作为相互作用粒子系统的酶动力学反应:随机平均和参数推断

Arnab Ganguly, Wasiur R. KhudaBukhsh
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引用次数: 0

摘要

我们考虑了多级迈克尔-门顿(MM)型酶动力学反应的随机模型,该模型描述了底物分子通过若干中间产物转化为产物的过程。这些反应网络的高维、多性质给计算带来了巨大挑战,尤其是在反应速率的统计估算方面。如果没有关于系统状态的直接数据,而只能获得产物形成时间的随机样本,那么这种困难就会进一步加大。为了解决这个问题,我们分两个阶段进行。首先,在某些类似于准稳态近似(QSSA)文献的技术假设下,我们证明了两个渐近结果:一个是随机平均原理,它可以得到一个低维模型;另一个是函数中心极限定理,它可以量化相关的波动。接下来,为了对原始 MM 反应网络的参数进行统计推断,我们建立了一个涉及相互作用粒子系统(IPS)的数学框架,并证明了一个混沌传播结果,使我们能够写出一个乘积形式的似然函数。基于 IPS 的推理方法的新颖之处在于,它不需要系统的状态信息,只需随机抽样乘积形式时间即可工作。我们提供了数值示例来说明理论结果的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Enzyme kinetic reactions as interacting particle systems: Stochastic averaging and parameter inference
We consider a stochastic model of multistage Michaelis--Menten (MM) type enzyme kinetic reactions describing the conversion of substrate molecules to a product through several intermediate species. The high-dimensional, multiscale nature of these reaction networks presents significant computational challenges, especially in statistical estimation of reaction rates. This difficulty is amplified when direct data on system states are unavailable, and one only has access to a random sample of product formation times. To address this, we proceed in two stages. First, under certain technical assumptions akin to those made in the Quasi-steady-state approximation (QSSA) literature, we prove two asymptotic results: a stochastic averaging principle that yields a lower-dimensional model, and a functional central limit theorem that quantifies the associated fluctuations. Next, for statistical inference of the parameters of the original MM reaction network, we develop a mathematical framework involving an interacting particle system (IPS) and prove a propagation of chaos result that allows us to write a product-form likelihood function. The novelty of the IPS-based inference method is that it does not require information about the state of the system and works with only a random sample of product formation times. We provide numerical examples to illustrate the efficacy of the theoretical results.
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