异质性干细胞再生的数学建模：从细胞分裂到沃丁顿表观遗传景观
Mathematical modeling of heterogeneous stem cell regeneration: from cell division to Waddington's epigenetic landscape
AI总结：
本章系统比较了基于拉格朗日坐标和欧拉坐标的细胞分裂建模策略，提出用微分-积分方程刻画沃丁顿表观遗传景观，并结合单细胞RNA测序数据的低维测量连接静态数据与组织发育动态过程。
摘要：
干细胞再生是大多数自我更新组织在发育和维持组织稳态过程中的关键生物学过程。在建立干细胞再生和组织发育的数学模型时，细胞分裂是连接不同尺度生物学过程并导致细胞群体数量和细胞表观遗传状态变化的核心过程。本章重点介绍生物系统中细胞分裂建模的主要策略。拉格朗日坐标建模方法考虑每个细胞内的基因网络动力学以及细胞分裂过程中细胞状态和模型参数的随机变化。相比之下，欧拉坐标建模方法通过微分-积分方程描述具有相同表观遗传状态的细胞群体数量的演化。这些策略分别关注不同尺度的动力学，并由此产生了两种建模沃丁顿表观遗传景观的方法：福克-普朗克方程方法和微分-积分方程方法。微分-积分方程方法基于细胞增殖、凋亡、分化以及细胞分裂过程中表观遗传状态转变的简单假设，来描述细胞群体密度的演化。此外，机器学习方法可以基于单细胞RNA测序数据建立细胞的低维宏观测量。这些低维测量可以量化细胞的表观遗传状态，并成为静态单细胞RNA测序数据与组织发育过程动态方程之间的连接。本章提出的微分-积分方程为理解组织发育和肿瘤进展的复杂生物学过程提供了一种合理的方法。
英文摘要：
Stem cell regeneration is a crucial biological process for most self-renewing tissues during the development and maintenance of tissue homeostasis. In developing the mathematical models of stem cell regeneration and tissue development, cell division is the core process connecting different scale biological processes and leading to changes in cell population number and the epigenetic state of cells. This chapter focuses on the primary strategies for modeling cell division in biological systems. The Lagrange coordinate modeling approach considers gene network dynamics within each cell and random changes in cell states and model parameters during cell division. In contrast, the Euler coordinate modeling approach formulates the evolution of cell population numbers with the same epigenetic state via a differential-integral equation. These strategies focus on different scale dynamics, respectively, and result in two methods of modeling Waddington's epigenetic landscape: the Fokker-Planck equation and the differential-integral equation approaches. The differential-integral equation approach formulates the evolution of cell population density based on simple assumptions in cell proliferation, apoptosis, differentiation, and epigenetic state transitions during cell division. Moreover, machine learning methods can establish low-dimensional macroscopic measurements of a cell based on single-cell RNA sequencing data. The low dimensional measurements can quantify the epigenetic state of cells and become connections between static single-cell RNA sequencing data with dynamic equations for tissue development processes. The differential-integral equation presented in this chapter provides a reasonable approach to understanding the complex biological processes of tissue development and tumor progression.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
