Differential equation models of biochemical networks are frequently associated with a large degree of uncertainty in parameters and/or initial conditions. However, estimating the impact of this uncertainty on model predictions via Monte Carlo simulation is computationally demanding. A more efficient approach could be to track a system of low-order statistical moments of the state. Unfortunately, when the underlying model is nonlinear, the system of moment equations is infinite-dimensional and cannot be solved without a moment closure approximation which may introduce bias in the moment dynamics. Here, we present a new method to study the time evolution of the desired moments for nonlinear systems with polynomial rate laws. Our approach is based on solving a system of low-order moment equations by substituting the higher-order moments with Monte Carlo-based estimates from a small number of simulations, and using an extended Kalman filter to counteract Monte Carlo noise. Our algorithm provides more accurate and robust results compared to traditional Monte Carlo and moment closure techniques, and we expect that it will be widely useful for the quantification of uncertainty in biochemical model predictions.

生化网络的微分方程模型经常与参数和/或初始条件的高度不确定性相关联。然而，通过蒙特卡罗模拟估计这种不确定性对模型预测的影响在计算上要求很高。一种更有效的方法可能是跟踪状态的低阶统计矩系统。不幸的是，当基础模型是非线性时，矩方程系统是无限维的，如果没有矩闭合近似就无法求解，这可能会在矩动力学中引入偏差。在这里，我们提出了一种新方法来研究具有多项式速率定律的非线性系统所需矩的时间演化。我们的方法基于求解一个低阶矩方程系统，方法是用少量模拟的基于蒙特卡罗的估计替换高阶矩，并使用扩展卡尔曼滤波器来抵消蒙特卡罗噪声。与传统的蒙特卡罗和矩闭合技术相比，我们的算法提供了更准确和稳健的结果，我们预计它将广泛用于量化生化模型预测中的不确定性。