51
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Tian J, Wang L, Da LT. Atomic resolution of short-range sliding dynamics of thymine DNA glycosylase along DNA minor-groove for lesion recognition. Nucleic Acids Res 2021; 49:1278-1293. [PMID: 33469643 PMCID: PMC7897493 DOI: 10.1093/nar/gkaa1252] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2020] [Revised: 12/10/2020] [Accepted: 12/15/2020] [Indexed: 02/06/2023] Open
Abstract
Thymine DNA glycosylase (TDG), as a repair enzyme, plays essential roles in maintaining the genome integrity by correcting several mismatched/damaged nucleobases. TDG acquires an efficient strategy to search for the lesions among a vast number of cognate base pairs. Currently, atomic-level details of how TDG translocates along DNA as it approaches the lesion site and the molecular mechanisms of the interplay between TDG and DNA are still elusive. Here, by constructing the Markov state model based on hundreds of molecular dynamics simulations with an integrated simulation time of ∼25 μs, we reveal the rotation-coupled sliding dynamics of TDG along a 9 bp DNA segment containing one G·T mispair. We find that TDG translocates along DNA at a relatively faster rate when distant from the lesion site, but slows down as it approaches the target, accompanied by deeply penetrating into the minor-groove, opening up the mismatched base pair and significantly sculpturing the DNA shape. Moreover, the electrostatic interactions between TDG and DNA are found to be critical for mediating the TDG translocation. Notably, several uncharacterized TDG residues are identified to take part in regulating the conformational switches of TDG occurred in the site-transfer process, which warrants further experimental validations.
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Affiliation(s)
- Jiaqi Tian
- Key Laboratory of Systems Biomedicine (Ministry of Education), Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
| | - Lingyan Wang
- Key Laboratory of Systems Biomedicine (Ministry of Education), Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
| | - Lin-Tai Da
- Key Laboratory of Systems Biomedicine (Ministry of Education), Shanghai Center for Systems Biomedicine, Shanghai Jiao Tong University, 800 Dongchuan Road, Shanghai 200240, China
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52
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He Z, Paul F, Roux B. A critical perspective on Markov state model treatments of protein-protein association using coarse-grained simulations. J Chem Phys 2021; 154:084101. [PMID: 33639768 PMCID: PMC7902085 DOI: 10.1063/5.0039144] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Atomic-level information is essential to explain the specific interactions governing protein–protein recognition in terms of structure and dynamics. Of particular interest is a characterization of the time-dependent kinetic aspects of protein–protein association and dissociation. A powerful framework to characterize the dynamics of complex molecular systems is provided by Markov State Models (MSMs). The central idea is to construct a reduced stochastic model of the full system by defining a set of conformational featured microstates and determining the matrix of transition probabilities between them. While a MSM framework can sometimes be very effective, different combinations of input featurization and simulation methods can significantly affect the robustness and the quality of the information generated from MSMs in the context of protein association. Here, a systematic examination of a variety of MSMs methodologies is undertaken to clarify these issues. To circumvent the uncertainties caused by sampling issues, we use a simplified coarse-grained model of the barnase–barstar protein complex. A sensitivity analysis is proposed to identify the microstates of an MSM that contribute most to the error in conjunction with the transition-based reweighting analysis method for a more efficient and accurate MSM construction.
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Affiliation(s)
- Ziwei He
- Department of Chemistry, The University of Chicago, 5735 S Ellis Ave., Chicago, Illinois 60637, USA
| | - Fabian Paul
- Department of Biochemistry and Molecular Biology, The University of Chicago, 929 E. 57th Street W225, Chicago, Illinois 60637, USA
| | - Benoît Roux
- Department of Chemistry, The University of Chicago, 5735 S Ellis Ave., Chicago, Illinois 60637, USA
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53
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Jia Z, Chen J. Specific PIP 2 binding promotes calcium activation of TMEM16A chloride channels. Commun Biol 2021; 4:259. [PMID: 33637964 PMCID: PMC7910439 DOI: 10.1038/s42003-021-01782-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2020] [Accepted: 02/01/2021] [Indexed: 11/09/2022] Open
Abstract
TMEM16A is a widely expressed Ca2+-activated Cl− channel that regulates crucial physiological functions including fluid secretion, neuronal excitability, and smooth muscle contraction. There is a critical need to understand the molecular mechanisms of TMEM16A gating and regulation. However, high-resolution TMEM16A structures have failed to reveal an activated state with an unobstructed permeation pathway even with saturating Ca2+. This has been attributed to the requirement of PIP2 for preventing TMEM16A desensitization. Here, atomistic simulations show that specific binding of PIP2 to TMEM16A can lead to spontaneous opening of the permeation pathway in the Ca2+-bound state. The predicted activated state is highly consistent with a wide range of mutagenesis and functional data. It yields a maximal Cl− conductance of ~1 pS, similar to experimental estimates, and recapitulates the selectivity of larger SCN− over Cl−. The resulting molecular mechanism of activation provides a basis for understanding the interplay of multiple signals in controlling TMEM16A channel function. Chen and Jia investigate the synergistic regulating role of Ca2+ binding and the signaling lipid PIP2 in TMEM16A channel gating. Their study is significant as it provides new insights into the activated state of TMEM16A and highlights an example of functional importance of lipids in regulating membrane-associated proteins.
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Affiliation(s)
- Zhiguang Jia
- Department of Chemistry, University of Massachusetts, Amherst, MA, USA.,Department of Biochemistry and Molecular Biology, University of Massachusetts, Amherst, MA, USA
| | - Jianhan Chen
- Department of Chemistry, University of Massachusetts, Amherst, MA, USA. .,Department of Biochemistry and Molecular Biology, University of Massachusetts, Amherst, MA, USA.
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54
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Ahalawat N, Mondal J. An Appraisal of Computer Simulation Approaches in Elucidating Biomolecular Recognition Pathways. J Phys Chem Lett 2021; 12:633-641. [PMID: 33382941 DOI: 10.1021/acs.jpclett.0c02785] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
Computer simulation approaches in biomolecular recognition processes have come a long way. In this Perspective, we highlight a series of recent success stories in which computer simulations have played a remarkable role in elucidating the atomic resolution mechanism of kinetic processes of protein-ligand binding in a quantitative fashion. In particular, we show that a robust combination of unbiased simulation, harnessed by a high-fidelity computing environment, and Markov state modeling approaches has been instrumental in revealing novel protein-ligand recognition pathways in multiple systems. We also elucidate the role of recent developments in enhanced sampling approaches in providing the much-needed impetus in accelerating simulation of the ligand recognition process. We identify multiple key issues, including force fields and the sampling bottleneck, which are currently preventing the field from achieving quantitative reconstruction of experimental measurements. Finally, we suggest a possible way forward via adoption of multiscale approaches and coarse-grained simulations as next steps toward efficient elucidation of ligand binding kinetics.
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Affiliation(s)
- Navjeet Ahalawat
- Department of Molecular Biology, Biotechnology and Bioinformatics, Chaudhary Charan Singh, Haryana Agricultural University, Hisar 125004, India
| | - Jagannath Mondal
- Tata Institute of Fundamental Research, Center for Interdisciplinary Sciences, Hyderabad 500046, India
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55
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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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56
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Abstract
Molecular dynamics simulations can now routinely access the microsecond timescale, making feasible direct sampling of ligand association events. While Markov State Model (MSM) approaches offer a useful framework for analyzing such trajectory data to gain insight into binding mechanisms, accurate modeling of ligand association pathways and kinetics must be done carefully. We describe methods and good practices for constructing MSMs of ligand binding from unbiased trajectory data and discuss how to use time-lagged independent component analysis (tICA) to build informative models, using as an example recent simulation work to model the binding of phenylalanine to the regulatory ACT domain dimer of phenylalanine hydroxylase. We describe a variety of methods for estimating association rates from MSMs and discuss how to distinguish between conformational selection and induced-fit mechanisms using MSMs. In addition, we review some examples of MSMs constructed to elucidate the mechanisms by which p53 transactivation domain (TAD) and related peptides bind the oncoprotein MDM2.
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Affiliation(s)
- Yunhui Ge
- Department of Chemistry, Temple University, Philadelphia, PA, USA
| | - Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, PA, USA.
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57
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Pant S, Smith Z, Wang Y, Tajkhorshid E, Tiwary P. Confronting pitfalls of AI-augmented molecular dynamics using statistical physics. J Chem Phys 2020; 153:234118. [PMID: 33353347 PMCID: PMC7863682 DOI: 10.1063/5.0030931] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/25/2020] [Accepted: 11/29/2020] [Indexed: 12/31/2022] Open
Abstract
Artificial intelligence (AI)-based approaches have had indubitable impact across the sciences through the ability to extract relevant information from raw data. Recently, AI has also found use in enhancing the efficiency of molecular simulations, wherein AI derived slow modes are used to accelerate the simulation in targeted ways. However, while typical fields where AI is used are characterized by a plethora of data, molecular simulations, per construction, suffer from limited sampling and thus limited data. As such, the use of AI in molecular simulations can suffer from a dangerous situation where the AI-optimization could get stuck in spurious regimes, leading to incorrect characterization of the reaction coordinate (RC) for the problem at hand. When such an incorrect RC is then used to perform additional simulations, one could start to deviate progressively from the ground truth. To deal with this problem of spurious AI-solutions, here, we report a novel and automated algorithm using ideas from statistical mechanics. It is based on the notion that a more reliable AI-solution will be one that maximizes the timescale separation between slow and fast processes. To learn this timescale separation even from limited data, we use a maximum caliber-based framework. We show the applicability of this automatic protocol for three classic benchmark problems, namely, the conformational dynamics of a model peptide, ligand-unbinding from a protein, and folding/unfolding energy landscape of the C-terminal domain of protein G. We believe that our work will lead to increased and robust use of trustworthy AI in molecular simulations of complex systems.
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Affiliation(s)
- Shashank Pant
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, Department of Biochemistry, Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | | | | | - Emad Tajkhorshid
- NIH Center for Macromolecular Modeling and Bioinformatics, Beckman Institute for Advanced Science and Technology, Department of Biochemistry, Center for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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58
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Copperman J, Zuckerman DM. Accelerated Estimation of Long-Timescale Kinetics from Weighted Ensemble Simulation via Non-Markovian "Microbin" Analysis. J Chem Theory Comput 2020; 16:6763-6775. [PMID: 32990438 PMCID: PMC8045600 DOI: 10.1021/acs.jctc.0c00273] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Abstract
The weighted ensemble (WE) simulation strategy provides unbiased sampling of nonequilibrium processes, such as molecular folding or binding, but the extraction of rate constants relies on characterizing steady-state behavior. Unfortunately, WE simulations of sufficiently complex systems will not relax to steady state on observed simulation times. Here, we show that a postsimulation clustering of molecular configurations into "microbins" using methods developed in the Markov State Model (MSM) community can yield unbiased kinetics from WE data before steady-state convergence of the WE simulation itself. Because WE trajectories are directional and not equilibrium distributed, the history-augmented MSM (haMSM) formulation can be used, which yields the mean first-passage time (MFPT) without bias for arbitrarily small lag times. Accurate kinetics can be obtained while bypassing the often prohibitive convergence requirements of the nonequilibrium weighted ensemble. We validate the method in a simple diffusive process on a two-dimensional (2D) random energy landscape and then analyze atomistic protein folding simulations using WE molecular dynamics. We report significant progress toward the unbiased estimation of protein folding times and pathways, though key challenges remain.
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Affiliation(s)
- Jeremy Copperman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239, United States
| | - Daniel M Zuckerman
- Department of Biomedical Engineering, Oregon Health and Science University, Portland, Oregon 97239, United States
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59
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Wang X, Unarta IC, Cheung PPH, Huang X. Elucidating molecular mechanisms of functional conformational changes of proteins via Markov state models. Curr Opin Struct Biol 2020; 67:69-77. [PMID: 33126140 DOI: 10.1016/j.sbi.2020.10.005] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/29/2020] [Revised: 09/28/2020] [Accepted: 10/07/2020] [Indexed: 01/01/2023]
Abstract
Functional conformational changes of proteins can facilitate numerous biological events in cells. The Markov state model (MSM) built from molecular dynamics simulations provide a powerful approach to study them. We here introduce a protocol that is tailor-made for constructing MSMs to study the functional conformational changes of proteins. In this protocol, one of the important steps is to select proper molecular features that can collectively describe the slowest timescales of conformational changes of interest. We recommend spectral oASIS, the modified version of oASIS, as a promising approach for automatic feature selection. Recently developed deep learning methods could also serve efficient approaches for selecting features and finding collective variables. Using DNA repair enzymes and RNA polymerases as examples, we review recent applications of MSMs to elucidate molecular mechanisms of functional conformational changes. Finally, we discuss remaining challenges and future perspectives for constructing MSMs to study functional conformational changes of proteins.
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Affiliation(s)
- Xiaowei Wang
- The Hong Kong University of Science and Technology-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China; Department of Chemistry, Center of Systems Biology and Human Health, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Ilona Christy Unarta
- Bioengineering Graduate Program, The Hong Kong University of Science and Technology, Kowloon, 4Hong Kong Center for Neurodegenerative Diseases, Hong Kong
| | - Peter Pak-Hang Cheung
- The Hong Kong University of Science and Technology-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China; Department of Chemistry, Center of Systems Biology and Human Health, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Kowloon, Hong Kong
| | - Xuhui Huang
- The Hong Kong University of Science and Technology-Shenzhen Research Institute, Hi-Tech Park, Nanshan, Shenzhen 518057, China; Department of Chemistry, Center of Systems Biology and Human Health, State Key Laboratory of Molecular Neuroscience, The Hong Kong University of Science and Technology, Kowloon, Hong Kong; Bioengineering Graduate Program, The Hong Kong University of Science and Technology, Kowloon, 4Hong Kong Center for Neurodegenerative Diseases, Hong Kong.
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60
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Lorpaiboon C, Thiede EH, Webber RJ, Weare J, Dinner AR. Integrated Variational Approach to Conformational Dynamics: A Robust Strategy for Identifying Eigenfunctions of Dynamical Operators. J Phys Chem B 2020; 124:9354-9364. [PMID: 32955887 PMCID: PMC7955702 DOI: 10.1021/acs.jpcb.0c06477] [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] [Indexed: 12/15/2022]
Abstract
One approach to analyzing the dynamics of a physical system is to search for long-lived patterns in its motions. This approach has been particularly successful for molecular dynamics data, where slowly decorrelating patterns can indicate large-scale conformational changes. Detecting such patterns is the central objective of the variational approach to conformational dynamics (VAC), as well as the related methods of time-lagged independent component analysis and Markov state modeling. In VAC, the search for slowly decorrelating patterns is formalized as a variational problem solved by the eigenfunctions of the system's transition operator. VAC computes solutions to this variational problem by optimizing a linear or nonlinear model of the eigenfunctions using time series data. Here, we build on VAC's success by addressing two practical limitations. First, VAC can give poor eigenfunction estimates when the lag time parameter is chosen poorly. Second, VAC can overfit when using flexible parametrizations such as artificial neural networks with insufficient regularization. To address these issues, we propose an extension that we call integrated VAC (IVAC). IVAC integrates over multiple lag times before solving the variational problem, making its results more robust and reproducible than VAC's.
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Affiliation(s)
- Chatipat Lorpaiboon
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
| | - Erik Henning Thiede
- Flatiron Institute, New York, New York 60637, United States; Department of Computer Science, University of Chicago, Chicago, Illinois 60637, United States
| | - Robert J. Webber
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
| | - Jonathan Weare
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, United States
| | - Aaron R. Dinner
- Department of Chemistry and James Franck Institute, University of Chicago, Chicago, Illinois 60637, United States
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61
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Affiliation(s)
- Francesco Cocina
- Biochemistry Department, University of Zurich, Zurich CH-8057, Switzerland
| | - Andreas Vitalis
- Biochemistry Department, University of Zurich, Zurich CH-8057, Switzerland
| | - Amedeo Caflisch
- Biochemistry Department, University of Zurich, Zurich CH-8057, Switzerland
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62
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Tian H, Tao P. ivis Dimensionality Reduction Framework for Biomacromolecular Simulations. J Chem Inf Model 2020; 60:4569-4581. [PMID: 32820912 DOI: 10.1021/acs.jcim.0c00485] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Molecular dynamics (MD) simulations have been widely applied to study macromolecules including proteins. However, the high dimensionality of the data sets produced by simulations makes thorough analysis difficult and further hinders a deeper understanding of biomacromolecules. To gain more insights into the protein structure-function relations, appropriate dimensionality reduction methods are needed to project simulations onto low-dimensional spaces. Linear dimensionality reduction methods, such as principal component analysis (PCA) and time-structure-based independent component analysis (t-ICA), could not preserve sufficient structural information. Though better than linear methods, nonlinear methods, such as t-distributed stochastic neighbor embedding (t-SNE), still suffer from the limitations in avoiding system noise and keeping inter-cluster relations. ivis is a novel deep learning-based dimensionality reduction method originally developed for single-cell data sets. Here, we applied this framework for the study of light, oxygen, and voltage (LOV) domains of diatom Phaeodactylum tricornutum aureochrome 1a (PtAu1a). Compared with other methods, ivis is shown to be superior in constructing a Markov state model (MSM), preserving information of both local and global distances, and maintaining similarity between high and low dimensions with the least information loss. Moreover, the ivis framework is capable of providing new perspectives for deciphering residue-level protein allostery through the feature weights in the neural network. Overall, ivis is a promising member of the analysis toolbox for proteins.
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Affiliation(s)
- Hao Tian
- Department of Chemistry, Center for Research Computing, Center for Drug Discovery, Design, and Delivery (CD4), Southern Methodist University, Dallas, Texas 75205, United States
| | - Peng Tao
- Department of Chemistry, Center for Research Computing, Center for Drug Discovery, Design, and Delivery (CD4), Southern Methodist University, Dallas, Texas 75205, United States
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63
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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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64
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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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65
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Klus S, Nüske F, Hamzi B. Kernel-Based Approximation of the Koopman Generator and Schrödinger Operator. ENTROPY 2020; 22:e22070722. [PMID: 33286494 PMCID: PMC7517260 DOI: 10.3390/e22070722] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/27/2020] [Revised: 06/25/2020] [Accepted: 06/26/2020] [Indexed: 01/01/2023]
Abstract
Many dimensionality and model reduction techniques rely on estimating dominant eigenfunctions of associated dynamical operators from data. Important examples include the Koopman operator and its generator, but also the Schrödinger operator. We propose a kernel-based method for the approximation of differential operators in reproducing kernel Hilbert spaces and show how eigenfunctions can be estimated by solving auxiliary matrix eigenvalue problems. The resulting algorithms are applied to molecular dynamics and quantum chemistry examples. Furthermore, we exploit that, under certain conditions, the Schrödinger operator can be transformed into a Kolmogorov backward operator corresponding to a drift-diffusion process and vice versa. This allows us to apply methods developed for the analysis of high-dimensional stochastic differential equations to quantum mechanical systems.
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Affiliation(s)
- Stefan Klus
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
- Correspondence:
| | - Feliks Nüske
- Department of Mathematics, Paderborn University, 33098 Paderborn, Germany;
| | - Boumediene Hamzi
- Department of Mathematics, Imperial College London, London SW7 2AZ, UK;
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66
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George A, Purnaprajna M, Athri P. Laplacian score and genetic algorithm based automatic feature selection for Markov State Models in adaptive sampling based molecular dynamics. PEERJ PHYSICAL CHEMISTRY 2020. [DOI: 10.7717/peerj-pchem.9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
Adaptive sampling molecular dynamics based on Markov State Models use short parallel MD simulations to accelerate simulations, and are proven to identify hidden conformers. The accuracy of the predictions provided by it depends on the features extracted from the simulated data that is used to construct it. The identification of the most important features in the trajectories of the simulated system has a considerable effect on the results.
Methods
In this study, we use a combination of Laplacian scoring and genetic algorithms to obtain an optimized feature subset for the construction of the MSM. The approach is validated on simulations of three protein folding complexes, and two protein ligand binding complexes.
Results
Our experiments show that this approach produces better results when the number of samples is significantly lesser than the number of features extracted. We also observed that this method mitigates over fitting that occurs due to high dimensionality of large biosystems with shorter simulation times.
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Affiliation(s)
- Anu George
- Department of Computer Science & Engineering, Amrita School of Engineering, Bengaluru, Amrita Vishwa Vidyapeetham, India
| | - Madhura Purnaprajna
- Department of Computer Science & Engineering, Amrita School of Engineering, Bengaluru, Amrita Vishwa Vidyapeetham, India
| | - Prashanth Athri
- Department of Computer Science & Engineering, Amrita School of Engineering, Bengaluru, Amrita Vishwa Vidyapeetham, India
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67
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Ngo VA, Sarkar S, Neale C, Garcia AE. How Anionic Lipids Affect Spatiotemporal Properties of KRAS4B on Model Membranes. J Phys Chem B 2020; 124:5434-5453. [PMID: 32438809 DOI: 10.1021/acs.jpcb.0c02642] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
RAS proteins are small membrane-anchored GTPases that regulate key cellular signaling networks. It has been recently shown that different anionic lipid types can affect the spatiotemporal properties of RAS through dimerization/clustering and signaling fidelity. To understand the effects of anionic lipids on key spatiotemporal properties of RAS, we dissected 1 ms of data from all-atom molecular dynamics simulations for KRAS4B on two model anionic lipid membranes that have 30% of POPS mixed with neutral POPC and 8% of PIP2 mixed with POPC. We unveiled the orientation space of KRAS4B, whose kinetics were slower and more distinguishable on the membrane containing PIP2 than the membrane containing POPS. Particularly, the PIP2-mixed membrane can differentiate a third kinetic orientation state from the other two known orientation states. We observed that each orientation state may yield different binding modes with an RAF kinase, which is required for activating the MAPK/ERK signaling pathway. However, an overall occluded probability, for which RAF kinases cannot bind KRAS4B, remains unchanged on the two different membranes. We identified rare fast diffusion modes of KRAS4B that appear coupled with orientations exposed to cytosolic RAF. Particularly, on the membrane having PIP2, we found nonlinear correlations between the orientation states and the conformations of the cationic farnesylated hypervariable region, which acts as an anchor in the membrane. Using diffusion coefficients estimated from the all-atom simulations, we quantified the effect of PIP2 and POPS on the KRAS4B dimerization via Green's function reaction dynamics simulations, in which the averaged dimerization rate is 12.5% slower on PIP2-mixed membranes.
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Affiliation(s)
- Van A Ngo
- Center for Nonlinear Studies (CNLS), Los Alamos National Lab, Los Alamos, New Mexico 87545, United States
| | - Sumantra Sarkar
- Center for Nonlinear Studies (CNLS), Los Alamos National Lab, Los Alamos, New Mexico 87545, United States
| | - Chris Neale
- Theoretical Biology and Biophysics Group, T-6, Los Alamos National Lab, Los Alamos, New Mexico 87545, United States
| | - Angel E Garcia
- Center for Nonlinear Studies (CNLS), Los Alamos National Lab, Los Alamos, New Mexico 87545, United States
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68
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Pattis JG, May ER. Markov State Model of Lassa Virus Nucleoprotein Reveals Large Structural Changes during the Trimer to Monomer Transition. Structure 2020; 28:548-554.e3. [PMID: 32234493 DOI: 10.1016/j.str.2020.03.002] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2019] [Revised: 01/23/2020] [Accepted: 03/09/2020] [Indexed: 12/14/2022]
Abstract
Lassa virus contains a nucleoprotein (NP) that encapsulates the viral genomic RNA forming the ribonucleoprotein (RNP). The NP forms trimers that do not bind RNA, but a structure of only the NP N-terminal domain was co-crystallized with RNA bound. These structures suggested a model in which the NP forms a trimer to keep the RNA gate closed, but then is triggered to undergo a change to a form competent for RNA binding. Here, we investigate the scenario in which the trimer is disrupted to observe whether monomeric NP undergoes significant conformational changes. From multi-microsecond molecular dynamics simulations and an adaptive sampling scheme to sample the conformational space, a Markov state model (MSM) is constructed. The MSM reveals an energetically favorable conformational change, with the most significant changes occurring at the domain interface. These results support a model in which significant structural reorganization of the NP is required for RNP formation.
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Affiliation(s)
- Jason G Pattis
- Department of Molecular and Cell Biology, University of Connecticut, Storrs, CT 06269, USA
| | - Eric R May
- Department of Molecular and Cell Biology, University of Connecticut, Storrs, CT 06269, USA.
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69
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Lim NM, Osato M, Warren GL, Mobley DL. Fragment Pose Prediction Using Non-equilibrium Candidate Monte Carlo and Molecular Dynamics Simulations. J Chem Theory Comput 2020; 16:2778-2794. [PMID: 32167763 PMCID: PMC7325745 DOI: 10.1021/acs.jctc.9b01096] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023]
Abstract
Part of early stage drug discovery involves determining how molecules may bind to the target protein. Through understanding where and how molecules bind, chemists can begin to build ideas on how to design improvements to increase binding affinities. In this retrospective study, we compare how computational approaches like docking, molecular dynamics (MD) simulations, and a non-equilibrium candidate Monte Carlo (NCMC)-based method (NCMC + MD) perform in predicting binding modes for a set of 12 fragment-like molecules, which bind to soluble epoxide hydrolase. We evaluate each method's effectiveness in identifying the dominant binding mode and finding additional binding modes (if any). Then, we compare our predicted binding modes to experimentally obtained X-ray crystal structures. We dock each of the 12 small molecules into the apo-protein crystal structure and then run simulations up to 1 μs each. Small and fragment-like molecules likely have smaller energy barriers separating different binding modes by virtue of relatively fewer and weaker interactions relative to drug-like molecules and thus likely undergo more rapid binding mode transitions. We expect, thus, to see more rapid transitions between binding modes in our study. Following this, we build Markov State Models to define our stable ligand binding modes. We investigate if adequate sampling of ligand binding modes and transitions between them can occur at the microsecond timescale using traditional MD or a hybrid NCMC+MD simulation approach. Our findings suggest that even with small fragment-like molecules, we fail to sample all the crystallographic binding modes using microsecond MD simulations, but using NCMC+MD, we have better success in sampling the crystal structure while obtaining the correct populations.
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Affiliation(s)
- Nathan M Lim
- Department of Pharmaceutical Sciences, University of California-Irvine, Irvine, California 92697, United States
| | - Meghan Osato
- Department of Pharmaceutical Sciences, University of California-Irvine, Irvine, California 92697, United States
| | - Gregory L Warren
- OpenEye Scientific Software, Santa Fe, New Mexico 87508, United States
| | - David L Mobley
- Department of Pharmaceutical Sciences, University of California-Irvine, Irvine, California 92697, United States
- Department of Chemistry, University of California-Irvine, Irvine, California 92697, United States
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70
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Umeda R, Satouh Y, Takemoto M, Nakada-Nakura Y, Liu K, Yokoyama T, Shirouzu M, Iwata S, Nomura N, Sato K, Ikawa M, Nishizawa T, Nureki O. Structural insights into tetraspanin CD9 function. Nat Commun 2020; 11:1606. [PMID: 32231207 PMCID: PMC7105497 DOI: 10.1038/s41467-020-15459-7] [Citation(s) in RCA: 100] [Impact Index Per Article: 25.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2019] [Accepted: 03/06/2020] [Indexed: 01/16/2023] Open
Abstract
Tetraspanins play critical roles in various physiological processes, ranging from cell adhesion to virus infection. The members of the tetraspanin family have four membrane-spanning domains and short and large extracellular loops, and associate with a broad range of other functional proteins to exert cellular functions. Here we report the crystal structure of CD9 and the cryo-electron microscopic structure of CD9 in complex with its single membrane-spanning partner protein, EWI-2. The reversed cone-like molecular shape of CD9 generates membrane curvature in the crystalline lipid layers, which explains the CD9 localization in regions with high membrane curvature and its implications in membrane remodeling. The molecular interaction between CD9 and EWI-2 is mainly mediated through the small residues in the transmembrane region and protein/lipid interactions, whereas the fertilization assay revealed the critical involvement of the LEL region in the sperm-egg fusion, indicating the different dependency of each binding domain for other partner proteins. Tetraspanins play critical roles in various physiological processes, ranging from cell adhesion to virus infection. Here authors report the crystal structure of CD9 and the cryo-electron microscopic structure of CD9 in complex with its single membrane-spanning partner protein, EWI-2.
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Affiliation(s)
- Rie Umeda
- Department of Biological Sciences Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan
| | - Yuhkoh Satouh
- Laboratory of Molecular Traffic, Institute for Molecular and Cellular Regulation (IMCR), Gunma University, Maebashi, 371-8512, Japan.,Research Institute for Microbial Diseases, Osaka University, 3-1 Yamadaoka, Suita, Osaka, Japan
| | - Mizuki Takemoto
- Department of Biological Sciences Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan.,Preferred Networks, Inc., Bunkyo-ku, Tokyo, Japan
| | - Yoshiko Nakada-Nakura
- Department of Cell Biology, Graduate School of Medicine, Kyoto University, Kyoto, Japan
| | - Kehong Liu
- Department of Cell Biology, Graduate School of Medicine, Kyoto University, Kyoto, Japan
| | - Takeshi Yokoyama
- Laboratory for Protein Functional and Structural Biology, RIKEN Center for Biosystems Dynamics Research, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa, 230-0045, Japan
| | - Mikako Shirouzu
- Laboratory for Protein Functional and Structural Biology, RIKEN Center for Biosystems Dynamics Research, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama, Kanagawa, 230-0045, Japan
| | - So Iwata
- Department of Cell Biology, Graduate School of Medicine, Kyoto University, Kyoto, Japan.,RIKEN SPring-8 Center, 1-1-1 Kouto, Sayo-cho, Sayo-gun, Hyogo, Japan
| | - Norimichi Nomura
- Department of Cell Biology, Graduate School of Medicine, Kyoto University, Kyoto, Japan
| | - Ken Sato
- Laboratory of Molecular Traffic, Institute for Molecular and Cellular Regulation (IMCR), Gunma University, Maebashi, 371-8512, Japan.,Gunma University Initiative for Advanced Research (GIAR), Gunma University, Maebashi, 371-8512, Japan
| | - Masahito Ikawa
- Research Institute for Microbial Diseases, Osaka University, 3-1 Yamadaoka, Suita, Osaka, Japan
| | - Tomohiro Nishizawa
- Department of Biological Sciences Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan. .,Precursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology, Bunkyo-ku, Tokyo, Japan.
| | - Osamu Nureki
- Department of Biological Sciences Graduate School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, Japan.
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71
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Abstract
Machine learning (ML) is transforming all areas of science. The complex and time-consuming calculations in molecular simulations are particularly suitable for an ML revolution and have already been profoundly affected by the application of existing ML methods. Here we review recent ML methods for molecular simulation, with particular focus on (deep) neural networks for the prediction of quantum-mechanical energies and forces, on coarse-grained molecular dynamics, on the extraction of free energy surfaces and kinetics, and on generative network approaches to sample molecular equilibrium structures and compute thermodynamics. To explain these methods and illustrate open methodological problems, we review some important principles of molecular physics and describe how they can be incorporated into ML structures. Finally, we identify and describe a list of open challenges for the interface between ML and molecular simulation.
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Affiliation(s)
- 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 and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA;
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit, University of Luxembourg, 1511 Luxembourg, Luxembourg;
| | - Klaus-Robert Müller
- Department of Computer Science, Technical University Berlin, 10587 Berlin, Germany; .,Max-Planck-Institut für Informatik, 66123 Saarbrücken, Germany.,Department of Brain and Cognitive Engineering, Korea University, Seoul 136-713, South Korea
| | - Cecilia Clementi
- Department of Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany; .,Department of Chemistry and Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA; .,Department of Physics, Rice University, Houston, Texas 77005, USA
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72
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Wan H, Voelz VA. Adaptive Markov state model estimation using short reseeding trajectories. J Chem Phys 2020; 152:024103. [PMID: 31941308 DOI: 10.1063/1.5142457] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
In the last decade, advances in molecular dynamics (MD) and Markov State Model (MSM) methodologies have made possible accurate and efficient estimation of kinetic rates and reactive pathways for complex biomolecular dynamics occurring on slow time scales. A promising approach to enhanced sampling of MSMs is to use "adaptive" methods, in which new MD trajectories are "seeded" preferentially from previously identified states. Here, we investigate the performance of various MSM estimators applied to reseeding trajectory data, for both a simple 1D free energy landscape and mini-protein folding MSMs of WW domain and NTL9(1-39). Our results reveal the practical challenges of reseeding simulations and suggest a simple way to reweight seeding trajectory data to better estimate both thermodynamic and kinetic quantities.
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Affiliation(s)
- Hongbin Wan
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
| | - Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122, USA
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73
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Aldukhi F, Deb A, Zhao C, Moffett AS, Shukla D. Molecular Mechanism of Brassinosteroid Perception by the Plant Growth Receptor BRI1. J Phys Chem B 2020; 124:355-365. [PMID: 31873025 DOI: 10.1021/acs.jpcb.9b09377] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
Abstract
Brassinosteroids (BRs) are essential phytohormones, which bind to the plant receptor, BRI1, to regulate various physiological processes. The molecular mechanism of the perception of BRs by the ectodomain of BRI1 remains not fully understood. It also remains elusive why a substantial difference in biological activity exists between the BRs. In this work, we study the binding mechanisms of the two most bioactive BRs, brassinolide (BLD) and castasterone (CAT), using molecular dynamics simulations. We report free-energy landscapes of the binding processes of both ligands, as well as detailed ligand binding pathways. Our results suggest that CAT has a lower binding affinity compared to BLD due to its inability to form hydrogen-bonding interactions with a tyrosine residue in the island domain of BRI1. We uncover a conserved nonproductive binding state for both BLD and CAT, which is more stable for CAT and may further contribute to the bioactivity difference. Finally, we validate past observations about the conformational restructuring and ordering of the island domain upon BLD binding. Overall, this study provides new insights into the fundamental mechanism of the perception of the two most bioactive BRs, which may create new avenues for genetic and agrochemical control of their signaling cascade.
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Affiliation(s)
| | - Aniket Deb
- Department of Food Technology and Biochemical Engineering , Jadavpur University , Kolkata , West Bengal 700032 , India
| | | | | | - Diwakar Shukla
- National Center for Supercomputing Applications , Urbana , Illinois 61801 , United States
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74
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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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75
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Affiliation(s)
- Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Berlin, Germany
- Department of Physics, Freie Universität Berlin, Berlin, Germany
| | - Edina Rosta
- Department of Chemistry, Kings College London, London, England
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76
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Cheng KJ, Selvam B, Chen LQ, Shukla D. Distinct Substrate Transport Mechanism Identified in Homologous Sugar Transporters. J Phys Chem B 2019; 123:8411-8418. [DOI: 10.1021/acs.jpcb.9b08257] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023]
Affiliation(s)
- Kevin J. Cheng
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana−Champaign, Champaign, Illinois 61801, United States
| | - Balaji Selvam
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, Champaign, Illinois 61801, United States
| | - Li-Qing Chen
- Department of Plant Biology, University of Illinois at Urbana−Champaign, Champaign, Illinois 61801, United States
| | - Diwakar Shukla
- Center for Biophysics and Quantitative Biology, University of Illinois at Urbana−Champaign, Champaign, Illinois 61801, United States
- Department of Chemical and Biomolecular Engineering, University of Illinois at Urbana−Champaign, Champaign, Illinois 61801, United States
- Department of Plant Biology, University of Illinois at Urbana−Champaign, Champaign, Illinois 61801, United States
- NIH Center for Macromolecular Modeling and Bioinformatics, University of Illinois at Urbana−Champaign, Champaign, Illinois 61801, United States
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana−Champaign, Champaign, Illinois 61801, United States
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77
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Sidky H, Chen W, Ferguson AL. High-Resolution Markov State Models for the Dynamics of Trp-Cage Miniprotein Constructed Over Slow Folding Modes Identified by State-Free Reversible VAMPnets. J Phys Chem B 2019; 123:7999-8009. [DOI: 10.1021/acs.jpcb.9b05578] [Citation(s) in RCA: 23] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Hythem Sidky
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
| | - Wei Chen
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States
| | - Andrew L. Ferguson
- Pritzker School of Molecular Engineering, University of Chicago, Chicago, Illinois 60637, United States
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78
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Recent Progress towards Chemically-Specific Coarse-Grained Simulation Models with Consistent Dynamical Properties. COMPUTATION 2019. [DOI: 10.3390/computation7030042] [Citation(s) in RCA: 34] [Impact Index Per Article: 6.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
Coarse-grained (CG) models can provide computationally efficient and conceptually simple characterizations of soft matter systems. While generic models probe the underlying physics governing an entire family of free-energy landscapes, bottom-up CG models are systematically constructed from a higher-resolution model to retain a high level of chemical specificity. The removal of degrees of freedom from the system modifies the relationship between the relative time scales of distinct dynamical processes through both a loss of friction and a “smoothing” of the free-energy landscape. While these effects typically result in faster dynamics, decreasing the computational expense of the model, they also obscure the connection to the true dynamics of the system. The lack of consistent dynamics is a serious limitation for CG models, which not only prevents quantitatively accurate predictions of dynamical observables but can also lead to qualitatively incorrect descriptions of the characteristic dynamical processes. With many methods available for optimizing the structural and thermodynamic properties of chemically-specific CG models, recent years have seen a stark increase in investigations addressing the accurate description of dynamical properties generated from CG simulations. In this review, we present an overview of these efforts, ranging from bottom-up parameterizations of generalized Langevin equations to refinements of the CG force field based on a Markov state modeling framework. We aim to make connections between seemingly disparate approaches, while laying out some of the major challenges as well as potential directions for future efforts.
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79
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Husic BE, Noé F. Deflation reveals dynamical structure in nondominant reaction coordinates. J Chem Phys 2019. [DOI: 10.1063/1.5099194] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Brooke E. Husic
- Department of Mathematics and Computer Science, Freie Universität, 14195 Berlin, Germany
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
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80
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Zhao L, Ouyang Y, Li Q, Zhang Z. Modulation of p53 N-terminal transactivation domain 2 conformation ensemble and kinetics by phosphorylation. J Biomol Struct Dyn 2019; 38:2613-2623. [DOI: 10.1080/07391102.2019.1637784] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Likun Zhao
- College of Life Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Yanhua Ouyang
- College of Life Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Qian Li
- College of Life Sciences, University of Chinese Academy of Sciences, Beijing, China
| | - Zhuqing Zhang
- College of Life Sciences, University of Chinese Academy of Sciences, Beijing, China
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81
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Selvam B, Yu YC, Chen LQ, Shukla D. Molecular Basis of the Glucose Transport Mechanism in Plants. ACS CENTRAL SCIENCE 2019; 5:1085-1096. [PMID: 31263768 PMCID: PMC6598156 DOI: 10.1021/acscentsci.9b00252] [Citation(s) in RCA: 31] [Impact Index Per Article: 6.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2019] [Indexed: 05/04/2023]
Abstract
The SWEET family belongs to a class of transporters in plants that undergoes large conformational changes to facilitate transport of sugar molecules across the cell membrane (SWEET, Sugars Will Eventually Be Exported Transporter). However, the structures of their functionally relevant conformational states in the transport cycle have not been reported. In this study, we have characterized the conformational dynamics and complete transport cycle of glucose in the OsSWEET2b transporter using extensive molecular dynamics simulations. Using Markov state models, we estimated the free energy barrier associated with different states as well as for the glucose transport mechanism. SWEETs undergo a structural transition to outward-facing (OF), occluded (OC), and inward-facing (IF) and strongly support an alternate access transport mechanism. The glucose diffuses freely from outside to inside the cell without causing major conformational changes which means that the conformations of glucose unbound and bound snapshots are exactly the same for OF, OC, and IF states. We identified a network of hydrophobic core residues at the center of the transporter that restricts the glucose entry to the cytoplasmic side and acts as an intracellular hydrophobic gate. The mechanistic predictions from molecular dynamics simulations are validated using site-directed mutagenesis experiments. Our simulation also revealed hourglass-like intermediate states making the pore radius narrower at the center. This work provides new fundamental insights into how substrate-transporter interactions actively change the free energy landscape of the transport cycle to facilitate enhanced transport activity.
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Affiliation(s)
- Balaji Selvam
- Department
of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Ya-Chi Yu
- Department
of Plant Biology, University of Illinois
at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Li-Qing Chen
- Department
of Plant Biology, University of Illinois
at Urbana-Champaign, Urbana, Illinois 61801, United States
| | - Diwakar Shukla
- Department
of Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Department
of Plant Biology, University of Illinois
at Urbana-Champaign, Urbana, Illinois 61801, United States
- Center
for Biophysics and Quantitative Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- NIH
Center for Macromolecular Modeling and Bioinformatics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- Beckman
Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, United States
- E-mail:
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82
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Cingolani G, McCauley M, Lobley A, Bryer AJ, Wesolowski J, Greco DL, Lokareddy RK, Ronzone E, Perilla JR, Paumet F. Structural basis for the homotypic fusion of chlamydial inclusions by the SNARE-like protein IncA. Nat Commun 2019; 10:2747. [PMID: 31227715 PMCID: PMC6588587 DOI: 10.1038/s41467-019-10806-9] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2018] [Accepted: 05/29/2019] [Indexed: 11/29/2022] Open
Abstract
Many intracellular bacteria, including Chlamydia, establish a parasitic membrane-bound organelle inside the host cell that is essential for the bacteria’s survival. Chlamydia trachomatis forms inclusions that are decorated with poorly characterized membrane proteins known as Incs. The prototypical Inc, called IncA, enhances Chlamydia pathogenicity by promoting the homotypic fusion of inclusions and shares structural and functional similarity to eukaryotic SNAREs. Here, we present the atomic structure of the cytoplasmic domain of IncA, which reveals a non-canonical four-helix bundle. Structure-based mutagenesis, molecular dynamics simulation, and functional cellular assays identify an intramolecular clamp that is essential for IncA-mediated homotypic membrane fusion during infection. Chlamydia trachomatis forms membrane-bound inclusions inside the host cell that are decorated with IncA, a SNARE-like protein that promotes the fusion of inclusions. Here, Cingolani et al. show that the protein folds into a non-canonical four-helix bundle and identify an intramolecular clamp required for membrane fusion.
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Affiliation(s)
- Gino Cingolani
- Thomas Jefferson University, Department of Biochemistry and Molecular Biology, Philadelphia, PA, 19107, USA. .,Institute of Biomembranes and Bioenergetics, National Research Council, Via Amendola 165/A, 70126, Bari, Italy.
| | - Michael McCauley
- Thomas Jefferson University, Department of Microbiology and Immunology, Philadelphia, PA, 19107, USA.,Janssen Research and Development, Spring House, PA, 19477, USA
| | - Anna Lobley
- Thomas Jefferson University, Department of Microbiology and Immunology, Philadelphia, PA, 19107, USA
| | - Alexander J Bryer
- The University of Delaware, Department of Chemistry and Biochemistry, Newark, DE, 19716, USA
| | - Jordan Wesolowski
- Thomas Jefferson University, Department of Microbiology and Immunology, Philadelphia, PA, 19107, USA
| | - Deanna L Greco
- The University of Delaware, Department of Chemistry and Biochemistry, Newark, DE, 19716, USA
| | - Ravi K Lokareddy
- Thomas Jefferson University, Department of Biochemistry and Molecular Biology, Philadelphia, PA, 19107, USA
| | - Erik Ronzone
- Thomas Jefferson University, Department of Microbiology and Immunology, Philadelphia, PA, 19107, USA.,VUE Health, Boston, MA, 02110, USA
| | - Juan R Perilla
- The University of Delaware, Department of Chemistry and Biochemistry, Newark, DE, 19716, USA
| | - Fabienne Paumet
- Thomas Jefferson University, Department of Microbiology and Immunology, Philadelphia, PA, 19107, USA.
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83
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Scherer MK, Husic BE, Hoffmann M, Paul F, Wu H, Noé F. Variational selection of features for molecular kinetics. J Chem Phys 2019; 150:194108. [PMID: 31117766 DOI: 10.1063/1.5083040] [Citation(s) in RCA: 40] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Abstract
The modeling of atomistic biomolecular simulations using kinetic models such as Markov state models (MSMs) has had many notable algorithmic advances in recent years. The variational principle has opened the door for a nearly fully automated toolkit for selecting models that predict the long time-scale kinetics from molecular dynamics simulations. However, one yet-unoptimized step of the pipeline involves choosing the features, or collective variables, from which the model should be constructed. In order to build intuitive models, these collective variables are often sought to be interpretable and familiar features, such as torsional angles or contact distances in a protein structure. However, previous approaches for evaluating the chosen features rely on constructing a full MSM, which in turn requires additional hyperparameters to be chosen, and hence leads to a computationally expensive framework. Here, we present a method to optimize the feature choice directly, without requiring the construction of the final kinetic model. We demonstrate our rigorous preprocessing algorithm on a canonical set of 12 fast-folding protein simulations and show that our procedure leads to more efficient model selection.
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Affiliation(s)
- Martin K Scherer
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Brooke E Husic
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Moritz Hoffmann
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Fabian Paul
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Hao Wu
- School of Mathematical Sciences, Tongji University, Shanghai 200092, People's Republic of China
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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84
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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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85
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Dämgen MA, Biggin PC. Computational methods to examine conformational changes and ligand-binding properties: Examples in neurobiology. Neurosci Lett 2019. [DOI: 10.1016/j.neulet.2018.03.004] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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86
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Paul F, Wu H, Vossel M, de Groot BL, Noé F. Identification of kinetic order parameters for non-equilibrium dynamics. J Chem Phys 2019; 150:164120. [PMID: 31042914 PMCID: PMC6486394 DOI: 10.1063/1.5083627] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2018] [Accepted: 04/04/2019] [Indexed: 12/17/2022] Open
Abstract
A popular approach to analyze the dynamics of high-dimensional many-body systems, such as macromolecules, is to project the trajectories onto a space of slowly varying collective variables, where subsequent analyses are made, such as clustering or estimation of free energy profiles or Markov state models. However, existing "dynamical" dimension reduction methods, such as the time-lagged independent component analysis (TICA), are only valid if the dynamics obeys detailed balance (microscopic reversibility) and typically require long, equilibrated simulation trajectories. Here, we develop a dimension reduction method for non-equilibrium dynamics based on the recently developed Variational Approach for Markov Processes (VAMP) by Wu and Noé. VAMP is illustrated by obtaining a low-dimensional description of a single file ion diffusion model and by identifying long-lived states from molecular dynamics simulations of the KcsA channel protein in an external electrochemical potential. This analysis provides detailed insights into the coupling of conformational dynamics, the configuration of the selectivity filter, and the conductance of the channel. We recommend VAMP as a replacement for the less general TICA method.
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Affiliation(s)
- Fabian Paul
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Hao Wu
- Tongji University, School of Mathematical Sciences, Shanghai 200092, People's Republic of China
| | - Maximilian Vossel
- Max Planck Institute for Biophysical Chemistry, Am Fassberg 11 D-37077 Göttingen, Germany
| | - Bert L de Groot
- Max Planck Institute for Biophysical Chemistry, Am Fassberg 11 D-37077 Göttingen, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 6, 14195 Berlin, Germany
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87
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Dewetting Controls Plant Hormone Perception and Initiation of Drought Resistance Signaling. Structure 2019; 27:692-702.e3. [DOI: 10.1016/j.str.2018.12.005] [Citation(s) in RCA: 32] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Revised: 11/19/2018] [Accepted: 12/05/2018] [Indexed: 11/23/2022]
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88
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Bacci M, Caflisch A, Vitalis A. On the removal of initial state bias from simulation data. J Chem Phys 2019; 150:104105. [PMID: 30876362 DOI: 10.1063/1.5063556] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/30/2022] Open
Abstract
Classical atomistic simulations of biomolecules play an increasingly important role in molecular life science. The structure of current computing architectures favors methods that run multiple trajectories at once without requiring extensive communication between them. Many advanced sampling strategies in the field fit this mold. These approaches often rely on an adaptive logic and create ensembles of comparatively short trajectories whose starting points are not distributed according to the correct Boltzmann weights. This type of bias is notoriously difficult to remove, and Markov state models (MSMs) are one of the few strategies available for recovering the correct kinetics and thermodynamics from these ensembles of trajectories. In this contribution, we analyze the performance of MSMs in the thermodynamic reweighting task for a hierarchical set of systems. We show that MSMs can be rigorous tools to recover the correct equilibrium distribution for systems of sufficiently low dimensionality. This is conditional upon not tampering with local flux imbalances found in the data. For a real-world application, we find that a pure likelihood-based inference of the transition matrix produces the best results. The removal of the bias is incomplete, however, and for this system, all tested MSMs are outperformed by an alternative albeit less general approach rooted in the ideas of statistical resampling. We conclude by formulating some recommendations for how to address the reweighting issue in practice.
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Affiliation(s)
- Marco Bacci
- University of Zurich, Department of Biochemistry, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Amedeo Caflisch
- University of Zurich, Department of Biochemistry, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
| | - Andreas Vitalis
- University of Zurich, Department of Biochemistry, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
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89
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Acharyya A, Ge Y, Wu H, DeGrado WF, Voelz VA, Gai F. Exposing the Nucleation Site in α-Helix Folding: A Joint Experimental and Simulation Study. J Phys Chem B 2019; 123:1797-1807. [PMID: 30694671 DOI: 10.1021/acs.jpcb.8b12220] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
One of the fundamental events in protein folding is α-helix formation, which involves sequential development of a series of helical hydrogen bonds between the backbone C═O group of residues i and the -NH group of residues i + 4. While we now know a great deal about α-helix folding dynamics, a key question that remains to be answered is where the productive helical nucleation event occurs. Statistically, a helical nucleus (or the first helical hydrogen-bond) can form anywhere within the peptide sequence in question; however, the one that leads to productive folding may only form at a preferred location. This consideration is based on the fact that the α-helical structure is inherently asymmetric, due to the specific alignment of the helical hydrogen bonds. While this hypothesis is plausible, validating it is challenging because there is not an experimental observable that can be used to directly pinpoint the location of the productive nucleation process. Therefore, in this study we combine several techniques, including peptide cross-linking, laser-induced temperature-jump infrared spectroscopy, and molecular dynamics simulations, to tackle this challenge. Taken together, our experimental and simulation results support an α-helix folding mechanism wherein the productive nucleus is formed at the N-terminus, which propagates toward the C-terminal end of the peptide to yield the folded structure. In addition, our results show that incorporation of a cross-linker can lead to formation of differently folded conformations, underscoring the need for all-atom simulations to quantitatively assess the proposed cross-linking design.
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Affiliation(s)
- Arusha Acharyya
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
| | - Yunhui Ge
- Department of Chemistry , Temple University , Philadelphia , Pennsylvania 19122 , United States
| | - Haifan Wu
- Department of Pharmaceutical Chemistry , University of California , San Francisco , California 94158 , United States
| | - William F DeGrado
- Department of Pharmaceutical Chemistry , University of California , San Francisco , California 94158 , United States
| | - Vincent A Voelz
- Department of Chemistry , Temple University , Philadelphia , Pennsylvania 19122 , United States
| | - Feng Gai
- Department of Chemistry , University of Pennsylvania , Philadelphia , Pennsylvania 19104 , United States
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90
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Wayment-Steele HK, Pande VS. Note: Variational encoding of protein dynamics benefits from maximizing latent autocorrelation. J Chem Phys 2019; 149:216101. [PMID: 30525733 DOI: 10.1063/1.5043303] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
As deep Variational Auto-Encoder (VAE) frameworks become more widely used for modeling biomolecular simulation data, we emphasize the capability of the VAE architecture to concurrently maximize the time scale of the latent space while inferring a reduced coordinate, which assists in finding slow processes as according to the variational approach to conformational dynamics. We provide evidence that the VDE framework [Hernández et al., Phys. Rev. E 97, 062412 (2018)], which uses this autocorrelation loss along with a time-lagged reconstruction loss, obtains a variationally optimized latent coordinate in comparison with related loss functions. We thus recommend leveraging the autocorrelation of the latent space while training neural network models of biomolecular simulation data to better represent slow processes.
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Affiliation(s)
| | - Vijay S Pande
- Department of Bioengineering, Stanford University, Stanford, California 94305, USA
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91
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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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92
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Ge Y, Borne E, Stewart S, Hansen MR, Arturo EC, Jaffe EK, Voelz VA. Simulations of the regulatory ACT domain of human phenylalanine hydroxylase (PAH) unveil its mechanism of phenylalanine binding. J Biol Chem 2018; 293:19532-19543. [PMID: 30287685 DOI: 10.1074/jbc.ra118.004909] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2018] [Revised: 09/17/2018] [Indexed: 12/20/2022] Open
Abstract
Phenylalanine hydroxylase (PAH) regulates phenylalanine (Phe) levels in mammals to prevent neurotoxicity resulting from high Phe concentrations as observed in genetic disorders leading to hyperphenylalaninemia and phenylketonuria. PAH senses elevated Phe concentrations by transient allosteric Phe binding to a protein-protein interface between ACT domains of different subunits in a PAH tetramer. This interface is present in an activated PAH (A-PAH) tetramer and absent in a resting-state PAH (RS-PAH) tetramer. To investigate this allosteric sensing mechanism, here we used the GROMACS molecular dynamics simulation suite on the Folding@home computing platform to perform extensive molecular simulations and Markov state model (MSM) analysis of Phe binding to ACT domain dimers. These simulations strongly implicated a conformational selection mechanism for Phe association with ACT domain dimers and revealed protein motions that act as a gating mechanism for Phe binding. The MSMs also illuminate a highly mobile hairpin loop, consistent with experimental findings also presented here that the PAH variant L72W does not shift the PAH structural equilibrium toward the activated state. Finally, simulations of ACT domain monomers are presented, in which spontaneous transitions between resting-state and activated conformations are observed, also consistent with a mechanism of conformational selection. These mechanistic details provide detailed insight into the regulation of PAH activation and provide testable hypotheses for the development of new allosteric effectors to correct structural and functional defects in PAH.
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Affiliation(s)
- Yunhui Ge
- From the Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122
| | - Elias Borne
- Fox Chase Cancer Center, Temple University Health System, Philadelphia, Pennsylvania 19111, and
| | - Shannon Stewart
- Fox Chase Cancer Center, Temple University Health System, Philadelphia, Pennsylvania 19111, and
| | - Michael R Hansen
- Fox Chase Cancer Center, Temple University Health System, Philadelphia, Pennsylvania 19111, and
| | - Emilia C Arturo
- Fox Chase Cancer Center, Temple University Health System, Philadelphia, Pennsylvania 19111, and.,Drexel University College of Medicine, Philadelphia, Pennsylvania 19129
| | - Eileen K Jaffe
- Fox Chase Cancer Center, Temple University Health System, Philadelphia, Pennsylvania 19111, and
| | - Vincent A Voelz
- From the Department of Chemistry, Temple University, Philadelphia, Pennsylvania 19122,
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93
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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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94
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Ahalawat N, Mondal J. Assessment and optimization of collective variables for protein conformational landscape: GB1 β-hairpin as a case study. J Chem Phys 2018; 149:094101. [PMID: 30195312 DOI: 10.1063/1.5041073] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Collective variables (CVs), when chosen judiciously, can play an important role in recognizing rate-limiting processes and rare events in any biomolecular systems. However, high dimensionality and inherent complexities associated with such biochemical systems render the identification of an optimal CV a challenging task, which in turn precludes the elucidation of an underlying conformational landscape in sufficient details. In this context, a relevant model system is presented by a 16-residue β-hairpin of GB1 protein. Despite being the target of numerous theoretical and computational studies for understanding the protein folding, the set of CVs optimally characterizing the conformational landscape of the β-hairpin of GB1 protein has remained elusive, resulting in a lack of consensus on its folding mechanism. Here we address this by proposing a pair of optimal CVs which can resolve the underlying free energy landscape of the GB1 hairpin quite efficiently. Expressed as a linear combination of a number of traditional CVs, the optimal CV for this system is derived by employing the recently introduced time-structured independent component analysis approach on a large number of independent unbiased simulations. By projecting the replica-exchange simulated trajectories along these pair of optimized CVs, the resulting free energy landscape of this system is able to resolve four distinct well-separated metastable states encompassing the extensive ensembles of folded, unfolded, and molten globule states. Importantly, the optimized CVs were found to be capable of automatically recovering a novel partial helical state of this protein, without needing to explicitly invoke helicity as a constituent CV. Furthermore, a quantitative sensitivity analysis of each constituent in the optimized CV provided key insights on the relative contributions of the constituent CVs in the overall free energy landscapes. Finally, the kinetic pathways connecting these metastable states, constructed using a Markov state model, provide an optimum description of the underlying folding mechanism of the peptide. Taken together, this work offers a quantitatively robust approach toward comprehensive mapping of the underlying folding landscape of a quintessential model system along its optimized CV.
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Affiliation(s)
- Navjeet Ahalawat
- Tata Institute of Fundamental Research, Center for Interdisciplinary Sciences, Hyderabad 500107, India
| | - Jagannath Mondal
- Tata Institute of Fundamental Research, Center for Interdisciplinary Sciences, Hyderabad 500107, India
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95
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Liang H, Zhou G, Ge Y, D'Ambrosio EA, Eidem TM, Blanchard C, Shehatou C, Chatare VK, Dunman PM, Valentine AM, Voelz VA, Grimes CL, Andrade RB. Elucidating the inhibition of peptidoglycan biosynthesis in Staphylococcus aureus by albocycline, a macrolactone isolated from Streptomyces maizeus. Bioorg Med Chem 2018; 26:3453-3460. [PMID: 29805074 PMCID: PMC6008248 DOI: 10.1016/j.bmc.2018.05.017] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/14/2018] [Revised: 05/02/2018] [Accepted: 05/12/2018] [Indexed: 02/01/2023]
Abstract
Antibiotic resistance is a serious threat to global public health, and methicillin-resistant Staphylococcus aureus (MRSA) is a poignant example. The macrolactone natural product albocycline, derived from various Streptomyces strains, was recently identified as a promising antibiotic candidate for the treatment of both MRSA and vancomycin-resistant S. aureus (VRSA), which is another clinically relevant and antibiotic resistant strain. Moreover, it was hypothesized that albocycline's antimicrobial activity was derived from the inhibition of peptidoglycan (i.e., bacterial cell wall) biosynthesis. Herein, preliminary mechanistic studies are performed to test the hypothesis that albocycline inhibits MurA, the enzyme that catalyzes the first step of peptidoglycan biosynthesis, using a combination of biological assays alongside molecular modeling and simulation studies. Computational modeling suggests albocycline exists as two conformations in solution, and computational docking of these conformations to an ensemble of simulated receptor structures correctly predicted preferential binding to S. aureus MurA-the enzyme that catalyzes the first step of peptidoglycan biosynthesis-over Escherichia coli (E. coli) MurA. Albocycline isolated from the producing organism (Streptomyces maizeus) weakly inhibited S. aureus MurA (IC50 of 480 μM) but did not inhibit E. coli MurA. The antimicrobial activity of albocycline against resistant S. aureus strains was superior to that of vancomycin, preferentially inhibiting Gram-positive organisms. Albocycline was not toxic to human HepG2 cells in MTT assays. While these studies demonstrate that albocycline is a promising lead candidate against resistant S. aureus, taken together they suggest that MurA is not the primary target, and further work is necessary to identify the major biological target.
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Affiliation(s)
- Hai Liang
- Department of Chemistry and Biochemistry, University of Delaware, Newark, DE 19716, United States
| | - Guangfeng Zhou
- Department of Chemistry, Temple University, Philadelphia, PA 19122, United States
| | - Yunhui Ge
- Department of Chemistry, Temple University, Philadelphia, PA 19122, United States
| | - Elizabeth A D'Ambrosio
- Department of Chemistry and Biochemistry, University of Delaware, Newark, DE 19716, United States
| | - Tess M Eidem
- Department of Microbiology and Immunology, University of Rochester School of Medicine and Dentistry, Rochester, NY 14642, United States
| | - Catlyn Blanchard
- Department of Microbiology and Immunology, University of Rochester School of Medicine and Dentistry, Rochester, NY 14642, United States
| | - Cindy Shehatou
- Department of Microbiology and Immunology, University of Rochester School of Medicine and Dentistry, Rochester, NY 14642, United States
| | - Vijay K Chatare
- Department of Chemistry, Temple University, Philadelphia, PA 19122, United States
| | - Paul M Dunman
- Department of Microbiology and Immunology, University of Rochester School of Medicine and Dentistry, Rochester, NY 14642, United States
| | - Ann M Valentine
- Department of Chemistry, Temple University, Philadelphia, PA 19122, United States
| | - Vincent A Voelz
- Department of Chemistry, Temple University, Philadelphia, PA 19122, United States
| | - Catherine L Grimes
- Department of Chemistry and Biochemistry, University of Delaware, Newark, DE 19716, United States
| | - Rodrigo B Andrade
- Department of Chemistry, Temple University, Philadelphia, PA 19122, United States.
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96
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Hernández CX, Wayment-Steele HK, Sultan MM, Husic BE, Pande VS. Variational encoding of complex dynamics. Phys Rev E 2018; 97:062412. [PMID: 30011547 DOI: 10.1103/physreve.97.062412] [Citation(s) in RCA: 89] [Impact Index Per Article: 14.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2017] [Indexed: 11/07/2022]
Abstract
Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged covariate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of the variational autoencoder (VAE), which is able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.
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Affiliation(s)
| | | | - Mohammad M Sultan
- Chemistry Department, Stanford University, Stanford, California, USA
| | - Brooke E Husic
- Chemistry Department, Stanford University, Stanford, California, USA
| | - Vijay S Pande
- Biophysics Program, Stanford University, Stanford, California, USA.,Chemistry Department, Stanford University, Stanford, California, USA
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97
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Sultan MM, Kiss G, Pande VS. Towards simple kinetic models of functional dynamics for a kinase subfamily. Nat Chem 2018; 10:903-909. [PMID: 29988151 DOI: 10.1038/s41557-018-0077-9] [Citation(s) in RCA: 46] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2017] [Accepted: 05/08/2018] [Indexed: 11/09/2022]
Abstract
Kinases are ubiquitous enzymes involved in the regulation of critical cellular pathways. However, in silico modelling of the conformational ensembles of these enzymes is difficult due to inherent limitations and the cost of computational approaches. Recent algorithmic advances combined with homology modelling and parallel simulations have enabled researchers to address this computational sampling bottleneck. Here, we present the results of molecular dynamics studies for seven Src family kinase (SFK) members: Fyn, Lyn, Lck, Hck, Fgr, Yes and Blk. We present a sequence invariant extension to Markov state models, which allows us to quantitatively compare the structural ensembles of the seven kinases. Our findings indicate that in the absence of their regulatory partners, SFK members have similar in silico dynamics with active state populations ranging from 4 to 40% and activation timescales in the hundreds of microseconds. Furthermore, we observe several potentially druggable intermediate states, including a pocket next to the adenosine triphosphate binding site that could potentially be targeted via a small-molecule inhibitor.
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Affiliation(s)
| | - Gert Kiss
- Department of Chemistry, Stanford University, Stanford, CA, USA.,Center for Molecular Analysis and Design, Stanford University, Stanford, CA, USA.,Revolution Medicines, Redwood City, CA, USA
| | - Vijay S Pande
- Department of Bioengineering, Stanford University, Stanford, CA, USA.
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98
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Wehmeyer C, Noé F. Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics. J Chem Phys 2018; 148:241703. [PMID: 29960344 DOI: 10.1063/1.5011399] [Citation(s) in RCA: 170] [Impact Index Per Article: 28.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Inspired by the success of deep learning techniques in the physical and chemical sciences, we apply a modification of an autoencoder type deep neural network to the task of dimension reduction of molecular dynamics data. We can show that our time-lagged autoencoder reliably finds low-dimensional embeddings for high-dimensional feature spaces which capture the slow dynamics of the underlying stochastic processes-beyond the capabilities of linear dimension reduction techniques.
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Affiliation(s)
- Christoph Wehmeyer
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
| | - Frank Noé
- Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany
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99
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Sinitskiy AV, Pande VS. Computer Simulations Predict High Structural Heterogeneity of Functional State of NMDA Receptors. Biophys J 2018; 115:841-852. [PMID: 30029773 DOI: 10.1016/j.bpj.2018.06.023] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2018] [Accepted: 06/18/2018] [Indexed: 01/07/2023] Open
Abstract
N-methyl-D-aspartate receptors (NMDARs)-i.e., transmembrane proteins expressed in neurons-play a central role in the molecular mechanisms of learning and memory formation. It is unclear how the known atomic structures of NMDARs determined by x-ray crystallography and electron cryomicroscopy (18 published Protein Data Bank entries) relate to the functional states of NMDARs inferred from electrophysiological recordings (multiple closed, open, preopen, etc. states). We address this problem by using molecular dynamics simulations at atomic resolution, a method successfully applied in the past to much smaller biomolecules. Our simulations predict that several conformations of NMDARs with experimentally determined geometries, including four "nonactive" electron cryomicroscopy structures, rapidly interconvert on submicrosecond timescales and therefore may correspond to the same functional state of the receptor (specifically, one of the closed states). This conclusion is not trivial because these conformational transitions involve changes in certain interatomic distances as large as tens of Å. The simulations also predict differences in the conformational dynamics of the apo and holo (i.e., agonist and coagonist bound) forms of the receptor on the microsecond timescale. To our knowledge, five new conformations of NMDARs, with geometries joining various features from different known experimental structures, are also predicted by the model. The main limitation of this work stems from its limited sampling (30 μs of aggregate length of molecular dynamics trajectories). Though this level significantly exceeds the sampling in previous simulations of parts of NMDARs, it is still much lower than the sampling recently achieved for smaller biomolecules (up to a few milliseconds), thus precluding, in particular, the observation of transitions between different functional states of NMDARs. Despite this limitation, such computational predictions may guide further experimental studies on the structure, dynamics, and function of NMDARs, for example by suggesting optimal locations of spectroscopic probes. Overall, atomic resolution simulations provide, to our knowledge, a novel perspective on the structure and dynamics of NMDARs, complementing information obtained by experimental methods.
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Affiliation(s)
- Anton V Sinitskiy
- Department of Bioengineering, Stanford University, Stanford, California.
| | - Vijay S Pande
- Department of Bioengineering, Stanford University, Stanford, California.
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100
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Husic BE, Pande VS. Note: MSM lag time cannot be used for variational model selection. J Chem Phys 2018; 147:176101. [PMID: 29117698 DOI: 10.1063/1.5002086] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The variational principle for conformational dynamics has enabled the systematic construction of Markov state models through the optimization of hyperparameters by approximating the transfer operator. In this note, we discuss why the lag time of the operator being approximated must be held constant in the variational approach.
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Affiliation(s)
- Brooke E Husic
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
| | - Vijay S Pande
- Department of Chemistry, Stanford University, Stanford, California 94305, USA
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