arXiv subjects

Umberto Lupo

Publications and source records attributed to Umberto Lupo.

12 recordsLinked to original sources

arXiv2024

DiffPaSS -- High-performance differentiable pairing of protein sequences using soft scores

Identifying interacting partners from two sets of protein sequences has important applications in computational biology. Interacting partners share similarities across species due to their common evolutionary history, and feature correlations in amino acid usage due to the need to maintain complementary interaction interfaces. Thus, the problem of finding interacting pairs can be formulated as searching for a pairing of sequences that maximizes a sequence similarity or a coevolution score. Several methods have been developed to address this problem, applying different approximate optimization methods to different scores. We introduce DiffPaSS, a differentiable framework for flexible, fast, and hyperparameter-free optimization for pairing interacting biological sequences, which can be applied to a wide variety of scores. We apply it to a benchmark prokaryotic dataset, using mutual information and neighbor graph alignment scores. DiffPaSS outperforms existing algorithms for optimizing the same scores. We demonstrate the usefulness of our paired alignments for the prediction of protein complex structure. DiffPaSS does not require sequences to be aligned, and we also apply it to non-aligned sequences from T cell receptors.

q-bio.BM↗

arXiv2023

Pairing interacting protein sequences using masked language modeling

Predicting which proteins interact together from amino-acid sequences is an important task. We develop a method to pair interacting protein sequences which leverages the power of protein language models trained on multiple sequence alignments, such as MSA Transformer and the EvoFormer module of AlphaFold. We formulate the problem of pairing interacting partners among the paralogs of two protein families in a differentiable way. We introduce a method called DiffPALM that solves it by exploiting the ability of MSA Transformer to fill in masked amino acids in multiple sequence alignments using the surrounding context. MSA Transformer encodes coevolution between functionally or structurally coupled amino acids. We show that it captures inter-chain coevolution, while it was trained on single-chain data, which means that it can be used out-of-distribution. Relying on MSA Transformer without fine-tuning, DiffPALM outperforms existing coevolution-based pairing methods on difficult benchmarks of shallow multiple sequence alignments extracted from ubiquitous prokaryotic protein datasets. It also outperforms an alternative method based on a state-of-the-art protein language model trained on single sequences. Paired alignments of interacting protein sequences are a crucial ingredient of supervised deep learning methods to predict the three-dimensional structure of protein complexes. DiffPALM substantially improves the structure prediction of some eukaryotic protein complexes by AlphaFold-Multimer, without significantly deteriorating any of those we tested. It also achieves competitive performance with using orthology-based pairing.

q-bio.BM↗

arXiv2023

Impact of phylogeny on structural contact inference from protein sequence data

Local and global inference methods have been developed to infer structural contacts from multiple sequence alignments of homologous proteins. They rely on correlations in amino-acid usage at contacting sites. Because homologous proteins share a common ancestry, their sequences also feature phylogenetic correlations, which can impair contact inference. We investigate this effect by generating controlled synthetic data from a minimal model where the importance of contacts and of phylogeny can be tuned. We demonstrate that global inference methods, specifically Potts models, are more resilient to phylogenetic correlations than local methods, based on covariance or mutual information. This holds whether or not phylogenetic corrections are used, and may explain the success of global methods. We analyse the roles of selection strength and of phylogenetic relatedness. We show that sites that mutate early in the phylogeny yield false positive contacts. We consider natural data and realistic synthetic data, and our findings generalise to these cases. Our results highlight the impact of phylogeny on contact prediction from protein sequences and illustrate the interplay between the rich structure of biological data and inference.

q-bio.BM↗

arXiv2022

Generative power of a protein language model trained on multiple sequence alignments

Computational models starting from large ensembles of evolutionarily related protein sequences capture a representation of protein families and learn constraints associated to protein structure and function. They thus open the possibility for generating novel sequences belonging to protein families. Protein language models trained on multiple sequence alignments, such as MSA Transformer, are highly attractive candidates to this end. We propose and test an iterative method that directly employs the masked language modeling objective to generate sequences using MSA Transformer. We demonstrate that the resulting sequences score as well as natural sequences, for homology, coevolution and structure-based measures. For large protein families, our synthetic sequences have similar or better properties compared to sequences generated by Potts models, including experimentally-validated ones. Moreover, for small protein families, our generation method based on MSA Transformer outperforms Potts models. Our method also more accurately reproduces the higher-order statistics and the distribution of sequences in sequence space of natural data than Potts models. MSA Transformer is thus a strong candidate for protein sequence generation and protein design.

q-bio.BM↗

arXiv2022

Protein language models trained on multiple sequence alignments learn phylogenetic relationships

Self-supervised neural language models with attention have recently been applied to biological sequence data, advancing structure, function and mutational effect prediction. Some protein language models, including MSA Transformer and AlphaFold's EvoFormer, take multiple sequence alignments (MSAs) of evolutionarily related proteins as inputs. Simple combinations of MSA Transformer's row attentions have led to state-of-the-art unsupervised structural contact prediction. We demonstrate that similarly simple, and universal, combinations of MSA Transformer's column attentions strongly correlate with Hamming distances between sequences in MSAs. Therefore, MSA-based language models encode detailed phylogenetic relationships. We further show that these models can separate coevolutionary signals encoding functional and structural constraints from phylogenetic correlations reflecting historical contingency. To assess this, we generate synthetic MSAs, either without or with phylogeny, from Potts models trained on natural MSAs. We find that unsupervised contact prediction is substantially more resilient to phylogenetic noise when using MSA Transformer versus inferred Potts models.

q-bio.BM↗

arXiv2022

ICLR 2022 Challenge for Computational Geometry and Topology: Design and Results

This paper presents the computational challenge on differential geometry and topology that was hosted within the ICLR 2022 workshop ``Geometric and Topological Representation Learning". The competition asked participants to provide implementations of machine learning algorithms on manifolds that would respect the API of the open-source software Geomstats (manifold part) and Scikit-Learn (machine learning part) or PyTorch. The challenge attracted seven teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

cs.CG↗

arXiv2022

Persistence Steenrod modules

It has long been envisioned that the strength of the barcode invariant of filtered cellular complexes could be increased using cohomology operations. Leveraging recent advances in the computation of Steenrod squares, we introduce a new family of computable invariants on mod 2 persistent cohomology termed $Sq^k$-barcodes. We present a complete algorithmic pipeline for their computation and illustrate their real-world applicability using the space of conformations of the cyclo-octane molecule.

math.AT↗

arXiv2021

ICLR 2021 Challenge for Computational Geometry & Topology: Design and Results

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

cs.CG↗

arXiv2021

giotto-ph: A Python Library for High-Performance Computation of Persistent Homology of Vietoris-Rips Filtrations

We introduce giotto-ph, a high-performance, open-source software package for the computation of Vietoris-Rips barcodes. giotto-ph is based on Morozov and Nigmetov's lockfree (multicore) implementation of Ulrich Bauer's Ripser package. It also contains a re-working of the GUDHI library's implementation of Boissonnat and Pritam's Edge Collapser, which can be used as a pre-processing step to dramatically reduce overall run-times in certain scenarios. Our contribution is twofold: on the one hand, we integrate existing state-of-the-art ideas coherently in a single library and provide Python bindings to the C++ code. On the other hand, we increase parallelization opportunities and improve overall performance by adopting more efficient data structures. Our persistent homology backend establishes a new state of the art, surpassing even GPU-accelerated implementations such as Ripser++ when using as few as 5-10 CPU cores. Furthermore, our implementation of Edge Collapser has fewer software dependencies and improved run-times relative to GUDHI's original implementation.

cs.CG↗

arXiv2021

giotto-tda: A Topological Data Analysis Toolkit for Machine Learning and Data Exploration

We introduce giotto-tda, a Python library that integrates high-performance topological data analysis with machine learning via a scikit-learn-compatible API and state-of-the-art C++ implementations. The library's ability to handle various types of data is rooted in a wide range of preprocessing techniques, and its strong focus on data exploration and interpretability is aided by an intuitive plotting API. Source code, binaries, examples, and documentation can be found at https://github.com/giotto-ai/giotto-tda.

cs.LG↗

arXiv2018

On the global "two-sided" characteristic Cauchy problem for linear wave equations on manifolds

The global characteristic initial value problem for linear wave equations on globally hyperbolic Lorentzian manifolds is examined, for a class of smooth initial value hypersurfaces satisfying favourable global properties. First it is shown that, if geometrically well-motivated restrictions are placed on the supports of the (smooth) initial datum and of the (smooth) inhomogeneous term, then there exists a continuous global solution which is smooth "on each side" of the initial value hypersurface. A uniqueness result in Sobolev regularity $H^{1/2+\varepsilon}_\mathrm{loc}$ is proved among solutions supported in the union of the causal past and future of the initial value hypersurface, and whose product with the indicator function of the causal future (resp. past) of the hypersurface is past compact (resp. future compact). An explicit representation formula for solutions is obtained, which prominently features an invariantly defined, densitised version of the null expansion of the hypersurface. Finally, applications to quantum field theory on curved spacetimes are briefly discussed.

math-ph↗

arXiv2016

Non-existence of isometry-invariant Hadamard states for a Kruskal black hole in a box and for massless fields on 1+1 Minkowski spacetime with a uniformly accelerating mirror

We conjecture that (when the notion of Hadamard state is suitably adapted) there is no isometry-invariant Hadamard state for the massive or massless covariant Klein-Gordon equation defined on the region of the Kruskal spacetime to the left of a surface of constant Schwarzschild radius in the right Schwarzschild wedge when Dirichlet boundary conditions are put on that surface. We also prove that, with a suitable definition for 'boost-invariant Hadamard state' (which we call 'strongly boost-invariant globally-Hadamard') which takes into account both the existence of the timelike boundary and the special massless 1+1 infra-red pathology, there is no such state for the massless wave equation on the region of 1+1 Minkowski space to the left of an eternally uniformly accelerating mirror -- with Dirichlet boundary conditions. This result is significant because such a state does exist if there is also a symmetrically placed decelerating mirror in the left wedge (and the region to the left of this mirror is excluded). We expect a similar existence result to hold for Kruskal when there are symmetrically placed spherical boxes in both right and left Schwarzschild wedges. Our Kruskal no-go conjecture raises basic questions about the black holes in boxes considered in black hole thermodynamics. If true, it would lend further support to the conclusion of B.S. Kay 'Instability of enclosed horizons', Gen. Rel. Grav. 47, 1-27 (2015) (arXiv: 1310.7395) that the nearest thing to a description of a black hole in equilibrium in a box in terms of a classical spacetime with quantum fields propagating on it has, for the classical spacetime, the exterior Schwarzschild solution, with the classical spacetime picture breaking down near the horizon. An appendix points out the existence of, and partially fills, a gap in the proofs of the theorems in B.S. Kay and R.M. Wald Phys. Rep. 207, 49-136 (1991).

gr-qc↗