基于广义Markov跳变系统理论的DNA计算系统分析与控制

As a new type of biological computing model, DNA computing has been widely concerned by the scientific community. Its significance lies in the fact that DNA can be used as a computational medium for solving mathematical problems. The process of DNA computing involves a large number of molecular chemical reactions and exhibits a certain degree of uncertainty and randomness. At the same time, the reaction process of DNA computing is constrained by the principle of mass conservation. In this project, stochastic differential-algebraic equations are used to construct the singular Markovian jump system model of DNA computing. The structure and dynamics of DNA computing system are analyzed, the mechanism of impulse behavior is revealed, the positive boundedness and the stochastic stability of solution are derived. A hybrid impulsive control strategy is proposed to eliminate the negative effects of impulse behavior on system performance. A T-S fuzzy controller is designed to ensure the stochastic admissibility of the closed-loop system. When the operating mode signal is out of order during the transmission process, disordered control scheme is employed to guarantee the reliability of DNA computing. To verify the rationality and validity of the given methods, biochemical reaction experiments will be carried out for DNA strand displacement, enzyme digestion reactions, and so on. The research results will provide new methods for the modeling, analysis and design of DNA computing system, which have important theoretical significance and potential application value.

作为一种新型的生物计算模型，DNA计算受到了科学界的广泛关注。其意义在于DNA可以作为计算的介质而用于解决数学问题。DNA计算过程涉及大量的分子化学反应，具有一定的不确定性和随机性。与此同时，DNA计算的化学反应过程受质量守恒定律的约束。本项目拟利用随机微分代数方程，构建DNA计算的广义Markov跳变系统模型。分析DNA计算系统的结构和动力学特性，揭示脉冲行为的产生机制，给出系统解的正向有界性和随机稳定性判据。设计混杂脉冲控制器，消除脉冲行为对系统性能的不利影响。设计T-S模糊控制器，使得闭环系统随机容许。当模态运行信号发生传输紊乱时，设计错序控制器，保证DNA计算过程的可靠性。针对DNA计算过程中的链置换反应、酶切反应等，开展生化反应实验，验证设计方法的合理性和有效性。研究成果将为DNA计算系统的建模、分析与设计提供新方法，具有重要的理论意义和潜在应用价值。

本项目从DNA计算的系统动力学角度入手，将DNA分子、生物酶、外部反应条件等相关数据看成一个整体，并对其进行模型构建和系统动态行为定性分析，进而对其反应过程进行反馈控制，以保证DNA计算生化反应的顺利进行。本项目在DNA计算系统模型构建、DNA计算系统定性分析、DNA计算系统反馈控制等方向开展了相应的研究。具体成果有：建立了带有Lévy过程的熵驱动放大器（EDA）电路反应广义系统模型；构建了两类带有时滞参数的DNA链置换反应系统模型；构建了带有随机扰动的DNA催化反应系统模型；分析了EDA电路反应结束和持续的充分条件以及不同噪声强度下EDA电路反应中ThTSignal的反应活性；探究了时滞参数对DNA链置换反应的动态影响，得到了系统存在Hopf分岔的临界条件；研究了带有周期解的DNA催化反应模型的动力学特性，分析了系统解的全局吸引性；研究了一类不确定广义Markov跳变系统的混杂脉冲控制问题；提出了一种酶辅助切割调控策略，揭示了DNA电路中信号的传递机制；基于DNA链置换反应网络，构造了二自由度PID控制器并应用到减法门系统；基于化学反应网络设计了一系列分子器件，确保了系统的响应跟踪和扰动抑制性能。项目组出版专著1部；在IEEE Transactions on NanoBioscience、BMC Bioinformatics、Molecular Systems Design & Engineering等国际权威期刊及会议上发表论文16篇，其中SCI收录10篇；申请受理发明专利6项，在论文发表、专利申请等方面超额完成了预期目标。