Kim Keun-Young, Wang Jin
Department of Physics and Astronomy, State University of New York Stony Brook, Stony Brook, New York, United States of America.
PLoS Comput Biol. 2007 Mar 30;3(3):e60. doi: 10.1371/journal.pcbi.0030060. Epub 2007 Feb 14.
Finding a multidimensional potential landscape is the key for addressing important global issues, such as the robustness of cellular networks. We have uncovered the underlying potential energy landscape of a simple gene regulatory network: a toggle switch. This was realized by explicitly constructing the steady state probability of the gene switch in the protein concentration space in the presence of the intrinsic statistical fluctuations due to the small number of proteins in the cell. We explored the global phase space for the system. We found that the protein synthesis rate and the unbinding rate of proteins to the gene were small relative to the protein degradation rate; the gene switch is monostable with only one stable basin of attraction. When both the protein synthesis rate and the unbinding rate of proteins to the gene are large compared with the protein degradation rate, two global basins of attraction emerge for a toggle switch. These basins correspond to the biologically stable functional states. The potential energy barrier between the two basins determines the time scale of conversion from one to the other. We found as the protein synthesis rate and protein unbinding rate to the gene relative to the protein degradation rate became larger, the potential energy barrier became larger. This also corresponded to systems with less noise or the fluctuations on the protein numbers. It leads to the robustness of the biological basins of the gene switches. The technique used here is general and can be applied to explore the potential energy landscape of the gene networks.
找到一个多维势能景观是解决重要全球问题的关键，比如细胞网络的稳健性。我们揭示了一个简单基因调控网络——双稳开关的潜在能量景观。这是通过在存在由于细胞内蛋白质数量少而产生的内在统计涨落的情况下，明确构建蛋白质浓度空间中基因开关的稳态概率来实现的。我们探索了该系统的全局相空间。我们发现，相对于蛋白质降解速率，蛋白质合成速率和蛋白质与基因的解离速率较小；基因开关是单稳态的，只有一个稳定吸引盆。当蛋白质合成速率和蛋白质与基因的解离速率相对于蛋白质降解速率都很大时，双稳开关会出现两个全局吸引盆。这些吸引盆对应于生物学上稳定的功能状态。两个吸引盆之间的势能屏障决定了从一个状态转换到另一个状态的时间尺度。我们发现，随着蛋白质合成速率以及蛋白质与基因的解离速率相对于蛋白质降解速率变得更大，势能屏障也变得更大。这也对应于噪声或蛋白质数量波动较小的系统。这导致了基因开关生物学吸引盆的稳健性。这里使用的技术具有通用性，可应用于探索基因网络的势能景观。
