Geometry of gene regulatory dynamics
Geometry of gene regulatory dynamics
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DOI：
10.1073/pnas.2109729118
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发表时间：
2021-09-21
影响因子：
11.1
通讯作者：
Siggia, Eric D.
中科院分区：
文献类型：
--
作者：
Rand, David A.;Raju, Archishman;Siggia, Eric D.
胚胎发育导致从卵到成虫的复杂性的可重复和有序的外观。不同细胞类型的连续分化阐述了这种复杂性，这是基因网络活动的结果，沃丁顿将其比作流过一个景观的水流，其中山谷代表着不同的命运。几何方法允许正式表示这样的景观和编纂类型的行为，导致微分方程系统。Smale及其同事的研究结果表明，包含基因网络模型的系统可以用黎曼度量表示为潜在梯度，证明了Waddington的隐喻。在这里，我们扩展这种表示，包括参数依赖性和枚举所有三路细胞的决定，可实现通过调整最多两个参数，这可以概括为包括在组织中的空间坐标。由此列举了单元状态与模型参数的所有图。我们统一了一些标准模型的空间格局形成表示他们在潜在的形式（即，地形高程）。图灵系统似乎是非势的，但在适当的变量的动力学是低维和潜在的。时间无关嵌入恢复原始变量。侧抑制由具有许多不稳定方向的鞍点描述。果蝇眼睛模式的模型表现为一种弛豫现象。几何推理为开发提供了直观的动态模型，这些模型很好地适应了时间推移数据。
Embryonic development leads to the reproducible and ordered appearance of complexity from egg to adult. The successive differentiation of different cell types that elaborate this complexity results from the activity of gene networks and was likened by Waddington to a flow through a landscape in which valleys represent alternative fates. Geometric methods allow the formal representation of such landscapes and codify the types of behaviors that result from systems of differential equations. Results from Smale and coworkers imply that systems encompassing gene network models can be represented as potential gradients with a Riemann metric, justifying the Waddington metaphor. Here, we extend this representation to include parameter dependence and enumerate all three-way cellular decisions realizable by tuning at most two parameters, which can be generalized to include spatial coordinates in a tissue. All diagrams of cell states vs. model parameters are thereby enumerated. We unify a number of standard models for spatial pattern formation by expressing them in potential form (i.e., as topographic elevation). Turing systems appear nonpotential, yet in suitable variables the dynamics are low dimensional and potential. A time-independent embedding recovers the original variables. Lateral inhibition is described by a saddle point with many unstable directions. A model for the patterning of the Drosophila eye appears as relaxation in a bistable potential. Geometric reasoning provides intuitive dynamic models for development that are well adapted to fit time-lapse data.