Sequence Space Research Articles

Recent Progress in the Synthesis of α‐Hydroxy Carbonyl Compounds with ThDP‐dependent Carboligases

AbstractThiamine diphosphate (ThDP) dependent carboligases catalyze the formation of carbon‐carbon bonds. These enzymes are prominent biocatalysts for the production of valuable α‐hydroxy carbonyl compounds, which serve as key building blocks in the synthesis of various pharmaceuticals and fine chemicals. Carboligases act in selective manner to afford regio‐ and stereochemically defined products from simple starting materials. This review explores the catalytic prowess of carboligases for synthetic purposes and is aimed at providing a selection tool of enzymes for particular sets of substrates or desired products. The comprehensive overview encompasses structural insights, relationships of the currently known sequence space and practical applications with a focus on recent literature, showcasing carboligases as potent tools for sustainable and efficient synthesis.

Ultrahigh Throughput Evolution of Tryptophan Synthase in Droplets via an Aptamer Sensor.

Tryptophan synthase catalyzes the synthesis of a wide array of noncanonical amino acids and is an attractive target for directed evolution. Droplet microfluidics offers an ultrahigh throughput approach to directed evolution (up to 107 experiments per day), enabling the search for biocatalysts in wider regions of sequence space with reagent consumption minimized to the picoliter volume (per library member). While the majority of screening campaigns in this format on record relied on an optically active reaction product, a new assay is needed for tryptophan synthase. Tryptophan is not fluorogenic in the visible light spectrum and thus falls outside the scope of conventional droplet microfluidic readouts, which are incompatible with UV light detection at high throughput. Here, we engineer a tryptophan DNA aptamer into a sensor to quantitatively report on tryptophan production in droplets. The utility of the sensor was validated by identifying five-fold improved tryptophan synthases from ∼100,000 protein variants. More generally, this work establishes the use of DNA-aptamer sensors with a fluorogenic read-out in widening the scope of droplet microfluidic evolution.

Relative Uniform Convergence of Sequence of Functions Related to ℓp-Spaces Defined by Orlicz Functions

The Orlicz function-defined sequence spaces of functions by relative uniform convergence of sequences related to p-absolutely summable spaces are a new concept that is introduced in this article. We look at its various attributes, such as solidity, completeness, and symmetry. We also look at a few insertional connections involving these spaces.

Machine learning enabled design features of antimicrobial peptides selectively targeting peri-implant disease progression

Peri-implantitis is a complex infectious disease that manifests as progressive loss of alveolar bone around the dental implants and hyper-inflammation associated with microbial dysbiosis. Using antibiotics in treating peri-implantitis is controversial because of antibiotic resistance threats, the non-selective suppression of pathogens and commensals within the microbial community, and potentially serious systemic sequelae. Therefore, conventional treatment for peri-implantitis comprises mechanical debridement by nonsurgical or surgical approaches with adjunct local microbicidal agents. Consequently, current treatment options may not prevent relapses, as the pathogens either remain unaffected or quickly re-emerge after treatment. Successful mitigation of disease progression in peri-implantitis requires a specific mode of treatment capable of targeting keystone pathogens and restoring bacterial community balance toward commensal species. Antimicrobial peptides (AMPs) hold promise as alternative therapeutics through their bacterial specificity and targeted inhibitory activity. However, peptide sequence space exhibits complex relationships such as sparse vector encoding of sequences, including combinatorial and discrete functions describing peptide antimicrobial activity. In this paper, we generated a transparent Machine Learning (ML) model that identifies sequence-function relationships based on rough set theory using simple summaries of the hydropathic features of AMPs. Comparing the hydropathic features of peptides according to their differential activity for different classes of bacteria empowered predictability of antimicrobial targeting. Enriching the sequence diversity by a genetic algorithm, we generated numerous candidate AMPs designed for selectively targeting pathogens and predicted their activity using classifying rough sets. Empirical growth inhibition data is iteratively fed back into our ML training to generate new peptides, resulting in increasingly more rigorous rules for which peptides match targeted inhibition levels for specific bacterial strains. The subsequent top scoring candidates were empirically tested for their inhibition against keystone and accessory peri-implantitis pathogens as well as an oral commensal bacterium. A novel peptide, VL-13, was confirmed to be selectively active against a keystone pathogen. Considering the continually increasing number of oral implants placed each year and the complexity of the disease progression, prevalence of peri-implant diseases continues to rise. Our approach offers transparent ML-enabled paths towards developing antimicrobial peptide-based therapies targeting the changes in the microbial communities that can beneficially impact disease progression.

The Impact of Metagenomics on Biocatalysis.

In the ever-growing demand for sustainable ways to produce high-value small molecules, biocatalysis has come to the forefront of greener routes to these chemicals. As such, the need to constantly find and optimise suitable biocatalysts for specific transformations has never been greater. Metagenome mining has been shown to rapidly expand the toolkit of promiscuous enzymes needed for new transformations, without requiring protein engineering steps. If protein engineering is needed, the metagenomic candidate can often provide a better starting point for engineering than a previously discovered enzyme on the open database or from literature, for instance. In this review, we highlight where metagenomics has made substantial impact on the area of biocatalysis in recent years. We review the discovery of enzymes in previously unexplored or 'hidden' sequence space, leading to the characterisation of enzymes with enhanced properties that originate from natural selection pressures in native environments.

The Impact of Metagenomics on Biocatalysis

AbstractIn the ever‐growing demand for sustainable ways to produce high‐value small molecules, biocatalysis has come to the forefront of greener routes to these chemicals. As such, the need to constantly find and optimise suitable biocatalysts for specific transformations has never been greater. Metagenome mining has been shown to rapidly expand the toolkit of promiscuous enzymes needed for new transformations, without requiring protein engineering steps. If protein engineering is needed, the metagenomic candidate can often provide a better starting point for engineering than a previously discovered enzyme on the open database or from literature, for instance. In this review, we highlight where metagenomics has made substantial impact on the area of biocatalysis in recent years. We review the discovery of enzymes in previously unexplored or ‘hidden’ sequence space, leading to the characterisation of enzymes with enhanced properties that originate from natural selection pressures in native environments.

Solvability of infinite system of implicit fractional integral equations of two variables in tempered sequence spaces via generalized Darbo’s fixed point theorem

Solvability of infinite system of implicit fractional integral equations of two variables in tempered sequence spaces via generalized Darbo’s fixed point theorem

Solvability of infinite systems of Caputo–Hadamard fractional differential equations in the triple sequence space $$c^3(\triangle )$$

Solvability of infinite systems of Caputo–Hadamard fractional differential equations in the triple sequence space $$c^3(\triangle )$$

Discovery and characterization of l-DOPA 2,3-dioxygenase from Streptomyces hygroscopicus jingganensis

The largest natural reservoir of untapped carbon can be found in the cell-wall strengthening, plant woody-tissue polymer, lignin - a polymer of catechols or 1,2-dihydroxybenzene monomers. The catecholic carbon of lignin could be valorized into feedstocks and natural products by way of catabolic and biosynthetic transformations, including the oxygen-dependent cleavage reaction of extradiol dioxygenase (EDX) enzymes. The EDX l-DOPA 2,3-dioxygenase was first discovered as part of a biosynthetic gene cluster to the natural product antibiotic, lincomycin, and also contributes to the biosyntheses of anthramycin, sibiromycin, tomaymycin, porothramycin and hormaomycin. Using these l-DOPA 2,3-dioxygenases as a starting point, we searched sequence space in order to identify new sources of dioxygenase driven natural product diversity. A “vicinal-oxygen-chelate (VOC) family protein” from Streptomyces hygroscopicus jingganensis was identified using bioinformatic methods and biochemically investigated for dioxygenase activity against a suite of natural and synthetic catechols. Steady-state oxygen consumption assays were used to screen and identify substrates, and a steady-state kinetic model of oxygen consumption was developed to evaluate activity of the S. hygroscopicus jingganensis VOC-family-protein with respect to activity of l-DOPA 2,3-dioxygenases from Streptomyces lincolnensis and Streptomyces sclerotialus. Lastly, these data were integrated with steady-state kinetic methods to observe the formation of the EDX cleavage product with UV–visible spectroscopy. The genomic context and enzymatic activity of the S. hygroscopicus jingganensis VOC family protein are consistent with a l-DOPA 2,3-dioxygenase contained within a cryptic biosynthetic pathway.

ROUGH LACUNARY STATISTICAL ANALYSIS OF ORDER OF η OF TRIPLE DIFFERENCE SEQUENCE SPACES

We generalized the concepts in the probability of rough lacunary statistical analysis of order η by introducing the difference operator Δ_γ^α of fractional order, where α is a proper fraction and γ=(γ_mnk ) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence θ and arbitrary sequence p=(p_rst ) of strictly positive real numbers and investigate the topological structures of related with triple difference sequence spaces. The main focus of the present paper is to generalize rough lacunary statistical analysis of order η of triple difference sequence spaces and give the relations between statistical analysis and lacunary statistical analysis of order η.

On Some New Normed Narayana Sequence Spaces

In this paper, we first establish the regular matrix $N$ using Narayana numbers. Then, we create new normed sequence spaces $Z(N)$ using the matrix $ N$ and demonstrate that these spaces are linearly isomorphic to $Z$ where $Z\in\{c_0, c, \ell_p, \ell_\infty\}$. Additionally, we provide inclusion relations for the spaces $c_0(N)$, $c(N)$, $\ell_p(N)$, and $\ell_\infty(N)$. Furthermore, we construct the Schauder bases of the $c_0(N)$, $c(N)$, and $\ell_p(N)$. Finally, we compute the $\alpha$-, $\beta$-, and $\gamma$-duals of these spaces and characterize the classes $(Z(N),X)$ for the certain choice of the sequence space $X$.

Evolutionary accessibility of random and structured fitness landscapes

Biological evolution can be conceptualized as a search process in the space of gene sequences guided by the fitness landscape, a mapping that assigns a measure of reproductive value to each genotype. Here, we discuss probabilistic models of fitness landscapes with a focus on their evolutionary accessibility, where a path in a fitness landscape is said to be accessible if the fitness values encountered along the path increase monotonically. For uncorrelated (random) landscapes with independent and identically distributed fitness values, the probability of existence of accessible paths between genotypes at a distance linear in the sequence length L becomes nonzero at a nontrivial threshold value of the fitness difference between the initial and final genotypes, which can be explicitly computed for large classes of genotype graphs. The behaviour of uncorrelated random landscapes is contrasted with landscape models that display additional, biologically motivated structural features. In particular, landscapes defined by a tradeoff between adaptation to environmental extremes have been found to display a combinatorially large number of accessible paths to all local fitness maxima. We show that this property is characteristic of a broad class of models that satisfy a certain global constraint, and provide further examples from this class.

A study on some paranormed sequence spaces due to Lambda–Pascal matrix

A study on some paranormed sequence spaces due to Lambda–Pascal matrix

A note on Köthe–Toeplitz duals and multiplier spaces of sequence spaces involving bicomplex numbers

Abstract In this paper, we generalize the notions of the Köthe–Toeplitz duals of sequence spaces by introducing the concepts of bicomplex α-dual, bicomplex β-dual and bicomplex γ-dual, and also we compute them for some bicomplex sequence spaces l p ⁢ ( 𝔹 ⁢ ℂ ) {l_{p}(\mathbb{BC})} for 1 ≤ p ≤ ∞ {1\leq p\leq\infty} , c 0 ⁢ ( 𝔹 ⁢ ℂ ) {c_{0}(\mathbb{BC})} and c ⁢ ( 𝔹 ⁢ ℂ ) {c(\mathbb{BC})} . Furthermore, we define a concept of bicomplex multiplier space as the bicomplex version of multiplier space of two sequence spaces and support this definition with examples.

Some new Cesàro sequence spaces of order α

UDC 517.98 We introduce the spaces ℓ ∞ ( C α ) , f ( C α ) , and f 0 ( C α ) of Ces\`{a}ro bounded, Ces\`{a}ro almost convergent, and Ces\`{a}ro almost null sequences of order α , respectively. Moreover, we establish some inclusion relations for these spaces and determine the α -, β - and γ -duals of the spaces ℓ ∞ ( C α ) and f ( C α ) . Finally, we characterize the classes of matrix transformations from the space f ( C α ) to any sequence space Y and from any sequence space Y to the space f ( C α ) .

Two-sided estimates of Lebesgue constants for spaces of functions of generalized bounded variation and Hölder spaces

A proof of two-sided estimates of Lebesgue constants for spaces Hω⋂BV(X), where Hω is the Hölder space and BV(X) is the space of functions of bounded variation constructed from the symmetric space of sequences X. Choosing different spaces of sequences as X, we obtained new criteria for the convergence of classical Fourier series.

Tree Search-Based Evolutionary Bandits for Protein Sequence Optimization

While modern biotechnologies allow synthesizing new proteins and function measurements at scale, efficiently exploring a protein sequence space and engineering it remains a daunting task due to the vast sequence space of any given protein. Protein engineering is typically conducted through an iterative process of adding mutations to the wild-type or lead sequences, recombination of mutations, and running new rounds of screening. To enhance the efficiency of such a process, we propose a tree search-based bandit learning method, which expands a tree starting from the initial sequence with the guidance of a bandit machine learning model. Under simplified assumptions and a Gaussian Process prior, we provide theoretical analysis and a Bayesian regret bound, demonstrating that the method can efficiently discover a near-optimal design. The full algorithm is compatible with a suite of randomized tree search heuristics, machine learning models, pre-trained embeddings, and bandit techniques. We test various instances of the algorithm across benchmark protein datasets using simulated screens. Experiment results demonstrate that the algorithm is both sample-efficient, diversity-promoting, and able to find top designs using reasonably small mutation counts.

ESRL: Efficient Sampling-Based Reinforcement Learning for Sequence Generation

Applying Reinforcement Learning (RL) to sequence generation models enables the direct optimization of long-term rewards (e.g., BLEU and human feedback), but typically requires large-scale sampling over a space of action sequences. This is a computational challenge as presented by the practice of sequence generation problems, such as machine translation, where we often deal with a large action space (e.g., a vocabulary) and a long action sequence (e.g., a translation). In this work, we introduce two-stage sampling and dynamic sampling approaches to improve the sampling efficiency during training sequence generation models via RL. We experiment with our approaches on the traditional sequence generation tasks, including machine translation and abstractive summarization. Furthermore, we evaluate our approaches in RL from human feedback (RLHF) through training a large language model using the reward model. Experimental results show that the efficient sampling-based RL, referred to as ESRL, can outperform all baselines in terms of both training efficiency and memory consumption. Notably, ESRL yields consistent performance gains over the strong REINFORCE, minimum risk training, and proximal policy optimization methods. The code is available at https://github.com/wangclnlp/DeepSpeed-Chat-Extension/examples/esrl.

Designing Biological Sequences without Prior Knowledge Using Evolutionary Reinforcement Learning

Designing novel biological sequences with desired properties is a significant challenge in biological science because of the extra large search space. The traditional design process usually involves multiple rounds of costly wet lab evaluations. To reduce the need for expensive wet lab experiments, machine learning methods are used to aid in designing biological sequences. However, the limited availability of biological sequences with known properties hinders the training of machine learning models, significantly restricting their applicability and performance. To fill this gap, we present ERLBioSeq, an Evolutionary Reinforcement Learning algorithm for BIOlogical SEQuence design. ERLBioSeq leverages the capability of reinforcement learning to learn without prior knowledge and the potential of evolutionary algorithms to enhance the exploration of reinforcement learning in the large search space of biological sequences. Additionally, to enhance the efficiency of biological sequence design, we developed a predictor for sequence screening in the biological sequence design process, which incorporates both the local and global sequence information. We evaluated the proposed method on three main types of biological sequence design tasks, including the design of DNA, RNA, and protein. The results demonstrate that the proposed method achieves significant improvement compared to the existing state-of-the-art methods.

Some degenerate binomial sequence spaces and related matrix transformations and compactness

Some degenerate binomial sequence spaces and related matrix transformations and compactness