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A Monte Carlo method for in silico modeling and visualization of Waddington’s epigenetic landscape with intermediate details
Biosystems ( IF 1.6 ) Pub Date : 2020-10-17 , DOI: 10.1016/j.biosystems.2020.104275
Xiaomeng Zhang 1 , Ket Hing Chong 1 , Lin Zhu 2 , Jie Zheng 2
Affiliation  

Waddington’s epigenetic landscape is a classic metaphor for describing the cellular dynamics during the development modulated by gene regulation. Quantifying Waddington’s epigenetic landscape by mathematical modeling would be useful for understanding the mechanisms of cell fate determination. A few computational methods have been proposed for quantitative modeling of landscape; however, to model and visualize the landscape of a high dimensional gene regulatory system with realistic details is still challenging. Here, we propose a Monte Carlo method for modeling the Waddington’s epigenetic landscape of a gene regulatory network (GRN). The method estimates the probability distribution of cellular states by collecting a large number of time-course simulations with random initial conditions. By projecting all the trajectories into a 2-dimensional plane of dimensions i and j, we can approximately calculate the quasi-potential U(xi,xj,)=ln P(xi,xj,), where P(xi,xj,) is the estimated probability of an equilibrium steady state or a non-equilibrium state. Compared to the state-of-the-art methods, our Monte Carlo method can quantify the global potential landscape (or emergence behavior) of GRN for a high dimensional system. The potential landscapes show that not only attractors represent stability, but the paths between attractors are also part of the stability or robustness of biological systems. We demonstrate the novelty and reliability of our method by plotting the potential landscapes of a few published models of GRN.



中文翻译:

具有中间细节的 Waddington 表观遗传景观的计算机模拟和可视化的 Monte Carlo 方法

Waddington 的表观遗传景观是描述由基因调控调节的发育过程中细胞动力学的经典隐喻。通过数学建模量化 Waddington 的表观遗传景观将有助于理解细胞命运决定的机制。已经提出了一些用于景观定量建模的计算方法;然而,用逼真的细节对高维基因调控系统的景观进行建模和可视化仍然具有挑战性。在这里,我们提出了一种蒙特卡罗方法,用于对基因调控网络 (GRN) 的 Waddington 表观遗传景观进行建模。该方法通过收集大量具有随机初始条件的时间过程模拟来估计细胞状态的概率分布。一世j,我们可以近似计算准势 (X一世,Xj,)=-输入 (X一世,Xj,), 在哪里 (X一世,Xj,)是平衡稳态或非平衡状态的估计概率。与最先进的方法相比,我们的蒙特卡罗方法可以量化高维系统的 GRN 的全球潜在景观(或涌现行为)。潜在的景观表明,不仅吸引子代表稳定性,而且吸引子之间的路径也是生物系统稳定性或稳健性的一部分。我们通过绘制一些已发布的 GRN 模型的潜在景观来证明我们方法的新颖性和可靠性。

更新日期:2020-10-30
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