速率无关的表观遗传学：用于模拟表观遗传反应的热力学一致框架
Rate-Independent Epigenetics: a thermodynamically consistent framework for modelling epigenetic response
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中文总结 AI 辅助
该研究提出速率无关的表观遗传学框架，在速率无关系统理论内建模表观遗传变化，与热力学原理一致。通过假设能量演化原理得出控制方程，建立相关解的存在性等，构建变分时间积分器并证明其性质，还通过实例展示框架研究多稳定性等的能力。
中文摘要 AI 辅助
表观遗传变化是染色质状态的可遗传、长期且可主动逆转的修饰，具有记忆、阈值激活和滞后等速率无关的耗散演化特征。我们提出了一个数学框架——速率无关的表观遗传学，它在速率无关系统理论内对表观遗传变化进行建模，并与热力学定律所确定的两个基本原理相一致。在此框架中，一个模型由表观遗传构型的状态空间、依赖于状态和外部载荷的储能泛函以及编码表观遗传机制对变化的阻力的 1 齐次耗散势指定。假设能量演化原理，无需进一步的建模假设即可得出控制方程。能量平衡是精确的能量守恒，耗散势的 1 齐次性导致非负的最小（经济）耗散。在自然强制性和连续性假设下，我们建立了能量解的存在性，并通过粘性消失建立了平衡粘性解的存在性，这些解解决了表观遗传开关处能量公式的模糊性；在凸性下以及在标量情况下在温和的有限多重性条件下唯一性成立。然后我们构建了一个变分时间积分器，证明了它向能量解的收敛性和全局能量一致性估计。该框架在标量线性回跳算子、具有双阱能量势的示例以及非线性问题上进行了说明，展示了该框架研究多稳定性场景和灾难性开关的能力，并证明了理论结果成立。所提出的框架可被视为一个更丰富的包含粘性耗散特征的热力学一致理论的骨架。
英文摘要
Epigenetic changes -- heritable, long-lived, yet actively reversible modifications of the chromatin state -- display memory, threshold activation and hysteresis, features that are the hallmark of rate-independent dissipative evolution. We propose a mathematical framework, Rate-Independent Epigenetics, that models epigenetic change within the theory of rate-independent systems and is consistent with two fundamental principles identified with the laws of thermodynamics. In this framework, a model is specified by a state space of epigenetic configurations, a stored-energy functional depending on the state and on an external loading, and a 1-homogeneous dissipation potential encoding the resistance of the epigenetic machinery to change. Assuming an energetic evolution principle, the governing equations follow, with no further modelling hypotheses. The energy balance is exact energy conservation, and the 1-homogeneity of the dissipation potential forces a non-negative, minimal (economical) dissipation. Under natural coercivity and continuity assumptions we establish existence of energetic solutions and, via vanishing viscosity, of balanced-viscosity solutions that resolve the ambiguity of the energetic formulation at epigenetic switches; uniqueness holds under convexity and, in the scalar case, under a mild finite-multiplicity condition. We then build a variational time integrator, prove its convergence to energetic solutions and a global energy-consistency estimate. The framework is illustrated on the scalar linear play operator, on an example with a double-well energetic potential, showing the ability of the framework to study multi-stability scenarios and catastrophic switches and on a nonlinear problem, proving that the theoretical results hold. The presented framework can be seen as a skeleton for a richer thermodynamically-consistent theory incorporating viscous dissipation features.
