表观遗传景观上的随机梯度下降：细胞可塑性、肿瘤异质性与适应度渐近无关性的统一框架

中文摘要 AI 辅助

表型可塑性，即细胞在状态之间切换的能力，是发育、分化和治疗耐药性的核心。尽管它在多个尺度上被建模，从区室常微分方程到表型结构偏微分方程和单细胞随机方程，但连接这些描述的框架仍然缺失。我们提出了这样一个框架。从一个包含非线性生长和表型间线性转变的通用$n$区室常微分方程模型出发，我们通过一个关于最近定理的新的、初等的且可推广的证明表明，在均匀竞争下，长期群体分布仅由转变速率决定。所有表型在饱和时变得选择中性，生长过程中适应度差异的印记以显式速率消退。将转变限制为相邻状态可将模型转化为表型结构反应-扩散-平流偏微分方程的离散化。在这个连续介质模型中，扩散和平流由切换速率识别，适应度仍然渐近无关。将平流速度解释为有效表观遗传势的负梯度，可将偏微分方程转化为福克-普朗克方程，并将单细胞轨迹转化为表型景观上的朗之万意义上的随机梯度下降（SGD）。非局部转变，如突变，通过积分微分项纳入，产生一个包含反应、梯度流、扩散和跳跃的统一模型。状态依赖噪声重塑有效景观而不改变底层势。这为癌症提供了一条通往增强可塑性的途径，而静态的单细胞快照无法将其与改变的景观区分开来。该框架为Waddington景观提供了物理解释，其中细胞执行SGD，而癌症对应于被破坏的景观。

英文摘要

Phenotypic plasticity, the ability of cells to switch between states, is central to development, differentiation, and therapy resistance. Although it is modeled at several scales, from compartmental ODEs to phenotype-structured PDEs and single-cell stochastic equations, a framework connecting these descriptions is missing. We present such a framework. Starting from a general $n$-compartment ODE model encompassing nonlinear growth and linear transitions between phenotypes, we show, with a new, elementary and generalizable proof of a recent theorem, that under uniform competition, the long-term population distribution is solely governed by transition rates. All phenotypes become selectively neutral at saturation, and the imprint of fitness differences during growth fades at an explicit rate. Restricting transitions to neighboring states transforms the model into a discretization of a phenotype-structured reaction-diffusion-advection PDE. In this continuum model, diffusion and advection are identified from switching rates, and fitness remains asymptotically irrelevant. Interpreting the advection velocity as the negative gradient of an effective epigenetic potential transforms the PDE into a Fokker--Planck equation and converts single-cell trajectories into stochastic gradient descent (SGD) in the Langevin sense on the phenotypic landscape. Non-local transitions, such as mutations, are incorporated via an integro-differential term, yielding a unified model with reaction, gradient flow, diffusion, and jumps. State-dependent noise reshapes the effective landscape without altering the underlying potential. This gives cancer a route to elevated plasticity that static, single-cell snapshots cannot distinguish from a changed landscape. This framework provides a physical interpretation of Waddington's landscape, where cells perform SGD, and cancer corresponds to a corrupted landscape.

发表机构

• Instituto de Matemática e Computação, Universidade Federal de Itajubá（伊塔朱巴联邦大学数学与计算研究所）
• Carl Gustav Carus School of Medicine, Technische Universität Dresden（德累斯顿工业大学卡尔·古斯塔夫·卡斯医学院）

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