Crumière Anne, Sablik Mathieu
Institut de Mathématiques de Luminy, Campus de Luminy, Marseille Cedex 9, France.
Biosystems. 2008 Oct-Nov;94(1-2):102-8. doi: 10.1016/j.biosystems.2008.05.037. Epub 2008 Aug 3.
We discuss a rule proposed by the biologist Thomas according to which the possibility for a genetic network (represented by a signed directed graph called a regulatory graph) to have several stable states implies the existence of a positive circuit. This result is already known for different models, differential or discrete formalism, but always with a network of genes contained in a single cell. Thus, we can ask about the validity of this rule for a system containing several cells and with intercellular genetic interactions. In this paper, we consider the genetic interactions between several cells located on a d-dimensional lattice, i.e., each point of lattice represents a cell to which we associate the expression level of n genes contained in this cell. With this configuration, we show that the existence of a positive circuit is a necessary condition for a specific form of multistationarity, which naturally corresponds to spatial differentiation. We then illustrate this theorem through the example of the formation of sense organs in Drosophila.
我们讨论生物学家托马斯提出的一条规则，根据该规则，遗传网络（由称为调控图的带符号有向图表示）具有多个稳定状态的可能性意味着存在正回路。这个结果对于不同的模型，无论是微分形式还是离散形式，都是已知的，但总是针对单个细胞中包含的基因网络。因此，我们可以询问这条规则对于包含多个细胞且具有细胞间遗传相互作用的系统是否有效。在本文中，我们考虑位于d维晶格上的多个细胞之间的遗传相互作用，即晶格的每个点代表一个细胞，我们将该细胞中包含的n个基因的表达水平与之关联。通过这种配置，我们表明正回路的存在是一种特定形式的多稳态的必要条件，这种多稳态自然对应于空间分化。然后，我们通过果蝇感觉器官形成的例子来说明这个定理。
