Sequence Space Research Articles

Epistasis facilitates functional evolution in an ancient transcription factor.

A protein's genetic architecture - the set of causal rules by which its sequence produces its functions - also determines its possible evolutionary trajectories. Prior research has proposed that the genetic architecture of proteins is very complex, with pervasive epistatic interactions that constrain evolution and make function difficult to predict from sequence. Most of this work has analyzed only the direct paths between two proteins of interest - excluding the vast majority of possible genotypes and evolutionary trajectories - and has considered only a single protein function, leaving unaddressed the genetic architecture of functional specificity and its impact on the evolution of new functions. Here, we develop a new method based on ordinal logistic regression to directly characterize the global genetic determinants of multiple protein functions from 20-state combinatorial deep mutational scanning (DMS) experiments. We use it to dissect the genetic architecture and evolution of a transcription factor's specificity for DNA, using data from a combinatorial DMS of an ancient steroid hormone receptor's capacity to activate transcription from two biologically relevant DNA elements. We show that the genetic architecture of DNA recognition consists of a dense set of main and pairwise effects that involve virtually every possible amino acid state in the protein-DNA interface, but higher-order epistasis plays only a tiny role. Pairwise interactions enlarge the set of functional sequences and are the primary determinants of specificity for different DNA elements. They also massively expand the number of opportunities for single-residue mutations to switch specificity from one DNA target to another. By bringing variants with different functions close together in sequence space, pairwise epistasis therefore facilitates rather than constrains the evolution of new functions.

Epistasis facilitates functional evolution in an ancient transcription factor

A protein’s genetic architecture – the set of causal rules by which its sequence produces its functions – also determines its possible evolutionary trajectories. Prior research has proposed that the genetic architecture of proteins is very complex, with pervasive epistatic interactions that constrain evolution and make function difficult to predict from sequence. Most of this work has analyzed only the direct paths between two proteins of interest – excluding the vast majority of possible genotypes and evolutionary trajectories – and has considered only a single protein function, leaving unaddressed the genetic architecture of functional specificity and its impact on the evolution of new functions. Here, we develop a new method based on ordinal logistic regression to directly characterize the global genetic determinants of multiple protein functions from 20-state combinatorial deep mutational scanning (DMS) experiments. We use it to dissect the genetic architecture and evolution of a transcription factor’s specificity for DNA, using data from a combinatorial DMS of an ancient steroid hormone receptor’s capacity to activate transcription from two biologically relevant DNA elements. We show that the genetic architecture of DNA recognition consists of a dense set of main and pairwise effects that involve virtually every possible amino acid state in the protein-DNA interface, but higher-order epistasis plays only a tiny role. Pairwise interactions enlarge the set of functional sequences and are the primary determinants of specificity for different DNA elements. They also massively expand the number of opportunities for single-residue mutations to switch specificity from one DNA target to another. By bringing variants with different functions close together in sequence space, pairwise epistasis therefore facilitates rather than constrains the evolution of new functions.

Pseudotyped virus infection of multiplexed ACE2 libraries reveals SARS-CoV-2 variant shifts in receptor usage.

Pairwise compatibility between virus and host proteins can dictate the outcome of infection. During transmission, both inter- and intraspecies variabilities in receptor protein sequences can impact cell susceptibility. Many viruses possess mutable viral entry proteins and the patterns of host compatibility can shift as the viral protein sequence changes. This combinatorial sequence space between virus and host is poorly understood, as traditional experimental approaches lack the throughput to simultaneously test all possible combinations of protein sequences. Here, we created a pseudotyped virus infection assay where a multiplexed target-cell library of host receptor variants can be assayed simultaneously using a DNA barcode sequencing readout. We applied this assay to test a panel of 30 ACE2 orthologs or human sequence mutants for infectability by the original SARS-CoV-2 spike protein or the Alpha, Beta, Gamma, Delta, and Omicron BA1 variant spikes. We compared these results to an analysis of the structural shifts that occurred for each variant spike's interface with human ACE2. Mutated residues were directly involved in the largest shifts, although there were also widespread indirect effects altering interface structure. The N501Y substitution in spike conferred a large structural shift for interaction with ACE2, which was partially recreated by indirect distal substitutions in Delta, which does not harbor N501Y. The structural shifts from N501Y greatly influenced the set of animal orthologs the variant spike was capable of interacting with. Out of the thirteen non-human orthologs, ten exhibited unique patterns of variant-specific compatibility, demonstrating that spike sequence changes during human transmission can toggle ACE2 compatibility and potential susceptibility of other animal species, and cumulatively increase overall compatibilities as new variants emerge. These experiments provide a blueprint for similar large-scale assessments of protein compatibility during entry by diverse viruses. This dataset demonstrates the complex compatibility relationships that occur between variable interacting host and virus proteins.

Exploration of three Dyadobacter fermentans enzymes uncovers molecular activity determinants in CE15

Glucuronoyl esterases (GEs) are serine-type hydrolase enzymes belonging to carbohydrate esterase family 15 (CE15), and they play a central role in the reduction of recalcitrance in plant cell walls by cleaving ester linkages between glucuronoxylan and lignin in lignocellulose. Recent studies have suggested that bacterial CE15 enzymes are more heterogeneous in terms of sequence, structure, and substrate preferences than their fungal counterparts. However, the sequence space of bacterial GEs has still not been fully explored, and further studies on diverse enzymes could provide novel insights into new catalysts of biotechnological interest. To expand our knowledge on this family of enzymes, we investigated three unique CE15 members encoded by Dyadobacter fermentans NS114T, a Gram-negative bacterium found endophytically in maize/corn (Zea mays). The enzymes are dissimilar, sharing ≤ 39% sequence identity to each other‚ and were considerably different in their activities towards synthetic substrates. Combined analysis of their primary sequences and structural predictions aided in establishing hypotheses regarding specificity determinants within CE15, and these were tested using enzyme variants attempting to shift the activity profiles. Together, the results expand our existing knowledge of CE15, shed light into the molecular determinants defining specificity, and support the recent thesis that diverse GEs encoded by a single microorganism may have evolved to fulfil different physiological functions.Key points• D. fermentans encodes three CE15 enzymes with diverse sequences and specificities• The Region 2 inserts in bacterial GEs may directly influence enzyme activity• Rational amino acid substitutions improved the poor activity of the DfCE15A enzyme

Computation-Driven Rational Design of Self-Assembled Short Peptides for Catalytic Hydrogen Production.

Self-assembling peptides represent a captivating area of study in nanotechnology and biomaterials. This interest is largely driven by their unique properties and the vast application potential across various fields such as catalytic functions. However, design complexities, including high-dimensional sequence space and structural diversity, pose significant challenges in the study of such systems. In this work, we explored the possibility of self-assembled peptides to catalyze the hydrolysis of hydrosilane for hydrogen production using ab initio calculations and carried out wet-lab experiments to confirm the feasibility of these catalytic reactions under ambient conditions. Further, we delved into the nuanced interplay between sequence, structural conformation, and catalytic activity by combining modeling with experimental techniques such as transmission electron microscopy and nuclear magnetic resonance and proposed a dual mode of the microstructure of the catalytic center. Our results reveal that although research in this area is still at an early stage, the development of self-assembled peptide catalysts for hydrogen production has the potential to provide a more sustainable and efficient alternative to conventional hydrogen production methods. In addition, this work also demonstrates that a computation-driven rational design supplemented by experimental validation is an effective protocol for conducting research on functional self-assembled peptides.

THE SET OF ELEMENTARY TENSORS IS WEAKLY CLOSED IN PROJECTIVE TENSOR PRODUCTS

Abstract We prove that the set of elementary tensors is weakly closed in the projective tensor product of two Banach spaces. As a result, we answer a question of Rodríguez and Rueda Zoca [‘Weak precompactness in projective tensor products’, Indag. Math. (N.S.)35(1) (2024), 60–75], proving that if $(x_n) \subset X$ and $(y_n) \subset Y$ are two weakly null sequences such that $(x_n \otimes y_n)$ converges weakly in $X \widehat {\otimes }_\pi Y$ , then $(x_n \otimes y_n)$ is also weakly null.

Banach spaces of sequences arising from infinite matrices

Banach spaces of sequences arising from infinite matrices

Matrix Transformation and Compactness on q-Catalan Sequence Spaces

This article intends to develop q-Catalan sequence spaces l p ( C ( q ) ) and l ∞ ( C ( q ) ) due to q-Catalan matrix C ( q ) in l p and l ∞ , respectively. Apart from obtaining some basic topological properties and Schauder basis, we compute α-, β-, and γ-duals of the spaces l p ( C ( q ) ) and l ∞ ( C ( q ) ) . We state and prove a theorem that characterize certain matrix classes (X, Y), where X is either of the space l p ( C ( q ) ) or l ∞ ( C ( q ) ) and Y ∈ { l ∞ , c 0 , c , l 1 } . The final section is devoted to determination of certain conditions by which a matrix operator becomes compact.

Relative uniform convergence of p-absolutely summable sequence of functions

In this article we introduce the notion of relative uniform convergence of p-absolutely summable sequence of functions. We have investigated its different properties such as solidness, symmetric, convergence-free, monotonic etc. We have established some inclusion relations involving this sequence space.

Redefining the bacteriophage mv4 site-specific recombination system and the sequence specificity of its attB and core-attP sites.

Through their involvement in the integration and excision of a large number of mobile genetic elements, such as phages and integrative and conjugative elements (ICEs), site-specific recombination systems based on heterobivalent tyrosine recombinases play a major role in genome dynamics and evolution. However, despite hundreds of these systems having been identified in genome databases, very few have been described in detail, with none from phages that infect Bacillota (formerly Firmicutes). In this study, we reanalyzed the recombination module of Lactobacillus delbrueckii subsp. bulgaricus phage mv4, previously considered atypical compared with classical systems. Our results reveal that mv4 integrase is a 369 aa protein with all the structural hallmarks of recombinases from the Tn916 family and that it cooperatively interacts with its recombination sites. Using randomized DNA libraries, NGS sequencing, and other molecular approaches, we show that the 21-bp core-attP and attB sites have structural similarities to classical systems only if considering the nucleotide degeneracy, with two 7-bp inverted regions corresponding to mv4Int core-binding sites surrounding a 7-bp strand-exchange region. We also examined the different compositional constraints in the core-binding regions, which define the sequence space of permissible recombination sites.

Selection of a promiscuous minimalist cAMP phosphodiesterase from a library of de novo designed proteins.

The ability of unevolved amino acid sequences to become biological catalysts was key to the emergence of life on Earth. However, billions of years of evolution separate complex modern enzymes from their simpler early ancestors. To probe how unevolved sequences can develop new functions, we use ultrahigh-throughput droplet microfluidics to screen for phosphoesterase activity amidst a library of more than one million sequences based on a de novo designed 4-helix bundle. Characterization of hits revealed that acquisition of function involved a large jump in sequence space enriching for truncations that removed >40% of the protein chain. Biophysical characterization of a catalytically active truncated protein revealed that it dimerizes into an α-helical structure, with the gain of function accompanied by increased structural dynamics. The identified phosphodiesterase is a manganese-dependent metalloenzyme that hydrolyses a range of phosphodiesters. It is most active towards cyclic AMP, with a rate acceleration of ~109 and a catalytic proficiency of >1014 M-1, comparable to larger enzymes shaped by billions of years of evolution.

Robust genetic codes enhance protein evolvability.

The standard genetic code defines the rules of translation for nearly every life form on Earth. It also determines the amino acid changes accessible via single-nucleotide mutations, thus influencing protein evolvability-the ability of mutation to bring forth adaptive variation in protein function. One of the most striking features of the standard genetic code is its robustness to mutation, yet it remains an open question whether such robustness facilitates or frustrates protein evolvability. To answer this question, we use data from massively parallel sequence-to-function assays to construct and analyze 6 empirical adaptive landscapes under hundreds of thousands of rewired genetic codes, including those of codon compression schemes relevant to protein engineering and synthetic biology. We find that robust genetic codes tend to enhance protein evolvability by rendering smooth adaptive landscapes with few peaks, which are readily accessible from throughout sequence space. However, the standard genetic code is rarely exceptional in this regard, because many alternative codes render smoother landscapes than the standard code. By constructing low-dimensional visualizations of these landscapes, which each comprise more than 16 million mRNA sequences, we show that such alternative codes radically alter the topological features of the network of high-fitness genotypes. Whereas the genetic codes that optimize evolvability depend to some extent on the detailed relationship between amino acid sequence and protein function, we also uncover general design principles for engineering nonstandard genetic codes for enhanced and diminished evolvability, which may facilitate directed protein evolution experiments and the bio-containment of synthetic organisms, respectively.

Two new fibonomial difference sequence spaces and related dual properties

Two new fibonomial difference sequence spaces and related dual properties

Stability of Krein-von Neumann self-adjoint operator extension under unbounded perturbations

We have considered a fourth order difference operator defined on the Hilbert space of square summable sequences on N. We investigated the stability of existence of Krein-von Neumann self-adjoint extension of difference operators under bounded and unbounded coefficients. Using asymptotic summation based on discretised Levinson's theorem and appropriate smoothness and decay conditions, we have shown that unlike the case of deficiency indices and discrete spectrum, the existence of positive self-adjoint operator extensions is stable under unbounded perturbations. These results now exhaustively characterise the spectral and structural properties of difference operators with unbounded coefficients.

Towards parsimonious generative modeling of RNA families.

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.

On Some New Sequence Spaces and Their Duals

In this study, we defined some new sequence spaces using regular Tribonacci matrix. We examined some properties of these spaces such as completeness, Schauder basis. We have identified α−,β−, and γ−duals of the newly created spaces.

A study on Fibo-Pascal sequence spaces and associated matrix transformations and applications of Hausdorff measure of non-compactness

Abstract In this article, we introduce Fibo-Pascal sequence spaces P p F {P_{p}^{F}} , 0 &lt; p &lt; ∞ {0&lt;p&lt;\infty} , and P ∞ F {P_{\infty}^{F}} through the utilization of the Fibo-Pascal matrix P F {P^{F}} . We establish that both P p F {P_{p}^{F}} and P ∞ F {P_{\infty}^{F}} are BK-spaces, enjoying a linear isomorphism with the classical spaces ℓ p {\ell_{p}} and ℓ ∞ {\ell_{\infty}} , respectively. Further contributing to the depth of our investigation, we proceed to derive the Schauder basis of the space P p F {P_{p}^{F}} , alongside an exhaustive computation of the α-, β-, and γ-duals for both spaces P p F {P_{p}^{F}} and P ∞ F {P_{\infty}^{F}} . Additionally, we undertake the task of characterizing certain classes of matrix mappings pertaining to the spaces P p F {P_{p}^{F}} and P ∞ F {P_{\infty}^{F}} . The final section of this study is dedicated to the meticulous characterization of compact operators acting in the spaces P 1 F {P_{1}^{F}} , P p F {P_{p}^{F}} , and P ∞ F {P_{\infty}^{F}} by using Hausdorff measure of non-compactness.

Statistically convergent difference sequences of bi-complex numbers

Abstract In this article we introduce the notion of statistical convergence difference sequences of bi-complex numbers. Some properties of these sequence spaces like BC-module, Banach BC-module, BC-balanced set, BC-convex set, solidness, and symetricity are studied.

A paranormed fractional ordered Euler–Riesz difference sequence space

In this study, we introduce a novel sequence space denoted as [Formula: see text] with a fractional order [Formula: see text]. This new space is defined by the matrix [Formula: see text], which is a composition of the Euler–Riesz matrix [Formula: see text] and the fractional ordered difference operator [Formula: see text]. We explore its topological properties along with its [Formula: see text]-, [Formula: see text]-, and [Formula: see text]-duals. Furthermore, we provide characterizations for certain matrix mappings from [Formula: see text] to the sequence spaces of Maddox.

Comparative Analysis of Deep Generative Model for Industrial Enzyme Design

Abstract: Although enzymes have the advantage of efficient catalysis, natural enzymes lack stability in industrial environments and do not even meet the required catalytic reactions. This prompted us to urgently de novo design new enzymes. Computational design is a powerful tool, allowing rapid and efficient exploration of sequence space and facilitating the design of novel enzymes tailored to specific conditions and requirements. It is beneficial to de novo design industrial enzymes using computational methods. Currently, only one tool explicitly designed for the enzyme-only generation performs unsatisfactorily. We have selected several general protein sequence design tools and systematically evaluated their effectiveness when applied to specific industrial enzymes. We investigated the literature related to protein generation. We summarized the computational methods used for sequence generation into three categories: structure-conditional sequence generation, sequence generation without structural constraints, and co-generation of sequence and structure. To effectively evaluate the ability of six computational tools to generate enzyme sequences, we first constructed a luciferase dataset named Luc_64. Then we assessed the quality of enzyme sequences generated by these methods on this dataset, including amino acid distribution, EC number validation, etc. We also assessed sequences generated by structure-based methods on existing public datasets using sequence recovery rates and root-mean-square deviation (RMSD) from a sequence and structure perspective. In the functionality dataset, Luc_64, ABACUS-R, and ProteinMPNN stood out for producing sequences with amino acid distributions and functionalities closely matching those of naturally occurring luciferase enzymes, suggesting their effectiveness in preserving essential enzymatic characteristics. Across both benchmark datasets, ABACUS-R and ProteinMPNN, have also exhibited the highest sequence recovery rates, indicating their superior ability to generate sequences closely resembling the original enzyme structures. Our study provides a crucial reference for researchers selecting appropriate enzyme sequence design tools, highlighting the strengths and limitations of each tool in generating accurate and functional enzyme sequences. ProteinMPNN and ABACUS-R emerged as the most effective tools in our evaluation, offering high accuracy in sequence recovery and RMSD and maintaining the functional integrity of enzymes through accurate amino acid distribution. Meanwhile, the performance of protein general tools for migration to specific industrial enzymes was fairly evaluated on our specific industrial enzyme benchmark.