1
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Spiriti J, Wong CF. Quantitative Prediction of Dissociation Rates of PYK2 Ligands Using Umbrella Sampling and Milestoning. J Chem Theory Comput 2024; 20:4029-4044. [PMID: 38640609 DOI: 10.1021/acs.jctc.4c00192] [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: 04/21/2024]
Abstract
We used umbrella sampling and the milestoning simulation method to study the dissociation of multiple ligands from protein kinase PYK2. The activation barriers obtained from the potential of mean force of the umbrella sampling simulations correlated well with the experimental dissociation rates. Using the zero-temperature string method, we obtained optimized paths along the free-energy surfaces for milestoning simulations of three ligands with a similar structure. The milestoning simulations gave an absolute dissociation rate within 2 orders of magnitude of the experimental value for two ligands but at least 3 orders of magnitude too high for the third. Despite the similarity in their structures, the ligands took different pathways to exit from the binding site of PYK2, making contact with different sets of residues. In addition, the protein experienced different conformational changes for dissociation of the three ligands.
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Affiliation(s)
- Justin Spiriti
- Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, Missouri 63121, United States
| | - Chung F Wong
- Department of Chemistry and Biochemistry, University of Missouri-St. Louis, St. Louis, Missouri 63121, United States
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2
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Dietschreit JCB, Diestler DJ, Gómez-Bombarelli R. Entropy and Energy Profiles of Chemical Reactions. J Chem Theory Comput 2023; 19:5369-5379. [PMID: 37535443 DOI: 10.1021/acs.jctc.3c00448] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/05/2023]
Abstract
The description of chemical processes at the molecular level is often facilitated by the use of reaction coordinates or collective variables (CVs). The CV measures the progress of the reaction and allows the construction of profiles that track how specific properties evolve as the reaction progresses. Whereas CVs are routinely used, especially alongside enhanced sampling techniques, the links among reaction profiles, thermodynamic state functions, and reaction rate constants are not rigorously exploited. Here, we report a unified treatment of such reaction profiles. Tractable expressions are derived for the free-energy, internal-energy, and entropy profiles as functions of only the CV. We demonstrate the ability of this treatment to extract quantitative insight from the entropy and internal-energy profiles of various real-world physicochemical processes, including intramolecular organic reactions, ionic transport in superionic electrolytes, and molecular transport in nanoporous materials.
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Affiliation(s)
- Johannes C B Dietschreit
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
| | - Dennis J Diestler
- University of Nebraska-Lincoln, Lincoln, Nebraska 68583, United States
| | - Rafael Gómez-Bombarelli
- Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States
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3
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Ojha AA, Srivastava A, Votapka LW, Amaro RE. Selectivity and Ranking of Tight-Binding JAK-STAT Inhibitors Using Markovian Milestoning with Voronoi Tessellations. J Chem Inf Model 2023; 63:2469-2482. [PMID: 37023323 PMCID: PMC10131228 DOI: 10.1021/acs.jcim.2c01589] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/08/2023]
Abstract
Janus kinases (JAK), a group of proteins in the nonreceptor tyrosine kinase (NRTKs) family, play a crucial role in growth, survival, and angiogenesis. They are activated by cytokines through the Janus kinase-signal transducer and activator of a transcription (JAK-STAT) signaling pathway. JAK-STAT signaling pathways have significant roles in the regulation of cell division, apoptosis, and immunity. Identification of the V617F mutation in the Janus homology 2 (JH2) domain of JAK2 leading to myeloproliferative disorders has stimulated great interest in the drug discovery community to develop JAK2-specific inhibitors. However, such inhibitors should be selective toward JAK2 over other JAKs and display an extended residence time. Recently, novel JAK2/STAT5 axis inhibitors (N-(1H-pyrazol-3-yl)pyrimidin-2-amino derivatives) have displayed extended residence times (hours or longer) on target and adequate selectivity excluding JAK3. To facilitate a deeper understanding of the kinase-inhibitor interactions and advance the development of such inhibitors, we utilize a multiscale Markovian milestoning with Voronoi tessellations (MMVT) approach within the Simulation-Enabled Estimation of Kinetic Rates v.2 (SEEKR2) program to rank order these inhibitors based on their kinetic properties and further explain the selectivity of JAK2 inhibitors over JAK3. Our approach investigates the kinetic and thermodynamic properties of JAK-inhibitor complexes in a user-friendly, fast, efficient, and accurate manner compared to other brute force and hybrid-enhanced sampling approaches.
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Affiliation(s)
- Anupam Anand Ojha
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Ambuj Srivastava
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Lane William Votapka
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Rommie E Amaro
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
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4
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Abstract
This Perspective reviews the use of Transition Path Sampling methods to study enzymatically catalyzed chemical reactions. First applied by our group to an enzymatic reaction over 15 years ago, the method has uncovered basic principles in enzymatic catalysis such as the protein promoting vibration, and it has also helped harmonize such ideas as electrostatic preorganization with dynamic views of enzyme function. It is now being used to help uncover principles of protein design necessary to artificial enzyme creation.
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Affiliation(s)
- Steven D Schwartz
- Department of Chemistry and Biochemistry University of Arizona Tucson, Arizona 85721, United States
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5
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Ruzmetov T, Montes R, Sun J, Chen SH, Tang Z, Chang CEA. Binding Kinetics Toolkit for Analyzing Transient Molecular Conformations and Computing Free Energy Landscapes. J Phys Chem A 2022; 126:8761-8770. [DOI: 10.1021/acs.jpca.2c05499] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Talant Ruzmetov
- Department of Chemistry, University of California at Riverside, Riverside, California92521, United States
| | - Ruben Montes
- Department of Chemistry, University of California at Riverside, Riverside, California92521, United States
| | - Jianan Sun
- Department of Chemistry, University of California at Riverside, Riverside, California92521, United States
| | - Si-Han Chen
- Department of Chemistry, University of California at Riverside, Riverside, California92521, United States
| | - Zhiye Tang
- Department of Chemistry, University of California at Riverside, Riverside, California92521, United States
| | - Chia-en A. Chang
- Department of Chemistry, University of California at Riverside, Riverside, California92521, United States
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6
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Li W. Energy Decomposition along the Reaction Coordinate: Theory and Applications to Nonequilibrium Ensembles of Trajectories. J Phys Chem A 2022; 126:7763-7773. [PMID: 36214522 DOI: 10.1021/acs.jpca.2c04130] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
A theoretical framework is proposed for an energy decomposition scheme along the reaction coordinate, in which the ensemble average of the potential energy weighted with reactive flux intensity is decomposed into energy components at the per-coordinate level. The decomposed energy quantity is demonstrated to be closely related to the free energy along the reaction coordinate, and its connection to the emergent potential energy is provided. In the application to alanine dipeptide under vacuum, illustrative calculations were performed in three nonequilibrium ensembles of trajectories: (1) transition path ensemble sampled with transition path sampling; (2) ensemble of short trajectories initiated from configurations around the transition-state region; and (3) ensemble of short trajectories shooting from configurations in several transition paths. The energy components on each coordinate were found to be consistent among the three ensembles of trajectories, indicating a broad applicability of the approach in biomolecular studies. In addition, the free energies along an optimized reaction coordinate obtained with these nonequilibrium ensembles were largely overlapped with a reference free energy calculated from a long equilibrium trajectory.
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Affiliation(s)
- Wenjin Li
- Institute for Advanced Study, Shenzhen University, Shenzhen518060, China
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7
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Berezhkovskii AM, Szabo A. Relations among Unidirectional Fluxes at Equilibrium, Committors, and First Passage and Transition Path Times. J Phys Chem B 2022; 126:6624-6628. [PMID: 36037104 DOI: 10.1021/acs.jpcb.2c03757] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
For multidimensional diffusive dynamics, we algebraically derive remarkable analytical expressions that relate the mean first passage and transition path times between two dividing surfaces with the number of unidirectional transitions per unit time (fluxes) at equilibrium between the two surfaces and the committor (the probability of reaching one surface before the other). In one dimension, such relationships can be easily derived because analytical expressions for all the above-mentioned quantities can be found. This is not possible in higher dimensions, and at first sight, the problem seems much harder. We circumvent the difficulty that the equations determining the mean first passage and transition path times cannot be solved analytically by multiplying these equations by the committor, integrating both sides and finally using the divergence theorem. A byproduct of our derivation is an analytical expression for the starting point distribution over which individual first passage and transition path times must be averaged. It turns out that this distribution is not the Boltzmann one, but it has a simple physical interpretation.
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Affiliation(s)
- Alexander M Berezhkovskii
- Section of Molecular Transport, Eunice Kennedy Shriver National Institute of Child Health and Human development, National Institutes of Health, Bethesda, Maryland 20892, United States
| | - Attila Szabo
- Laboratory of Chemical Physics, National institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 20892, United States
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8
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Votapka LW, Stokely AM, Ojha AA, Amaro RE. SEEKR2: Versatile Multiscale Milestoning Utilizing the OpenMM Molecular Dynamics Engine. J Chem Inf Model 2022; 62:3253-3262. [PMID: 35759413 PMCID: PMC9277580 DOI: 10.1021/acs.jcim.2c00501] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
We present SEEKR2
(simulation-enabled estimation of kinetic rates
version 2)—the latest iteration in the family of SEEKR programs
for using multiscale simulation methods to computationally estimate
the kinetics and thermodynamics of molecular processes, in particular,
ligand-receptor binding. SEEKR2 generates equivalent, or improved,
results compared to the earlier versions of SEEKR but with significant
increases in speed and capabilities. SEEKR2 has also been built with
greater ease of usability and with extensible features to enable future
expansions of the method. Now, in addition to supporting simulations
using NAMD, calculations may be run with the fast and extensible OpenMM
simulation engine. The Brownian dynamics portion of the calculation
has also been upgraded to Browndye 2. Furthermore, this version of
SEEKR supports hydrogen mass repartitioning, which significantly reduces
computational cost, while showing little, if any, loss of accuracy
in the predicted kinetics.
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Affiliation(s)
- Lane W Votapka
- University of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093, United States
| | - Andrew M Stokely
- University of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093, United States
| | - Anupam A Ojha
- University of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093, United States
| | - Rommie E Amaro
- University of California, San Diego, 9500 Gilman Dr., La Jolla, California 92093, United States
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9
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Li W. Time-Lagged Flux in the Transition Path Ensemble: Flux Maximization and Relation to Transition Path Theory. J Phys Chem A 2022; 126:3797-3810. [PMID: 35670470 DOI: 10.1021/acs.jpca.2c02221] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The transition path ensemble is of special interest in reaction coordinate identification as it consists of reactive trajectories that start from the reactant state and end in the product one. As a theoretical framework for describing the transition path ensemble, the transition path theory has been introduced more than 10 years ago, and so far, its applications have only been illustrated in several low-dimensional systems. Given the transition path ensemble, expressions for calculating flux, current (a vector field), and principal curves are derived here in the space of collective variables from the transition path theory, and they are applicable to time series obtained from molecular dynamics simulations of high-dimensional systems, i.e., the position coordinates as a function of time in the transition path ensemble. The connection of the transition path theory is made to a density-weighted average flux, a quantity proposed in a previous work to appraise the relevance of a coordinate to the reaction coordinate [Li, W. J. Chem. Phys. 2022, 156, 054117]. Most importantly, as an extension of the existing quantities, time-lagged quantities such as flux and current are also proposed. The main insights and objects provided by these time-lagged quantities are illustrated in the application to the alanine peptide in vacuum.
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Affiliation(s)
- Wenjin Li
- Institute for Advanced Study, Shenzhen University, Shenzhen 518060, China
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10
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Cardenas AE, Drexler CI, Nechushtai R, Mittler R, Friedler A, Webb LJ, Elber R. Peptide Permeation across a Phosphocholine Membrane: An Atomically Detailed Mechanism Determined through Simulations and Supported by Experimentation. J Phys Chem B 2022; 126:2834-2849. [PMID: 35388695 PMCID: PMC9074375 DOI: 10.1021/acs.jpcb.1c10966] [Citation(s) in RCA: 15] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Cell-penetrating peptides (CPPs) facilitate translocation across biological membranes and are of significant biological and medical interest. Several CPPs can permeate into specific cells and organelles. We examine the incorporation and translocation of a novel anticancer CPP in a dioleoylphosphatidylcholine (DOPC) lipid bilayer membrane. The peptide, NAF-144-67, is a short fragment of a transmembrane protein, consisting of hydrophobic N-terminal and charged C-terminal segments. Experiments using fluorescently labeled NAF-144-67 in ∼100 nm DOPC vesicles and atomically detailed simulations conducted with Milestoning support a model in which a significant barrier for peptide-membrane entry is found at the interface between the aqueous solution and membrane. The initial step is the insertion of the N-terminal segment and the hydrophobic helix into the membrane, passing the hydrophilic head groups. Both experiments and simulations suggest that the free energy difference in the first step of the permeation mechanism in which the hydrophobic helix crosses the phospholipid head groups is -0.4 kcal mol-1 slightly favoring motion into the membrane. Milestoning calculations of the mean first passage time and the committor function underscore the existence of an early polar barrier followed by a diffusive barrierless motion in the lipid tail region. Permeation events are coupled to membrane fluctuations that are examined in detail. Our study opens the way to investigate in atomistic resolution the molecular mechanism, kinetics, and thermodynamics of CPP permeation to diverse membranes.
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Affiliation(s)
- Alfredo E Cardenas
- Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Chad I Drexler
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Rachel Nechushtai
- The Alexander Silberman Institute of Life Sciences, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat-Ram, Jerusalem 91904, Israel
| | - Ron Mittler
- The Department of Surgery, University of Missouri School of Medicine, Christopher S. Bond Life Sciences Center, University of Missouri, 1201 Rollins Street, Columbia, Missouri 65201, United States
| | - Assaf Friedler
- The Institute of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat-Ram, Jerusalem 91904, Israel
| | - Lauren J Webb
- Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Ron Elber
- Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States.,Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
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11
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Yue Z, Bernardi A, Li C, Mironenko AV, Swanson JMJ. Toward a Multipathway Perspective: pH-Dependent Kinetic Selection of Competing Pathways and the Role of the Internal Glutamate in Cl -/H + Antiporters. J Phys Chem B 2021; 125:7975-7984. [PMID: 34260231 PMCID: PMC8409247 DOI: 10.1021/acs.jpcb.1c03304] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Canonical descriptions of multistep biomolecular transformations generally follow a single-pathway viewpoint, with a series of transitions through intermediates converting reactants to products or repeating a conformational cycle. However, mounting evidence suggests that more complexity and pathway heterogeneity are mechanistically relevant due to the statistical distribution of multiple interconnected rate processes. Making sense of such pathway complexity remains a significant challenge. To better understand the role and relevance of pathway heterogeneity, we herein probe the chemical reaction network of a Cl-/H+ antiporter, ClC-ec1, and analyze reaction pathways using multiscale kinetic modeling (MKM). This approach allows us to describe the nature of the competing pathways and how they change as a function of pH. We reveal that although pH-dependent Cl-/H+ transport rates are largely regulated by the charge state of amino acid E148, the charge state of E203 determines relative contributions from coexisting pathways and can shift the flux pH-dependence. The selection of pathways via E203 explains how ionizable mutations (D/H/K/R) would impact the ClC-ec1 bioactivity from a kinetic perspective and lends further support to the indispensability of an internal glutamate in ClC antiporters. Our results demonstrate how quantifying the kinetic selection of competing pathways under varying conditions leads to a deeper understanding of the Cl-/H+ exchange mechanism and can suggest new approaches for mechanistic control.
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Affiliation(s)
- Zhi Yue
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Frank Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Austen Bernardi
- Department of Chemistry, Biological Chemistry Program, and Center for Cell and Genome Science, The University of Utah, Salt Lake City, Utah 84112, United States
| | - Chenghan Li
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Frank Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Alexander V. Mironenko
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Frank Institute, and Institute for Biophysical Dynamics, The University of Chicago, Chicago, Illinois 60637, United States
| | - Jessica M. J. Swanson
- Department of Chemistry, Biological Chemistry Program, and Center for Cell and Genome Science, The University of Utah, Salt Lake City, Utah 84112, United States
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12
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Narayan B, Buchete NV, Elber R. Computer Simulations of the Dissociation Mechanism of Gleevec from Abl Kinase with Milestoning. J Phys Chem B 2021; 125:5706-5715. [PMID: 33930271 DOI: 10.1021/acs.jpcb.1c00264] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
Gleevec (a.k.a., imatinib) is an important anticancer (e.g., chronic myeloid leukemia) chemotherapeutic drug due to its inhibitory interaction with the Abl kinase. Here, we use atomically detailed simulations within the Milestoning framework to study the molecular dissociation mechanism of Gleevec from Abl kinase. We compute the dissociation free energy profile, the mean first passage time for unbinding, and explore the transition state ensemble of conformations. The milestones form a multidimensional network with average connectivity of about 2.93, which is significantly higher than the connectivity for a one-dimensional reaction coordinate. The free energy barrier for Gleevec dissociation is estimated to be ∼10 kcal/mol, and the exit time is ∼55 ms. We examined the transition state conformations using both, the committor and transition function. We show that near the transition state the highly conserved salt bridge K217 and E286 is transiently broken. Together with the calculated free energy profile, these calculations can advance the understanding of the molecular interaction mechanisms between Gleevec and Abl kinase and play a role in future drug design and optimization studies.
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Affiliation(s)
- Brajesh Narayan
- School of Physics, University College Dublin, Belfield, Dublin 4, Ireland.,Institute for Discovery, University College Dublin, Belfield, Dublin 4, Ireland
| | - Nicolae-Viorel Buchete
- School of Physics, University College Dublin, Belfield, Dublin 4, Ireland.,Institute for Discovery, University College Dublin, Belfield, Dublin 4, Ireland
| | - Ron Elber
- Oden Institute for Computational Engineering and Science, Department of Chemistry, University of Texas at Austin, Austin Texas 78712, United States
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13
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Abstract
The protein HIV Reverse Transcriptase (HIV RT) synthesizes a DNA strand according to a template. During the synthesis, the polymerase slides on the double stranded DNA to allow the entry of a new nucleotide to the active site. We use Molecular Dynamics simulations to estimate the free energy profile and the time scale of the DNA-protein's relative displacement in the complex's closed state. We illustrate that the presence of the catalytic magnesium slows down the process. Upon removing the catalytic magnesium ion, the process is rapid and significantly faster than reopening the active site in preparation for the new substrate. We speculate that magnesium regulates DNA translocation. The magnesium locks the DNA into a specific orientation during the chemical addition of the nucleotide. The release of Mg2+ eases DNA sliding and the acceptance of a new substrate.
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Affiliation(s)
- Hao Wang
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, The University of Texas at Austin, Austin, Texas 78712, United States.,Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, United States
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14
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Abstract
Molecular dynamics (MD) simulations have become increasingly useful in the modern drug development process. In this review, we give a broad overview of the current application possibilities of MD in drug discovery and pharmaceutical development. Starting from the target validation step of the drug development process, we give several examples of how MD studies can give important insights into the dynamics and function of identified drug targets such as sirtuins, RAS proteins, or intrinsically disordered proteins. The role of MD in antibody design is also reviewed. In the lead discovery and lead optimization phases, MD facilitates the evaluation of the binding energetics and kinetics of the ligand-receptor interactions, therefore guiding the choice of the best candidate molecules for further development. The importance of considering the biological lipid bilayer environment in the MD simulations of membrane proteins is also discussed, using G-protein coupled receptors and ion channels as well as the drug-metabolizing cytochrome P450 enzymes as relevant examples. Lastly, we discuss the emerging role of MD simulations in facilitating the pharmaceutical formulation development of drugs and candidate drugs. Specifically, we look at how MD can be used in studying the crystalline and amorphous solids, the stability of amorphous drug or drug-polymer formulations, and drug solubility. Moreover, since nanoparticle drug formulations are of great interest in the field of drug delivery research, different applications of nano-particle simulations are also briefly summarized using multiple recent studies as examples. In the future, the role of MD simulations in facilitating the drug development process is likely to grow substantially with the increasing computer power and advancements in the development of force fields and enhanced MD methodologies.
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15
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Kannan D, Sharpe DJ, Swinburne TD, Wales DJ. Optimal dimensionality reduction of Markov chains using graph transformation. J Chem Phys 2020; 153:244108. [PMID: 33380101 DOI: 10.1063/5.0025174] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Markov chains can accurately model the state-to-state dynamics of a wide range of complex systems, but the underlying transition matrix is ill-conditioned when the dynamics feature a separation of timescales. Graph transformation (GT) provides a numerically stable method to compute exact mean first passage times (MFPTs) between states, which are the usual dynamical observables in continuous-time Markov chains (CTMCs). Here, we generalize the GT algorithm to discrete-time Markov chains (DTMCs), which are commonly estimated from simulation data, for example, in the Markov state model approach. We then consider the dimensionality reduction of CTMCs and DTMCs, which aids model interpretation and facilitates more expensive computations, including sampling of pathways. We perform a detailed numerical analysis of existing methods to compute the optimal reduced CTMC, given a partitioning of the network into metastable communities (macrostates) of nodes (microstates). We show that approaches based on linear algebra encounter numerical problems that arise from the requisite metastability. We propose an alternative approach using GT to compute the matrix of intermicrostate MFPTs in the original Markov chain, from which a matrix of weighted intermacrostate MFPTs can be obtained. We also propose an approximation to the weighted-MFPT matrix in the strongly metastable limit. Inversion of the weighted-MFPT matrix, which is better conditioned than the matrices that must be inverted in alternative dimensionality reduction schemes, then yields the optimal reduced Markov chain. The superior numerical stability of the GT approach therefore enables us to realize optimal Markovian coarse-graining of systems with rare event dynamics.
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Affiliation(s)
- Deepti Kannan
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Daniel J Sharpe
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Thomas D Swinburne
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | - David J Wales
- Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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16
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Elber R, Fathizadeh A, Ma P, Wang H. Modeling molecular kinetics with Milestoning. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2020. [DOI: 10.1002/wcms.1512] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
Affiliation(s)
- Ron Elber
- Department of Chemistry, The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
| | - Arman Fathizadeh
- The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
| | - Piao Ma
- Department of Chemistry University of Texas at Austin Austin Texas USA
| | - Hao Wang
- The Oden Institute for Computational Engineering and Sciences University of Texas at Austin Austin Texas USA
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17
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Elber R. Milestoning: An Efficient Approach for Atomically Detailed Simulations of Kinetics in Biophysics. Annu Rev Biophys 2020; 49:69-85. [PMID: 32375019 DOI: 10.1146/annurev-biophys-121219-081528] [Citation(s) in RCA: 37] [Impact Index Per Article: 9.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Recent advances in theory and algorithms for atomically detailed simulations open the way to the study of the kinetics of a wide range of molecular processes in biophysics. The theories propose a shift from the traditionally very long molecular dynamic trajectories, which are exact but may not be efficient in the study of kinetics, to the use of a large number of short trajectories. The short trajectories exploit a mapping to a mesh in coarse space and allow for efficient calculations of kinetics and thermodynamics. In this review, I focus on one theory: Milestoning is a theory and an algorithm that offers a hierarchical calculation of properties of interest, such as the free energy profile and the mean first passage time. Approximations to the true long-time dynamics can be computed efficiently and assessed at different steps of the investigation. The theory is discussed and illustrated using two biophysical examples: ion permeation through a phospholipid membrane and protein translocation through a channel.
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Affiliation(s)
- Ron Elber
- Oden Institute for Computational Engineering and Sciences, Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA;
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18
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Ma P, Elber R, Makarov DE. Value of Temporal Information When Analyzing Reaction Coordinates. J Chem Theory Comput 2020; 16:6077-6090. [PMID: 32841001 PMCID: PMC7881391 DOI: 10.1021/acs.jctc.0c00678] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/04/2023]
Abstract
Reaction coordinates chart pathways from reactants to products of chemical reactions. Determination of reaction coordinates from ensembles of molecular trajectories has thus been the focus of many studies. A widely used and insightful choice of a reaction coordinate is the committor function, defined as the probability that a trajectory will reach the product before the reactant. Here, we consider alternatives to the committor function that add useful mechanistic information, the mean first passage time, and the exit time to the product. We further derive a simple relationship between the functions of the committor, the mean first passage time, and the exit time. We illustrate the diversity of mechanisms predicted by alternative reaction coordinates with several toy problems and with a simple model of protein searching for a specific DNA motif.
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Affiliation(s)
- Piao Ma
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| | - Ron Elber
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
- Oden Institute for Computational Engineering and Sciences, Austin, Texas 78712, United States
| | - Dmitrii E Makarov
- Department of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
- Oden Institute for Computational Engineering and Sciences, Austin, Texas 78712, United States
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19
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Cottone G, Chiodo L, Maragliano L. Thermodynamics and Kinetics of Ion Permeation in Wild-Type and Mutated Open Active Conformation of the Human α7 Nicotinic Receptor. J Chem Inf Model 2020; 60:5045-5056. [PMID: 32803965 PMCID: PMC8011927 DOI: 10.1021/acs.jcim.0c00549] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Abstract
![]()
Molecular
studies of human pentameric ligand-gated ion channels
(LGICs) expressed in neurons and at neuromuscular junctions are of
utmost importance in the development of therapeutic strategies for
neurological disorders. We focus here on the nicotinic acetylcholine
receptor nAChR-α7, a homopentameric channel widely expressed
in the human brain, with a proven role in a wide spectrum of disorders
including schizophrenia and Alzheimer’s disease. By exploiting
an all-atom structural model of the full (transmembrane and extracellular)
protein in the open, agonist-bound conformation we recently developed,
we evaluate the free energy and the mean first passage time of single-ion
permeation using molecular dynamics simulations and the milestoning
method with Voronoi tessellation. The results for the wild-type channel
provide the first available mapping of the potential of mean force
in the full-length α7 nAChR, reveal its expected cationic nature,
and are in good agreement with simulation data for other channels
of the LGIC family and with experimental data on nAChRs. We then investigate
the role of a specific mutation directly related to ion selectivity
in LGICs, the E-1′ → A-1′ substitution at the
cytoplasmatic selectivity filter. We find that the mutation strongly
affects sodium and chloride permeation in opposite directions, leading
to a complete inversion of selectivity, at variance with the limited
experimental results available that classify this mutant as cationic.
We thus provide structural determinants for the observed cationic-to-anionic
inversion, revealing a key role of the protonation state of residue
rings far from the mutation, in the proximity of the hydrophobic channel
gate.
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Affiliation(s)
- Grazia Cottone
- Department of Physics and Chemistry-Emilio Segrè, University of Palermo, Viale delle Scienze Ed. 17, 90128 Palermo, Italy
| | - Letizia Chiodo
- Department of Engineering, Campus Bio-Medico University of Rome, Via Á. del Portillo 21, 00128 Rome, Italy
| | - Luca Maragliano
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi, 10, 16132 Genova, Italy.,IRCCS Ospedale Policlinico San Martino, Largo Rosanna Benzi, 10, 16132 Genova, Italy
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20
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Jagger BR, Ojha AA, Amaro RE. Predicting Ligand Binding Kinetics Using a Markovian Milestoning with Voronoi Tessellations Multiscale Approach. J Chem Theory Comput 2020; 16:5348-5357. [DOI: 10.1021/acs.jctc.0c00495] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- Benjamin R. Jagger
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, United States
| | - Anupam A. Ojha
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, United States
| | - Rommie E. Amaro
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093, United States
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21
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Wang H, Elber R. Milestoning with wind: Exploring the impact of a biasing potential in exact calculation of kinetics. J Chem Phys 2020; 152:224105. [PMID: 32534551 DOI: 10.1063/5.0011050] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
We consider the algorithm wind-assisted reweighted Milestoning of Grazioli and Andricioaei [J. Chem. Phys 149(8), 084103 (2018)], expand it, and assess its performance. We derive exact expressions for underdamped and overdamped Langevin dynamics and examine its efficiency for a simple model system (Mueller's potential) and for bond breaking in solution. The use of a biasing force (wind) significantly enhances the sampling of otherwise rare trajectories but also introduces an exponential weight to the trajectories that significantly impact the value of the statistics. In our examples, computing averages and standard deviations are not better using wind compared to straightforward Milestoning. However, the biasing force is useful for highly steep energy landscapes. On these landscapes, the probability of sampling straightforward Milestoning trajectories, which overcome the barrier, is low and the biasing force enables the observations of these rare events.
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Affiliation(s)
- Hao Wang
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, Texas 78712, USA
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22
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Wang H, Huang N, Dangerfield T, Johnson KA, Gao J, Elber R. Exploring the Reaction Mechanism of HIV Reverse Transcriptase with a Nucleotide Substrate. J Phys Chem B 2020; 124:4270-4283. [PMID: 32364738 DOI: 10.1021/acs.jpcb.0c02632] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/17/2023]
Abstract
Enzymatic reactions consist of several steps: (i) a weak binding event of the substrate to the enzyme, (ii) an induced fit or a protein conformational transition upon ligand binding, (iii) the chemical reaction, and (iv) the release of the product. Here we focus on step iii of the reaction of a DNA polymerase, HIV RT, with a nucleotide. We determine the rate and the free energy profile for the addition of a nucleotide to a DNA strand using a combination of a QM/MM model, the string method, and exact Milestoning. The barrier height and the time scale of the reaction are consistent with experiment. We show that the observables (free energies and mean first passage time) converge rapidly, as a function of the Milestoning iteration number. We also consider the substitution of an oxygen of the incoming nucleotide by a nonbridging sulfur atom and its impact on the enzymatic reaction. This substitution has been suggested in the past as a tool to examine the influence of the chemical step on the overall rate. Our joint computational and experimental study suggests that the impact of the substitution is small. Computationally, the differences between the two are within the estimated error bars. Experiments suggest a small difference. Finally, we examine step i, the weak binding of the nucleotide to the protein surface. We suggest that this step has only a small contribution to the selectivity of the enzyme. Comments are made on the impact of these steps on the overall mechanism.
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Affiliation(s)
- Hao Wang
- Oden Institute for Computational Engineering and Sciences, University of Texas, Austin Texas 78712, United States
| | - Nathan Huang
- Department of Molecular Biosciences, University of Texas, Austin, Texas 78712, United States
| | - Tyler Dangerfield
- Department of Molecular Biosciences, University of Texas, Austin, Texas 78712, United States
| | - Kenneth A Johnson
- Department of Molecular Biosciences, University of Texas, Austin, Texas 78712, United States
| | - Jiali Gao
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas, Austin Texas 78712, United States.,Department of Chemistry, University of Texas, Austin, Texas 78712, United States
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23
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Narayan B, Fathizadeh A, Templeton C, He P, Arasteh S, Elber R, Buchete NV, Levy RM. The transition between active and inactive conformations of Abl kinase studied by rock climbing and Milestoning. Biochim Biophys Acta Gen Subj 2020; 1864:129508. [PMID: 31884066 PMCID: PMC7012767 DOI: 10.1016/j.bbagen.2019.129508] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/29/2019] [Revised: 12/11/2019] [Accepted: 12/19/2019] [Indexed: 12/12/2022]
Abstract
BACKGROUND Kinases are a family of enzymes that catalyze the transfer of the ɤ-phosphate group from ATP to a protein's residue. Malfunctioning kinases are involved in many health problems such as cardiovascular diseases, diabetes, and cancer. Kinases transitions between multiple conformations of inactive to active forms attracted considerable interest. METHOD A reaction coordinate is computed for the transition between the active to inactive conformation in Abl kinase with a focus on the DFG-in to DFG-out flip. The method of Rock Climbing is used to construct a path locally, which is subsequently optimized using a functional of the entire path. The discrete coordinate sets along the reaction path are used in a Milestoning calculation of the free energy landscape and the rate of the transition. RESULTS The estimated transition times are between a few milliseconds and seconds, consistent with simulations of the kinetics and with indirect experimental data. The activation requires the transient dissociation of the salt bridge between Lys271 and Glu286. The salt bridge reforms once the DFG motif is stabilized by a locked conformation of Phe382. About ten residues are identified that contribute significantly to the process and are included as part of the reaction space. CONCLUSIONS The transition from DFG-in to DFG-out in Abl kinase was simulated using atomic resolution of a fully solvated protein yielding detailed description of the kinetics and the mechanism of the DFG flip. The results are consistent with other computational methods that simulate the kinetics and with some indirect experimental measurements. GENERAL SIGNIFICANCE The activation of kinases includes a conformational transition of the DFG motif that is important for enzyme activity but is not accessible to conventional Molecular Dynamics. We propose a detailed mechanism for the transition, at a timescale longer than conventional MD, using a combination of reaction path and Milestoning algorithms. The mechanism includes local structural adjustments near the binding site as well as collective interactions with more remote residues.
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Affiliation(s)
- Brajesh Narayan
- School of Physics, University College Dublin, Belfield, Dublin 4, Ireland
| | - Arman Fathizadeh
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, 201 E. 24(th) Street, 1 University Station (C0200), Austin, TX 78712-1229, USA
| | - Clark Templeton
- McKetta Department of Chemical Engineering, University of Texas at Austin, 200 E. Dean Keaton St. Stop C0400, Austin, TX 78712-1589, USA
| | - Peng He
- Department of Chemistry, Temple University, 1801 N Broad Street, Philadelphia, PA 19122, USA
| | - Shima Arasteh
- Department of Chemistry, Temple University, 1801 N Broad Street, Philadelphia, PA 19122, USA
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, 201 E. 24(th) Street, 1 University Station (C0200), Austin, TX 78712-1229, USA; Department of Chemistry, University of Texas at Austin, 2506 Speedway STOP A5300, Austin, TX 78712-1224, USA.
| | | | - Ron M Levy
- Department of Chemistry, Temple University, 1801 N Broad Street, Philadelphia, PA 19122, USA
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24
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Jagger BR, Kochanek SE, Haldar S, Amaro RE, Mulholland AJ. Multiscale simulation approaches to modeling drug-protein binding. Curr Opin Struct Biol 2020; 61:213-221. [PMID: 32113133 DOI: 10.1016/j.sbi.2020.01.014] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2019] [Revised: 01/16/2020] [Accepted: 01/21/2020] [Indexed: 01/19/2023]
Abstract
Simulations can provide detailed insight into the molecular processes involved in drug action, such as protein-ligand binding, and can therefore be a valuable tool for drug design and development. Processes with a large range of length and timescales may be involved, and understanding these different scales typically requires different types of simulation methodology. Ideally, simulations should be able to connect across scales, to analyze and predict how changes at one scale can influence another. Multiscale simulation methods, which combine different levels of treatment, are an emerging frontier with great potential in this area. Here we review multiscale frameworks of various types, and selected applications to biomolecular systems with a focus on drug-ligand binding.
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Affiliation(s)
- Benjamin R Jagger
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, United States
| | - Sarah E Kochanek
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, United States
| | - Susanta Haldar
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, BS8 1TS, UK
| | - Rommie E Amaro
- Department of Chemistry and Biochemistry, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093, United States.
| | - Adrian J Mulholland
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol, BS8 1TS, UK.
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25
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Kells A, Koskin V, Rosta E, Annibale A. Correlation functions, mean first passage times, and the Kemeny constant. J Chem Phys 2020; 152:104108. [PMID: 32171226 DOI: 10.1063/1.5143504] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Markov processes are widely used models for investigating kinetic networks. Here, we collate and present a variety of results pertaining to kinetic network models in a unified framework. The aim is to lay out explicit links between several important quantities commonly studied in the field, including mean first passage times (MFPTs), correlation functions, and the Kemeny constant. We provide new insights into (i) a simple physical interpretation of the Kemeny constant, (ii) a relationship to infer equilibrium distributions and rate matrices from measurements of MFPTs, and (iii) a protocol to reduce the dimensionality of kinetic networks based on specific requirements that the MFPTs in the coarse-grained system should satisfy. We prove that this protocol coincides with the one proposed by Hummer and Szabo [J. Phys. Chem. B 119, 9029 (2014)], and it leads to a variational principle for the Kemeny constant. Finally, we introduce a modification of this protocol, which preserves the Kemeny constant. Our work underpinning the theoretical aspects of kinetic networks will be useful in applications including milestoning and path sampling algorithms in molecular simulations.
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Affiliation(s)
- Adam Kells
- Department of Chemistry, Kings College London, London, United Kingdom
| | - Vladimir Koskin
- Department of Chemistry, Kings College London, London, United Kingdom
| | - Edina Rosta
- Department of Chemistry, Kings College London, London, United Kingdom
| | - Alessia Annibale
- Department of Mathematics, Kings College London, London, United Kingdom
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26
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Tang Z, Chen SH, Chang CEA. Transient States and Barriers from Molecular Simulations and the Milestoning Theory: Kinetics in Ligand-Protein Recognition and Compound Design. J Chem Theory Comput 2020; 16:1882-1895. [PMID: 32031801 DOI: 10.1021/acs.jctc.9b01153] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022]
Abstract
This study presents a novel computational approach to study molecular recognition and binding kinetics for drug-like compounds dissociating from a flexible protein system. The intermediates and their free energy profile during ligand association and dissociation processes control ligand-protein binding kinetics and bring a more complete picture of ligand-protein binding. The method applied the milestoning theory to extract kinetics and thermodynamics information from running short classical molecular dynamics (MD) simulations for frames from a given dissociation path. High-dimensional ligand-protein motions (3N-6 degrees of freedom) during ligand dissociation were reduced by use of principal component modes for assigning more than 100 milestones, and classical MD runs were allowed to travel multiple milestones to efficiently obtain ensemble distribution of initial structures for MD simulations and estimate the transition time and rate during ligand traveling between milestones. We used five pyrazolourea ligands and cyclin-dependent kinase 8 with cyclin C (CDK8/CycC) as our model system as well as metadynamics and a pathway search method to sample dissociation pathways. With our strategy, we constructed the free energy profile for highly mobile biomolecular systems. The computed binding free energy and residence time correctly ranked the pyrazolourea ligand series, in agreement with experimental data. Guided by a barrier of a ligand passing an αC helix and activation loop, we introduced one hydroxyl group to parent compounds to design our ligands with increased residence time and validated our prediction by experiments. This work provides a novel and robust approach to investigate dissociation kinetics of large and flexible systems for understanding unbinding mechanisms and designing new small-molecule drugs with desired binding kinetics.
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Affiliation(s)
- Zhiye Tang
- Department of Chemistry, University of California Riverside, Riverside, California 92521, United States
| | - Si-Han Chen
- Department of Chemistry, University of California Riverside, Riverside, California 92521, United States
| | - Chia-En A Chang
- Department of Chemistry, University of California Riverside, Riverside, California 92521, United States
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27
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Wei W, Elber R. ScMile: A Script to Investigate Kinetics with Short Time Molecular Dynamics Trajectories and the Milestoning Theory. J Chem Theory Comput 2020; 16:860-874. [PMID: 31922745 PMCID: PMC7031965 DOI: 10.1021/acs.jctc.9b01030] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023]
Abstract
Studies of complex and rare events in condensed phase systems continue to attract considerable attention. Milestoning is a useful theory and algorithm to investigate the long-time dynamics of activated molecular events. It is based on launching a large number of short trajectories and statistical analysis of the outcome. The implementation of the theory in a computer script is described that enables more efficient Milestoning calculation, reducing user time and errors, and automating a significant fraction of the algorithm. The script exploits a molecular dynamics engine, which at present is NAMD, to run the short trajectories. However, since the script is external to the engine, the script can be easily adapted to different molecular dynamics codes. The outcomes of the short trajectories are analyzed to obtain a kinetic and thermodynamic description of the entire process. While many examples of Milestoning were published in the past, we provide two simple examples (a conformational transition of alanine dipeptide in a vacuum and aqueous solution) to illustrate the use of the script.
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Affiliation(s)
- Wei Wei
- Oden Institute for Computational Engineering and Sciences , University of Texas at Austin , Austin , Texas 78712 , United States
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences , University of Texas at Austin , Austin , Texas 78712 , United States
- Department of Chemistry , The University of Texas at Austin , Austin , Texas 78712 , United States
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28
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Gershenson A, Gosavi S, Faccioli P, Wintrode PL. Successes and challenges in simulating the folding of large proteins. J Biol Chem 2020; 295:15-33. [PMID: 31712314 PMCID: PMC6952611 DOI: 10.1074/jbc.rev119.006794] [Citation(s) in RCA: 28] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Computational simulations of protein folding can be used to interpret experimental folding results, to design new folding experiments, and to test the effects of mutations and small molecules on folding. However, whereas major experimental and computational progress has been made in understanding how small proteins fold, research on larger, multidomain proteins, which comprise the majority of proteins, is less advanced. Specifically, large proteins often fold via long-lived partially folded intermediates, whose structures, potentially toxic oligomerization, and interactions with cellular chaperones remain poorly understood. Molecular dynamics based folding simulations that rely on knowledge of the native structure can provide critical, detailed information on folding free energy landscapes, intermediates, and pathways. Further, increases in computational power and methodological advances have made folding simulations of large proteins practical and valuable. Here, using serpins that inhibit proteases as an example, we review native-centric methods for simulating the folding of large proteins. These synergistic approaches range from Gō and related structure-based models that can predict the effects of the native structure on folding to all-atom-based methods that include side-chain chemistry and can predict how disease-associated mutations may impact folding. The application of these computational approaches to serpins and other large proteins highlights the successes and limitations of current computational methods and underscores how computational results can be used to inform experiments. These powerful simulation approaches in combination with experiments can provide unique insights into how large proteins fold and misfold, expanding our ability to predict and manipulate protein folding.
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Affiliation(s)
- Anne Gershenson
- Department of Biochemistry and Molecular Biology, University of Massachusetts, Amherst, Massachusetts 01003; Molecular and Cellular Biology Graduate Program, University of Massachusetts, Amherst, Massachusetts 01003.
| | - Shachi Gosavi
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences, Tata Institute of Fundamental Research, Bangalore-560065, India.
| | - Pietro Faccioli
- Dipartimento di Fisica, Universitá degli Studi di Trento, 38122 Povo (Trento), Italy; Trento Institute for Fundamental Physics and Applications, 38123 Povo (Trento), Italy.
| | - Patrick L Wintrode
- Department of Pharmaceutical Sciences, University of Maryland School of Pharmacy, Baltimore, Maryland 21201.
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29
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Fathizadeh A, Kogan M, Anderson CM, Webb LJ, Elber R. Defect-Assisted Permeation Through a Phospholipid Membrane: Experimental and Computational Study of the Peptide WKW. J Phys Chem B 2019; 123:6792-6798. [PMID: 31304755 PMCID: PMC6687544 DOI: 10.1021/acs.jpcb.9b05414] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
We investigate membrane permeation by the peptide WKW that is amidated at its C-terminus and therefore carries a positive charge of +2. To facilitate an efficient calculation, we introduce a novel set of simple coarse variables that measure permeation depth and membrane distortion. The phospholipid head groups shift toward the center of the membrane, following the permeating peptide, and create a defect that assists permeation. The Milestoning algorithm was used in the new coarse space to compute the free-energy profile and the mean first passage time. The barrier was lower than expected from a simple continuum estimate. This behavior is consistent with the known behavior of positively charged cell-penetrating peptides, and is explained by a detailed mechanism of defect formation and propagation revealed by the simulations.
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Affiliation(s)
- Arman Fathizadeh
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin. TX, 78712
| | - Molly Kogan
- Department of Chemistry, University of Texas at Austin, Austin TX, 78712
| | - Cari M. Anderson
- Department of Chemistry, University of Texas at Austin, Austin TX, 78712
| | - Lauren J. Webb
- Department of Chemistry, University of Texas at Austin, Austin TX, 78712
| | - Ron Elber
- Oden Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin. TX, 78712
- Department of Chemistry, University of Texas at Austin, Austin TX, 78712
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30
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Marrink SJ, Corradi V, Souza PC, Ingólfsson HI, Tieleman DP, Sansom MS. Computational Modeling of Realistic Cell Membranes. Chem Rev 2019; 119:6184-6226. [PMID: 30623647 PMCID: PMC6509646 DOI: 10.1021/acs.chemrev.8b00460] [Citation(s) in RCA: 410] [Impact Index Per Article: 82.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/23/2018] [Indexed: 12/15/2022]
Abstract
Cell membranes contain a large variety of lipid types and are crowded with proteins, endowing them with the plasticity needed to fulfill their key roles in cell functioning. The compositional complexity of cellular membranes gives rise to a heterogeneous lateral organization, which is still poorly understood. Computational models, in particular molecular dynamics simulations and related techniques, have provided important insight into the organizational principles of cell membranes over the past decades. Now, we are witnessing a transition from simulations of simpler membrane models to multicomponent systems, culminating in realistic models of an increasing variety of cell types and organelles. Here, we review the state of the art in the field of realistic membrane simulations and discuss the current limitations and challenges ahead.
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Affiliation(s)
- Siewert J. Marrink
- Groningen
Biomolecular Sciences and Biotechnology Institute & Zernike Institute
for Advanced Materials, University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| | - Valentina Corradi
- Centre
for Molecular Simulation and Department of Biological Sciences, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Paulo C.T. Souza
- Groningen
Biomolecular Sciences and Biotechnology Institute & Zernike Institute
for Advanced Materials, University of Groningen, Nijenborgh 7, 9747 AG Groningen, The Netherlands
| | - Helgi I. Ingólfsson
- Biosciences
and Biotechnology Division, Physical and Life Sciences Directorate, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94550, United States
| | - D. Peter Tieleman
- Centre
for Molecular Simulation and Department of Biological Sciences, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Mark S.P. Sansom
- Department
of Biochemistry, University of Oxford, South Parks Road, Oxford OX1 3QU, U.K.
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31
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Thirumalai D, Hyeon C, Zhuravlev PI, Lorimer GH. Symmetry, Rigidity, and Allosteric Signaling: From Monomeric Proteins to Molecular Machines. Chem Rev 2019; 119:6788-6821. [DOI: 10.1021/acs.chemrev.8b00760] [Citation(s) in RCA: 51] [Impact Index Per Article: 10.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- D. Thirumalai
- Department of Chemistry, The University of Texas, Austin, Texas 78712, United States
| | - Changbong Hyeon
- Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
| | - Pavel I. Zhuravlev
- Biophysics Program, Institute for Physical Science and Technology and Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States
| | - George H. Lorimer
- Biophysics Program, Institute for Physical Science and Technology and Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, United States
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32
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Zhou X, Zhu F. Calculating Single-Channel Permeability and Conductance from Transition Paths. J Chem Inf Model 2019; 59:777-785. [PMID: 30688447 DOI: 10.1021/acs.jcim.8b00914] [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]
Abstract
Permeability and conductance are the major transport properties of membrane channels, quantifying the rate of channel crossing by the solute. It is highly desirable to calculate these quantities in all-atom molecular dynamics simulations. When the solute crossing rate is low, however, direct methods would require prohibitively long simulations, and one thus typically adopts alternative strategies based on the free energy of single solute along the channel. Here we present a new method to calculate the crossing rate by initiating unbiased trajectories in which the solute is released at the free energy barrier. In this method, the total time the solute spends in the barrier region during a channel crossing (transition path) is used to determine the kinetic rate. Our method achieves a significantly higher statistical accuracy than the classical reactive flux method, especially for diffusive barrier crossing. Our test on ion permeation through a carbon nanotube verifies that the method correctly predicts the crossing rate and reproduces the spontaneous crossing events as in long equilibrium simulations. The rigorous and efficient method here will be valuable for quantitatively connecting simulations to experimental measurement of membrane channels.
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Affiliation(s)
- Xiaoyan Zhou
- Department of Physics , Zhejiang Normal University , Jinhua 321004 , China.,Department of Physics , Indiana University Purdue University Indianapolis , 402 North Blackford Street , Indianapolis , Indiana 46202 , United States
| | - Fangqiang Zhu
- Department of Physics , Indiana University Purdue University Indianapolis , 402 North Blackford Street , Indianapolis , Indiana 46202 , United States
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33
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Berezhkovskii AM, Szabo A. Committors, first-passage times, fluxes, Markov states, milestones, and all that. J Chem Phys 2019; 150:054106. [PMID: 30736684 PMCID: PMC6910584 DOI: 10.1063/1.5079742] [Citation(s) in RCA: 39] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2018] [Accepted: 01/05/2019] [Indexed: 11/14/2022] Open
Abstract
Milestoning on a one-dimensional potential starts by choosing a set of points, called milestones, and initiating short trajectories from each milestone, which are terminated when they reach an adjacent milestone for the first time. From the average duration of these trajectories and the probabilities of where they terminate, a rate matrix can be constructed and then used to calculate the mean first-passage time (MFPT) between any two milestones. All these MFPT's turn out to be exact. Here we adopt a point of view from which this remarkable result is not unexpected. In addition, we clarify the nature of the "states" whose interconversion is described by the rate matrix constructed using information obtained from short trajectories and provide a microscopic expression for the "equilibrium population" of these states in terms of equilibrium averages of the committors.
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Affiliation(s)
- Alexander M. Berezhkovskii
- Mathematical and Statistical Computing Laboratory, Office of Intramural Research, Center for Information Technology, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Attila Szabo
- Laboratory of Chemical Physics, National institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland 208192, USA
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Viswanath S, Sali A. Optimizing model representation for integrative structure determination of macromolecular assemblies. Proc Natl Acad Sci U S A 2019; 116:540-545. [PMID: 30587581 PMCID: PMC6329962 DOI: 10.1073/pnas.1814649116] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
Integrative structure determination of macromolecular assemblies requires specifying the representation of the modeled structure, a scoring function for ranking alternative models based on diverse types of data, and a sampling method for generating these models. Structures are often represented at atomic resolution, although ad hoc simplified representations based on generic guidelines and/or trial and error are also used. In contrast, we introduce here the concept of optimizing representation. To illustrate this concept, the optimal representation is selected from a set of candidate representations based on an objective criterion that depends on varying amounts of information available for different parts of the structure. Specifically, an optimal representation is defined as the highest-resolution representation for which sampling is exhaustive at a precision commensurate with the precision of the representation. Thus, the method does not require an input structure and is applicable to any input information. We consider a space of representations in which a representation is a set of nonoverlapping, variable-length segments (i.e., coarse-grained beads) for each component protein sequence. We also implement a method for efficiently finding an optimal representation in our open-source Integrative Modeling Platform (IMP) software (https://integrativemodeling.org/). The approach is illustrated by application to three complexes of two subunits and a large assembly of 10 subunits. The optimized representation facilitates exhaustive sampling and thus can produce a more accurate model and a more accurate estimate of its uncertainty for larger structures than were possible previously.
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Affiliation(s)
- Shruthi Viswanath
- Department of Bioengineering and Therapeutic Sciences, University of California, San Francisco, CA 94143;
| | - Andrej Sali
- Department of Bioengineering and Therapeutic Sciences, University of California, San Francisco, CA 94143;
- Department of Pharmaceutical Chemistry, University of California, San Francisco, CA 94143
- California Institute of Quantitative Biosciences, University of California, San Francisco, CA 94143
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35
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Fathizadeh A, Elber R. Ion Permeation through a Phospholipid Membrane: Transition State, Path Splitting, and Calculation of Permeability. J Chem Theory Comput 2019; 15:720-730. [PMID: 30474968 PMCID: PMC6467798 DOI: 10.1021/acs.jctc.8b00882] [Citation(s) in RCA: 21] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We investigate the thermodynamics and kinetics of the permeation of a potassium ion through a phospholipid membrane. We illustrate that the conventional reaction coordinate (the position of the ion along the normal to the membrane plane) is insufficient to capture essential elements of the process. It is necessary to add coarse variables that measure membrane distortion. New coarse variables are suggested, and a two-dimensional coarse-space is proposed to describe the permeation. We illustrate path splitting and two transition states of comparable barrier heights. The alternative pathways differ by the extent of water solvation of the ion-phosphate pairs. The permeation process cannot be described by a local one-dimensional reaction coordinate, and a network formulation is more appropriate. We use Milestoning with Voronoi tessellation in two dimensions to quantify the equilibrium and rate of the permeation of the positively charged ion. The permeation coefficient is computed and compared favorably to experiment.
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Affiliation(s)
- Arman Fathizadeh
- Institute for Computational Engineering and Sciences , University of Texas at Austin , Austin , Texas 78712 , United States
| | - Ron Elber
- Institute for Computational Engineering and Sciences , University of Texas at Austin , Austin , Texas 78712 , United States
- Department of Chemistry , University of Texas at Austin , Austin , Texas 78712 , United States
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36
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Templeton C, Elber R. Why Does RNA Collapse? The Importance of Water in a Simulation Study of Helix-Junction-Helix Systems. J Am Chem Soc 2018; 140:16948-16951. [PMID: 30465606 DOI: 10.1021/jacs.8b11111] [Citation(s) in RCA: 16] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Using computer simulations, we consider the balance of thermodynamic forces that collapse RNA. A model helix-junction-helix (HJH) construct is used to investigate the transition from an extended to a collapsed conformation. Conventional Molecular Dynamics and Milestoning Simulations are used to study the free energy profile of the process for two ion concentrations. We illustrate that HJH folds to a collapsed state with two types of counterions (Mg2+ and K+). By dissecting the free energy landscape into energetic and entropic contributions, we illustrate that the electrostatic forces between the RNA and the mobile ions do not drive the RNA to a collapsed state. Instead, entropy gains from water expulsion near the neighborhood of the RNA provide the stabilization free energy that tilt HJH into more compact structures. Further simulations of a three-helix hammerhead ribozyme show a similar behavior and support the idea of collapse due to increased gain in water entropy.
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Affiliation(s)
- Clark Templeton
- Department of Chemical Engineering , University of Texas at Austin , Austin , Texas 78712 , United States
| | - Ron Elber
- Institute for Computational Engineering and Science, Department of Chemistry , University of Texas at Austin , Austin , Texas 78712 , United States
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37
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Dickson BM. Erroneous Rates and False Statistical Confirmations from Infrequent Metadynamics and Other Equivalent Violations of the Hyperdynamics Paradigm. J Chem Theory Comput 2018; 15:78-83. [DOI: 10.1021/acs.jctc.8b00848] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Bradley M. Dickson
- Center for Epigenetics, Van Andel Research Institute, Grand Rapids, Michigan 49503, United States
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38
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Ma P, Cardenas AE, Chaudhari MI, Elber R, Rempe SB. Probing Translocation in Mutants of the Anthrax Channel: Atomically Detailed Simulations with Milestoning. J Phys Chem B 2018; 122:10296-10305. [PMID: 30338689 DOI: 10.1021/acs.jpcb.8b08304] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Anthrax toxin consists of a cation channel and two protein factors. Translocation of the anthrax protein factors from endosomal to the cytosolic compartment is a complex process which utilizes the cation channel. An atomically detailed understanding of the function of the anthrax translocation machinery is incomplete. We report atomically detailed simulations of the lethal factor and channel mutants. Kinetic and thermodynamic properties of early events in the translocation process are computed within the Milestoning theory and algorithm. Several mutants of the channel illustrate that long-range electrostatic interactions provide the dominant driving force for translocation. No external energy input is required because the lower pH in the endosome relative to the cytosol drives the initial translocation process forward. Channel mutants with variable sizes cause smaller effects on translocation events relative to charge manipulations. Comparison with available experimental data is provided.
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Affiliation(s)
| | | | - Mangesh I Chaudhari
- Biological and Engineering Sciences , Sandia National Laboratories , Albuquerque , New Mexico 87185 , United States
| | | | - Susan B Rempe
- Biological and Engineering Sciences , Sandia National Laboratories , Albuquerque , New Mexico 87185 , United States
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39
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Jagger BR, Lee CT, Amaro RE. Quantitative Ranking of Ligand Binding Kinetics with a Multiscale Milestoning Simulation Approach. J Phys Chem Lett 2018; 9:4941-4948. [PMID: 30070844 PMCID: PMC6443090 DOI: 10.1021/acs.jpclett.8b02047] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/07/2023]
Abstract
Efficient prediction and ranking of small molecule binders by their kinetic ( kon and koff) and thermodynamic ( Δ G) properties can be a valuable metric for drug lead optimization, as these quantities are often indicators of in vivo efficacy. We have previously described a hybrid molecular dynamics, Brownian dynamics, and milestoning model, Simulation Enabled Estimation of Kinetic Rates (SEEKR), that can predict kon's, koff's, and Δ G's. Here we demonstrate the effectiveness of this approach for ranking a series of seven small molecule compounds for the model system, β-cyclodextrin, based on predicted kon's and koff's. We compare our results using SEEKR to experimentally determined rates as well as rates calculated using long time scale molecular dynamics simulations and show that SEEKR can effectively rank the compounds by koff and Δ G with reduced computational cost. We also provide a discussion of convergence properties and sensitivities of calculations with SEEKR to establish "best practices" for its future use.
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Affiliation(s)
- Benjamin R Jagger
- Department of Chemistry and Biochemistry , University of California, San Diego , 9500 Gilman Drive , La Jolla , California 92093-0340 , United States
| | - Christopher T Lee
- Department of Chemistry and Biochemistry , University of California, San Diego , 9500 Gilman Drive , La Jolla , California 92093-0340 , United States
| | - Rommie E Amaro
- Department of Chemistry and Biochemistry , University of California, San Diego , 9500 Gilman Drive , La Jolla , California 92093-0340 , United States
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40
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Mayes HB, Lee S, White AD, Voth GA, Swanson JMJ. Multiscale Kinetic Modeling Reveals an Ensemble of Cl -/H + Exchange Pathways in ClC-ec1 Antiporter. J Am Chem Soc 2018; 140:1793-1804. [PMID: 29332400 PMCID: PMC5812667 DOI: 10.1021/jacs.7b11463] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Despite several years of research, the ion exchange mechanisms in chloride/proton antiporters and many other coupled transporters are not yet understood at the molecular level. Here, we present a novel approach to kinetic modeling and apply it to ion exchange in ClC-ec1. Our multiscale kinetic model is developed by (1) calculating the state-to-state rate coefficients with reactive and polarizable molecular dynamics simulations, (2) optimizing these rates in a global kinetic network, and (3) predicting new electrophysiological results. The model shows that the robust Cl:H exchange ratio (2.2:1) can indeed arise from kinetic coupling without large protein conformational changes, indicating a possible facile evolutionary connection to chloride channels. The E148 amino acid residue is shown to couple chloride and proton transport through protonation-dependent blockage of the central anion binding site and an anion-dependent pKa value, which influences proton transport. The results demonstrate how an ensemble of different exchange pathways, as opposed to a single series of transitions, culminates in the macroscopic observables of the antiporter, such as transport rates, chloride/proton stoichiometry, and pH dependence.
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Affiliation(s)
- Heather B Mayes
- Department of Chemistry, The University of Chicago , Chicago, Illinois 60637, United States.,Department of Chemical Engineering, University of Michigan , Ann Arbor, Michigan 48109, United States
| | - Sangyun Lee
- Department of Chemistry, The University of Chicago , Chicago, Illinois 60637, United States.,Computational Biology Center, IBM Thomas J. Watson Research Center , Yorktown Heights, New York 10598, United States
| | - Andrew D White
- Department of Chemistry, The University of Chicago , Chicago, Illinois 60637, United States.,Department of Chemical Engineering, University of Rochester , Rochester, New York 14627-0166, United States
| | - Gregory A Voth
- Department of Chemistry, The University of Chicago , Chicago, Illinois 60637, United States.,James Franck Institute and Institute for Biophysical Dynamics, The University of Chicago , Chicago, Illinois 60637, United States
| | - Jessica M J Swanson
- Department of Chemistry, The University of Chicago , Chicago, Illinois 60637, United States
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41
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Ma P, Cardenas AE, Chaudhari MI, Elber R, Rempe SB. The Impact of Protonation on Early Translocation of Anthrax Lethal Factor: Kinetics from Molecular Dynamics Simulations and Milestoning Theory. J Am Chem Soc 2017; 139:14837-14840. [PMID: 29019235 PMCID: PMC5656527 DOI: 10.1021/jacs.7b07419] [Citation(s) in RCA: 29] [Impact Index Per Article: 4.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
We report atomically detailed molecular dynamics simulations of the permeation of the lethal factor (LF) N-terminal segment through the anthrax channel. The N-terminal chain is unstructured and leads the permeation process for the LF protein. The simulations were conducted in explicit solvent with milestoning theory, making it possible to extract kinetic information from nanosecond to millisecond time scales. We illustrate that the initial event is strongly influenced by the protonation states of the permeating amino acids. While the N-terminal segment passes easily at high protonation state through the anthrax channel (and the ϕ clamp), the initial permeation represents a critical step, which can be irreversible and establishes a hook in the channel mouth.
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Affiliation(s)
- Piao Ma
- Department of Chemistry, University of Texas at Austin, Austin, TX, 78712
| | - Alfredo E. Cardenas
- Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, 78712
| | - Mangesh I. Chaudhari
- Biological and Engineering Sciences, Sandia National Laboratories, Albuquerque, NM 87185
| | - Ron Elber
- Department of Chemistry, University of Texas at Austin, Austin, TX, 78712
- Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, 78712
| | - Susan B. Rempe
- Biological and Engineering Sciences, Sandia National Laboratories, Albuquerque, NM 87185
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42
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Atis M, Johnson KA, Elber R. Pyrophosphate Release in the Protein HIV Reverse Transcriptase. J Phys Chem B 2017; 121:9557-9565. [PMID: 28926712 DOI: 10.1021/acs.jpcb.7b08320] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
Abstract
Enzymatic reactions usually occur in several steps: a step of substrate binding to the surface of the protein, a step of protein reorganization around the substrate and conduction of a chemical reaction, and a step of product release. The release of inorganic phosphate-PPi-from the matrix of the protein HIV reverse transcriptase is investigated computationally. Atomically detailed simulations with explicit solvent are analyzed to obtain the free energy profile, mean first passage time, and detailed molecular mechanisms of PPi escape. A challenge for the computations is of time scales. The experimental time scale of the process of interest is in milliseconds, and straightforward molecular dynamics simulations are in sub-microseconds. To overcome the time scale gap, we use the algorithm of Milestoning along a reaction coordinate to compute the overall free energy profile and rate. The methods of locally enhanced sampling and steered molecular dynamics determine plausible reaction coordinates. The observed molecular mechanism couples the transfer of the PPi to positively charged lysine side chains that are found on the exit pathway and to an exiting magnesium ion. In accord with experimental findings, the release rate is comparable to the chemical step, allowing for variations in substrate (DNA or RNA template) in which the release becomes rate determining.
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Affiliation(s)
- Murat Atis
- Institute for Computational Engineering and Sciences, The University of Texas at Austin , Austin, Texas 78712, United States
| | - Kenneth A Johnson
- Department of Molecular Biosciences, The University of Texas at Austin , Austin, Texas 78712, United States
| | - Ron Elber
- Institute for Computational Engineering and Sciences, The University of Texas at Austin , Austin, Texas 78712, United States.,Department of Chemistry, The University of Texas at Austin , Austin, Texas 78712, United States
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