Integrative BioSystems Institute and Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, 313 Ferst Drive, Suite 4103, Atlanta, GA 30332-0535, United States.
J Biotechnol. 2010 Sep 1;149(3):154-65. doi: 10.1016/j.jbiotec.2009.12.016. Epub 2010 Jan 8.
Recent trends suggest that future biotechnology will increasingly rely on mathematical models of the biological systems under investigation. In particular, metabolic engineering will make wider use of metabolic pathway models in stoichiometric or fully kinetic format. A significant obstacle to the use of pathway models is the identification of suitable process descriptions and their parameters. We recently showed that, at least under favorable conditions, Dynamic Flux Estimation (DFE) permits the numerical characterization of fluxes from sets of metabolic time series data. However, DFE does not prescribe how to convert these numerical results into functional representations. In some cases, Michaelis-Menten rate laws or canonical formats are well suited, in which case the estimation of parameter values is easy. However, in other cases, appropriate functional forms are not evident, and exhaustive searches among all possible candidate models are not feasible. We show here how piecewise power-law functions of one or more variables offer an effective default solution for the almost unbiased representation of uni- and multivariate time series data. The results of an automated algorithm for their determination are piecewise power-law fits, whose accuracy is only limited by the available data. The individual power-law pieces may lead to discontinuities at break points or boundaries between sub-domains. In many practical applications, these boundary gaps do not cause problems. Potential smoothing techniques, based on differential inclusions and Filippov's theory, are discussed in Appendix A.
最近的趋势表明，未来的生物技术将越来越依赖于所研究的生物系统的数学模型。特别是，代谢工程将更广泛地使用代谢途径模型，无论是在计量格式还是在全动力学格式中。途径模型应用的一个显著障碍是合适的过程描述及其参数的识别。我们最近表明，至少在有利条件下，动态通量估计（DFE）允许从代谢时间序列数据集数值特征化通量。然而，DFE 并没有规定如何将这些数值结果转换为功能表示。在某些情况下，米氏动力学定律或规范格式非常适用，在这种情况下，参数值的估计很容易。然而，在其他情况下，合适的功能形式并不明显，并且对所有可能的候选模型进行详尽搜索是不可行的。我们在这里展示了一个或多个变量的分段幂律函数如何为单变量和多变量时间序列数据的几乎无偏表示提供有效默认解决方案。其确定的自动算法的结果是分段幂律拟合，其准确性仅受可用数据的限制。各个幂律部分可能在子域之间的断点或边界处导致不连续。在许多实际应用中，这些边界间隙不会造成问题。基于微分包含和 Filippov 理论的潜在平滑技术在附录 A 中进行了讨论。
