Institut de Mathématiques de Luminy, Marseille, France.
J Theor Biol. 2011 Feb 7;270(1):177-84. doi: 10.1016/j.jtbi.2010.09.017. Epub 2010 Sep 22.
This paper deals with the generalized logical framework defined by René Thomas in the 70's to qualitatively represent the dynamics of regulatory networks. In this formalism, a regulatory network is represented as a graph, where nodes denote regulatory components (basically genes) and edges denote regulations between these components. Discrete variables are associated to regulatory components accounting for their levels of expression. In most cases, Boolean variables are enough, but some situations may require further values. Despite this fact, the majority of tools dedicated to the analysis of logical models are restricted to the Boolean case. A formal Boolean mapping of multivalued logical models is a natural way of extending the applicability of these tools. Three decades ago, a multivalued to Boolean variable mapping was proposed by P. Van Ham. Since then, all works related to multivalued logical models and using a Boolean representation rely on this particular mapping. We formally show in this paper that this mapping is actually the sole, up to cosmetic changes, that could preserve the regulatory structures of the underlying graphs as well as their dynamical behaviours.
本文讨论了 René Thomas 在 70 年代定义的广义逻辑框架，用于定性表示调控网络的动态。在这个形式主义中，调控网络表示为一个图，其中节点表示调控组件（基本上是基因），边表示这些组件之间的调控关系。离散变量与调控组件相关联，用于表示它们的表达水平。在大多数情况下，布尔变量就足够了，但有些情况可能需要进一步的值。尽管如此，大多数专门用于分析逻辑模型的工具都仅限于布尔情况。对多值逻辑模型进行形式布尔映射是扩展这些工具适用性的自然方法。三十年前，P. Van Ham 提出了一种多值到布尔变量的映射。从那时起，所有与多值逻辑模型相关的工作以及使用布尔表示都依赖于这种特殊的映射。我们在本文中正式证明，这种映射实际上是唯一的，除了外观上的变化，可以保留底层图的调控结构及其动态行为。
