1
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Schwartz R, Zev S, Major DT. Differential Substrate Sensing in Terpene Synthases from Plants and Microorganisms: Insight from Structural, Bioinformatic, and EnzyDock Analyses. Angew Chem Int Ed Engl 2024; 63:e202400743. [PMID: 38556463 DOI: 10.1002/anie.202400743] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2024] [Revised: 03/26/2024] [Accepted: 03/26/2024] [Indexed: 04/02/2024]
Abstract
Terpene synthases (TPSs) catalyze the first step in the formation of terpenoids, which comprise the largest class of natural products in nature. TPSs employ a family of universal natural substrates, composed of isoprenoid units bound to a diphosphate moiety. The intricate structures generated by TPSs are the result of substrate binding and folding in the active site, enzyme-controlled carbocation reaction cascades, and final reaction quenching. A key unaddressed question in class I TPSs is the asymmetric nature of the diphosphate-(Mg2+)3 cluster, which forms a critical part of the active site. In this asymmetric ion cluster, two diphosphate oxygen atoms protrude into the active site pocket. The substrate hydrocarbon tail, which is eventually molded into terpenes, can bind to either of these oxygen atoms, yet to which is unknown. Herein, we employ structural, bioinformatics, and EnzyDock docking tools to address this enigma. We bring initial data suggesting that this difference is rooted in evolutionary differences between TPSs. We hypothesize that this alteration in binding, and subsequent chemistry, is due to TPSs originating from plants or microorganisms. We further suggest that this difference can cast light on the frequent observation that the chiral products or intermediates of plant and bacterial terpene synthases represent opposite enantiomers.
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Affiliation(s)
- Renana Schwartz
- Department of Chemistry and Institute for Nanotechnology & Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Shani Zev
- Department of Chemistry and Institute for Nanotechnology & Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel
| | - Dan T Major
- Department of Chemistry and Institute for Nanotechnology & Advanced Materials, Bar-Ilan University, Ramat-Gan, 52900, Israel
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2
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Park Y, Metzger BP, Thornton JW. The simplicity of protein sequence-function relationships. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2023.09.02.556057. [PMID: 37732229 PMCID: PMC10508729 DOI: 10.1101/2023.09.02.556057] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/22/2023]
Abstract
How complicated is the genetic architecture of proteins - the set of causal effects by which sequence determines function? High-order epistatic interactions among residues are thought to be pervasive, making a protein's function difficult to predict or understand from its sequence. Most studies, however, used methods that overestimate epistasis, because they analyze genetic architecture relative to a designated reference sequence - causing measurement noise and small local idiosyncrasies to propagate into pervasive high-order interactions - or have not effectively accounted for global nonlinearity in the sequence-function relationship. Here we present a new reference-free method that jointly estimates global nonlinearity and specific epistatic interactions across a protein's entire genotype-phenotype map. This method yields a maximally efficient explanation of a protein's genetic architecture and is more robust than existing methods to measurement noise, partial sampling, and model misspecification. We reanalyze 20 combinatorial mutagenesis experiments from a diverse set of proteins and find that additive and pairwise effects, along with a simple nonlinearity to account for limited dynamic range, explain a median of 96% of total variance in measured phenotypes (and >92% in every case). Only a tiny fraction of genotypes are strongly affected by third- or higher-order epistasis. Genetic architecture is also sparse: the number of terms required to explain the vast majority of variance is smaller than the number of genotypes by many orders of magnitude. The sequence-function relationship in most proteins is therefore far simpler than previously thought, opening the way for new and tractable approaches to characterize it.
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Affiliation(s)
- Yeonwoo Park
- Committee on Genetics, Genomics, and Systems Biology, University of Chicago, Chicago, IL 60637
- Current affiliation: Center for RNA Research, Institute for Basic Science, Seoul, Republic of Korea 08826
| | - Brian P.H. Metzger
- Department of Ecology and Evolution, University of Chicago, Chicago, IL 60637
- Current affiliation: Department of Biological Sciences, Purdue University, West Lafayette, IN 47907
| | - Joseph W. Thornton
- Department of Ecology and Evolution, University of Chicago, Chicago, IL 60637
- Department of Human Genetics, University of Chicago, Chicago, IL 60637
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3
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Nartey C, Koo HJ, Laurendon C, Shaik HZ, O’maille P, Noel JP, Morcos F. Coevolutionary Information Captures Catalytic Functions and Reveals Divergent Roles of Terpene Synthase Interdomain Connections. Biochemistry 2024; 63:355-366. [PMID: 38206111 PMCID: PMC10851433 DOI: 10.1021/acs.biochem.3c00578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/24/2023] [Revised: 12/22/2023] [Accepted: 12/27/2023] [Indexed: 01/12/2024]
Abstract
Inferring the historical and biophysical causes of diversity within protein families is a complex puzzle. A key to unraveling this problem is characterizing the rugged topography of sequence-function adaptive landscapes. Using biochemical data from a 29 = 512 combinatorial library of tobacco 5-epi-aristolochene synthase (TEAS) mutants engineered to make the native major product of Egyptian henbane premnaspirodiene synthase (HPS) and a complementary 512 mutant HPS library, we address the question of how product specificity is controlled. These data sets reveal that HPS is far more robust and resistant to mutations than TEAS, where most mutants are promiscuous. We also combine experimental data with a sequence Potts Hamiltonian model and direct coupling analysis to quantify mutant fitness. Our results demonstrate that the Hamiltonian captures variation in product outputs across both libraries, clusters native family members based on their substrate specificities, and exposes the divergent catalytic roles of couplings between the catalytic and noncatalytic domains of TEAS versus HPS. Specifically, we found that the role of the interdomain connectivities in specifying product output is more important in TEAS than connectivities within the catalytic domain. Despite being 75% identical, this property is not shared by HPS, where connectivities within the catalytic domain are more important for specificity. By solving the X-ray crystal structure of HPS, we assessed structural bases for their interdomain network differences. Last, we calculate the product profile Shannon entropies of the two libraries, which showcases that site-site connectivities also play divergent roles in catalytic accuracy.
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Affiliation(s)
- Charisse
M. Nartey
- Department
of Biological Sciences, The University of
Texas at Dallas, Richardson, Texas 75080, United States
| | - Hyun Jo Koo
- Howard
Hughes Medical Institute, The Salk Institute for Biological Studies, Jack H. Skirball Center for Chemical Biology and Proteomics, 10010 North Torrey Pines Road, La Jolla, California 92037, United States
| | - Caroline Laurendon
- John
Innes Centre, Department of Metabolic Biology, Norwich Research Park, Norwich NR4 7UH, U.K.
| | - Hana Z. Shaik
- Department
of Bioengineering, The University of Texas
at Dallas, Richardson, Texas 75080, United States
| | - Paul O’maille
- John
Innes Centre, Institute of Food Research, Food & Health Programme, Norwich Research Park, Norwich NR4 7UA, U.K.
| | - Joseph P. Noel
- Howard
Hughes Medical Institute, The Salk Institute for Biological Studies, Jack H. Skirball Center for Chemical Biology and Proteomics, 10010 North Torrey Pines Road, La Jolla, California 92037, United States
| | - Faruck Morcos
- Department
of Biological Sciences, The University of
Texas at Dallas, Richardson, Texas 75080, United States
- Department
of Bioengineering, The University of Texas
at Dallas, Richardson, Texas 75080, United States
- Center for
Systems Biology, The University of Texas
at Dallas, Richardson, Texas 75080, United States
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4
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Alvarez S, Nartey CM, Mercado N, de la Paz JA, Huseinbegovic T, Morcos F. In vivo functional phenotypes from a computational epistatic model of evolution. Proc Natl Acad Sci U S A 2024; 121:e2308895121. [PMID: 38285950 PMCID: PMC10861889 DOI: 10.1073/pnas.2308895121] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2023] [Accepted: 12/19/2023] [Indexed: 01/31/2024] Open
Abstract
Computational models of evolution are valuable for understanding the dynamics of sequence variation, to infer phylogenetic relationships or potential evolutionary pathways and for biomedical and industrial applications. Despite these benefits, few have validated their propensities to generate outputs with in vivo functionality, which would enhance their value as accurate and interpretable evolutionary algorithms. We demonstrate the power of epistasis inferred from natural protein families to evolve sequence variants in an algorithm we developed called sequence evolution with epistatic contributions (SEEC). Utilizing the Hamiltonian of the joint probability of sequences in the family as fitness metric, we sampled and experimentally tested for in vivo [Formula: see text]-lactamase activity in Escherichia coli TEM-1 variants. These evolved proteins can have dozens of mutations dispersed across the structure while preserving sites essential for both catalysis and interactions. Remarkably, these variants retain family-like functionality while being more active than their wild-type predecessor. We found that depending on the inference method used to generate the epistatic constraints, different parameters simulate diverse selection strengths. Under weaker selection, local Hamiltonian fluctuations reliably predict relative changes to variant fitness, recapitulating neutral evolution. SEEC has the potential to explore the dynamics of neofunctionalization, characterize viral fitness landscapes, and facilitate vaccine development.
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Affiliation(s)
- Sophia Alvarez
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX75080
| | - Charisse M. Nartey
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX75080
| | - Nicholas Mercado
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX75080
| | | | - Tea Huseinbegovic
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX75080
| | - Faruck Morcos
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX75080
- Department of Bioengineering, University of Texas at Dallas, Richardson, TX75080
- Center for Systems Biology, University of Texas at Dallas, Richardson, TX75080
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5
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Fannjiang C, Listgarten J. Is Novelty Predictable? Cold Spring Harb Perspect Biol 2024; 16:a041469. [PMID: 38052497 PMCID: PMC10835614 DOI: 10.1101/cshperspect.a041469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/07/2023]
Abstract
Machine learning-based design has gained traction in the sciences, most notably in the design of small molecules, materials, and proteins, with societal applications ranging from drug development and plastic degradation to carbon sequestration. When designing objects to achieve novel property values with machine learning, one faces a fundamental challenge: how to push past the frontier of current knowledge, distilled from the training data into the model, in a manner that rationally controls the risk of failure. If one trusts learned models too much in extrapolation, one is likely to design rubbish. In contrast, if one does not extrapolate, one cannot find novelty. Herein, we ponder how one might strike a useful balance between these two extremes. We focus in particular on designing proteins with novel property values, although much of our discussion is relevant to machine learning-based design more broadly.
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Affiliation(s)
- Clara Fannjiang
- Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA
| | - Jennifer Listgarten
- Department of Electrical Engineering and Computer Sciences, University of California, Berkeley, California 94720, USA
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6
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Buda K, Miton CM, Tokuriki N. Pervasive epistasis exposes intramolecular networks in adaptive enzyme evolution. Nat Commun 2023; 14:8508. [PMID: 38129396 PMCID: PMC10739712 DOI: 10.1038/s41467-023-44333-5] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2023] [Accepted: 12/08/2023] [Indexed: 12/23/2023] Open
Abstract
Enzyme evolution is characterized by constant alterations of the intramolecular residue networks supporting their functions. The rewiring of these network interactions can give rise to epistasis. As mutations accumulate, the epistasis observed across diverse genotypes may appear idiosyncratic, that is, exhibit unique effects in different genetic backgrounds. Here, we unveil a quantitative picture of the prevalence and patterns of epistasis in enzyme evolution by analyzing 41 fitness landscapes generated from seven enzymes. We show that >94% of all mutational and epistatic effects appear highly idiosyncratic, which greatly distorted the functional prediction of the evolved enzymes. By examining seemingly idiosyncratic changes in epistasis along adaptive trajectories, we expose several instances of higher-order, intramolecular rewiring. Using complementary structural data, we outline putative molecular mechanisms explaining higher-order epistasis along two enzyme trajectories. Our work emphasizes the prevalence of epistasis and provides an approach to exploring this phenomenon through a molecular lens.
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Affiliation(s)
- Karol Buda
- Michael Smith Laboratories, University of British Columbia, Vancouver, Canada
| | - Charlotte M Miton
- Michael Smith Laboratories, University of British Columbia, Vancouver, Canada
| | - Nobuhiko Tokuriki
- Michael Smith Laboratories, University of British Columbia, Vancouver, Canada.
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7
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Arya S, George AB, O’Dwyer JP. Sparsity of higher-order landscape interactions enables learning and prediction for microbiomes. Proc Natl Acad Sci U S A 2023; 120:e2307313120. [PMID: 37991947 PMCID: PMC10691334 DOI: 10.1073/pnas.2307313120] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2023] [Accepted: 10/16/2023] [Indexed: 11/24/2023] Open
Abstract
Microbiome engineering offers the potential to leverage microbial communities to improve outcomes in human health, agriculture, and climate. To translate this potential into reality, it is crucial to reliably predict community composition and function. But a brute force approach to cataloging community function is hindered by the combinatorial explosion in the number of ways we can combine microbial species. An alternative is to parameterize microbial community outcomes using simplified, mechanistic models, and then extrapolate these models beyond where we have sampled. But these approaches remain data-hungry, as well as requiring an a priori specification of what kinds of mechanisms are included and which are omitted. Here, we resolve both issues by introducing a mechanism-agnostic approach to predicting microbial community compositions and functions using limited data. The critical step is the identification of a sparse representation of the community landscape. We then leverage this sparsity to predict community compositions and functions, drawing from techniques in compressive sensing. We validate this approach on in silico community data, generated from a theoretical model. By sampling just [Formula: see text]1% of all possible communities, we accurately predict community compositions out of sample. We then demonstrate the real-world application of our approach by applying it to four experimental datasets and showing that we can recover interpretable, accurate predictions on composition and community function from highly limited data.
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Affiliation(s)
- Shreya Arya
- Department of Physics, University of Illinois, Urbana-Champaign, Urbana, IL61801
| | - Ashish B. George
- Center for Artificial Intelligence and Modeling, Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL61801
- Broad Institute of Massachusetts Institute of Technology and Harvard, Cambridge, MA0214
- Department of Plant Biology, University of Illinois, Urbana-Champaign, Urbana, IL61801
| | - James P. O’Dwyer
- Center for Artificial Intelligence and Modeling, Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL61801
- Department of Plant Biology, University of Illinois, Urbana-Champaign, Urbana, IL61801
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8
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Alvarez S, Nartey CM, Mercado N, de la Paz A, Huseinbegovic T, Morcos F. In vivo functional phenotypes from a computational epistatic model of evolution. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.05.24.542176. [PMID: 37292895 PMCID: PMC10245989 DOI: 10.1101/2023.05.24.542176] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
Computational models of evolution are valuable for understanding the dynamics of sequence variation, to infer phylogenetic relationships or potential evolutionary pathways and for biomedical and industrial applications. Despite these benefits, few have validated their propensities to generate outputs with in vivo functionality, which would enhance their value as accurate and interpretable evolutionary algorithms. We demonstrate the power of epistasis inferred from natural protein families to evolve sequence variants in an algorithm we developed called Sequence Evolution with Epistatic Contributions. Utilizing the Hamiltonian of the joint probability of sequences in the family as fitness metric, we sampled and experimentally tested for in vivo β -lactamase activity in E. coli TEM-1 variants. These evolved proteins can have dozens of mutations dispersed across the structure while preserving sites essential for both catalysis and interactions. Remarkably, these variants retain family-like functionality while being more active than their WT predecessor. We found that depending on the inference method used to generate the epistatic constraints, different parameters simulate diverse selection strengths. Under weaker selection, local Hamiltonian fluctuations reliably predict relative changes to variant fitness, recapitulating neutral evolution. SEEC has the potential to explore the dynamics of neofunctionalization, characterize viral fitness landscapes and facilitate vaccine development.
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Affiliation(s)
- Sophia Alvarez
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX 75080, USA
| | - Charisse M. Nartey
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX 75080, USA
| | - Nicholas Mercado
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX 75080, USA
| | - Alberto de la Paz
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX 75080, USA
| | - Tea Huseinbegovic
- School of Natural Sciences and Mathematics, University of Texas at Dallas, Richardson, TX 75080, USA
| | - Faruck Morcos
- Department of Biological Sciences, University of Texas at Dallas, Richardson, TX 75080, USA
- Department of Bioengineering, University of Texas at Dallas, Richardson, TX 75080, USA
- Center for Systems Biology, University of Texas at Dallas, Richardson, TX 75080, USA
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9
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Rebholz Z, Lancaster J, Larose H, Khrimian A, Luck K, Sparks ME, Gendreau KL, Shewade L, Köllner TG, Weber DC, Gundersen-Rindal DE, O'Maille P, Morozov AV, Tholl D. Ancient origin and conserved gene function in terpene pheromone and defense evolution of stink bugs and hemipteran insects. INSECT BIOCHEMISTRY AND MOLECULAR BIOLOGY 2023; 152:103879. [PMID: 36470318 DOI: 10.1016/j.ibmb.2022.103879] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/04/2022] [Revised: 11/24/2022] [Accepted: 11/25/2022] [Indexed: 06/17/2023]
Abstract
Insects use diverse arrays of small molecules such as metabolites of the large class of terpenes for intra- and inter-specific communication and defense. These molecules are synthesized by specialized metabolic pathways; however, the origin of enzymes involved in terpene biosynthesis and their evolution in insect genomes is still poorly understood. We addressed this question by investigating the evolution of isoprenyl diphosphate synthase (IDS)-like genes with terpene synthase (TPS) function in the family of stink bugs (Pentatomidae) within the large order of piercing-sucking Hemipteran insects. Stink bugs include species of global pest status, many of which emit structurally related 15-carbon sesquiterpenes as sex or aggregation pheromones. We provide evidence for the emergence of IDS-type TPS enzymes at the onset of pentatomid evolution over 100 million years ago, coinciding with the evolution of flowering plants. Stink bugs of different geographical origin maintain small IDS-type families with genes of conserved TPS function, which stands in contrast to the diversification of TPS genes in plants. Expanded gene mining and phylogenetic analysis in other hemipteran insects further provides evidence for an ancient emergence of IDS-like genes under presumed selection for terpene-mediated chemical interactions, and this process occurred independently from a similar evolution of IDS-type TPS genes in beetles. Our findings further suggest differences in TPS diversification in insects and plants in conjunction with different modes of gene functionalization in chemical interactions.
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Affiliation(s)
- Zarley Rebholz
- Department of Biological Sciences, Virginia Tech, Latham Hall, 220 Ag Quad Lane, Blacksburg, VA, 24061, USA
| | - Jason Lancaster
- Department of Biological Sciences, Virginia Tech, Latham Hall, 220 Ag Quad Lane, Blacksburg, VA, 24061, USA
| | - Hailey Larose
- Department of Biological Sciences, Virginia Tech, Latham Hall, 220 Ag Quad Lane, Blacksburg, VA, 24061, USA
| | - Ashot Khrimian
- Invasive Insect Biocontrol and Behavior Laboratory, USDA Agricultural Research Service, Beltsville, MD, 20705, USA
| | - Katrin Luck
- Department of Biochemistry, Max Planck Institute for Chemical Ecology, Hans-Knöll-Strasse 8, D-07745, Jena, Germany
| | - Michael E Sparks
- Invasive Insect Biocontrol and Behavior Laboratory, USDA Agricultural Research Service, Beltsville, MD, 20705, USA
| | - Kerry L Gendreau
- Department of Biological Sciences, Virginia Tech, Latham Hall, 220 Ag Quad Lane, Blacksburg, VA, 24061, USA
| | - Leena Shewade
- SRI International, Biosciences Division, 333 Ravenswood Avenue, Menlo Park, CA, 94025-3493, USA
| | - Tobias G Köllner
- Department of Biochemistry, Max Planck Institute for Chemical Ecology, Hans-Knöll-Strasse 8, D-07745, Jena, Germany
| | - Donald C Weber
- Invasive Insect Biocontrol and Behavior Laboratory, USDA Agricultural Research Service, Beltsville, MD, 20705, USA
| | - Dawn E Gundersen-Rindal
- Invasive Insect Biocontrol and Behavior Laboratory, USDA Agricultural Research Service, Beltsville, MD, 20705, USA
| | - Paul O'Maille
- SRI International, Biosciences Division, 333 Ravenswood Avenue, Menlo Park, CA, 94025-3493, USA
| | - Alexandre V Morozov
- Department of Physics & Astronomy and Center for Quantitative Biology, Rutgers University, 136 Frelinghuysen Rd., Piscataway, NJ, 08854-8019, USA
| | - Dorothea Tholl
- Department of Biological Sciences, Virginia Tech, Latham Hall, 220 Ag Quad Lane, Blacksburg, VA, 24061, USA.
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10
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On the sparsity of fitness functions and implications for learning. Proc Natl Acad Sci U S A 2022; 119:2109649118. [PMID: 34937698 PMCID: PMC8740588 DOI: 10.1073/pnas.2109649118] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 11/11/2021] [Indexed: 01/05/2023] Open
Abstract
The properties of proteins and other biological molecules are encoded in large part in the sequence of amino acids or nucleotides that defines them. Increasingly, researchers estimate functions that map sequences to a particular property using machine learning and related statistical approaches. However, an important question remains unanswered: How many experimental measurements are needed in order to accurately learn these “fitness” functions? We leverage perspectives from the fields of biophysics, evolutionary biology, and signal processing to develop a theoretical framework that enables us to make progress on answering this question. We demonstrate that this framework can be used to make useful calculations on real-world data and suggest how these calculations may be used to guide experiments. Fitness functions map biological sequences to a scalar property of interest. Accurate estimation of these functions yields biological insight and sets the foundation for model-based sequence design. However, the fitness datasets available to learn these functions are typically small relative to the large combinatorial space of sequences; characterizing how much data are needed for accurate estimation remains an open problem. There is a growing body of evidence demonstrating that empirical fitness functions display substantial sparsity when represented in terms of epistatic interactions. Moreover, the theory of Compressed Sensing provides scaling laws for the number of samples required to exactly recover a sparse function. Motivated by these results, we develop a framework to study the sparsity of fitness functions sampled from a generalization of the NK model, a widely used random field model of fitness functions. In particular, we present results that allow us to test the effect of the Generalized NK (GNK) model’s interpretable parameters—sequence length, alphabet size, and assumed interactions between sequence positions—on the sparsity of fitness functions sampled from the model and, consequently, the number of measurements required to exactly recover these functions. We validate our framework by demonstrating that GNK models with parameters set according to structural considerations can be used to accurately approximate the number of samples required to recover two empirical protein fitness functions and an RNA fitness function. In addition, we show that these GNK models identify important higher-order epistatic interactions in the empirical fitness functions using only structural information.
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11
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Aghazadeh A, Nisonoff H, Ocal O, Brookes DH, Huang Y, Koyluoglu OO, Listgarten J, Ramchandran K. Epistatic Net allows the sparse spectral regularization of deep neural networks for inferring fitness functions. Nat Commun 2021; 12:5225. [PMID: 34471113 PMCID: PMC8410946 DOI: 10.1038/s41467-021-25371-3] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2020] [Accepted: 07/27/2021] [Indexed: 11/18/2022] Open
Abstract
Despite recent advances in high-throughput combinatorial mutagenesis assays, the number of labeled sequences available to predict molecular functions has remained small for the vastness of the sequence space combined with the ruggedness of many fitness functions. While deep neural networks (DNNs) can capture high-order epistatic interactions among the mutational sites, they tend to overfit to the small number of labeled sequences available for training. Here, we developed Epistatic Net (EN), a method for spectral regularization of DNNs that exploits evidence that epistatic interactions in many fitness functions are sparse. We built a scalable extension of EN, usable for larger sequences, which enables spectral regularization using fast sparse recovery algorithms informed by coding theory. Results on several biological landscapes show that EN consistently improves the prediction accuracy of DNNs and enables them to outperform competing models which assume other priors. EN estimates the higher-order epistatic interactions of DNNs trained on massive sequence spaces-a computational problem that otherwise takes years to solve.
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Affiliation(s)
- Amirali Aghazadeh
- Department of Electrical Engineering and Computer Sciences, Berkeley, CA, USA
| | | | - Orhan Ocal
- Department of Electrical Engineering and Computer Sciences, Berkeley, CA, USA
| | - David H Brookes
- Biophysics Graduate Group, University of California, Berkeley, CA, USA
| | - Yijie Huang
- Department of Electrical Engineering and Computer Sciences, Berkeley, CA, USA
| | - O Ozan Koyluoglu
- Department of Electrical Engineering and Computer Sciences, Berkeley, CA, USA
| | - Jennifer Listgarten
- Department of Electrical Engineering and Computer Sciences, Berkeley, CA, USA
- Center for Computational Biology, Berkeley, CA, USA
| | - Kannan Ramchandran
- Department of Electrical Engineering and Computer Sciences, Berkeley, CA, USA.
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12
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Miton CM, Buda K, Tokuriki N. Epistasis and intramolecular networks in protein evolution. Curr Opin Struct Biol 2021; 69:160-168. [PMID: 34077895 DOI: 10.1016/j.sbi.2021.04.007] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Revised: 04/01/2021] [Accepted: 04/21/2021] [Indexed: 12/01/2022]
Abstract
Proteins are molecular machines composed of complex, highly connected amino acid networks. Their functional optimization requires the reorganization of these intramolecular networks by evolution. In this review, we discuss the mechanisms by which epistasis, that is, the dependence of the effect of a mutation on the genetic background, rewires intramolecular interactions to alter protein function. Deciphering the biophysical basis of epistasis is crucial to our understanding of evolutionary dynamics and the elucidation of sequence-structure-function relationships. We featured recent studies that provide insights into the molecular mechanisms giving rise to epistasis, particularly at the structural level. These studies illustrate the convoluted and fascinating nature of the intramolecular networks co-opted by epistasis during the evolution of protein function.
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Affiliation(s)
- Charlotte M Miton
- Michael Smith Laboratories, University of British Columbia, Vancouver, V6T 1Z4, BC, Canada
| | - Karol Buda
- Michael Smith Laboratories, University of British Columbia, Vancouver, V6T 1Z4, BC, Canada
| | - Nobuhiko Tokuriki
- Michael Smith Laboratories, University of British Columbia, Vancouver, V6T 1Z4, BC, Canada.
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