Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.
Customized Steady-State Constraints for Parameter Estimation in Non-Linear Ordinary Differential Equation Models.
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DOI：
10.3389/fcell.2016.00041
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发表时间：
2016
影响因子：
5.5
通讯作者：
Kaschek D
中科院分区：
文献类型：
--
作者：
Rosenblatt M;Timmer J;Kaschek D
常微分方程模型已经成为分析动力系统和理解潜在机制的一种广泛的方法。模型参数通常是未知的，并且必须从实验数据估计，例如通过最大似然估计。特别是，生物系统的模型包含了大量的参数。为了降低参数空间的维度，在参数估计过程中加入了稳态信息。对于非线性模型，解析的稳态计算通常会导致无法获得闭合解的高阶多项式方程。这可以通过求解动力学参数的稳态方程来绕过，这导致了具有相对简单解的线性方程组。同时避免了稳态解的多重性，否则会给优化带来问题。然而，当求解动力学参数时，对于特定的模型规范，稳态约束往往变为负值，从而产生新类型的优化问题。在这里，我们提出了一种基于图论的算法，通过逐步消除动态变量之间的循环依赖关系来推导非负的解析稳态表达式。该算法通过构造避免了多个稳态解。我们表明，我们的方法适用于包含抑制项、质量作用方程和Hill-型动力学方程的大多数常见的生化反应网络。通过比较不同的包含稳态信息的解析方法和数值方法的参数估计性能，我们发现我们的方法特别适合于保证高的优化成功率。
Ordinary differential equation models have become a wide-spread approach to analyze dynamical systems and understand underlying mechanisms. Model parameters are often unknown and have to be estimated from experimental data, e.g., by maximum-likelihood estimation. In particular, models of biological systems contain a large number of parameters. To reduce the dimensionality of the parameter space, steady-state information is incorporated in the parameter estimation process. For non-linear models, analytical steady-state calculation typically leads to higher-order polynomial equations for which no closed-form solutions can be obtained. This can be circumvented by solving the steady-state equations for kinetic parameters, which results in a linear equation system with comparatively simple solutions. At the same time multiplicity of steady-state solutions is avoided, which otherwise is problematic for optimization. When solved for kinetic parameters, however, steady-state constraints tend to become negative for particular model specifications, thus, generating new types of optimization problems. Here, we present an algorithm based on graph theory that derives non-negative, analytical steady-state expressions by stepwise removal of cyclic dependencies between dynamical variables. The algorithm avoids multiple steady-state solutions by construction. We show that our method is applicable to most common classes of biochemical reaction networks containing inhibition terms, mass-action and Hill-type kinetic equations. Comparing the performance of parameter estimation for different analytical and numerical methods of incorporating steady-state information, we show that our approach is especially well-tailored to guarantee a high success rate of optimization.