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Hayes RL, Cervantes LF, Abad Santos JC, Samadi A, Vilseck JZ, Brooks CL. How to Sample Dozens of Substitutions per Site with λ Dynamics. J Chem Theory Comput 2024. [PMID: 38976796 DOI: 10.1021/acs.jctc.4c00514] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/10/2024]
Abstract
Alchemical free energy methods are useful in computer-aided drug design and computational protein design because they provide rigorous statistical mechanics-based estimates of free energy differences from molecular dynamics simulations. λ dynamics is a free energy method with the ability to characterize combinatorial chemical spaces spanning thousands of related systems within a single simulation, which gives it a distinct advantage over other alchemical free energy methods that are mostly limited to pairwise comparisons. Recently developed methods have improved the scalability of λ dynamics to perturbations at many sites; however, the size of chemical space that can be explored at each individual site has previously been limited to fewer than ten substituents. As the number of substituents increases, the volume of alchemical space corresponding to nonphysical alchemical intermediates grows exponentially relative to the size corresponding to the physical states of interest. Beyond nine substituents, λ dynamics simulations become lost in an alchemical morass of intermediate states. In this work, we introduce new biasing potentials that circumvent excessive sampling of intermediate states by favoring sampling of physical end points relative to alchemical intermediates. Additionally, we present a more scalable adaptive landscape flattening algorithm for these larger alchemical spaces. Finally, we show that this potential enables more efficient sampling in both protein and drug design test systems with up to 24 substituents per site, enabling, for the first time, simultaneous simulation of all 20 amino acids.
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Affiliation(s)
- Ryan L Hayes
- Department of Chemical and Biomolecular Engineering, University of California Irvine, Irvine, California 92697, United States
- Department of Pharmaceutical Sciences, University of California Irvine, Irvine, California 92697, United States
| | - Luis F Cervantes
- Department of Medicinal Chemistry, College of Pharmacy, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Justin Cruz Abad Santos
- Department of Chemical and Biomolecular Engineering, University of California Irvine, Irvine, California 92697, United States
| | - Amirmasoud Samadi
- Department of Chemical and Biomolecular Engineering, University of California Irvine, Irvine, California 92697, United States
| | - Jonah Z Vilseck
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, Indiana 46202, United States
- Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indianapolis, Indiana 46202, United States
| | - Charles L Brooks
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Biophysics Program, University of Michigan, Ann Arbor, Michigan 48109, United States
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Hu R, Zhang J, Kang Y, Wang Z, Pan P, Deng Y, Hsieh CY, Hou T. Comprehensive, Open-Source, and Automated Workflow for Multisite λ-Dynamics in Lead Optimization. J Chem Theory Comput 2024; 20:1465-1478. [PMID: 38300792 DOI: 10.1021/acs.jctc.3c01154] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2024]
Abstract
Multisite λ-dynamics (MSLD) is a highly efficient binding free energy calculation method that samples multiple ligands in a single round by assigning different λ values to the alchemical part of each ligand. This method holds great promise for lead optimization (LO) in drug discovery. However, the complex data preparation and simulation process limits its widespread application in diverse protein-ligand systems. To address this challenge, we developed a comprehensive, open-source, and automated workflow for MSLD calculations based on the BLaDE dynamics engine. This workflow incorporates the Ligand Internal and Cartesian coordinate reconstruction-based alignment algorithm (LIC-align) and an optimized maximum common substructure (MCS) search algorithm to accurately generate MSLD multiple topologies with ideal perturbation patterns. Furthermore, our workflow is highly modularized, allowing straightforward integration and extension of various simulation techniques, and is highly accessible to nonexperts. This workflow was validated by calculating the relative binding free energies of large-scale congeneric ligands, many of which have large perturbing groups. The agreement between the calculations and experiments was excellent, with an average unsigned error of 1.08 ± 0.47 kcal/mol. More than 57.1% of the ligands had an error of less than 1.0 kcal/mol, and the perturbations of 6 targets were fully connected via the calculations, while those of 2 targets were connected via both calculations and experimental data. The Pearson correlation coefficient reached 0.88, indicating that the MSLD workflow provides accurate predictions that can guide lead optimization in drug discovery. We also examined the impact of single-site versus multisite perturbations, ligand grouping by perturbing group size, and the position of the anchor atom on the MSLD performance. By integrating our proposed LIC-align and optimized MCS search algorithm along with the coping strategies to handle challenging molecular substructures, our workflow can handle many realistic scenarios more reasonably than all previously published methods. Moreover, we observed that our MSLD workflow achieved similar accuracy to free energy perturbation (FEP) while improving computational efficiency by over 1 order of magnitude in speedup. These findings provide valuable insights and strategies for further MSLD development, making MSLD a competitive tool for lead optimization.
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Affiliation(s)
- Renling Hu
- Innovation Institute for Artificial Intelligence in Medicine of Zhejiang University, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
- Polytechnic Institute, Zhejiang University, Hangzhou 310058, Zhejiang, China
- CarbonSilicon AI Technology Co., Ltd., Hangzhou 310018, Zhejiang, China
| | - Jintu Zhang
- Innovation Institute for Artificial Intelligence in Medicine of Zhejiang University, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Yu Kang
- Innovation Institute for Artificial Intelligence in Medicine of Zhejiang University, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Zhe Wang
- Innovation Institute for Artificial Intelligence in Medicine of Zhejiang University, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Peichen Pan
- Innovation Institute for Artificial Intelligence in Medicine of Zhejiang University, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Yafeng Deng
- CarbonSilicon AI Technology Co., Ltd., Hangzhou 310018, Zhejiang, China
| | - Chang-Yu Hsieh
- Innovation Institute for Artificial Intelligence in Medicine of Zhejiang University, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
| | - Tingjun Hou
- Innovation Institute for Artificial Intelligence in Medicine of Zhejiang University, College of Pharmaceutical Sciences, Zhejiang University, Hangzhou 310058, Zhejiang, China
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Liu X, Brooks Iii CL. Enhanced Sampling of Buried Charges in Free Energy Calculations Using Replica Exchange with Charge Tempering. J Chem Theory Comput 2024; 20:1051-1061. [PMID: 38232295 DOI: 10.1021/acs.jctc.3c00993] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2024]
Abstract
Buried ionizable groups in proteins often play important structural and functional roles. However, it is generally challenging to study the detailed molecular mechanisms solely based on experimental measurements. Free energy calculations using atomistic simulations, on the other hand, complement experimental studies and can provide high temporal and spatial resolution information that can lead to mechanistic insights. Nevertheless, it is also well recognized that sufficient sampling of such atomistic simulations can be challenging, considering that structural changes related to the buried charges may be very slow. In the present study, we describe a simple but effective enhanced sampling technique called replica exchange with charge tempering (REChgT) with a novel free energy method, multisite λ dynamics (MSλD), to study two systems containing buried charges, pKa prediction of a small molecule, orotate, in complex with the dihydroorotate dehydrogenase, and relative stability of a Glu-Lys pair buried in the hydrophobic core of two variants of Staphylococcal nuclease. Compared to the original MSλD simulations, the usage of REChgT dramatically increases sampling in both conformational and alchemical spaces, which directly translates into a significant reduction of wall time to converge the free energy calculations. This study highlights the importance of sufficient sampling toward developing improved free energy methods.
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Affiliation(s)
- Xiaorong Liu
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
| | - Charles L Brooks Iii
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109, United States
- Biophysics Program, University of Michigan, Ann Arbor, Michigan 48109, United States
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Angelo M, Zhang W, Vilseck JZ, Aoki ST. In silico λ-dynamics predicts protein binding specificities to modified RNAs. BIORXIV : THE PREPRINT SERVER FOR BIOLOGY 2024:2024.01.26.577511. [PMID: 38328125 PMCID: PMC10849657 DOI: 10.1101/2024.01.26.577511] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/09/2024]
Abstract
RNA modifications shape gene expression through a smorgasbord of chemical changes to canonical RNA bases. Although numbering in the hundreds, only a few RNA modifications are well characterized, in part due to the absence of methods to identify modification sites. Antibodies remain a common tool to identify modified RNA and infer modification sites through straightforward applications. However, specificity issues can result in off-target binding and confound conclusions. This work utilizes in silico λ-dynamics to efficiently estimate binding free energy differences of modification-targeting antibodies between a variety of naturally occurring RNA modifications. Crystal structures of inosine and N6-methyladenosine (m6A) targeting antibodies bound to their modified ribonucleosides were determined and served as structural starting points. λ-Dynamics was utilized to predict RNA modifications that permit or inhibit binding to these antibodies. In vitro RNA-antibody binding assays supported the accuracy of these in silico results. High agreement between experimental and computed binding propensities demonstrated that λ-dynamics can serve as a predictive screen for antibody specificity against libraries of RNA modifications. More importantly, this strategy is an innovative way to elucidate how hundreds of known RNA modifications interact with biological molecules without the limitations imposed by in vitro or in vivo methodologies.
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Affiliation(s)
- Murphy Angelo
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, 635 Barnhill Drive, Indianapolis, IN 46202, USA
| | - Wen Zhang
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, 635 Barnhill Drive, Indianapolis, IN 46202, USA
- Melvin and Bren Simon Cancer Center, 535 Barnhill Drive, Indianapolis, IN 46202, USA
| | - Jonah Z. Vilseck
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, 635 Barnhill Drive, Indianapolis, IN 46202, USA
- Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indianapolis, IN 46202, USA
| | - Scott T. Aoki
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, 635 Barnhill Drive, Indianapolis, IN 46202, USA
- Melvin and Bren Simon Cancer Center, 535 Barnhill Drive, Indianapolis, IN 46202, USA
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Robo MT, Hayes RL, Ding X, Pulawski B, Vilseck JZ. Fast free energy estimates from λ-dynamics with bias-updated Gibbs sampling. Nat Commun 2023; 14:8515. [PMID: 38129400 PMCID: PMC10740020 DOI: 10.1038/s41467-023-44208-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Accepted: 12/04/2023] [Indexed: 12/23/2023] Open
Abstract
Relative binding free energy calculations have become an integral computational tool for lead optimization in structure-based drug design. Classical alchemical methods, including free energy perturbation or thermodynamic integration, compute relative free energy differences by transforming one molecule into another. However, these methods have high operational costs due to the need to perform many pairwise perturbations independently. To reduce costs and accelerate molecular design workflows, we present a method called λ-dynamics with bias-updated Gibbs sampling. This method uses dynamic biases to continuously sample between multiple ligand analogues collectively within a single simulation. We show that many relative binding free energies can be determined quickly with this approach without compromising accuracy. For five benchmark systems, agreement to experiment is high, with root mean square errors near or below 1.0 kcal mol-1. Free energy results are consistent with other computational approaches and within statistical noise of both methods (0.4 kcal mol-1 or less). Notably, large efficiency gains over thermodynamic integration of 18-66-fold for small perturbations and 100-200-fold for whole aromatic ring substitutions are observed. The rapid determination of relative binding free energies will enable larger chemical spaces to be more readily explored and structure-based drug design to be accelerated.
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Affiliation(s)
- Michael T Robo
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, IN, 46202, USA
- Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indianapolis, IN, 46202, USA
- Indiana Biosciences Research Institute, 1210 Waterway Blvd Ste. 2000, Indianapolis, IN, 46202, USA
| | - Ryan L Hayes
- Chemical and Biomolecular Engineering, University of California, Irvine, California, 92617, USA
- Pharmaceutical Sciences, University of California, Irvine, CA, 92617, USA
| | - Xinqiang Ding
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
- Department of Chemistry, Tufts University, Medford, MA, 02144, USA
| | - Brian Pulawski
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, IN, 46202, USA
| | - Jonah Z Vilseck
- Department of Biochemistry and Molecular Biology, Indiana University School of Medicine, Indianapolis, IN, 46202, USA.
- Center for Computational Biology and Bioinformatics, Indiana University School of Medicine, Indianapolis, IN, 46202, USA.
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Fu H, Chipot C, Shao X, Cai W. Standard Binding Free-Energy Calculations: How Far Are We from Automation? J Phys Chem B 2023; 127:10459-10468. [PMID: 37824848 DOI: 10.1021/acs.jpcb.3c04370] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/14/2023]
Abstract
Recent success stories suggest that in silico protein-ligand binding free-energy calculations are approaching chemical accuracy. However, their widespread application remains limited by the extensive human intervention required, posing challenges for the neophyte. As such, it is critical to develop automated workflows for estimating protein-ligand binding affinities with minimum personal involvement. Key human efforts include setting up and tuning enhanced-sampling or alchemical-transformation algorithms as a preamble to computational binding free-energy estimations. Additionally, preparing input files, bookkeeping, and postprocessing represent nontrivial tasks. In this Perspective, we discuss recent progress in automating standard binding free-energy calculations, featuring the development of adaptive or parameter-free algorithms, standardization of binding free-energy calculation workflows, and the implementation of user-friendly software. We also assess the current state of automated standard binding free-energy calculations and evaluate the limitations of existing methods. Last, we outline the requirements for future algorithms and workflows to facilitate automated free-energy calculations for diverse protein-ligand complexes.
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Affiliation(s)
- Haohao Fu
- State Key Laboratory of Medicinal Chemical Biology, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Christophe Chipot
- Laboratoire International Associé CNRS and University of Illinois at Urbana-Champaign, UMR no. 7019, Université de Lorraine, BP 70239, F-54506 Vandoeuvre-lès-Nancy, France
- Department of Physics, University of Illinois at Urbana-Champaign, 1110 West Green Street, Urbana, Illinois 61801, United States
- Department of Chemistry, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States
- Department of Chemistry, The University of Hawai'i at Ma̅noa, 2545 McCarthy Mall, Honolulu, Hawaii 96822, United States
| | - Xueguang Shao
- State Key Laboratory of Medicinal Chemical Biology, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
| | - Wensheng Cai
- State Key Laboratory of Medicinal Chemical Biology, Tianjin Key Laboratory of Biosensing and Molecular Recognition, Research Center for Analytical Sciences, Frontiers Science Center for New Organic Matter, College of Chemistry, Nankai University, Tianjin 300071, China
- Haihe Laboratory of Sustainable Chemical Transformations, Tianjin 300192, China
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Champion C, Gall R, Ries B, Rieder SR, Barros EP, Riniker S. Accelerating Alchemical Free Energy Prediction Using a Multistate Method: Application to Multiple Kinases. J Chem Inf Model 2023; 63:7133-7147. [PMID: 37948537 PMCID: PMC10685456 DOI: 10.1021/acs.jcim.3c01469] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/13/2023] [Revised: 10/23/2023] [Accepted: 10/23/2023] [Indexed: 11/12/2023]
Abstract
Alchemical free-energy methods based on molecular dynamics (MD) simulations have become important tools to identify modifications of small organic molecules that improve their protein binding affinity during lead optimization. The routine application of pairwise free-energy methods to rank potential binders from best to worst is impacted by the combinatorial increase in calculations to perform when the number of molecules to assess grows. To address this fundamental limitation, our group has developed replica-exchange enveloping distribution sampling (RE-EDS), a pathway-independent multistate method, enabling the calculation of alchemical free-energy differences between multiple ligands (N > 2) from a single MD simulation. In this work, we apply the method to a set of four kinases with diverse binding pockets and their corresponding inhibitors (42 in total), chosen to showcase the general applicability of RE-EDS in prospective drug design campaigns. We show that for the targets studied, RE-EDS is able to model up to 13 ligands simultaneously with high sampling efficiency, leading to a substantial decrease in computational cost when compared to pairwise methods.
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Affiliation(s)
- Candide Champion
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - René Gall
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | | | - Salomé R. Rieder
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Emilia P. Barros
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Sereina Riniker
- Department of Chemistry and
Applied Biosciences, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
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Buckner J, Liu X, Chakravorty A, Wu Y, Cervantes LF, Lai TT, Brooks CL. pyCHARMM: Embedding CHARMM Functionality in a Python Framework. J Chem Theory Comput 2023; 19:3752-3762. [PMID: 37267404 PMCID: PMC10504603 DOI: 10.1021/acs.jctc.3c00364] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
CHARMM is rich in methodology and functionality as one of the first programs addressing problems of molecular dynamics and modeling of biological macromolecules and their partners, e.g., small molecule ligands. When combined with the highly developed CHARMM parameters for proteins, nucleic acids, small molecules, lipids, sugars, and other biologically relevant building blocks, and the versatile CHARMM scripting language, CHARMM has been a trendsetting platform for modeling studies of biological macromolecules. To further enhance the utility of accessing and using CHARMM functionality in increasingly complex workflows associated with modeling biological systems, we introduce pyCHARMM, Python bindings, functions, and modules to complement and extend the extensive set of modeling tools and methods already available in CHARMM. These include access to CHARMM function-generated variables associated with the system (psf), coordinates, velocities and forces, atom selection variables, and force field related parameters. The ability to augment CHARMM forces and energies with energy terms or methods derived from machine learning or other sources, written in Python, CUDA, or OpenCL and expressed as Python callable routines is introduced together with analogous functions callable during dynamics calculations. Integration of Python-based graphical engines for visualization of simulation models and results is also accessible. Loosely coupled parallelism is available for workflows such as free energy calculations, using MBAR/TI approaches or high-throughput multisite λ-dynamics (MSλD) free energy methods, string path optimization calculations, replica exchange, and molecular docking with a new Python-based CDOCKER module. CHARMM accelerated platform kernels through the CHARMM/OpenMM API, CHARMM/DOMDEC, and CHARMM/BLaDE API are also readily integrated into this Python framework. We anticipate that pyCHARMM will be a robust platform for the development of comprehensive and complex workflows utilizing Python and its extensive functionality as well as an optimal platform for users to learn molecular modeling methods and practices within a Python-friendly environment such as Jupyter Notebooks.
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Affiliation(s)
- Joshua Buckner
- Department of Chemistry, University of Michigan, Ann Arbor, MI
| | - Xiaorong Liu
- Department of Chemistry, University of Michigan, Ann Arbor, MI
| | | | - Yujin Wu
- Department of Chemistry, University of Michigan, Ann Arbor, MI
| | - Luis F. Cervantes
- Department of Medicinal Chemistry, University of Michigan, Ann Arbor, MI
| | - Thanh T. Lai
- Biophysics Program, University of Michigan, Ann Arbor, MI
| | - Charles L. Brooks
- Department of Chemistry, University of Michigan, Ann Arbor, MI
- Biophysics Program, University of Michigan, Ann Arbor, MI
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Liu X, Tsang PK, Soellner MB, Brooks CL. QSAR via Multisite λ-Dynamics in the Orphaned TSSK1B Kinase. Protein Sci 2023; 32:e4623. [PMID: 36906820 PMCID: PMC10031809 DOI: 10.1002/pro.4623] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2022] [Revised: 02/18/2023] [Accepted: 03/08/2023] [Indexed: 03/13/2023]
Abstract
Multisite λ-dynamics (MSλD) is a novel method for the calculation of relative free energies of binding for ligands to their targeted receptors. It can be readily used to examine a large number of molecules with multiple functional groups at multiple sites around a common core. This makes MSλD a powerful tool in structure-based drug design. In the present study, MSλD is applied to calculate the relative binding free energies of 1296 inhibitors to the testis specific serine kinase 1B (TSSK1B), a validated target for male contraception. For this system, MSλD requires significantly fewer computational resources compared to traditional free energy methods like free energy perturbation or thermodynamic integration. From MSλD simulations, we examined whether modifications of a ligand at two different sites are coupled or not. Based on our calculations, we established a quantitative structure-activity relationship (QSAR) for this set of molecules and identified a site in the ligand where further modification, such as adding more polar groups, may lead to increased binding affinity. This article is protected by copyright. All rights reserved.
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Affiliation(s)
- Xiaorong Liu
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan, 48109, USA
| | - Pui Ki Tsang
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan, 48109, USA
| | - Matthew B Soellner
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan, 48109, USA
| | - Charles L Brooks
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan, 48109, USA
- Biophysics Program, University of Michigan, Ann Arbor, Michigan, 48109, USA
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