Kuepfer Lars, Sauer Uwe, Parrilo Pablo A
Institute of Molecular Systems Biology, ETH Zürich, CH-8093 Zürich, Switzerland.
BMC Bioinformatics. 2007 Jan 15;8:12. doi: 10.1186/1471-2105-8-12.
Current approaches to parameter estimation are often inappropriate or inconvenient for the modelling of complex biological systems. For systems described by nonlinear equations, the conventional approach is to first numerically integrate the model, and then, in a second a posteriori step, check for consistency with experimental constraints. Hence, only single parameter sets can be considered at a time. Consequently, it is impossible to conclude that the "best" solution was identified or that no good solution exists, because parameter spaces typically cannot be explored in a reasonable amount of time.
We introduce a novel approach based on semidefinite programming to directly identify consistent steady state concentrations for systems consisting of mass action kinetics, i.e., polynomial equations and inequality constraints. The duality properties of semidefinite programming allow to rigorously certify infeasibility for whole regions of parameter space, thus enabling the simultaneous multi-dimensional analysis of entire parameter sets.
Our algorithm reduces the computational effort of parameter estimation by several orders of magnitude, as illustrated through conceptual sample problems. Of particular relevance for systems biology, the approach can discriminate between structurally different candidate models by proving inconsistency with the available data.
当前的参数估计方法对于复杂生物系统的建模往往不合适或不方便。对于由非线性方程描述的系统，传统方法是首先对模型进行数值积分，然后在第二步后验步骤中检查与实验约束的一致性。因此，一次只能考虑单个参数集。因此，不可能得出已确定“最佳”解决方案或不存在良好解决方案的结论，因为通常无法在合理的时间内探索参数空间。
我们引入了一种基于半定规划的新方法，以直接确定由质量作用动力学组成的系统的一致稳态浓度，即多项式方程和不等式约束。半定规划的对偶性质允许严格证明参数空间的整个区域不可行，从而能够对整个参数集进行同时多维分析。
我们的算法将参数估计的计算工作量减少了几个数量级，如概念性示例问题所示。对于系统生物学特别相关的是，该方法可以通过证明与现有数据不一致来区分结构不同的候选模型。
