Ling Hong, Samarasinghe Sandhya, Kulasiri Don
German Cancer Research Centre, Heildelberg, Germany; Centre for Advanced Computational Solutions (C-fACS), Lincoln University, Christchurch, New Zealand.
Biosystems. 2013 Dec;114(3):191-205. doi: 10.1016/j.biosystems.2013.08.004. Epub 2013 Sep 5.
Understanding the control of cellular networks consisting of gene and protein interactions and their emergent properties is a central activity of Systems Biology research. For this, continuous, discrete, hybrid, and stochastic methods have been proposed. Currently, the most common approach to modelling accurate temporal dynamics of networks is ordinary differential equations (ODE). However, critical limitations of ODE models are difficulty in kinetic parameter estimation and numerical solution of a large number of equations, making them more suited to smaller systems. In this article, we introduce a novel recurrent artificial neural network (RNN) that addresses above limitations and produces a continuous model that easily estimates parameters from data, can handle a large number of molecular interactions and quantifies temporal dynamics and emergent systems properties. This RNN is based on a system of ODEs representing molecular interactions in a signalling network. Each neuron represents concentration change of one molecule represented by an ODE. Weights of the RNN correspond to kinetic parameters in the system and can be adjusted incrementally during network training. The method is applied to the p53-Mdm2 oscillation system - a crucial component of the DNA damage response pathways activated by a damage signal. Simulation results indicate that the proposed RNN can successfully represent the behaviour of the p53-Mdm2 oscillation system and solve the parameter estimation problem with high accuracy. Furthermore, we presented a modified form of the RNN that estimates parameters and captures systems dynamics from sparse data collected over relatively large time steps. We also investigate the robustness of the p53-Mdm2 system using the trained RNN under various levels of parameter perturbation to gain a greater understanding of the control of the p53-Mdm2 system. Its outcomes on robustness are consistent with the current biological knowledge of this system. As more quantitative data become available on individual proteins, the RNN would be able to refine parameter estimation and mapping of temporal dynamics of individual signalling molecules as well as signalling networks as a system. Moreover, RNN can be used to modularise large signalling networks.
理解由基因和蛋白质相互作用及其涌现特性组成的细胞网络的控制是系统生物学研究的核心活动。为此，人们提出了连续、离散、混合和随机方法。目前，对网络精确时间动态进行建模的最常用方法是常微分方程（ODE）。然而，ODE模型的关键局限性在于动力学参数估计困难以及大量方程的数值求解，这使得它们更适合较小的系统。在本文中，我们引入了一种新颖的递归人工神经网络（RNN），该网络解决了上述局限性，并生成了一个连续模型，该模型能够轻松地从数据中估计参数，能够处理大量分子相互作用，并量化时间动态和涌现系统特性。这种RNN基于一个表示信号网络中分子相互作用的ODE系统。每个神经元代表由一个ODE表示的一种分子的浓度变化。RNN的权重对应于系统中的动力学参数，并且可以在网络训练期间逐步调整。该方法应用于p53-Mdm2振荡系统——由损伤信号激活的DNA损伤反应途径的关键组成部分。仿真结果表明，所提出的RNN能够成功地表示p53-Mdm2振荡系统的行为，并高精度地解决参数估计问题。此外，我们提出了一种RNN的改进形式，该形式能够从在相对较大时间步长上收集的稀疏数据中估计参数并捕捉系统动态。我们还使用训练好的RNN在各种参数扰动水平下研究p53-Mdm2系统的鲁棒性，以更好地理解p53-Mdm2系统的控制。其关于鲁棒性的结果与该系统当前的生物学知识一致。随着关于单个蛋白质的更多定量数据可用，RNN将能够完善单个信号分子以及作为一个系统的信号网络的时间动态的参数估计和映射。此外，RNN可用于对大型信号网络进行模块化。
