1
|
Domingues TS, Coifman R, Haji-Akbari A. Estimating Position-Dependent and Anisotropic Diffusivity Tensors from Molecular Dynamics Trajectories: Existing Methods and Future Outlook. J Chem Theory Comput 2024; 20:4427-4455. [PMID: 38815171 DOI: 10.1021/acs.jctc.4c00148] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/01/2024]
Abstract
Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in characterizing such spatial heterogeneities and probing the impact of confinement on materials' properties. For static properties, this is a straightforward task and can be achieved via simple spatial binning. Such an approach, however, cannot be readily applied to transport coefficients due to lack of natural extensions of autocorrelations used for their calculation in the bulk. The prime example of this challenge is diffusivity, which, in the bulk, can be readily estimated from the particles' mobility statistics, which satisfy the Fokker-Planck equation. Under confinement, however, such statistics will follow the Smoluchowski equation, which lacks a closed-form analytical solution. This brief review explores the rich history of estimating profiles of the diffusivity tensor from MD simulations and discusses various approximate methods and algorithms developed for this purpose. Besides discussing heuristic extensions of bulk methods, we overview more rigorous algorithms, including kernel-based methods, Bayesian approaches, and operator discretization techniques. Additionally, we outline methods based on applying biasing potentials or imposing constraints on tracer particles. Finally, we discuss approaches that estimate diffusivity from mean first passage time or committor probability profiles, a conceptual framework originally developed in the context of collective variable spaces describing rare events in computational chemistry and biology. In summary, this paper offers a concise survey of diverse approaches for estimating diffusivity from MD trajectories, highlighting challenges and opportunities in this area.
Collapse
Affiliation(s)
- Tiago S Domingues
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, United States
| | - Ronald Coifman
- Department of Mathematics, Yale University, New Haven, Connecticut 06520, United States
- Department of Computer Science, Yale University, New Haven, Connecticut 06520, United States
| | - Amir Haji-Akbari
- Department of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06520, United States
| |
Collapse
|
2
|
Raza S, Sievertsen TH, Okumoto S, Vermaas JV. Passive permeability controls synthesis for the allelochemical sorgoleone in sorghum root exudate. PHYTOCHEMISTRY 2024; 217:113891. [PMID: 37844789 DOI: 10.1016/j.phytochem.2023.113891] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/07/2023] [Revised: 10/04/2023] [Accepted: 10/07/2023] [Indexed: 10/18/2023]
Abstract
Competition for soil nutrients and water with other plants foster competition within the biosphere for access to these limited resources. The roots for the common grain sorghum produce multiple small molecules that are released via root exudates into the soil to compete with other plants. Sorgoleone is one such compound, which suppresses weed growth near sorghum by acting as a quinone analog and interferes with photosynthesis. Since sorghum also grows photosynthetically, and may be susceptible to sorgoleone action if present in tissues above ground, it is essential to exude sorgoleone efficiently. However, since the P450 enzymes that synthesize sorgoleone are intracellular, the release mechanism for sorgoleone remain unclear. In this study, we conducted an in silico assessment for sorgoleone and its precursors to passively permeate biological membranes. To facilitate accurate simulation, CHARMM parameters were newly optimized for sorgoleone and its precursors. These parameters were used to conduct 1 μs of unbiased molecular dynamics simulations to compare the permeability of sorgoleone with its precursors molecules. We find that interleaflet transfer is maximized for sorgoleone, suggesting that the precursor molecules may remain in the same leaflet for access by biosynthetic P450 enzymes. Since no sorgoleone was extracted during unbiased simulations, we compute a permeability coefficient using the inhomogeneous solubility diffusion model. The requisite free energy and diffusivity profiles for sorgoleone through a sorghum membrane model were determined through Replica Exchange Umbrella Sampling (REUS) simulations. The REUS calculations highlight that any soluble sorgoleone would quickly insert into a lipid bilayer, and would readily transit. When sorgoleone forms aggregates in root exudate as indicated by our equilibrium simulations, aggregate formation would lower the effective concentration in aqueous solution, creating a concentration gradient that would facilitate passive transport. This suggests that sorgoleone synthesis occurs within sorghum root cells and that sorgoleone is exuded by permeating through the cell membrane without the need for a transport protein once the extracellular sorgoleone aggregate is formed.
Collapse
Affiliation(s)
- Saad Raza
- Plant Research Laboratory, College of Natural Science, Michigan State University, East Lansing, 48824, MI, USA
| | - Troy H Sievertsen
- Department of Biochemistry and Molecular Biology, College of Natural Science, Michigan State University, East Lansing, 48824, MI, USA
| | - Sakiko Okumoto
- Department of Soil and Crop Sciences, College of Agriculture and Life Sciences, Texas A&M University, College Station, 77843, TX, USA
| | - Josh V Vermaas
- Plant Research Laboratory, College of Natural Science, Michigan State University, East Lansing, 48824, MI, USA; Department of Biochemistry and Molecular Biology, College of Natural Science, Michigan State University, East Lansing, 48824, MI, USA.
| |
Collapse
|
3
|
Raza S, Miller M, Hamberger B, Vermaas JV. Plant Terpenoid Permeability through Biological Membranes Explored via Molecular Simulations. J Phys Chem B 2023; 127:1144-1157. [PMID: 36717085 PMCID: PMC9923751 DOI: 10.1021/acs.jpcb.2c07209] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023]
Abstract
Plants synthesize small molecule diterpenes composed of 20 carbons from precursor isopentenyl diphosphate and dimethylallyl disphosphate, manufacturing diverse compounds used for defense, signaling, and other functions. Industrially, diterpenes are used as natural aromas and flavoring, as pharmaceuticals, and as natural insecticides or repellents. Despite diterpene ubiquity in plant systems, it remains unknown how plants control diterpene localization and transport. For many other small molecules, plant cells maintain transport proteins that control compound compartmentalization. However, for most diterpene compounds, specific transport proteins have not been identified, and so it has been hypothesized that diterpenes may cross biological membranes passively. Through molecular simulation, we study membrane transport for three complex diterpenes from among the many made by members of the Lamiaceae family to determine their permeability coefficient across plasma membrane models. To facilitate accurate simulation, the intermolecular interactions for leubethanol, abietic acid, and sclareol were parametrized through the standard CHARMM methodology for incorporation into molecular simulations. To evaluate the effect of membrane composition on permeability, we simulate the three diterpenes in two membrane models derived from sorghum and yeast lipidomics data. We track permeation events within our unbiased simulations, and compare implied permeation coefficients with those calculated from Replica Exchange Umbrella Sampling calculations using the inhomogeneous solubility diffusion model. The diterpenes are observed to permeate freely through these membranes, indicating that a transport protein may not be needed to export these small molecules from plant cells. Moreover, the permeability is observed to be greater for plant-like membrane compositions when compared against animal-like membrane models. Increased permeability for diterpene molecules in plant membranes suggest that plants have tailored their membranes to facilitate low-energy transport processes for signaling molecules.
Collapse
Affiliation(s)
- Saad Raza
- Plant
Research Laboratory, College of Natural Science, Michigan State University, East LansingMichigan48824, United States
| | - Mykayla Miller
- Department
of Chemistry and Biochemistry, California
State University, Fullerton, Fullerton, California92831, United States
| | - Björn Hamberger
- Department
Of Biochemistry and Molecular Biology, College of Natural Science, Michigan State University, East LansingMichigan48824, United States
| | - Josh V. Vermaas
- Plant
Research Laboratory, College of Natural Science, Michigan State University, East LansingMichigan48824, United States,Department
Of Biochemistry and Molecular Biology, College of Natural Science, Michigan State University, East LansingMichigan48824, United States,E-mail: . Phone: +1 (517) 884-6937
| |
Collapse
|
4
|
Vermaas JV, Crowley MF, Beckham GT. Molecular simulation of lignin-related aromatic compound permeation through gram-negative bacterial outer membranes. J Biol Chem 2022; 298:102627. [PMID: 36273587 PMCID: PMC9720347 DOI: 10.1016/j.jbc.2022.102627] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Revised: 10/14/2022] [Accepted: 10/15/2022] [Indexed: 12/12/2022] Open
Abstract
Lignin, an abundant aromatic heteropolymer in secondary plant cell walls, is the single largest source of renewable aromatics in the biosphere. Leveraging this resource for renewable bioproducts through targeted microbial action depends on lignin fragment uptake by microbial hosts and subsequent enzymatic action to obtain the desired product. Recent computational work has emphasized that bacterial inner membranes are permeable to many aromatic compounds expected from lignin depolymerization processes. In this study, we expand on these findings through simulations for 42 lignin-related compounds across a gram-negative bacterial outer membrane model. Unbiased simulation trajectories indicate that spontaneous crossing for the full outer membrane is relatively rare at molecular simulation timescales, primarily due to preferential membrane partitioning and slow diffusion within the lipopolysaccharide layer within the outer membrane. Membrane partitioning and permeability coefficients were determined through replica exchange umbrella sampling simulations to overcome sampling limitations. We find that the glycosylated lipopolysaccharides found in the outer membrane increase the permeation barrier to many lignin-related compounds, particularly the most hydrophobic compounds. However, the effect is relatively modest; at industrially relevant concentrations, uncharged lignin-related compounds will readily diffuse across the outer membrane without the need for specific porins. Together, our results provide insight into the permeability of the bacterial outer membrane for assessing lignin fragment uptake and the future production of renewable bioproducts.
Collapse
Affiliation(s)
- Josh V. Vermaas
- Biosciences Center, National Renewable Energy Laboratory, Golden, Colorado, USA,National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA,MSU-DOE Plant Research Laboratory, Michigan State University, East Lansing, Michigan, USA,Department of Biochemistry and Molecular Biology, Michigan State University, East Lansing, Michigan, USA,For correspondence: Josh V. Vermaas; Michael F. Crowley; Gregg T. Beckham
| | - Michael F. Crowley
- Renewable Resources and Enabling Sciences Center, National Renewable Energy, Laboratory, Golden, Colorado, USA,For correspondence: Josh V. Vermaas; Michael F. Crowley; Gregg T. Beckham
| | - Gregg T. Beckham
- Renewable Resources and Enabling Sciences Center, National Renewable Energy, Laboratory, Golden, Colorado, USA,For correspondence: Josh V. Vermaas; Michael F. Crowley; Gregg T. Beckham
| |
Collapse
|
5
|
Nagai T, Okazaki S. Global diffusion of hydrogen molecules in the heterogeneous structure of polymer electrolytes for fuel cells: Dynamic Monte Carlo combined with molecular dynamics calculations. J Chem Phys 2022; 157:054502. [DOI: 10.1063/5.0096574] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Using our recently developed dynamic Monte Carlo (MC) method [Nagai et al., J. Chem Phys. 156, 154506 (2022)], we investigated global diffusion of hydrogen molecules over structural heterogeneities of polymer electrolyte membranes in fuel cells. The three-dimensional position-dependent free energies and the diffusion constants of the hydrogen molecules, required by the present dynamic MC calculations, were taken from our previous study [Nagai et al., J. Chem. Phys. 156, 044507 (2022)] and newly evaluated in this work, respectively. The calculations enabled evaluating the hydrogen dynamics over long-time scales, including global diffusion constants. Based on the calculated global diffusion constants and free energies, the permeability of hydrogen molecules was estimated via the solubility-diffusion model. The estimated values were in good agreement with reported experimental data, thus validating the present methodology. The analysis of the Monte Carlo trajectories indicated that the main permeation paths are located in the polymer and interfacial phases, although the water phase may make a non-negligible contribution to mass transport.
Collapse
Affiliation(s)
- Tetsuro Nagai
- Graduate School of Frontier Sciences, The University of Tokyo Graduate School of Frontier Sciences, Japan
| | - Susumu Okazaki
- Department of Advanced Materials Science, University of Tokyo Graduate School of Frontier Sciences Department of Advanced Materials Science, Japan
| |
Collapse
|
6
|
Nagai T, Yoshimori A, Okazaki S. Dynamic Monte Carlo calculation generating particle trajectories that satisfy the diffusion equation for heterogeneous systems with a position-dependent diffusion coefficient and free energy. J Chem Phys 2022; 156:154506. [PMID: 35459306 DOI: 10.1063/5.0086949] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
A series of new Monte Carlo (MC) transition probabilities was investigated that could produce molecular trajectories statistically satisfying the diffusion equation with a position-dependent diffusion coefficient and potential energy. The MC trajectories were compared with the numerical solution of the diffusion equation by calculating the time evolution of the probability distribution and the mean first passage time, which exhibited excellent agreement. The method is powerful when investigating, for example, the long-distance and long-time global transportation of a molecule in heterogeneous systems by coarse-graining them into one-particle diffusive molecular motion with a position-dependent diffusion coefficient and free energy. The method can also be applied to many-particle dynamics.
Collapse
Affiliation(s)
- Tetsuro Nagai
- Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan
| | - Akira Yoshimori
- Department of Physics, Niigata University, Niigata 950-2181, Japan
| | - Susumu Okazaki
- Department of Advanced Materials Science, Graduate School of Frontier Sciences, The University of Tokyo, Kashiwa 277-8561, Japan
| |
Collapse
|
7
|
Yamaguchi T. Coupling between Translational Diffusion of a Solute and Dynamics of the Heterogeneous Structure: Higher Alcohols and Ionic Liquids. J Phys Chem B 2022; 126:3125-3134. [PMID: 35438995 DOI: 10.1021/acs.jpcb.2c01053] [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
Translational diffusion of nonpolar monoatomic solutes in a room-temperature ionic liquid and 1-octanol was studied by molecular dynamics simulation. The diffusion coefficient was evaluated in two different ways: (1) from the mean-square displacement of a freely diffusing solute and (2) from the time correlation function of force acting on a fixed solute. The diffusion of the free solute is much greater than the prediction of the Stokes-Einstein (SE) relation when the size of the solute is small, as has been reported by many experimental works. In contrast, the friction on fixed small solutes follows the SE relation. The mechanism of the solute diffusion in both solvents was then analyzed based on the coupling between the translational motion of the solute and the collective dynamics of the heterogeneous intermediate-range structure characteristic to these solvents. Analysis revealed that the coupling is present in all systems, but the relaxation is fast in the cases of free and small solutes. This suggests that the coupling can relax through the motion of the solute when the solute is free and small, while the relaxation of the heterogeneous structure itself is required for large or fixed solutes. The difference in the relaxation dynamics of the friction on the solute and the shear viscosity is explained as the coupling with different dynamic modes of the solvent. Therefore, the validity of the SE relation may not be a good criterion to judge whether the mechanisms of the diffusion and the viscosity are the same or not.
Collapse
Affiliation(s)
- Tsuyoshi Yamaguchi
- Graduate School of Engineering, Nagoya University, Chikusa, Nagoya 464-8603, Japan
| |
Collapse
|