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

马萨诸塞州理工学院的Jianshu Cao得到了理论和计算化学项目探索性研究的小额资助，用于研究开发一种方法，将复杂的化学反应分解为不可约的方案，该方案为一类反应提供通用结构，并且对子方案的变化保持不变。不可约通用格式的概念有助于动力学行为的分析和分类，并便于对实验测量结果的解释。这项工作包括三个阶段。 1.一阶动力学网络通过识别两个动力学基序来分解，即，连续链式反应和分支反应。系统地串联链式反应和侧分支，研究人员可以将复杂的反应简化为一般形式，其中每个环节代表与复杂的等待时间分布函数相关的子方案。当动力学步骤在子方案内改变时，等待时间分布函数相应地改变，但总体通用方案和相关动态量将保持相同的函数形式。 2.一个高阶动力学网络，然后扩展其稳态解的速率方程，保留了完整的非线性的平均浓度的动态行为。稳定状态附近的相关性和波动近似的线性形式的解决方案，直接相关的动态行为和响应测量的稳定性分析方法的方法。在线性化网络中，反馈或前馈机制定义了第三个基序，它将非局部性引入线性动力学，是理解多稳定性和振荡的核心。3.在研究的最后一部分中，正在开发一种分层处理非线性动力学网络，并充分考虑与单细胞实验相关的数量统计。投影算子作为一种形式化的技术正在被探索，它可以将复杂的动力学网络系统地简化为具有非线性耦合的一般模型，通过将所得到的方法应用于生物学中感兴趣的复杂反应网络，这项工作正在产生更广泛的影响。 学生培训也受到了积极的影响，曹正努力通过他为碲化物研讨会开发的课程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.