Zhou Joseph Xu, Samal Areejit, d'Hérouël Aymeric Fouquier, Price Nathan D, Huang Sui
Institute for Systems Biology, Seattle, WA, USA; Kavli Institute for Theoretical Physics, UC Santa Barbara, CA, USA.
Institute for Systems Biology, Seattle, WA, USA; The Institute of Mathematical Sciences, Chennai, India; The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.
Biosystems. 2016 Apr-May;142-143:15-24. doi: 10.1016/j.biosystems.2016.03.002. Epub 2016 Mar 7.
Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, originally developed for continuous systems, are not suitable for discrete-valued networks which are important tools to study complex systems. In this paper, we provide a framework to quantify the landscape for discrete Boolean networks (BNs). We apply our framework to study pancreas cell differentiation where an ensemble of BN models is considered based on the structure of a minimal GRN for pancreas development. We impose biologically motivated structural constraints (corresponding to specific type of Boolean functions) and dynamical constraints (corresponding to stable attractor states) to limit the space of BN models for pancreas development. In addition, we enforce a novel functional constraint corresponding to the relative ordering of attractor states in BN models to restrict the space of BN models to the biological relevant class. We find that BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics of pancreas cell differentiation. This framework can also determine the genes' influence on cell state transitions, and thus can facilitate the rational design of cell reprogramming protocols.
细胞类型重编程方面的进展重新唤起了人们对沃丁顿表观遗传景观概念的兴趣。最近，研究人员开发了准势理论来表示沃丁顿景观。从细胞的基因调控网络（GRN）中的相互作用推导出来的准势U(x)，量化了网络状态的相对稳定性，而网络状态决定了多稳态动力系统中状态转变所需的努力。然而，最初为连续系统开发的准势景观并不适用于离散值网络，而离散值网络是研究复杂系统的重要工具。在本文中，我们提供了一个框架来量化离散布尔网络（BN）的景观。我们应用我们的框架来研究胰腺细胞分化，其中基于胰腺发育的最小GRN的结构考虑了一组BN模型。我们施加了具有生物学动机的结构约束（对应于特定类型的布尔函数）和动力学约束（对应于稳定吸引子状态），以限制胰腺发育的BN模型空间。此外，我们实施了一种与BN模型中吸引子状态的相对排序相对应的新功能约束，将BN模型的空间限制在生物学相关的类别中。我们发现，具有通道化/符号兼容布尔函数的BN最能捕捉胰腺细胞分化的动态。这个框架还可以确定基因对细胞状态转变的影响，从而有助于合理设计细胞重编程方案。
