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Article ; Online: Biophysical Inference of Epistasis and the Effects of Mutations on Protein Stability and Function.

Otwinowski, Jakub

2018 Volume 35, Issue 10, Page(s) 2345–2354

Abstract: Understanding the relationship between protein sequence, function, and stability is a fundamental problem in biology. The essential function of many proteins that fold into a specific structure is their ability to bind to a ligand, which can be assayed ... ...

Abstract	Understanding the relationship between protein sequence, function, and stability is a fundamental problem in biology. The essential function of many proteins that fold into a specific structure is their ability to bind to a ligand, which can be assayed for thousands of mutated variants. However, binding assays do not distinguish whether mutations affect the stability of the binding interface or the overall fold. Here, we introduce a statistical method to infer a detailed energy landscape of how a protein folds and binds to a ligand by combining information from many mutated variants. We fit a thermodynamic model describing the bound, unbound, and unfolded states to high quality data of protein G domain B1 binding to IgG-Fc. We infer distinct folding and binding energies for each mutation providing a detailed view of how mutations affect binding and stability across the protein. We accurately infer the folding energy of each variant in physical units, validated by independent data, whereas previous high-throughput methods could only measure indirect changes in stability. While we assume an additive sequence-energy relationship, the binding fraction is epistatic due its nonlinear relation to energy. Despite having no epistasis in energy, our model explains much of the observed epistasis in binding fraction, with the remaining epistasis identifying conformationally dynamic regions.
MeSH term(s)	Amino Acid Sequence ; Animals ; Computer Simulation/statistics & numerical data ; Epistasis, Genetic/physiology ; Evolution, Molecular ; Humans ; Ligands ; Mutation ; Protein Conformation ; Protein Folding ; Protein Stability ; Proteins/genetics ; Proteins/physiology ; Structure-Activity Relationship ; Thermodynamics
Chemical Substances	Ligands ; Proteins
Language	English
Publishing date	2018-08-16
Publishing country	United States
Document type	Journal Article ; Research Support, N.I.H., Extramural
ZDB-ID	998579-7
ISSN	1537-1719 ; 0737-4038
ISSN (online)	1537-1719
ISSN	0737-4038
DOI	10.1093/molbev/msy141
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Book ; Online: Contrastive losses as generalized models of global epistasis

Brookes, David H. / Otwinowski, Jakub / Sinai, Sam

2023

Abstract: Fitness functions map large combinatorial spaces of biological sequences to properties of interest. Inferring these multimodal functions from experimental data is a central task in modern protein engineering. Global epistasis models are an effective and ... ...

Abstract	Fitness functions map large combinatorial spaces of biological sequences to properties of interest. Inferring these multimodal functions from experimental data is a central task in modern protein engineering. Global epistasis models are an effective and physically-grounded class of models for estimating fitness functions from observed data. These models assume that a sparse latent function is transformed by a monotonic nonlinearity to emit measurable fitness. Here we demonstrate that minimizing contrastive loss functions, such as the Bradley-Terry loss, is a simple and flexible technique for extracting the sparse latent function implied by global epistasis. We argue by way of a fitness-epistasis uncertainty principle that the nonlinearities in global epistasis models can produce observed fitness functions that do not admit sparse representations, and thus may be inefficient to learn from observations when using a Mean Squared Error (MSE) loss (a common practice). We show that contrastive losses are able to accurately estimate a ranking function from limited data even in regimes where MSE is ineffective. We validate the practical utility of this insight by showing contrastive loss functions result in consistently improved performance on benchmark tasks.
Keywords	Quantitative Biology - Populations and Evolution ; Computer Science - Machine Learning
Subject code	006
Publishing date	2023-05-04
Publishing country	us
Document type	Book ; Online
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Article ; Online: Learning the shape of protein microenvironments with a holographic convolutional neural network.

Pun, Michael N / Ivanov, Andrew / Bellamy, Quinn / Montague, Zachary / LaMont, Colin / Bradley, Philip / Otwinowski, Jakub / Nourmohammad, Armita

Proceedings of the National Academy of Sciences of the United States of America

2024 Volume 121, Issue 6, Page(s) e2300838121

Abstract: Proteins play a central role in biology from immune recognition to brain activity. While major advances in machine learning have improved our ability to predict protein structure from sequence, determining protein function from its sequence or structure ... ...

Abstract	Proteins play a central role in biology from immune recognition to brain activity. While major advances in machine learning have improved our ability to predict protein structure from sequence, determining protein function from its sequence or structure remains a major challenge. Here, we introduce holographic convolutional neural network (H-CNN) for proteins, which is a physically motivated machine learning approach to model amino acid preferences in protein structures. H-CNN reflects physical interactions in a protein structure and recapitulates the functional information stored in evolutionary data. H-CNN accurately predicts the impact of mutations on protein stability and binding of protein complexes. Our interpretable computational model for protein structure-function maps could guide design of novel proteins with desired function.
MeSH term(s)	Algorithms ; Neural Networks, Computer ; Proteins/genetics ; Machine Learning ; Amino Acids
Chemical Substances	Proteins ; Amino Acids
Language	English
Publishing date	2024-02-01
Publishing country	United States
Document type	Journal Article
ZDB-ID	209104-5
ISSN	1091-6490 ; 0027-8424
ISSN (online)	1091-6490
ISSN	0027-8424
DOI	10.1073/pnas.2300838121
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Article ; Online: Information-Geometric Optimization with Natural Selection.

Otwinowski, Jakub / LaMont, Colin H / Nourmohammad, Armita

Entropy (Basel, Switzerland)

2020 Volume 22, Issue 9

Abstract: Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between classical population genetics of quantitative traits and evolutionary ... ...

Abstract	Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between classical population genetics of quantitative traits and evolutionary optimization, and formulate a new evolutionary algorithm. Optimization of a continuous objective function is analogous to searching for high fitness phenotypes on a fitness landscape. We describe how natural selection moves a population along the non-Euclidean gradient that is induced by the population on the fitness landscape (the natural gradient). We show how selection is related to Newton's method in optimization under quadratic fitness landscapes, and how selection increases fitness at the cost of reducing diversity. We describe the generation of new phenotypes and introduce an operator that recombines the whole population to generate variants. Finally, we introduce a proof-of-principle algorithm that combines natural selection, our recombination operator, and an adaptive method to increase selection and find the optimum. The algorithm is extremely simple in implementation; it has no matrix inversion or factorization, does not require storing a covariance matrix, and may form the basis of more general model-based optimization algorithms with natural gradient updates.
Language	English
Publishing date	2020-08-31
Publishing country	Switzerland
Document type	Journal Article
ZDB-ID	2014734-X
ISSN	1099-4300 ; 1099-4300
ISSN (online)	1099-4300
ISSN	1099-4300
DOI	10.3390/e22090967
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Article ; Online: Design of an optimal combination therapy with broadly neutralizing antibodies to suppress HIV-1.

LaMont, Colin / Otwinowski, Jakub / Vanshylla, Kanika / Gruell, Henning / Klein, Florian / Nourmohammad, Armita

eLife

2022 Volume 11

Abstract: Infusion of broadly neutralizing antibodies (bNAbs) has shown promise as an alternative to anti-retroviral therapy against HIV. A key challenge is to suppress viral escape, which is more effectively achieved with a combination of bNAbs. Here, we propose ... ...

Abstract	Infusion of broadly neutralizing antibodies (bNAbs) has shown promise as an alternative to anti-retroviral therapy against HIV. A key challenge is to suppress viral escape, which is more effectively achieved with a combination of bNAbs. Here, we propose a computational approach to predict the efficacy of a bNAb therapy based on the population genetics of HIV escape, which we parametrize using high-throughput HIV sequence data from bNAb-naive patients. By quantifying the mutational target size and the fitness cost of HIV-1 escape from bNAbs, we predict the distribution of rebound times in three clinical trials. We show that a cocktail of three bNAbs is necessary to effectively suppress viral escape, and predict the optimal composition of such bNAb cocktail. Our results offer a rational therapy design for HIV, and show how genetic data can be used to predict treatment outcomes and design new approaches to pathogenic control.
MeSH term(s)	Antibodies, Neutralizing ; Broadly Neutralizing Antibodies ; HIV Antibodies ; HIV Infections/drug therapy ; HIV-1/genetics ; Humans
Chemical Substances	Antibodies, Neutralizing ; Broadly Neutralizing Antibodies ; HIV Antibodies
Language	English
Publishing date	2022-07-19
Publishing country	England
Document type	Journal Article ; Research Support, U.S. Gov't, Non-P.H.S. ; Research Support, Non-U.S. Gov't
ZDB-ID	2687154-3
ISSN	2050-084X ; 2050-084X
ISSN (online)	2050-084X
ISSN	2050-084X
DOI	10.7554/eLife.76004
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Book ; Online: Information-geometric optimization with natural selection

Otwinowski, Jakub / LaMont, Colin

2019

Abstract: Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a new ... ...

Abstract	Evolutionary algorithms, inspired by natural evolution, aim to optimize difficult objective functions without computing derivatives. Here we detail the relationship between population genetics and evolutionary optimization and formulate a new evolutionary algorithm. Optimization of a continuous objective function is analogous to searching for high fitness phenotypes on a fitness landscape. We summarize how natural selection moves a population along the non-euclidean gradient that is induced by the population on the fitness landscape (the natural gradient). Under normal approximations common in quantitative genetics, we show how selection is related to Newton's method in optimization. We find that intermediate selection is most informative of the fitness landscape. We describe the generation of new phenotypes and introduce an operator that recombines the whole population to generate variants that preserve normal statistics. Finally, we introduce a proof-of-principle algorithm that combines natural selection, our recombination operator, and an adaptive method to increase selection. Our algorithm is similar to covariance matrix adaptation and natural evolutionary strategies in optimization, and has similar performance. The algorithm is extremely simple in implementation with no matrix inversion or factorization, does not require storing a covariance matrix, and may form the basis of more general model-based optimization algorithms with natural gradient updates. Comment: changed title
Keywords	Quantitative Biology - Populations and Evolution ; Computer Science - Neural and Evolutionary Computing
Subject code	518
Publishing date	2019-12-06
Publishing country	us
Document type	Book ; Online
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Article ; Online: Inferring the shape of global epistasis.

Otwinowski, Jakub / McCandlish, David M / Plotkin, Joshua B

Proceedings of the National Academy of Sciences of the United States of America

2018 Volume 115, Issue 32, Page(s) E7550–E7558

Abstract: Genotype-phenotype relationships are notoriously complicated. Idiosyncratic interactions between specific combinations of mutations occur and are difficult to predict. Yet it is increasingly clear that many interactions can be understood in terms of ... ...

Abstract	Genotype-phenotype relationships are notoriously complicated. Idiosyncratic interactions between specific combinations of mutations occur and are difficult to predict. Yet it is increasingly clear that many interactions can be understood in terms of global epistasis. That is, mutations may act additively on some underlying, unobserved trait, and this trait is then transformed via a nonlinear function to the observed phenotype as a result of subsequent biophysical and cellular processes. Here we infer the shape of such global epistasis in three proteins, based on published high-throughput mutagenesis data. To do so, we develop a maximum-likelihood inference procedure using a flexible family of monotonic nonlinear functions spanned by an I-spline basis. Our analysis uncovers dramatic nonlinearities in all three proteins; in some proteins a model with global epistasis accounts for virtually all of the measured variation, whereas in others we find substantial local epistasis as well. This method allows us to test hypotheses about the form of global epistasis and to distinguish variance components attributable to global epistasis, local epistasis, and measurement error.
MeSH term(s)	Epistasis, Genetic ; Evolution, Molecular ; Genetic Fitness ; Genotype ; Models, Genetic ; Models, Statistical ; Mutation ; Nonlinear Dynamics ; Phenotype
Language	English
Publishing date	2018-07-23
Publishing country	United States
Document type	Journal Article ; Research Support, N.I.H., Extramural ; Research Support, Non-U.S. Gov't ; Research Support, U.S. Gov't, Non-P.H.S.
ZDB-ID	209104-5
ISSN	1091-6490 ; 0027-8424
ISSN (online)	1091-6490
ISSN	0027-8424
DOI	10.1073/pnas.1804015115
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Article ; Online: Clonal interference and Muller's ratchet in spatial habitats.

Otwinowski, Jakub / Krug, Joachim

Physical biology

2014 Volume 11, Issue 5, Page(s) 56003

Abstract: Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones. Recent theoretical studies have pointed out that the resulting fitness dynamics is analogous to ... ...

Abstract	Competition between independently arising beneficial mutations is enhanced in spatial populations due to the linear rather than exponential growth of clones. Recent theoretical studies have pointed out that the resulting fitness dynamics is analogous to a surface growth process, where new layers nucleate and spread stochastically, leading to the build up of scale-invariant roughness. This scenario differs qualitatively from the standard view of adaptation in that the speed of adaptation becomes independent of population size while the fitness variance does not. Here we exploit recent progress in the understanding of surface growth processes to obtain precise predictions for the universal, non-Gaussian shape of the fitness distribution for one-dimensional habitats, which are verified by simulations. When the mutations are deleterious rather than beneficial the problem becomes a spatial version of Muller's ratchet. In contrast to the case of well-mixed populations, the rate of fitness decline remains finite even in the limit of an infinite habitat, provided the ratio [Formula: see text] between the deleterious mutation rate and the square of the (negative) selection coefficient is sufficiently large. Using, again, an analogy to surface growth models we show that the transition between the stationary and the moving state of the ratchet is governed by directed percolation.
MeSH term(s)	Adaptation, Biological ; Biological Evolution ; Ecosystem ; Genetic Fitness ; Genetic Variation ; Models, Genetic ; Mutation
Language	English
Publishing date	2014-08-26
Publishing country	England
Document type	Journal Article ; Research Support, Non-U.S. Gov't ; Research Support, U.S. Gov't, Non-P.H.S.
ZDB-ID	2133216-2
ISSN	1478-3975 ; 1478-3967
ISSN (online)	1478-3975
ISSN	1478-3967
DOI	10.1088/1478-3975/11/5/056003
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Article ; Online: Inferring fitness landscapes by regression produces biased estimates of epistasis.

Otwinowski, Jakub / Plotkin, Joshua B

Proceedings of the National Academy of Sciences of the United States of America

2014 Volume 111, Issue 22, Page(s) E2301–9

Abstract: The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is to sample as ... ...

Abstract	The genotype-fitness map plays a fundamental role in shaping the dynamics of evolution. However, it is difficult to directly measure a fitness landscape in practice, because the number of possible genotypes is astronomical. One approach is to sample as many genotypes as possible, measure their fitnesses, and fit a statistical model of the landscape that includes additive and pairwise interactive effects between loci. Here, we elucidate the pitfalls of using such regressions by studying artificial but mathematically convenient fitness landscapes. We identify two sources of bias inherent in these regression procedures, each of which tends to underestimate high fitnesses and overestimate low fitnesses. We characterize these biases for random sampling of genotypes as well as samples drawn from a population under selection in the Wright-Fisher model of evolutionary dynamics. We show that common measures of epistasis, such as the number of monotonically increasing paths between ancestral and derived genotypes, the prevalence of sign epistasis, and the number of local fitness maxima, are distorted in the inferred landscape. As a result, the inferred landscape will provide systematically biased predictions for the dynamics of adaptation. We identify the same biases in a computational RNA-folding landscape as well as regulatory sequence binding data treated with the same fitting procedure. Finally, we present a method to ameliorate these biases in some cases.
MeSH term(s)	Drug Resistance/genetics ; Epistasis, Genetic/genetics ; Evolution, Molecular ; Genetic Fitness/genetics ; Genotype ; Models, Genetic ; RNA Folding/genetics ; Regression Analysis ; Selection, Genetic/genetics
Language	English
Publishing date	2014-05-19
Publishing country	United States
Document type	Journal Article ; Research Support, Non-U.S. Gov't ; Research Support, U.S. Gov't, Non-P.H.S.
ZDB-ID	209104-5
ISSN	1091-6490 ; 0027-8424
ISSN (online)	1091-6490
ISSN	0027-8424
DOI	10.1073/pnas.1400849111
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Article ; Online: Major antigenic site B of human influenza H3N2 viruses has an evolving local fitness landscape.

Wu, Nicholas C / Otwinowski, Jakub / Thompson, Andrew J / Nycholat, Corwin M / Nourmohammad, Armita / Wilson, Ian A

Nature communications

2020 Volume 11, Issue 1, Page(s) 1233

Abstract: Antigenic drift of influenza virus hemagglutinin (HA) is enabled by facile evolvability. However, HA antigenic site B, which has become immunodominant in recent human H3N2 influenza viruses, is also evolutionarily constrained by its involvement in ... ...

Abstract	Antigenic drift of influenza virus hemagglutinin (HA) is enabled by facile evolvability. However, HA antigenic site B, which has become immunodominant in recent human H3N2 influenza viruses, is also evolutionarily constrained by its involvement in receptor binding. Here, we employ deep mutational scanning to probe the local fitness landscape of HA antigenic site B in six different human H3N2 strains spanning from 1968 to 2016. We observe that the fitness landscape of HA antigenic site B can be very different between strains. Sequence variants that exhibit high fitness in one strain can be deleterious in another, indicating that the evolutionary constraints of antigenic site B have changed over time. Structural analysis suggests that the local fitness landscape of antigenic site B can be reshaped by natural mutations via modulation of the receptor-binding mode. Overall, these findings elucidate how influenza virus continues to explore new antigenic space despite strong functional constraints.
MeSH term(s)	Animals ; Antigens, Viral/genetics ; Antigens, Viral/immunology ; Antigens, Viral/metabolism ; Binding Sites/genetics ; Crystallography, X-Ray ; DNA Mutational Analysis ; Dogs ; Evolution, Molecular ; HEK293 Cells ; Hemagglutinin Glycoproteins, Influenza Virus/genetics ; Hemagglutinin Glycoproteins, Influenza Virus/immunology ; Hemagglutinin Glycoproteins, Influenza Virus/metabolism ; Humans ; Influenza A Virus, H3N2 Subtype/genetics ; Influenza A Virus, H3N2 Subtype/immunology ; Influenza A Virus, H3N2 Subtype/metabolism ; Madin Darby Canine Kidney Cells ; Mutation ; Protein Domains/genetics ; Protein Domains/immunology ; RNA, Viral/genetics ; RNA, Viral/isolation & purification ; Receptors, Cell Surface/metabolism ; Reverse Transcriptase Polymerase Chain Reaction ; Sequence Analysis, DNA
Chemical Substances	Antigens, Viral ; Hemagglutinin Glycoproteins, Influenza Virus ; RNA, Viral ; Receptors, Cell Surface ; sialic acid receptor
Language	English
Publishing date	2020-03-06
Publishing country	England
Document type	Journal Article ; Research Support, N.I.H., Extramural ; Research Support, Non-U.S. Gov't
ZDB-ID	2553671-0
ISSN	2041-1723 ; 2041-1723
ISSN (online)	2041-1723
ISSN	2041-1723
DOI	10.1038/s41467-020-15102-5
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