Regression analysis for constraining free parameters in electrophysiological models of cardiac cells.
Regression analysis for constraining free parameters in electrophysiological models of cardiac cells.
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DOI：
10.1371/journal.pcbi.1000914
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发表时间：
2010-09-02
影响因子：
4.3
通讯作者：
Sobie EA
中科院分区：
文献类型：
--
作者：
Sarkar AX;Sobie EA
计算生物学中的一个主要挑战是约束数学模型中的自由参数。调整参数以使给定的模型输出更真实，有时会对其他模型行为产生意外和不希望的影响。在这里，我们扩展了一个基于回归的参数敏感性分析的方法，并表明，一个简单的程序可以唯一地定义在一个众所周知的模型的人心室肌细胞的离子电导。通过随机化离子电导，运行重复模拟以测量生理输出，然后分别收集随机化参数和模拟结果作为“输入”和“输出”矩阵，来分析模型的参数灵敏度。多变量回归导出矩阵，其元素指示电导的变化如何影响模型输出。我们在这里表明，如果线性无关的输出的数量等于输入的数量，回归矩阵可以被反转。这是重要的，因为它意味着逆矩阵可以指定生成模型输出的特定组合所需的离子电导。将这一想法应用于所测试的肌细胞模型，我们发现大多数离子电导可以精确地指定（16个参数中有12个的R2 > 0.77）。我们还将这种方法应用于心力衰竭引起的电生理变化的测试案例，发现大多数参数的变化都可以很好地预测。我们使用贝叶斯方法补充了我们的研究结果，以证明模型参数不能使用有限的输出来指定，但如果考虑多个输出，则可以成功地约束它们。我们的研究结果建立在坚实的数学基础上，基于直觉的过程同时将模型的输出与多个数据集相匹配。更一般地说，这种方法显示出作为在电生理学和其他生物学领域中定义模型参数的工具的希望。生物过程的数学模型通常包含许多从实验中未知的自由参数。选择这些参数的值，虽然在现实的计算模型的建设中的一个重要步骤，经常使用一个特设的方法，这是一个组合的直觉和试错。本文提出了一种基于线性代数的约束数学模型中自由参数的新方法。我们证明了这种方法的效用，通过模拟与模型的人类心脏细胞。其基本前提是，如果模型只被要求概括一个或几个生物行为，参数的值可能是模糊的;然而，如果模型必须同时匹配实验数据的许多特征，则可以唯一地确定自由参数。结果表明，如果计算模型是现实的，他们必须在同一时间与几组数据进行比较。这种新的方法应该作为一个有价值的工具，有兴趣的研究人员在开发现实的数学模型的生物过程。
A major challenge in computational biology is constraining free parameters in mathematical models. Adjusting a parameter to make a given model output more realistic sometimes has unexpected and undesirable effects on other model behaviors. Here, we extend a regression-based method for parameter sensitivity analysis and show that a straightforward procedure can uniquely define most ionic conductances in a well-known model of the human ventricular myocyte. The model's parameter sensitivity was analyzed by randomizing ionic conductances, running repeated simulations to measure physiological outputs, then collecting the randomized parameters and simulation results as “input” and “output” matrices, respectively. Multivariable regression derived a matrix whose elements indicate how changes in conductances influence model outputs. We show here that if the number of linearly-independent outputs equals the number of inputs, the regression matrix can be inverted. This is significant, because it implies that the inverted matrix can specify the ionic conductances that are required to generate a particular combination of model outputs. Applying this idea to the myocyte model tested, we found that most ionic conductances could be specified with precision (R2 > 0.77 for 12 out of 16 parameters). We also applied this method to a test case of changes in electrophysiology caused by heart failure and found that changes in most parameters could be well predicted. We complemented our findings using a Bayesian approach to demonstrate that model parameters cannot be specified using limited outputs, but they can be successfully constrained if multiple outputs are considered. Our results place on a solid mathematical footing the intuition-based procedure simultaneously matching a model's output to several data sets. More generally, this method shows promise as a tool to define model parameters, in electrophysiology and in other biological fields. Mathematical models of biological processes generally contain many free parameters that are not known from experiments. Choosing values for these parameters, although an important step in the construction of realistic computational models, is frequently performed using an ad hoc approach that is a combination of intuition and trial and error. We have developed a novel method for constraining free parameters in mathematical models based on the techniques of linear algebra. We demonstrate this method's utility through simulations with a model of a human heart cell. The underlying premise is that if the model is only asked to recapitulate one or a few biological behaviors, the values of the parameters may be ambiguous; however, if the model must simultaneously match many features of experimental data, the free parameters can be determined uniquely. The results demonstrate that if computational models are to be realistic, they must be compared with several sets of data at the same time. This new method should serve as a valuable tool for investigators interested in developing realistic mathematical models of biological processes.
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影响因子：
20.1
作者：
LUO, CH;RUDY, Y
通讯作者：
RUDY, Y
DOI：
10.1016/j.pbiomolbio.2004.02.002
发表时间：
2004-06-01
影响因子：
3.8
作者：
Dokos, S;Lovell, NH
通讯作者：
Lovell, NH
影响因子：
4.3
作者：
Druckmann, Shaul;Banitt, Yoav;Gidon, Albert;Schurmann, Felix;Markram, Henry;Segev, Idan
通讯作者：
Segev, Idan
DOI：
10.1152/ajpheart.00731.2001
发表时间：
2002-06-01
影响因子：
4.8
作者：
Bernus, O;Wilders, R;Panfilov, AV
通讯作者：
Panfilov, AV
影响因子：
25
作者：
Prinz, AA;Bucher, D;Marder, E
通讯作者：
Marder, E