arXiv subjects

Frank Noe

Publications and source records attributed to Frank Noe.

12 recordsLinked to original sources

arXiv2025

Accelerating scientific discovery with the common task framework

Machine learning (ML) and artificial intelligence (AI) algorithms are transforming and empowering the characterization and control of dynamic systems in the engineering, physical, and biological sciences. These emerging modeling paradigms require comparative metrics to evaluate a diverse set of scientific objectives, including forecasting, state reconstruction, generalization, and control, while also considering limited data scenarios and noisy measurements. We introduce a common task framework (CTF) for science and engineering, which features a growing collection of challenge data sets with a diverse set of practical and common objectives. The CTF is a critically enabling technology that has contributed to the rapid advance of ML/AI algorithms in traditional applications such as speech recognition, language processing, and computer vision. There is a critical need for the objective metrics of a CTF to compare the diverse algorithms being rapidly developed and deployed in practice today across science and engineering.

cs.LG↗

arXiv2024

The need to implement FAIR principles in biomolecular simulations

This letter illustrates the opinion of the molecular dynamics (MD) community on the need to adopt a new FAIR paradigm for the use of molecular simulations. It highlights the necessity of a collaborative effort to create, establish, and sustain a database that allows findability, accessibility, interoperability, and reusability of molecular dynamics simulation data. Such a development would democratize the field and significantly improve the impact of MD simulations on life science research. This will transform our working paradigm, pushing the field to a new frontier. We invite you to support our initiative at the MDDB community (https://mddbr.eu/community/) Now published as: Amaro, R.E., et al. The need to implement FAIR principles in biomolecular simulations. Nat Methods (2025) https://doi.org/10.1038/s41592-025-02635-0

q-bio.BM↗

arXiv2020

TorchMD: A deep learning framework for molecular simulations

Molecular dynamics simulations provide a mechanistic description of molecules by relying on empirical potentials. The quality and transferability of such potentials can be improved leveraging data-driven models derived with machine learning approaches. Here, we present TorchMD, a framework for molecular simulations with mixed classical and machine learning potentials. All of force computations including bond, angle, dihedral, Lennard-Jones and Coulomb interactions are expressed as PyTorch arrays and operations. Moreover, TorchMD enables learning and simulating neural network potentials. We validate it using standard Amber all-atom simulations, learning an ab-initio potential, performing an end-to-end training and finally learning and simulating a coarse-grained model for protein folding. We believe that TorchMD provides a useful tool-set to support molecular simulations of machine learning potentials. Code and data are freely available at \url{github.com/torchmd}.

physics.chem-ph↗

arXiv2019

Machine Learning of coarse-grained Molecular Dynamics Force Fields

Atomistic or ab-initio molecular dynamics simulations are widely used to predict thermodynamics and kinetics and relate them to molecular structure. A common approach to go beyond the time- and length-scales accessible with such computationally expensive simulations is the definition of coarse-grained molecular models. Existing coarse-graining approaches define an effective interaction potential to match defined properties of high-resolution models or experimental data. In this paper, we reformulate coarse-graining as a supervised machine learning problem. We use statistical learning theory to decompose the coarse-graining error and cross-validation to select and compare the performance of different models. We introduce CGnets, a deep learning approach, that learns coarse-grained free energy functions and can be trained by a force matching scheme. CGnets maintain all physically relevant invariances and allow one to incorporate prior physics knowledge to avoid sampling of unphysical structures. We show that CGnets can capture all-atom explicit-solvent free energy surfaces with models using only a few coarse-grained beads and no solvent, while classical coarse-graining methods fail to capture crucial features of the free energy surface. Thus, CGnets are able to capture multi-body terms that emerge from the dimensionality reduction.

physics.comp-ph↗

arXiv2019

Deep Generative Markov State Models

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-sized vector indicating the membership to metastable (long-lived) states, (ii) a Markov chain that governs the transitions between metastable states and facilitates analysis of the long-time dynamics, and (iii) a generative part that samples the conditional distribution of configurations in the next time step. The model can be operated in a recursive fashion to generate trajectories to predict the system evolution from a defined starting state and propose new configurations. The DeepGenMSM is demonstrated to provide accurate estimates of the long-time kinetics and generate valid distributions for molecular dynamics (MD) benchmark systems. Remarkably, we show that DeepGenMSMs are able to make long time-steps in molecular configuration space and generate physically realistic structures in regions that were not seen in training data.

stat.ML↗

arXiv2016

Reversible Markov chain estimation using convex-concave programming

We present a convex-concave reformulation of the reversible Markov chain estimation problem and outline an efficient numerical scheme for the solution of the resulting problem based on a primal-dual interior point method for monotone variational inequalities. Extensions to situations in which information about the stationary vector is available can also be solved via the convex- concave reformulation. The method can be generalized and applied to the discrete transition matrix reweighting analysis method to perform inference from independent chains with specified couplings between the stationary probabilities. The proposed approach offers a significant speed-up compared to a fixed-point iteration for a number of relevant applications.

physics.data-an↗

arXiv2015

Efficient estimation of rare-event kinetics

The efficient calculation of rare-event kinetics in complex dynamical systems, such as the rate and pathways of ligand dissociation from a protein, is a generally unsolved problem. Markov state models can systematically integrate ensembles of short simulations and thus effectively parallelize the computational effort, but the rare events of interest still need to be spontaneously sampled in the data. Enhanced sampling approaches, such as parallel tempering or umbrella sampling, can accelerate the computation of equilibrium expectations massively - but sacrifice the ability to compute dynamical expectations. In this work we establish a principle to combine knowledge of the equilibrium distribution with kinetics from fast "downhill" relaxation trajectories using reversible Markov models. This approach is general as it does not invoke any specific dynamical model, and can provide accurate estimates of the rare event kinetics. Large gains in sampling efficiency can be achieved whenever one direction of the process occurs more rapid than its reverse, making the approach especially attractive for downhill processes such as folding and binding in biomolecules.

physics.chem-ph↗

arXiv2015

Kinetic distance and kinetic maps from molecular dynamics simulation

Characterizing macromolecular kinetics from molecular dynamics (MD) simulations requires a distance metric that can distinguish slowly-interconverting states. Here we build upon diffusion map theory and define a kinetic distance for irreducible Markov processes that quantifies how slowly molecular conformations interconvert. The kinetic distance can be computed given a model that approximates the eigenvalues and eigenvectors (reaction coordinates) of the MD Markov operator. Here we employ the time-lagged independent component analysis (TICA). The TICA components can be scaled to provide a kinetic map in which the Euclidean distance corresponds to the kinetic distance. As a result, the question of how many TICA dimensions should be kept in a dimensionality reduction approach becomes obsolete, and one parameter less needs to be specified in the kinetic model construction. We demonstrate the approach using TICA and Markov state model (MSM) analyses for illustrative models, protein conformation dynamics in bovine pancreatic trypsin inhibitor and protein-inhibitor association in trypsin and benzamidine.

physics.comp-ph↗

arXiv2013

Spectral rate theory for projected two-state kinetics

Classical rate theories often fail in cases where the observable(s) or order parameter(s) used are poor reaction coordinates or the observed signal is deteriorated by noise, such that no clear separation between reactants and products is possible. Here, we present a general spectral two-state rate theory for ergodic dynamical systems in thermal equilibrium that explicitly takes into account how the system is observed. The theory allows the systematic estimation errors made by standard rate theories to be understood and quantified. We also elucidate the connection of spectral rate theory with the popular Markov state modeling (MSM) approach for molecular simulation studies. An optimal rate estimator is formulated that gives robust and unbiased results even for poor reaction coordinates and can be applied to both computer simulations and single-molecule experiments. No definition of a dividing surface is required. Another result of the theory is a model-free definition of the reaction coordinate quality (RCQ). The RCQ can be bounded from below by the directly computable observation quality (OQ), thus providing a measure allowing the RCQ to be optimized by tuning the experimental setup. Additionally, the respective partial probability distributions can be obtained for the reactant and product states along the observed order parameter, even when these strongly overlap. The effects of both filtering (averaging) and uncorrelated noise are also examined. The approach is demonstrated on numerical examples and experimental single-molecule force probe data of the p5ab RNA hairpin and the apo-myoglobin protein at low pH, here focusing on the case of two-state kinetics.

physics.data-an↗

arXiv2013

Projected and Hidden Markov Models for calculating kinetics and metastable states of complex molecules

Markov state models (MSMs) have been successful in computing metastable states, slow relaxation timescales and associated structural changes, and stationary or kinetic experimental observables of complex molecules from large amounts of molecular dynamics simulation data. However, MSMs approximate the true dynamics by assuming a Markov chain on a clusters discretization of the state space. This approximation is difficult to make for high-dimensional biomolecular systems, and the quality and reproducibility of MSMs has therefore been limited. Here, we discard the assumption that dynamics are Markovian on the discrete clusters. Instead, we only assume that the full phase- space molecular dynamics is Markovian, and a projection of this full dynamics is observed on the discrete states, leading to the concept of Projected Markov Models (PMMs). Robust estimation methods for PMMs are not yet available, but we derive a practically feasible approximation via Hidden Markov Models (HMMs). It is shown how various molecular observables of interest that are often computed from MSMs can be computed from HMMs / PMMs. The new framework is applicable to both, simulation and single-molecule experimental data. We demonstrate its versatility by applications to educative model systems, an 1 ms Anton MD simulation of the BPTI protein, and an optical tweezer force probe trajectory of an RNA hairpin.

physics.chem-ph↗

arXiv2013

Spatiotemporal model of a key step in endocytosis: SNX9 recruitment via phosphoinositides

Clathrin mediated endocytosis (CME) is an ubiquitous cellular pathway that regulates central aspects of cell physiology such as nutrient uptake, modulation of signal transduction, synaptic transmission and membrane turn-over. Endocytic vesicle formation depends on the timed production of specific phosphoinositides and their interactions with various endocytic proteins. Recently, it has been found that phosphatidylinositol-3,4-bisphosphate (PI(3,4)P2) produced by the class II phosphatidylinositol 3-kinase C2alpha plays a key role in the recruitment of the PX-BAR domain protein SNX9, which is proposed to play a role in the constriction of the endocytic vesicle neck [Posor et al, Nature 499, p233 (2013)]. Interestingly, SNX9 and its close paralog SNX18 are not fully specific to PI(3,4)P2 but can also bind other phospholipids, in particular to PI(4,5)P2, an abundant plasma membrane lipid required for the recruitment of many endocytic proteins. In order to understand the dynamical interplay between phospholipids and endocytic proteins, we developed a computational model of the temporal changes in the population of the phosphoinositide-associated endocytic proteins and their spatial distribution at a clathrin-coated pit (CCP). The model resolves single molecules in time and space, and incorporates the complex interplay of proteins and lipids, as well as their movement within the CCP. We find that the comparably small differences in lipid binding affinities of endocytic proteins are amplified by competition among them, allowing for the selective enrichment of SNX9 at late stage CCPs as a result of timed PI(3,4)P2 production.

q-bio.BM↗

arXiv2013

Efficient Bayesian estimation of Markov model transition matrices with given stationary distribution

Direct simulation of biomolecular dynamics in thermal equilibrium is challenging due to the metastable nature of conformation dynamics and the computational cost of molecular dynamics. Biased or enhanced sampling methods may improve the convergence of expectation values of equilibrium probabilities and expectation values of stationary quantities significantly. Unfortunately the convergence of dynamic observables such as correlation functions or timescales of conformational transitions relies on direct equilibrium simulations. Markov state models are well suited to describe both, stationary properties and properties of slow dynamical processes of a molecular system, in terms of a transition matrix for a jump process on a suitable discretiza- tion of continuous conformation space. Here, we introduce statistical estimation methods that allow a priori knowledge of equilibrium probabilities to be incorporated into the estimation of dynamical observables. Both, maximum likelihood methods and an improved Monte Carlo sampling method for reversible transition ma- trices with fixed stationary distribution are given. The sampling approach is applied to a toy example as well as to simulations of the MR121-GSGS-W peptide, and is demonstrated to converge much more rapidly than a previous approach in [F. Noe, J. Chem. Phys. 128, 244103 (2008)]

physics.chem-ph↗