SGER: A new approach to the decomposition of complex chemical kinetics

麻省理工学院的曹建树得到了理论和计算化学研究计划中的一小笔探索性研究补助金的支持，该基金旨在开发一种方法，将复杂的化学反应分解成不可约的方案，该方案为一类反应提供类属结构，并且不随子方案的变化而变化。不可约一般格式的概念有助于动态行为的分析和分类，并有助于解释实验测量。这项工作包括三个阶段。1.通过识别两个动力学基元，即顺序链式反应和支化反应，对一级动力学网络进行分解。研究人员系统地将链式反应和侧枝反应串联在一起，然后可以将复杂的反应简化为其一般形式，其中每个环节代表与复杂等待时间分布函数相关联的子方案。当子方案内的动力学步骤改变时，等待时间分布函数相应地改变，但总体通用方案和相关的动态量将保持相同的函数形式。2.然后围绕速率方程的稳态解展开一个高阶动力学网络，该网络保留了平均浓度动态行为的完全非线性。稳态附近的相关性和波动被近似为解的线性形式，这种方法直接与动态行为和响应测量的稳定性分析方法相关。在线性化网络中，反馈或前馈机制定义了第三个基元，它将非定域性引入到线性动力学中，并且是理解多稳定性和振荡的核心。3.在研究的最后部分，正在开发一种充分考虑与单细胞实验相关的数量统计的非线性动力学网络的分级处理方法。投影算子是一种将复杂的动力学网络系统化为具有非线性耦合的通用方案的形式化技术，通过将所得到的方法应用于生物学中复杂的相互作用的反应网络，这项工作正在产生更广泛的影响。学生培训也受到了积极影响，曹正在努力通过他正在为Telluride研讨会开发的课程来进一步传播他的研究成果。

Jianshu Cao of the Massachusetts Institute of Technology is supported by a Small Grant for Exploratory Research from the Theoretical and Computational Chemistry program for research to develop a method to decompose complex chemical reactions into irreducible schemes that provide the generic structures for a class of reactions and are invariant to changes made to the sub-schemes. The concept of irreducible generic schemes is helpful in the analysis and classification of dynamic behavior and facilitates the interpretation of experimental measurements. The work consists of three stages. 1. A first-order kinetic network is decomposed by identifying two kinetic motifs, i.e., sequential chain reactions and branching reactions. Systematically concatenating chain reactions and side-branches, the investigators can then reduce a complex reaction to its generic form, each link of which represents a sub-scheme associated with a complex waiting time distribution function. When a kinetic step is altered within a sub-scheme, the waiting time distribution function changes accordingly, but the overall generic scheme and related dynamic quantities will remain the same functional forms. 2. A high-order kinetic network is then expanded around its steady state solution to the rate equation, which retains the full non-linearity in the dynamic behavior of average concentration. The correlations and fluctuations near the steady state are approximated by a linear form for the solution, an approach directly related to stability analysis methods for dynamic behavior and response measurements. In linearized networks, the feed-back or feed-forward mechanism defines a third motif, which introduces non-locality into linear kinetics and is central for understanding multi-stability and oscillations. 3. In the last part of the research, a hierarchical treatment of non-linear kinetic networks with a full account of number statistics relevant to single cell experiments is being developed. The projection operator is being explored as a formal technique to systematically reduce a complex kinetic network to a generic scheme with non-linear couplings.The work is having a broader impact through application of the resulting methods to complx reaction networks of interets in biology. Student training is also being positively impacted and Cao is making an effort to further disseminate the results of his research through a course he is developing for the Telluride Workshop.