arXiv subjects

Enrico Trizio

Publications and source records attributed to Enrico Trizio.

12 recordsLinked to original sources

arXiv2026

Let's Stalk About Membranes: Committor-Based Enhanced Sampling of Stalk Formation

Membrane fusion is essential for cellular communication and function, and understanding how two lipid bilayers merge is key to informing therapeutic strategies. Functionalized nanoparticles have recently emerged as synthetic fusogens, but the molecular mechanisms driving this process remain unclear, partly because fusion involves transitions over high free-energy barriers, difficult to capture in molecular simulations. While enhanced sampling methods can address this problem, they also rely on the definition of collective variables, which are especially hard to define for fusion, as it arises from the collective rearrangement of many molecules and cannot be easily reduced to a simple intuitive coordinate. Here, we study stalk formation, the first step of fusion, mediated by an amphiphilic gold nanoparticle, by employing an enhanced sampling strategy based on the committor function, machine-learned through a self-consistent procedure. This method requires minimal prior knowledge of the system and leverages the learned committor function as an effective collective variable, enabling uniform sampling of the entire pathway. From the resulting reactive trajectories and extensive transition region sampling, we obtain converged free-energy estimates and mechanistic insight into stalk formation.

cond-mat.soft↗

arXiv2026

Ceci n'est pas un committor, yet it samples like one: efficient sampling via approximated committor functions

Atomistic simulations are widely used to investigate reactive processes but are often limited by the rare event problem due to kinetic bottlenecks. We recently introduced an enhanced sampling approach based on the committor function, machine-learned following a variational principle. This method combines a transition-state-oriented bias potential, expressed as a functional of the committor, with a metadynamics-like bias along a committor-based collective variable, enabling uniform exploration of reaction pathways. In its original formulation, the committor is represented by a neural network that takes physical descriptors as input and is trained by minimizing a functional involving gradients with respect to atomic coordinates, which can be computationally demanding in some cases. Here, we propose a simplified learning criterion formulated entirely in the descriptor space, which bypasses the need for explicit and costly coordinate gradients and provides a relaxed upper bound to the original variational principle. Although this approach does not formally target the exact committor, we show that it retains robust sampling performance while significantly reducing computational costs, thus enabling the study of processes that would be practically unfeasible using the original formulation.

physics.comp-ph↗

arXiv2025

Committors without Descriptors

The study of rare events is one of the major challenges in atomistic simulations, and several enhanced sampling methods towards its solution have been proposed. Recently, it has been suggested that the use of the committor, which provides a precise formal description of rare events, could be of use in this context. We have recently followed up on this suggestion and proposed a committor-based method that promotes frequent transitions between the metastable states of the system and allows extensive sampling of the process transition state ensemble. One of the strengths of our approach is being self-consistent and semi-automatic, exploiting a variational criterion to iteratively optimize a neural-network-based parametrization of the committor, which uses a set of physical descriptors as input. Here, we further automate this procedure by combining our previous method with the expressive power of graph neural networks, which can directly process atomic coordinates rather than descriptors. Besides applications on benchmark systems, we highlight the advantages of a graph-based approach in describing the role of solvent molecules in systems, such as ion pair dissociation or ligand binding.

physics.comp-ph↗

arXiv2025

Enhanced Sampling in the Age of Machine Learning: Algorithms and Applications

Molecular dynamics simulations hold great promise for providing insight into the microscopic behavior of complex molecular systems. However, their effectiveness is often constrained by long timescales associated with rare events. Enhanced sampling methods have been developed to address these challenges, and recent years have seen a growing integration with machine learning techniques. This review provides a comprehensive overview of how they are reshaping the field, with a particular focus on the data-driven construction of collective variables. Furthermore, these techniques have also improved biasing schemes and unlocked novel strategies via reinforcement learning and generative approaches. In addition to methodological advances, we highlight applications spanning different areas such as biomolecular processes, ligand binding, catalytic reactions, and phase transitions. We conclude by outlining future directions aimed at enabling more automated strategies for rare-event sampling.

physics.comp-ph↗

arXiv2024

Advanced simulations with PLUMED: OPES and Machine Learning Collective Variables

Many biological processes occur on time scales longer than those accessible to molecular dynamics simulations. Identifying collective variables (CVs) and introducing an external potential to accelerate them is a popular approach to address this problem. In particular, $\texttt{PLUMED}$ is a community-developed library that implements several methods for CV-based enhanced sampling. This chapter discusses two recent developments that have gained popularity in recent years. The first is the On-the-fly Probability Enhanced Sampling (OPES) method as a biasing scheme. This provides a unified approach to enhanced sampling able to cover many different scenarios: from free energy convergence to the discovery of metastable states, from rate calculation to generalized ensemble simulation. The second development concerns the use of machine learning (ML) approaches to determine CVs by learning the relevant variables directly from simulation data. The construction of these variables is facilitated by the $\texttt{mlcolvar}$ library, which allows them to be optimized in Python and then used to enhance sampling thanks to a native interface inside $\texttt{PLUMED}$. For each of these methods, in addition to a brief introduction, we provide guidelines, practical suggestions and point to examples from the literature to facilitate their use in the study of the process of interest.

physics.comp-ph↗

arXiv2024

Everything everywhere all at once: a probability-based enhanced sampling approach to rare events

The problem of studying rare events is central to many areas of computer simulations. In a recent paper [Kang, P., et al., Nat. Comput. Sci. 4, 451-460, 2024], we have shown that a powerful way of solving this problem passes through the computation of the committor function, and we have demonstrated how the committor can be iteratively computed in a variational way and the transition state ensemble efficiently sampled. Here, we greatly ameliorate this procedure by combining it with a metadynamics-like enhanced sampling approach in which a logarithmic function of the committor is used as a collective variable. This integrated procedure leads to an accurate and balanced sampling of the free energy surface in which transition states and metastable basins are studied with the same thoroughness. We also show that our approach can be used in cases in which competing reactive paths are possible and intermediate metastable are encountered. In addition, we demonstrate how physical insights can be obtained from the optimized committor model and the sampled data, thus providing a full characterization of the rare event under study. We ascribe the success of this approach to the use of a probability-based description of rare events.

physics.comp-ph↗

arXiv2024

Descriptors-free Collective Variables From Geometric Graph Neural Networks

Enhanced sampling simulations make the computational study of rare events feasible. A large family of such methods crucially depends on the definition of some collective variables (CVs) that could provide a low-dimensional representation of the relevant physics of the process. Recently, many methods have been proposed to semi-automatize the CV design by using machine learning tools to learn the variables directly from the simulation data. However, most methods are based on feed-forward neural networks and require as input some user-defined physical descriptors. Here, we propose to bypass this step using a graph neural network to directly use the atomic coordinates as input for the CV model. This way, we achieve a fully automatic approach to CV determination that provides variables invariant under the relevant symmetries, especially the permutational one. Furthermore, we provide different analysis tools to favor the physical interpretation of the final CV. We prove the robustness of our approach using different methods from the literature for the optimization of the CV, and we prove its efficacy on several systems, including a small peptide, an ion dissociation in explicit solvent, and a simple chemical reaction.

physics.comp-ph↗

arXiv2024

Computing the Committor with the Committor: an Anatomy of the Transition State Ensemble

Determining the kinetic bottlenecks that make transitions between metastable states difficult is key to understanding important physical problems like crystallization, chemical reactions, or protein folding. In all these phenomena, the system spends a considerable amount of time in one metastable state before making a rare but important transition to a new state. The rarity of these events makes their direct simulation challenging, if not impossible. We propose a method to explore the distribution of configurations that the system passes as it translocates from one metastable basin to another. We shall refer to this set of configurations as the transition state ensemble. We base our method on the committor function and the variational principle to which it obeys. We find the minimum of the variational principle via a self-consistent procedure that does not require any input besides the knowledge of the initial and final state. Right from the start, our procedure focuses on sampling the transition state ensemble and allows harnessing a large number of such configurations. With the help of the variational principle, we perform a detailed analysis of the transition state ensemble, ranking quantitatively the degrees of freedom mostly involved in the transition and opening the way for a systematic approach for the interpretation of simulation results and the construction of collective variables.

physics.comp-ph↗

arXiv2023

Structure and polymerization of liquid sulfur across the $\lambda$-transition

The anomalous $\lambda$-transition of liquid sulfur, which is supposed to be related to the transformation of eight-membered sulfur rings into long polymeric chains, has attracted considerable attention. However, a detailed description of the underlying dynamical polymerization process is still missing. Here, we study the structures and the mechanism of the polymerization processes of liquid sulfur across the $\lambda$-transition as well as its reverse process of formation of the rings. We do so by performing ab-initio-quality molecular dynamics simulations thanks to a combination of machine learning potentials and state-of-the-art enhanced sampling techniques. With our approach, we obtain structural results that are in good agreement with the experiments and we report precious dynamical insights into the mechanisms involved in the process.

cond-mat.soft↗

arXiv2023

A unified framework for machine learning collective variables for enhanced sampling simulations: $\texttt{mlcolvar}$

Identifying a reduced set of collective variables is critical for understanding atomistic simulations and accelerating them through enhanced sampling techniques. Recently, several methods have been proposed to learn these variables directly from atomistic data. Depending on the type of data available, the learning process can be framed as dimensionality reduction, classification of metastable states or identification of slow modes. Here we present $\texttt{mlcolvar}$, a Python library that simplifies the construction of these variables and their use in the context of enhanced sampling through a contributed interface to the PLUMED software. The library is organized modularly to facilitate the extension and cross-contamination of these methodologies. In this spirit, we developed a general multi-task learning framework in which multiple objective functions and data from different simulations can be combined to improve the collective variables. The library's versatility is demonstrated through simple examples that are prototypical of realistic scenarios.

physics.comp-ph↗

arXiv2023

Deep Learning Collective Variables from Transition Path Ensemble

The study of the rare transitions that take place between long lived metastable states is a major challenge in molecular dynamics simulations. Many of the methods suggested to address this problem rely on the identification of the slow modes of the system which are referred to as collective variables. Recently machine learning methods have been used to learn the collective variables as functions of a large number of physical descriptors. Among many such methods Deep Targeted Discriminant Analysis has proven to be useful. This collective variable is built from data harvested in short unbiased simulation in the two basins. Here we enrich the set of data on which the Deep Targeted Discriminant Analysis collective variable is built by adding data coming from the transition path ensemble. These are collected from a number of reactive trajectories obtained using the On-the-fly Probability Enhanced Sampling Flooding method. The collective variables thus trained, lead to a more accurate sampling and faster convergence. The performance of these new collective variables is tested on a number of representative examples.

physics.chem-ph↗

arXiv2021

From enhanced sampling to reaction profiles

The determination of efficient collective variables is crucial to the success of many enhanced sampling methods. As inspired by previous discrimination approaches, we first collect a set of data from the different metastable basins. The data are then projected with the help of a neural network into a low-dimensional manifold in which data from different basins are well discriminated. This is here guaranteed by imposing that the projected data follows a preassigned distribution. The collective variables thus obtained lead to an efficient sampling and often allow reducing the number of collective variables in a multi-basin scenario. We first check the validity of the method in two-state systems. We then move to multi-step chemical processes. In the latter case, at variance with previous approaches, one single collective variable suffices, leading not only to computational efficiency but to a very clear representation of the reaction free energy profile.

physics.comp-ph↗