至关重要的。敏感度分析是了解模型的行为如何取决于参数值的过程。敏感度分析同时量化了预测的确定性，并阐明了驱动计算模型的潜在生物学机制。虽然灵敏度分析被普遍认为是建模中的一个重要步骤，但如何最好地利用现有的差分灵敏度方法往往不清楚。在这篇手稿中，我们解释和比较各种差异敏感性方法，希望最佳实践将被广泛采用。我们强调现有软件的相对优势及其局限性。我们还提出了一种新的计算微分灵敏度的数值方法。
Differential sensitivity analysis is indispensable in fitting parameters, understanding uncertainty, and forecasting the results of both thought and lab experiments. Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to determine which method is best suited for a particular model. In this paper, we explain a variety of differential sensitivity methods and assess their value in some typical biological models. First, we explain the mathematical basis for three numerical methods: adjoint sensitivity analysis, complex perturbation sensitivity analysis, and forward mode sensitivity analysis. We then carry out four instructive case studies. (a) The CARRGO model for tumor-immune interaction highlights the additional information that differential sensitivity analysis provides beyond traditional naive sensitivity methods, (b) the deterministic SIR model demonstrates the value of using second-order sensitivity in refining model predictions, (c) the stochastic SIR model shows how differential sensitivity can be attacked in stochastic modeling, and (d) a discrete birth-death-migration model illustrates how the complex perturbation method of differential sensitivity can be generalized to a broader range of biological models. Finally, we compare the speed, accuracy, and ease of use of these methods. We find that forward mode automatic differentiation has the quickest computational time, while the complex perturbation method is the simplest to implement and the most generalizable. Over the past few decades, mathematical modeling has become an indispensable tool in the biologist’s toolbox. From deterministic to stochastic to statistical models, computational modeling is ubiquitous in almost every field of biology. Because model parameter estimates are often noisy or depend on poorly understood interactions, it is crucial to examine how both quantitative and qualitative predictions change as parameter estimates change, especially as the number of parameters increases. Sensitivity analysis is the process of understanding how a model’s behavior depends on parameter values. Sensitivity analysis simultaneously quantifies prediction certainty and clarifies the underlying biological mechanisms that drive computational models. While sensitivity analysis is universally recognized to be an important step in modeling, it is often unclear how to best leverage the available differential sensitivity methods. In this manuscript we explain and compare various differential sensitivity methods in the hope that best practices will be widely adopted. We stress the relative advantages of existing software and their limitations. We also present a new numerical technique for computing differential sensitivity.
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影响因子：
4.3
作者：
Lillacci G;Khammash M
通讯作者：
Khammash M
影响因子：
2.7
作者：
Hindmarsh, AC;Brown, PN;Woodward, CS
通讯作者：
Woodward, CS
影响因子：
10.2
作者：
Dorman, KS;Sinsheimer, JS;Lange, K
通讯作者：
Lange, K
影响因子：
10.2
作者：
HENRICI, P
通讯作者：
HENRICI, P
影响因子：
6.1
作者：
Landeros, Alfonso;Stutz, Timothy;Sehl, Mary E.
通讯作者：
Sehl, Mary E.