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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. 

Abstract Understanding how mutations render a drug ineffective is a problem of immense relevance. Often the mechanism through which mutations cause drug resistance can be explained purely through thermodynamics. However, the more perplexing situation is when two proteins have the same drug binding affinities but different residence times. In this work, we demonstrate how all‐atom molecular dynamics simulations using recent developments grounded in statistical mechanics can provide a detailed mechanistic rationale for such variances. We discover dissociation mechanisms for the anti‐cancer drug Imatinib (Gleevec) against wild‐type and the N368S mutant of Abl kinase. We show how this point mutation triggers far‐reaching changes in the protein's flexibility and leads to a different, much faster, drug dissociation pathway. We believe that this work marks an efficient and scalable approach to obtain mechanistic insight into resistance mutations in biomolecular receptors that are hard to explain using a structural perspective. 

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. 

The study of phenomena such as protein folding and conformational changes in molecules is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary tool for the study of transition processes in biomolecules, but it is hampered by a huge timescale gap between the processes of interest and atomic vibrations that dictate the time step size. Therefore, it is imperative to combine MD simulations with other techniques in order to quantify the transition processes taking place on large timescales. In this work, the diffusion map with Mahalanobis kernel, a meshless approach for approximating the Backward Kolmogorov Operator (BKO) in collective variables, is upgraded to incorporate standard enhanced sampling techniques, such as metadynamics. The resulting algorithm, which we call the target measure Mahalanobis diffusion map (tm-mmap), is suitable for a moderate number of collective variables in which one can approximate the diffusion tensor and free energy. Imposing appropriate boundary conditions allows use of the approximated BKO to solve for the committor function and utilization of transition path theory to find the reactive current delineating the transition channels and the transition rate. The proposed algorithm, tm-mmap, is tested on the two-dimensional Moro–Cardin two-well system with position-dependent diffusion coefficient and on alanine dipeptide in two collective variables where the committor, the reactive current, and the transition rate are compared to those computed by the finite element method (FEM). Finally, tm-mmap is applied to alanine dipeptide in four collective variables where the use of finite elements is infeasible. 

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.