具有绝对浓度鲁棒性的随机模型化学系统的有限时间分布
Finite time distributions of stochastically modeled chemical systems with absolute concentration robustness
摘要：
最近的研究在实验和数学界都集中在生化相互作用系统，满足“绝对浓度鲁棒性”（ACR）的属性。ACR性质首先在实验上发现，在许多不同的系统中，观察到平衡时关键系统组分的浓度对系统的总浓度水平是稳健的。后续的数学工作集中在生化系统的确定性模型，并演示了如何利用化学反应网络理论来解释这种鲁棒性。后来的数学工作集中在同一类反应网络的行为上，尽管假设动力学是随机的。在随机假设下，证明了只要系统是保守的，系统将经历概率为1的灭绝事件，表现出与确定性设置完全不同的长期行为。在这里，我们考虑一个一般类的随机模型，交叉与类ACR系统以前研究。我们考虑一个特定的系统标度在紧凑的时间间隔，并证明，在这种标度的限制下，ACR物种的丰度分布收敛到一定的产品形式的泊松分布，其平均值是ACR值的确定性模型。这一结果是在协议与最近的acrutures有关的行为赋予随机动力学的ACR网络，并有助于解决冲突的理论结果有关的确定性和随机模型在这种情况下。
英文摘要：
Recent research in both the experimental and mathematical communities has focused on biochemical interaction systems that satisfy an "absolute concentration robustness" (ACR) property. The ACR property was first discovered experimentally when, in a number of different systems, the concentrations of key system components at equilibrium were observed to be robust to the total concentration levels of the system. Followup mathematical work focused on deterministic models of biochemical systems and demonstrated how chemical reaction network theory can be utilized to explain this robustness. Later mathematical work focused on the behavior of this same class of reaction networks, though under the assumption that the dynamics were stochastic. Under the stochastic assumption, it was proven that the system will undergo an extinction event with a probability of one so long as the system is conservative, showing starkly different long-time behavior than in the deterministic setting. Here we consider a general class of stochastic models that intersects with the class of ACR systems studied previously. We consider a specific system scaling over compact time intervals and prove that in a limit of this scaling the distribution of the abundances of the ACR species converges to a certain product-form Poisson distribution whose mean is the ACR value of the deterministic model. This result is in agreement with recent conjectures pertaining to the behavior of ACR networks endowed with stochastic kinetics, and helps to resolve the conflicting theoretical results pertaining to deterministic and stochastic models in this setting.
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