论文标题
与混合反馈的代谢途径的定性行为
Qualitative Behavior of a Metabolic Pathway with Hybrid Feedback
论文作者
论文摘要
我们研究模型的定性行为，以代表代谢网络中的局部调节。该模型基于[A. Goelzer，F。BekkalBrikci，I。Martin-Verstraete等人，BMC Syst Biol 2（2008），第1--18页]。在这类调节中，代谢物效应子是代谢途径的终产物。我们假设根据代谢物效应子的浓度在零和正值之间切换途径的输入。将开关系统视为差分包含，我们证明它会收敛到全球均匀均匀稳定的平衡点，根据输入的正值，到达滑动模式或在滑动模式周围振荡。最后，我们表明，在任何情况下，开关系统的解决方案是具有光滑或分段线性输入的方程序列解决方案的极限。
We study the qualitative behavior of a model to represent local regulation in a metabolic network. The model is based on the end-product control structure introduced in [A. Goelzer, F. Bekkal Brikci, I. Martin-Verstraete et al., BMC Syst Biol 2 (2008), pp. 1--18]. In this class of regulation, the metabolite effector is the end-product of a metabolic pathway. We suppose the input to the pathway to switch between zero and a positive value according to the concentration of the metabolite effector. Considering the switched system as a differential inclusion, we prove that it converges to a globally uniformly asymptotically stable equilibrium point, reaches the sliding mode or oscillates around the sliding mode depending on the positive value of the input. Finally, we show that in any case the solution of the switched system is the limit of solutions of equation sequences with smooth or piecewise linear inputs.
