"Layer-by-layer" Unsupervised Clustering of Statistically Relevant Fluctuations in Noisy Time-series Data of Complex Dynamical Systems

Complex systems are typically characterized by intricate internal dynamics that are often hard to elucidate. Ideally, this requires methods that allow to detect and classify in unsupervised way the microscopic dynamical events occurring in the system. However, decoupling statistically relevant fluctuations from the internal noise remains most often non-trivial. Here we describe "Onion Clustering": a simple, iterative unsupervised clustering method that efficiently detects and classifies statistically relevant fluctuations in noisy time-series data. We demonstrate its efficiency by analyzing simulation and experimental trajectories of various systems with complex internal dynamics, ranging from the atomic- to the microscopic-scale, in- and out-of-equilibrium. The method is based on an iterative detect-classify-archive approach. In similar way as peeling the external (evident) layer of an onion reveals the internal hidden ones, the method performs a first detection and classification of the most populated dynamical environment in the system and of its characteristic noise. The signal of such dynamical cluster is then removed from the time-series data and the remaining part, cleared-out from its noise, is analyzed again. At every iteration, the detection of hidden dynamical sub-domains is facilitated by an increasing (and adaptive) relevance-to-noise ratio. The process iterates until no new dynamical domains can be uncovered, revealing, as an output, the number of clusters that can be effectively distinguished/classified in statistically robust way as a function of the time-resolution of the analysis. Onion Clustering is general and benefits from clear-cut physical interpretability. We expect that it will help analyzing a variety of complex dynamical systems and time-series data.Comment: 29 pages, 9 figures. Errors in labels in Fig5 correcte

A Data-Driven Dimensionality Reduction Approach to Compare and Classify Lipid Force Fields

Molecular dynamics simulations of all-atom and coarse-grained lipid bilayer models are increasingly used to obtain useful insights for understanding the structural dynamics of these assemblies. In this context, one crucial point concerns the comparison of the performance and accuracy of classical force fields (FFs), which sometimes remains elusive. To date, the assessments performed on different classical potentials are mostly based on the comparison with experimental observables, which typically regard average properties. However, local differences of the structure and dynamics, which are poorly captured by average measurements, can make a difference, but these are nontrivial to catch. Here, we propose an agnostic way to compare different FFs at different resolutions (atomistic, united-atom, and coarse-grained), by means of a high-dimensional similarity metrics built on the framework of Smooth Overlap of Atomic Position (SOAP). We compare and classify a set of 13 FFs, modeling 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) bilayers. Our SOAP kernel-based metrics allows us to compare, discriminate, and correlate different FFs at different model resolutions in an unbiased, high-dimensional way. This also captures differences between FFs in modeling nonaverage events (originating from local transitions), for example, the liquid-to-gel phase transition in dipalmitoylphosphatidylcholine (DPPC) bilayers, for which our metrics allows us to identify nucleation centers for the phase transition, highlighting some intrinsic resolution limitations in implicit versus explicit solvent FFs

Detecting dynamic domains and local fluctuations in complex molecular systems via timelapse neighbors shuffling

Many complex molecular systems owe their properties to local dynamic rearrangements or fluctuations that, despite the rise of machine learning (ML) and sophisticated structural descriptors, remain often difficult to detect. Here we show an ML framework based on a new descriptor, named Local Environments and Neighbors Shuffling (LENS), which allows identifying dynamic domains and detecting local fluctuations in a variety of systems via tracking how much the surrounding of each molecular unit changes over time in terms of neighbor individuals. Statistical analysis of the LENS time-series data allows to blindly detect different dynamic domains within various types of molecular systems with, e.g., liquid-like, solid-like, or diverse dynamics, and to track local fluctuations emerging within them in an efficient way. The approach is found robust, versatile, and, given the abstract definition of the LENS descriptor, capable of shedding light on the dynamic complexity of a variety of (not necessarily molecular) systems

Automatic Middle-Out Optimisation of Coarse-Grained Lipid Force Fields

Automatic data-driven approaches are increasingly used to develop accurate molecular models. But the parameters of such automatically-optimised models are typically untransferable. Using a multi-reference approach in combination with an automatic optimisation engine (SwarmCGM), here we show that it is possible to optimise coarse-grained (CG) lipid models that are also transferable, generating optimised lipid force fields. The parameters of the CG lipid models are iteratively and simultaneously optimised against higher-resolution simulations (bottom-up) and experimental data (top-down references). Including different types of lipid bilayers in the training set guarantees the transferability of the optimised force field parameters. Tested against state-of-the-art CG lipid force fields, we demonstrate that SwarmCGM can systematically improve their parameters, enhancing the agreement with the experiments even for lipid types not included in the training set. The approach is general and can be used to improve existing CG lipid force fields, as well as to develop new custom ones.Comment: Paper (Pages 1-16) + Supporting Information (Pages 17-40

Supramolecular Semiconductivity through Emerging Ionic Gates in Ion–Nanoparticle Superlattices

The self-assembly of nanoparticles driven by small molecules or ions may produce colloidal superlattices with features and properties reminiscent of those of metals or semiconductors. However, to what extent the properties of such supramolecular crystals actually resemble those of atomic materials often remains unclear. Here, we present coarse-grained molecular simulations explicitly demonstrating how a behavior evocative of that of semiconductors may emerge in a colloidal superlattice. As a case study, we focus on gold nanoparticles bearing positively charged groups that self-assemble into FCC crystals via mediation by citrate counterions. In silico ohmic experiments show how the dynamically diverse behavior of the ions in different superlattice domains allows the opening of conductive ionic gates above certain levels of applied electric fields. The observed binary conductive/nonconductive behavior is reminiscent of that of conventional semiconductors, while, at a supramolecular level, crossing the "band gap " requires a sufficient electrostatic stimulus to break the intermolecular interactions and make ions diffuse throughout the superlattice's cavities

TimeSOAP: Tracking high-dimensional fluctuations in complex molecular systems via time variations of SOAP spectra

Many molecular systems and physical phenomena are controlled by local fluctuations and microscopic dynamical rearrangements of the constitutive interacting units that are often difficult to detect. This is the case, for example, of phase transitions, phase equilibria, nucleation events, and defect propagation, to mention a few. A detailed comprehension of local atomic environments and of their dynamic rearrangements is essential to understand such phenomena and also to draw structure-property relationships useful to unveil how to control complex molecular systems. Considerable progress in the development of advanced structural descriptors [e.g., Smooth Overlap of Atomic Position (SOAP), etc.] has certainly enhanced the representation of atomic-scale simulations data. However, despite such efforts, local dynamic environment rearrangements still remain difficult to elucidate. Here, exploiting the structurally rich description of atomic environments of SOAP and building on the concept of time-dependent local variations, we developed a SOAP-based descriptor, TimeSOAP (τSOAP), which essentially tracks time variations in local SOAP environments surrounding each molecule (i.e., each SOAP center) along ensemble trajectories. We demonstrate how analysis of the time-series τSOAP data and of their time derivatives allows us to detect dynamic domains and track instantaneous changes of local atomic arrangements (i.e., local fluctuations) in a variety of molecular systems. The approach is simple and general, and we expect that it will help shed light on a variety of complex dynamical phenomena

Machine learning of microscopic structure-dynamics relationships in complex molecular systems

In many complex molecular systems, the macroscopic ensemble's properties are controlled by microscopic dynamic events (or fluctuations) that are often difficult to detect via pattern-recognition approaches. Discovering the relationships between local structural environments and the dynamical events originating from them would allow unveiling microscopic level structure-dynamics relationships fundamental to understand the macroscopic behavior of complex systems. Here we show that, by coupling advanced structural (e.g., Smooth Overlap of Atomic Positions, SOAP) with local dynamical descriptors (e.g., Local Environment and Neighbor Shuffling, LENS) in a unique dataset, it is possible to improve both individual SOAP- and LENS-based analyses, obtaining a more complete characterization of the system under study. As representative examples, we use various molecular systems with diverse internal structural dynamics. On the one hand, we demonstrate how the combination of structural and dynamical descriptors facilitates decoupling relevant dynamical fluctuations from noise, overcoming the intrinsic limits of the individual analyses. Furthermore, machine learning approaches also allow extracting from such combined structural/dynamical dataset useful microscopic-level relationships, relating key local dynamical events (e.g., LENS fluctuations) occurring in the systems to the local structural (SOAP) environments they originate from. Given its abstract nature, we believe that such an approach will be useful in revealing hidden microscopic structure-dynamics relationships fundamental to rationalize the behavior of a variety of complex systems, not necessarily limited to the atomistic and molecular scales