1
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Sisk TR, Robustelli P. Folding-upon-binding pathways of an intrinsically disordered protein from a deep Markov state model. Proc Natl Acad Sci U S A 2024; 121:e2313360121. [PMID: 38294935 PMCID: PMC10861926 DOI: 10.1073/pnas.2313360121] [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: 08/10/2023] [Accepted: 11/22/2023] [Indexed: 02/02/2024] Open
Abstract
A central challenge in the study of intrinsically disordered proteins is the characterization of the mechanisms by which they bind their physiological interaction partners. Here, we utilize a deep learning-based Markov state modeling approach to characterize the folding-upon-binding pathways observed in a long timescale molecular dynamics simulation of a disordered region of the measles virus nucleoprotein NTAIL reversibly binding the X domain of the measles virus phosphoprotein complex. We find that folding-upon-binding predominantly occurs via two distinct encounter complexes that are differentiated by the binding orientation, helical content, and conformational heterogeneity of NTAIL. We observe that folding-upon-binding predominantly proceeds through a multi-step induced fit mechanism with several intermediates and do not find evidence for the existence of canonical conformational selection pathways. We observe four kinetically separated native-like bound states that interconvert on timescales of eighty to five hundred nanoseconds. These bound states share a core set of native intermolecular contacts and stable NTAIL helices and are differentiated by a sequential formation of native and non-native contacts and additional helical turns. Our analyses provide an atomic resolution structural description of intermediate states in a folding-upon-binding pathway and elucidate the nature of the kinetic barriers between metastable states in a dynamic and heterogenous, or "fuzzy", protein complex.
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Affiliation(s)
- Thomas R. Sisk
- Department of Chemistry, Dartmouth College, Hanover, NH03755
| | - Paul Robustelli
- Department of Chemistry, Dartmouth College, Hanover, NH03755
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2
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Brotzakis ZF. Cryo-electron Microscopy and Molecular Modeling Methods to Characterize the Dynamics of Tau Bound to Microtubules. Methods Mol Biol 2024; 2754:77-90. [PMID: 38512661 DOI: 10.1007/978-1-0716-3629-9_4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/23/2024]
Abstract
The electron microscopy metainference integrative structural biology method enables the combination of cryo-electron microscopy electron density maps with molecular modeling techniques such as molecular dynamics to unveil the atomistic biomolecular structural ensemble and the error in the map data in an efficient manner. Here we illustrate the electron microscopy metainference protocol and analysis used to elucidate the atomistic structural ensemble of the microtubule-associated protein tau bound to microtubules by using state-of-the-art molecular mechanic force field and the electron density map.
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3
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Bebon R, Godec A. Controlling Uncertainty of Empirical First-Passage Times in the Small-Sample Regime. PHYSICAL REVIEW LETTERS 2023; 131:237101. [PMID: 38134782 DOI: 10.1103/physrevlett.131.237101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/20/2023] [Revised: 10/18/2023] [Accepted: 10/31/2023] [Indexed: 12/24/2023]
Abstract
We derive general bounds on the probability that the empirical first-passage time τ[over ¯]_{n}≡∑_{i=1}^{n}τ_{i}/n of a reversible ergodic Markov process inferred from a sample of n independent realizations deviates from the true mean first-passage time by more than any given amount in either direction. We construct nonasymptotic confidence intervals that hold in the elusive small-sample regime and thus fill the gap between asymptotic methods and the Bayesian approach that is known to be sensitive to prior belief and tends to underestimate uncertainty in the small-sample setting. We prove sharp bounds on extreme first-passage times that control uncertainty even in cases where the mean alone does not sufficiently characterize the statistics. Our concentration-of-measure-based results allow for model-free error control and reliable error estimation in kinetic inference, and are thus important for the analysis of experimental and simulation data in the presence of limited sampling.
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Affiliation(s)
- Rick Bebon
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany
| | - Aljaž Godec
- Mathematical bioPhysics Group, Max Planck Institute for Multidisciplinary Sciences, 37077 Göttingen, Germany
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4
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Faidon Brotzakis Z, Löhr T, Truong S, Hoff S, Bonomi M, Vendruscolo M. Determination of the Structure and Dynamics of the Fuzzy Coat of an Amyloid Fibril of IAPP Using Cryo-Electron Microscopy. Biochemistry 2023; 62:2407-2416. [PMID: 37477459 PMCID: PMC10433526 DOI: 10.1021/acs.biochem.3c00010] [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: 01/10/2023] [Revised: 06/03/2023] [Indexed: 07/22/2023]
Abstract
In recent years, major advances in cryo-electron microscopy (cryo-EM) have enabled the routine determination of complex biomolecular structures at atomistic resolution. An open challenge for this approach, however, concerns large systems that exhibit continuous dynamics. To address this problem, we developed the metadynamic electron microscopy metainference (MEMMI) method, which incorporates metadynamics, an enhanced conformational sampling approach, into the metainference method of integrative structural biology. MEMMI enables the simultaneous determination of the structure and dynamics of large heterogeneous systems by combining cryo-EM density maps with prior information through molecular dynamics, while at the same time modeling the different sources of error. To illustrate the method, we apply it to elucidate the dynamics of an amyloid fibril of the islet amyloid polypeptide (IAPP). The resulting conformational ensemble provides an accurate description of the structural variability of the disordered region of the amyloid fibril, known as fuzzy coat. The conformational ensemble also reveals that in nearly half of the structural core of this amyloid fibril, the side chains exhibit liquid-like dynamics despite the presence of the highly ordered network backbone of hydrogen bonds characteristic of the cross-β structure of amyloid fibrils.
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Affiliation(s)
- Z. Faidon Brotzakis
- Centre
for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K.
| | - Thomas Löhr
- Centre
for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K.
| | - Steven Truong
- Centre
for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K.
| | - Samuel Hoff
- Department
of Structural Biology and Chemistry, Institut
Pasteur, Université Paris Cité CNRS UMR 3528, 75015 Paris, France
| | - Massimiliano Bonomi
- Department
of Structural Biology and Chemistry, Institut
Pasteur, Université Paris Cité CNRS UMR 3528, 75015 Paris, France
| | - Michele Vendruscolo
- Centre
for Misfolding Diseases, Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K.
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5
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Sisk T, Robustelli P. Folding-upon-binding pathways of an intrinsically disordered protein from a deep Markov state model. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2023:2023.07.21.550103. [PMID: 37546728 PMCID: PMC10401938 DOI: 10.1101/2023.07.21.550103] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/08/2023]
Abstract
A central challenge in the study of intrinsically disordered proteins is the characterization of the mechanisms by which they bind their physiological interaction partners. Here, we utilize a deep learning based Markov state modeling approach to characterize the folding-upon-binding pathways observed in a long-time scale molecular dynamics simulation of a disordered region of the measles virus nucleoprotein NTAIL reversibly binding the X domain of the measles virus phosphoprotein complex. We find that folding-upon-binding predominantly occurs via two distinct encounter complexes that are differentiated by the binding orientation, helical content, and conformational heterogeneity of NTAIL. We do not, however, find evidence for the existence of canonical conformational selection or induced fit binding pathways. We observe four kinetically separated native-like bound states that interconvert on time scales of eighty to five hundred nanoseconds. These bound states share a core set of native intermolecular contacts and stable NTAIL helices and are differentiated by a sequential formation of native and non-native contacts and additional helical turns. Our analyses provide an atomic resolution structural description of intermediate states in a folding-upon-binding pathway and elucidate the nature of the kinetic barriers between metastable states in a dynamic and heterogenous, or "fuzzy", protein complex.
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Affiliation(s)
- Thomas Sisk
- Dartmouth College, Department of Chemistry, Hanover, NH, 03755
| | - Paul Robustelli
- Dartmouth College, Department of Chemistry, Hanover, NH, 03755
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6
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Mardt A, Hempel T, Clementi C, Noé F. Deep learning to decompose macromolecules into independent Markovian domains. Nat Commun 2022; 13:7101. [PMID: 36402768 PMCID: PMC9675806 DOI: 10.1038/s41467-022-34603-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/16/2022] [Accepted: 10/27/2022] [Indexed: 11/21/2022] Open
Abstract
The increasing interest in modeling the dynamics of ever larger proteins has revealed a fundamental problem with models that describe the molecular system as being in a global configuration state. This notion limits our ability to gather sufficient statistics of state probabilities or state-to-state transitions because for large molecular systems the number of metastable states grows exponentially with size. In this manuscript, we approach this challenge by introducing a method that combines our recent progress on independent Markov decomposition (IMD) with VAMPnets, a deep learning approach to Markov modeling. We establish a training objective that quantifies how well a given decomposition of the molecular system into independent subdomains with Markovian dynamics approximates the overall dynamics. By constructing an end-to-end learning framework, the decomposition into such subdomains and their individual Markov state models are simultaneously learned, providing a data-efficient and easily interpretable summary of the complex system dynamics. While learning the dynamical coupling between Markovian subdomains is still an open issue, the present results are a significant step towards learning Ising models of large molecular complexes from simulation data.
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Affiliation(s)
- Andreas Mardt
- grid.14095.390000 0000 9116 4836Freie Universität Berlin, Department of Mathematics and Computer Science, Berlin, Germany
| | - Tim Hempel
- grid.14095.390000 0000 9116 4836Freie Universität Berlin, Department of Mathematics and Computer Science, Berlin, Germany ,grid.14095.390000 0000 9116 4836Freie Universität Berlin, Department of Physics, Berlin, Germany
| | - Cecilia Clementi
- grid.14095.390000 0000 9116 4836Freie Universität Berlin, Department of Physics, Berlin, Germany ,grid.21940.3e0000 0004 1936 8278Rice University, Department of Chemistry, Houston, TX USA ,grid.509984.90000 0004 5907 3802Rice University, Center for Theoretical Biological Physics, Houston, TX USA
| | - Frank Noé
- grid.14095.390000 0000 9116 4836Freie Universität Berlin, Department of Mathematics and Computer Science, Berlin, Germany ,grid.14095.390000 0000 9116 4836Freie Universität Berlin, Department of Physics, Berlin, Germany ,grid.21940.3e0000 0004 1936 8278Rice University, Department of Chemistry, Houston, TX USA ,Microsoft Research AI4Science, Berlin, Germany
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7
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A litmus test for classifying recognition mechanisms of transiently binding proteins. Nat Commun 2022; 13:3792. [PMID: 35778416 PMCID: PMC9249894 DOI: 10.1038/s41467-022-31374-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Accepted: 06/15/2022] [Indexed: 11/17/2022] Open
Abstract
Partner recognition in protein binding is critical for all biological functions, and yet, delineating its mechanism is challenging, especially when recognition happens within microseconds. We present a theoretical and experimental framework based on straight-forward nuclear magnetic resonance relaxation dispersion measurements to investigate protein binding mechanisms on sub-millisecond timescales, which are beyond the reach of standard rapid-mixing experiments. This framework predicts that conformational selection prevails on ubiquitin’s paradigmatic interaction with an SH3 (Src-homology 3) domain. By contrast, the SH3 domain recognizes ubiquitin in a two-state binding process. Subsequent molecular dynamics simulations and Markov state modeling reveal that the ubiquitin conformation selected for binding exhibits a characteristically extended C-terminus. Our framework is robust and expandable for implementation in other binding scenarios with the potential to show that conformational selection might be the design principle of the hubs in protein interaction networks. The authors provide a litmus test for the recognition mechanism of transiently binding proteins based on nuclear magnetic resonance and find a conformational selection binding mechanism through concentration-dependent kinetics of ubiquitin and SH3.
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8
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Kolloff C, Mazur A, Marzinek JK, Bond PJ, Olsson S, Hiller S. Motional clustering in supra-τ c conformational exchange influences NOE cross-relaxation rate. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2022; 338:107196. [PMID: 35367892 DOI: 10.1016/j.jmr.2022.107196] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/15/2021] [Revised: 03/01/2022] [Accepted: 03/13/2022] [Indexed: 06/14/2023]
Abstract
Biomolecular spin relaxation processes, such as the NOE, are commonly modeled by rotational τc-tumbling combined with fast motions on the sub-τc timescale. Motions on the supra-τc timescale, in contrast, are considered to be completely decorrelated to the molecular tumbling and therefore invisible. Here, we show how supra-τc dynamics can nonetheless influence the NOE build-up between methyl groups. This effect arises because supra-τc motions can cluster the fast-motion ensembles into discrete states, affecting distance averaging as well as the fast-motion order parameter and hence the cross-relaxation rate. We present a computational approach to estimate methyl-methyl cross-relaxation rates from extensive (>100×τc) all-atom molecular dynamics (MD) trajectories on the example of the 723-residue protein Malate Synthase G. The approach uses Markov state models (MSMs) to resolve transitions between metastable states and thus to discriminate between sub-τc and supra-τc conformational exchange. We find that supra-τc exchange typically increases NOESY cross-peak intensities. The methods described in this work extend the theory of modeling sub-μs dynamics in spin relaxation and thus contribute to a quantitative estimation of NOE cross-relaxation rates from MD simulations, eventually leading to increased precision in structural and functional studies of large proteins.
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Affiliation(s)
- Christopher Kolloff
- Biozentrum, Universität Basel, Spitalstrasse 41, Basel 4056, Switzerland; Department of Computer Science and Engineering, Chalmers University of Technology, Rännvägen 6, Göteborg 412 58, Sweden.
| | - Adam Mazur
- Biozentrum, Universität Basel, Spitalstrasse 41, Basel 4056, Switzerland.
| | - Jan K Marzinek
- Bioinformatics Institute (A∗STAR), 30 Biopolis Street, #07-01 Matrix, Singapore 138671, Singapore.
| | - Peter J Bond
- Bioinformatics Institute (A∗STAR), 30 Biopolis Street, #07-01 Matrix, Singapore 138671, Singapore; National University of Singapore, Department of Biological Sciences, 14 Science Drive 4, Singapore 117543, Singapore.
| | - Simon Olsson
- Department of Computer Science and Engineering, Chalmers University of Technology, Rännvägen 6, Göteborg 412 58, Sweden.
| | - Sebastian Hiller
- Biozentrum, Universität Basel, Spitalstrasse 41, Basel 4056, Switzerland.
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9
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Hoffmann M, Scherer M, Hempel T, Mardt A, de Silva B, Husic BE, Klus S, Wu H, Kutz N, Brunton SL, Noé F. Deeptime: a Python library for machine learning dynamical models from time series data. MACHINE LEARNING: SCIENCE AND TECHNOLOGY 2022. [DOI: 10.1088/2632-2153/ac3de0] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Abstract
Generation and analysis of time-series data is relevant to many quantitative fields ranging from economics to fluid mechanics. In the physical sciences, structures such as metastable and coherent sets, slow relaxation processes, collective variables, dominant transition pathways or manifolds and channels of probability flow can be of great importance for understanding and characterizing the kinetic, thermodynamic and mechanistic properties of the system. Deeptime is a general purpose Python library offering various tools to estimate dynamical models based on time-series data including conventional linear learning methods, such as Markov state models (MSMs), Hidden Markov Models and Koopman models, as well as kernel and deep learning approaches such as VAMPnets and deep MSMs. The library is largely compatible with scikit-learn, having a range of Estimator classes for these different models, but in contrast to scikit-learn also provides deep Model classes, e.g. in the case of an MSM, which provide a multitude of analysis methods to compute interesting thermodynamic, kinetic and dynamical quantities, such as free energies, relaxation times and transition paths. The library is designed for ease of use but also easily maintainable and extensible code. In this paper we introduce the main features and structure of the deeptime software. Deeptime can be found under https://deeptime-ml.github.io/.
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10
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Ueda T, Imai S, Shimada I. Function-related dynamics of GPCRs. JOURNAL OF MAGNETIC RESONANCE (SAN DIEGO, CALIF. : 1997) 2022; 336:107164. [PMID: 35168190 DOI: 10.1016/j.jmr.2022.107164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Revised: 01/29/2022] [Accepted: 02/03/2022] [Indexed: 06/14/2023]
Abstract
G protein-coupled receptors (GPCRs) include various neurotransmitters and hormones, and over 30% of modern drugs target GPCRs. The number of GPCR crystal structures has rapidly increased, and many structures of GPCRs in complexes with their binding partners are being solved by cryo-electron microscopy. However, crystallographic or cryo-electron microscopy data alone cannot fully explain the important features of GPCR signaling determined experimentally. Recent studies have suggested that GPCRs are structurally dynamic, and exchange between multiple conformations. In this respect, NMR methods provide information about the dynamics of proteins over a wide range of frequencies, in aqueous solutions at nearphysiological temperatures. Although NMR studies of GPCRs are challenging due to their innate instability and relatively large molecular weights, recent methodological advances have enabled us to observe the NMR signals of various GPCRs. These NMR studies revealed that GPCRs exist in function-related equilibria between locally different conformations that are simultaneously populated. Here we will describe solution NMR studies that have clarified the function-related conformational dynamics of two GPCRs, β2 adrenergic receptor and adenosine A2A receptor.
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Affiliation(s)
- Takumi Ueda
- Graduate School of Pharmaceutical Sciences, The University of Tokyo, Tokyo, Japan
| | - Shunsuke Imai
- Center for Biosystems Dynamics Research (BDR), RIKEN, Kanagawa, Japan
| | - Ichio Shimada
- Graduate School of Pharmaceutical Sciences, The University of Tokyo, Tokyo, Japan; Center for Biosystems Dynamics Research (BDR), RIKEN, Kanagawa, Japan.
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11
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Irrgang ME, Davis C, Kasson PM. gmxapi: A GROMACS-native Python interface for molecular dynamics with ensemble and plugin support. PLoS Comput Biol 2022; 18:e1009835. [PMID: 35157693 PMCID: PMC8880871 DOI: 10.1371/journal.pcbi.1009835] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2021] [Revised: 02/25/2022] [Accepted: 01/16/2022] [Indexed: 11/19/2022] Open
Abstract
Gmxapi provides an integrated, native Python API for both standard and advanced molecular dynamics simulations in GROMACS. The Python interface permits multiple levels of integration with the core GROMACS libraries, and legacy support is provided via an interface that mimics the command-line syntax, so that all GROMACS commands are fully available. Gmxapi has been officially supported since the GROMACS 2019 release and is enabled by default in current versions of the software. Here we describe gmxapi 0.3 and later. Beyond simply wrapping GROMACS library operations, the API permits several advanced operations that are not feasible using the prior command-line interface. First, the API allows custom user plugin code within the molecular dynamics force calculations, so users can execute custom algorithms without modifying the GROMACS source. Second, the Python interface allows tasks to be dynamically defined, so high-level algorithms for molecular dynamics simulation and analysis can be coordinated with loop and conditional operations. Gmxapi makes GROMACS more accessible to custom Python scripting while also providing support for high-level data-flow simulation algorithms that were previously feasible only in external packages.
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Affiliation(s)
- M. Eric Irrgang
- Departments of Molecular Physiology and Biomedical Engineering, University of Virginia, Charlottesville, Virginia, United States of America
| | - Caroline Davis
- Departments of Molecular Physiology and Biomedical Engineering, University of Virginia, Charlottesville, Virginia, United States of America
| | - Peter M. Kasson
- Departments of Molecular Physiology and Biomedical Engineering, University of Virginia, Charlottesville, Virginia, United States of America
- Science for Life Laboratory, Department of Cell and Molecular Biology, Uppsala University, Uppsala, Sweden
- * E-mail:
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12
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Kamenik AS, Linker SM, Riniker S. Enhanced sampling without borders: on global biasing functions and how to reweight them. Phys Chem Chem Phys 2022; 24:1225-1236. [PMID: 34935813 PMCID: PMC8768491 DOI: 10.1039/d1cp04809k] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/20/2021] [Accepted: 12/14/2021] [Indexed: 12/17/2022]
Abstract
Molecular dynamics (MD) simulations are a powerful tool to follow the time evolution of biomolecular motions in atomistic resolution. However, the high computational demand of these simulations limits the timescales of motions that can be observed. To resolve this issue, so called enhanced sampling techniques are developed, which extend conventional MD algorithms to speed up the simulation process. Here, we focus on techniques that apply global biasing functions. We provide a broad overview of established enhanced sampling methods and promising new advances. As the ultimate goal is to retrieve unbiased information from biased ensembles, we also discuss benefits and limitations of common reweighting schemes. In addition to concisely summarizing critical assumptions and implications, we highlight the general application opportunities as well as uncertainties of global enhanced sampling.
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Affiliation(s)
- Anna S Kamenik
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Stephanie M Linker
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
| | - Sereina Riniker
- Laboratory of Physical Chemistry, ETH Zurich, Vladimir-Prelog-Weg 2, 8093 Zurich, Switzerland.
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13
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Gu H, Wang W, Cao S, Unarta IC, Yao Y, Sheong FK, Huang X. RPnet: a reverse-projection-based neural network for coarse-graining metastable conformational states for protein dynamics. Phys Chem Chem Phys 2022; 24:1462-1474. [PMID: 34985469 DOI: 10.1039/d1cp03622j] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Abstract
The Markov State Model (MSM) is a powerful tool for modeling long timescale dynamics based on numerous short molecular dynamics (MD) simulation trajectories, which makes it a useful tool for elucidating the conformational changes of biological macromolecules. By partitioning the phase space into discretized states and estimating the probabilities of inter-state transitions based on short MD trajectories, one can construct a kinetic network model that could be used to extrapolate long-timescale kinetics if the Markovian condition is met. However, meeting the Markovian condition often requires hundreds or even thousands of states (microstates), which greatly hinders the comprehension of the conformational dynamics of complex biomolecules. Kinetic lumping algorithms can coarse grain numerous microstates into a handful of metastable states (macrostates), which would greatly facilitate the elucidation of biological mechanisms. In this work, we have developed a reverse-projection-based neural network (RPnet) to lump microstates into macrostates, by making use of a physics-based loss function that is based on the projection operator framework of conformational dynamics. By recognizing that microstate and macrostate transition modes can be related through a projection process, we have developed a reverse-projection scheme to directly compare the microstate and macrostate dynamics. Based on this reverse-projection scheme, we designed a loss function that allows the effective assessment of the quality of a given kinetic lumping. We then make use of a neural network to efficiently minimize this loss function to obtain an optimized set of macrostates. We have demonstrated the power of our RPnet in analyzing the dynamics of a numerical 2D potential, alanine dipeptide, and the clamp opening of an RNA polymerase. In all these systems, we have illustrated that our method could yield comparable or better results than competing methods in terms of state partitioning and reproduction of slow dynamics. We expect that our RPnet holds promise in analyzing the conformational dynamics of biological macromolecules.
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Affiliation(s)
- Hanlin Gu
- Department of Mathematics, Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Wei Wang
- Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong.
| | - Siqin Cao
- Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong.
| | - Ilona Christy Unarta
- Department of Chemical and Biological Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Yuan Yao
- Department of Mathematics, Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Fu Kit Sheong
- Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong. .,Institute for Advanced Study, Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Xuhui Huang
- Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong. .,Department of Chemical and Biological Engineering, Hong Kong University of Science and Technology, Kowloon, Hong Kong
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14
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Beyerle ER, Guenza MG. Identifying the leading dynamics of ubiquitin: A comparison between the tICA and the LE4PD slow fluctuations in amino acids' position. J Chem Phys 2021; 155:244108. [PMID: 34972386 DOI: 10.1063/5.0059688] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Molecular Dynamics (MD) simulations of proteins implicitly contain the information connecting the atomistic molecular structure and proteins' biologically relevant motion, where large-scale fluctuations are deemed to guide folding and function. In the complex multiscale processes described by MD trajectories, it is difficult to identify, separate, and study those large-scale fluctuations. This problem can be formulated as the need to identify a small number of collective variables that guide the slow kinetic processes. The most promising method among the ones used to study the slow leading processes in proteins' dynamics is the time-structure based on time-lagged independent component analysis (tICA), which identifies the dominant components in a noisy signal. Recently, we developed an anisotropic Langevin approach for the dynamics of proteins, called the anisotropic Langevin Equation for Protein Dynamics or LE4PD-XYZ. This approach partitions the protein's MD dynamics into mostly uncorrelated, wavelength-dependent, diffusive modes. It associates with each mode a free-energy map, where one measures the spatial extension and the time evolution of the mode-dependent, slow dynamical fluctuations. Here, we compare the tICA modes' predictions with the collective LE4PD-XYZ modes. We observe that the two methods consistently identify the nature and extension of the slowest fluctuation processes. The tICA separates the leading processes in a smaller number of slow modes than the LE4PD does. The LE4PD provides time-dependent information at short times and a formal connection to the physics of the kinetic processes that are missing in the pure statistical analysis of tICA.
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Affiliation(s)
- E R Beyerle
- Institute for Fundamental Science and Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97403, USA
| | - M G Guenza
- Institute for Fundamental Science and Department of Chemistry and Biochemistry, University of Oregon, Eugene, Oregon 97403, USA
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15
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Mardt A, Noé F. Progress in deep Markov state modeling: Coarse graining and experimental data restraints. J Chem Phys 2021; 155:214106. [PMID: 34879670 DOI: 10.1063/5.0064668] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recent advances in deep learning frameworks have established valuable tools for analyzing the long-timescale behavior of complex systems, such as proteins. In particular, the inclusion of physical constraints, e.g., time-reversibility, was a crucial step to make the methods applicable to biophysical systems. Furthermore, we advance the method by incorporating experimental observables into the model estimation showing that biases in simulation data can be compensated for. We further develop a new neural network layer in order to build a hierarchical model allowing for different levels of details to be studied. Finally, we propose an attention mechanism, which highlights important residues for the classification into different states. We demonstrate the new methodology on an ultralong molecular dynamics simulation of the Villin headpiece miniprotein.
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Affiliation(s)
- Andreas Mardt
- Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany
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16
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Nierzwicki Ł, Palermo G. Molecular Dynamics to Predict Cryo-EM: Capturing Transitions and Short-Lived Conformational States of Biomolecules. Front Mol Biosci 2021; 8:641208. [PMID: 33884260 PMCID: PMC8053777 DOI: 10.3389/fmolb.2021.641208] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/13/2020] [Accepted: 02/15/2021] [Indexed: 12/21/2022] Open
Abstract
Single-particle cryogenic electron microscopy (cryo-EM) has revolutionized the field of the structural biology, providing an access to the atomic resolution structures of large biomolecular complexes in their near-native environment. Today's cryo-EM maps can frequently reach the atomic-level resolution, while often containing a range of resolutions, with conformationally variable regions obtained at 6 Å or worse. Low resolution density maps obtained for protein flexible domains, as well as the ensemble of coexisting conformational states arising from cryo-EM, poses new challenges and opportunities for Molecular Dynamics (MD) simulations. With the ability to describe the biomolecular dynamics at the atomic level, MD can extend the capabilities of cryo-EM, capturing the conformational variability and predicting biologically relevant short-lived conformational states. Here, we report about the state-of-the-art MD procedures that are currently used to refine, reconstruct and interpret cryo-EM maps. We show the capability of MD to predict short-lived conformational states, finding remarkable confirmation by cryo-EM structures subsequently solved. This has been the case of the CRISPR-Cas9 genome editing machinery, whose catalytically active structure has been predicted through both long-time scale MD and enhanced sampling techniques 2 years earlier than cryo-EM. In summary, this contribution remarks the ability of MD to complement cryo-EM, describing conformational landscapes and relating structural transitions to function, ultimately discerning relevant short-lived conformational states and providing mechanistic knowledge of biological function.
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Affiliation(s)
- Łukasz Nierzwicki
- Department of Bioengineering, University of California, Riverside, CA, United States
| | - Giulia Palermo
- Department of Bioengineering, University of California, Riverside, CA, United States
- Department of Chemistry, University of California, Riverside, CA, United States
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17
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Kulik M, Mori T, Sugita Y. Multi-Scale Flexible Fitting of Proteins to Cryo-EM Density Maps at Medium Resolution. Front Mol Biosci 2021; 8:631854. [PMID: 33842541 PMCID: PMC8025875 DOI: 10.3389/fmolb.2021.631854] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/21/2020] [Accepted: 01/26/2021] [Indexed: 11/13/2022] Open
Abstract
Structure determination using cryo-electron microscopy (cryo-EM) medium-resolution density maps is often facilitated by flexible fitting. Avoiding overfitting, adjusting force constants driving the structure to the density map, and emulating complex conformational transitions are major concerns in the fitting. To address them, we develop a new method based on a three-step multi-scale protocol. First, flexible fitting molecular dynamics (MD) simulations with coarse-grained structure-based force field and replica-exchange scheme between different force constants replicas are performed. Second, fitted Cα atom positions guide the all-atom structure in targeted MD. Finally, the all-atom flexible fitting refinement in implicit solvent adjusts the positions of the side chains in the density map. Final models obtained via the multi-scale protocol are significantly better resolved and more reliable in comparison with long all-atom flexible fitting simulations. The protocol is useful for multi-domain systems with intricate structural transitions as it preserves the secondary structure of single domains.
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Affiliation(s)
- Marta Kulik
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Japan
| | - Takaharu Mori
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Japan
| | - Yuji Sugita
- Theoretical Molecular Science Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Japan.,RIKEN Center for Computational Science, Kobe, Japan.,RIKEN Center for Biosystems Dynamics Research, Kobe, Japan
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18
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Sicard F, Koskin V, Annibale A, Rosta E. Position-Dependent Diffusion from Biased Simulations and Markov State Model Analysis. J Chem Theory Comput 2021; 17:2022-2033. [DOI: 10.1021/acs.jctc.0c01151] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Affiliation(s)
- François Sicard
- Department of Chemistry, King’s College London, SE1 1DB London, U.K
- Department of Physics and Astronomy, University College London, WC1E 6BT London, U.K
| | - Vladimir Koskin
- Department of Chemistry, King’s College London, SE1 1DB London, U.K
- Department of Physics and Astronomy, University College London, WC1E 6BT London, U.K
| | - Alessia Annibale
- Department of Mathematics, King’s College London, SE11 6NJ London, U.K
| | - Edina Rosta
- Department of Chemistry, King’s College London, SE1 1DB London, U.K
- Department of Physics and Astronomy, University College London, WC1E 6BT London, U.K
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19
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Hays JM, Boland E, Kasson PM. Inference of Joint Conformational Distributions from Separately Acquired Experimental Measurements. J Phys Chem Lett 2021; 12:1606-1611. [PMID: 33596657 PMCID: PMC8310705 DOI: 10.1021/acs.jpclett.0c03623] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
Flexible proteins serve vital roles in a multitude of biological processes. However, determining their full conformational ensembles is extremely difficult because this requires detailed knowledge about the heterogeneity of the protein's degrees of freedom. Label-based experiments such as double electron-electron resonance (DEER) are very useful in studying flexible proteins, as they provide distributional data on heterogeneity. These experiments are typically performed separately, so information about correlation between distributions is lost. We have developed a method to recover correlation information using nonequilibrium work estimates in molecular dynamics refinement. We tested this method on a simple model of an alternating-access transporter for which the true joint distributions are known, and it successfully recovered the true joint distribution. We also applied our method to the protein syntaxin-1a, where it discarded physically implausible conformations. Our method thus provides a way to recover correlation structure in separate experimental measurements of conformational ensembles and refines the resulting structural ensemble.
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Affiliation(s)
- Jennifer M. Hays
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
- Department of Molecular Physiology, University of Virginia, Charlottesville, VA, USA
| | - Emily Boland
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
- Department of Molecular Physiology, University of Virginia, Charlottesville, VA, USA
| | - Peter M. Kasson
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, USA
- Department of Molecular Physiology, University of Virginia, Charlottesville, VA, USA
- Science for Life Laboratory, Department of Cell and Molecular Biology, Uppsala, 75124 Sweden
- Corresponding Author:
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20
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Raich L, Meier K, Günther J, Christ CD, Noé F, Olsson S. Discovery of a hidden transient state in all bromodomain families. Proc Natl Acad Sci U S A 2021; 118:e2017427118. [PMID: 33468647 PMCID: PMC7848705 DOI: 10.1073/pnas.2017427118] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Bromodomains (BDs) are small protein modules that interact with acetylated marks in histones. These posttranslational modifications are pivotal to regulate gene expression, making BDs promising targets to treat several diseases. While the general structure of BDs is well known, their dynamical features and their interplay with other macromolecules are poorly understood, hampering the rational design of potent and selective inhibitors. Here, we combine extensive molecular dynamics simulations, Markov state modeling, and available structural data to reveal a transiently formed state that is conserved across all BD families. It involves the breaking of two backbone hydrogen bonds that anchor the ZA-loop with the αA helix, opening a cryptic pocket that partially occludes the one associated to histone binding. By analyzing more than 1,900 experimental structures, we unveil just two adopting the hidden state, explaining why it has been previously unnoticed and providing direct structural evidence for its existence. Our results suggest that this state is an allosteric regulatory switch for BDs, potentially related to a recently unveiled BD-DNA-binding mode.
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Affiliation(s)
- Lluís Raich
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
| | - Katharina Meier
- Computational Molecular Design, Pharmaceuticals, R&D, Bayer AG, 42096 Wuppertal, Germany
| | - Judith Günther
- Computational Molecular Design, Pharmaceuticals, R&D, Bayer AG, 13342 Berlin, Germany
| | - Clara D Christ
- Computational Molecular Design, Pharmaceuticals, R&D, Bayer AG, 13342 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany;
- Department of Chemistry, Rice University, Houston, TX 77005
| | - Simon Olsson
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany;
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21
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Brotzakis ZF, Vendruscolo M, Bolhuis PG. A method of incorporating rate constants as kinetic constraints in molecular dynamics simulations. Proc Natl Acad Sci U S A 2021; 118:e2012423118. [PMID: 33376207 PMCID: PMC7812743 DOI: 10.1073/pnas.2012423118] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Abstract
From the point of view of statistical mechanics, a full characterization of a molecular system requires an accurate determination of its possible states, their populations, and the respective interconversion rates. Toward this goal, well-established methods increase the accuracy of molecular dynamics simulations by incorporating experimental information about states using structural restraints and about populations using thermodynamics restraints. However, it is still unclear how to include experimental knowledge about interconversion rates. Here, we introduce a method of imposing known rate constants as constraints in molecular dynamics simulations, which is based on a combination of the maximum-entropy and maximum-caliber principles. Starting from an existing ensemble of trajectories, obtained from either molecular dynamics or enhanced trajectory sampling, this method provides a minimally perturbed path distribution consistent with the kinetic constraints, as well as modified free energy and committor landscapes. We illustrate the application of the method to a series of model systems, including all-atom molecular simulations of protein folding. Our results show that by combining experimental rate constants and molecular dynamics simulations, this approach enables the determination of transition states, reaction mechanisms, and free energies. We anticipate that this method will extend the applicability of molecular simulations to kinetic studies in structural biology and that it will assist the development of force fields to reproduce kinetic and thermodynamic observables. Furthermore, this approach is generally applicable to a wide range of systems in biology, physics, chemistry, and material science.
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Affiliation(s)
- Z Faidon Brotzakis
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Michele Vendruscolo
- Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, United Kingdom
| | - Peter G Bolhuis
- van't Hoff Institute for Molecular Sciences, University of Amsterdam, 1090 GD Amsterdam, The Netherlands
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22
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Löhr T, Kohlhoff K, Heller GT, Camilloni C, Vendruscolo M. A kinetic ensemble of the Alzheimer's Aβ peptide. NATURE COMPUTATIONAL SCIENCE 2021; 1:71-78. [PMID: 38217162 DOI: 10.1038/s43588-020-00003-w] [Citation(s) in RCA: 30] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2020] [Accepted: 11/24/2020] [Indexed: 01/15/2024]
Abstract
The conformational and thermodynamic properties of disordered proteins are commonly described in terms of structural ensembles and free energy landscapes. To provide information on the transition rates between the different states populated by these proteins, it would be desirable to generalize this description to kinetic ensembles. Approaches based on the theory of stochastic processes can be particularly suitable for this purpose. Here, we develop a Markov state model and apply it to determine a kinetic ensemble of Aβ42, a disordered peptide associated with Alzheimer's disease. Through the Google Compute Engine, we generated 315-µs all-atom molecular dynamics trajectories. Using a probabilistic-based definition of conformational states in a neural network approach, we found that Aβ42 is characterized by inter-state transitions on the microsecond timescale, exhibiting only fully unfolded or short-lived, partially folded states. Our results illustrate how kinetic ensembles provide effective information about the structure, thermodynamics and kinetics of disordered proteins.
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Affiliation(s)
- Thomas Löhr
- Department of Chemistry, University of Cambridge, Cambridge, UK
| | | | | | - Carlo Camilloni
- Dipartimento di Bioscienze, Università degli Studi di Milano, Milano, Italy
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23
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Strotz D, Orts J, Kadavath H, Friedmann M, Ghosh D, Olsson S, Chi CN, Güntert P, Vögeli B, Riek R. Protein Allostery at Atomic Resolution. Angew Chem Int Ed Engl 2020; 59:22132-22139. [PMID: 32797659 PMCID: PMC9202374 DOI: 10.1002/anie.202008734] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2020] [Revised: 07/23/2020] [Indexed: 08/15/2023]
Abstract
Protein allostery is a phenomenon involving the long range coupling between two distal sites in a protein. In order to elucidate allostery at atomic resoluion on the ligand-binding WW domain of the enzyme Pin1, multistate structures were calculated from exact nuclear Overhauser effect (eNOE). In its free form, the protein undergoes a microsecond exchange between two states, one of which is predisposed to interact with its parent catalytic domain. In presence of the positive allosteric ligand, the equilibrium between the two states is shifted towards domain-domain interaction, suggesting a population shift model. In contrast, the allostery-suppressing ligand decouples the side-chain arrangement at the inter-domain interface thereby reducing the inter-domain interaction. As such, this mechanism is an example of dynamic allostery. The presented distinct modes of action highlight the power of the interplay between dynamics and function in the biological activity of proteins.
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Affiliation(s)
- Dean Strotz
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
| | - Julien Orts
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
| | - Harindranath Kadavath
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
| | - Michael Friedmann
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
| | - Dhiman Ghosh
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
| | - Simon Olsson
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Celestine N. Chi
- Department of Medical Biochemistry and Microbiology, Uppsala Biomedical Center, Uppsala University, 751 23 Uppsala, Sweden
| | - Peter Güntert
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
- Institute of Biophysical Chemistry, Center for Biomolecular Magnetic Resonance, and Frankfurt Institute for Advanced Studies, J.W. Goethe-Universität, Max-von-Laue-Str. 9, 60438 Frankfurt am Main, Germany
- Graduate School of Science, Tokyo Metropolitan University, Hachioji, Tokyo 192-0397, Japan
| | - Beat Vögeli
- Department of Biochemistry and Molecular Genetics, University of Colorado at Denver, 12801 East 17 Avenue, Aurora, CO 80045, USA
| | - Roland Riek
- Laboratory of Physical Chemistry, Swiss Federal Institute of Technology, ETH-Hönggerberg, CH-8093 Zürich, Switzerland
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24
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Strotz D, Orts J, Kadavath H, Friedmann M, Ghosh D, Olsson S, Chi CN, Pokharna A, Güntert P, Vögeli B, Riek R. Protein Allostery at Atomic Resolution. Angew Chem Int Ed Engl 2020. [DOI: 10.1002/ange.202008734] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Affiliation(s)
- Dean Strotz
- Laboratory of Physical Chemistry Swiss Federal Institute of Technology ETH-Hönggerberg 8093 Zürich Switzerland
| | - Julien Orts
- Laboratory of Physical Chemistry Swiss Federal Institute of Technology ETH-Hönggerberg 8093 Zürich Switzerland
| | - Harindranath Kadavath
- Laboratory of Physical Chemistry Swiss Federal Institute of Technology ETH-Hönggerberg 8093 Zürich Switzerland
| | - Michael Friedmann
- Laboratory of Physical Chemistry Swiss Federal Institute of Technology ETH-Hönggerberg 8093 Zürich Switzerland
| | - Dhiman Ghosh
- Laboratory of Physical Chemistry Swiss Federal Institute of Technology ETH-Hönggerberg 8093 Zürich Switzerland
| | - Simon Olsson
- Department of Mathematics and Computer Science Freie Universität Berlin Arnimallee 6 14195 Berlin Germany
| | - Celestine N. Chi
- Department of Medical Biochemistry and Microbiology Uppsala Biomedical Center Uppsala University 751 23 Uppsala Sweden
| | - Aditya Pokharna
- Laboratory of Physical Chemistry Swiss Federal Institute of Technology ETH-Hönggerberg 8093 Zürich Switzerland
| | - Peter Güntert
- Laboratory of Physical Chemistry Swiss Federal Institute of Technology ETH-Hönggerberg 8093 Zürich Switzerland
- Institute of Biophysical Chemistry Center for Biomolecular Magnetic Resonance, and Frankfurt Institute for Advanced Studies J.W. Goethe-Universität Max-von-Laue-Str. 9 60438 Frankfurt am Main Germany
- Graduate School of Science Tokyo Metropolitan University, Hachioji Tokyo 192-0397 Japan
| | - Beat Vögeli
- Department of Biochemistry and Molecular Genetics University of Colorado at Denver 12801 East 17th Avenue Aurora CO 80045 USA
| | - Roland Riek
- Laboratory of Physical Chemistry Swiss Federal Institute of Technology ETH-Hönggerberg 8093 Zürich Switzerland
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25
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Ulcickas JRW, Cao Z, Rong J, Bouman CA, Slipchenko LV, Buzzard GT, Simpson GJ. Multiagent Consensus Equilibrium in Molecular Structure Determination. J Phys Chem A 2020; 124:9105-9112. [PMID: 32975942 DOI: 10.1021/acs.jpca.0c07282] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Multiagent consensus equilibrium (MACE) is demonstrated for the integration of experimental observables as constraints in molecular structure determination and for the systematic merging of multiple computational architectures. MACE is founded on simultaneously determining the equilibrium point between multiple experimental and/or computational agents; the returned state description (e.g., atomic coordinates for molecular structure) represents the intersection of each manifold and is not equivalent to the average optimum state for each agent. The moment of inertia, determined directly from microwave spectroscopy measurements, serves to illustrate the mechanism through which MACE evaluations merge experimental and quantum chemical modeling. MACE results reported combine gradient descent optimization of each ab initio agent with an agent that predicts the chemical structure based on root-mean-square deviation of the predicted inertia tensor with experimentally measured moments of inertia. Successful model fusion for several small molecules was achieved as well as the larger molecule solketal. Fusing a model of moment of inertia, an underdetermined predictor of structure, with low cost computational methods yielded structure determination performance comparable to standard computational methods such as MP2/cc-pVTZ and greater agreement with experimental observables.
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Affiliation(s)
- James R W Ulcickas
- Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907, United States
| | - Ziyi Cao
- Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907, United States
| | - Jiayue Rong
- Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907, United States
| | - Charles A Bouman
- Department of Electrical and Computer Engineering, Purdue University, 465 Northwestern Ave, West Lafayette, Indiana 47907, United States
| | - Lyudmila V Slipchenko
- Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907, United States
| | - Gregery T Buzzard
- Department of Mathematics, Purdue University, 150 North University Street, West Lafayette, Indiana 47907, United States
| | - Garth J Simpson
- Department of Chemistry, Purdue University, 560 Oval Drive, West Lafayette, Indiana 47907, United States
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26
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Target search and recognition mechanisms of glycosylase AlkD revealed by scanning FRET-FCS and Markov state models. Proc Natl Acad Sci U S A 2020; 117:21889-21895. [PMID: 32820079 PMCID: PMC7486748 DOI: 10.1073/pnas.2002971117] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
DNA glycosylase repairs DNA damage to maintain the genome integrity, and thus it is essential for the survival of all organisms. However, it remains a long-standing puzzle how glycosylase diffuses along the genomic DNA to locate the sparse and aberrant lesion sites efficiently and accurately in the genome containing numerous base pairs. Previously, only the high-speed–low-accuracy search mode has been characterized experimentally, while the low-speed–high-accuracy mode is undetectable. Here, we observed the low-speed mode of glycosylase AlkD translocating, and further dissected its molecular mechanisms. To achieve this, we developed an integrated platform by combining scanning FRET-FCS with Markov state model. We expect that this platform can be widely applied to investigate other glycosylases and DNA-binding proteins. DNA glycosylase is responsible for repairing DNA damage to maintain the genome stability and integrity. However, how glycosylase can efficiently and accurately recognize DNA lesions across the enormous DNA genome remains elusive. It has been hypothesized that glycosylase translocates along the DNA by alternating between a fast but low-accuracy diffusion mode and a slow but high-accuracy mode when searching for DNA lesions. However, the slow mode has not been successfully characterized due to the limitation in the spatial and temporal resolutions of current experimental techniques. Using a newly developed scanning fluorescence resonance energy transfer (FRET)–fluorescence correlation spectroscopy (FCS) platform, we were able to observe both slow and fast modes of glycosylase AlkD translocating on double-stranded DNA (dsDNA), reaching the temporal resolution of microsecond and spatial resolution of subnanometer. The underlying molecular mechanism of the slow mode was further elucidated by Markov state model built from extensive all-atom molecular dynamics simulations. We found that in the slow mode, AlkD follows an asymmetric diffusion pathway, i.e., rotation followed by translation. Furthermore, the essential role of Y27 in AlkD diffusion dynamics was identified both experimentally and computationally. Our results provided mechanistic insights on how conformational dynamics of AlkD–dsDNA complex coordinate different diffusion modes to accomplish the search for DNA lesions with high efficiency and accuracy. We anticipate that the mechanism adopted by AlkD to search for DNA lesions could be a general one utilized by other glycosylases and DNA binding proteins.
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27
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Ligand-bound glutamine binding protein assumes multiple metastable binding sites with different binding affinities. Commun Biol 2020; 3:419. [PMID: 32747735 PMCID: PMC7400645 DOI: 10.1038/s42003-020-01149-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2020] [Accepted: 07/14/2020] [Indexed: 11/08/2022] Open
Abstract
Protein dynamics plays key roles in ligand binding. However, the microscopic description of conformational dynamics-coupled ligand binding remains a challenge. In this study, we integrate molecular dynamics simulations, Markov state model (MSM) analysis and experimental methods to characterize the conformational dynamics of ligand-bound glutamine binding protein (GlnBP). We show that ligand-bound GlnBP has high conformational flexibility and additional metastable binding sites, presenting a more complex energy landscape than the scenario in the absence of ligand. The diverse conformations of GlnBP demonstrate different binding affinities and entail complex transition kinetics, implicating a concerted ligand binding mechanism. Single molecule fluorescence resonance energy transfer measurements and mutagenesis experiments are performed to validate our MSM-derived structure ensemble as well as the binding mechanism. Collectively, our study provides deeper insights into the protein dynamics-coupled ligand binding, revealing an intricate regulatory network underlying the apparent binding affinity. Zhang, Wu, Feng et al. show that ligand-bound glutamine binding protein assumes multiple metastable binding sites, presenting a more dynamic energy landscape than its ligand-free form. This study provides insights into the ligand-binding mechanisms coupled with protein dynamics that underly the apparent binding affinity.
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28
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Verkhivker GM, Agajanian S, Hu G, Tao P. Allosteric Regulation at the Crossroads of New Technologies: Multiscale Modeling, Networks, and Machine Learning. Front Mol Biosci 2020; 7:136. [PMID: 32733918 PMCID: PMC7363947 DOI: 10.3389/fmolb.2020.00136] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/01/2020] [Accepted: 06/08/2020] [Indexed: 12/12/2022] Open
Abstract
Allosteric regulation is a common mechanism employed by complex biomolecular systems for regulation of activity and adaptability in the cellular environment, serving as an effective molecular tool for cellular communication. As an intrinsic but elusive property, allostery is a ubiquitous phenomenon where binding or disturbing of a distal site in a protein can functionally control its activity and is considered as the "second secret of life." The fundamental biological importance and complexity of these processes require a multi-faceted platform of synergistically integrated approaches for prediction and characterization of allosteric functional states, atomistic reconstruction of allosteric regulatory mechanisms and discovery of allosteric modulators. The unifying theme and overarching goal of allosteric regulation studies in recent years have been integration between emerging experiment and computational approaches and technologies to advance quantitative characterization of allosteric mechanisms in proteins. Despite significant advances, the quantitative characterization and reliable prediction of functional allosteric states, interactions, and mechanisms continue to present highly challenging problems in the field. In this review, we discuss simulation-based multiscale approaches, experiment-informed Markovian models, and network modeling of allostery and information-theoretical approaches that can describe the thermodynamics and hierarchy allosteric states and the molecular basis of allosteric mechanisms. The wealth of structural and functional information along with diversity and complexity of allosteric mechanisms in therapeutically important protein families have provided a well-suited platform for development of data-driven research strategies. Data-centric integration of chemistry, biology and computer science using artificial intelligence technologies has gained a significant momentum and at the forefront of many cross-disciplinary efforts. We discuss new developments in the machine learning field and the emergence of deep learning and deep reinforcement learning applications in modeling of molecular mechanisms and allosteric proteins. The experiment-guided integrated approaches empowered by recent advances in multiscale modeling, network science, and machine learning can lead to more reliable prediction of allosteric regulatory mechanisms and discovery of allosteric modulators for therapeutically important protein targets.
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Affiliation(s)
- Gennady M. Verkhivker
- Graduate Program in Computational and Data Sciences, Schmid College of Science and Technology, Chapman University, Orange, CA, United States
- Department of Biomedical and Pharmaceutical Sciences, Chapman University School of Pharmacy, Irvine, CA, United States
| | - Steve Agajanian
- Graduate Program in Computational and Data Sciences, Schmid College of Science and Technology, Chapman University, Orange, CA, United States
| | - Guang Hu
- Center for Systems Biology, Department of Bioinformatics, School of Biology and Basic Medical Sciences, Soochow University, Suzhou, China
| | - Peng Tao
- Department of Chemistry, Center for Drug Discovery, Design, and Delivery (CD4), Center for Scientific Computation, Southern Methodist University, Dallas, TX, United States
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29
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Jagger BR, Kochanek SE, Haldar S, Amaro RE, Mulholland AJ. Multiscale simulation approaches to modeling drug-protein binding. Curr Opin Struct Biol 2020; 61:213-221. [PMID: 32113133 DOI: 10.1016/j.sbi.2020.01.014] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2019] [Revised: 01/16/2020] [Accepted: 01/21/2020] [Indexed: 01/19/2023]
Abstract
Simulations can provide detailed insight into the molecular processes involved in drug action, such as protein-ligand binding, and can therefore be a valuable tool for drug design and development. Processes with a large range of length and timescales may be involved, and understanding these different scales typically requires different types of simulation methodology. Ideally, simulations should be able to connect across scales, to analyze and predict how changes at one scale can influence another. Multiscale simulation methods, which combine different levels of treatment, are an emerging frontier with great potential in this area. Here we review multiscale frameworks of various types, and selected applications to biomolecular systems with a focus on drug-ligand binding.
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Affiliation(s)
- Benjamin R Jagger
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, United States
| | - Sarah E Kochanek
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, United States
| | - Susanta Haldar
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, BS8 1TS, UK
| | - Rommie E Amaro
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, United States.
| | - Adrian J Mulholland
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, BS8 1TS, UK.
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30
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Matsunaga Y, Sugita Y. Use of single-molecule time-series data for refining conformational dynamics in molecular simulations. Curr Opin Struct Biol 2020; 61:153-159. [DOI: 10.1016/j.sbi.2019.12.022] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Revised: 12/24/2019] [Accepted: 12/27/2019] [Indexed: 12/18/2022]
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31
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Dixit PD, Lyashenko E, Niepel M, Vitkup D. Maximum Entropy Framework for Predictive Inference of Cell Population Heterogeneity and Responses in Signaling Networks. Cell Syst 2020; 10:204-212.e8. [PMID: 31864963 PMCID: PMC7047530 DOI: 10.1016/j.cels.2019.11.010] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2018] [Revised: 07/30/2019] [Accepted: 11/25/2019] [Indexed: 12/13/2022]
Abstract
Predictive models of signaling networks are essential for understanding cell population heterogeneity and designing rational interventions in disease. However, using computational models to predict heterogeneity of signaling dynamics is often challenging because of the extensive variability of biochemical parameters across cell populations. Here, we describe a maximum entropy-based framework for inference of heterogeneity in dynamics of signaling networks (MERIDIAN). MERIDIAN estimates the joint probability distribution over signaling network parameters that is consistent with experimentally measured cell-to-cell variability of biochemical species. We apply the developed approach to investigate the response heterogeneity in the EGFR/Akt signaling network. Our analysis demonstrates that a significant fraction of cells exhibits high phosphorylated Akt (pAkt) levels hours after EGF stimulation. Our findings also suggest that cells with high EGFR levels predominantly contribute to the subpopulation of cells with high pAkt activity. We also discuss how MERIDIAN can be extended to accommodate various experimental measurements.
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Affiliation(s)
- Purushottam D Dixit
- Department of Systems Biology, Columbia University, New York, NY, USA; Department of Physics, University of Florida, Gainesville, FL, USA.
| | - Eugenia Lyashenko
- Department of Systems Biology, Columbia University, New York, NY, USA
| | - Mario Niepel
- Laboratory of Systems Pharmacology, HMS LINCS Center, Harvard Medical School, Boston, MA 02115, USA
| | - Dennis Vitkup
- Department of Systems Biology, Columbia University, New York, NY, USA; Department of Biomedical Informatics, Columbia University, New York, NY, USA; Center for Computational Biology and Bioinformatics, Columbia University, New York, NY, USA.
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32
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Bradshaw RT, Marinelli F, Faraldo-Gómez JD, Forrest LR. Interpretation of HDX Data by Maximum-Entropy Reweighting of Simulated Structural Ensembles. Biophys J 2020; 118:1649-1664. [PMID: 32105651 PMCID: PMC7136279 DOI: 10.1016/j.bpj.2020.02.005] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/17/2019] [Revised: 01/28/2020] [Accepted: 02/05/2020] [Indexed: 01/12/2023] Open
Abstract
Hydrogen-deuterium exchange combined with mass spectrometry (HDX-MS) is a widely applied biophysical technique that probes the structure and dynamics of biomolecules without the need for site-directed modifications or bio-orthogonal labels. The mechanistic interpretation of HDX data, however, is often qualitative and subjective, owing to a lack of quantitative methods to rigorously translate observed deuteration levels into atomistic structural information. To help address this problem, we have developed a methodology to generate structural ensembles that faithfully reproduce HDX-MS measurements. In this approach, an ensemble of protein conformations is first generated, typically using molecular dynamics simulations. A maximum-entropy bias is then applied post hoc to the resulting ensemble such that averaged peptide-deuteration levels, as predicted by an empirical model, agree with target values within a given level of uncertainty. We evaluate this approach, referred to as HDX ensemble reweighting (HDXer), for artificial target data reflecting the two major conformational states of a binding protein. We demonstrate that the information provided by HDX-MS experiments and by the model of exchange are sufficient to recover correctly weighted structural ensembles from simulations, even when the relevant conformations are rarely observed. Degrading the information content of the target data—e.g., by reducing sequence coverage, by averaging exchange levels over longer peptide segments, or by incorporating different sources of uncertainty—reduces the structural accuracy of the reweighted ensemble but still allows for useful insights into the distinctive structural features reflected by the target data. Finally, we describe a quantitative metric to rank candidate structural ensembles according to their correspondence with target data and illustrate the use of HDXer to describe changes in the conformational ensemble of the membrane protein LeuT. In summary, HDXer is designed to facilitate objective structural interpretations of HDX-MS data and to inform experimental approaches and further developments of theoretical exchange models.
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Affiliation(s)
- Richard T Bradshaw
- Computational Structural Biology Section, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, Maryland
| | - Fabrizio Marinelli
- Theoretical Molecular Biophysics Unit, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland
| | - José D Faraldo-Gómez
- Theoretical Molecular Biophysics Unit, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland.
| | - Lucy R Forrest
- Computational Structural Biology Section, National Institute of Neurological Disorders and Stroke, National Institutes of Health, Bethesda, Maryland.
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33
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Orioli S, Larsen AH, Bottaro S, Lindorff-Larsen K. How to learn from inconsistencies: Integrating molecular simulations with experimental data. PROGRESS IN MOLECULAR BIOLOGY AND TRANSLATIONAL SCIENCE 2020; 170:123-176. [PMID: 32145944 DOI: 10.1016/bs.pmbts.2019.12.006] [Citation(s) in RCA: 48] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/28/2022]
Abstract
Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modeling tool to interpret experimental measurements, and to use experimental data to refine our biophysical models. Thus, explicit integration and synergy between molecular simulations and experiments is fundamental for furthering our understanding of biological processes. This is especially true in the case where discrepancies between measured and simulated observables emerge. In this chapter, we provide an overview of some of the core ideas behind methods that were developed to improve the consistency between experimental information and numerical predictions. We distinguish between situations where experiments are used to refine our understanding and models of specific systems, and situations where experiments are used more generally to refine transferable models. We discuss different philosophies and attempt to unify them in a single framework. Until now, such integration between experiments and simulations have mostly been applied to equilibrium data, and we discuss more recent developments aimed to analyze time-dependent or time-resolved data.
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Affiliation(s)
- Simone Orioli
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark; Structural Biophysics, Niels Bohr Institute, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Andreas Haahr Larsen
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark; Structural Biophysics, Niels Bohr Institute, Faculty of Science, University of Copenhagen, Copenhagen, Denmark
| | - Sandro Bottaro
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark; Atomistic Simulations Laboratory, Istituto Italiano di Tecnologia, Genova, Italy
| | - Kresten Lindorff-Larsen
- Structural Biology and NMR Laboratory & Linderstrøm-Lang Centre for Protein Science, Department of Biology, University of Copenhagen, Copenhagen, Denmark.
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34
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Wan H, Ge Y, Razavi A, Voelz VA. Reconciling Simulated Ensembles of Apomyoglobin with Experimental Hydrogen/Deuterium Exchange Data Using Bayesian Inference and Multiensemble Markov State Models. J Chem Theory Comput 2020; 16:1333-1348. [PMID: 31917926 DOI: 10.1021/acs.jctc.9b01240] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/08/2023]
Abstract
Hydrogen/deuterium exchange (HDX) is a powerful technique to investigate protein conformational dynamics at amino acid resolution. Because HDX provides a measurement of solvent exposure of backbone hydrogens, ensemble-averaged over potentially slow kinetic processes, it has been challenging to use HDX protection factors to refine structural ensembles obtained from molecular dynamics simulations. This entails dual challenges: (1) identifying structural observables that best correlate with backbone amide protection from exchange and (2) restraining these observables in molecular simulations to model ensembles consistent with experimental measurements. Here, we make significant progress on both fronts. First, we describe an improved predictor of HDX protection factors from structural observables in simulated ensembles, parametrized from ultralong molecular dynamics simulation trajectory data, with a Bayesian inference approach used to retain the full posterior distribution of model parameters. We next present a new method for obtaining simulated ensembles in agreement with experimental HDX protection factors, in which molecular simulations are performed at various temperatures and restraint biases and used to construct multiensemble Markov State Models (MSMs). Finally, the BICePs (Bayesian Inference of Conformational Populations) algorithm is then used with our HDX protection factor predictor to infer which thermodynamic ensemble agrees best with the experiment and estimate populations of each conformational state in the MSM. To illustrate the approach, we use a combination of HDX protection factor restraints and chemical shift restraints to model the conformational ensemble of apomyoglobin at pH 6. The resulting ensemble agrees well with the experiment and gives insight into the all-atom structure of disordered helices F and H in the absence of heme.
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Affiliation(s)
- Hongbin Wan
- Department of Chemistry , Temple University , Philadelphia , Pennsylvania 19122 , United States
| | - Yunhui Ge
- Department of Chemistry , Temple University , Philadelphia , Pennsylvania 19122 , United States
| | - Asghar Razavi
- Department of Chemistry , Temple University , Philadelphia , Pennsylvania 19122 , United States
| | - Vincent A Voelz
- Department of Chemistry , Temple University , Philadelphia , Pennsylvania 19122 , United States
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35
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Juárez-Jiménez J, Gupta AA, Karunanithy G, Mey ASJS, Georgiou C, Ioannidis H, De Simone A, Barlow PN, Hulme AN, Walkinshaw MD, Baldwin AJ, Michel J. Dynamic design: manipulation of millisecond timescale motions on the energy landscape of cyclophilin A. Chem Sci 2020; 11:2670-2680. [PMID: 34084326 PMCID: PMC8157532 DOI: 10.1039/c9sc04696h] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2019] [Accepted: 01/14/2020] [Indexed: 12/21/2022] Open
Abstract
Proteins need to interconvert between many conformations in order to function, many of which are formed transiently, and sparsely populated. Particularly when the lifetimes of these states approach the millisecond timescale, identifying the relevant structures and the mechanism by which they interconvert remains a tremendous challenge. Here we introduce a novel combination of accelerated MD (aMD) simulations and Markov state modelling (MSM) to explore these 'excited' conformational states. Applying this to the highly dynamic protein CypA, a protein involved in immune response and associated with HIV infection, we identify five principally populated conformational states and the atomistic mechanism by which they interconvert. A rational design strategy predicted that the mutant D66A should stabilise the minor conformations and substantially alter the dynamics, whereas the similar mutant H70A should leave the landscape broadly unchanged. These predictions are confirmed using CPMG and R1ρ solution state NMR measurements. By efficiently exploring functionally relevant, but sparsely populated conformations with millisecond lifetimes in silico, our aMD/MSM method has tremendous promise for the design of dynamic protein free energy landscapes for both protein engineering and drug discovery.
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Affiliation(s)
- Jordi Juárez-Jiménez
- EaStCHEM School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ UK
| | - Arun A Gupta
- EaStCHEM School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ UK
| | - Gogulan Karunanithy
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford South Parks Road Oxford OX1 3QZ UK
| | - Antonia S J S Mey
- EaStCHEM School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ UK
| | - Charis Georgiou
- EaStCHEM School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ UK
| | - Harris Ioannidis
- EaStCHEM School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ UK
| | - Alessio De Simone
- EaStCHEM School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ UK
| | - Paul N Barlow
- EaStCHEM School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ UK
| | - Alison N Hulme
- EaStCHEM School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ UK
| | - Malcolm D Walkinshaw
- School of Biological Sciences Michael Swann Building, Max Born Crescent Edinburgh EH9 3BF UK
| | - Andrew J Baldwin
- Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford South Parks Road Oxford OX1 3QZ UK
| | - Julien Michel
- EaStCHEM School of Chemistry, University of Edinburgh David Brewster Road Edinburgh EH9 3FJ UK
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36
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Hamilton GL, Alper J, Sanabria H. Reporting on the future of integrative structural biology ORAU workshop. FRONT BIOSCI-LANDMRK 2020; 25:43-68. [PMID: 31585877 PMCID: PMC7323472 DOI: 10.2741/4794] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
Integrative and hybrid methods have the potential to bridge long-standing knowledge gaps in structural biology. These methods will have a prominent role in the future of the field as we make advances toward a complete, unified representation of biology that spans the molecular and cellular scales. The Department of Physics and Astronomy at Clemson University hosted The Future of Integrative Structural Biology workshop on April 29, 2017 and partially sponsored by partially sponsored by a program of the Oak Ridge Associated Universities (ORAU). The workshop brought experts from multiple structural biology disciplines together to discuss near-term steps toward the goal of a molecular atlas of the cell. The discussion focused on the types of structural data that should be represented, how this data should be represented, and how the time domain might be incorporated into such an atlas. The consensus was that an explorable, map-like Virtual Cell, containing both spatial and temporal data bridging the atomic and cellular length scales obtained by multiple experimental methods, represents the best path toward a complete atlas of the cell.
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Affiliation(s)
- George L Hamilton
- Physics and Astronomy, Clemson University, 216 Kinard Lab, Clemson, S.C. USA
| | - Joshua Alper
- Physics and Astronomy, Clemson University, 302B Kinard Lab, Clemson, S.C. 29634-0978. USA
| | - Hugo Sanabria
- Physics and Astronomy, Clemson University, 214 Kinard Lab, Clemson, S.C. 29634-0978. USA,
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37
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Noé F. Machine Learning for Molecular Dynamics on Long Timescales. MACHINE LEARNING MEETS QUANTUM PHYSICS 2020. [DOI: 10.1007/978-3-030-40245-7_16] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
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38
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Bernardi RC, Durner E, Schoeler C, Malinowska KH, Carvalho BG, Bayer EA, Luthey-Schulten Z, Gaub HE, Nash MA. Mechanisms of Nanonewton Mechanostability in a Protein Complex Revealed by Molecular Dynamics Simulations and Single-Molecule Force Spectroscopy. J Am Chem Soc 2019; 141:14752-14763. [PMID: 31464132 PMCID: PMC6939381 DOI: 10.1021/jacs.9b06776] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
![]()
Can molecular dynamics
simulations predict the mechanical behavior of protein complexes?
Can simulations decipher the role of protein domains of unknown function
in large macromolecular complexes? Here, we employ a wide-sampling
computational approach to demonstrate that molecular dynamics simulations,
when carefully performed and combined with single-molecule atomic
force spectroscopy experiments, can predict and explain the behavior
of highly mechanostable protein complexes. As a test case, we studied
a previously unreported homologue from Ruminococcus flavefaciens called X-module-Dockerin (XDoc) bound to its partner Cohesin (Coh).
By performing dozens of short simulation replicas near the rupture
event, and analyzing dynamic network fluctuations, we were able to
generate large simulation statistics and directly compare them with
experiments to uncover the mechanisms involved in mechanical stabilization.
Our single-molecule force spectroscopy experiments show that the XDoc-Coh
homologue complex withstands forces up to 1 nN at loading rates of
105 pN/s. Our simulation results reveal that this remarkable
mechanical stability is achieved by a protein architecture that directs
molecular deformation along paths that run perpendicular to the pulling
axis. The X-module was found to play a crucial role in shielding the
adjacent protein complex from mechanical rupture. These mechanisms
of protein mechanical stabilization have potential applications in
biotechnology for the development of systems exhibiting shear enhanced
adhesion or tunable mechanics.
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Affiliation(s)
- Rafael C Bernardi
- Beckman Institute for Advanced Science and Technology , University of Illinois at Urbana-Champaign , Urbana , Illinois 61801 , United States
| | - Ellis Durner
- Lehrstuhl für Angewandte Physik and Center for Nanoscience , Ludwig-Maximilians-Universität , 80799 Munich , Germany
| | - Constantin Schoeler
- Lehrstuhl für Angewandte Physik and Center for Nanoscience , Ludwig-Maximilians-Universität , 80799 Munich , Germany
| | - Klara H Malinowska
- Lehrstuhl für Angewandte Physik and Center for Nanoscience , Ludwig-Maximilians-Universität , 80799 Munich , Germany
| | - Bruna G Carvalho
- School of Chemical Engineering , University of Campinas , 13083-852 Campinas , Brazil
| | - Edward A Bayer
- Department of Biomolecular Sciences , Weizmann Institute of Science , 76100 Rehovot , Israel
| | - Zaida Luthey-Schulten
- Beckman Institute for Advanced Science and Technology , University of Illinois at Urbana-Champaign , Urbana , Illinois 61801 , United States.,Department of Chemistry , University of Illinois at Urbana-Champaign , Urbana , Illinois 61801 , United States
| | - Hermann E Gaub
- Lehrstuhl für Angewandte Physik and Center for Nanoscience , Ludwig-Maximilians-Universität , 80799 Munich , Germany
| | - Michael A Nash
- Department of Chemistry , University of Basel , 4058 Basel , Switzerland.,Department of Biosystems Science and Engineering , ETH Zurich , 4058 Basel , Switzerland
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39
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Feng CJ, Dhayalan B, Tokmakoff A. Refinement of Peptide Conformational Ensembles by 2D IR Spectroscopy: Application to Ala‒Ala‒Ala. Biophys J 2019; 114:2820-2832. [PMID: 29925019 DOI: 10.1016/j.bpj.2018.05.003] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2018] [Revised: 04/27/2018] [Accepted: 05/02/2018] [Indexed: 10/28/2022] Open
Abstract
Characterizing ensembles of intrinsically disordered proteins is experimentally challenging because of the ill-conditioned nature of ensemble determination with limited data and the intrinsic fast dynamics of the conformational ensemble. Amide I two-dimensional infrared (2D IR) spectroscopy has picosecond time resolution to freeze structural ensembles as needed for probing disordered-protein ensembles and conformational dynamics. Also, developments in amide I computational spectroscopy now allow a quantitative and direct prediction of amide I spectra based on conformational distributions drawn from molecular dynamics simulations, providing a route to ensemble refinement against experimental spectra. We performed a Bayesian ensemble refinement method on Ala-Ala-Ala against isotope-edited Fourier-transform infrared spectroscopy and 2D IR spectroscopy and tested potential factors affecting the quality of ensemble refinements. We found that isotope-edited 2D IR spectroscopy provides a stringent constraint on Ala-Ala-Ala conformations and returns consistent conformational ensembles with the dominant ppII conformer across varying prior distributions from many molecular dynamics force fields and water models. The dominant factor influencing ensemble refinements is the systematic frequency uncertainty from spectroscopic maps. However, the uncertainty of conformer populations can be significantly reduced by incorporating 2D IR spectra in addition to traditional Fourier-transform infrared spectra. Bayesian ensemble refinement against isotope-edited 2D IR spectroscopy thus provides a route to probe equilibrium-complex protein ensembles and potentially nonequilibrium conformational dynamics.
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Affiliation(s)
- Chi-Jui Feng
- Department of Chemistry, James Franck Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois
| | - Balamurugan Dhayalan
- Department of Chemistry, James Franck Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois
| | - Andrei Tokmakoff
- Department of Chemistry, James Franck Institute and Institute for Biophysical Dynamics, University of Chicago, Chicago, Illinois.
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40
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Provasi D. Ligand-Binding Calculations with Metadynamics. METHODS IN MOLECULAR BIOLOGY (CLIFTON, N.J.) 2019; 2022:233-253. [PMID: 31396906 DOI: 10.1007/978-1-4939-9608-7_10] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Abstract
All-atom molecular dynamics simulations can capture the dynamic degrees of freedom that characterize molecular recognition, the knowledge of which constitutes the cornerstone of rational approaches to drug design and optimization. In particular, enhanced sampling algorithms, such as metadynamics, are powerful tools to dramatically reduce the computational cost required for a mechanistic description of the binding process. Here, we describe the essential details characterizing these simulation strategies, focusing on the critical step of identifying suitable reaction coordinates, as well as on the different analysis algorithms to estimate binding affinity and residence times. We conclude with a survey of published applications that provides explicit examples of successful simulations for several targets.
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Affiliation(s)
- Davide Provasi
- Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, NY, USA.
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41
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Abstract
Most current molecular dynamics simulation and analysis methods rely on the idea that the molecular system can be represented by a single global state (e.g., a Markov state in a Markov state model [MSM]). In this approach, molecules can be extensively sampled and analyzed when they only possess a few metastable states, such as small- to medium-sized proteins. However, this approach breaks down in frustrated systems and in large protein assemblies, where the number of global metastable states may grow exponentially with the system size. To address this problem, we here introduce dynamic graphical models (DGMs) that describe molecules as assemblies of coupled subsystems, akin to how spins interact in the Ising model. The change of each subsystem state is only governed by the states of itself and its neighbors. DGMs require fewer parameters than MSMs or other global state models; in particular, we do not need to observe all global system configurations to characterize them. Therefore, DGMs can predict previously unobserved molecular configurations. As a proof of concept, we demonstrate that DGMs can faithfully describe molecular thermodynamics and kinetics and predict previously unobserved metastable states for Ising models and protein simulations.
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Affiliation(s)
- Simon Olsson
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany;
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany;
- Department of Physics, Freie Universität Berlin, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, TX 77005
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42
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Hays JM, Cafiso DS, Kasson PM. Hybrid Refinement of Heterogeneous Conformational Ensembles Using Spectroscopic Data. J Phys Chem Lett 2019; 10:3410-3414. [PMID: 31181934 PMCID: PMC6605767 DOI: 10.1021/acs.jpclett.9b01407] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
Multistructured biomolecular systems play crucial roles in a wide variety of cellular processes but have resisted traditional methods of structure determination, which often resolve only a few low-energy states. High-resolution structure determination using experimental methods that yield distributional data remains extremely difficult, especially when the underlying conformational ensembles are quite heterogeneous. We have therefore developed a method to integrate sparse, multimultimodal spectroscopic data to obtain high-resolution estimates of conformational ensembles. We have tested our method by incorporating double electron-electron resonance data on the soluble N-ethylmaleimide-sensitive factor attachment receptor (SNARE) protein syntaxin-1a into biased molecular dynamics simulations. We find that our method substantially outperforms existing state-of-the-art methods in capturing syntaxin's open-closed conformational equilibrium and further yields new conformational states that are consistent with experimental data and may help in understanding syntaxin's function. Our improved methods for refining heterogeneous conformational ensembles from spectroscopic data will greatly accelerate the structural understanding of such systems.
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Affiliation(s)
- Jennifer M. Hays
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, 22903
- Department of Molecular Physiology and Biophysics, University of Virginia, Charlottesville, VA, 22903
| | - David S. Cafiso
- Department of Molecular Physiology and Biophysics, University of Virginia, Charlottesville, VA, 22903
- Department of Chemistry, University of Virginia, Charlottesville, VA, 22903
| | - Peter M. Kasson
- Department of Biomedical Engineering, University of Virginia, Charlottesville, VA, 22903
- Department of Molecular Physiology and Biophysics, University of Virginia, Charlottesville, VA, 22903
- Science for Life Laboratory, Department of Cell and Molecular Biology, Uppsala University, 75124 Uppsala,
Sweden
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43
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Chen S, Wiewiora RP, Meng F, Babault N, Ma A, Yu W, Qian K, Hu H, Zou H, Wang J, Fan S, Blum G, Pittella-Silva F, Beauchamp KA, Tempel W, Jiang H, Chen K, Skene RJ, Zheng YG, Brown PJ, Jin J, Luo C, Chodera JD, Luo M. The dynamic conformational landscape of the protein methyltransferase SETD8. eLife 2019; 8:45403. [PMID: 31081496 PMCID: PMC6579520 DOI: 10.7554/elife.45403] [Citation(s) in RCA: 26] [Impact Index Per Article: 5.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/22/2019] [Accepted: 05/08/2019] [Indexed: 12/27/2022] Open
Abstract
Elucidating the conformational heterogeneity of proteins is essential for understanding protein function and developing exogenous ligands. With the rapid development of experimental and computational methods, it is of great interest to integrate these approaches to illuminate the conformational landscapes of target proteins. SETD8 is a protein lysine methyltransferase (PKMT), which functions in vivo via the methylation of histone and nonhistone targets. Utilizing covalent inhibitors and depleting native ligands to trap hidden conformational states, we obtained diverse X-ray structures of SETD8. These structures were used to seed distributed atomistic molecular dynamics simulations that generated a total of six milliseconds of trajectory data. Markov state models, built via an automated machine learning approach and corroborated experimentally, reveal how slow conformational motions and conformational states are relevant to catalysis. These findings provide molecular insight on enzymatic catalysis and allosteric mechanisms of a PKMT via its detailed conformational landscape. Our cells contain thousands of proteins that perform many different tasks. Such tasks often involve significant changes in the shape of a protein that allow it to interact with other proteins or ligands. Understanding these shape changes can be an essential step for predicting and manipulating how proteins work or designing new drugs. Some changes in protein shape happen quickly, whereas others take longer. Existing experimental approaches generally only capture some, but not all, of the different shapes an individual protein adopts. A family of proteins known as protein lysine methyltransferases (PKMTs) help to regulate the activities of other proteins by adding small tags called methyl groups to specific positions on their target proteins. PKMTs play important roles in many life processes including in activating genes, maintaining stem cells and controlling how organs develop. It is important for cells to properly control the activity of PKMTs because too much, or too little, activity can promote cancers and neurological diseases. For example, genetic mutations that increase the levels of a PKMT known as SETD8 appear to promote the progression of some breast cancers and childhood leukemia. There is a pressing need to develop new drugs that can inhibit SETD8 and other PKMTs in human patients. However, these efforts are hindered by the lack of understanding of exactly how the shape of PKMT proteins change as they operate in cells. Chen, Wiewiora et al. used a technique called X-ray crystallography to generate structural models of the human SETD8 protein in the presence or absence of native or foreign ligands. These models were used to develop computer simulations of how the shape of SETD8 changes as it operates. Further computational analysis and laboratory experiments revealed how slow changes in the shape of SETD8 contribute to the ability of the protein to attach methyl groups to other proteins. This work is a significant stepping-stone to developing a complete model of how the SETD8 protein works, as well as understanding how genetic mutations may affect the protein’s role in the body. The next step is to refine the model by integrating data from other approaches including biophysical models and mathematical calculations of the energy associated with the shape changes, with a long-term goal to better understand and then manipulate the function of SETD8.
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Affiliation(s)
- Shi Chen
- Tri-Institutional PhD Program in Chemical Biology, Memorial Sloan Kettering Cancer Center, New York, United States.,Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Rafal P Wiewiora
- Tri-Institutional PhD Program in Chemical Biology, Memorial Sloan Kettering Cancer Center, New York, United States.,Computational and Systems Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Fanwang Meng
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China
| | - Nicolas Babault
- Mount Sinai Center for Therapeutics Discovery, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Oncological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Tisch Cancer Institute, Icahn School of Medicine at Mount Sinai, New York, United States
| | - Anqi Ma
- Mount Sinai Center for Therapeutics Discovery, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Oncological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Tisch Cancer Institute, Icahn School of Medicine at Mount Sinai, New York, United States
| | - Wenyu Yu
- Structural Genomics Consortium, University of Toronto, Toronto, Canada
| | - Kun Qian
- Department of Pharmaceutical and Biomedical Sciences, University of Georgia, Athens, United States
| | - Hao Hu
- Department of Pharmaceutical and Biomedical Sciences, University of Georgia, Athens, United States
| | - Hua Zou
- Takeda California, Science Center Drive, San Diego, United States
| | - Junyi Wang
- Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Shijie Fan
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Gil Blum
- Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Fabio Pittella-Silva
- Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Kyle A Beauchamp
- Computational and Systems Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Wolfram Tempel
- Structural Genomics Consortium, University of Toronto, Toronto, Canada
| | - Hualiang Jiang
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Kaixian Chen
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China.,University of Chinese Academy of Sciences, Beijing, China
| | - Robert J Skene
- Takeda California, Science Center Drive, San Diego, United States
| | - Yujun George Zheng
- Department of Pharmaceutical and Biomedical Sciences, University of Georgia, Athens, United States
| | - Peter J Brown
- Structural Genomics Consortium, University of Toronto, Toronto, Canada
| | - Jian Jin
- Mount Sinai Center for Therapeutics Discovery, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Pharmacological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Department of Oncological Sciences, Icahn School of Medicine at Mount Sinai, New York, United States.,Tisch Cancer Institute, Icahn School of Medicine at Mount Sinai, New York, United States
| | - Cheng Luo
- Drug Discovery and Design Center, CAS Key Laboratory of Receptor Research, State Key Laboratory of Drug Research, Shanghai Institute of Materia Medica, Chinese Academy of Sciences, Shanghai, China.,University of Chinese Academy of Sciences, Beijing, China
| | - John D Chodera
- Computational and Systems Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States
| | - Minkui Luo
- Chemical Biology Program, Memorial Sloan Kettering Cancer Center, New York, United States.,Program of Pharmacology, Weill Cornell Medical College of Cornell University, New York, United States
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44
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Sengupta U, Carballo-Pacheco M, Strodel B. Automated Markov state models for molecular dynamics simulations of aggregation and self-assembly. J Chem Phys 2019; 150:115101. [DOI: 10.1063/1.5083915] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Affiliation(s)
- Ushnish Sengupta
- Institute of Complex Systems: Structural Biochemistry (ICS-6), Forschungszentrum Jülich, 52425 Jülich, Germany
- Department of Engineering, University of Cambridge, Cambridge CB2 1PZ, United Kingdom
| | - Martín Carballo-Pacheco
- Institute of Complex Systems: Structural Biochemistry (ICS-6), Forschungszentrum Jülich, 52425 Jülich, Germany
- AICES Graduate School, RWTH Aachen University, Schinkelstraße 2, 52062 Aachen, Germany
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Birgit Strodel
- Institute of Complex Systems: Structural Biochemistry (ICS-6), Forschungszentrum Jülich, 52425 Jülich, Germany
- Institute of Theoretical and Computational Chemistry, Heinrich Heine University Düsseldorf, 40225 Düsseldorf, Germany
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45
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Dixit PD. Introducing User-Prescribed Constraints in Markov Chains for Nonlinear Dimensionality Reduction. Neural Comput 2019; 31:980-997. [PMID: 30883279 DOI: 10.1162/neco_a_01184] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Stochastic kernel-based dimensionality-reduction approaches have become popular in the past decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified by the kernel through row normalization. However, in many cases, it is desirable to impose user-specified stationary-state and dynamical constraints on the Markov chain. Unfortunately, no systematic framework exists to impose such user-defined constraints. Here, based on our previous work on inference of Markov models, we introduce a path entropy maximization based approach to derive the transition probabilities of Markov chains using a kernel and additional user-specified constraints. We illustrate the usefulness of these Markov chains with examples.
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Affiliation(s)
- Purushottam D Dixit
- Department of Systems Biology, Columbia University, New York, NY 10032, U.S.A.
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46
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Nussinov R, Tsai CJ, Shehu A, Jang H. Computational Structural Biology: Successes, Future Directions, and Challenges. Molecules 2019; 24:molecules24030637. [PMID: 30759724 PMCID: PMC6384756 DOI: 10.3390/molecules24030637] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/11/2019] [Revised: 02/05/2019] [Accepted: 02/10/2019] [Indexed: 02/06/2023] Open
Abstract
Computational biology has made powerful advances. Among these, trends in human health have been uncovered through heterogeneous 'big data' integration, and disease-associated genes were identified and classified. Along a different front, the dynamic organization of chromatin is being elucidated to gain insight into the fundamental question of genome regulation. Powerful conformational sampling methods have also been developed to yield a detailed molecular view of cellular processes. when combining these methods with the advancements in the modeling of supramolecular assemblies, including those at the membrane, we are finally able to get a glimpse into how cells' actions are regulated. Perhaps most intriguingly, a major thrust is on to decipher the mystery of how the brain is coded. Here, we aim to provide a broad, yet concise, sketch of modern aspects of computational biology, with a special focus on computational structural biology. We attempt to forecast the areas that computational structural biology will embrace in the future and the challenges that it may face. We skirt details, highlight successes, note failures, and map directions.
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Affiliation(s)
- Ruth Nussinov
- Computational Structural Biology Section, Basic Science Program, Frederick National Laboratory for Cancer Research, Frederick, MD 21702, USA.
- Sackler Institute of Molecular Medicine, Department of Human Genetics and Molecular Medicine, Sackler School of Medicine, Tel Aviv University, Tel Aviv 69978, Israel.
| | - Chung-Jung Tsai
- Computational Structural Biology Section, Basic Science Program, Frederick National Laboratory for Cancer Research, Frederick, MD 21702, USA.
| | - Amarda Shehu
- Departments of Computer Science, Department of Bioengineering, and School of Systems Biology, George Mason University, Fairfax, VA 22030, USA.
| | - Hyunbum Jang
- Computational Structural Biology Section, Basic Science Program, Frederick National Laboratory for Cancer Research, Frederick, MD 21702, USA.
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47
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Mittal S, Shukla D. Maximizing Kinetic Information Gain of Markov State Models for Optimal Design of Spectroscopy Experiments. J Phys Chem B 2018; 122:10793-10805. [DOI: 10.1021/acs.jpcb.8b07076] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
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48
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Selvam B, Mittal S, Shukla D. Free Energy Landscape of the Complete Transport Cycle in a Key Bacterial Transporter. ACS CENTRAL SCIENCE 2018; 4:1146-1154. [PMID: 30276247 PMCID: PMC6161048 DOI: 10.1021/acscentsci.8b00330] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/24/2018] [Indexed: 05/21/2023]
Abstract
PepTSo is a proton-coupled bacterial symporter, from the major facilitator superfamily (MFS), which transports di-/tripeptide molecules. The recently obtained crystal structure of PepTSo provides an unprecedented opportunity to gain an understanding of functional insights of the substrate transport mechanism. Binding of the proton and peptide molecule induces conformational changes into occluded (OC) and outward-facing (OF) states, which we are able to characterize using molecular dynamics (MD) simulations. The structural knowledge of the OC and OF state is important to fully understand the major energy barrier associated with the transport cycle. In order to gain functional insight into the interstate dynamics, we performed extensive all atom MD simulations. The Markov state model was constructed to identify the free energy barriers between the states, and kinetic information on intermediate pathways was obtained using the transition pathway theory (TPT). TPT shows that the OF state is obtained by the movement of TM1 and TM7 at the extracellular side approximately 12-16 Å away from each other, and the inward movement of TM4 and TM10 at the intracellular halves to 3-4 Å characterizes the OC state. Helix distance distributions obtained from MD simulations were compared with experimental double electron-electron resonance spectroscopy and were found to be in excellent agreement with previous studies. We also predicted the optimal positions for placement of methane thiosulfonate spin label probes to capture the slowest protein dynamics. Our finding sheds light on the conformational cycle of this key membrane transporter and the functional relationships between the multiple intermediate states.
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Affiliation(s)
- Balaji Selvam
- Department of Chemical and Biomolecular Engineering, Center for Biophysics and Quantitative
Biology, and Department
of Plant Biology, University of Illinois
at Urbana-Champaign, Urbana, Illinois, United States
| | - Shriyaa Mittal
- Department of Chemical and Biomolecular Engineering, Center for Biophysics and Quantitative
Biology, and Department
of Plant Biology, University of Illinois
at Urbana-Champaign, Urbana, Illinois, United States
| | - Diwakar Shukla
- Department of Chemical and Biomolecular Engineering, Center for Biophysics and Quantitative
Biology, and Department
of Plant Biology, University of Illinois
at Urbana-Champaign, Urbana, Illinois, United States
- E-mail:
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49
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Vögeli B, Vugmeyster L. Distance-independent Cross-correlated Relaxation and Isotropic Chemical Shift Modulation in Protein Dynamics Studies. Chemphyschem 2018; 20:178-196. [PMID: 30110510 DOI: 10.1002/cphc.201800602] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/22/2018] [Indexed: 01/09/2023]
Abstract
Cross-correlated relaxation (CCR) in multiple-quantum coherences differs from other relaxation phenomena in its theoretical ability to be mediated across an infinite distance. The two interfering relaxation mechanisms may be dipolar interactions, chemical shift anisotropies, chemical shift modulations or quadrupolar interactions. These properties make multiple-quantum CCR an attractive probe for structure and dynamics of biomacromolecules not accessible from other measurements. Here, we review the use of multiple-quantum CCR measurements in dynamics studies of proteins. We compile a list of all experiments proposed for CCR rate measurements, provide an overview of the theory with a focus on protein dynamics, and present applications to various protein systems.
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Affiliation(s)
- Beat Vögeli
- Department of Biochemistry and Molecular Genetics, University of Colorado at Denver, 12801 East 17th Avenue, Aurora, CO, 80045, United States
| | - Liliya Vugmeyster
- Department of Chemistry, University of Colorado at Denver, 1201 Laurimer Street Denver, CO, 80204, United States
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50
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Bottaro S, Lindorff-Larsen K. Biophysical experiments and biomolecular simulations: A perfect match? Science 2018; 361:355-360. [DOI: 10.1126/science.aat4010] [Citation(s) in RCA: 135] [Impact Index Per Article: 22.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Abstract
A fundamental challenge in biological research is achieving an atomic-level description and mechanistic understanding of the function of biomolecules. Techniques for biomolecular simulations have undergone substantial developments, and their accuracy and scope have expanded considerably. Progress has been made through an increasingly tight integration of experiments and simulations, with experiments being used to refine simulations and simulations used to interpret experiments. Here we review the underpinnings of this progress, including methods for more efficient conformational sampling, accuracy of the physical models used, and theoretical approaches to integrate experiments and simulations. These developments are enabling detailed studies of complex biomolecular assemblies.
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