Title: A Sensitivity Analysis Methodology for Rule-Based Stochastic Chemical Systems Show Chinese title

Title: 基于规则的随机化学系统的敏感性分析方法论

Abstract: In this study, we introduce a sensitivity analysis methodology for stochastic systems in chemistry, where dynamics are often governed by random processes. Our approach is based on gradient estimation via finite differences, averaging simulation outcomes, and analyzing variability under intrinsic noise. We characterize gradient uncertainty as an angular range within which all plausible gradient directions are expected to lie. This uncertainty measure adaptively guides the number of simulations performed for each nominal-perturbation pair of points in order to minimize unnecessary computations while maintaining robustness. Systematically exploring a range of parameter values across the parameter space, rather than focusing on a single value, allows us to identify not only sensitive parameters but also regions of parameter space associated with different levels of sensitivity. These results are visualized through vector field plots to offer an intuitive representation of local sensitivity across parameter space. Additionally, global sensitivity coefficients are computed to capture overall trends. Flexibility regarding the choice of output observable measures is another key feature of our method: while traditional sensitivity analyses often focus on species concentrations, our framework allows for the definition of a large range of problem-specific observables. This makes it broadly applicable in diverse chemical and biochemical scenarios. We demonstrate our approach on two systems: classical Michaelis-Menten kinetics and a rule-based model of the formose reaction, using the cheminformatics software M{\O}D for Gillespie-based stochastic simulations. Show Chinese abstract

Abstract: 在本研究中，我们引入了一种针对化学随机系统的敏感性分析方法，其中动力学通常由随机过程主导。 我们的方法基于通过有限差分进行梯度估计，平均模拟结果，并在内在噪声下分析变异性。 我们将梯度不确定性表征为一个角度范围，在该范围内预期所有可能的梯度方向都位于其中。 这种不确定性度量自适应地指导每个名义扰动点对的模拟次数，以在保持鲁棒性的同时减少不必要的计算。 系统地探索参数空间中的参数值范围，而不是专注于单个值，使我们不仅能够识别敏感参数，还能识别与不同敏感性水平相关的参数空间区域。 这些结果通过矢量场图进行可视化，以提供参数空间中局部敏感性的直观表示。 此外，计算全局敏感性系数以捕捉整体趋势。 关于输出可观测度量的选择具有灵活性是我们的方法的另一个关键特征：虽然传统的敏感性分析通常关注物种浓度，但我们的框架允许定义大量问题特定的可观测量。 这使其在各种化学和生化场景中具有广泛的应用性。 我们通过两个系统演示了我们的方法：经典的米氏动力学和一个形式为M{\O }D的基于规则的甲醛反应模型，使用化学生物信息学软件进行基于Gillespie的随机模拟。