Most studies of motifs of biological regulatory networks focus on the analysis of asymptotical behaviours (attractors, and even often only stable states), but transient properties are rarely addressed. In the line of our previous study devoted to isolated circuits (Remy et al. in Bioinformatics (Oxford, England) 19(Suppl. 2):172–178, 2003 ), we consider chorded circuits, that are motifs made of an elementary positive or negative circuit with a chord, possibly a self-loop. We provide detailed descriptions of the boolean dynamics of chorded circuits versus isolated circuits, under the synchronous and asynchronous updating schemes within the logical formalism. To this end, we address the description of the trajectories in the dynamics of isolated circuits with coding techniques and adapt them for chorded circuits. The use of the logical modeling gives access to mathematical tools (group actions, analysis of recurrent sequences, coding of trajectories, specific abacus...) allowing complete analytical analysis of basic yet important motifs. In particular, we show that whatever the chosen updating rule, the dynamics depends on a small number of parameters.

中文翻译：

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由孤立和弦电路产生的布尔动力学的组合探索

大多数对生物调节网络基序的研究都集中在渐近行为（吸引子，甚至通常只有稳定状态）的分析上，但很少涉及瞬态特性。在我们之前致力于隔离电路的研究中（Remy 等人在 Bioinformatics (Oxford, England) 19(Suppl. 2):172–178, 2003 中），我们考虑和弦电路，即由基本正数构成的主题或带和弦的负电路，可能是自循环。我们在逻辑形式中的同步和异步更新方案下提供了和弦电路与隔离电路的布尔动态的详细描述。为此，我们使用编码技术解决了隔离电路动力学中轨迹的描述，并使它们适用于和弦电路。使用逻辑建模可以访问数学工具（小组行动、循环序列分析、轨迹编码、特定算盘......），允许对基本但重要的主题进行完整的分析分析。特别是，我们表明无论选择何种更新规则，动态都取决于少量参数。