Luo Xiaosheng, Xu Liufang, Han Bo, Wang Jin
Applied Science Department at Little Rock, University of Arkansas, Little Rock, Arkansas, United States of America.
Biophysics & Complex System Center and Theoretical Physics Center, Department of Physics, Jilin University, Changchun, Jilin, China.
PLoS Comput Biol. 2017 Sep 11;13(9):e1005710. doi: 10.1371/journal.pcbi.1005710. eCollection 2017 Sep.
Using fission yeast cell cycle as an example, we uncovered that the non-equilibrium network dynamics and global properties are determined by two essential features: the potential landscape and the flux landscape. These two landscapes can be quantified through the decomposition of the dynamics into the detailed balance preserving part and detailed balance breaking non-equilibrium part. While the funneled potential landscape is often crucial for the stability of the single attractor networks, we have uncovered that the funneled flux landscape is crucial for the emergence and maintenance of the stable limit cycle oscillation flow. This provides a new interpretation of the origin for the limit cycle oscillations: There are many cycles and loops existed flowing through the state space and forming the flux landscapes, each cycle with a probability flux going through the loop. The limit cycle emerges when a loop stands out and carries significantly more probability flux than other loops. We explore how robustness ratio (RR) as the gap or steepness versus averaged variations or roughness of the landscape, quantifying the degrees of the funneling of the underlying potential and flux landscapes. We state that these two landscapes complement each other with one crucial for stabilities of states on the cycle and the other crucial for the stability of the flow along the cycle. The flux is directly related to the speed of the cell cycle. This allows us to identify the key factors and structure elements of the networks in determining the stability, speed and robustness of the fission yeast cell cycle oscillations. We see that the non-equilibriumness characterized by the degree of detailed balance breaking from the energy pump quantified by the flux is the cause of the energy dissipation for initiating and sustaining the replications essential for the origin and evolution of life. Regulating the cell cycle speed is crucial for designing the prevention and curing strategy of cancer.
以裂殖酵母细胞周期为例，我们发现非平衡网络动力学和全局特性由两个基本特征决定：势能景观和通量景观。这两种景观可以通过将动力学分解为保持细致平衡的部分和打破细致平衡的非平衡部分来量化。虽然漏斗状的势能景观通常对单吸引子网络的稳定性至关重要，但我们发现漏斗状的通量景观对稳定极限环振荡流的出现和维持至关重要。这为极限环振荡的起源提供了一种新的解释：在状态空间中存在许多循环和回路，形成通量景观，每个循环都有一个概率通量通过该回路。当一个回路脱颖而出并携带比其他回路显著更多的概率通量时，极限环就会出现。我们探索了作为景观的差距或陡度与平均变化或粗糙度之比的鲁棒性比率（RR），以量化潜在势能和通量景观的漏斗程度。我们指出，这两种景观相互补充，一种对循环上状态的稳定性至关重要，另一种对沿循环流动的稳定性至关重要。通量与细胞周期的速度直接相关。这使我们能够识别网络中决定裂殖酵母细胞周期振荡的稳定性、速度和鲁棒性的关键因素和结构要素。我们看到，以通量量化的能量泵打破细致平衡的程度所表征的非平衡是启动和维持生命起源和进化所必需的复制的能量耗散的原因。调节细胞周期速度对于设计癌症的预防和治疗策略至关重要。
