Multistability and natural biological variability can result in significant heterogeneity within a cell population, leading to challenges in understanding and modulating cell behavior. Energy landscapes can offer qualitatively intuitive visualizations of cell phenotype and facilitate a more quantitative understanding of cellular dynamics, but current methods for landscape generation are mathematically involved and often require specific system properties (e.g., ergodicity or independent gene/protein probability distributions) that do not always hold. Here, we present a simple kinetic Monte Carlo-based method for landscape generation from a system of ordinary differential equations using only simulation trajectories initialized throughout the phase space of interest. The resulting landscape produces three quantitative features relevant to understanding cell behavior: stability (reflected by the depth or potential of landscape valleys), velocity (representing average directional movement on the landscape), and variance in velocity (indicative of landscape positions with heterogeneous movements). We applied this method to a genetic toggle switch, a core decision-making network in binary cellular responses, to elucidate effects of biologically relevant intrinsic and extrinsic cues. Intrinsic noise, such as stochasticity in transcription-translation and differences in cell cycle position, manifests through changes in valley width and position, reflecting increased population heterogeneity and more probabilistic cell fate transitions. The landscapes also capture the effect of an external inducer, revealing a quantitative correlation between the rate of cell fate transition and the energy barrier above a threshold inducer concentration determined by the permissivity of the valley. Further, in tracking dynamically changing landscapes under time-varying external cues, we unexpectedly found that an oscillatory inducer input can modulate cell fate heterogeneity and lead to periodic cell fate transitions entrained to the input frequency, depending on the intrinsic degradation rate of the switch. The landscape generation approach outlined herein is generalizable to other network topologies and may provide new quantitative insights into their dynamics.

中文翻译：

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基于轨迹的基因调控网络能量景观

多稳定性和自然生物变异性会导致细胞群内的显着异质性，从而对理解和调节细胞行为带来挑战。能量景观可以提供细胞表型的定性直观可视化，并有助于对细胞动力学进行更定量的理解，但目前用于景观生成的方法在数学上涉及并且通常需要特定的系统属性（例如，遍历性或独立的基因/蛋白质概率分布）永远持有。在这里，我们提出了一种简单的基于动力学蒙特卡罗的方法，用于从常微分方程系统中生成景观，该系统仅使用在整个感兴趣相空间中初始化的模拟轨迹。由此产生的景观产生与理解细胞行为相关的三个定量特征：稳定性（由景观山谷的深度或潜力反映）、速度（代表景观上的平均定向运动）和速度变化（指示具有异质运动的景观位置） . 我们将此方法应用于遗传切换开关，这是二元细胞反应中的核心决策网络，以阐明生物学相关的内在和外在线索的影响。内在噪声，例如转录翻译的随机性和细胞周期位置的差异，通过谷宽和位置的变化表现出来，反映了群体异质性的增加和细胞命运转变的概率。景观还捕捉到了外部诱因的影响，揭示了细胞命运转变率与高于阈值诱导剂浓度的能垒之间的定量相关性，该阈值诱导剂浓度由谷​​的许可率决定。此外，在随时间变化的外部线索下跟踪动态变化的景观时，我们意外地发现，振荡诱导剂输入可以调节细胞命运的异质性，并导致周期性的细胞命运转变被输入频率所夹带，这取决于开关的内在退化率。本文概述的景观生成方法可推广到其他网络拓扑，并可能为其动态提供新的定量见解。在随时间变化的外部线索下跟踪动态变化的景观时，我们出乎意料地发现，振荡诱导剂输入可以调节细胞命运的异质性，并导致周期性的细胞命运转变与输入频率有关，这取决于开关的内在退化率。本文概述的景观生成方法可推广到其他网络拓扑，并可能为其动态提供新的定量见解。在随时间变化的外部线索下跟踪动态变化的景观时，我们出乎意料地发现，振荡诱导剂输入可以调节细胞命运的异质性，并导致周期性的细胞命运转变与输入频率有关，这取决于开关的内在退化率。本文概述的景观生成方法可推广到其他网络拓扑，并可能为其动态提供新的定量见解。