Lab of Systems Biology, Department of Electrical Engineering, National Tsing Hua University, Hsinchu 30013, Taiwan.
Math Biosci. 2011 Oct;233(2):111-25. doi: 10.1016/j.mbs.2011.07.001. Epub 2011 Jul 19.
Some current promoter libraries have been developed for synthetic gene networks. But an efficient method to engineer a synthetic gene network with some desired behaviors by selecting adequate promoters from these promoter libraries has not been presented. Thus developing a systematic method to efficiently employ promoter libraries to improve the engineering of synthetic gene networks with desired behaviors is appealing for synthetic biologists. In this study, a synthetic gene network with intrinsic parameter fluctuations and environmental disturbances in vivo is modeled by a nonlinear stochastic system. In order to engineer a synthetic gene network with a desired behavior despite intrinsic parameter fluctuations and environmental disturbances in vivo, a multiobjective H(2)/H(∞) reference tracking (H(2) optimal tracking and H(∞) noise filtering) design is introduced. The H(2) optimal tracking can make the tracking errors between the behaviors of a synthetic gene network and the desired behaviors as small as possible from the minimum mean square error point of view, and the H(∞) noise filtering can attenuate all possible noises, from the worst-case noise effect point of view, to achieve a desired noise filtering ability. If the multiobjective H(2)/H(∞) reference tracking design is satisfied, the synthetic gene network can robustly and optimally track the desired behaviors, simultaneously. First, based on the dynamic gene regulation, the existing promoter libraries are redefined by their promoter activities so that they can be efficiently selected in the design procedure. Then a systematic method is developed to select an adequate promoter set from the redefined promoter libraries to synthesize a gene network satisfying these two design objectives. But the multiobjective H(2)/H(∞) reference tracking design problem needs to solve a difficult Hamilton-Jacobi Inequality (HJI)-constrained optimization problem. Therefore, the fuzzy approximation method is employed to simplify the HJI-constrained optimization problem to an equivalent linear matrix inequality (LMI)-constrained optimization problem, which can be easily solved by selecting an adequate promoter set from the redefined promoter libraries using the LMI toolbox in Matlab. Based on the confirmation of in silico design examples, we can select an adequate promoter set from the redefined promoter libraries to achieve the multiobjective H(2)/H(∞) reference tracking design. The proposed method can reduce the number of trial-and-error experiments in selecting an adequate promoter set for a synthetic gene network with desired behaviors. With the rapid increase of promoter libraries, this systematic method will accelerate progress of synthetic biology design.
一些现有的启动子文库已经被开发出来用于合成基因网络。但是，还没有提出一种有效的方法来通过从这些启动子文库中选择合适的启动子来设计具有某些所需行为的合成基因网络。因此，开发一种系统的方法来有效地利用启动子文库来改进具有所需行为的合成基因网络的工程设计对于合成生物学家来说是很有吸引力的。在这项研究中，通过非线性随机系统对体内具有内在参数波动和环境干扰的合成基因网络进行建模。为了设计具有所需行为的合成基因网络，尽管存在体内的内在参数波动和环境干扰，引入了多目标 H(2)/H(∞)参考跟踪(H(2)最优跟踪和 H(∞)噪声滤波)设计。H(2)最优跟踪可以使合成基因网络的行为与期望行为之间的跟踪误差尽可能小，从均方误差最小的角度来看，而 H(∞)噪声滤波可以衰减所有可能的噪声，从最坏情况噪声效应的角度来看，以实现期望的噪声滤波能力。如果满足多目标 H(2)/H(∞)参考跟踪设计，则合成基因网络可以同时稳健地、最优地跟踪期望行为。首先，基于动态基因调控，通过其启动子活性重新定义现有的启动子文库，以便在设计过程中能够有效地选择。然后，开发了一种系统的方法来从重新定义的启动子文库中选择合适的启动子集来合成满足这两个设计目标的基因网络。但是，多目标 H(2)/H(∞)参考跟踪设计问题需要解决一个困难的哈密顿-雅可比不等式(HJI)约束优化问题。因此，采用模糊逼近方法将 HJI 约束优化问题简化为等效的线性矩阵不等式(LMI)约束优化问题，然后使用 Matlab 中的 LMI 工具箱从重新定义的启动子文库中选择合适的启动子集，很容易解决这个问题。基于计算机设计实例的验证，我们可以从重新定义的启动子文库中选择合适的启动子集来实现多目标 H(2)/H(∞)参考跟踪设计。该方法可以减少为具有所需行为的合成基因网络选择合适启动子集的试验和错误实验的次数。随着启动子文库的快速增加，这种系统的方法将加速合成生物学设计的进展。
