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Structural ensembles of disordered proteins from hierarchical chain growth and simulation. Curr Opin Struct Biol 2023; 78:102501. [PMID: 36463772 DOI: 10.1016/j.sbi.2022.102501] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/31/2022] [Revised: 10/26/2022] [Accepted: 10/28/2022] [Indexed: 12/03/2022]
Abstract
Disordered proteins and nucleic acids play key roles in cellular function and disease. Here, we review recent advances in the computational exploration of the conformational dynamics of flexible biomolecules. While atomistic molecular dynamics (MD) simulation has seen a lot of improvement in recent years, large-scale computing resources and careful validation are required to simulate full-length disordered biopolymers in solution. As a computationally efficient alternative, hierarchical chain growth (HCG) combines pre-sampled chain fragments in a statistically reproducible manner into ensembles of full-length atomically detailed biomolecular structures. Experimental data can be integrated during and after chain assembly. Applications to the neurodegeneration-linked proteins α-synuclein, tau, and TDP-43, including as condensate, illustrate the use of HCG. We conclude by highlighting the emerging connections to AI-based structural modeling including AlphaFold2.
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2
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Stelzl L, Pietrek LM, Holla A, Oroz J, Sikora M, Köfinger J, Schuler B, Zweckstetter M, Hummer G. Global Structure of the Intrinsically Disordered Protein Tau Emerges from Its Local Structure. JACS AU 2022; 2:673-686. [PMID: 35373198 PMCID: PMC8970000 DOI: 10.1021/jacsau.1c00536] [Citation(s) in RCA: 34] [Impact Index Per Article: 17.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Indexed: 05/13/2023]
Abstract
The paradigmatic disordered protein tau plays an important role in neuronal function and neurodegenerative diseases. To disentangle the factors controlling the balance between functional and disease-associated conformational states, we build a structural ensemble of the tau K18 fragment containing the four pseudorepeat domains involved in both microtubule binding and amyloid fibril formation. We assemble 129-residue-long tau K18 chains with atomic detail from an extensive fragment library constructed with molecular dynamics simulations. We introduce a reweighted hierarchical chain growth (RHCG) algorithm that integrates experimental data reporting on the local structure into the assembly process in a systematic manner. By combining Bayesian ensemble refinement with importance sampling, we obtain well-defined ensembles and overcome the problem of exponentially varying weights in the integrative modeling of long-chain polymeric molecules. The resulting tau K18 ensembles capture nuclear magnetic resonance (NMR) chemical shift and J-coupling measurements. Without further fitting, we achieve very good agreement with measurements of NMR residual dipolar couplings. The good agreement with experimental measures of global structure such as single-molecule Förster resonance energy transfer (FRET) efficiencies is improved further by ensemble refinement. By comparing wild-type and mutant ensembles, we show that pathogenic single-point P301L, P301S, and P301T mutations shift the population from the turn-like conformations of the functional microtubule-bound state to the extended conformations of disease-associated tau fibrils. RHCG thus provides us with an atomically detailed view of the population equilibrium between functional and aggregation-prone states of tau K18, and demonstrates that global structural characteristics of this intrinsically disordered protein emerge from its local structure.
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Affiliation(s)
- Lukas
S. Stelzl
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
- Faculty
of Biology, Johannes Gutenberg University
Mainz, Gresemundweg 2, 55128 Mainz, Germany
- KOMET 1, Institute of Physics, Johannes
Gutenberg University Mainz, 55099 Mainz, Germany
- Institute of Molecular Biology (IMB), 55128 Mainz, Germany
| | - Lisa M. Pietrek
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
| | - Andrea Holla
- Department
of Biochemistry, University of Zurich, 8057 Zurich, Switzerland
| | - Javier Oroz
- German
Center for Neurodegenerative Diseases (DZNE), von-Siebold-Str. 3a, 37075 Göttingen, Germany
- Rocasolano
Institute for Physical Chemistry, CSIC, Serrano 119, 28006 Madrid, Spain
| | - Mateusz Sikora
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
- Faculty
of Physics, University of Vienna, Kolingasse 14-16, 1090 Vienna, Austria
| | - Jürgen Köfinger
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
| | - Benjamin Schuler
- Department
of Biochemistry, University of Zurich, 8057 Zurich, Switzerland
- Department
of Physics, University of Zurich, 8057 Zurich, Switzerland
| | - Markus Zweckstetter
- German
Center for Neurodegenerative Diseases (DZNE), von-Siebold-Str. 3a, 37075 Göttingen, Germany
- Department
for NMR-based Structural Biology, Max Planck
Institute for Multidisciplinary Sciences, Am Faßberg 11, 37077 Göttingen, Germany
| | - Gerhard Hummer
- Department
of Theoretical Biophysics, Max Planck Institute
of Biophysics, Max-von-Laue-Straße 3, 60438 Frankfurt am Main, Germany
- Institute
for Biophysics, Goethe University Frankfurt, Max-von-Laue-Straße 9, 60438 Frankfurt am Main, Germany
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3
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Spiriti J, Subramanian SR, Palli R, Wu M, Zuckerman DM. Middle-way flexible docking: Pose prediction using mixed-resolution Monte Carlo in estrogen receptor α. PLoS One 2019; 14:e0215694. [PMID: 31013302 PMCID: PMC6478315 DOI: 10.1371/journal.pone.0215694] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/31/2019] [Accepted: 04/06/2019] [Indexed: 12/17/2022] Open
Abstract
There is a vast gulf between the two primary strategies for simulating protein-ligand interactions. Docking methods significantly limit or eliminate protein flexibility to gain great speed at the price of uncontrolled inaccuracy, whereas fully flexible atomistic molecular dynamics simulations are expensive and often suffer from limited sampling. We have developed a flexible docking approach geared especially for highly flexible or poorly resolved targets based on mixed-resolution Monte Carlo (MRMC), which is intended to offer a balance among speed, protein flexibility, and sampling power. The binding region of the protein is treated with a standard atomistic force field, while the remainder of the protein is modeled at the residue level with a Gō model that permits protein flexibility while saving computational cost. Implicit solvation is used. Here we assess three facets of the MRMC approach with implications for other docking studies: (i) the role of receptor flexibility in cross-docking pose prediction; (ii) the use of non-equilibrium candidate Monte Carlo (NCMC) and (iii) the use of pose-clustering in scoring. We examine 61 co-crystallized ligands of estrogen receptor α, an important cancer target known for its flexibility. We also compare the performance of the MRMC approach with Autodock smina. Adding protein flexibility, not surprisingly, leads to significantly lower total energies and stronger interactions between protein and ligand, but notably we document the important role of backbone flexibility in the improvement. The improved backbone flexibility also leads to improved performance relative to smina. Somewhat unexpectedly, our implementation of NCMC leads to only modestly improved sampling of ligand poses. Overall, the addition of protein flexibility improves the performance of docking, as measured by energy-ranked poses, but we do not find significant improvements based on cluster information or the use of NCMC. We discuss possible improvements for the model including alternative coarse-grained force fields, improvements to the treatment of solvation, and adding additional types of NCMC moves.
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Affiliation(s)
- Justin Spiriti
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR 97239, United States of America
| | - Sundar Raman Subramanian
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA 15260, United States of America
| | - Rohith Palli
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA 15260, United States of America
| | - Maria Wu
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, PA 15260, United States of America
| | - Daniel M. Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, OR 97239, United States of America
- * E-mail:
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4
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Donovan-Maiye RM, Langmead CJ, Zuckerman DM. Systematic Testing of Belief-Propagation Estimates for Absolute Free Energies in Atomistic Peptides and Proteins. J Chem Theory Comput 2018; 14:426-443. [PMID: 29185777 PMCID: PMC5933972 DOI: 10.1021/acs.jctc.7b00775] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023]
Abstract
Motivated by the extremely high computing costs associated with estimates of free energies for biological systems using molecular simulations, we further the exploration of existing "belief propagation" (BP) algorithms for fixed-backbone peptide and protein systems. The precalculation of pairwise interactions among discretized libraries of side-chain conformations, along with representation of protein side chains as nodes in a graphical model, enables direct application of the BP approach, which requires only ∼1 s of single-processor run time after the precalculation stage. We use a "loopy BP" algorithm, which can be seen as an approximate generalization of the transfer-matrix approach to highly connected (i.e., loopy) graphs, and it has previously been applied to protein calculations. We examine the application of loopy BP to several peptides as well as the binding site of the T4 lysozyme L99A mutant. The present study reports on (i) the comparison of the approximate BP results with estimates from unbiased estimators based on the Amber99SB force field; (ii) investigation of the effects of varying library size on BP predictions; and (iii) a theoretical discussion of the discretization effects that can arise in BP calculations. The data suggest that, despite their approximate nature, BP free-energy estimates are highly accurate-indeed, they never fall outside confidence intervals from unbiased estimators for the systems where independent results could be obtained. Furthermore, we find that libraries of sufficiently fine discretization (which diminish library-size sensitivity) can be obtained with standard computing resources in most cases. Altogether, the extremely low computing times and accurate results suggest the BP approach warrants further study.
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Affiliation(s)
| | - Christopher J Langmead
- Computational Biology Department, Carnegie Mellon University , Pittsburgh, Pennsylvania 15213, United States
| | - Daniel M Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University , Portland, Oregon 97239, United States
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5
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Mittal A, Lyle N, Harmon TS, Pappu RV. Hamiltonian Switch Metropolis Monte Carlo Simulations for Improved Conformational Sampling of Intrinsically Disordered Regions Tethered to Ordered Domains of Proteins. J Chem Theory Comput 2014; 10:3550-3562. [PMID: 25136274 PMCID: PMC4132852 DOI: 10.1021/ct5002297] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2014] [Indexed: 02/06/2023]
Abstract
![]()
There
is growing interest in the topic of intrinsically disordered
proteins (IDPs). Atomistic Metropolis Monte Carlo (MMC) simulations
based on novel implicit solvation models have yielded useful insights
regarding sequence-ensemble relationships for IDPs modeled as autonomous
units. However, a majority of naturally occurring IDPs are tethered
to ordered domains. Tethering introduces additional energy scales
and this creates the challenge of broken ergodicity for standard MMC
sampling or molecular dynamics that cannot be readily alleviated by
using generalized tempering methods. We have designed, deployed, and
tested our adaptation of the Nested Markov Chain Monte Carlo sampling
algorithm. We refer to our adaptation as Hamiltonian Switch Metropolis
Monte Carlo (HS-MMC) sampling. In this method, transitions out of
energetic traps are enabled by the introduction of an auxiliary Markov
chain that draws conformations for the disordered region from a Boltzmann
distribution that is governed by an alternative potential function
that only includes short-range steric repulsions and conformational
restraints on the ordered domain. We show using multiple, independent
runs that the HS-MMC method yields conformational distributions that
have similar and reproducible statistical properties, which is in
direct contrast to standard MMC for equivalent amounts of sampling.
The method is efficient and can be deployed for simulations of a range
of biologically relevant disordered regions that are tethered to ordered
domains.
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Affiliation(s)
- Anuradha Mittal
- Department of Biomedical Engineering and Center for Biological Systems Engineering and Department of Physics, Washington University in St. Louis One Brookings Drive , Campus Box 1097, St. Louis, Missouri 63130, United States
| | - Nicholas Lyle
- Department of Biomedical Engineering and Center for Biological Systems Engineering and Department of Physics, Washington University in St. Louis One Brookings Drive , Campus Box 1097, St. Louis, Missouri 63130, United States
| | - Tyler S Harmon
- Department of Biomedical Engineering and Center for Biological Systems Engineering and Department of Physics, Washington University in St. Louis One Brookings Drive , Campus Box 1097, St. Louis, Missouri 63130, United States
| | - Rohit V Pappu
- Department of Biomedical Engineering and Center for Biological Systems Engineering and Department of Physics, Washington University in St. Louis One Brookings Drive , Campus Box 1097, St. Louis, Missouri 63130, United States
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Roberts CC, Chang CEA. Ligand Binding Pathway Elucidation for Cryptophane Host-Guest Complexes. J Chem Theory Comput 2013; 9:2010-9. [PMID: 26583550 DOI: 10.1021/ct301023m] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
Modeling binding pathways can provide insight into molecular recognition, including kinetic mechanisms, barriers to binding, and gating effects. This work represents a novel computational approach, Hopping Minima, for the determination of conformational transitions of single molecules as well as binding pathways for molecular complexes. The method begins by thoroughly sampling a set of conformational minima for a molecular system. The natural motions of the system are modeled using the normal modes of the sampled minima. The natural motions are utilized to connect conformational minima and are finally combined to form association/binding pathways in the case of molecular complexes. We provide an implementation and example application of the method using alanine dipeptide and a set of chemical host-guest systems: two cryptophane hosts with two guest cations, trimethylammonium and tetramethylammonium. Our results demonstrate that conformational transitions can be modeled and extended to find binding pathways as well as energetic information relevant to the minimum conformations involved. This approach has advantages over simulation-based methods for studying systems with slow binding processes and can help design molecules with preferred binding kinetics.
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Affiliation(s)
- Christopher C Roberts
- Department of Chemistry, University of California, Riverside, California 92521, United States
| | - Chia-En A Chang
- Department of Chemistry, University of California, Riverside, California 92521, United States
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7
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Mamonov AB, Lettieri S, Ding Y, Sarver JL, Palli R, Cunningham TF, Saxena S, Zuckerman DM. Tunable, mixed-resolution modeling using library-based Monte Carlo and graphics processing units. J Chem Theory Comput 2012; 8:2921-2929. [PMID: 23162384 PMCID: PMC3496292 DOI: 10.1021/ct300263z] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Building on our recently introduced library-based Monte Carlo (LBMC) approach, we describe a flexible protocol for mixed coarse-grained (CG)/all-atom (AA) simulation of proteins and ligands. In the present implementation of LBMC, protein side chain configurations are pre-calculated and stored in libraries, while bonded interactions along the backbone are treated explicitly. Because the AA side chain coordinates are maintained at minimal run-time cost, arbitrary sites and interaction terms can be turned on to create mixed-resolution models. For example, an AA region of interest such as a binding site can be coupled to a CG model for the rest of the protein. We have additionally developed a hybrid implementation of the generalized Born/surface area (GBSA) implicit solvent model suitable for mixed-resolution models, which in turn was ported to a graphics processing unit (GPU) for faster calculation. The new software was applied to study two systems: (i) the behavior of spin labels on the B1 domain of protein G (GB1) and (ii) docking of randomly initialized estradiol configurations to the ligand binding domain of the estrogen receptor (ERα). The performance of the GPU version of the code was also benchmarked in a number of additional systems.
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8
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Lettieri S, Zuckerman DM. Accelerating molecular Monte Carlo simulations using distance and orientation-dependent energy tables: tuning from atomistic accuracy to smoothed "coarse-grained" models. J Comput Chem 2011; 33:268-75. [PMID: 22120971 DOI: 10.1002/jcc.21970] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/24/2011] [Accepted: 09/25/2011] [Indexed: 11/09/2022]
Abstract
Typically, the most time consuming part of any atomistic molecular simulation is the repeated calculation of distances, energies, and forces between pairs of atoms. However, many molecules contain nearly rigid multi-atom groups such as rings and other conjugated moieties, whose rigidity can be exploited to significantly speed-up computations. The availability of GB-scale random-access memory (RAM) offers the possibility of tabulation (precalculation) of distance- and orientation-dependent interactions among such rigid molecular bodies. Here, we perform an investigation of this energy tabulation approach for a fluid of atomistic-but rigid-benzene molecules at standard temperature and density. In particular, using O(1) GB of RAM, we construct an energy look-up table, which encompasses the full range of allowed relative positions and orientations between a pair of whole molecules. We obtain a hardware-dependent speed-up of a factor of 24-50 as compared to an ordinary ("exact") Monte Carlo simulation and find excellent agreement between energetic and structural properties. Second, we examine the somewhat reduced fidelity of results obtained using energy tables based on much less memory use. Third, the energy table serves as a convenient platform to explore potential energy smoothing techniques, akin to coarse-graining. Simulations with smoothed tables exhibit near atomistic accuracy while increasing diffusivity. The combined speed-up in sampling from tabulation and smoothing exceeds a factor of 100. For future applications, greater speed-ups can be expected for larger rigid groups, such as those found in biomolecules.
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Affiliation(s)
- Steven Lettieri
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
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