标题： 基于能量景观的理论框架，用于理解动态组分相互作用下生命系统功能的出现 显示英文标题

标题： An energy landscape-based theoretical framework for understanding the emergence of functions in a living system under the dynamical component interaction

摘要： 在由相互作用组分（如分子、细胞和组织）组成的生物系统中，每个组分通常会根据与周围组分的相互作用自适应地改变其内部状态。 例如，单独的组织在受到机械相互作用的影响时，表现出组件级别的自适应行为，如生长和重塑，从而产生多组织系统的功能。 随着组分的自适应行为，它们的相互作用表现出动态变化，这些变化强烈影响系统功能的出现。 为了理解由于组分级别的自适应行为导致的系统功能如何出现，本研究提出了一种理论框架，该框架对由于单个组分的自适应行为引起的组分之间相互作用的动力学进行了形式化。 为了对自适应内部状态的变化进行建模，我们为每个组分分配了一个能量景观及其相关的能量速率景观，从而得到了自适应行为的广义梯度流模型。 然后，我们通过制定由于单个组分的自适应行为导致的每个组分环境状态的时间变化，来表示相互作用的动力学。 通过使用在形态变化下机械相互作用的简化组织模型进行案例研究，我们的理论框架表明，由于单个组织形态变化而产生的施加力的时间变化决定了系统功能的出现。 这些发现表明，基于能量和能量速率景观的时间变化来表达相互作用动力学，为理解系统功能如何从组分级别的自适应行为中出现提供了一个强有力的理论框架。 显示英文摘要

摘要： In a living system composed of interacting components such as molecules, cells, and tissues, each component often adaptively changes its internal states in response to interactions with its surrounding components. For example, individual tissues exhibit component-level adaptive behavior, such as growth and remodeling, in response to their mechanical interactions, resulting in the emergence of functions of a multi-tissue system. Along with the adaptive behavior of the components, their interactions exhibit dynamical changes, which strongly influence the emergence of system functions. To understand how the emergence of system functions occurs from such dynamical interactions due to component-level adaptive behavior, this study proposes a theoretical framework that formulates the dynamics of interactions among components due to the adaptive behavior of individual components. For modeling the adaptive internal state changes, we assign an energy landscape and its associated energy rate landscape for each component, leading to the generalized gradient flow model of adaptive behavior. Then, we represent interaction dynamics based on temporal changes in these energy and energy rate landscapes by formulating temporal changes in the environmental states of each component due to the adaptive behavior of individual components. Through case studies using simplified models of mechanically interacting tissues under morphological changes, our theoretical framework demonstrates that temporal changes in applied forces due to morphological changes of individual tissues determine the emergence of system functions. These findings highlight that expressing interaction dynamics based on temporal changes in energy and energy rate landscapes offers a powerful theoretical framework for understanding how system functions emerge from component-level adaptive behavior.