scholarly journals Higher-order epistatic networks underlie the evolutionary fitness landscape of a xenobiotic-degrading enzyme

2018 ◽  
Author(s):  
Gloria Yang ◽  
Dave W Anderson ◽  
Florian Baier ◽  
Elias Dohmen ◽  
Nansook Hong ◽  
...  
Keyword(s):  
Fitness Landscape ◽  
Interaction Network ◽  
Higher Order ◽  
Intramolecular Interactions ◽  
Evolutionary Mechanisms ◽  
Methyl Parathion Hydrolase ◽  
Degrading Enzyme ◽  
Adaptive Landscapes ◽  
Necessary And Sufficient ◽  
Enzyme Functions

AbstractCharacterizing the adaptive landscapes that encompass the emergence of novel enzyme functions can provide molecular insights into both enzymatic and evolutionary mechanisms. Here, we combine ancestral protein reconstruction with biochemical, structural, and mutational analyses to characterize the functional evolution of methyl-parathion hydrolase (MPH), a xenobiotic organophosphate-degrading enzyme. We identify five mutations that are necessary and sufficient for the evolution of MPH from an ancestral dihydrocoumarin hydrolase. In-depth analyses of the adaptive landscapes encompassing this evolutionary transition revealed that a complex interaction network, defined in part by higher-order epistasis, determined the adaptive pathways that were available. By also characterizing the adaptive landscapes in terms of their functional activity towards three other OP substrates, we reveal that subtle differences in substrate substituents drastically alter the enzyme’s epistatic network by changing its intramolecular interactions. Our work suggests that the mutations function collectively to enable substrate recognition via subtle structural repositioning.

Higher-order epistasis shapes the fitness landscape of a xenobiotic-degrading enzyme

2019 ◽  
Vol 15 (11) ◽  
pp. 1120-1128 ◽  
Author(s):  
Gloria Yang ◽  
Dave W Anderson ◽  
Florian Baier ◽  
Elias Dohmen ◽  
Nansook Hong ◽  
...  
Keyword(s):  
Fitness Landscape ◽  
Higher Order ◽  
Degrading Enzyme

scholarly journals Author Correction: Higher-order epistasis shapes the fitness landscape of a xenobiotic-degrading enzyme

2020 ◽  
Vol 16 (8) ◽  
pp. 930-930
Author(s):  
Gloria Yang ◽  
Dave W. Anderson ◽  
Florian Baier ◽  
Elias Dohmen ◽  
Nansook Hong ◽  
...  
Keyword(s):  
Fitness Landscape ◽  
Higher Order ◽  
Degrading Enzyme

scholarly journals Variational Problems with Time Delay and Higher-Order Distributed-Order Fractional Derivatives with Arbitrary Kernels

Mathematics ◽  
2021 ◽  
Vol 9 (14) ◽  
pp. 1665
Author(s):  
Fátima Cruz ◽  
Ricardo Almeida ◽  
Natália Martins
Keyword(s):  
Time Delay ◽  
Fractional Derivatives ◽  
Variational Problems ◽  
Higher Order ◽  
Sufficient Optimality Conditions ◽  
Fractional Operator ◽  
Different Types ◽  
Generalized Fractional Derivatives ◽  
Necessary And Sufficient ◽  
Distributed Order

In this work, we study variational problems with time delay and higher-order distributed-order fractional derivatives dealing with a new fractional operator. This fractional derivative combines two known operators: distributed-order derivatives and derivatives with respect to another function. The main results of this paper are necessary and sufficient optimality conditions for different types of variational problems. Since we are dealing with generalized fractional derivatives, from this work, some well-known results can be obtained as particular cases.

Partial Higher-Order Specifications1

1992 ◽  
Vol 16 (2) ◽  
pp. 101-126
Author(s):  
Egidio Astesiano ◽  
Maura Cerioli
Keyword(s):  
Sufficient Conditions ◽  
Higher Order ◽  
Necessary And Sufficient Conditions ◽  
Important Case ◽  
Deduction System ◽  
Closure Properties ◽  
Inference System ◽  
Conditional Specification ◽  
Necessary And Sufficient

In this paper the classes of extensional models of higher-order partial conditional specifications are studied, with the emphasis on the closure properties of these classes. Further it is shown that any equationally complete inference system for partial conditional specifications may be extended to an inference system for partial higher-order conditional specifications, which is equationally complete w.r.t. the class of all extensional models. Then, applying some previous results, a deduction system is proposed, equationally complete for the class of extensional models of a partial conditional specification. Finally, turning the attention to the special important case of termextensional models, it is first shown a sound and equationally complete inference system and then necessary and sufficient conditions are given for the existence of free models, which are also free in the class of term-generated extensional models.

scholarly journals The topology of evolutionary novelty and innovation in macroevolution

2017 ◽  
Vol 372 (1735) ◽  
pp. 20160422 ◽  
Author(s):  
Douglas H. Erwin
Keyword(s):  
Evolutionary Theory ◽  
Fitness Landscape ◽  
Conceptual Metaphor ◽  
Functional Trait ◽  
Evolutionary Change ◽  
Evolutionary Novelty ◽  
Adaptive Landscapes ◽  
George Gaylord Simpson

Sewall Wright's fitness landscape introduced the concept of evolutionary spaces in 1932. George Gaylord Simpson modified this to an adaptive, phenotypic landscape in 1944 and since then evolutionary spaces have played an important role in evolutionary theory through fitness and adaptive landscapes, phenotypic and functional trait spaces, morphospaces and related concepts. Although the topology of such spaces is highly variable, from locally Euclidean to pre-topological, evolutionary change has often been interpreted as a search through a pre-existing space of possibilities, with novelty arising by accessing previously inaccessible or difficult to reach regions of a space. Here I discuss the nature of evolutionary novelty and innovation within the context of evolutionary spaces, and argue that the primacy of search as a conceptual metaphor ignores the generation of new spaces as well as other changes that have played important evolutionary roles. This article is part of the themed issue ‘Process and pattern in innovations from cells to societies’.

scholarly journals Completeness Theorems for Elliptic Equations of Higher Order with Constant Coefficients

2007 ◽  
Vol 14 (1) ◽  
pp. 81-97
Author(s):  
Alberto Cialdea
Keyword(s):  
Elliptic Equation ◽  
Bounded Domain ◽  
Elliptic Equations ◽  
Complete System ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Polynomial Solutions ◽  
Constant Coefficients ◽  
Necessary And Sufficient ◽  
Completeness Theorems

Abstract Let {ω𝑘 } be a complete system of polynomial solutions of the elliptic equation ∑|α|⩽2𝑚 aα 𝐷 α 𝑢 = 0, aα being real constants. We give necessary and sufficient conditions for the completeness of the system in [𝐿𝑝(∂Ω)]𝑚, where Ω ⊂ is a bounded domain such that is connected and ∂Ω ∈ 𝐶1.

scholarly journals Higher-order optimality conditions for a minimax

1996 ◽  
Vol 54 (3) ◽  
pp. 509-516 ◽  
Author(s):  
Do Van Luu ◽  
W. Oettli
Keyword(s):  
Optimality Conditions ◽  
Minimax Problem ◽  
Higher Order ◽  
Regularity Conditions ◽  
Sufficient Optimality Conditions ◽  
Basic Assumptions ◽  
Necessary And Sufficient ◽  
Inequality Type

Higher-order necessary and sufficient optimality conditions for a nonsmooth minimax problem with infinitely many constraints of inequality type are established under suitable basic assumptions and regularity conditions.

scholarly journals Environmental changes bridge evolutionary valleys

2016 ◽  
Vol 2 (1) ◽  
pp. e1500921 ◽  
Author(s):  
Barrett Steinberg ◽  
Marc Ostermeier
Keyword(s):  
Antibiotic Resistance ◽  
Negative Selection ◽  
Environmental Changes ◽  
Fitness Landscape ◽  
Antibiotic Resistance Gene ◽  
Evolutionary Strategies ◽  
Evolutionary Mechanisms ◽  
Inaccessible Area ◽  
Evolutionary Pathways ◽  
Open Question

In the basic fitness landscape metaphor for molecular evolution, evolutionary pathways are presumed to follow uphill steps of increasing fitness. How evolution can cross fitness valleys is an open question. One possibility is that environmental changes alter the fitness landscape such that low-fitness sequences reside on a hill in alternate environments. We experimentally test this hypothesis on the antibiotic resistance gene TEM-15 β-lactamase by comparing four evolutionary strategies shaped by environmental changes. The strategy that included initial steps of selecting for low antibiotic resistance (negative selection) produced superior alleles compared with the other three strategies. We comprehensively examined possible evolutionary pathways leading to one such high-fitness allele and found that an initially deleterious mutation is key to the allele’s evolutionary history. This mutation is an initial gateway to an otherwise relatively inaccessible area of sequence space and participates in higher-order, positive epistasis with a number of neutral to slightly beneficial mutations. The ability of negative selection and environmental changes to provide access to novel fitness peaks has important implications for natural evolutionary mechanisms and applied directed evolution.

scholarly journals Covariant Fitness Clusters Reveal Structural Evolution of SARS-CoV-2 Polymerase Across the Human Population

2022 ◽  
Author(s):  
Chao Wang ◽  
Nadia Elghobashi-Meinhardt ◽  
William E Balch
Keyword(s):  
Fitness Landscape ◽  
Structural Evolution ◽  
Gaussian Process Regression ◽  
Binding Motif ◽  
Learning Approach ◽  
Spatial Covariance ◽  
Evolutionary Mechanisms ◽  
Viral Genomes ◽  
Machine Learning Approach ◽  
Rapid Spread

Understanding the fitness landscape of viral mutations is crucial for uncovering the evolutionary mechanisms contributing to pandemic behavior. Here, we apply a Gaussian process regression (GPR) based machine learning approach that generates spatial covariance (SCV) relationships to construct stability fitness landscapes for the RNA-dependent RNA polymerase (RdRp) of SARS-CoV-2. GPR generated fitness scores capture on a residue-by-residue basis a covariant fitness cluster centered at the C487-H642-C645-C646 Zn2+ binding motif that iteratively evolves since the early phase pandemic. In the Alpha and Delta variant of concern (VOC), multi-residue SCV interactions in the NiRAN domain form a second fitness cluster contributing to spread. Strikingly, a novel third fitness cluster harboring a Delta VOC basal mutation G671S augments RdRp structural plasticity to potentially promote rapid spread through viral load. GPR principled SCV provides a generalizable tool to mechanistically understand evolution of viral genomes at atomic resolution contributing to fitness at the pathogen-host interface.

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