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A theorem of Arens and Calderon states that if A is a commutative Banach algebra with Jacobson radical Rad(A), and if a0,..., an ∈ A with a0 2 Rad(A) and a1 an invertible element of A, then there exists y ∈ Rad(A) such that ... n this paper, we give extensions of this result to commutative non-normed topological algebras, as this is vital for extending an embedding theorem of Allan in [2] regarding the embedding of the formal power series algebra C[[X]] into a commutative Banach algebra. [ABSTRACT FROM AUTHOR]

We present a general survey on formal power series over topological algebras, along with some perspectives which are not easily found in the literature. [ABSTRACT FROM AUTHOR]

The accurate prediction of binding between T cell receptors (TCR) and their cognate epitopes is key to understanding the adaptive immune response and developing immunotherapies. Current methods face two significant limitations: the shortage of comprehensive high-quality data and the bias introduced by the selection of the negative training data commonly used in the supervised learning approaches. We propose a method, Transformer-based Unsupervised Language model for Interacting Peptides and T cell receptors (TULIP), that addresses both limitations by leveraging incomplete data and unsupervised learning and using the transformer architecture of language models. Our model is flexible and integrates all possible data sources, regardless of their quality or completeness. We demonstrate the existence of a bias introduced by the sampling procedure used in previous supervised approaches, emphasizing the need for an unsupervised approach. TULIP recognizes the specific TCRs binding an epitope, performing well on unseen epitopes. Our model outperforms state-of-the-art models and offers a promising direction for the development of more accurate TCR epitope recognition models., Competing Interests: Competing interests statement:The authors declare no competing interest.

Generative probabilistic models emerge as a new paradigm in data-driven, evolution-informed design of biomolecular sequences. This paper introduces a novel approach, called Edge Activation Direct Coupling Analysis (eaDCA), tailored to the characteristics of RNA sequences, with a strong emphasis on simplicity, efficiency, and interpretability. eaDCA explicitly constructs sparse coevolutionary models for RNA families, achieving performance levels comparable to more complex methods while utilizing a significantly lower number of parameters. Our approach demonstrates efficiency in generating artificial RNA sequences that closely resemble their natural counterparts in both statistical analyses and SHAPE-MaP experiments, and in predicting the effect of mutations. Notably, eaDCA provides a unique feature: estimating the number of potential functional sequences within a given RNA family. For example, in the case of cyclic di-AMP riboswitches (RF00379), our analysis suggests the existence of approximately 1039 functional nucleotide sequences. While huge compared to the known <4000 natural sequences, this number represents only a tiny fraction of the vast pool of nearly 1082 possible nucleotide sequences of the same length (136 nucleotides). These results underscore the promise of sparse and interpretable generative models, such as eaDCA, in enhancing our understanding of the expansive RNA sequence space., (© The Author(s) 2024. Published by Oxford University Press on behalf of Nucleic Acids Research.)

Objectives: Despite their life-saving capabilities, cerebrospinal fluid (CSF) shunts exhibit high failure rates, with a large fraction of failures attributed to the regulating valve. Due to a lack of methods for the detailed analysis of valve malfunctions, failure mechanisms are not well understood, and valves often have to be surgically explanted on the mere suspicion of malfunction. The presented pilot study aims to demonstrate radiological methods for comprehensive analysis of CSF shunt valves, considering both the potential for failure analysis in design optimization, and for future clinical in-vivo application to reduce the number of required shunt revision surgeries. The proposed method could also be utilized to develop and support in situ repair methods (e.g. by lysis or ultrasound) of malfunctioning CSF shunt valves., Materials and Methods: The primary methods described are contrast-enhanced radiographic time series of CSF shunt valves, taken in a favorable projection geometry at low radiation dose, and the machine-learning-based diagnosis of CSF shunt valve obstructions. Complimentarily, we investigate CT-based methods capable of providing accurate ground truth for the training of such diagnostic tools. Using simulated test and training data, the performance of the machine-learning diagnostics in identifying and localizing obstructions within a shunt valve is evaluated regarding per-pixel sensitivity and specificity, the Dice similarity coefficient, and the false positive rate in the case of obstruction free test samples., Results: Contrast enhanced subtraction radiography allows high-resolution, time-resolved, low-dose analysis of fluid transport in CSF shunt valves. Complementarily, photon-counting micro-CT allows to investigate valve obstruction mechanisms in detail, and to generate valid ground truth for machine learning-based diagnostics. Machine-learning-based detection of valve obstructions in simulated radiographies shows promising results, with a per-pixel sensitivity >70%, per-pixel specificity >90%, a median Dice coefficient >0.8 and <10% false positives at a detection threshold of 0.5., Conclusions: This ex-vivo study demonstrates obstruction detection in cerebro-spinal fluid shunt valves, combining radiological methods with machine learning under conditions compatible to future in-vivo application. Results indicate that high-resolution contrast-enhanced subtraction radiography, possibly including time-series data, combined with machine-learning image analysis, has the potential to strongly improve the diagnostics of CSF shunt valve failures. The presented method is in principle suitable for in-vivo application, considering both measurement geometry and radiological dose. Further research is needed to validate these results on real-world data and to refine the employed methods. In combination, the presented methods enable comprehensive analysis of valve failure mechanisms, paving the way for improved product development and clinical diagnostics of CSF shunt valves., Competing Interests: Declaration of competing interest This work was supported by a hardware loan of DECTRIS AG of Baden-Daettwil, Switzerland, who provided the photon-counting detectors employed in the current study. Martin Pichotka: Shareholder of speCTive GmbH, Freiburg, Germany. Moritz Weigt: Shareholder of speCTive GmbH, Freiburg, Germany. Christopher L. Schlett: Speaker Bureau by Siemens Healthineers and Bayer Healthcare. All other authors declare no competing interests., (Copyright © 2023 The Author(s). Published by Elsevier GmbH.. All rights reserved.)

Metabolic magnetic resonance imaging (MRI) using hyperpolarized (HP) pyruvate is becoming a non-invasive technique for diagnosing, staging, and monitoring response to treatment in cancer and other diseases. The clinically established method for producing HP pyruvate, dissolution dynamic nuclear polarization, however, is rather complex and slow. Signal Amplification By Reversible Exchange (SABRE) is an ultra-fast and low-cost method based on fast chemical exchange. Here, for the first time, we demonstrate not only in vivo utility, but also metabolic MRI with SABRE. We present a novel routine to produce aqueous HP [1- 13 C]pyruvate-d 3 for injection in 6 minutes. The injected solution was sterile, non-toxic, pH neutral and contained ≈30 mM [1- 13 C]pyruvate-d 3 polarized to ≈11 % (residual 250 mM methanol and 20 μM catalyst). It was obtained by rapid solvent evaporation and metal filtering, which we detail in this manuscript. This achievement makes HP pyruvate MRI available to a wide biomedical community for fast metabolic imaging of living organisms., (© 2023 The Authors. Angewandte Chemie International Edition published by Wiley-VCH GmbH.)

Motivation: Being able to artificially design novel proteins of desired function is pivotal in many biological and biomedical applications. Generative statistical modeling has recently emerged as a new paradigm for designing amino acid sequences, including in particular models and embedding methods borrowed from natural language processing (NLP). However, most approaches target single proteins or protein domains, and do not take into account any functional specificity or interaction with the context. To extend beyond current computational strategies, we develop a method for generating protein domain sequences intended to interact with another protein domain. Using data from natural multidomain proteins, we cast the problem as a translation problem from a given interactor domain to the new domain to be generated, i.e. we generate artificial partner sequences conditional on an input sequence. We also show in an example that the same procedure can be applied to interactions between distinct proteins., Results: Evaluating our model's quality using diverse metrics, in part related to distinct biological questions, we show that our method outperforms state-of-the-art shallow autoregressive strategies. We also explore the possibility of fine-tuning pretrained large language models for the same task and of using Alphafold 2 for assessing the quality of sampled sequences., Availability and Implementation: Data and code on https://github.com/barthelemymp/Domain2DomainProteinTranslation., (© The Author(s) 2023. Published by Oxford University Press.)

Predicting protein-protein interactions from sequences is an important goal of computational biology. Various sources of information can be used to this end. Starting from the sequences of two interacting protein families, one can use phylogeny or residue coevolution to infer which paralogs are specific interaction partners within each species. We show that these two signals can be combined to improve the performance of the inference of interaction partners among paralogs. For this, we first align the sequence-similarity graphs of the two families through simulated annealing, yielding a robust partial pairing. We next use this partial pairing to seed a coevolution-based iterative pairing algorithm. This combined method improves performance over either separate method. The improvement obtained is striking in the difficult cases where the average number of paralogs per species is large or where the total number of sequences is modest., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2023 Gandarilla-Pérez et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Dehydroamino acids are important structural motifs and biosynthetic intermediates for natural products. Many bioactive natural products of nonribosomal origin contain dehydroamino acids; however, the biosynthesis of dehydroamino acids in most nonribosomal peptides is not well understood. Here, we provide biochemical and bioinformatic evidence in support of the role of a unique class of condensation domains in dehydration (C modAA ). We also obtain the crystal structure of a C modAA domain, which is part of the nonribosomal peptide synthetase AmbE in the biosynthesis of the antibiotic methoxyvinylglycine. Biochemical analysis reveals that AmbE-C modAA modifies a peptide substrate that is attached to the donor carrier protein. Mutational studies of AmbE-C modAA identify several key residues for activity, including four residues that are mostly conserved in the C modAA subfamily. Alanine mutation of these conserved residues either significantly increases or decreases AmbE activity. AmbE exhibits a dimeric conformation, which is uncommon and could enable transfer of an intermediate between different protomers. Our discovery highlights a central dehydrating function for C modAA domains that unifies dehydroamino acid biosynthesis in diverse nonribosomal peptide pathways. Our work also begins to shed light on the mechanism of C modAA domains. Understanding C modAA domain function may facilitate identification of new natural products that contain dehydroamino acids and enable engineering of dehydroamino acids into nonribosomal peptides.

Characterizing the effect of mutations is key to understand the evolution of protein sequences and to separate neutral amino-acid changes from deleterious ones. Epistatic interactions between residues can lead to a context dependence of mutation effects. Context dependence constrains the amino-acid changes that can contribute to polymorphism in the short term, and the ones that can accumulate between species in the long term. We use computational approaches to accurately predict the polymorphisms segregating in a panel of 61,157 Escherichia coli genomes from the analysis of distant homologues. By comparing a context-aware Direct-Coupling Analysis modelling to a non-epistatic approach, we show that the genetic context strongly constrains the tolerable amino acids in 30% to 50% of amino-acid sites. The study of more distant species suggests the gradual build-up of genetic context over long evolutionary timescales by the accumulation of small epistatic contributions., (© 2022. The Author(s).)

The emergence of new variants of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is a major concern given their potential impact on the transmissibility and pathogenicity of the virus as well as the efficacy of therapeutic interventions. Here, we predict the mutability of all positions in SARS-CoV-2 protein domains to forecast the appearance of unseen variants. Using sequence data from other coronaviruses, preexisting to SARS-CoV-2, we build statistical models that not only capture amino acid conservation but also more complex patterns resulting from epistasis. We show that these models are notably superior to conservation profiles in estimating the already observable SARS-CoV-2 variability. In the receptor binding domain of the spike protein, we observe that the predicted mutability correlates well with experimental measures of protein stability and that both are reliable mutability predictors (receiver operating characteristic areas under the curve ∼0.8). Most interestingly, we observe an increasing agreement between our model and the observed variability as more data become available over time, proving the anticipatory capacity of our model. When combined with data concerning the immune response, our approach identifies positions where current variants of concern are highly overrepresented. These results could assist studies on viral evolution and future viral outbreaks and, in particular, guide the exploration and anticipation of potentially harmful future SARS-CoV-2 variants., Competing Interests: The authors declare no competing interest., (Copyright © 2022 the Author(s). Published by PNAS.)

During their evolution, proteins explore sequence space via an interplay between random mutations and phenotypic selection. Here, we build upon recent progress in reconstructing data-driven fitness landscapes for families of homologous proteins, to propose stochastic models of experimental protein evolution. These models predict quantitatively important features of experimentally evolved sequence libraries, like fitness distributions and position-specific mutational spectra. They also allow us to efficiently simulate sequence libraries for a vast array of combinations of experimental parameters like sequence divergence, selection strength, and library size. We showcase the potential of the approach in reanalyzing two recent experiments to determine protein structure from signals of epistasis emerging in experimental sequence libraries. To be detectable, these signals require sufficiently large and sufficiently diverged libraries. Our modeling framework offers a quantitative explanation for different outcomes of recently published experiments. Furthermore, we can forecast the outcome of time- and resource-intensive evolution experiments, opening thereby a way to computationally optimize experimental protocols., (© The Author(s) 2021. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.)

Background: Boltzmann machines are energy-based models that have been shown to provide an accurate statistical description of domains of evolutionary-related protein and RNA families. They are parametrized in terms of local biases accounting for residue conservation, and pairwise terms to model epistatic coevolution between residues. From the model parameters, it is possible to extract an accurate prediction of the three-dimensional contact map of the target domain. More recently, the accuracy of these models has been also assessed in terms of their ability in predicting mutational effects and generating in silico functional sequences., Results: Our adaptive implementation of Boltzmann machine learning, adabmDCA, can be generally applied to both protein and RNA families and accomplishes several learning set-ups, depending on the complexity of the input data and on the user requirements. The code is fully available at https://github.com/anna-pa-m/adabmDCA . As an example, we have performed the learning of three Boltzmann machines modeling the Kunitz and Beta-lactamase2 protein domains and TPP-riboswitch RNA domain., Conclusions: The models learned by adabmDCA are comparable to those obtained by state-of-the-art techniques for this task, in terms of the quality of the inferred contact map as well as of the synthetically generated sequences. In addition, the code implements both equilibrium and out-of-equilibrium learning, which allows for an accurate and lossless training when the equilibrium one is prohibitive in terms of computational time, and allows for pruning irrelevant parameters using an information-based criterion., (© 2021. The Author(s).)

Generative models emerge as promising candidates for novel sequence-data driven approaches to protein design, and for the extraction of structural and functional information about proteins deeply hidden in rapidly growing sequence databases. Here we propose simple autoregressive models as highly accurate but computationally efficient generative sequence models. We show that they perform similarly to existing approaches based on Boltzmann machines or deep generative models, but at a substantially lower computational cost (by a factor between 10 2 and 10 3 ). Furthermore, the simple structure of our models has distinctive mathematical advantages, which translate into an improved applicability in sequence generation and evaluation. Within these models, we can easily estimate both the probability of a given sequence, and, using the model's entropy, the size of the functional sequence space related to a specific protein family. In the example of response regulators, we find a huge number of ca. 10 68 possible sequences, which nevertheless constitute only the astronomically small fraction 10 -80 of all amino-acid sequences of the same length. These findings illustrate the potential and the difficulty in exploring sequence space via generative sequence models., (© 2021. The Author(s).)

Crabs of the family Camptandriidae are the most dominant burrowing crabs inhabiting arid mangrove forests of the Persian Gulf. They play important roles in the structuring and functioning of mangrove ecosystems by modulating biogeochemical processes and cycling of nutrients, serving as important ecosystem engineers. We analysed stable carbon ( 13 C) and nitrogen ( 15 N) isotope values of three camptandriid crabs ( Opusia indica , Nasima dotilliformis, and Manningis arabicum ) and their potential food sources in the Hara Biosphere Reserve, northern Persian Gulf. A Bayesian mixing model was used to estimate the contribution of potential food sources for consumers. The results showed that to some degree, all the four sources selected contributed to the camptandriid diets, but microphytobenthos made the most important contributions to the diet of the consumers. Mangroves do not appear to be a significant source of carbon in the diet of camptandriid crabs in the arid mangrove system of the Persian Gulf. Rather, they offer favourable growing conditions, thus boosting microphytobenthos production and availability for consumers which prefer a high nutritional and palatable source.