Exploring the landscape of model representations

The success of any physical model critically depends upon adopting an appropriate representation for the phenomenon of interest. Unfortunately, it remains generally challenging to identify the essential degrees of freedom or, equivalently, the proper order parameters for describing complex phenomena. Here we develop a statistical physics framework for exploring and quantitatively characterizing the space of order parameters for representing physical systems. Specifically, we examine the space of low-resolution representations that correspond to particle based coarse-grained (CG) models for a simple microscopic model of protein fluctuations. We employ Monte Carlo (MC) methods to sample this space and determine the density of states for CG representations as a function of their ability to preserve the configurational information, I, and large-scale fluctuations, Q, of the microscopic model. These two metrics are uncorrelated in high-resolution representations but become anticorrelated at lower resolutions. Moreover, our MC simulations suggest an emergent length scale for coarse-graining proteins, as well as a qualitative distinction between good and bad representations of proteins. Finally, we relate our work to recent approaches for clustering graphs and detecting communities in networks.

任一物理模型的成功构建，关键在于为所研究的物理现象选取恰当的表征方式。遗憾的是，当前要识别描述复杂现象所需的核心自由度，或等价地确定恰当的序参量（order parameters），仍普遍具有挑战性。本研究构建了一套统计物理框架，用于探索并定量表征用于描述物理系统的序参量空间。具体而言，我们针对一个简化的蛋白质涨落微观模型，研究了与之对应的基于粒子的粗粒度（coarse-grained, CG）模型所对应的低分辨率表征空间。我们采用蒙特卡洛（Monte Carlo, MC）方法对该空间进行采样，并基于CG表征保留微观模型的构型信息I与大尺度涨落Q的能力，计算其态密度。这两项评价指标在高分辨率表征中互不相关，但在低分辨率表征中呈现负相关关系。此外，我们的MC模拟结果表明，蛋白质粗粒化过程存在一个涌现特征长度尺度，同时可区分出优质与劣质的蛋白质表征方式。最后，我们将本研究与近期的图聚类与网络社区检测方法建立关联。