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Phase transitions are ubiquitous across life, yet hard to quantify and describe accurately. In this work, we develop an approach for characterizing generic attributes of phase transitions from very limited observations made deep within different phases’ domains of stability. Our approach is called thermodynamic maps (TM), which combines statistical mechanics and molecular simulations with score-based generative models. TM enable learning the temperature dependence of arbitrary thermodynamic observables across a wide range of temperatures. We show its usefulness by calculating phase transition attributes such as melting temperature, temperature-dependent heat capacities, and critical exponents. For instance, we demonstrate the ability of TM to infer the ferromagnetic phase transition of the Ising model, including temperature-dependent heat capacity and critical exponents, despite never having seen samples from the transition region. In addition, we efficiently characterize the temperature-dependent conformational ensemble and compute melting curves of the two RNA systems: a GCAA tetraloop and the HIV-TAR RNA, which are notoriously hard to sample due to glassy-like energy landscapes. 

Abstract In recent years, predictive machine learning models have gained prominence across various scientific domains. However, their black-box nature necessitates establishing trust in them before accepting their predictions as accurate. One promising strategy involves employing explanation techniques that elucidate the rationale behind a model’s predictions in a way that humans can understand. However, assessing the degree of human interpretability of these explanations is a nontrivial challenge. In this work, we introduce interpretation entropy as a universal solution for evaluating the human interpretability of any linear model. Using this concept and drawing inspiration from classical thermodynamics, we present Thermodynamics-inspired Explainable Representations of AI and other black-box Paradigms, a method for generating optimally human-interpretable explanations in a model-agnostic manner. We demonstrate the wide-ranging applicability of this method by explaining predictions from various black-box model architectures across diverse domains, including molecular simulations, text, and image classification. 

Using simulations or experiments performed at some set of temperatures to learn about the physics or chemistry at some other arbitrary temperature is a problem of immense practical and theoretical relevance. Here we develop a framework based on statistical mechanics and generative artificial intelligence that allows solving this problem. Specifically, we work with denoising diffusion probabilistic models and show how these models in combination with replica exchange molecular dynamics achieve superior sampling of the biomolecular energy landscape at temperatures that were never simulated without assuming any particular slow degrees of freedom. The key idea is to treat the temperature as a fluctuating random variable and not a control parameter as is usually done. This allows us to directly sample from the joint probability distribution in configuration and temperature space. The results here are demonstrated for a chirally symmetric peptide and single-strand RNA undergoing conformational transitions in all-atom water. We demonstrate how we can discover transition states and metastable states that were previously unseen at the temperature of interest and even bypass the need to perform further simulations for a wide range of temperatures. At the same time, any unphysical states are easily identifiable through very low Boltzmann weights. The procedure while shown here for a class of molecular simulations should be more generally applicable to mixing information across simulations and experiments with varying control parameters. 

Abstract Recurrent neural networks have seen widespread use in modeling dynamical systems in varied domains such as weather prediction, text prediction and several others. Often one wishes to supplement the experimentally observed dynamics with prior knowledge or intuition about the system. While the recurrent nature of these networks allows them to model arbitrarily long memories in the time series used in training, it makes it harder to impose prior knowledge or intuition through generic constraints. In this work, we present a path sampling approach based on principle of Maximum Caliber that allows us to include generic thermodynamic or kinetic constraints into recurrent neural networks. We show the method here for a widely used type of recurrent neural network known as long short-term memory network in the context of supplementing time series collected from different application domains. These include classical Molecular Dynamics of a protein and Monte Carlo simulations of an open quantum system continuously losing photons to the environment and displaying Rabi oscillations. Our method can be easily generalized to other generative artificial intelligence models and to generic time series in different areas of physical and social sciences, where one wishes to supplement limited data with intuition or theory based corrections. 

In computational physics, chemistry, and biology, the implementation of new techniques in shared and open-source software lowers barriers to entry and promotes rapid scientific progress. However, effectively training new software users presents several challenges. Common methods like direct knowledge transfer and in-person workshops are limited in reach and comprehensiveness. Furthermore, while the COVID-19 pandemic highlighted the benefits of online training, traditional online tutorials can quickly become outdated and may not cover all the software’s functionalities. To address these issues, here we introduce “PLUMED Tutorials,” a collaborative model for developing, sharing, and updating online tutorials. This initiative utilizes repository management and continuous integration to ensure compatibility with software updates. Moreover, the tutorials are interconnected to form a structured learning path and are enriched with automatic annotations to provide broader context. This paper illustrates the development, features, and advantages of PLUMED Tutorials, aiming to foster an open community for creating and sharing educational resources. 

We report the molecular recognition properties of Pillar[ n ]MaxQ (P[ n ]MQ) toward a series of (methylated) amino acids, amino acid amides, and post-translationally modified peptides by a combination of 1 H NMR, isothermal titration calorimetry, indicator displacement assays, and molecular dynamics simulations. We find that P6MQ is a potent receptor for N -methylated amino acid side chains. P6MQ recognized the H3K4Me 3 peptide with K d = 16 nM in phosphate buffered saline.