Cao2013 - Application of ABSIS in the the enzymatic futile cycle

Michael Samoilov, Sergey Plyasunov & Adam P. Arkin. Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. Proceedings of the National Academy of Sciences 102, 7 (2005).

Critical events that occur rarely in biological processes are of great importance, but are challenging to study using Monte Carlo simulation. By introducing biases to reaction selection and reaction rates, weighted stochastic simulation algorithms based on importance sampling allow rare events to be sampled more effectively. However, existing methods do not address the important issue of barrier crossing, which often arises from multistable networks and systems with complex probability landscape. In addition, the proliferation of parameters and the associated computing cost pose significant problems. Here we introduce a general theoretical framework for obtaining optimized biases in sampling individual reactions for estimating probabilities of rare events. We further describe a practical algorithm called adaptively biased sequential importance sampling (ABSIS) method for efficient probability estimation. By adopting a look-ahead strategy and by enumerating short paths from the current state, we estimate the reaction-specific and state-specific forward and backward moving probabilities of the system, which are then used to bias reaction selections. The ABSIS algorithm can automatically detect barrier-crossing regions, and can adjust bias adaptively at different steps of the sampling process, with bias determined by the outcome of exhaustively generated short paths. In addition, there are only two bias parameters to be determined, regardless of the number of the reactions and the complexity of the network. We have applied the ABSIS method to four biochemical networks: the birth-death process, the reversible isomerization, the bistable Schlögl model, and the enzymatic futile cycle model. For comparison, we have also applied the finite buffer discrete chemical master equation (dCME) method recently developed to obtain exact numerical solutions of the underlying discrete chemical master equations of these problems. This allows us to assess sampling results objectively by comparing simulation results with true answers. Overall, ABSIS can accurately and efficiently estimate rare event probabilities for all examples, often with smaller variance than other importance sampling algorithms. The ABSIS method is general and can be applied to study rare events of other stochastic networks with complex probability landscape.

迈克尔·萨莫伊洛夫（Michael Samoilov）、谢尔盖·普利亚苏诺夫（Sergey Plyasunov）与亚当·P·阿金（Adam P. Arkin）。《通过噪声诱导双稳性与振荡实现酶促无效循环中的随机放大与信号传导》，《美国国家科学院院刊》（Proceedings of the National Academy of Sciences），102卷第7期，2005年。

生物过程中罕见发生的关键事件具有重要研究价值，却难以通过蒙特卡洛（Monte Carlo）模拟开展研究。基于重要性采样（importance sampling）的加权随机模拟算法，通过对反应选择与反应速率引入偏置，能够更高效地对罕见事件进行采样。然而，现有方法并未解决关键的势垒穿越问题——这类问题常出现在多稳态网络与具有复杂概率景观的系统中。此外，参数激增与随之而来的计算成本也带来了严峻挑战。本研究提出了一个通用理论框架，用于在单个反应的采样过程中获取最优偏置，以估算罕见事件的发生概率。我们进一步提出了一种名为自适应偏置序贯重要性采样（adaptively biased sequential importance sampling, ABSIS）的实用算法，用于高效完成概率估算。该算法采用前瞻策略，枚举当前状态下的短路径，进而估算系统针对特定反应与特定状态的正向、反向转移概率，并以此偏置反应选择过程。ABSIS算法可自动识别势垒穿越区域，并在采样过程的不同阶段自适应调整偏置，偏置由穷尽生成的短路径结果确定。此外，无论反应数量与网络复杂度如何，仅需确定两个偏置参数即可。我们将ABSIS方法应用于四类生化网络：生死过程、可逆异构化反应、双稳态施洛格尔（Schlögl）模型以及酶促无效循环模型。为进行对比验证，我们还采用了近期提出的有限缓冲离散化学主方程（discrete chemical master equation, dCME）方法，以获取上述问题对应的离散化学主方程的精确数值解。借此可将模拟结果与真实解进行比对，从而客观评估采样效果。总体而言，ABSIS算法可对所有测试案例的罕见事件概率实现精准高效的估算，其方差通常低于其他重要性采样算法。ABSIS方法具有通用性，可用于研究其他具有复杂概率景观的随机网络中的罕见事件。