Cryo-electron microscopy (cryo-EM) is capable of producing reconstructed 3D images of biomolecules at near-atomic resolution. As such, it represents one of the most promising imaging techniques in structural biology. However, raw cryo-EM images are only highly corrupted - noisy and band-pass filtered - 2D projections o…
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25 results for “biomolecules”
Review of mathematical representations for biomolecular data.
problem Complexity and high dimensionality of biomolecular datasets hinder ML applications.
method Developed low-dimensional and scalable mathematical representations using algebraic topology, differential geometry, and graph theory.
result Mathematical representations improve protein-ligand binding predictions and other biomolecular applications.
Current Flash X-ray single-particle diffraction Imaging (FXI) experiments, which operate on modern X-ray Free Electron Lasers (XFELs), can record millions of interpretable diffraction patterns from individual biomolecules per day. Due to the stochastic nature of the XFELs, those patterns will to a varying degree includ…
RNA foldings and Stuck Knotsmath.GT
Study uses knot theory to model RNA foldings, emphasizing both entanglement and intrachain interactions.
problem Modeling RNA foldings considering both entanglement and intrachain interactions.
method Combines knot theory with embedded rigid vertex graphs to emphasize both entanglement and intrachain interactions of RNA foldings.
result Defines and computes a coloring counting invariant for stuck links, providing explicit computations for arc diagrams of RNA foldings.
Study evaluates consistency of feature attribution in deep learning for multi-omics data.
problem Challenges in interpretability of deep learning models in biological research.
method Investigation of Shapley Additive Explanations (SHAP) on multi-view deep learning models applied to multi-omics data.
result SHAP rankings are sensitive to architecture and random initialization, suggesting caution.
Chirality for crooked curvescond-mat.soft
Tensor measures chirality for curves, even those with rough edges.
problem Quantifying chirality for complex, possibly irregular curves.
method Developed a tensorial chirality measure for rigid filaments and curves.
result A curve's chirality can be determined by its twist about perpendicular axes.
This review explores the use of machine learning in discovering collective variables for biomolecular dynamics.
problem Understanding the conformational dynamics and molecular recognition in biomolecules.
method Statistical analysis of high-dimensional spatiotemporal data generated from molecular dynamics simulations.
result Machine learning algorithms can be used to discover abstract collective variables that describe biomolecular dynamics.
A kernel-based approach to molecular conformation analysisphysics.comp-ph
We present a novel machine learning approach to understanding conformation dynamics of biomolecules. The approach combines kernel-based techniques that are popular in the machine learning community with transfer operator theory for analyzing dynamical systems in order to identify conformation dynamics based on molecula…
Nanowire field-effect sensors have recently been developed for label-free detection of biomolecules. In this work, we introduce a computational technique based on Bayesian estimation to determine the physical parameters of the sensor and, more importantly, the properties of the analyte molecules. To that end, we first …
Geometric vector perceptrons improve protein structure learning.
problem Learning from protein structure with efficient and natural representations.
method Introducing geometric vector perceptrons to extend dense layers for Euclidean vectors, integrating geometric and relational reasoning.
result Improves model quality assessment and computational protein design over existing methods.
The functions of proteins and RNAs are determined by a myriad of interactions between their constituent residues, but most quantitative models of how molecular phenotype depends on genotype must approximate this by simple additive effects. While recent models have relaxed this constraint to also account for pairwise in…
Solvents can induce helical knots in simulated biopolymer tubes.
problem Understanding how solvents influence the folding of biopolymers.
method Computer simulations using morphometric solvation techniques.
result Solvents can induce complex helical structures, including knots.
New method generates equilibrium glass configurations efficiently.
problem Sampling equilibrium configurations of amorphous materials is slow and difficult.
method Riemannian stochastic interpolation framework combining Riemannian stochastic interpolant and equivariant flow matching.
result Enforcing geometric and symmetry constraints significantly improves generative performance.
TorsionNet uses reinforcement learning to efficiently generate conformers of flexible molecules.
problem Efficiently generating diverse and representative conformer sets for flexible molecules.
method Sequential conformer search technique based on reinforcement learning under the rigid rotor approximation, trained via curriculum learning.
result TorsionNet outperforms chemoinformatics methods by 4x on large branched alkanes and several orders of magnitude on biopolymer lignin.
Geometric GNNs improve graph discrimination through GWL.
problem Discriminating geometric graphs embedded in Euclidean space.
method Proposed a geometric version of the Weisfeiler-Leman test (GWL) for geometric graphs.
result Characterized the expressive power of geometric GNNs based on physical symmetries.
Despite an explosion in the number of experimentally determined, atomically detailed structures of biomolecules, many critical tasks in structural biology remain data-limited. Whether performance in such tasks can be improved by using large repositories of tangentially related structural data remains an open question. …
Automates feature selection and weighting in molecular systems.
problem Optimal feature selection and alignment in molecular systems.
method Differentiable Information Imbalance (DII) method for automated feature ranking and scaling.
result Automated feature selection and scaling that preserves information content and interpretability.
Energy-based diffusion models improve molecular sampling and simulation.
problem Inconsistency between diffusion model scores and equilibrium distributions.
method Fokker-Planck regularization to enforce consistency.
result Improved consistency and efficient sampling of biomolecular systems.
Identification of high affinity drug-target interactions is a major research question in drug discovery. Proteins are generally represented by their structures or sequences. However, structures are available only for a small subset of biomolecules and sequence similarity is not always correlated with functional similar…
A new framework uses stochastic optimal control to estimate rare events more accurately.
problem Estimating rare events like chemical reactions in biomolecules is computationally challenging.
method The approach casts committor estimation as a stochastic optimal control problem, developing direct and off-policy Value Matching losses.
result The framework yields more accurate committor estimates, reaction rates, and equilibrium constants.
Accelerating the identification of informative reduced representations of proteins with deep learning for graphsphysics.comp-ph
Deep learning speeds up protein mapping entropy calculation.
problem Efficiently calculating the mapping entropy of protein structures.
method Deep graph networks for accelerating mapping entropy computation.
result Deep graph networks achieve a speedup factor of up to 10^5.
Cryo-EM reconstruction is reformulated as a stochastic inverse problem to handle structural heterogeneity.
problem Handling structural heterogeneity in cryo-EM 3D reconstruction.
method Formulated as a stochastic inverse problem over probability measures, using variational discrepancy and Wasserstein gradient flow.
result Validated approach using synthetic examples, demonstrating recovery of continuous structural distributions.
This paper finds efficient algorithms for approximating Markov networks with k-tree topologies.
problem Efficiently approximating Markov networks with complex topologies.
method Developed O(n^{k+1})-time algorithms for finding maximum spanning k-trees (MSkT) that retain certain subgraphs.
result Optimal approximation of Markov networks with k-tree topology is achieved in polynomial time.
Recent years have witnessed a trend that advanced mathematical tools, such as algebraic topology, differential geometry, graph theory, and partial differential equations, have been developed for describing biological macromolecules. These tools have considerably strengthened our ability to understand the molecular mech…
In this thesis we present the novel semi-supervised network-based algorithm P-Net, which is able to rank and classify patients with respect to a specific phenotype or clinical outcome under study. The peculiar and innovative characteristic of this method is that it builds a network of samples/patients, where the nodes …