超度量扩散、粗糙能量景观和跃迁网络
Ultrametric Diffusion, Rugged Energy Landscapes and Transition Networks
摘要：
在这篇文章中，我们介绍了超度量网络，它是使用主方程构造的标准马尔可夫状态模型的p-adic连续模拟。p-adic转移网络（或超度量网络）是一个复杂系统的模型，它由层次能量景观、能量景观上的马尔可夫过程和主方程组成。我们专注于两个不同盆地之间的过渡率是常数函数的网络，每个盆地内的跳跃过程是由一个p-adic径向函数控制。我们解决明确的柯西问题的主方程连接到这种类型的网络。这个问题的解决方案是网络对给定初始浓度的响应。如果连接到网络的马尔可夫过程是保守的，则网络的长期响应由马尔可夫链控制。如果这个过程不是保守的，网络就有吸收态。我们定义了一个吸收时间，它依赖于初始浓度，如果这个时间是有限的，网络在有限的时间内达到吸收状态。我们在网络的响应中确定了负责将网络带入吸收状态的术语，我们称之为快速转换模式。快速转换模式的存在是假设能量景观是超度量（分层）的结果，并且据我们所知，使用马尔可夫状态模型的标准方法无法获得该结果。如今，人们普遍认为蛋白质的天然状态是可以从任何其他状态快速到达的动力学枢纽。快速跃迁模式的存在意味着超度量网络上的某些状态作为动力学枢纽工作。
英文摘要：
In this article we introduce the ultrametric networks which are p-adic continuous analogues of the standard Markov state models constructed using master equations. A p-adic transition network (or an ultrametric network) is a model of a complex system consisting of a hierarchical energy landscape, a Markov process on the energy landscape, and a master equation. We focus on networks where the transition rates between two different basins are constant functions, and the jumping process inside of each basin is controlled by a p-adic radial function. We solve explicitly the Cauchy problem for the master equation attached to this type of networks. The solution of this problem is the network response to a given initial concentration. If the Markov process attached to the network is conservative, the long term response of the network is controlled by a Markov chain. If the process is not conservative the network has absorbing states. We define an absorbing time, which depends on the initial concentration, if this time is finite the network reaches an absorbing state in a finite time. We identify in the response of the network the terms responsible for bringing the network to an absorbing state, we call them the fast transition modes. The existence of the fast transition modes is a consequence of the assumption that the energy landscape is ultrametric (hierarchical), and to the best of our understanding this result cannot be obtained using standard methods of Markov state models. Nowadays, it is widely accepted that protein native states are kinetic hubs that can be reached quickly from any other state. The existence of fast transition modes implies that certain states on an ultrametric network work as kinetic hubs.
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。
