Sequence Space Research Articles

Certain topological properties for almost convergent Catalan-Motzkin sequence space

The purpose of this paper is to introduce a new almost convergent sequence space by means of a matrix involving Catalan and Motzkin numbers. It is demonstrated that this novel sequence space and the space of all almost convergent sequences are linearly isomorphic and the $\beta$-dual of this new space is deduced. In addition, by defining Catalan-Motzkin core of a complex-valued sequence, certain inclusion relations are derived for it.

Constructability-driven design of frame structures with state-space search methods

In the design of frames and trusses, the relationship between the structural form, the construction sequence, and the structural behavior during construction is rarely systematically considered. This paper proposes a method to systematically consider constructability in design, specifically focusing on minimizing the maximum displacement or stress during construction. The paper presents the formulation of the optimal assembly sequencing problem as a state-space search with a unique design of the search heuristic and constraint bounding schemes. It proposes three variants of heuristic search algorithms for finding a feasible sequence, a diverse set of feasible sequences, and an optimal sequence, respectively. These algorithms are tested on a case study structure to showcase their ability to navigate the combinatorial space of assembly sequences, and provide means for designers to incorporate sequence-related performance into conceptual structural design.

Massively parallel analysis of single-molecule dynamics on next-generation sequencing chips.

Single-molecule techniques are ideally poised to characterize complex dynamics but are typically limited to investigating a small number of different samples. However, a large sequence or chemical space often needs to be explored to derive a comprehensive understanding of complex biological processes. Here we describe multiplexed single-molecule characterization at the library scale (MUSCLE), a method that combines single-molecule fluorescence microscopy with next-generation sequencing to enable highly multiplexed observations of complex dynamics. We comprehensively profiled the sequence dependence of DNA hairpin properties and Cas9-induced target DNA unwinding-rewinding dynamics. The ability to explore a large sequence space for Cas9 allowed us to identify a number of target sequences with unexpected behaviors. We envision that MUSCLE will enable the mechanistic exploration of many fundamental biological processes.

Single-molecule structural and kinetic studies across sequence space.

At the core of molecular biology lies the intricate interplay between sequence, structure, and function. Single-molecule techniques provide in-depth dynamic insights into structure and function, but laborious assays impede functional screening of large sequence libraries. We introduce high-throughput Single-molecule Parallel Analysis for Rapid eXploration of Sequence space (SPARXS), integrating single-molecule fluorescence with next-generation sequencing. We applied SPARXS to study the sequence-dependent kinetics of the Holliday junction, a critical intermediate in homologous recombination. By examining the dynamics of millions of Holliday junctions, covering thousands of distinct sequences, we demonstrated the ability of SPARXS to uncover sequence patterns, evaluate sequence motifs, and construct thermodynamic models. SPARXS emerges as a versatile tool for untangling the mechanisms that underlie sequence-specific processes at the molecular scale.

Rational design of base, sugarand backbone modifications improves ADAR-mediated RNA editing.

AIMers are short, chemically modified oligonucleotides that induce A-to-I RNA editing through interaction with endogenous adenosine deaminases acting on RNA (ADAR) enzymes. Here, we describe the development of new AIMer designs with base, sugar and backbone modifications that improve RNA editing efficiency over our previous design. AIMers incorporating a novel pattern of backbone and 2' sugar modifications support enhanced editing efficiency across multiple sequences. Further efficiency gains were achieved through incorporation of an N-3-uridine (N3U), in place of cytidine (C), in the 'orphan base' position opposite the edit site. Molecular modeling suggests that N3U might enhance ADAR catalytic activity by stabilizing the AIMer-ADAR interaction and potentially reducing the energy required to flip the target base into the active site. Supporting this hypothesis, AIMers containing N3U consistently enhanced RNA editing over those containing C across multiple target sequences and multiple nearest neighbor sequence combinations. AIMers combining N3U and the novel pattern of 2' sugar chemistry and backbone modifications improved RNA editing both in vitro and in vivo. We provide detailed N3U synthesis methods and, for the first time, explore the impact of N3U and its analogs on ADAR-mediated RNA editing efficiency and targetable sequence space.

Addressing epistasis in the design of protein function

Mutations in protein active sites can dramatically improve function. The active site, however, is densely packed and extremely sensitive to mutations. Therefore, some mutations may only be tolerated in combination with others in a phenomenon known as epistasis. Epistasis reduces the likelihood of obtaining improved functional variants and dramatically slows natural and lab evolutionary processes. Research has shed light on the molecular origins of epistasis and its role in shaping evolutionary trajectories and outcomes. In addition, sequence- and AI-based strategies that infer epistatic relationships from mutational patterns in natural or experimental evolution data have been used to design functional protein variants. In recent years, combinations of such approaches and atomistic design calculations have successfully predicted highly functional combinatorial mutations in active sites. These were used to design thousands of functional active-site variants, demonstrating that, while our understanding of epistasis remains incomplete, some of the determinants that are critical for accurate design are now sufficiently understood. We conclude that the space of active-site variants that has been explored by evolution may be expanded dramatically to enhance natural activities or discover new ones. Furthermore, design opens the way to systematically exploring sequence and structure space and mutational impacts on function, deepening our understanding and control over protein activity.

Predicting monoclonal antibody binding sequences from a sparse sampling of all possible sequences

Previous work has shown that binding of target proteins to a sparse, unbiased sample of all possible peptide sequences is sufficient to train a machine learning model that can then predict, with statistically high accuracy, target binding to any possible peptide sequence of similar length. Here, highly sequence-specific molecular recognition is explored by measuring binding of 8 monoclonal antibodies (mAbs) with specific linear cognate epitopes to an array containing 121,715 near-random sequences about 10 residues in length. Network models trained on resulting sequence-binding values are used to predict the binding of each mAb to its cognate sequence and to an in silico generated one million random sequences. The model always ranks the binding of the cognate sequence in the top 100 sequences, and for 6 of the 8 mAbs, the cognate sequence ranks in the top ten. Practically, this approach has potential utility in selecting highly specific mAbs for therapeutics or diagnostics. More fundamentally, this demonstrates that very sparse random sampling of a large amino acid sequence spaces is sufficient to generate comprehensive models predictive of highly specific molecular recognition.

Some aspects of 𝜆-weak convergence using difference operator

Abstract In this paper, we introduce generalized difference weak sequence space classes by utilizing the difference operator Δ ı ȷ \Delta^{\jmath}_{\imath} and the de la Vallée–Poussin mean, denoted as [ ( V , λ ) w , Δ ı ȷ ] m [(\mathscr{V},\lambda)_{w},\Delta^{\jmath}_{\imath}]_{m} for m = 0 m=0 , 1, and ∞. Further, we explore some algebraic and topological properties of these spaces, including their nature as linear, normed, Banach, and BK spaces. Additionally, we examine properties such as solidity, symmetry, and monotonicity. Finally, we define and establish some inclusion relations among generalized difference weak statistical convergence, generalized difference weak 𝜆-statistical convergence, and generalized difference weak [ V , λ ] [\mathscr{V},\lambda] -convergence.

Nikishin’s theorem and factorization through Marcinkiewicz spaces

Consider L 0 L^0 , the F F -space of all equivalence classes of measurable functions on a finite measure space equipped with the topology of convergence in measure. Inspired by Nikishin’s classical result on the factorization of sublinear continuous operators from a Banach space to L 0 L^0 , we prove a theorem that characterizes those maps from any quasi-metric space into L 0 L^0 that factor strongly through Marcinkiewicz weighted spaces. We show applications to sublinear operators on a certain class of quasi-Banach spaces with generalized Rademacher type generated by Orlicz sequence spaces.

Machine learning-guided multi-site combinatorial mutagenesis enhances the thermostability of pectin lyase

Enhancing the thermostability of enzymes is crucial for industrial applications. Methods such as directed evolution are often limited by the huge sequence space and combinatorial explosion, making it difficult to obtain optimal mutants. In recent years, machine learning (ML)-guided protein engineering has become an attractive tool because of its ability to comprehensively explore the sequence space of enzymes and discover superior mutants. This study employed ML to perform combinatorial mutation design on the pectin lyase PMGL-Ba from Bacillus licheniformis, aiming to improve its thermostability. First, 18 single-point mutants with enhanced thermostability were identified through semi-rational design. Subsequently, the initial library containing a small number of low-order mutants was utilized to construct an ML model to explore the combinatorial sequence space (theoretically 196,608 mutants) of single-point mutants. The results showed that the ML-predicted second library was successfully enriched with highly thermostable combinatorial mutants. After one iteration of learning, the best-performing combinatorial mutant in the third library, P36, showed a 67-fold and 39-fold increase in half-life at 75 °C and 80 °C, respectively, as well as a 2.1-fold increase in activity. Structural analysis and molecular dynamics simulations provided insights into the improved performance of the engineered enzyme.

Sequence, Structure, and Functional Space of Drosophila De Novo Proteins.

During de novo emergence, new protein coding genes emerge from previously nongenic sequences. The de novo proteins they encode are dissimilar in composition and predicted biochemical properties to conserved proteins. However, functional de novo proteins indeed exist. Both identification of functional de novo proteins and their structural characterization are experimentally laborious. To identify functional and structured de novo proteins in silico, we applied recently developed machine learning based tools and found that most de novo proteins are indeed different from conserved proteins both in their structure and sequence. However, some de novo proteins are predicted to adopt known protein folds, participate in cellular reactions, and to form biomolecular condensates. Apart from broadening our understanding of de novo protein evolution, our study also provides a large set of testable hypotheses for focused experimental studies on structure and function of de novo proteins in Drosophila.

Systematic multi-trait AAV capsid engineering for efficient gene delivery

Broadening gene therapy applications requires manufacturable vectors that efficiently transduce target cells in humans and preclinical models. Conventional selections of adeno-associated virus (AAV) capsid libraries are inefficient at searching the vast sequence space for the small fraction of vectors possessing multiple traits essential for clinical translation. Here, we present Fit4Function, a generalizable machine learning (ML) approach for systematically engineering multi-trait AAV capsids. By leveraging a capsid library that uniformly samples the manufacturable sequence space, reproducible screening data are generated to train accurate sequence-to-function models. Combining six models, we designed a multi-trait (liver-targeted, manufacturable) capsid library and validated 88% of library variants on all six predetermined criteria. Furthermore, the models, trained only on mouse in vivo and human in vitro Fit4Function data, accurately predicted AAV capsid variant biodistribution in macaque. Top candidates exhibited production yields comparable to AAV9, efficient murine liver transduction, up to 1000-fold greater human hepatocyte transduction, and increased enrichment relative to AAV9 in a screen for liver transduction in macaques. The Fit4Function strategy ultimately makes it possible to predict cross-species traits of peptide-modified AAV capsids and is a critical step toward assembling an ML atlas that predicts AAV capsid performance across dozens of traits.

α-, β- and γ-duals of the sequence spaces formed by a regular matrix of Tetranacci numbers

Abstract The primary objective of this paper is to create a novel infinite Toeplitz matrix by leveraging Tetranacci numbers. This matrix serves as the foundation for defining new sequence spaces denoted as c 0 ⁢ ( G ) {c_{0}(G)} , c ⁢ ( G ) {c(G)} , ℓ ∞ ⁢ ( G ) {\ell_{\infty}(G)} , and ℓ p ⁢ ( G ) {\ell_{p}(G)} , where 1 ≤ p < ∞ {1\leq p<\infty} . By utilizing this newly constructed matrix, the paper also explores and examines various algebraic and topological properties inherent to the sequence spaces c 0 ⁢ ( G ) {c_{0}(G)} , c ⁢ ( G ) {c(G)} , ℓ ∞ ⁢ ( G ) {\ell_{\infty}(G)} , and ℓ p ⁢ ( G ) {\ell_{p}(G)} for values of p within the range of 1 ≤ p < ∞ {1\leq p<\infty} . At last, we also prove existence theorem with example for infinite systems of differential equations in ℓ p ⁢ ( G ) {\ell_{p}(G)} .

Deep-learning-based design of synthetic orthologs of SH3 signaling domains

Evolution-based deep generative models represent an exciting direction in understanding and designing proteins. An open question is whether such models can learn specialized functional constraints that control fitness in specific biological contexts. Here, we examine the ability of generative models to produce synthetic versions of Src-homology 3 (SH3) domains that mediate signaling in the Sho1 osmotic stress response pathway of yeast. We show that a variational autoencoder (VAE) model produces artificial sequences that experimentally recapitulate the function of natural SH3 domains. More generally, the model organizes all fungal SH3 domains such that locality in the model latent space (but not simply locality in sequence space) enriches the design of synthetic orthologs and exposes non-obvious amino acid constraints distributed near and far from the SH3 ligand-binding site. The ability of generative models to design ortholog-like functions invivo opens new avenues for engineering protein function in specific cellular contexts and environments.

De novo synthetic antimicrobial peptide design with a recurrent neural network.

Antibiotic resistance is recognized as an imminent and growing global health threat. New antimicrobial drugs are urgently needed due to the decreasing effectiveness of conventional small-molecule antibiotics. Antimicrobial peptides (AMPs), a class of host defense peptides, are emerging as promising candidates to address this need. The potential sequence space of amino acids is combinatorially vast, making it possible to extend the current arsenal of antimicrobial agents with a practically infinite number of new peptide-based candidates. However, mining naturally occurring AMPs, whether directly by wet lab screening methods or aided by bioinformatics prediction tools, has its theoretical limit regarding the number of samples or genomic/transcriptomic resources researchers have access to. Further, manually designing novel synthetic AMPs requires prior field knowledge, restricting its throughput. In silico sequence generation methods are gaining interest as a high-throughput solution to the problem. Here, we introduce AMPd-Up, a recurrent neural network based tool for de novo AMP design, and demonstrate its utility over existing methods. Validation of candidates designed by AMPd-Up through antimicrobial susceptibility testing revealed that 40 of the 58 generated sequences possessed antimicrobial activity against Escherichia coli and/or Staphylococcus aureus. These results illustrate that AMPd-Up can be used to design novel synthetic AMPs with potent activities.

Deep mutational scanning and machine learning for the analysis of antimicrobial-peptide features driving membrane selectivity.

Many antimicrobial peptides directly disrupt bacterial membranes yet can also damage mammalian membranes. It is therefore central to their therapeutic use that rules governing the membrane selectivity of antimicrobial peptides be deciphered. However, this is difficult even for short peptides owing to the large combinatorial space of amino acid sequences. Here we describe a method for measuring the loss or maintenance of antimicrobial-peptide activity for thousands of peptide-sequence variants simultaneously, and its application to Protegrin-1, a potent yet toxic antimicrobial peptide, to determine the positional importance and flexibility of residues across its sequence while identifying variants with changes in membrane selectivity. More bacterially selective variants maintained a membrane-bound secondary structure while avoiding aromatic residues and cysteine pairs. A machine-learning model trained with our datasets accurately predicted membrane-specific activities for over 5.7 million Protegrin-1 variants, and identified one variant that showed substantially reduced toxicity and retention of activity in a mouse model of intraperitoneal infection. The high-throughput methodology may help elucidate sequence-structure-function relationships in antimicrobial peptides and inform the design of peptide-based synthetic drugs.

A Markovian dynamics for Caenorhabditis elegans behavior across scales

How do we capture the breadth of behavior in animal movement, from rapid body twitches to aging? Using high-resolution videos of the nematode worm Caenorhabditis elegans, we show that a single dynamics connects posture-scale fluctuations with trajectory diffusion and longer-lived behavioral states. We take short posture sequences as an instantaneous behavioral measure, fixing the sequence length for maximal prediction. Within the space of posture sequences, we construct a fine-scale, maximum entropy partition so that transitions among microstates define a high-fidelity Markov model, which we also use as a means of principled coarse-graining. We translate these dynamics into movement using resistive force theory, capturing the statistical properties of foraging trajectories. Predictive across scales, we leverage the longest-lived eigenvectors of the inferred Markov chain to perform a top-down subdivision of the worm's foraging behavior, revealing both "runs-and-pirouettes" as well as previously uncharacterized finer-scale behaviors. We use our model to investigate the relevance of these fine-scale behaviors for foraging success, recovering a trade-off between local and global search strategies.

A Comparative Study driven by Spatial Performance and VR toward Wayfinding in Architectural Space: Healthcare Buildings as a Case Study

Healthcare buildings can be complicated to navigate, causing patients to experience stress and lose time if not adequately planned. This study aims to identify the relationship between the spatial layout in healthcare buildings and wayfinding for users, by utilizing Behavioral Sequence Analysis (BSA) and Space Syntax through Immersive Virtual Reality (iVR). The methodology is based on behavioral and spatial data and was tested by using the experimental setups in VR environments. Space syntax analysis is applied to collect spatial data. Experiments were conducted by assigning wayfinding tasks in virtual hospitals with various plan configurations. Behavioral data obtained from BSA was associated with the spatial data driven by the space syntax analysis to gain a comprehensive understanding of the participants’ wayfinding behavior. The results indicate that the semi-centralized floor plan layout with high visibility levels performs better in wayfinding while the decentralized layout with low visibility values performs worse.

Neural network extrapolation to distant regions of the protein fitness landscape

Machine learning (ML) has transformed protein engineering by constructing models of the underlying sequence-function landscape to accelerate the discovery of new biomolecules. ML-guided protein design requires models, trained on local sequence-function information, to accurately predict distant fitness peaks. In this work, we evaluate neural networks’ capacity to extrapolate beyond their training data. We perform model-guided design using a panel of neural network architectures trained on protein G (GB1)-Immunoglobulin G (IgG) binding data and experimentally test thousands of GB1 designs to systematically evaluate the models’ extrapolation. We find each model architecture infers markedly different landscapes from the same data, which give rise to unique design preferences. We find simpler models excel in local extrapolation to design high fitness proteins, while more sophisticated convolutional models can venture deep into sequence space to design proteins that fold but are no longer functional. We also find that implementing a simple ensemble of convolutional neural networks enables robust design of high-performing variants in the local landscape. Our findings highlight how each architecture’s inductive biases prime them to learn different aspects of the protein fitness landscape and how a simple ensembling approach makes protein engineering more robust.

η- Dual of generalized triple sequence space

η- Dual of generalized triple sequence space