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g_elpot: A Tool for Quantifying Biomolecular Electrostatics from Molecular Dynamics Trajectories
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Biomolecular Systems

g_elpot: A Tool for Quantifying Biomolecular Electrostatics from Molecular Dynamics Trajectories
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  • Andrei Y. Kostritskii*
    Andrei Y. Kostritskii
    Institute of Biological Information Processing (IBI-1), Molekular- und Zellphysiologie, and JARA-HPC, Forschungszentrum Jülich, 52425 Jülich, Germany
    Department of Physics, RWTH Aachen University, 52062 Aachen, Germany
    Institute of Clinical Pharmacology, RWTH Aachen University, 52062 Aachen, Germany
    *E-mail: [email protected]
  • Claudia Alleva
    Claudia Alleva
    Institute of Biological Information Processing (IBI-1), Molekular- und Zellphysiologie, and JARA-HPC, Forschungszentrum Jülich, 52425 Jülich, Germany
  • Saskia Cönen
    Saskia Cönen
    Institute of Biological Information Processing (IBI-1), Molekular- und Zellphysiologie, and JARA-HPC, Forschungszentrum Jülich, 52425 Jülich, Germany
    Institute of Clinical Pharmacology, RWTH Aachen University, 52062 Aachen, Germany
  • Jan-Philipp Machtens*
    Jan-Philipp Machtens
    Institute of Biological Information Processing (IBI-1), Molekular- und Zellphysiologie, and JARA-HPC, Forschungszentrum Jülich, 52425 Jülich, Germany
    Institute of Clinical Pharmacology, RWTH Aachen University, 52062 Aachen, Germany
    *E-mail: [email protected]. Phone: ++49 2461 614043.
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Journal of Chemical Theory and Computation

Cite this: J. Chem. Theory Comput. 2021, 17, 5, 3157–3167
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https://doi.org/10.1021/acs.jctc.0c01246
Published April 29, 2021

Copyright © 2021 The Authors. Published by American Chemical Society. This publication is licensed under

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Abstract

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Electrostatic forces drive a wide variety of biomolecular processes by defining the energetics of the interaction between biomolecules and charged substances. Molecular dynamics (MD) simulations provide trajectories that contain ensembles of structural configurations sampled by biomolecules and their environment. Although this information can be used for high-resolution characterization of biomolecular electrostatics, it has not yet been possible to calculate electrostatic potentials from MD trajectories in a way allowing for quantitative connection to energetics. Here, we present g_elpot, a GROMACS-based tool that utilizes the smooth particle mesh Ewald method to quantify the electrostatics of biomolecules by calculating potential within water molecules that are explicitly present in biomolecular MD simulations. g_elpot can extract the global distribution of the electrostatic potential from MD trajectories and measure its time course in functionally important regions of a biomolecule. To demonstrate that g_elpot can be used to gain biophysical insights into various biomolecular processes, we applied the tool to MD trajectories of the P2X3 receptor, TMEM16 lipid scramblases, the secondary-active transporter GltPh, and DNA complexed with cationic polymers. Our results indicate that g_elpot is well suited for quantifying electrostatics in biomolecular systems to provide a deeper understanding of its role in biomolecular processes.

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Copyright © 2021 The Authors. Published by American Chemical Society

Introduction

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Through shaping the energetics of the interaction between charged substances, electrostatics underlies the biological functions of many biomolecules. Detailed characterization of biomolecular electrostatics is required for a full understanding of diverse biological processes, such as ion transport across cell membranes, protein–ligand interactions, and the formation of biomolecular complexes. Both a biomolecule and its environment contribute to charge distribution and, thereby, to the electrostatic potential of a system. However, experimentally resolved structures rarely provide information on the dynamic biomolecular environment. In the absence of such information, the distribution of the electrostatic potential around a biomolecule can be evaluated by continuum methods based on the Poisson–Boltzmann (PB) equation. (1) Considerable insights into the biophysical properties of proteins and nucleic acids have been gained using continuum methods (1) implemented in a number of software packages, including the widely used DelPhi (2) and APBS. (3,4) However, due to their implicit representation of the biomolecular environment, continuum methods do not take into account a number of molecular-level phenomena (e.g., the orientation of solvent molecules at the interface with biomolecules (5) and the orientation of lipid headgroups around membrane proteins), which can significantly affect the electrostatics of the system. (6) Moreover, PB methods represent the environment in terms of electric permittivity, which is arbitrarily assigned to different parts of the system. (7,8) Lastly, calculations based on the PB equation ignore the natural dynamics of the studied biomolecules. These features limit the amount of quantitative details on biomolecular electrostatics that can be obtained using PB methods.
Nowadays, molecular dynamics (MD) simulations are commonly used to obtain information on the dynamics and functions of biomolecular systems at atomistic resolution. (9,10) During an MD simulation, the biomolecule and its environment sample the conformational space, with each trajectory frame containing information on the instantaneous distribution of electrostatic potential, as defined by the atomic positions. Due to the nanoscale size of the systems studied in MD simulations, periodic boundary conditions are commonly used to avoid undesirable edge effects. (8,11) In a periodic system, the long-range nature of the electrostatics makes the direct sum of contributions from the periodic copies only conditionally convergent. (8) This problem can be tackled by a number of approaches, (8,11) including widely used methods based on the Ewald summation. (12,13) Briefly, the potential is split into short- and long-range parts that converge in real and Fourier spaces, respectively. Whereas the short-range part has singularities at the atom positions, the long-range part can be used to calculate a smooth distribution of the electrostatic potential over the simulation box.
The idea of using the long-range part of the potential (calculated by the smooth particle mesh Ewald (SPME) method (13)) to characterize electrostatics in biomolecular systems based on the MD trajectories was first realized in the pmepot plug-in (14) of the visual molecular dynamics (VMD) package. (15) The plug-in generates a map of the average distribution of the long-range part of the SPME potential and, to the best of our knowledge, has so far been the only tool for extracting electrostatic potentials from MD trajectories. However, the resulting map can be substantially smeared due to the free translation and rotation of a biomolecule during an MD simulation. This smearing cannot be avoided by rotational fitting of the trajectory onto the reference structure prior to the SPME calculation because subsequent application of the periodic boundary conditions results in an artificial electrostatic-potential map. The smearing problem can be solved using short MD trajectories (16) or simulations with positional restraints applied to the biomolecule. (17) However, the absence of a fitting procedure limits the usage of pmepot mainly to the qualitative analysis of electrostatics in long MD simulations of free proteins and nucleic acids. Additionally, although MD trajectories inherently contain time-resolved information on a biomolecular system, pmepot can only derive the average distribution of the potential and not its time course. Furthermore, we will demonstrate that direct quantification of electrostatics from the long-range part of the SPME potential should be interpreted with caution due to its slow convergence over the parameters used for the calculations.
Here, we present the g_elpot tool, which overcomes the aforementioned limitations and enables the efficient quantitative analysis of electrostatic potential in biomolecular systems based on MD trajectories. On-the-fly fitting of trajectory frames enables the generation of high-resolution maps of electrostatic potential around biomolecules. Based on a computational scheme that harnesses the explicit water molecules present in an MD system, g_elpot generates the maps that are easily converted into convergent electrostatic-potential profiles. Using g_elpot, we characterized electrostatics in several biomolecular systems: the P2X3 receptor, human and fungal TMEM16 lipid scramblases, and supramolecular complexes of DNA with polycations. We also exploited the tool’s ability to extract time-resolved electrostatic potentials in arbitrary regions of a biomolecule to quantify the dependence of the electrostatic potential in the substrate-binding pocket on Na+ occupation in the Na+-coupled glutamate transporter homologue GltPh. Taken together, our results demonstrate that g_elpot is a convenient tool for the thorough quantification of electrostatics in diverse biomolecular systems.

Methods

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Quantification of Electrostatics Based on Water-Molecule Potentials

To decide whether it is electrostatically favorable for a charged solvable substance to locate at particular sites on a biomolecule, we consider the potential (Φ) created at a point (r) of a system with respect to the bulk solution
(1)
Defined relative to the bulk, this potential is conceptually equivalent to the PB potential with Dirichlet boundary conditions set to zero. However, in contrast to the PB potential, Φ(r) can be calculated for a particular configuration of a biomolecular system with explicit ions and solvent molecules. Averaging the potential over the MD trajectory, we obtain a distribution of the electrostatic potential while taking into account atomic details of the biomolecular environment.
Hereafter, we only consider the hydrated regions of the system because, in most biologically relevant processes, a charged soluble substance interacts with a biomolecule at a hydrated site. The local electrostatics at the water-populated regions of the system can be quantified by water-molecule potentials that are calculated at a certain point (rwm) within each water molecule, e.g., its center of geometry. The water-molecule potential can then be split into two parts
(2)
where ϕwm(rwm) accounts for the contribution of the water molecule itself to the potential and ϕsur(rwm) is the contribution of the rest of the system, i.e., the surroundings of the water molecule. In turn, we define the system bulk potential as
(3)
where ⟨···⟩bulk denotes averaging over all water molecules in the bulk region of the system. Thus
(4)
The contribution of the water molecule to the potential at rwm depends on the geometry of the water molecule but not on its position or surroundings. Therefore, if water molecules are assumed to have only small geometric fluctuations
(5)
and
(6)
Notably, in the case of absolutely rigid water molecules, the approximations in eqs 5 and 6 become equalities.
In a periodic point-charge system where the unit-cell edges are defined by vectors a1, a2, and a3, the distribution of electrostatic potential can be calculated with the SPME method (13) by splitting the potential into the long-range and short-range parts
(7)
where the long-range part is created by Gaussian-distributed charges ρ(r), approximating the original charge distribution
(8)
where N is the number of atoms, qi and ri are the charge and the position of an atom i, β is the inverse width of a Gaussian, and the outer sum is over n = n1a1 + n2a2 + n3a3, for all integers n1, n2, and n3. The long- and short-range parts of the potential converge in Fourier and real space, respectively. The higher the value of β, the faster the short-range part decays (Supporting Information Figure S1a); therefore, the value of the β parameter can be chosen such that the short-range part of the potential created by an atom is negligible at a predefined distance. In MD simulations, interatomic repulsion at short distances prevents atoms from overlapping and guarantees a nonzero distance between them. Therefore, the short-range part of the potential created at rwm by the atoms surrounding the water molecule can be made negligible by assigning β a value greater than some critical value βc, so
(9)
and Φ can be found as
(10)
Thus, the proper choice of β ensures that only the long-range part of the potential is enough to obtain a rigorous quantification of local electrostatics in the hydrated regions of the simulation system.

Implementation

g_elpot exploits the presence of explicit water molecules in MD simulations to generate detailed information on the electrostatics in a biomolecular system. First, the long-range part of the SPME potential is calculated on a regular grid (Figure 1, step 1), and then each water molecule is assigned a potential, referred to as the water-molecule potential (Figure 1, step 2). This potential is the average of the long-range SPME potentials at the grid nodes within a sphere of 0.15 nm radius around the center of geometry of the water molecule. The averaging smoothens the resulting potentials by suppressing changes in the potential caused by minor changes in the water-molecule geometry. Thus, provided that β ≥ βc, the water-molecule potential can be used to calculate the electrostatic potential created by the water molecule’s surroundings. To avoid smearing of the final electrostatic-potential map (which is built around a biomolecule), the trajectory frame is superimposed on the reference structure of the biomolecule (Figure 1, step 3). Each water-molecule potential is then added to the map nodes that are within 0.15 nm of the water molecule’s center of geometry. After all water-molecule potentials are added to the final electrostatic-potential map, the potential at each node is normalized by the number of contributing water molecules (Figure 1, step 4). This procedure is repeated for each frame of the trajectory, resulting in an average electrostatic-potential map around the biomolecule. g_elpot also generates a map that reports the fraction of trajectory frames in which a particular node has water molecules in its vicinity. Since this map is used to mask the dehydrated regions of a system, it is referred to as a water-occupancy map. As the water-occupancy map has the same dimensions as the electrostatic-potential map, combining both maps is a straightforward way to obtain the electrostatic-potential profile along a coordinate of interest, for instance, along the pore axis of an ion channel. Optionally, the water-molecule-based scheme can be switched off so that the final map is obtained by linear interpolation of the SPME potential instead of the average water-molecule potential. When calculated in this way, the electrostatic-potential map can be used to qualitatively describe the distribution of the electrostatic potential in nonhydrated regions of the system.

Figure 1

Figure 1. Water-based scheme to calculate the electrostatic potential. First, the long-range part of the potential is calculated by solving the Poisson equation on the grid using the SPME method. Second, each water molecule is assigned a potential averaged over a sphere around its center of geometry, resulting in a distribution of water-molecule potentials. Third, the frame is fitted onto the reference structure and the grid of the final electrostatic-potential map is built around the biomolecule. Fourth, the water-molecule potentials are distributed over the nodes of the electrostatic-potential map, followed by normalization of the node potential based on the number of contributing water molecules. The final map is used for the quantitative analysis of electrostatics, e.g., to generate a potential profile.

g_elpot can also provide time-resolved electrostatic potentials in predefined regions of a system. Each region is defined by a point (the center of geometry of a user-defined group), which is assigned with the average potential of water molecules within a sphere of user-defined radius (Supporting Information Figure S1b). To prevent discontinuity in the resulting time courses, if no water molecule is found within the sphere, then the point is assigned the potential of the nearest water molecule (Supporting Information Figure S1b). The time course of the total number of water molecules within the sphere is also recorded (Supporting Information Figure S1b) so that such dehydrated frames can be excluded from further analysis. To enable comparison with the bulk potential, a point representing the bulk solution must also be specified by the user in absolute coordinates. In practice, the bulk point is chosen based on the initial state of the system but is scaled at every simulation frame following a possible change in the size of the simulation box.
g_elpot is written in C/C++, with the fast Fourier transform as part of the SPME calculation done using FFTW library (18) version 3. OpenMP is used for optional thread parallelization over the trajectory frames. The tool is GROMACS based and, therefore, accepts input files in GROMACS formats. In particular, the atomic charges and reference conformation are read from a tpr file, and the trajectory can be in any GROMACS-supported format (including xtc, tng, trr, and pdb). The atomic groups used for the analysis are defined by the GROMACS-style index file. To apply g_elpot to trajectories generated by other simulation packages, the simulation files need to be converted into GROMACS formats first. In particular, NAMD (19) users can find the conversion instructions at the tool webpage provided below.

Availability and Usage

Source code, installation instructions, and usage recommendations can be found at: https://jugit.fz-juelich.de/computational-neurophysiology/g_elpot.

Simulation Details

P2X3 System

The human ionotropic cation-selective ATP receptor P2X3 was modeled based on its structure in the open state (20) (PDBID: 5SVK) and embedded in a 1-palmitoyl-2-oleoyl-phosphatidylcholine (POPC) bilayer using the g_membed functionality (21) in GROMACS. The ATP-binding ectodomain (residues 49–315) was cut off, and transmembrane helices were joined by two glycine residues. The system was simulated in GROMACS (22) version 2018 using a time step of 2 fs. A pressure of 1 bar was applied semi-isotropically with a Berendsen barostat (23) using a time constant of 5 ps. A temperature of 310 K was maintained with a velocity-rescaling thermostat. (24) Van der Waals interactions were calculated with the Lennard-Jones potential and a cutoff radius of 1.2 nm, with forces smoothly switched to zero in the range of 1.0–1.2 nm and no dispersion correction. The protein was described by the CHARMM36m (25) force field, lipids by the CHARMM36 force field, (26) and water by the TIP3P model. (27) Na+ and Cl were added to give a bulk concentration of approximately 150 mM NaCl. To maintain the open state of the P2X3 pore, position restraints were imposed on the backbone atoms of the upper parts of the transmembrane domains (residues 40–45 and 318–323). The production run of 1 μs was preceded by equilibration for about 100 ns: first with restraints on all heavy atoms and lipids in the z-direction, second on all heavy atoms, and third on backbone atoms only. Prior to analysis, the trajectory was sampled every 100 ps. In g_elpot calculations, the SPME grid size was 248 × 248 × 264, and the Cα atoms of residues 21–81 were used as the fitting group.

TMEM16 Systems

Crystal structures of nhTMEM16 (28) (PDBID: 4WIS) and human TMEM16K (29) (PDBID: 5OC9) were used to model the proteins, which were embedded in membranes composed of either pure POPC or a mixture of POPC with 1-palmitoyl-2-oleoyl-phosphatidylserine (POPS). CHARMM36 (26) and CHARMM36m (25) force field parameters were used for lipids and proteins, respectively. The systems were simulated for 1 μs each using GROMACS (22) version 2016 or 2018. Other simulation details are as previously published. (30) Prior to analysis, the trajectories were sampled every 100 ps. In g_elpot calculations, the SPME grid sizes were 360 × 360 × 312 and 390 × 390 × 312 in the nhTMEM16 and TMEM16K systems, respectively. Backbone atoms of residues 182–212, 219–246, 280–319, 324–358, 362–392, 431–464, 499–518, 523–546, 560–585, and 600–625 in nhTMEM16 and backbone atoms of residues 205–235, 239–273, 306–349, 354–388, 392–422, 425–460, 494–512, 517–540, 554–577, and 587–613 in TMEM16K were used as fitting groups.

GltPh Systems

The crystal structure of GltPh in the Na1/Na3-bound state (31) (PDBID: 7AHK) was used to model the protein, which was embedded in a POPC membrane using g_membed, (21) in accordance with the prediction from the Orientations of Proteins in Membranes database. (32) The apo- and Na1-bound states were created by removing the corresponding Na+ ions from the crystal structure. The AMBER99SB-ILDN, (33) Berger, (34) and Joung (35) parameters were used for protein, lipids, and ions, respectively. Simulations were conducted using GROMACS (22) version 5.1. Other simulation details are as previously published (31) (Supporting Information Table S1 shows the simulation times). Prior to the analysis, the trajectories were sampled every 1 ns. In g_elpot calculations, the SPME grid size was 320 × 320 × 272; all backbone atoms were used as the fitting group; and the aspartate-binding site used for time-resolved calculations of the potential was defined as a sphere of 0.7 nm radius around the center of geometry of Cα atoms of residues 276, 277, 278, 309, 394, and 401. Occupancy of the Na1 site was evaluated based on the minimum distance between Na+ ions and the center of mass of backbone oxygen atoms of residues 306, 310, and 401 and of side-chain oxygen atoms of residues 310, 312, and 405. The site was considered occupied if the distance was less than 0.5 nm.

DNA Systems

DNA was in the form of a Dickerson dodecamer (36) and was described by the AMBER parmbsc0 (37) force field. Free DNA in the 150 mM NaCl solution was simulated using GROMACS (22) version 2018. The free-DNA system was first equilibrated using a Berendsen barostat (23) with a time constant of 1 ps: a 5 ns run with restraints on all of the heavy atoms, followed by a 5 ns run with no restraints. The production run was carried out using a Parrinello–Rahman barostat (38) with a time constant of 1 ps. Supporting Information Table S2 shows simulation times for the DNA systems. Simulation details of the DNA–polycation systems can be found in Kondinskaia et al. (39) Prior to analysis, the trajectories were sampled every 100 ps. In g_elpot calculations, the SPME grid size was 200 × 200 × 200, and phosphorus atoms of the DNA molecule were used as the fitting group. To evaluate the equilibrium electrostatics of the complexes, the first 100 ns of the trajectories of DNA with polycations was discarded from the analysis.

Calculating the Electrostatic-Potential Profiles

Electrostatic-potential profiles were calculated by combining a map of the electrostatic potential with a water-occupancy map using the gridData module of the MDAnalysis library. (40) The Python script used to calculate these profiles is available on the tool webpage. The root-mean-square difference (RMSDiff) between two profiles was calculated as
(11)
where Φj(zi) is the potential at the zi position in the j-th profile, and the sum is taken over all of the positions.

Results and Discussion

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Electrostatics within the Cation-Selective Pore of the P2X3 Receptor

P2X receptors are a class of ATP-gated cation channels that are widely expressed in different cell types and essential for a number of physiological processes, including muscle contraction and nociception. (41,42) A functional receptor is formed by three subunits, with each belonging to one of the seven subtypes (41) (P2X1–P2X7) and consisting of two transmembrane helices and a large ATP-binding extracellular domain. (43) Here, we conducted a fully atomistic 1 μs MD simulation of the transmembrane part of the human P2X3 receptor trimer in the open conformation, which was recently resolved by X-ray crystallography. (20) To focus on quantification of electrostatics within the pore region of the receptor (Figure 2a), we substituted the extracellular ATP-binding domain with two glycine residues to connect the transmembrane helices. We then used g_elpot to calculate the electrostatic-potential profile along the P2X3 pore.

Figure 2

Figure 2. Calculation of the electrostatic potential within the pore of the P2X3 cation channel. (a) (Left) Structure of the P2X3 receptor transmembrane domain without the ATP-binding ectodomain and embedded in a lipid membrane. The oxygen and hydrogen atoms of water molecules and the phosphorus atoms around the protein are shown as red, white, and orange spheres, respectively. (Middle) The water-occupancy map, contoured at an occupancy level of 0.1. (Right) Electrostatic-potential map, obtained with β = 20 nm–1 and contoured at −400 mV. The maps were calculated from the first 100 ns block of the 1 μs trajectory. (b) Electrostatic-potential profiles along the P2X3 pore, calculated from the first 100 ns block of the 1 μs trajectory using different values for the β parameter. (c) Average electrostatic-potential profile along the P2X3 pore based on the whole 1 μs trajectory (β = 20 nm–1). Whiskers indicate the standard deviation of the potential, as calculated for 10 separate 100 ns blocks.

Figure 2a shows examples of the output water-occupancy and electrostatic-potential maps, as calculated from the first 100 ns block of the 1 μs trajectory. Using the water-occupancy map to mask regions with a low water presence (<10 % of frames), we calculated the electrostatic-potential profile along the P2X3 pore by averaging the potential map over the plane perpendicular to the pore axis (Figure 2b,c). Notably, the resulting profile was strongly dependent on the value used for the β parameter in g_elpot calculations (Figure 2b): the potential within the pore was positive if β was <10 nm–1. Higher β values led to more negative potentials, with the profiles converging at a β value of ≥20 nm–1. We also calculated the potential profiles using the raw long-range SPME potential combined with a water-density map produced using GROmaρs (44) (Supporting Information Figure S2a). Although the pore potential was positive at low β values and decreased upon increasing β, the profiles demonstrated poorer convergence over β compared with those calculated using water-based potentials with g_elpot (Supporting Information Figure S2b). A possible explanation for this is that during the trajectory, protein and lipid atoms overlap with the average water-density map and therefore contribute to the resulting potential profiles. However, due to differences in the configuration between water and nonwater molecules, the β parameter affects their internal potentials differently, leading to poorer convergence. As a β value of ≥20 nm–1 provided convergent results, we used it to calculate the average potential profile along the P2X3 pore from the whole 1 μs trajectory (Figure 2c). Consistent with the cation selectivity of the receptor, the electrostatic potential remained negative along the whole pore and reached its lowest values at the intracellular exit of the pore (Figure 2c). To test the convergence of the profiles generated by g_elpot in time, we split the 1 μs trajectory into 10, 50, 100, and 500 ns blocks and calculated an electrostatic-potential profile for each block (Supporting Information Figure S3a). We evaluated the deviation of the obtained profiles from the reference 1 μs profile and found that a trajectory as short as 50 ns is enough to generate a profile, which deviates from the reference on average by <20 mV (Supporting Information Figure S3b). Although in practice convergence of the calculation would always depend on the underlying MD trajectory, we assume that, if all of the relevant states of the system are sufficiently sampled, a trajectory as short as 50 ns would likely suffice to obtain a reasonable estimation of the electrostatic potential.
Our results suggest that use of a low β leads to an artificial electrostatic potential in proximity to nonwater substances and emphasize the importance of using the correct value for the β parameter in electrostatic calculations based on the Gaussian-distributed atomic charges in heterogeneous systems. In particular, a β of 2.5 nm–1, which has been commonly used in studies using pmepot, (45−48) led to the likely incorrect conclusion of a positive electrostatic potential in the cation-selective pore. We demonstrated that using a β value of 20 nm–1 is enough to obtain a convergent potential profile within the pore if the water-based scheme is used. The profile indicated that the negative potential of the pore is focused near its intracellular exit, which is lined by lipid headgroups (Figure 2a). Notably, these lipid headgroups coordinate Na+ ions permeating through the channel. (20,49) Thus, given the high affinity of Ca2+ ions to lipid headgroups, (50,51) our results suggest that the intracellular exit from the P2X3 pore can form a rather deep energetic well in the permeation pathway. Such a well would explain the relatively high Ca2+ permeability of P2X3 receptors, which underlies their role in sensory signal processing. (42,52) In summary, we have demonstrated the advantage of using the electrostatic potential calculated by our water-based method over the raw SPME potential in terms of convergence of the final electrostatic-potential profile, along with the general applicability of g_elpot for quantifying electrostatics in ion channels.

Electrostatics within the Proteolipidic Pores of TMEM16 Lipid Scramblases

TMEM16 lipid scramblases are Ca2+-activated proteins that facilitate the transport of lipids between the leaflets of the membrane. The headgroups of transported lipids slide along the transmembrane hydrophilic cavity exposed by each protomer to the hydrophobic core of the lipid bilayer. (30,53−55) Some lipid scramblases also operate as ion channels, (56) in which the ions permeate through a proteolipidic pore that is partly lined by the lipid headgroups. (30,54) Importantly, the ion selectivity of lipid scramblases is highly variable and depends on the amino acid composition of the pore as well as on the membrane lipid composition. (30) In theory, the distribution of the electrostatic potential within the pore could be used to identify the regions that contribute most to ion selectivity of lipid scramblases. However, the complex and dynamic structure of the proteolipidic pore makes it challenging to obtain comprehensive information on its electrostatic properties using experimental structures only, as they lack the details about lipid arrangement within the cavity. (28,29,57−60) In contrast, MD simulations dynamically sample different configurations of the pore-lining lipids. Here, we used g_elpot to calculate the electrostatic potential along the proteolipidic pores of fungal nhTMEM16 and human TMEM16K in neutral and anionic membranes to gain a better understanding of the connection between electrostatics and ion selectivity in TMEM16 lipid scramblases.
As TMEM16 lipid scramblases form dimers (Figure 3a) of independently acting protomers, (61,62) we first generated electrostatic-potential and water-occupancy maps around the whole protein and then separated the regions corresponding to the different protomers to calculate their electrostatic-potential profiles (Figure 3b,c). In the fully active state, the scramblase cavity is bound to two Ca2+ ions, which were partly hydrated in the simulations. Since the activating Ca2+ ions do not directly interact with the permeating ions, (30) we also excluded from the analysis the regions in direct proximity to the Ca2+ ions (distance of <5 Å). Figure 3b and Figure 3c illustrate the resulting masked water-occupancy maps in the nhTMEM16 and TMEM16K systems, respectively, and Figure 3d shows the final electrostatic-potential profiles along the pores of the TMEM16 lipid scramblases. In full agreement with the higher cation selectivity of nhTMEM16 in anionic compared with neutral membranes, (30) the potential within the nhTMEM16 pore is negative along the whole pore region in the POPC:POPS mixture and is significantly lower than the pore potential in the pure POPC membrane (Figure 3d). The most notable difference between the profiles is seen near the extracellular entrance of the pore (at 10–20 Å along the pore axis), where the potential is about 100 mV more negative in the POPC:POPS than in the POPC membrane. Interestingly, the potential in this region of nhTMEM16 in the POPC:POPS mixture is very similar to that of TMEM16K (Figure 3d). However, the potential in the intracellular part is much more negative in the TMEM16K pore than in the nhTMEM16 pore in either membrane, making the profile negative along the whole pore of TMEM16K and explaining its high cation selectivity. (30)

Figure 3

Figure 3. Electrostatic-potential profiles along the proteolipidic pore of TMEM16 lipid scramblases. (a) Dimeric structure of nhTMEM16 in a lipid membrane. Protomers are colored white and gray; phosphorus atoms are shown in orange. (b,c) Side views of nhTMEM16 in the mixed POPC:POPS membrane (b) and of TMEM16K in the POPC membrane (c), together with the examples of the masked water-occupancy maps used to calculate the electrostatic-potential profiles. The maps were contoured at an occupancy level of 0.1. Phosphorus atoms of POPC and POPS are shown in orange and cyan, respectively. (d) Average electrostatic-potential profiles along the proteolipidic pore of TMEM16K and nhTMEM16 in pure POPC and mixed POPC:POPS membranes. The profiles were averaged over 1 μs trajectories. Whiskers indicate the standard deviation of the potential, as calculated for 10 separate 100 ns blocks.

Using g_elpot on μs long MD trajectories overcame the limitations of static experimental structures related to the complex and dynamic nature of the proteolipidic pores of nhTMEM16 and TMEM16K. This enabled us to identify the regions responsible for the diverse ion selectivities of these lipid scramblases. We found that anionic lipids mainly affect the ion selectivity of nhTMEM16 by changing the electrostatic potential at the extracellular entrance to the pore. In this region, the negative potential of the nhTMEM16 pore embedded in the anionic membrane is very similar to that of TMEM16K, whose cation selectivity is further strengthened by the negative potential in the intracellular half of its pore. In summary, we have demonstrated that g_elpot is well suited to analyze electrostatics in biomolecular cavities with complex structures and identified the relationship between electrostatics and ion selectivity in TMEM16 lipid scramblases.

Electrostatics in the Substrate-Binding Site of the GltPh Transporter

Excitatory amino acid transporters (EAATs) transport released glutamate from the synaptic cleft back into neurons and glia cells, thereby terminating glutamatergic neurotransmission in the mammalian brain. EAATs are bifunctional homotrimeric proteins that operate as secondary-active transporters and Cl channels. (63−66) GltPh is a prokaryotic EAAT homologue that has been widely used to study the structural and functional properties of EAATs using MD simulations. (31,66−70) In EAATs, the transport cycle mediates the exchange of one glutamate together with three Na+ and one H+ against one K+. (64) In GltPh, aspartate instead of glutamate is transported together with three Na+ and the inward-to-outward re-translocation is uncoupled from K+ transport. (68,71)
Importantly, the binding of aspartate and Na+ to GltPh is temporally ordered: (31) (i) two Na+ bind consecutively to the Na1 and Na3 sites, (ii) the substrate binds, and (iii) the last Na+ binds to the Na2 site, inducing the conformational changes required to permit inward translocation. As aspartate and Na+ are oppositely charged but do not directly interact with each other when bound to GltPh, electrostatics has been proposed to play an important role in the ion–substrate coupling that defines the stoichiometry of transport. (31) Here, we quantified electrostatics in the aspartate-binding pocket of GltPh in different states to better understand and quantify the role of electrostatics in the energetics of substrate binding in glutamate transporters.
We first simulated GltPh in the apo, Na1, or Na1/Na3-bound states (Figure 4a), ensuring that all three protomers in the protein were in the same state at the start of the simulations (simulations were replicated three times for each state; Supporting Information Table S1). We then used g_elpot to extract time courses of the electrostatic potential in the aspartate-binding site (Figure 4b) from the resulting MD trajectories (Supporting Information Figure S4a). Notably, spontaneous binding of Na+ to the Na1 site (observed in the apo-state simulations; Supporting Information Figure S4b) correlated with an increase in the electrostatic potential of the aspartate-binding pocket (Figure 4b). To compare the electrostatic potential in the different states of GltPh, we split the time courses for each simulated protomer into 50 ns blocks and calculated the average potential in the aspartate-binding site depending on Na+ occupancy (Figure 4c). In simulations starting from the apo state, the protein was considered to be in the Na1-bound state if the average occupancy of the Na1 site in a trajectory block was higher than 0.5. A gradual increase in the potential was seen upon transition from the apo state via the Na1-bound state to the Na1/Na3-bound state. In the apo state, the substrate-binding pocket has negative potential with a median value of −50.7 mV. Although the potential increased upon Na+ binding to the Na1 site, it remained negative in most protomers, with a median value of −13.5 mV. Finally, the potential became positive (median value of 15.3 mV) when both the Na1 and Na3 sites were occupied.

Figure 4

Figure 4. Sodium binding increases the electrostatic potential at the aspartate-binding site of GltPh. (a) Structure of the aspartate-bound GltPh protomer in the outward-facing conformation shown together with different occupancy states of the binding sites. The aspartate molecule is shown in violet, and Na+ ions are shown as blue spheres. The violet cross in the apo panel indicates the position where the potential was measured. Membrane borders are shown schematically. (b) Time courses of electrostatic potential in the aspartate-binding site (violet) and Na+ occupancy of the Na1 site (blue) in one of the protomers upon spontaneous Na+ binding in an MD simulation initiated from the apo state. The time courses are shown as running averages with 50 ns windows. (c) Electrostatic potential in the aspartate-binding site in different states. Each data point is an average potential from a 50 ns block of a single protomer trajectory, whiskers indicate the 5th and 95th percentiles, and a median value is shown for each state.

Utilizing g_elpot enabled us to quantitatively confirm the previously proposed electrostatic coupling between Na+ and substrate binding in GltPh. (31) The negative potential in the apo- and Na1-bound states facilitates binding of the second Na+ to the Na3 site and energetically disfavors binding of the negatively charged aspartate to the binding pocket. In turn, binding of the second Na+ to the Na3 site reverses the sign of the potential, thus enabling efficient binding of the substrate. This highlights the important role of electrostatics in GltPh transport stoichiometry. In summary, we have demonstrated that the ability of g_elpot to extract time-resolved information on the local electrostatic potential from MD trajectories can provide insight into the energetics of dynamical processes, as demonstrated for the coupling of substrate binding to Na+ binding in the secondary-active transporter GltPh.

Local Effects of Polycations on DNA Electrostatics

The unique physicochemical properties of cationic polymers or polycations make them promising targets for various therapeutic applications, e.g., as antibacterial materials and gene-delivery vectors. (72) These applications are based on the ability of polycations to form complexes with negatively charged biological molecules, including anionic lipids and DNA. Although the binding efficiency of a polycation to anionic membranes or to DNA is mainly defined by its total charge, recent MD simulations have demonstrated that the precise arrangement of the resulting complexes strongly depends on the chemical structure of the polycation. (39,73,74) In particular, the cationic polymers polyvinylamine (PVA) and polyalylamine (PAA) differ structurally only in the length of the side chain of their monomers (Supporting Information Figure S5a) but have distinct binding patterns with a DNA molecule: (39) PAA mainly interacts with the DNA backbone, whereas PVA stably binds to the major groove (Figure 5a). Here, we took full advantage of the fitting functionality of g_elpot to quantify the electrostatics of the DNA grooves and thereby unravel the effects of the polycation-binding pattern on the local electrostatic potential of the resulting supramolecular complex. Since differences in the electrostatic properties of the minor and major grooves of DNA play an important role in DNA condensation, (75) we quantified both the groove-specific and global DNA electrostatics to decipher the effect of polycation-binding patterns on the local electrostatic potential of the resulting polyplex.

Figure 5

Figure 5. Local effects of polycations on DNA electrostatics. (a) Structure of DNA in complex with cationic polymers PVA (left) and PAA (right). The backbone and grooves of DNA are shown in red and white, respectively. Polymers are shown as spheres with nitrogen atoms in blue and carbon atoms in teal (PVA) and yellow (PAA); hydrogen atoms are omitted. (b) Radial distribution of electrostatic potential around the central axis of DNA either in free form or in complex with PVA or PAA, calculated either globally (top), or separately for major (middle) and minor (bottom) grooves. Whiskers indicate the standard deviation of the potential, calculated separately for 100 ns blocks.

The following scheme was used for groove-specific calculation of the electrostatic-potential profile around DNA. First, each phosphorus atom of the DNA strand was paired with the closest phosphorus atom from the complementary strand based on the interatomic distance along the long axis of the DNA molecule. Since DNA tails are flexible in MD simulations and can occasionally unwind, two phosphorus pairs from each end of the DNA molecule were excluded from the analysis (Supporting Information Figure S5b). The simulation box was then divided along the DNA long axis into 7 Å slabs centered on the center of geometry of each phosphorus pair. Each slab was then split into two subspaces, representing the major and minor grooves (Supporting Information Figure S5c). The subspaces were bounded by two parallel lines drawn through the paired phosphorus atoms on each strand and perpendicular to the line connecting them (Supporting Information Figure S5c).
To compare the effects of the different polycations on DNA electrostatics, we conducted a simulation with DNA in the free form to complement previous simulations of DNA with polycations. (39) When the radial distribution of the electrostatic potential around the central axis of the DNA helix was calculated globally, no significant difference was found between DNA in the free form and in complex with either PAA or PVA at distances larger than 1.2 nm (Figure 5b, top panel). Both polycations had only a minute effect on local minor-groove DNA electrostatics (Figure 5b, bottom panel); in contrast, the difference in their binding patterns resulted in rather distinct effects on the major-groove potential (Figure 5b, middle panel): PVA effectively screened the major groove, whereas PAA shifted the major-groove potential to slightly more negative values compared with the free DNA. This result suggests that polycations can interfere with the charge screening of DNA by Na+ ions. Importantly, the potential distributions differed up to 2.5 nm (i.e., more than twice the DNA radius) from the DNA central axis, suggesting that the polycations would influence the interactions between different DNA segments during condensation.
Thus, by using g_elpot, we found that the groove-specific electrostatics of DNA–polycation complexes are sensitive to small differences in the monomeric structures that determine the binding patterns of polycations to the DNA double helix. The fact that both PVA and PAA had only a minor impact on the global electrostatics of the DNA suggests that the charge density of the polycations may be insufficient to efficiently screen the negative charge of DNA. This is consistent with previous reports that linear polycations have a lower DNA-condensing efficiency than their branched forms. (72) Our calculations also demonstrated that in DNA in the free form, the minor groove creates a significantly greater negative potential compared with the major groove (Figure 5b). This suggests that polycations that effectively screen the minor groove (i.e., similar to histones (75,76)) may reduce the energetic penalty related to DNA condensation more efficiently than polycations that screen the major groove. In summary, we have demonstrated that the fitting functionality of g_elpot enables the quantification of local electrostatics around water-soluble molecules and provided high-resolution insights into the biophysical properties of DNA–polycation complexes.

Conclusions and Perspectives

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Electrostatics plays a substantial role in many biomolecular processes. Since atomic positions define the distribution of the electrostatic potential within a system, atomistic MD simulations are a rich source of detailed structural information that can be harnessed for the high-resolution characterization of electrostatics. In this work, we developed a computational scheme based on the presence of explicit water molecules in biomolecular MD systems for the reliable quantification of the electrostatics of biomolecules based on their MD trajectories. We implemented the scheme in a GROMACS-based (22) tool, called g_elpot, that can be used to generate high-resolution maps and time courses of the electrostatic potential from MD trajectories of biomolecular systems. We have demonstrated that this approach is well suited to gain insights into electrostatics in diverse biomolecular systems, including receptors, ion channels, transporters, and supramolecular complexes of DNA with polycations. We found that the intracellular exit of the P2X3 pore has the lowest electrostatic potential and may form an energetic well for permeating cations. We also identified the regions that define ion selectivity in the proteolipidic pores of ion-conducting TMEM16 lipid scramblases. Furthermore, we demonstrated that electrostatics influences ion–substrate coupling in the secondary-active transporter GltPh by using g_elpot to extract time courses of the electrostatic potential in the substrate-binding pocket. Finally, we quantified the specific effect of polycation-binding patterns on the electrostatics around the DNA major and minor grooves.
In addition to the examples reported here, g_elpot can be generally applied to study the electrostatics of any hydrated macromolecule, including globular proteins and carbon nanotubes. Moreover, owing to its ability to obtain time-resolved electrostatic potentials, the tool can be used in combination with functional mode analysis (77,78) to identify the structural determinants of electrostatic potential in the function-related regions of proteins. Finally, as it is becoming increasingly common to complement experimental structural studies with MD simulations, (20,29,79) g_elpot is an ideal tool for the initial biophysical characterization of newly resolved biomolecular structures. In conclusion, we anticipate that the insights gained with g_elpot will further advance our understanding of the mechanisms linking biomolecular structure and dynamics to physiological function.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.0c01246.

  • Dependence of the short-range part of the potential on β; convergence of P2X3 profiles calculated from the raw SPME potential; time convergence of the g_elpot calculations; raw data on the electrostatic potential and Na1 occupancy in the GltPh simulations; chemical structure of PVA and PAA; groove-specific division of space in DNA systems; and simulation times for DNA and GltPh systems (PDF)

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Author Information

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  • Corresponding Authors
    • Andrei Y. Kostritskii - Institute of Biological Information Processing (IBI-1), Molekular- und Zellphysiologie, and JARA-HPC, Forschungszentrum Jülich, 52425 Jülich, GermanyDepartment of Physics, RWTH Aachen University, 52062 Aachen, GermanyInstitute of Clinical Pharmacology, RWTH Aachen University, 52062 Aachen, GermanyOrcidhttp://orcid.org/0000-0001-5890-4123 Email: [email protected]
    • Jan-Philipp Machtens - Institute of Biological Information Processing (IBI-1), Molekular- und Zellphysiologie, and JARA-HPC, Forschungszentrum Jülich, 52425 Jülich, GermanyInstitute of Clinical Pharmacology, RWTH Aachen University, 52062 Aachen, GermanyOrcidhttp://orcid.org/0000-0003-1673-8571 Email: [email protected]
  • Authors
    • Claudia Alleva - Institute of Biological Information Processing (IBI-1), Molekular- und Zellphysiologie, and JARA-HPC, Forschungszentrum Jülich, 52425 Jülich, Germany
    • Saskia Cönen - Institute of Biological Information Processing (IBI-1), Molekular- und Zellphysiologie, and JARA-HPC, Forschungszentrum Jülich, 52425 Jülich, GermanyInstitute of Clinical Pharmacology, RWTH Aachen University, 52062 Aachen, Germany
  • Notes
    The authors declare no competing financial interest.

Acknowledgments

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The authors thank Dr. Andrey Gurtovenko for providing trajectories of DNA with polycations and Dr. Christoph Fahlke, Dr. Ralf Hausmann, and Piersilvio Longo for critically reading the manuscript. A.Y.K. thanks Diana Kondinskaia for fruitful discussions. This work was supported by the Deutsche Forschungsgemeinschaft (German Research Foundation) to J.-P.M. (MA 7525/1-2, as part of the Research Unit FOR 2518, DynIon, project P4; and MA 7525/2-1, as part of the Research Unit FOR 6046, project P2) and to Dr. Ralf Hausmann (HA 6095/1-2), the Jülich-Aachen Research Alliance Center for Simulation and Data Science (JARA-CSD) School for Simulation and Data Science (SSD), and by a grant from the Interdisciplinary Centre for Clinical Research within the faculty of Medicine at the RWTH Aachen University (IZKF TN1-3/IA532003). The authors gratefully acknowledge the computing time granted through JARA on the supercomputer JURECA at Forschungszentrum Jülich and the supercomputer CLAIX at RWTH Aachen University.

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  • Abstract

    Figure 1

    Figure 1. Water-based scheme to calculate the electrostatic potential. First, the long-range part of the potential is calculated by solving the Poisson equation on the grid using the SPME method. Second, each water molecule is assigned a potential averaged over a sphere around its center of geometry, resulting in a distribution of water-molecule potentials. Third, the frame is fitted onto the reference structure and the grid of the final electrostatic-potential map is built around the biomolecule. Fourth, the water-molecule potentials are distributed over the nodes of the electrostatic-potential map, followed by normalization of the node potential based on the number of contributing water molecules. The final map is used for the quantitative analysis of electrostatics, e.g., to generate a potential profile.

    Figure 2

    Figure 2. Calculation of the electrostatic potential within the pore of the P2X3 cation channel. (a) (Left) Structure of the P2X3 receptor transmembrane domain without the ATP-binding ectodomain and embedded in a lipid membrane. The oxygen and hydrogen atoms of water molecules and the phosphorus atoms around the protein are shown as red, white, and orange spheres, respectively. (Middle) The water-occupancy map, contoured at an occupancy level of 0.1. (Right) Electrostatic-potential map, obtained with β = 20 nm–1 and contoured at −400 mV. The maps were calculated from the first 100 ns block of the 1 μs trajectory. (b) Electrostatic-potential profiles along the P2X3 pore, calculated from the first 100 ns block of the 1 μs trajectory using different values for the β parameter. (c) Average electrostatic-potential profile along the P2X3 pore based on the whole 1 μs trajectory (β = 20 nm–1). Whiskers indicate the standard deviation of the potential, as calculated for 10 separate 100 ns blocks.

    Figure 3

    Figure 3. Electrostatic-potential profiles along the proteolipidic pore of TMEM16 lipid scramblases. (a) Dimeric structure of nhTMEM16 in a lipid membrane. Protomers are colored white and gray; phosphorus atoms are shown in orange. (b,c) Side views of nhTMEM16 in the mixed POPC:POPS membrane (b) and of TMEM16K in the POPC membrane (c), together with the examples of the masked water-occupancy maps used to calculate the electrostatic-potential profiles. The maps were contoured at an occupancy level of 0.1. Phosphorus atoms of POPC and POPS are shown in orange and cyan, respectively. (d) Average electrostatic-potential profiles along the proteolipidic pore of TMEM16K and nhTMEM16 in pure POPC and mixed POPC:POPS membranes. The profiles were averaged over 1 μs trajectories. Whiskers indicate the standard deviation of the potential, as calculated for 10 separate 100 ns blocks.

    Figure 4

    Figure 4. Sodium binding increases the electrostatic potential at the aspartate-binding site of GltPh. (a) Structure of the aspartate-bound GltPh protomer in the outward-facing conformation shown together with different occupancy states of the binding sites. The aspartate molecule is shown in violet, and Na+ ions are shown as blue spheres. The violet cross in the apo panel indicates the position where the potential was measured. Membrane borders are shown schematically. (b) Time courses of electrostatic potential in the aspartate-binding site (violet) and Na+ occupancy of the Na1 site (blue) in one of the protomers upon spontaneous Na+ binding in an MD simulation initiated from the apo state. The time courses are shown as running averages with 50 ns windows. (c) Electrostatic potential in the aspartate-binding site in different states. Each data point is an average potential from a 50 ns block of a single protomer trajectory, whiskers indicate the 5th and 95th percentiles, and a median value is shown for each state.

    Figure 5

    Figure 5. Local effects of polycations on DNA electrostatics. (a) Structure of DNA in complex with cationic polymers PVA (left) and PAA (right). The backbone and grooves of DNA are shown in red and white, respectively. Polymers are shown as spheres with nitrogen atoms in blue and carbon atoms in teal (PVA) and yellow (PAA); hydrogen atoms are omitted. (b) Radial distribution of electrostatic potential around the central axis of DNA either in free form or in complex with PVA or PAA, calculated either globally (top), or separately for major (middle) and minor (bottom) grooves. Whiskers indicate the standard deviation of the potential, calculated separately for 100 ns blocks.

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  • Supporting Information

    Supporting Information


    The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jctc.0c01246.

    • Dependence of the short-range part of the potential on β; convergence of P2X3 profiles calculated from the raw SPME potential; time convergence of the g_elpot calculations; raw data on the electrostatic potential and Na1 occupancy in the GltPh simulations; chemical structure of PVA and PAA; groove-specific division of space in DNA systems; and simulation times for DNA and GltPh systems (PDF)


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