利用DMRG进行化学主方程参数探索
Chemical master equation parameter exploration using DMRG
AI总结：
本文利用DMRG方法研究七种物质基因切换开关CRN模型的稳态双稳态特性，通过张量网络技术分析参数对双稳态的影响，并计算弛豫时间尺度。
摘要：
均匀混合的化学反应网络（CRNs）包含许多不同的化学物质，其数量在相关的方式下波动。虽然这些相关性通常通过蒙特卡罗采样随机轨迹来监测，但人们有兴趣系统地近似指数级大量的可能微状态的联合分布，使用张量网络或张量列车。我们利用张量网络策略来确定七种物质基因切换开关CRN模型的稳态是否支持双稳态，作为两种分解速率函数，这两种参数都是动力学模型的参数。我们强调张量网络解决方案如何捕捉随机波动的影响，超越均场分析，甚至在均场分析中产生显著偏离。这项工作还开发并展示了若干技术进步，使广泛类别的CRN的稳态可以以有利于参数探索的方式计算。我们证明，尽管具有非厄米特率算子和小谱间隙，稳态分布仍可通过普通密度矩阵重正化群（DMRG）算法计算，我们说明如何将该稳态分布高效投影到一个识别双模态的序参量，我们利用激发态DMRG计算双稳态的弛豫时间尺度。
英文摘要：
Well-mixed chemical reaction networks (CRNs) contain many distinct chemical species with copy numbers that fluctuate in correlated ways. While those correlations are typically monitored via Monte Carlo sampling of stochastic trajectories, there is interest in systematically approximating the joint distribution over the exponentially large number of possible microstates using tensor networks or tensor trains. We exploit the tensor network strategy to determine when the steady state of a seven-species gene toggle switch CRN model supports bistability as a function of two decomposition rates, both parameters of the kinetic model. We highlight how the tensor network solution captures the effects of stochastic fluctuations, going beyond mean field and indeed deviating meaningfully from a mean-field analysis. The work furthermore develops and demonstrates several technical advances that will allow steady-states of broad classes of CRNs to be computed in a manner conducive to parameter exploration. We show that the steady-state distributions can be computed via the ordinary density matrix renormalization group (DMRG) algorithm despite having a non-Hermitian rate operator with a small spectral gap, we illustrate how that steady-state distribution can be efficiently projected to an order parameter that identifies bimodality, and we employ excited-state DMRG to calculate a relaxation timescale for the bistability.
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