Making sense of complex systems through resolution, relevance, and mapping entropy

EXCOGITO, an Extensible Coarse-Graining Toolbox for the Investigation of Biomolecules by Means of Low-Resolution Representations

Bottom-up coarse-grained (CG) models proved to be essential to complement and sometimes even replace all-atom representations of soft matter systems and biological macromolecules. The development of low-resolution models takes the moves from the reduction of the degrees of freedom employed, that is, the definition of a mapping between a system's high-resolution description and its simplified counterpart. Even in the absence of an explicit parametrization and simulation of a CG model, the observation of the atomistic system in simpler terms can be informative: this idea is leveraged by the mapping entropy, a measure of the information loss inherent to the process of coarsening. Mapping entropy lies at the heart of the extensible coarse-graining toolbox, EXCOGITO, developed to perform a number of operations and analyses on molecular systems pivoting around the properties of mappings. EXCOGITO can process an all-atom trajectory to compute the mapping entropy, identify the mapping that minimizes it, and establish quantitative relations between a low-resolution representation and the geometrical, structural, and energetic features of the system. Here, the software, which is available free of charge under an open-source license, is presented and showcased to introduce potential users to its capabilities and usage.

Quality assessment and community detection methods for anonymized mobility data in the Italian Covid context

We discuss how to assess the reliability of partial, anonymized mobility data and compare two different methods to identify spatial communities based on movements: Greedy Modularity Clustering (GMC) and the novel Critical Variable Selection (CVS). These capture different aspects of mobility: direct population fluxes (GMC) and the probability for individuals to move between two nodes (CVS). As a test case, we consider movements of Italians before and during the SARS-Cov2 pandemic, using Facebook users' data and publicly available information from the Italian National Institute of Statistics (Istat) to construct daily mobility networks at the interprovincial level. Using the Perron-Frobenius (PF) theorem, we show how the mean stochastic network has a stationary population density state comparable with data from Istat, and how this ceases to be the case if even a moderate amount of pruning is applied to the network. We then identify the first two national lockdowns through temporal clustering of the mobility networks, define two representative graphs for the lockdown and non-lockdown conditions and perform optimal spatial community identification on both graphs using the GMC and CVS approaches. Despite the fundamental differences in the methods, the variation of information (VI) between them assesses that they return similar partitions of the Italian provincial networks in both situations. The information provided can be used to inform policy, for example, to define an optimal scale for lockdown measures. Our approach is general and can be applied to other countries or geographical scales.

Surveying the energy landscape of coarse-grained mappings

Simulations of soft materials often adopt low-resolution coarse-grained (CG) models. However, the CG representation is not unique and its impact upon simulated properties is poorly understood. In this work, we investigate the space of CG representations for ubiquitin, which is a typical globular protein with 72 amino acids. We employ Monte Carlo methods to ergodically sample this space and to characterize its landscape. By adopting the Gaussian network model as an analytically tractable atomistic model for equilibrium fluctuations, we exactly assess the intrinsic quality of each CG representation without introducing any approximations in sampling configurations or in modeling interactions. We focus on two metrics, the spectral quality and the information content, that quantify the extent to which the CG representation preserves low-frequency, large-amplitude motions and configurational information, respectively. The spectral quality and information content are weakly correlated among high-resolution representations but become strongly anticorrelated among low-resolution representations. Representations with maximal spectral quality appear consistent with physical intuition, while low-resolution representations with maximal information content do not. Interestingly, quenching studies indicate that the energy landscape of mapping space is very smooth and highly connected. Moreover, our study suggests a critical resolution below which a "phase transition" qualitatively distinguishes good and bad representations.