Sequence Space Research Articles

A New Paranormed Sequence Space Defined by Regular Bell Matrix

This paper aims to construct a new paranormed sequence space by the aid of a regular matrix of Bell numbers. As well, its special duals such as α−,β−,γ− duals are presented and Schauder basis is determined. Moreover, certain matrix classes for this space are characterized.

On Gradual Borel Summability Method of Rough Convergence of Triple Sequences of Beta Stancu Operators

We define the concept of rough limit set of a triple sequence space of beta Stancu operators of Borel summability of gradual real numbers and obtain the relation between the set of rough limit and the extreme limit points of a triple sequence space of beta Stancu operators of Borel summability method of gradual real numbers. Finally, we investigate some properties of the rough limit set of beta Stancu operators under which Borel summable sequence of gradual real numbers are convergent. Also, we give the results for Borel summability method of series of gradual real numbers.

New Banach Sequence Spaces Defined by Jordan Totient Function

In this study, a special lower triangular matrix derived by combining Riesz matrix and Jordan totient matrix is used to construct new Banach spaces. $\alpha-$,$\beta-$,$\gamma-$duals of the resulting spaces are obtained and some matrix operators are characterized.

Prediction of Mycotoxin Response of DNA-Wrapped Nanotube Sensor with Machine Learning

DNA-wrapped single-walled carbon nanotubes (SWCNTs) have demonstrated great versatility in their use as optical sensors. SWCNTs emit a near-infrared fluorescence that is responsive to even the slightest changes in the nanotube environment, enabling sensors that can respond to single-molecule fluctuations within the vicinity of their surfaces. The fluorescence response and surface interactions of these sensors are determined by the DNA wrapping sequence. However, the lack of information on the relationship between the DNA sequence and its effect on the SWCNT fluorescence remains a bottleneck for designing sequences that are specific to analytes of interest. We have recently demonstrated the use of directed volution to control the fluorescence response of SWCNTs through DNA design. Iterative cycles of DNA mutation, screening, and selection allowed us to evolve sequences that yield DNA-wrapped SWCNT sensors with a desired fluorescence response to mycotoxins.In this work, we apply the screening results of the DNA libraries used in this approach to train machine learning (ML) algorithms. Artificial neural network (ANN) and support vector machine (SVM) methods were used to predict the response of ssDNA-SWCNT sensors to a specific mycotoxin. The reliability of these models was further assessed through cross-validation. The ANN and SVM models with cross-validation were able to accurately classify the various DNA sequences as yielding either a high or low fluorescence response with an accuracy of 73 and 81%, respectively. The models were further used to predict the performance of alternative DNA sequences outside the initial training dataset, using the Hierarchy and k-means++ clustering methods to evaluate the similarity and dissimilarity of each DNA sequence. Compared to the SVM model, the ANN model showed an improved ability to predict high responses for dissimilar DNA sequences. We further applied a combinatorial approach based on SVM and ANN models to design new DNA sequences for improving sensor performance. The success of this approach was validated experimentally, demonstrating the rational design of improved sensors with 95% prediction accuracy.The application of ML algorithms to directed evolution libraries of DNA thus allows one to accurately map the performances of these sensors within a particular sequence space. The computational success of this mapping provides a framework for replacing current empirical approaches with the rational design of DNA sequences for SWCNT sensing. Keywords: Nano Biosensor, DNA-SWCNT, Mycotoxin, Machine learning, Directed evolution method.

Parallel evolution and enhanced virulence upon in vivo passage of an RNA virus in Drosophila melanogaster.

Virus evolution is strongly affected by antagonistic co-evolution of virus and host. Host immunity positively selects for viruses that evade the immune response, which in turn may drive counter-adaptations in host immune genes. We investigated how host immune pressure shapes virus populations, using the fruit fly Drosophila melanogaster and its natural pathogen Drosophila C virus (DCV), as a model. We performed an experimental evolution study in which DCV was serially passaged for ten generations in three fly genotypes differing in their antiviral RNAi response: wild-type flies and flies in which the endonuclease gene Dicer-2 was either overexpressed or inactivated. All evolved virus populations replicated more efficiently in vivo and were more virulent than the parental stock. The number of polymorphisms increased in all three host genotypes with passage number, which was most pronounced in Dicer-2 knockout flies. Mutational analysis showed strong parallel evolution, as mutations accumulated in a specific region of the VP3 capsid protein in every lineage in a host genotype-independent manner. The parental tyrosine at position ninety-five of VP3 was substituted with either one of five different amino acids in fourteen out of fifteen lineages. However, no consistent amino acid changes were observed in the viral RNAi suppressor gene 1A, nor elsewhere in the genome in any of the host backgrounds. Our study indicates that the RNAi response restricts the sequence space that can be explored by viral populations. Moreover, our study illustrates how evolution towards higher virulence can be a highly reproducible, yet unpredictable process.

De Novo Discovery of Cysteine Frameworks for Developing Multicyclic Peptide Libraries for Ligand Discovery.

Conserved cysteine frameworks are essential components of disulfide-rich peptides (DRPs), which dominantly define the structural diversity of both naturally occurring and de novo-designed DRPs. However, there are only very limited numbers of conserved cysteine frameworks, and general methods enabling de novo discovery of cysteine frameworks with robust foldability are still not available. Here, we devised a "touchstone"-based strategy that relies on chasing oxidative foldability between two individual disulfide-rich folds on the phage surface to discover new cysteine frameworks from random sequences. Unique cysteine frameworks with a high degree of compatibility with phage display systems and broad sequence tolerance were successfully identified, which were subsequently exploited for the development of multicyclic DRP libraries, enabling the rapid discovery of new peptide ligands with low-nanomolar and picomolar binding affinity. This study provides an unprecedented method for exploring and exploiting the sequence and structure space of DRPs that is not readily accessible by existing strategies, holding the potential to revolutionize the study of DRPs and significantly advance the design and discovery of multicyclic peptide ligands and drugs.

Hold out the genome: a roadmap to solving the cis-regulatory code.

Gene expression is regulated by transcription factors that work together to read cis-regulatory DNA sequences. The 'cis-regulatory code' - how cells interpret DNA sequences to determine when, where and how much genes should be expressed - has proven to be exceedingly complex. Recently, advances in the scale and resolution of functional genomics assays and machine learning have enabled substantial progress towards deciphering this code. However, the cis-regulatory code will probably never be solved if models are trained only on genomic sequences; regions of homology can easily lead to overestimation of predictive performance, and our genome is too short and has insufficient sequence diversity to learn all relevant parameters. Fortunately, randomly synthesized DNA sequences enable testing a far larger sequence space than exists in our genomes, and designed DNA sequences enable targeted queries to maximally improve the models. As the same biochemical principles are used to interpret DNA regardless of its source, models trained on these synthetic data can predict genomic activity, often better than genome-trained models. Here we provide an outlook on the field, and propose a roadmap towards solving the cis-regulatory code by a combination of machine learning and massively parallel assays using synthetic DNA.

An innovative orthogonal matrix based on nonlinear chaotic system for compressive sensing

Compressed sensing exploits the signal’s sparsity by non-uniform sampling to achieve high-quality signal reconstruction at low sampling rates. This work aims to show the efficient performance of chaotic binary orthogonal matrices (CBOM) in compressed sensing. The nonlinear, high dimensional, irregular, and high complexity properties of chaotic systems can provide more diverse and efficient ways of sampling and reconstructing signals. The CBOM construction method proposed in this paper is divided into two steps, in the first step, the real-valued sequence of a one-dimensional chaotic map is binarised using the proposed Threshold-Matching Symbol Algorithm (TMSA) to obtain a chaotic binary sequence (CBS). The i.i.d properties of the CBS were proved using the Perron–Frobenius operator and the properties of the joint probability. The binarized CBS conditionally preserves the pseudo-random of chaotic sequences, as evidenced by the derivation of the well-distribution measure and the k-order correlation measure. In the second step, the binarised sequence CBS was split and orthogonalized to construct CBOM, which satisfies low storage and correlation. We prove that CBOM obeys the Restricted Isometric Condition (RIP). The orthogonalization of the matrix will further reduce matrix column correlation and improve the quality of the reconstruction. Numerical simulation results show that the proposed matrix has considerable sampling efficiency, comparable to Gaussian and partial Hadamard matrices, close to the theoretical limit. Meanwhile, the generation and reconstruction time of the proposed matrix is smaller than other matrices. Our framework covers partial one-dimensional chaotic maps, including Chebyshev, Tent, Logistic, and so on. We can easily apply this paradigm to various fields.

Tailoring the Hybridization Density of DNA Biosensors through Tunable Surface Functionalization

AbstractDNA biosensors are promising candidates for the development of point‐of‐care diagnosis methods. They can be inserted in microfluidic platforms, are often non‐expensive, and can be produced for a variety of targeted analytes. However, their development faces several challenges, some of which arise from their surface design. Among the characteristics which affect the binding efficiency of DNA probes to their targeted genes, the packing density and lateral spacing of the probe sequences must be controlled to provide enough binding sites and avoid crowding effect. It has also been demonstrated that increasing the space between the probe and the substrate can enhance the sensitivity of the sensing surface. Herein, we describe a methodology to control the vertical distance between DNA probes and a glass support, and lateral spacing between the probes. Such functionalization strategy could help the development of sensing surface with high hybridization density, and therefore high sensitivity.

Riesz I-convergent sequence spaces

In this article we have introduced some new sequence spaces as a domain of triangular Riesz matrix, and study some of their algebraic and topological properties. Further, our work will devote to argue some inclosions regarding those fore-said sequence spaces.

SOME SUMMABILITY TECHNIQUES IN INFINITE SERIES & SEQUENCE

The study of summability techniques plays a vital role in the fields of Functional Analysis, Fourier series, and Engineering. This paper is mainly focused on the comparison between Cesaro summability and Able summability. Besides providing a theorem, and giving examples related to Able method and Cesaro method, we give a theorem to prove the completeness of a sequence space.

REC protein family expansion by the emergence of a new signaling pathway.

We explore when and why large classes of proteins expand into new sequence space. We used an unsupervised machine learning approach to observe the sequence landscape of REC domains of bacterial response regulator proteins. We find that within-gene recombination can switch effector domains and, consequently, change the regulatory context of the duplicated protein.

Generating Novel and Soluble Class II Fructose-1,6-Bisphosphate Aldolase with ProteinGAN

Fructose-1,6-bisphosphate aldolase (FBA) is an important enzyme involved in central carbon metabolism (CCM) with promising industrial applications. Artificial intelligence models like generative adversarial networks (GANs) can design novel sequences that differ from natural ones. To expand the sequence space of FBA, we applied the generative adversarial network (ProteinGAN) model for the de novo design of FBA in this study. First, we corroborated the viability of the ProteinGAN model through replicating the generation of functional MDH variants. The model was then applied to the design of class II FBA. Computational analysis showed that the model successfully captured features of natural class II FBA sequences while expanding sequence diversity. Experimental results validated soluble expression and activity for the generated FBAs. Among the 20 generated FBA sequences (identity ranging from 85% to 99% with the closest natural FBA sequences), 4 were successfully expressed as soluble proteins in E. coli, and 2 of these 4 were functional. We further proposed a filter based on sequence identity to the endogenous FBA of E. coli and reselected 10 sequences (sequence identity ranging from 85% to 95%). Among them, six were successfully expressed as soluble proteins, and five of these six were functional—a significant improvement compared to the previous results. Furthermore, one generated FBA exhibited activity that was 1.69fold the control FBA. This study demonstrates that enzyme design with GANs can generate functional protein variants with enhanced performance and unique sequences.

Enhancing luciferase activity and stability through generative modeling of natural enzyme sequences.

The availability of natural protein sequences synergized with generative AI provides new paradigms to engineer enzymes. Although active enzyme variants with numerous mutations have been designed using generative models, their performance often falls short of their wild type counterparts. Additionally, in practical applications, choosing fewer mutations that can rival the efficacy of extensive sequence alterations is usually more advantageous. Pinpointing beneficial single mutations continues to be a formidable task. In this study, using the generative maximum entropy model to analyze Renilla luciferase (RLuc) homologs, and in conjunction with biochemistry experiments, we demonstrated that natural evolutionary information could be used to predictively improve enzyme activity and stability by engineering the active center and protein scaffold, respectively. The success rate to improve either luciferase activity or stability of designed single mutants is ~50%. This finding highlights nature's ingenious approach to evolving proficient enzymes, wherein diverse evolutionary pressures are preferentially applied to distinct regions of the enzyme, ultimately culminating in an overall high performance. We also reveal an evolutionary preference in RLuc toward emitting blue light that holds advantages in terms of water penetration compared to other light spectra. Taken together, our approach facilitates navigation through enzyme sequence space and offers effective strategies for computer-aided rational enzyme engineering.

Harnessing generative AI to decode enzyme catalysis and evolution for enhanced engineering.

Enzymes, as paramount protein catalysts, occupy a central role in fostering remarkable progress across numerous fields. However, the intricacy of sequence-function relationships continues to obscure our grasp of enzyme behaviors and curtails our capabilities in rational enzyme engineering. Generative artificial intelligence (AI), known for its proficiency in handling intricate data distributions, holds the potential to offer novel perspectives in enzyme research. Generative models could discern elusive patterns within the vast sequence space and uncover new functional enzyme sequences. This review highlights the recent advancements in employing generative AI for enzyme sequence analysis. We delve into the impact of generative AI in predicting mutation effects on enzyme fitness, catalytic activity and stability, rationalizing the laboratory evolution of de novo enzymes, and decoding protein sequence semantics and their application in enzyme engineering. Notably, the prediction of catalytic activity and stability of enzymes using natural protein sequences serves as a vital link, indicating how enzyme catalysis shapes enzyme evolution. Overall, we foresee that the integration of generative AI into enzyme studies will remarkably enhance our knowledge of enzymes and expedite the creation of superior biocatalysts.

Leveraging attention-enhanced variational autoencoders: Novel approach for investigating latent space of aptamer sequences

Aptamers are increasingly recognized as potent alternatives to antibodies for diagnostic and therapeutic applications. The application of deep learning, particularly attention-based models, for aptamer (DNA/RNA) sequences is an innovative field. The ongoing advancements in aptamer sequencing technologies coupled with machine learning algorithms have resulted in novel developments. Further research is required to investigate the full potential of deep learning models and address the challenges associated with the generation of sequences, like the large search space of possible sequences. In this study, we propose a workflow that integrates an attention mechanism within a framework of a generative variational autoencoder, to generate novel sequences by expanding latent memory. They show 100 % novelty compared with the dataset, and approximately 88 % of them show negative values for the minimum free energy, which may indicate the likelihood of an RNA sequence folding into a functional structure. Because the field of aptamer discovery is affected by data scarcity, advanced strategies that facilitate the generation of diverse and superior sequences are necessitated. The utilization of our workflow can result in novel aptamers. Thus, investigations such as the present study can address the abovementioned challenge. Our research is anticipated to facilitate further discoveries and advancements in aptamer fields.

The Hahn sequence space generated by the Cesàro mean of order m

The Hahn sequence space generated by the Cesàro mean of order m

Student's Engagement in Mathematics Learning on Cesaro Sequence Spaces on Matrix Transformations

Abstract available with the full text.

Design and deep learning of synthetic B-cell-specific promoters.

Synthetic biology and deep learning synergistically revolutionize our ability for decoding and recoding DNA regulatory grammar. The B-cell-specific transcriptional regulation is intricate, and unlock the potential of B-cell-specific promoters as synthetic elements is important for B-cell engineering. Here, we designed and pooled synthesized 23640 B-cell-specific promoters that exhibit larger sequence space, B-cell-specific expression, and enable diverse transcriptional patterns in B-cells. By MPRA (Massively parallel reporter assays), we deciphered the sequence features that regulate promoter transcriptional, including motifs and motif syntax (their combination and distance). Finally, we built and trained a deep learning model capable of predicting the transcriptional strength of the immunoglobulin V gene promoter directly from sequence. Prediction of thousands of promoter variants identified in the global human population shows that polymorphisms in promoters influence the transcription of immunoglobulin V genes, which may contribute to individual differences in adaptive humoral immune responses. Our work helps to decipher the transcription mechanism in immunoglobulin genes and offers thousands of non-similar promoters for B-cell engineering.

Accelerating Biocatalysis Discovery with Machine Learning: A Paradigm Shift in Enzyme Engineering, Discovery, and Design.

Emerging computational tools promise to revolutionize protein engineering for biocatalytic applications and accelerate the development timelines previously needed to optimize an enzyme to its more efficient variant. For over a decade, the benefits of predictive algorithms have helped scientists and engineers navigate the complexity of functional protein sequence space. More recently, spurred by dramatic advances in underlying computational tools, the promise of faster, cheaper, and more accurate enzyme identification, characterization, and engineering has catapulted terms such as artificial intelligence and machine learning to the must-have vocabulary in the field. This Perspective aims to showcase the current status of applications in pharmaceutical industry and also to discuss and celebrate the innovative approaches in protein science by highlighting their potential in selected recent developments and offering thoughts on future opportunities for biocatalysis. It also critically assesses the technology's limitations, unanswered questions, and unmet challenges.