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Matsubara Y, Okabe R, Masayama R, Watanabe NM, Umakoshi H, Kasahara K, Matubayasi N. A methodology of quantifying membrane permeability based on returning probability theory and molecular dynamics simulation. J Chem Phys 2024; 161:024108. [PMID: 38984955 DOI: 10.1063/5.0214401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2024] [Accepted: 06/14/2024] [Indexed: 07/11/2024] Open
Abstract
We propose a theoretical approach to estimate the permeability coefficients of substrates (permeants) for crossing membranes from donor (D) phase to acceptor (A) phase by means of molecular dynamics (MD) simulation. A fundamental aspect of our approach involves reformulating the returning probability (RP) theory, a rigorous bimolecular reaction theory, to describe permeation phenomena. This reformulation relies on the parallelism between permeation and bimolecular reaction processes. In the present method, the permeability coefficient is represented in terms of the thermodynamic and kinetic quantities for the reactive (R) phase that exists within the inner region of a membrane. One can evaluate these quantities using multiple MD trajectories starting from phase R. We apply the RP theory to the permeation of ethanol and methylamine at different concentrations (infinitely dilute and 1 mol % conditions of permeants). Under the 1 mol% condition, the present method yields a larger permeability coefficient for ethanol (0.12 ± 0.01 cm s-1) than for methylamine (0.069 ± 0.006 cm s-1), while the values of the permeability coefficient are satisfactorily close to those obtained from the brute-force MD simulations (0.18 ± 0.03 and 0.052 ± 0.005 cm s-1 for ethanol and methylamine, respectively). Moreover, upon analyzing the thermodynamic and kinetic contributions to the permeability, we clarify that a higher concentration dependency of permeability for ethanol, as compared to methylamine, arises from the sensitive nature of ethanol's free-energy barrier within the inner region of the membrane against ethanol concentration.
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Affiliation(s)
- Yuya Matsubara
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Ryo Okabe
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Ren Masayama
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nozomi Morishita Watanabe
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Hiroshi Umakoshi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Kento Kasahara
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
| | - Nobuyuki Matubayasi
- Division of Chemical Engineering, Graduate School of Engineering Science, Osaka University, Toyonaka, Osaka 560-8531, Japan
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Mostofian B, Martin HJ, Razavi A, Patel S, Allen B, Sherman W, Izaguirre JA. Targeted Protein Degradation: Advances, Challenges, and Prospects for Computational Methods. J Chem Inf Model 2023; 63:5408-5432. [PMID: 37602861 PMCID: PMC10498452 DOI: 10.1021/acs.jcim.3c00603] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/27/2023] [Indexed: 08/22/2023]
Abstract
The therapeutic approach of targeted protein degradation (TPD) is gaining momentum due to its potentially superior effects compared with protein inhibition. Recent advancements in the biotech and pharmaceutical sectors have led to the development of compounds that are currently in human trials, with some showing promising clinical results. However, the use of computational tools in TPD is still limited, as it has distinct characteristics compared with traditional computational drug design methods. TPD involves creating a ternary structure (protein-degrader-ligase) responsible for the biological function, such as ubiquitination and subsequent proteasomal degradation, which depends on the spatial orientation of the protein of interest (POI) relative to E2-loaded ubiquitin. Modeling this structure necessitates a unique blend of tools initially developed for small molecules (e.g., docking) and biologics (e.g., protein-protein interaction modeling). Additionally, degrader molecules, particularly heterobifunctional degraders, are generally larger than conventional small molecule drugs, leading to challenges in determining drug-like properties like solubility and permeability. Furthermore, the catalytic nature of TPD makes occupancy-based modeling insufficient. TPD consists of multiple interconnected yet distinct steps, such as POI binding, E3 ligase binding, ternary structure interactions, ubiquitination, and degradation, along with traditional small molecule properties. A comprehensive set of tools is needed to address the dynamic nature of the induced proximity ternary complex and its implications for ubiquitination. In this Perspective, we discuss the current state of computational tools for TPD. We start by describing the series of steps involved in the degradation process and the experimental methods used to characterize them. Then, we delve into a detailed analysis of the computational tools employed in TPD. We also present an integrative approach that has proven successful for degrader design and its impact on project decisions. Finally, we examine the future prospects of computational methods in TPD and the areas with the greatest potential for impact.
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Affiliation(s)
- Barmak Mostofian
- OpenEye, Cadence Molecular Sciences, Boston, Massachusetts 02114 United States
| | - Holli-Joi Martin
- Laboratory
for Molecular Modeling, Division of Chemical Biology and Medicinal
Chemistry, Eshelman School of Pharmacy, University of North Carolina, Chapel Hill, North Carolina 27599 United States
| | - Asghar Razavi
- ENKO
Chem, Inc, Mystic, Connecticut 06355 United States
| | - Shivam Patel
- Psivant
Therapeutics, Boston, Massachusetts 02210 United States
| | - Bryce Allen
- Differentiated
Therapeutics, San Diego, California 92056 United States
| | - Woody Sherman
- Psivant
Therapeutics, Boston, Massachusetts 02210 United States
| | - Jesus A Izaguirre
- Differentiated
Therapeutics, San Diego, California 92056 United States
- Atommap
Corporation, New York, New York 10013 United States
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3
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Chipot C. Predictions from First-Principles of Membrane Permeability to Small Molecules: How Useful Are They in Practice? J Chem Inf Model 2023; 63:4533-4544. [PMID: 37449868 DOI: 10.1021/acs.jcim.3c00686] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/18/2023]
Abstract
Predicting from first-principles the rate of passive permeation of small molecules across the biological membrane represents a promising strategy for screening lead compounds upstream in the drug-discovery and development pipeline. One popular avenue for the estimation of permeation rates rests on computer simulations in conjunction with the inhomogeneous solubility-diffusion model, which requires the determination of the free-energy change and position-dependent diffusivity of the substrate along the translocation pathway through the lipid bilayer. In this Perspective, we will clarify the physical meaning of the membrane permeability inferred from such computer simulations, and how theoretical predictions actually relate to what is commonly measured experimentally. We will also examine why these calculations remain both technically challenging and overly computationally expensive, which has hitherto precluded their routine use in nonacademic settings. We finally synopsize possible research directions to meet these challenges, increase the predictive power of physics-based rates of passive permeation, and, by ricochet, improve their practical usefulness.
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Affiliation(s)
- Christophe Chipot
- Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche n◦7019, Université de Lorraine, 54500 Vandœuvre-lès-Nancy cedex, France
- Beckman Institute for Advanced Science and Technology, and Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61820, United States
- Department of Biochemistry and Molecular Biology, University of Chicago, Chicago, Illinois 60637, United States
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Kim N, Lee JH, Song Y, Lee JH, Schatz GC, Hwang H. Molecular Dynamics Simulation Study of the Protonation State Dependence of Glutamic Acid Transport through a Cyclic Peptide Nanotube. J Phys Chem B 2023. [PMID: 37369069 DOI: 10.1021/acs.jpcb.3c02285] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/29/2023]
Abstract
The effect of the protonation state of glutamic acid on its translocation through cyclic peptide nanotubes (CPNs) was assessed by using molecular dynamics (MD) simulations. Anionic (GLU-), neutral zwitterionic (GLU0), and cationic (GLU+) forms of glutamic acid were selected as three different protonation states for an analysis of energetics and diffusivity for acid transport across a cyclic decapeptide nanotube. Based on the solubility-diffusion model, permeability coefficients for the three protonation states of the acid were calculated and compared with experimental results for CPN-mediated glutamate transport through CPNs. Potential of mean force (PMF) calculations reveal that, due to the cation-selective nature of the lumen of CPNs, GLU-, so-called glutamate, shows significantly high free energy barriers, while GLU+ displays deep energy wells and GLU0 has mild free energy barriers and wells inside the CPN. The considerable energy barriers for GLU- inside CPNs are mainly attributed to unfavorable interactions with DMPC bilayers and CPNs and are reduced by favorable interactions with channel water molecules through attractive electrostatic interactions and hydrogen bonding. Unlike the distinct PMF curves, position-dependent diffusion coefficient profiles exhibit comparable frictional behaviors regardless of the charge status of three protonation states due to similar confined environments imposed by the lumen of the CPN. The calculated permeability coefficients for the three protonation states clearly demonstrate that glutamic acid has a strong protonation state dependence for its transport through CPNs, as determined by the energetics rather than the diffusivity of the protonation state. In addition, the permeability coefficients also imply that GLU- is unlikely to pass through a CPN due to the high energy barriers inside the CPN, which is in disagreement with experimental measurements, where a considerable amount of glutamate permeating through the CPN was detected. To resolve the discrepancy between this work and the experimental observations, several possibilities are proposed, including a large concentration gradient of glutamate between the inside and outside of lipid vesicles and bilayers in the experiments, the glutamate activity difference between our MD simulations and experiments, an overestimation of energy barriers due to the artifacts imposed in MD simulations, and/or finally a transformation of the protonation state from GLU- to GLU0 to reduce the energy barriers. Overall, our study demonstrates that the protonation state of glutamic acid has a strong effect on the transport of the acid and suggests a possible protonation state change for glutamate permeating through CPNs.
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Affiliation(s)
- Namho Kim
- Department of Biochemistry, Kangwon National University, Chuncheon, Gangwon-do 24341, Republic of Korea
| | - Ji Hye Lee
- Department of Chemistry and Institute for Molecular Science and Fusion Technology, Kangwon National University, Chuncheon, Gangwon-do 24341, Republic of Korea
| | - Yeonho Song
- Department of Chemistry and Institute for Molecular Science and Fusion Technology, Kangwon National University, Chuncheon, Gangwon-do 24341, Republic of Korea
| | - Jeong-Hyung Lee
- Department of Biochemistry, Kangwon National University, Chuncheon, Gangwon-do 24341, Republic of Korea
| | - George C Schatz
- Department of Chemistry, Northwestern University, 2145 Sheridan Rd, Evanston, Illinois 60208, United States
| | - Hyonseok Hwang
- Department of Chemistry and Institute for Molecular Science and Fusion Technology, Kangwon National University, Chuncheon, Gangwon-do 24341, Republic of Korea
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Vervust W, Zhang DT, van Erp TS, Ghysels A. Path sampling with memory reduction and replica exchange to reach long permeation timescales. Biophys J 2023:S0006-3495(23)00127-3. [PMID: 36809877 PMCID: PMC10398259 DOI: 10.1016/j.bpj.2023.02.021] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2022] [Revised: 01/13/2023] [Accepted: 02/15/2023] [Indexed: 02/23/2023] Open
Abstract
Assessing kinetics in biological processes with molecular dynamics simulations remains a computational and conceptual challenge, given the large time and length scales involved. For kinetic transport of biochemical compounds or drug molecules, the permeability through the phospholipid membranes is a key kinetic property, but long timescales are hindering the accurate computation. Technological advances in high-performance computing therefore need to be accompanied by theoretical and methodological developments. In this contribution, the replica exchange transition interface sampling (RETIS) methodology is shown to give perspective toward observing longer permeation pathways. It is first reviewed how RETIS, a path-sampling methodology that gives in principle exact kinetics, can be used to compute membrane permeability. Next, recent and current developments in three RETIS aspects are discussed: several new Monte Carlo moves in the path-sampling algorithm, memory reduction by reducing pathlengths, and exploitation of parallel computing with CPU-imbalanced replicas. Finally, the memory reduction presenting a new replica exchange implementation, coined REPPTIS, is showcased with a permeant needing to pass a membrane with two permeation channels, either representing an entropic or energetic barrier. The REPPTIS results showed clearly that inclusion of some memory and enhancing ergodic sampling via replica exchange moves are both necessary to obtain correct permeability estimates. In an additional example, ibuprofen permeation through a dipalmitoylphosphatidylcholine membrane was modeled. REPPTIS succeeded in estimating the permeability of this amphiphilic drug molecule with metastable states along the permeation pathway. In conclusion, the presented methodological advances allow for deeper insight into membrane biophysics even if the pathways are slow, as RETIS and REPPTIS push the permeability calculations to longer timescales.
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Affiliation(s)
- Wouter Vervust
- IBiTech - Biommeda Research Group, Faculty of Engineering and Architecture, Ghent University, Gent, Belgium
| | - Daniel T Zhang
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway
| | - Titus S van Erp
- Department of Chemistry, Norwegian University of Science and Technology, Trondheim, Norway
| | - An Ghysels
- IBiTech - Biommeda Research Group, Faculty of Engineering and Architecture, Ghent University, Gent, Belgium.
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Mitsuta Y, Asada T, Shigeta Y. Calculation of the permeability coefficients of small molecules through lipid bilayers by free-energy reaction network analysis following the explicit treatment of the internal conformation of the solute. Phys Chem Chem Phys 2022; 24:26070-26082. [PMID: 36268802 DOI: 10.1039/d2cp03678a] [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: 06/16/2023]
Abstract
Biomembrane permeation represents a major barrier to pharmacokinetics. During preclinical drug discovery, the coefficients of the permeation of molecules through lipid bilayers account for a valuable property of such molecules. Therefore, the control of the permeation of molecules through lipid bilayers is an essential factor in drug design, and the estimation of the permeation phenomena is a crucial study in pharmacy. Thus, there are many published studies on the theoretical estimations of permeation coefficients. Here, we propose a molecular dynamics (MD) simulation method for estimating the permeation of small molecules through lipid bilayers based on the free-energy reaction network (FERN) analysis. In this method, the collective variables (CVs) of the free energy calculations explicitly include the conformational changes in the rotational bonds of the solute molecules. The advantages of the present method over the other method are that it is possible to estimate reaction pathways and their reaction rates, i.e., permeation coefficients or passage times, in multidimensional space spanned by CVs though conventional methods such as the umbrella sampling method and target MDs often dealt with a few degrees of freedom. To demonstrate the efficacy of our method, we calculate the coefficients of the permeation of three small aromatic peptides, namely N-acetylphenylalanineamide (Ac-Phe-NH2 or NAFA), N-acetyltyrosineamide (Ac-Tyr-NH2 or NAYA), and N-acetyltryptophanamide (Ac-Trp-NH2 or NATA), through a 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayer. In these cases we adopted one CV for the permeation direction and four CVs for the internal rotational coordinates. The results reveal that the permeation coefficients of NAFA, NAYA, and NATA are 1.7 × 10-2, 0.51 × 10-4, and 5.7 × 10-4 cm s-1, respectively. Compared with the experimental data, our simulation results followed the same trend, i.e., NAFA > NATA > NAYA. By analyzing the structures of metastable points of the solute molecules, our simulation result reveals that the aforementioned trend is caused by the differences in stability among their rotamers. Furthermore, we evaluate the statistical fluctuation of the rotamers, and the time scale of flipping the side chain reveals that the structures rigidify as the ligand moves deeper into the membrane.
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Affiliation(s)
- Yuki Mitsuta
- Department of Chemistry, Osaka Prefecture University, 1-1, Gakuen-cho, Sakai, Osaka, 599-8531, Japan.
- RIMED, Osaka Prefecture University, 1-1, Gakuen-cho, Sakai, Osaka, 599-8531, Japan
| | - Toshio Asada
- Department of Chemistry, Osaka Prefecture University, 1-1, Gakuen-cho, Sakai, Osaka, 599-8531, Japan.
- RIMED, Osaka Prefecture University, 1-1, Gakuen-cho, Sakai, Osaka, 599-8531, Japan
| | - Yasuteru Shigeta
- Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki, 305-8577, Japan
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7
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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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Zhang S, Thompson JP, Xia J, Bogetti AT, York F, Skillman AG, Chong LT, LeBard DN. Mechanistic Insights into Passive Membrane Permeability of Drug-like Molecules from a Weighted Ensemble of Trajectories. J Chem Inf Model 2022; 62:1891-1904. [PMID: 35421313 PMCID: PMC9044451 DOI: 10.1021/acs.jcim.1c01540] [Citation(s) in RCA: 6] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
Passive permeability
of a drug-like molecule is a critical property
assayed early in a drug discovery campaign that informs a medicinal
chemist how well a compound can traverse biological membranes, such
as gastrointestinal epithelial or restrictive organ barriers, so it
can perform a specific therapeutic function. However, the challenge
that remains is the development of a method, experimental or computational,
which can both determine the permeation rate and provide mechanistic
insights into the transport process to help with the rational design
of any given molecule. Typically, one of the following three methods
are used to measure the membrane permeability: (1) experimental permeation
assays acting on either artificial or natural membranes; (2) quantitative
structure–permeability relationship models that rely on experimental
values of permeability or related pharmacokinetic properties of a
range of molecules to infer those for new molecules; and (3) estimation
of permeability from the Smoluchowski equation, where free energy
and diffusion profiles along the membrane normal are taken as input
from large-scale molecular dynamics simulations. While all these methods
provide estimates of permeation coefficients, they provide very little
information for guiding rational drug design. In this study, we employ
a highly parallelizable weighted ensemble (WE) path sampling strategy,
empowered by cloud computing techniques, to generate unbiased permeation
pathways and permeability coefficients for a set of drug-like molecules
across a neat 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphatidylcholine
membrane bilayer. Our WE method predicts permeability coefficients
that compare well to experimental values from an MDCK-LE cell line
and PAMPA assays for a set of drug-like amines of varying size, shape,
and flexibility. Our method also yields a series of continuous permeation
pathways weighted and ranked by their associated probabilities. Taken
together, the ensemble of reactive permeation pathways, along with
the estimate of the permeability coefficient, provides a clearer picture
of the microscopic underpinnings of small-molecule membrane permeation.
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Affiliation(s)
- She Zhang
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Jeff P Thompson
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Junchao Xia
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | - Anthony T Bogetti
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Forrest York
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
| | | | - Lillian T Chong
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - David N LeBard
- OpenEye Scientific, Santa Fe, New Mexico 87508, United States
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Lin YC, Luo YL. Unifying Single-Channel Permeability From Rare-Event Sampling and Steady-State Flux. Front Mol Biosci 2022; 9:860933. [PMID: 35495625 PMCID: PMC9043130 DOI: 10.3389/fmolb.2022.860933] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2022] [Accepted: 03/07/2022] [Indexed: 11/18/2022] Open
Abstract
Various all-atom molecular dynamics (MD) simulation methods have been developed to compute free energies and crossing rates of ions and small molecules through ion channels. However, a systemic comparison across different methods is scarce. Using a carbon nanotube as a model of small conductance ion channel, we computed the single-channel permeability for potassium ion using umbrella sampling, Markovian milestoning, and steady-state flux under applied voltage. We show that a slightly modified inhomogeneous solubility-diffusion equation yields a single-channel permeability consistent with the mean first passage time (MFPT) based method. For milestoning, applying cylindrical and spherical bulk boundary conditions yield consistent MFPT if factoring in the effective bulk concentration. The sensitivity of the MFPT to the output frequency of collective variables is highlighted using the convergence and symmetricity of the inward and outward MFPT profiles. The consistent transport kinetic results from all three methods demonstrated the robustness of MD-based methods in computing ion channel permeation. The advantages and disadvantages of each technique are discussed, focusing on the future applications of milestoning in more complex systems.
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Guardiani C, Cecconi F, Chiodo L, Cottone G, Malgaretti P, Maragliano L, Barabash ML, Camisasca G, Ceccarelli M, Corry B, Roth R, Giacomello A, Roux B. Computational methods and theory for ion channel research. ADVANCES IN PHYSICS: X 2022; 7:2080587. [PMID: 35874965 PMCID: PMC9302924 DOI: 10.1080/23746149.2022.2080587] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/28/2022] [Accepted: 05/15/2022] [Indexed: 06/15/2023] Open
Abstract
Ion channels are fundamental biological devices that act as gates in order to ensure selective ion transport across cellular membranes; their operation constitutes the molecular mechanism through which basic biological functions, such as nerve signal transmission and muscle contraction, are carried out. Here, we review recent results in the field of computational research on ion channels, covering theoretical advances, state-of-the-art simulation approaches, and frontline modeling techniques. We also report on few selected applications of continuum and atomistic methods to characterize the mechanisms of permeation, selectivity, and gating in biological and model channels.
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Affiliation(s)
- C. Guardiani
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
| | - F. Cecconi
- CNR - Istituto dei Sistemi Complessi, Rome, Italy and Istituto Nazionale di Fisica Nucleare, INFN, Roma1 section. 00185, Roma, Italy
| | - L. Chiodo
- Department of Engineering, Campus Bio-Medico University, Rome, Italy
| | - G. Cottone
- Department of Physics and Chemistry-Emilio Segrè, University of Palermo, Palermo, Italy
| | - P. Malgaretti
- Helmholtz Institute Erlangen-Nürnberg for Renewable Energy (IEK-11), Forschungszentrum Jülich, Erlangen, Germany
| | - L. Maragliano
- Department of Life and Environmental Sciences, Polytechnic University of Marche, Ancona, Italy, and Center for Synaptic Neuroscience and Technology, Istituto Italiano di Tecnologia, Genova, Italy
| | - M. L. Barabash
- Department of Materials Science and Nanoengineering, Rice University, Houston, TX 77005, USA
| | - G. Camisasca
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
- Dipartimento di Fisica, Università Roma Tre, Rome, Italy
| | - M. Ceccarelli
- Department of Physics and CNR-IOM, University of Cagliari, Monserrato 09042-IT, Italy
| | - B. Corry
- Research School of Biology, The Australian National University, Canberra, ACT 2600, Australia
| | - R. Roth
- Institut Für Theoretische Physik, Eberhard Karls Universität Tübingen, Tübingen, Germany
| | - A. Giacomello
- Dipartimento di Ingegneria Meccanica e Aerospaziale, Sapienza Università di Roma, Rome, Italy
| | - B. Roux
- Department of Biochemistry & Molecular Biology, University of Chicago, Chicago IL, USA
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11
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Ray D, Stone SE, Andricioaei I. Markovian Weighted Ensemble Milestoning (M-WEM): Long-Time Kinetics from Short Trajectories. J Chem Theory Comput 2021; 18:79-95. [PMID: 34910499 DOI: 10.1021/acs.jctc.1c00803] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We introduce a rare-event sampling scheme, named Markovian Weighted Ensemble Milestoning (M-WEM), which inlays a weighted ensemble framework within a Markovian milestoning theory to efficiently calculate thermodynamic and kinetic properties of long-time-scale biomolecular processes from short atomistic molecular dynamics simulations. M-WEM is tested on the Müller-Brown potential model, the conformational switching in alanine dipeptide, and the millisecond time-scale protein-ligand unbinding in a trypsin-benzamidine complex. Not only can M-WEM predict the kinetics of these processes with quantitative accuracy but it also allows for a scheme to reconstruct a multidimensional free-energy landscape along additional degrees of freedom, which are not part of the milestoning progress coordinate. For the ligand-receptor system, the experimental residence time, association and dissociation kinetics, and binding free energy could be reproduced using M-WEM within a simulation time of a few hundreds of nanoseconds, which is a fraction of the computational cost of other currently available methods, and close to 4 orders of magnitude less than the experimental residence time. Due to the high accuracy and low computational cost, the M-WEM approach can find potential applications in kinetics and free-energy-based computational drug design.
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Affiliation(s)
- Dhiman Ray
- Department of Chemistry, University of California Irvine, Irvine, California 92697, United States
| | - Sharon Emily Stone
- Department of Chemistry, University of California Irvine, Irvine, California 92697, United States
| | - Ioan Andricioaei
- Department of Chemistry, University of California Irvine, Irvine, California 92697, United States.,Department of Physics and Astronomy, University of California Irvine, Irvine, California 92697, United States
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12
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Róg T, Girych M, Bunker A. Mechanistic Understanding from Molecular Dynamics in Pharmaceutical Research 2: Lipid Membrane in Drug Design. Pharmaceuticals (Basel) 2021; 14:1062. [PMID: 34681286 PMCID: PMC8537670 DOI: 10.3390/ph14101062] [Citation(s) in RCA: 18] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2021] [Revised: 10/14/2021] [Accepted: 10/15/2021] [Indexed: 11/17/2022] Open
Abstract
We review the use of molecular dynamics (MD) simulation as a drug design tool in the context of the role that the lipid membrane can play in drug action, i.e., the interaction between candidate drug molecules and lipid membranes. In the standard "lock and key" paradigm, only the interaction between the drug and a specific active site of a specific protein is considered; the environment in which the drug acts is, from a biophysical perspective, far more complex than this. The possible mechanisms though which a drug can be designed to tinker with physiological processes are significantly broader than merely fitting to a single active site of a single protein. In this paper, we focus on the role of the lipid membrane, arguably the most important element outside the proteins themselves, as a case study. We discuss work that has been carried out, using MD simulation, concerning the transfection of drugs through membranes that act as biological barriers in the path of the drugs, the behavior of drug molecules within membranes, how their collective behavior can affect the structure and properties of the membrane and, finally, the role lipid membranes, to which the vast majority of drug target proteins are associated, can play in mediating the interaction between drug and target protein. This review paper is the second in a two-part series covering MD simulation as a tool in pharmaceutical research; both are designed as pedagogical review papers aimed at both pharmaceutical scientists interested in exploring how the tool of MD simulation can be applied to their research and computational scientists interested in exploring the possibility of a pharmaceutical context for their research.
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Affiliation(s)
- Tomasz Róg
- Department of Physics, University of Helsinki, 00014 Helsinki, Finland;
| | - Mykhailo Girych
- Department of Physics, University of Helsinki, 00014 Helsinki, Finland;
| | - Alex Bunker
- Drug Research Program, Division of Pharmaceutical Biosciences, Faculty of Pharmacy, University of Helsinki, 00014 Helsinki, Finland;
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13
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Jiang W, Lin YC, Botello-Smith W, Contreras JE, Harris AL, Maragliano L, Luo YL. Free energy and kinetics of cAMP permeation through connexin26 via applied voltage and milestoning. Biophys J 2021; 120:2969-2983. [PMID: 34214529 DOI: 10.1016/j.bpj.2021.06.024] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Revised: 04/08/2021] [Accepted: 06/17/2021] [Indexed: 11/18/2022] Open
Abstract
The connexin family is a diverse group of highly regulated wide-pore channels permeable to biological signaling molecules. Despite the critical roles of connexins in mediating selective molecular signaling in health and disease, the basis of molecular permeation through these pores remains unclear. Here, we report the thermodynamics and kinetics of binding and transport of a second messenger, adenosine-3',5'-cyclophosphate (cAMP), through a connexin26 hemichannel (Cx26). First, inward and outward fluxes of cAMP molecules solvated in KCl solution were obtained from 4 μs of ± 200 mV simulations. These fluxes data yielded a single-channel permeability of cAMP and cAMP/K+ permeability ratio consistent with experimentally measured values. The results from voltage simulations were then compared with the potential of mean force (PMF) and the mean first passage times (MFPTs) of a single cAMP without voltage, obtained from a total of 16.5 μs of Voronoi-tessellated Markovian milestoning simulations. Both the voltage simulations and the milestoning simulations revealed two cAMP-binding sites, for which the binding constants KD and dissociation rates koff were computed from PMF and MFPTs. The protein dipole inside the pore produces an asymmetric PMF, reflected in unequal cAMP MFPTs in each direction once within the pore. The free energy profiles under opposite voltages were derived from the milestoning PMF and revealed the interplay between voltage and channel polarity on the total free energy. In addition, we show how these factors influence the cAMP dipole vector during permeation, and how cAMP affects the local and nonlocal pore diameter in a position-dependent manner.
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Affiliation(s)
- Wenjuan Jiang
- Department of Pharmaceutical Sciences, College of Pharmacy, Western University of Health Sciences, Pomona, California
| | - Yi-Chun Lin
- Department of Pharmaceutical Sciences, College of Pharmacy, Western University of Health Sciences, Pomona, California
| | - Wesley Botello-Smith
- Department of Pharmaceutical Sciences, College of Pharmacy, Western University of Health Sciences, Pomona, California
| | - Jorge E Contreras
- Department of Physiology and Membrane Biology, School of Medicine, University of California, Davis, California.
| | - Andrew L Harris
- Department of Pharmacology, Physiology, and Neuroscience, New Jersey Medical School, Rutgers, The State University of New Jersey, Newark, New Jersey.
| | - Luca Maragliano
- Department of Life and Environmental Sciences, Polytechnic University of Marche, Ancona, Italy; Center for Synaptic Neuroscience and Technology, Italian Institute of Technology, Genoa, Italy.
| | - Yun Lyna Luo
- Department of Pharmaceutical Sciences, College of Pharmacy, Western University of Health Sciences, Pomona, California.
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14
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Davoudi S, Ghysels A. Sampling efficiency of the counting method for permeability calculations estimated with the inhomogeneous solubility-diffusion model. J Chem Phys 2021; 154:054106. [PMID: 33557559 DOI: 10.1063/5.0033476] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Permeability is a key property in various fields such as membrane technology for chemical separation and transport of substances through cell membranes. At the molecular scale, the counting method uses the number of membrane crossings in a conventional unbiased molecular dynamics simulation to predict the permeability. This contribution investigates under which conditions the counting method has insufficient statistics. An equation is derived for a compartmental model based on the inhomogeneous solubility-diffusion (Smoluchowski) model, giving insight into how the flux correlates with the solubility of permeants. This equation shows that a membrane crossing is a rare event not only when the membrane forms a large free energy barrier but also when the membrane forms a deep free energy well that traps permeants. Such a permeant trap has a high permeability; yet, the counting method suffers from poor statistics. To illustrate this, coarse-grained MD was run for 16 systems of dipalmitoylphosphatidylcholine bilayer membranes with different permeant types. The composition rule for permeability is shown to also hold for fluxes, and it is highlighted that the considered thickness of the membrane causes uncertainty in the permeability calculation of highly permeable membranes. In conclusion, a high permeability in itself is not an effective indicator of the sampling efficiency of the counting method, and caution should be taken for permeants whose solubility varies greatly over the simulation box. A practical consequence relevant in, e.g., drug design is that a drug with high membrane permeability might get trapped by membranes thus reducing its efficacy.
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Affiliation(s)
- Samaneh Davoudi
- IBiTech-BioMMeda Group, Ghent University, Corneel Heymanslaan 10, Block B-entrance 36, 9000 Gent, Belgium
| | - An Ghysels
- IBiTech-BioMMeda Group, Ghent University, Corneel Heymanslaan 10, Block B-entrance 36, 9000 Gent, Belgium
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15
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Alberini G, Benfenati F, Maragliano L. Structural Mechanism of ω-Currents in a Mutated Kv7.2 Voltage Sensor Domain from Molecular Dynamics Simulations. J Chem Inf Model 2021; 61:1354-1367. [PMID: 33570938 PMCID: PMC8023575 DOI: 10.1021/acs.jcim.0c01407] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Abstract
![]()
Activation of voltage-gated
ion channels is regulated by conformational
changes of the voltage sensor domains (VSDs), four water- and ion-impermeable
modules peripheral to the central, permeable pore domain. Anomalous
currents, defined as ω-currents, have been recorded in response
to mutations of residues on the VSD S4 helix and associated with ion
fluxes through the VSDs. In humans, gene defects in the potassium
channel Kv7.2 result in a broad range of epileptic disorders, from
benign neonatal seizures to severe epileptic encephalopathies. Experimental
evidence suggests that the R207Q mutation in S4, associated with peripheral
nerve hyperexcitability, induces ω-currents at depolarized potentials,
but the fine structural details are still elusive. In this work, we
use atom-detailed molecular dynamics simulations and a refined model
structure of the Kv7.2 VSD in the active conformation in a membrane/water
environment to study the effect of R207Q and four additional mutations
of proven clinical importance. Our results demonstrate that the R207Q
mutant shows the most pronounced increase of hydration in the internal
VSD cavity, a feature favoring the occurrence of ω-currents.
Free energy and kinetics calculations of sodium permeation through
the native and mutated VSD indicate as more favorable the formation
of a cationic current in the latter. Overall, our simulations establish
a mechanistic linkage between genetic variations and their physiological
outcome, by providing a computational description that includes both
thermodynamic and kinetic features of ion permeation associated with
ω-currents.
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Affiliation(s)
- Giulio Alberini
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi, 10, 16132 Genova, Italy.,Department of Experimental Medicine, Università degli Studi di Genova, Viale Benedetto XV, 3, 16132 Genova, Italy
| | - Fabio Benfenati
- 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
| | - Luca Maragliano
- Center for Synaptic Neuroscience and Technology (NSYN@UniGe), Istituto Italiano di Tecnologia, Largo Rosanna Benzi, 10, 16132 Genova, Italy.,Department of Life and Environmental Sciences, Polytechnic University of Marche, Via Brecce Bianche, 60131 Ancona, Italy
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16
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Riccardi E, Krämer A, van Erp TS, Ghysels A. Permeation Rates of Oxygen through a Lipid Bilayer Using Replica Exchange Transition Interface Sampling. J Phys Chem B 2020; 125:193-201. [DOI: 10.1021/acs.jpcb.0c09947] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Enrico Riccardi
- Department of Chemistry, Norwegian University of Science and Technology, Høgskoleringen 5, 7491 Trondheim, Norway
| | - Andreas Krämer
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, United States
| | - Titus S. van Erp
- Department of Chemistry, Norwegian University of Science and Technology, Høgskoleringen 5, 7491 Trondheim, Norway
- Center for Molecular Modeling (CMM), Ghent University, Technologiepark, Zwijnaarde, Ghent 9000, Belgium
| | - An Ghysels
- IBiTech, Faculty of Engineering and Architecture, Ghent University, Corneel Heymanslaan
10, Block B - entrance 36, 9000 Gent, Belgium
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17
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Krämer A, Ghysels A, Wang E, Venable RM, Klauda JB, Brooks BR, Pastor RW. Membrane permeability of small molecules from unbiased molecular dynamics simulations. J Chem Phys 2020; 153:124107. [PMID: 33003739 PMCID: PMC7519415 DOI: 10.1063/5.0013429] [Citation(s) in RCA: 30] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2020] [Accepted: 08/31/2020] [Indexed: 12/26/2022] Open
Abstract
Permeation of many small molecules through lipid bilayers can be directly observed in molecular dynamics simulations on the nano- and microsecond timescale. While unbiased simulations provide an unobstructed view of the permeation process, their feasibility for computing permeability coefficients depends on various factors that differ for each permeant. The present work studies three small molecules for which unbiased simulations of permeation are feasible within less than a microsecond, one hydrophobic (oxygen), one hydrophilic (water), and one amphiphilic (ethanol). Permeabilities are computed using two approaches: counting methods and a maximum-likelihood estimation for the inhomogeneous solubility diffusion (ISD) model. Counting methods yield nearly model-free estimates of the permeability for all three permeants. While the ISD-based approach is reasonable for oxygen, it lacks precision for water due to insufficient sampling and results in misleading estimates for ethanol due to invalid model assumptions. It is also demonstrated that simulations using a Langevin thermostat with collision frequencies of 1/ps and 5/ps yield oxygen permeabilities and diffusion constants that are lower than those using Nosé-Hoover by statistically significant margins. In contrast, permeabilities from trajectories generated with Nosé-Hoover and the microcanonical ensemble do not show statistically significant differences. As molecular simulations become more affordable and accurate, calculation of permeability for an expanding range of molecules will be feasible using unbiased simulations. The present work summarizes theoretical underpinnings, identifies pitfalls, and develops best practices for such simulations.
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Affiliation(s)
- Andreas Krämer
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - An Ghysels
- IBiTech - BioMMeda, Ghent University, Corneel Heymanslaan 10, Block B - Entrance 36, 9000 Gent, Belgium
| | - Eric Wang
- Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20740, USA
| | - Richard M. Venable
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Jeffery B. Klauda
- Department of Chemical and Biomolecular Engineering, University of Maryland, College Park, Maryland 20740, USA
| | - Bernard R. Brooks
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Richard W. Pastor
- Laboratory of Computational Biology, National Heart, Lung, and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
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18
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Martinotti C, Ruiz-Perez L, Deplazes E, Mancera RL. Molecular Dynamics Simulation of Small Molecules Interacting with Biological Membranes. Chemphyschem 2020; 21:1486-1514. [PMID: 32452115 DOI: 10.1002/cphc.202000219] [Citation(s) in RCA: 29] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/17/2020] [Revised: 05/22/2020] [Indexed: 12/12/2022]
Abstract
Cell membranes protect and compartmentalise cells and their organelles. The semi-permeable nature of these membranes controls the exchange of solutes across their structure. Characterising the interaction of small molecules with biological membranes is critical to understanding of physiological processes, drug action and permeation, and many biotechnological applications. This review provides an overview of how molecular simulations are used to study the interaction of small molecules with biological membranes, with a particular focus on the interactions of water, organic compounds, drugs and short peptides with models of plasma cell membrane and stratum corneum lipid bilayers. This review will not delve on other types of membranes which might have different composition and arrangement, such as thylakoid or mitochondrial membranes. The application of unbiased molecular dynamics simulations and enhanced sampling methods such as umbrella sampling, metadynamics and replica exchange are described using key examples. This review demonstrates how state-of-the-art molecular simulations have been used successfully to describe the mechanism of binding and permeation of small molecules with biological membranes, as well as associated changes to the structure and dynamics of these membranes. The review concludes with an outlook on future directions in this field.
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Affiliation(s)
- Carlo Martinotti
- School of Pharmacy and Biomedical Sciences, Curtin Health Innovation Research Institute and, Curtin Institute for Computation, Curtin University, Perth, WA 6845, Australia
| | - Lanie Ruiz-Perez
- School of Pharmacy and Biomedical Sciences, Curtin Health Innovation Research Institute and, Curtin Institute for Computation, Curtin University, Perth, WA 6845, Australia
| | - Evelyne Deplazes
- School of Life Sciences, University of Technology Sydney, Sydney, NSW 2007, Australia
| | - Ricardo L Mancera
- School of Pharmacy and Biomedical Sciences, Curtin Health Innovation Research Institute and, Curtin Institute for Computation, Curtin University, Perth, WA 6845, Australia
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19
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Ray D, Andricioaei I. Weighted ensemble milestoning (WEM): A combined approach for rare event simulations. J Chem Phys 2020; 152:234114. [DOI: 10.1063/5.0008028] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Affiliation(s)
- Dhiman Ray
- Department of Chemistry, University of California Irvine, California 92697, USA
| | - Ioan Andricioaei
- Department of Chemistry, University of California Irvine, California 92697, USA
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20
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Hoffmann C, Centi A, Menichetti R, Bereau T. Molecular dynamics trajectories for 630 coarse-grained drug-membrane permeations. Sci Data 2020; 7:51. [PMID: 32054852 PMCID: PMC7018832 DOI: 10.1038/s41597-020-0391-0] [Citation(s) in RCA: 12] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2019] [Accepted: 01/22/2020] [Indexed: 02/07/2023] Open
Abstract
The permeation of small-molecule drugs across a phospholipid membrane bears much interest both in the pharmaceutical sciences and in physical chemistry. Connecting the chemistry of the drug and the lipids to the resulting thermodynamic properties remains of immediate importance. Here we report molecular dynamics (MD) simulation trajectories using the coarse-grained (CG) Martini force field. A wide, representative coverage of chemistry is provided: across solutes-exhaustively enumerating all 105 CG dimers-and across six phospholipids. For each combination, umbrella-sampling simulations provide detailed structural information of the solute at all depths from the bilayer midplane to bulk water, allowing a precise reconstruction of the potential of mean force. Overall, the present database contains trajectories from 15,120 MD simulations. This database may serve the further identification of structure-property relationships between compound chemistry and drug permeability.
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Affiliation(s)
| | - Alessia Centi
- Max Planck Institute for Polymer Research, 55128, Mainz, Germany
| | - Roberto Menichetti
- Max Planck Institute for Polymer Research, 55128, Mainz, Germany
- Physics Department, University of Trento, 38123, Trento, Italy
- INFN-TIFPA, Trento Institute for Fundamental Physics and Applications, 38123, Trento, Italy
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, 55128, Mainz, Germany.
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21
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Fukunishi Y, Mashimo T, Kurosawa T, Wakabayashi Y, Nakamura HK, Takeuchi K. Prediction of Passive Membrane Permeability by Semi-Empirical Method Considering Viscous and Inertial Resistances and Different Rates of Conformational Change and Diffusion. Mol Inform 2020; 39:e1900071. [PMID: 31609549 PMCID: PMC7050510 DOI: 10.1002/minf.201900071] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2019] [Accepted: 09/22/2019] [Indexed: 12/24/2022]
Abstract
Membrane permeability is an important property of drugs in adsorption. Many prediction methods work well for small molecules, but the prediction of middle-molecule permeability is still difficult. In the present study, we modified a classical permeability model based on Fick's law to study passive membrane permeability. The model consisted of the distribution of solute from water to membrane and the diffusion of solute in each solvent. The diffusion coefficient is the inverse of the resistance, and we examined the inertial resistance in addition to the viscous resistance, the latter of which has been widely used in permeability prediction. Also, we examined three models changing the balance between the diffusion of solute in membrane and the conformational change of solute. The inertial resistance improved the prediction results in addition to the viscous resistance. The models worked well not only for small molecules but also for middle molecules, whose structures have more conformational freedom.
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Affiliation(s)
- Yoshifumi Fukunishi
- Molecular Profiling Research Center for Drug Discovery (molprof)National Institute of Advanced Industrial Science and Technology (AIST)2-3-26, Aomi, Koto-kuTokyo135-0064Japan
| | - Tadaaki Mashimo
- Technology Research Association for Next-Generation Natural Products Chemistry2-3-26, Aomi, Koto-kuTokyo135-0064Japan
- IMSBIO Co., Ltd.Owl Tower, 4–21-1, Higashi-Ikebukuro, Toshima-kuTokyo170-0013Japan
| | - Takashi Kurosawa
- Technology Research Association for Next-Generation Natural Products Chemistry2-3-26, Aomi, Koto-kuTokyo135-0064Japan
- Hitachi Solutions East Japan, 12–1 Ekimaehoncho, Kawasaki-ku, KawasakiKanagawa210-0007Japan
| | | | - Hironori K. Nakamura
- Biomodeling Research Co., Ltd.1-704-2 Uedanishi, Tenpaku-ku, NagoyaAichi468-0058Japan
| | - Koh Takeuchi
- Molecular Profiling Research Center for Drug Discovery (molprof)National Institute of Advanced Industrial Science and Technology (AIST)2-3-26, Aomi, Koto-kuTokyo135-0064Japan
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22
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Effects of Cholesterol on Water Permittivity of Biomimetic Ion Pair Amphiphile Bilayers: Interplay between Membrane Bending and Molecular Packing. Int J Mol Sci 2019; 20:ijms20133252. [PMID: 31269714 PMCID: PMC6651711 DOI: 10.3390/ijms20133252] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2019] [Revised: 06/28/2019] [Accepted: 06/28/2019] [Indexed: 02/04/2023] Open
Abstract
Ion pair amphiphile (IPA), a molecular complex composed of a pair of cationic and anionic amphiphiles, is an inexpensive phospholipid substitute to fabricate vesicles with various pharmaceutical applications. Modulating the physicochemical and permeation properties of IPA vesicles are important for carrier designs. Here, we applied molecular dynamics simulations to examine the cholesterol effects on the structures, mechanics, and water permittivity of hexadecyltrimethylammonium-dodecylsulfate (HTMA-DS) and dodecyltrimethylammonium- hexadecylsulfate (DTMA-HS) IPA bilayers. Structural and mechanical analyses indicate that both IPA systems are in gel phase at 298 K. Adding cholesterol induces alkyl chain ordering around the rigid sterol ring and increases the cavity density within the hydrophilic region of both IPA bilayers. Furthermore, the enhanced alkyl chain ordering and the membrane deformation energy induced by cholesterol increase the permeation free energy penalty. In contrast, cholesterol has minor effects on the water local diffusivities within IPA membranes. Overall, the cholesterol reduces the water permittivity of rigid IPA membranes due to the synergistic effects of increased alkyl chain ordering and enhanced membrane mechanical modulus. The results provide molecular insights into the effects of molecular packing and mechanical deformations on the water permittivity of biomimetic IPA membranes, which is critical for designing IPA vesicular carriers.
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23
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Lomize AL, Pogozheva ID. Physics-Based Method for Modeling Passive Membrane Permeability and Translocation Pathways of Bioactive Molecules. J Chem Inf Model 2019; 59:3198-3213. [PMID: 31259555 DOI: 10.1021/acs.jcim.9b00224] [Citation(s) in RCA: 37] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
Abstract
Assessment of permeability is a critical step in the drug development process for selection of drug candidates with favorable ADME properties. We have developed a novel physics-based method for fast computational modeling of passive permeation of diverse classes of molecules across lipid membranes. The method is based on heterogeneous solubility-diffusion theory and operates with all-atom 3D structures of solutes and the anisotropic solvent model of the lipid bilayer characterized by transbilayer profiles of dielectric and hydrogen bonding capacity parameters. The optimal translocation pathway of a solute is determined by moving an ensemble of representative conformations of the molecule through the dioleoyl-phosphatidylcholine (DOPC) bilayer and optimizing their rotational orientations in every point of the transmembrane trajectory. The method calculates (1) the membrane-bound state of the solute molecule; (2) free energy profile of the solute along the permeation pathway; and (3) the permeability coefficient obtained by integration over the transbilayer energy profile and assuming a constant size-dependent diffusivity along the membrane normal. The accuracy of the predictions was evaluated against experimental permeability coefficients measured in pure lipid membranes (for 78 compounds, R2 was 0.88 and rmse was 1.15 log units), PAMPA-DS (for 280 compounds, R2 was 0.75 and rmse was 1.59 log units), BBB (for 182 compounds, R2 was 0.69 and rmse was 0.87 log units), and Caco-2/MDCK assays (for 165 compounds, R2 was 0.52 and rmse was 0.89 log units).
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Affiliation(s)
- Andrei L Lomize
- Department of Medicinal Chemistry, College of Pharmacy , University of Michigan , 428 Church Street , Ann Arbor , Michigan 48109-1065 , United States
| | - Irina D Pogozheva
- Department of Medicinal Chemistry, College of Pharmacy , University of Michigan , 428 Church Street , Ann Arbor , Michigan 48109-1065 , United States
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Abstract
This Review illustrates the evaluation of permeability of lipid membranes from molecular dynamics (MD) simulation primarily using water and oxygen as examples. Membrane entrance, translocation, and exit of these simple permeants (one hydrophilic and one hydrophobic) can be simulated by conventional MD, and permeabilities can be evaluated directly by Fick's First Law, transition rates, and a global Bayesian analysis of the inhomogeneous solubility-diffusion model. The assorted results, many of which are applicable to simulations of nonbiological membranes, highlight the limitations of the homogeneous solubility diffusion model; support the utility of inhomogeneous solubility diffusion and compartmental models; underscore the need for comparison with experiment for both simple solvent systems (such as water/hexadecane) and well-characterized membranes; and demonstrate the need for microsecond simulations for even simple permeants like water and oxygen. Undulations, subdiffusion, fractional viscosity dependence, periodic boundary conditions, and recent developments in the field are also discussed. Last, while enhanced sampling methods and increasingly sophisticated treatments of diffusion add substantially to the repertoire of simulation-based approaches, they do not address directly the critical need for force fields with polarizability and multipoles, and constant pH methods.
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Affiliation(s)
- Richard M Venable
- Laboratory of Computational Biology, National Lung, Heart, and Blood Institute , National Institutes of Health , Bethesda , Maryland 20892 , United States
| | - Andreas Krämer
- Laboratory of Computational Biology, National Lung, Heart, and Blood Institute , National Institutes of Health , Bethesda , Maryland 20892 , United States
| | - Richard W Pastor
- Laboratory of Computational Biology, National Lung, Heart, and Blood Institute , National Institutes of Health , Bethesda , Maryland 20892 , United States
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25
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Affiliation(s)
| | - Tristan Bereau
- Max Planck Institute for Polymer Research, Mainz, Germany
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26
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Rivel T, Ramseyer C, Yesylevskyy S. The asymmetry of plasma membranes and their cholesterol content influence the uptake of cisplatin. Sci Rep 2019; 9:5627. [PMID: 30948733 PMCID: PMC6449338 DOI: 10.1038/s41598-019-41903-w] [Citation(s) in RCA: 81] [Impact Index Per Article: 16.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2018] [Accepted: 03/18/2019] [Indexed: 12/20/2022] Open
Abstract
The composition of the plasma membrane of malignant cells is thought to influence the cellular uptake of cisplatin and to take part in developing resistance to this widespread anti-cancer drug. In this work we study the permeation of cisplatin through the model membranes of normal and cancer cells using molecular dynamics simulations. A special attention is paid to lipid asymmetry and cholesterol content of the membranes. The loss of lipid asymmetry, which is common for cancer cells, leads to a decrease in their permeability to cisplatin by one order of magnitude in comparison to the membranes of normal cells. The change in the cholesterol molar ratio from 0% to 33% also decreases the permeability of the membrane by approximately one order of magnitude. The permeability of pure DOPC membrane is 5-6 orders of magnitude higher than one of the membranes with realistic lipid composition, which makes it as an inadequate model for the studies of drug permeability.
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Affiliation(s)
- Timothée Rivel
- Laboratoire Chrono Environnement UMR CNRS 6249, Université de Bourgogne Franche-Comté, 16 route de Gray, 25030, Besançon, Cedex, France.
| | - Christophe Ramseyer
- Laboratoire Chrono Environnement UMR CNRS 6249, Université de Bourgogne Franche-Comté, 16 route de Gray, 25030, Besançon, Cedex, France
| | - Semen Yesylevskyy
- Laboratoire Chrono Environnement UMR CNRS 6249, Université de Bourgogne Franche-Comté, 16 route de Gray, 25030, Besançon, Cedex, France.,Department of Physics of Biological Systems, Institute of Physics of the National Academy of Sciences of Ukraine, Prospect Nauky 46, 03028, Kyiv, Ukraine
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Enkavi G, Javanainen M, Kulig W, Róg T, Vattulainen I. Multiscale Simulations of Biological Membranes: The Challenge To Understand Biological Phenomena in a Living Substance. Chem Rev 2019; 119:5607-5774. [PMID: 30859819 PMCID: PMC6727218 DOI: 10.1021/acs.chemrev.8b00538] [Citation(s) in RCA: 173] [Impact Index Per Article: 34.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
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Biological
membranes are tricky to investigate. They are complex
in terms of molecular composition and structure, functional
over a wide range of time scales, and characterized
by nonequilibrium conditions. Because of all of these
features, simulations are a great technique to study biomembrane
behavior. A significant part of the functional processes
in biological membranes takes place at the molecular
level; thus computer simulations are the method of
choice to explore how their properties emerge from specific
molecular features and how the interplay among the numerous
molecules gives rise to function over spatial and
time scales larger than the molecular ones. In this
review, we focus on this broad theme. We discuss the current
state-of-the-art of biomembrane simulations that, until
now, have largely focused on a rather narrow picture
of the complexity of the membranes. Given this, we
also discuss the challenges that we should unravel in the
foreseeable future. Numerous features such as the actin-cytoskeleton
network, the glycocalyx network, and nonequilibrium
transport under ATP-driven conditions have so far
received very little attention; however, the potential
of simulations to solve them would be exceptionally high. A
major milestone for this research would be that one day
we could say that computer simulations genuinely research
biological membranes, not just lipid bilayers.
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Affiliation(s)
- Giray Enkavi
- Department of Physics , University of Helsinki , P.O. Box 64, FI-00014 Helsinki , Finland
| | - Matti Javanainen
- Department of Physics , University of Helsinki , P.O. Box 64, FI-00014 Helsinki , Finland.,Institute of Organic Chemistry and Biochemistry of the Czech Academy of Sciences , Flemingovo naḿesti 542/2 , 16610 Prague , Czech Republic.,Computational Physics Laboratory , Tampere University , P.O. Box 692, FI-33014 Tampere , Finland
| | - Waldemar Kulig
- Department of Physics , University of Helsinki , P.O. Box 64, FI-00014 Helsinki , Finland
| | - Tomasz Róg
- Department of Physics , University of Helsinki , P.O. Box 64, FI-00014 Helsinki , Finland.,Computational Physics Laboratory , Tampere University , P.O. Box 692, FI-33014 Tampere , Finland
| | - Ilpo Vattulainen
- Department of Physics , University of Helsinki , P.O. Box 64, FI-00014 Helsinki , Finland.,Computational Physics Laboratory , Tampere University , P.O. Box 692, FI-33014 Tampere , Finland.,MEMPHYS-Center for Biomembrane Physics
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28
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Menichetti R, Kanekal KH, Bereau T. Drug-Membrane Permeability across Chemical Space. ACS CENTRAL SCIENCE 2019; 5:290-298. [PMID: 30834317 PMCID: PMC6396385 DOI: 10.1021/acscentsci.8b00718] [Citation(s) in RCA: 50] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/05/2018] [Indexed: 05/05/2023]
Abstract
Unraveling the relation between the chemical structure of small druglike compounds and their rate of passive permeation across lipid membranes is of fundamental importance for pharmaceutical applications. The elucidation of a comprehensive structure-permeability relationship expressed in terms of a few molecular descriptors is unfortunately hampered by the overwhelming number of possible compounds. In this work, we reduce a priori the size and diversity of chemical space to solve an analogous-but smoothed out-structure-property relationship problem. This is achieved by relying on a physics-based coarse-grained model that reduces the size of chemical space, enabling a comprehensive exploration of this space with greatly reduced computational cost. We perform high-throughput coarse-grained (HTCG) simulations to derive a permeability surface in terms of two simple molecular descriptors-bulk partitioning free energy and pK a. The surface is constructed by exhaustively simulating all coarse-grained compounds that are representative of small organic molecules (ranging from 30 to 160 Da) in a high-throughput scheme. We provide results for acidic, basic, and zwitterionic compounds. Connecting back to the atomic resolution, the HTCG predictions for more than 500 000 compounds allow us to establish a clear connection between specific chemical groups and the resulting permeability coefficient, enabling for the first time an inverse design procedure. Our results have profound implications for drug synthesis: the predominance of commonly employed chemical moieties narrows down the range of permeabilities.
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Affiliation(s)
| | | | - Tristan Bereau
- Max Planck Institute for
Polymer Research, 55128 Mainz, Germany
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29
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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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30
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De Vos O, Venable RM, Van Hecke T, Hummer G, Pastor RW, Ghysels A. Membrane Permeability: Characteristic Times and Lengths for Oxygen and a Simulation-Based Test of the Inhomogeneous Solubility-Diffusion Model. J Chem Theory Comput 2018; 14:3811-3824. [PMID: 29894626 DOI: 10.1021/acs.jctc.8b00115] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023]
Abstract
The balance of normal and radial (lateral) diffusion of oxygen in phospholipid membranes is critical for biological function. Based on the Smoluchowski equation for the inhomogeneous solubility-diffusion model, Bayesian analysis (BA) can be applied to molecular dynamics trajectories of oxygen to extract the free energy and the normal and radial diffusion profiles. This paper derives a theoretical formalism to convert these profiles into characteristic times and lengths associated with entering, escaping, or completely crossing the membrane. The formalism computes mean first passage times and holds for any process described by rate equations between discrete states. BA of simulations of eight model membranes with varying lipid composition and temperature indicate that oxygen travels 3 to 5 times further in the radial than in the normal direction when crossing the membrane in a time of 15 to 32 ns, thereby confirming the anisotropy of passive oxygen transport in membranes. Moreover, the preceding times and distances estimated from the BA are compared to the aggregate of 280 membrane exits explicitly observed in the trajectories. BA predictions for the distances of oxygen radial diffusion within the membrane are statistically indistinguishable from the corresponding simulation values, yet BA oxygen exit times from the membrane interior are approximately 20% shorter than the simulation values, averaged over seven systems. The comparison supports the BA approach and, therefore, the applicability of the Smoluchowski equation to membrane diffusion. Given the shorter trajectories required for the BA, these results validate the BA as a computationally attractive alternative to direct observation of exits when estimating characteristic times and radial distances. The effect of collective membrane undulations on the BA is also discussed.
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Affiliation(s)
- Oriana De Vos
- Center for Molecular Modeling , Ghent University , Technologiepark 903 , 9052 Gent , Belgium
| | - Richard M Venable
- Laboratory of Computational Biology , National Heart Lung Blood Institute, National Institutes of Health , Bethesda , Maryland 20892 , United States
| | - Tanja Van Hecke
- Department of Information Technology , Ghent University , 9000 Gent , Belgium
| | - Gerhard Hummer
- Department of Theoretical Biophysics , Max Planck Institute of Biophysics , 60438 Frankfurt am Main , Germany.,Institute for Biophysics , Goethe University Frankfurt , 60438 Frankfurt am Main , Germany
| | - Richard W Pastor
- Laboratory of Computational Biology , National Heart Lung Blood Institute, National Institutes of Health , Bethesda , Maryland 20892 , United States
| | - An Ghysels
- Center for Molecular Modeling , Ghent University , Technologiepark 903 , 9052 Gent , Belgium
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31
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Amaro RE, Mulholland AJ. Multiscale Methods in Drug Design Bridge Chemical and Biological Complexity in the Search for Cures. Nat Rev Chem 2018; 2:0148. [PMID: 30949587 PMCID: PMC6445369 DOI: 10.1038/s41570-018-0148] [Citation(s) in RCA: 94] [Impact Index Per Article: 15.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023]
Abstract
Drug action is inherently multiscale: it connects molecular interactions to emergent properties at cellular and larger scales. Simulation techniques at each of these different scales are already central to drug design and development, but methods capable of connecting across these scales will extend understanding of complex mechanisms and the ability to predict biological effects. Improved algorithms, ever-more-powerful computing architectures and the accelerating growth of rich datasets are driving advances in multiscale modeling methods capable of bridging chemical and biological complexity from the atom to the cell. Particularly exciting is the development of highly detailed, structure-based, physical simulations of biochemical systems, which are now able to access experimentally relevant timescales for large systems and, at the same time, achieve unprecedented accuracy. In this Perspective, we discuss how emerging data-rich, physics-based multiscale approaches are of the cusp of realizing long-promised impact in the discovery, design and development of novel therapeutics. We highlight emerging methods and applications in this growing field, and outline how different scales can be combined in practical modelling and simulation strategies.
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Affiliation(s)
- Rommie E Amaro
- Department of Chemistry and Biochemistry, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0304
| | - Adrian J Mulholland
- Centre for Computational Chemistry, School of Chemistry, University of Bristol, Bristol BS8 1TS, UK
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32
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Votapka LW, Jagger BR, Heyneman AL, Amaro RE. SEEKR: Simulation Enabled Estimation of Kinetic Rates, A Computational Tool to Estimate Molecular Kinetics and Its Application to Trypsin-Benzamidine Binding. J Phys Chem B 2017; 121:3597-3606. [PMID: 28191969 PMCID: PMC5562489 DOI: 10.1021/acs.jpcb.6b09388] [Citation(s) in RCA: 62] [Impact Index Per Article: 8.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
We present the Simulation Enabled Estimation of Kinetic Rates (SEEKR) package, a suite of open-source scripts and tools designed to enable researchers to perform multiscale computation of the kinetics of molecular binding, unbinding, and transport using a combination of molecular dynamics, Brownian dynamics, and milestoning theory. To demonstrate its utility, we compute the kon, koff, and ΔGbind for the protein trypsin with its noncovalent binder, benzamidine, and examine the kinetics and other results generated in the context of the new software, and compare our findings to previous studies performed on the same system. We compute a kon estimate of (2.1 ± 0.3) × 107 M-1 s-1, a koff estimate of 83 ± 14 s-1, and a ΔGbind of -7.4 ± 0.1 kcal·mol-1, all of which compare closely to the experimentally measured values of 2.9 × 107 M-1 s-1, 600 ± 300 s-1, and -6.71 ± 0.05 kcal·mol-1, respectively.
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Affiliation(s)
- Lane W. Votapka
- Laufer Center for Physical and Quantitative Biology, Stony Brook University, Stony Brook, NY 11794
- University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093
| | | | | | - Rommie E. Amaro
- University of California San Diego, 9500 Gilman Dr., La Jolla, CA 92093
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33
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Dickson CJ, Hornak V, Pearlstein RA, Duca JS. Structure–Kinetic Relationships of Passive Membrane Permeation from Multiscale Modeling. J Am Chem Soc 2016; 139:442-452. [DOI: 10.1021/jacs.6b11215] [Citation(s) in RCA: 80] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Callum J. Dickson
- Computer-Aided Drug Discovery,
Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Viktor Hornak
- Computer-Aided Drug Discovery,
Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Robert A. Pearlstein
- Computer-Aided Drug Discovery,
Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Jose S. Duca
- Computer-Aided Drug Discovery,
Global Discovery Chemistry, Novartis Institutes for BioMedical Research, 181 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
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34
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Nitschke N, Atkovska K, Hub JS. Accelerating potential of mean force calculations for lipid membrane permeation: System size, reaction coordinate, solute-solute distance, and cutoffs. J Chem Phys 2016; 145:125101. [DOI: 10.1063/1.4963192] [Citation(s) in RCA: 23] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/15/2023] Open
Affiliation(s)
- Naomi Nitschke
- Institute for Microbiology and Genetics, Georg-August-University Göttingen, Justus-von-Liebig-Weg 11, 37077 Göttingen, Germany
| | - Kalina Atkovska
- Institute for Microbiology and Genetics, Georg-August-University Göttingen, Justus-von-Liebig-Weg 11, 37077 Göttingen, Germany
| | - Jochen S. Hub
- Institute for Microbiology and Genetics, Georg-August-University Göttingen, Justus-von-Liebig-Weg 11, 37077 Göttingen, Germany
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