Ahmad Jamil, Bourdon Jérémie, Eveillard Damien, Fromentin Jonathan, Roux Olivier, Sinoquet Christine
IRCCyN, UMR CNRS, Ecole Centrale de Nantes, France.
Biosystems. 2009 Dec;98(3):149-59. doi: 10.1016/j.biosystems.2009.05.002. Epub 2009 May 13.
The modelling of gene regulatory networks (GRNs) has classically been addressed through very different approaches. Among others, extensions of Thomas's asynchronous Boolean approach have been proposed, to better fit the dynamics of biological systems: genes may reach different discrete expression levels, depending on the states of other genes, called the regulators: thus, activations and inhibitions are triggered conditionally on the proper expression levels of these regulators. In contrast, some fine-grained propositions have focused on the molecular level as modelling the evolution of biological compound concentrations through differential equation systems. Both approaches are limited. The first one leads to an oversimplification of the system, whereas the second is incapable to tackle large GRNs. In this context, hybrid paradigms, that mix discrete and continuous features underlying distinct biological properties, achieve significant advances for investigating biological properties. One of these hybrid formalisms proposes to focus, within a GRN abstraction, on the time delay to pass from a gene expression level to the next. Until now, no research work has been carried out, which attempts to benefit from the modelling of a GRN by differential equations, converting it into a multi-valued logical formalism of Thomas, with the aim of performing biological applications. This paper fills this gap by describing a whole pipelined process which orchestrates the following stages: (i) model conversion from a piece-wise affine differential equation (PADE) modelization scheme into a discrete model with focal points, (ii) characterization of subgraphs through a graph simplification phase which is based on probabilistic criteria, (iii) conversion of the subgraphs into parametric linear hybrid automata, (iv) analysis of dynamical properties (e.g. cyclic behaviours) using hybrid model-checking techniques. The present work is the outcome of a methodological investigation launched to cope with the GRN responsible for the reaction of Escherichia coli bacterium to carbon starvation. As expected, we retrieve a remarkable cycle already exhibited by a previous analysis of the PADE model. Above all, hybrid model-checking enables us to infer temporal properties, whose biological signification is then discussed.
基因调控网络（GRN）的建模传统上采用了非常不同的方法。其中，有人提出了托马斯异步布尔方法的扩展，以更好地拟合生物系统的动态：基因可能会根据其他基因（称为调节因子）的状态达到不同的离散表达水平；因此，激活和抑制是根据这些调节因子的适当表达水平有条件地触发的。相比之下，一些细粒度的提议则侧重于分子水平，即通过微分方程系统对生物化合物浓度的演变进行建模。这两种方法都有局限性。第一种方法导致系统过度简化，而第二种方法无法处理大型GRN。在这种情况下，混合范式结合了不同生物学特性背后的离散和连续特征，在研究生物学特性方面取得了显著进展。其中一种混合形式主义建议在GRN抽象中关注从一个基因表达水平过渡到下一个水平的时间延迟。到目前为止，还没有研究工作尝试从通过微分方程对GRN进行建模中受益，并将其转换为托马斯的多值逻辑形式主义，以进行生物学应用。本文通过描述一个完整的流水线过程填补了这一空白，该过程编排了以下阶段：（i）从分段仿射微分方程（PADE）建模方案转换为具有焦点的离散模型，（ii）通过基于概率标准的图形简化阶段对子图进行特征化，（iii）将子图转换为参数线性混合自动机，（iv）使用混合模型检查技术分析动态特性（例如循环行为）。目前的工作是为应对负责大肠杆菌对碳饥饿反应的GRN而开展的方法学研究的成果。不出所料，我们检索到了先前对PADE模型分析中已经展示的一个显著循环。最重要的是，混合模型检查使我们能够推断时间特性，然后讨论其生物学意义。
