arXiv subjects

Pilar Cossio

Publications and source records attributed to Pilar Cossio.

At least 19 recordsLinked to original sources

arXiv2026

On the discretization of the object space in inverse problems with application to cryo-electron microscopy

In many inverse problems, the aim is to recover a probability distribution on a latent (or object state) space from indirect, noisy observations. When the observations can be modelled as noisy samples from the mixing latent distribution, the recovery problem is a deconvolution problem on the space of probability measures. A common strategy is to fix a finite set of candidate points and estimate a weight for each, turning the problem into a finite-dimensional concave maximum likelihood problem on the simplex. We study the combined effect of this discretization and of the noise in the context of cryo-electron microscopy (cryo-EM), where the candidate points are biomolecular conformations and the weights describe the relative frequency of each conformation. Our results pertain to both statistical and algorithmic aspects of the estimator. We analyze the weight-recovery problem in which the candidate states and their likelihoods are known. A nearby pair of candidates forces a near-null direction. More generally, the grid and the noise level impose a uniform lower bound on the achievable Kullback--Leibler divergence between observation densities, even with infinite data. The finite-grid estimator is asymptotically normal when its population target is in the interior of the simplex; at a boundary target, its limit is a cone-projected Gaussian. Finally, the exact proximal form of Expectation--Maximization leads to a global high-noise comparison between an early iterate and a KL-penalized likelihood, without a basin assumption or a linearization of the recursion. Tests on synthetic images of the Hsp90 molecule illustrate the theoretical findings and translate them into practical guidelines for interpreting reweighted ensembles.

stat.ME↗

arXiv2026

Measurement-limited learning of conformational heterogeneity in cryo-electron microscopy

Cryogenic electron microscopy images sample individual biomolecules from their conformational landscapes, offering a route to infer the distributions underlying molecular mechanisms. However, because images are indirect measurements, they limit which features of an underlying landscape are statistically identifiable. In ensemble reweighting, this problem appears as a choice of resolution: conformational space is discretized into representative structures whose population weights are inferred from images. Adding structures increases nominal resolution, but nearby conformations may generate overlapping image distributions and indistinguishable weights. Here, we develop an information-theoretic framework that selects representative conformations by maximizing mutual information between ensemble weights and images under a probabilistic forward model. Analytically, we show in a one-dimensional Gaussian model that measurement noise sets the optimal spacing. Applied to molecular conformations sampled from simulation, the framework constructs near-optimal ensembles that span heterogeneity while avoiding redundancy. Thus, the measurement process induces a maximally learnable coarse graining of conformation space.

physics.bio-ph↗

arXiv2026

Stepping up enhanced rate calculations with EATR-flooding

Several recent methods have shown that it is possible to compute rate constants of very slow biomolecular processes using simulations where a time-dependent bias is added along one or several collective variables (CVs). We previously reported the exponential average time-dependent rate (EATR) method, which can improve upon these approaches by accounting for how efficiently the external biasing potential modifies the observed rate using a learned CV-quality factor $\gamma$. This results in more accurate rate estimates using the same data when biasing a suboptimal coordinate. However, as formulated EATR depended on the biasing potential varying over time to properly determine the biasing efficiency, which limits the method's applicability to quasi-static biasing schemes such as ``flooding'' or on-the-fly probability enhanced sampling (OPES). Here, we present the EATR-flooding approach, which generalizes our method by replacing the need for a time dependent bias by instead varying (stepping up) the strength of the biasing potential across multiple sets of simulations. We implement this approach as an open-source Python library, and demonstrate that this approach is accurate without substantial loss of efficiency compared to standard EATR for a coarse-grained protein system, and also show good performance on a fully atomistic cavity-ligand model. Two additional appealing features of EATR-flooding are an internal check for over-biasing and the fact that only a single $\gamma$ parameter is predicted for a given choice of CVs, as compared to our earlier results where $\gamma$ empirically depended on biasing rate. Finally, we believe EATR-flooding applies not only to OPES simulations but more generally to CV biasing enhanced sampling approaches, making it broadly useful.

physics.chem-ph↗

arXiv2026

MIMIC: A Generative Multimodal Foundation Model for Biomolecules

Biological function emerges from coupled constraints across sequence, structure, regulation, evolution, and cellular context, yet most foundation models in biology are trained within one modality or for a fixed forward task. We present MIMIC, a generative multimodal foundation model trained on our newly curated and aligned dataset, LORE, linking nucleic acid, protein, evolutionary, structural, regulatory, and semantic/contextual modalities within partially observed biomolecular states. MIMIC uses a split-track encoder-decoder architecture to condition on arbitrary subsets of observed modalities and reconstruct or generate missing components of molecular state across the genome, transcriptome, and proteome. Multimodal conditioning consistently improves MIMIC's sequence reconstruction relative to sequence-only inputs, while its learned representations enable state-of-the-art performance on RNA and protein downstream tasks. MIMIC achieves state-of-the-art splicing prediction, and its joint generative formulation enables isoform-aware inference that further improves performance. Beyond prediction, the same generative framework supports constrained design. For RNA, MIMIC identifies corrective edits in a clinically relevant HBB splice-disrupting mutation without reverting it by using evolutionary and structural signals. For proteins, jointly conditioning on shape and surface chemistry of PD-L1 and hACE2 binding sites produces diverse, high-confidence sequences with strong in silico support for target binding. Finally, MIMIC uses experimental context as semantic conditioning to model assay-dependent RNA chemical probing, rather than treating context as a fixed output. Together, these results position MIMIC's aligned multimodal generative modeling as a strong foundation for unifying representation learning, conditional prediction, and constrained biomolecular design within a single model.

cs.AI↗

arXiv2026

Robust Inference-Time Steering of Protein Diffusion Models via Embedding Optimization

A core challenge in structural biophysics is generating biomolecular conformations that are both physically plausible and consistent with experimental measurements. While sequence-to-structure diffusion models provide powerful priors, posterior sampling methods steer generation by perturbing atomic coordinates with gradients from experimental likelihoods. However, when the target lies in a low-density region of the prior, these methods require aggressive upweighting of the likelihood that can destabilize sampling and be sensitive to hyperparameters. We propose EmbedOpt, an inference-time steering framework that introduces an orthogonal optimization axis: rather than performing posterior sampling under a fixed prior, EmbedOpt directly optimizes the prior by updating the model's conditional embedding. This embedding space encodes rich coevolutionary signals, so optimizing it shifts the structural prior to align with experimental constraints. Empirically, EmbedOpt matches coordinate-based posterior sampling baselines on sparse distance constraints and outperforms them on cryo-electron microscopy map fitting, including real, noisy experimental ones. Furthermore, EmbedOpt's smooth optimization behavior yields robustness to hyperparameters spanning two orders of magnitude and enables comparable performance with fewer diffusion steps. Code is available at https://github.com/rs-station/embedopt.

cs.LG↗

arXiv2025

Quantitative and Predictive Folding Models from Limited Single-Molecule Data Using Simulation-Based Inference

The study of biomolecular folding has been greatly advanced by single-molecule force spectroscopy (SMFS), which enables the observation of the dynamics of individual molecules. However, extracting quantitative models of fundamental properties such as folding landscapes from SMFS data is very challenging due to instrumental noise, linker artifacts, and the inherent stochasticity of the process, often requiring extensive datasets and complex calibration. Here, we introduce a framework based on simulation-based inference (SBI) that overcomes these limitations by integrating physics-based modeling with deep learning. We first apply this framework to analyze constant-force measurements of a DNA hairpin. From a single experimental trajectory of only two seconds, we successfully reconstruct the hairpin's free energy landscape and folding dynamics, obtaining results in close agreement with established deconvolution methods that require 10-100 times more data. Furthermore, we demonstrate the generality of our approach by applying it to a riboswitch aptamer featuring multiple states and tertiary contacts, resolving the profile of a landscape featuring four metastable states from a single trajectory. The Bayesian nature of this approach robustly quantifies uncertainties for all inferred parameters, including diffusion coefficients and linker stiffness, without needing independent measurements of instrument properties. The inferred models are predictive, generating simulated trajectories that quantitatively reproduce experimental thermodynamics and kinetics. The ability to derive statistically robust models from minimal datasets is crucial for investigating complex biomolecular systems where extensive data collection is impractical, paving the way for novel applications of SMFS.

physics.chem-ph↗

arXiv2025

Cryo-em images are intrinsically low dimensional

Simulation-based inference provides a powerful framework for cryo-electron microscopy, employing neural networks in methods like CryoSBI to infer biomolecular conformations via learned latent representations. This latent space represents a rich opportunity, encoding valuable information about the physical system and the inference process. Harnessing this potential hinges on understanding the underlying geometric structure of these representations. We investigate this structure by applying manifold learning techniques to CryoSBI representations of hemagglutinin (simulated and experimental). We reveal that these high-dimensional data inherently populate low-dimensional, smooth manifolds, with simulated data effectively covering the experimental counterpart. By characterizing the manifold's geometry using Diffusion Maps and identifying its principal axes of variation via coordinate interpretation methods, we establish a direct link between the latent structure and key physical parameters. Discovering this intrinsic low-dimensionality and interpretable geometric organization not only validates the CryoSBI approach but enables us to learn more from the data structure and provides opportunities for improving future inference strategies by exploiting this revealed manifold geometry.

q-bio.QM↗

arXiv2024

PLUMED Tutorials: a collaborative, community-driven learning ecosystem

In computational physics, chemistry, and biology, the implementation of new techniques in a 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.

physics.ed-ph↗

arXiv2024

Estimating the tails of the spectrum of the Hessian of the log-likelihood for \textit{ab-initio} single-particle reconstruction in electron cryomicroscopy

Electron cryomicroscopy (cryo-EM) is a technique in structural biology used to reconstruct accurate volumetric maps of molecules. One step of the cryo-EM pipeline involves solving an inverse-problem. This inverse-problem, referred to as \textit{ab-initio} single-particle reconstruction, takes as input a collection of 2d-images -- each a projection of a molecule from an unknown viewing-angle -- and attempts to reconstruct the 3d-volume representing the underlying molecular density. Most methods for solving this inverse-problem search for a solution which optimizes a posterior likelihood of generating the observed image-data, given the reconstructed volume. Within this framework, it is natural to study the Hessian of the log-likelihood: the eigenvectors and eigenvalues of the Hessian determine how the likelihood changes with respect to perturbations in the solution, and can give insight into the sensitivity of the solution to aspects of the input. In this paper we describe a simple strategy for estimating the smallest eigenvalues and eigenvectors (i.e., the `softest modes') of the Hessian of the log-likelihood for the \textit{ab-initio} single-particle reconstruction problem. This strategy involves rewriting the log-likelihood as a 3d-integral. This interpretation holds in the low-noise limit, as well as in many practical scenarios which allow for noise-marginalization. Once we have estimated the softest modes, we can use them to perform many kinds of sensitivity analysis. For example, we can determine which parts of the reconstructed volume are trustworthy, and which are unreliable, and how this unreliability might depend on the data-set and the imaging parameters. We believe that this kind of analysis can be used alongside more traditional strategies for sensitivity analysis, as well as in other applications, such as free-energy estimation.

q-bio.QM↗

arXiv2024

Simulation-based inference of single-molecule experiments

Single-molecule experiments are a unique tool to characterize the structural dynamics of biomolecules. However, reconstructing molecular details from noisy single-molecule data is challenging. Simulation-based inference (SBI) integrates statistical inference, physics-based simulators, and machine learning and is emerging as a powerful framework for analysing complex experimental data. Recent advances in deep learning have accelerated the development of new SBI methods, enabling the application of Bayesian inference to an ever-increasing number of scientific problems. Here, we review the nascent application of SBI to the analysis of single-molecule experiments. We introduce parametric Bayesian inference and discuss its limitations. We then overview emerging deep-learning-based SBI methods to perform Bayesian inference for complex models encoded in computer simulators. We illustrate the first applications of SBI to single-molecule force-spectroscopy and cryo-electron microscopy experiments. SBI allows us to leverage powerful computer algorithms modeling complex biomolecular phenomena to connect scientific models and experiments in a principled way.

physics.chem-ph↗

arXiv2024

CryoBench: Diverse and challenging datasets for the heterogeneity problem in cryo-EM

Cryo-electron microscopy (cryo-EM) is a powerful technique for determining high-resolution 3D biomolecular structures from imaging data. Its unique ability to capture structural variability has spurred the development of heterogeneous reconstruction algorithms that can infer distributions of 3D structures from noisy, unlabeled imaging data. Despite the growing number of advanced methods, progress in the field is hindered by the lack of standardized benchmarks with ground truth information and reliable validation metrics. Here, we introduce CryoBench, a suite of datasets, metrics, and benchmarks for heterogeneous reconstruction in cryo-EM. CryoBench includes five datasets representing different sources of heterogeneity and degrees of difficulty. These include conformational heterogeneity generated from designed motions of antibody complexes or sampled from a molecular dynamics simulation, as well as compositional heterogeneity from mixtures of ribosome assembly states or 100 common complexes present in cells. We then analyze state-of-the-art heterogeneous reconstruction tools, including neural and non-neural methods, assess their sensitivity to noise, and propose new metrics for quantitative evaluation. We hope that CryoBench will be a foundational resource for accelerating algorithmic development and evaluation in the cryo-EM and machine learning communities. Project page: https://cryobench.cs.princeton.edu.

cs.CV↗

arXiv2024

Active learning of Boltzmann samplers and potential energies with quantum mechanical accuracy

Extracting consistent statistics between relevant free-energy minima of a molecular system is essential for physics, chemistry and biology. Molecular dynamics (MD) simulations can aid in this task but are computationally expensive, especially for systems that require quantum accuracy. To overcome this challenge, we develop an approach combining enhanced sampling with deep generative models and active learning of a machine learning potential (MLP). We introduce an adaptive Markov chain Monte Carlo framework that enables the training of one Normalizing Flow (NF) and one MLP per state, achieving rapid convergence towards the Boltzmann distribution. Leveraging the trained NF and MLP models, we compute thermodynamic observables such as free-energy differences or optical spectra. We apply this method to study the isomerization of an ultrasmall silver nanocluster, belonging to a set of systems with diverse applications in the fields of medicine and catalysis.

physics.chem-ph↗

arXiv2024

Good rates from bad coordinates: the exponential average time-dependent rate approach

Our ability to calculate rates of biochemical processes using molecular dynamics simulations is severely limited by the fact that the time scales for reactions, or changes in conformational state, scale exponentially with the relevant free-energy barriers. In this work, we improve upon a recently proposed rate estimator that allows us to predict transition times with molecular dynamics simulations biased to rapidly explore one or several collective variables. This approach relies on the idea that not all bias goes into promoting transitions, and along with the rate, it estimates a concomitant scale factor for the bias termed the collective variable biasing efficiency $γ$. First, we demonstrate mathematically that our new formulation allows us to derive the commonly used Infrequent Metadynamics (iMetaD) estimator when using a perfect collective variable, $γ=1$. After testing it on a model potential, we then study the unfolding behavior of a previously well characterized coarse-grained protein, which is sufficiently complex that we can choose many different collective variables to bias, but which is sufficiently simple that we are able to compute the unbiased rate dire ctly. For this system, we demonstrate that our new Exponential Average Time-Dependent Rate (EATR) estimator converges to the true rate more rapidly as a function of bias deposition time than does the previous iMetaD approach, even for bias deposition times that are short. We also show that the $γ$ parameter can serve as a good metric for assessing the quality of the biasing coordinate. Finally, we demonstrate that the approach works when combining multiple less-than-optimal bias coordinates.

physics.chem-ph↗

arXiv2023

Microscopic Theory, Analysis, and Interpretation of Conductance Histograms in Molecular Junctions

Molecular electronics break-junction experiments are widely used to investigate fundamental physics and chemistry at the nanoscale. Reproducibility in these experiments relies on measuring conductance on thousands of freshly formed molecular junctions, yielding a broad histogram of conductance events. Experiments typically focus on the most probable conductance, while the information content of the conductance histogram has remained unclear. Here, we develop a theory for the conductance histogram, which accurately fits experimental data and augments the information content that can be extracted, by merging the theory of force-spectroscopy with molecular conductance. Specifically, we propose a microscopic model of the junction evolution under the modulation of external mechanical forces and combine it with the non-equilibrium stochastic features of junction rupture and formation. Our formulation captures contributions to the conductance dispersion that emerge due to changes in the conductance during the mechanical elongation inherent to the experiments. The final histogram shape is determined by the statistics of junction rupture and formation. The procedure yields analytical equations for the conductance histogram in terms of parameters that describe the free-energy profile of the junction, its mechanical manipulation, and the ability of the molecule to transport charge. All physical parameters that define our microscopic model can be obtained from separate conductance and rupture force measurements on molecular junctions. Further, the predicted behavior with respect to physical parameters can be used to test the range of validity of the microscopic model, understand the conductance histograms, and design molecular junction experiments with enhanced resolution and molecular devices with more reproducible conductance properties.

physics.chem-ph↗

arXiv2022

Ensemble reweighting using Cryo-EM particles

Cryo-electron microscopy (cryo-EM) has recently become a premier method for obtaining high-resolution structures of biological macromolecules. However, it is limited to biomolecular samples with low conformational heterogeneity, where all the conformations can be well-sampled at many projection angles. While cryo-EM technically provides single-molecule data for heterogeneous molecules, most existing reconstruction tools cannot extract the full distribution of possible molecular configurations. To overcome these limitations, we build on a prior Bayesian approach and develop an ensemble refinement framework that estimates the ensemble density from a set of cryo-EM particles by reweighting a prior ensemble of conformations, e.g., from molecular dynamics simulations or structure prediction tools. Our work is a general approach to recovering the equilibrium probability density of the biomolecule directly in conformational space from single-molecule data. To validate the framework, we study the extraction of state populations and free energies for a simple toy model and from synthetic cryo-EM images of a simulated protein that explores multiple folded and unfolded conformations.

q-bio.BM↗

arXiv2022

Simulation-based inference of single-molecule force spectroscopy

Single-molecule force spectroscopy (smFS) is a powerful approach to studying molecular self-organization. However, the coupling of the molecule with the ever-present experimental device introduces artifacts, that complicates the interpretation of these experiments. Performing statistical inference to learn hidden molecular properties is challenging because these measurements produce non-Markovian time-series, and even minimal models lead to intractable likelihoods. To overcome these challenges, we developed a computational framework built on novel statistical methods called simulation-based inference (SBI). SBI enabled us to directly estimate the Bayesian posterior, and extract reduced quantitative models from smFS, by encoding a mechanistic model into a simulator in combination with probabilistic deep learning. Using synthetic data, we could systematically disentangle the measurement of hidden molecular properties from experimental artifacts. The integration of physical models with machine learning density estimation is general, transparent, easy to use, and broadly applicable to other types of biophysical experiments.

physics.chem-ph↗

arXiv2022

Ab initio metadynamics determination of temperature-dependent free-energy landscape in ultrasmall silver clusters

Ab initio metadynamics enables extracting free-energy landscapes having the accuracy of first principles electronic structure methods. We introduce an interface between the PLUMED code that computes free-energy landscapes and enhanced-sampling algorithms and the ASE module, which includes several ab initio electronic structure codes. The interface is validated with a Lennard-Jones cluster free-energy landscape calculation by averaging multiple short metadynamics trajectories. We use this interface and analysis to estimate the free-energy landscape of Ag5 and Ag6 clusters at 10, 100 and 300 K with the radius of gyration and coordination number as collective variables, finding at most tens of meV in error. Relative free-energy differences between the planar and non-planar isomers of both clusters decrease with temperature, in agreement with previously proposed stabilization of non-planar isomers. Interestingly, we find that Ag6 is the smallest silver cluster where entropic effects at room temperature boost the non planar isomer probability to a competing state. The new ASE-PLUMED interface enables simulating nanosystem electronic properties at more realistic temperature-dependent conditions.

cond-mat.mtrl-sci↗

arXiv2021

Transition rates, survival probabilities, and quality of bias from time-dependent biased simulations

Simulations with an adaptive time-dependent bias, such as metadynamics, enable an efficient exploration of the conformational space of a system. However, the dynamic information of the system is altered by the bias. With infrequent metadynamics it is possible to recover the transition rate of crossing a barrier, if the collective variables are ideal and there is no bias deposition near the transition state. Unfortunately, for simulations of complex molecules, these conditions are not always fulfilled. To overcome these limitations, and inspired by single-molecule force spectroscopy, we developed a method based on Kramers' theory for calculating the barrier-crossing rate when a time-dependent bias is added to the system. We assess the quality of the bias parameter by measuring how efficiently the bias accelerates the transitions compared to ideal behavior. We present approximate analytical expressions of the survival probability that accurately reproduce the barrier-crossing time statistics, and enable the extraction of the unbiased transition rate even for challenging cases, where previous methods fail.

physics.bio-ph↗