8 research outputs found
Functional Maps Representation on Product Manifolds
We consider the tasks of representing, analyzing and manipulating maps
between shapes. We model maps as densities over the product manifold of the
input shapes; these densities can be treated as scalar functions and therefore
are manipulable using the language of signal processing on manifolds. Being a
manifold itself, the product space endows the set of maps with a geometry of
its own, which we exploit to define map operations in the spectral domain; we
also derive relationships with other existing representations (soft maps and
functional maps). To apply these ideas in practice, we discretize product
manifolds and their Laplace--Beltrami operators, and we introduce localized
spectral analysis of the product manifold as a novel tool for map processing.
Our framework applies to maps defined between and across 2D and 3D shapes
without requiring special adjustment, and it can be implemented efficiently
with simple operations on sparse matrices.Comment: Accepted to Computer Graphics Foru
Functional maps representation on product manifolds
We consider the tasks of representing, analysing and manipulating maps between shapes. We model maps as densities over the product manifold of the input shapes; these densities can be treated as scalar functions and therefore are manipulable using the language of signal processing on manifolds. Being a manifold itself, the product space endows the set of maps with a geometry of its own, which we exploit to define map operations in the spectral domain; we also derive relationships with other existing representations (soft maps and functional maps). To apply these ideas in practice, we discretize product manifolds and their Laplace–Beltrami operators, and we introduce localized spectral analysis of the product manifold as a novel tool for map processing. Our framework applies to maps defined between and across 2D and 3D shapes without requiring special adjustment, and it can be implemented efficiently with simple operations on sparse matrices
DiffDock-PP: Rigid Protein-Protein Docking with Diffusion Models
Understanding how proteins structurally interact is crucial to modern
biology, with applications in drug discovery and protein design. Recent machine
learning methods have formulated protein-small molecule docking as a generative
problem with significant performance boosts over both traditional and deep
learning baselines. In this work, we propose a similar approach for rigid
protein-protein docking: DiffDock-PP is a diffusion generative model that
learns to translate and rotate unbound protein structures into their bound
conformations. We achieve state-of-the-art performance on DIPS with a median
C-RMSD of 4.85, outperforming all considered baselines. Additionally,
DiffDock-PP is faster than all search-based methods and generates reliable
confidence estimates for its predictions. Our code is publicly available at
Comment: ICLR Machine Learning for Drug Discovery (MLDD) Workshop 202
DockGame: Cooperative Games for Multimeric Rigid Protein Docking
Protein interactions and assembly formation are fundamental to most
biological processes. Predicting the assembly structure from constituent
proteins -- referred to as the protein docking task -- is thus a crucial step
in protein design applications. Most traditional and deep learning methods for
docking have focused mainly on binary docking, following either a search-based,
regression-based, or generative modeling paradigm. In this paper, we focus on
the less-studied multimeric (i.e., two or more proteins) docking problem. We
introduce DockGame, a novel game-theoretic framework for docking -- we view
protein docking as a cooperative game between proteins, where the final
assembly structure(s) constitute stable equilibria w.r.t. the underlying game
potential. Since we do not have access to the true potential, we consider two
approaches - i) learning a surrogate game potential guided by physics-based
energy functions and computing equilibria by simultaneous gradient updates, and
ii) sampling from the Gibbs distribution of the true potential by learning a
diffusion generative model over the action spaces (rotations and translations)
of all proteins. Empirically, on the Docking Benchmark 5.5 (DB5.5) dataset,
DockGame has much faster runtimes than traditional docking methods, can
generate multiple plausible assembly structures, and achieves comparable
performance to existing binary docking baselines, despite solving the harder
task of coordinating multiple protein chains.Comment: Under Revie
DiffDock: Diffusion Steps, Twists, and Turns for Molecular Docking
Predicting the binding structure of a small molecule ligand to a protein -- a
task known as molecular docking -- is critical to drug design. Recent deep
learning methods that treat docking as a regression problem have decreased
runtime compared to traditional search-based methods but have yet to offer
substantial improvements in accuracy. We instead frame molecular docking as a
generative modeling problem and develop DiffDock, a diffusion generative model
over the non-Euclidean manifold of ligand poses. To do so, we map this manifold
to the product space of the degrees of freedom (translational, rotational, and
torsional) involved in docking and develop an efficient diffusion process on
this space. Empirically, DiffDock obtains a 38% top-1 success rate (RMSD<2A) on
PDBBind, significantly outperforming the previous state-of-the-art of
traditional docking (23%) and deep learning (20%) methods. Moreover, DiffDock
has fast inference times and provides confidence estimates with high selective
accuracy.Comment: Under revie