Langevin dynamics simulations of charged model phosphatidylinositol lipids in the presence of diffusion barriers: toward an atomic level understanding of corralling of PIP2 by protein fences in biological membranes
© Lee et al.; licensee BioMed Central Ltd. 2014
Received: 15 May 2014
Accepted: 4 November 2014
Published: 26 November 2014
The polyvalent acidic lipid phosphatidylinositol, 4,5-bisphosphate (PIP2) is important for many cellular functions. It has been suggested that different pools of PIP2 exist in the cytoplasmic leaflet of the plasma membrane, and that such pooling could play a role in the regulation of PIP2. The mechanism of fencing, however, is not understood.
This study presents the results of Langevin dynamics simulations of PIP2 to elucidate some of the molecular level considerations that must be applied to models for fencing. For each simulation, a pool of PIP2 (modeled as charged spheres) was placed in containments with boundaries modeled as a single row of rods (steric or electrostatic) or rigid protein filaments. It is shown that even a small gap (20 Å, which is 1.85 times larger than the diameter of a PIP2 sphere) leads to poor steric blocking, and that electrostatic blockage is only effective at very high charge density. Filaments of human septin, yeast septin, and actin also failed to provide adequate blockage when placed on the membrane surface. The two septins do provide high blockage consistent with experiment and with phenomenological considerations of permeability when they are buried 9 Å and 12 Å below the membrane surface, respectively. In contrast, burial does not improve blockage by the “arch-shaped” actin filaments. Free energy estimates using implicit membrane-solvent models indicate that burial of the septins to about 10 Å can be achieved without penetration of charged residues into the hydrophobic region of the membrane.
These results imply that a functioning fence assembled from protein filaments must either be buried well below the membrane surface, have more than a single row, or contain additional components that fill small gaps in the filaments.
Phosphatidylinositol 4,5-bisphosphate (PIP2) participates in numerous cellular processes such as generation of second messengers, activation of ion channels, endocytosis, and exocytosis ,. Although PIP2 occupies only ~2% of the phospholipids on the inner leaflet, there is experimental evidence that the local concentration is significantly enhanced in the regions where exo-, endo-, and phagocytosis occur ,; in the case of the forming phagosome, the local concentration is increased about 3-fold to ~6%. More generally, the pooling of PIP2 into specific compartments could allow it to participate in many different cellular functions.
Two different mechanisms of PIP2 pooling have been proposed: protein-fencing and protein-binding. In the so-called “protein-fence” hypothesis ,, membrane-bound or transmembrane proteins form a boundary that greatly hinders escape of PIP2 from the corral. Protein fences have been implicated in restriction in diffusion of membrane proteins and lipids . The alternative “protein-binding” hypothesis, or “reduced diffusion constant hypothesis”, is that peptides or proteins within the corral bind PIP2, which substantially reduces its diffusion constant, and thereby prevents its escape . For example, PIP2 could be bound through simple electrostatic interactions to clusters of basic residues, which exist on many proteins involved in endo-, exo-, and phagocytosis, such as syntaxin and the MARCKS protein ,. Recent measurements of PIP2 diffusion in nascent phagosomes by Golebiewska et al. , have provided unambiguous support for the protein-fence hypothesis in at least this system; diffusion within the corral is similar to other regions in the plasma membrane (and not very different from pure lipid liposomes), but diffusion out of the corral is reduced by a factor of at least 100 (1% of free diffusion). The molecular composition of the fence, however, was not determined.
What makes a good fence? An arrangement of actin filaments would seem to be a suitable candidate. Actin lies on the surface of the nascent phagosomes noted above and is highly negatively charged, as is PIP2. Hence, an unbroken row of actin filaments could in principle provide both steric and electrostatic barriers to PIP2 diffusion. However, fencing remained after actin was experimentally removed from nascent phagosomes, and computer simulations of PIP2-like charged spheres on a membrane surface indicated essentially unimpeded diffusion through an atomic-level model fence composed of actin .
This paper extends the aforementioned simulations to evaluate both rod-like and atomic models of protein fences. The PIP2 molecules are represented as charged spheres and simulated by Langevin dynamics (LD), which involves generating stochastic trajectories for individual particles consistent with the Langevin equation ,. LD is a close variant of Brownian dynamics , and the results of the simulations (ratios of relaxation times) would be similar for the two methods . The rod-like fences consist of a row of spheres each comparable to the size of PIP2. Steric interactions are isolated by placing the rod-like fences with different sizes of gaps (missing spheres) on the diffusion plane. Electrostatic interactions are probed by charging the spheres (either negatively or positively) and raising the row above the plane to eliminate steric interactions.
While the results of these simulations could be obtained using diffusion equations, a simulation-based solution is pedagogical and provides insight into more complex shapes and arrangements. In addition, the atomic-level particle simulations were performed with actin and two other fence candidates, human septin and yeast septin, at different levels of burial with respect to the diffusion plane. All-atom simulations suitable for studying these systems are not presently possible in terms of time and length scales. Hence, the protein fence is represented by a field on a grid and assumed to be rigid; water and all other membrane components are treated implicitly; i.e., only the PIP2-like spheres are simulated. For simplicity, only the single-row fence is considered and the possibility that peptide or other membrane components can bind to the protein filaments and fill in gaps is not explored.
By way of outline, the details of the modeling and simulation are described in the following section. The Results and Discussion section presents and analyzes the decay functions obtained from the simulations, and relates them with the experimental permeability.
Langevin dynamics of PIP2
The systems are enclosed by hard wall boundaries modeled by a harmonic restraint potential with a force constant of 100 kcal/mol/Å2 with XY dimensions of 1,400 Å (-475 < X < 925 Å) × 1,000 Å for rod-like steric fence, 1,400 Å × 450 Å for rod-like electrostatic fence, and 1,400 Å × 750 Å for the protein fences. Fences were located parallel to the Y-axis at X = 0 (Figure 1a). The “corral” extends from -475 Å < X < 0 Å for all the systems. Simulations were initialized with 438, 197, and 329 PIP2-like spheres in the rod-like steric, rod-like electrostatic, and protein corrals (X < 0), respectively; these values correspond to the 6% concentrations of PIP2 if restricted inside the corral or 2% if distributed uniformly in the whole PIP2-accessible region. LD simulations were carried out with a position independent collision frequency γ = 1 ps-1, temperature T = 300 K, and a time step of 5 fs. The PIP2 spheres were equilibrated for 25 ns and constrained to remain in the corral, and then simulated for 10.0 μs without constraints. Different random seeds were used to generate 20 independent trajectories for the rod-like fences and 30 for the protein fences. The diffusion constant D = k B T/mγ = 2.4 ×10-5 cm2/s is over 10 times faster than the experimental value . However, because only the ratios of hindered to free diffusion are considered, this large value of D does not alter the conclusions, and is computationally efficient. Note also that D is the same throughout the region, although the effective diffusion constant may be enhanced or retarded in the vicinity of the fence, and is larger in the beginning of the trajectory arising from repulsion of the changed particles in the corral.
Lastly, Brownian dynamics would have been equally acceptable for this study, but it is not available in CHARMM , the simulation package used.
As noted in the Background section, the rod-like models were simulated to quantify the general blockade characteristics for purely steric and electrostatic potentials. Steric fences (Figure 1b) of length L = 1,000 Å were developed by placing impenetrable spheres with no charge and gaps specified by the fence opening length (L open) on the diffusion plane. Simulations were performed with L open = 10, 20, 30, 40, 50, 100, 200, and 500 Å to model increasingly porous fences, and L open = 1,000 Å to model free diffusion. The electrostatic fences (Figure 1c) are single-lined charged spheres with charges (q = ±0.05e, ±0.10e, ±0.50e, and ±1.00e) and heights above the diffusion plane (h = 2, 5, 7, and 10 Å).
An actin fence was built from an X-ray fiber based model (PDB:2ZWH) of Oda et al.  and by adding additional monomers with 166.4° rotations and 27.6 Å translations along the fence axis to generate an actin filament. A human septin fence was built from the hexameric biological unit (Sept7-Sept6-Sept2-Sept2-Sept6-Sept7) in PDB:2QAG . Missing coordinates of some residues in PDB:2QAG were reconstructed using I-TASSER , a protein structure prediction tool. The model structure was then aligned to the original PDB to determine the best-fit structure. Additional biological units were placed by 253.2 Å translations along the fence axis to generate a human septin filament.
There is no reported PDB structure for octameric yeast septin, but the full sequence and the octameric biological unit (Cdc11-Cdc12-Cdc3-Cdc10-Cdc10-Cdc3-Cdc12-Cdc11) of the protein is available. Atomic coordinates of the full sequence were generated using I-TASSER and the best-fit structure was selected from the alignment to the human septin model. The sequence identity between the subunits of yeast septin and human septin ranges from 32% to 38% (comparison in Protein BLAST ), which supports the similar structures to each other. Additional biological units were placed by 338.7 Å translations along the fence axis to generate a yeast septin filament.
The resulting septin structures form a long filamentous rod. The binding surfaces of the septins to the lipid membrane are assumed to be the one with the polybasic region that is conserved among septin family and its subunits (Additional file 1: Figure S1), thereby electrostatic attraction is expected to enhance the binding of the septins to the anionic lipid ,. The septins contain long C-terminal extensions that are believed to play a key role in binding with the other septins to make parallel filament bundle . The C-terminal extensions were excluded here because they appear to contribute little to the single filament formation and binding of the septins to the membrane.
Continuum electrostatics based effective potentials
Note that ϕ PHIX and U CORE were computed once before the LD simulations, and their energies and forces were calculated using the 3rd-order B-spline interpolation during the simulations ,. The preparation of the simulation system (PDB manipulation), calculation of the potential maps (PBEQ module), and LD simulations were performed using CHARMM  and CHARMM-GUI (http://www.charmm-gui.org) .
where Γ is the gamma function defined as . The retardation of diffusion is then quantified by the concentration relaxation time ratio ξ = < τ free >/< τ >, where < τ free > is the relaxation time in the absence of a barrier, i.e., free diffusion.
where C ref is set to the bulk concentration under equilibrium (2%). The PMF represents the potential profile in the presence of PIP2 molecules in the equilibrated simulation system.
Results and Discussion
Additional file 1: Figure S2 shows the characteristics of the rod-like fences. The steric fences range from nearly continuous to 50% breached (Additional file 1: Figure S2A), and the electrostatic fences from strongly negative to strongly positive (Additional file 1: Figure S2B). The positive (attractive potential well) and negative charges (repulsive potential barrier) yield symmetric electrostatic potential profiles (Additional file 1: Figure S2C).
The concentration relaxation time ratio ξ is plotted as a function of Zmin in Figure 7. Consistent from the potential maps in Figure 6, fencing is ineffective when Zmin = 0 Å. This result is anticipated from the steric rod models, where even a small gap results in nearly free diffusion (Figure 3). Actin has a pronounced arch-shape (Figure 2a), which leaves unblocked fence even with the deepest burial (Figure 6a, Zmin = -15 v). Consequently, all the actin fence results show significant PIP2 escape out of corral (Figure 7) for all burial depths. Septins provide essentially complete blockage (ξ ≈ zero) when Zmin = -9 Å for the human septin fence and Zmin = -12 Å for the yeast septin fence. Specifically, the potential maps calculated at Zmin = -9 Å for the human septin fence and Zmin = -12 Å for the yeast septin fence (Figure 6d) show the “blanket coverage” required for blockage found in the rod-like fence studies. Interestingly, human and yeast septin block PIP2 diffusion in different ways as revealed by the comparison of the steric (U CORE) and electrostatic (ϕ PHIX) potentials. U CORE from the human septin fence at Zmin = -9 Å provides complete coverage. In contrast, narrow gaps in U CORE from yeast septin fence at Zmin = -12 Å are filled in by ϕ PHIX for complete blockade.
Phenomenological treatment of permeability
Let us assume, for simplicity, a square corral of 1 μm per side. From Hilgemann's analysis , we can also assume that there are 100 kinases inside the corral and each kinase produces 100 PIP2 molecules per second, hence production rate is of 104 molecules/(μm2⋅s). The permeability P through a fence region can be defined as P = k ⋅ D/d, where k is the partition coefficient of PIP2 from the bulk membrane into the fence region, D is the diffusion coefficient, and d is the thickness of the fence region. Assuming d = 5 nm and D =1 μm2/s (in the bulk region ), P = 200 k μm/s. The flux per unit length F of PIP2 out of the fence can be simplified using Fick's law as F = P (C i - C o ), where C i (from our rigid-protein model, 105 μm-2) is the areal concentration of PIP2 inside the fence and C o (3 × 104 μm-2) that in the bulk. The steady-state PIP2 flux out of the corral can be estimated as F = 1.4 × 107k / (μm⋅s). As the condition for the corral to act as a barrier maintaining the concentrated pool of PIP2, the outward flux should be kept below of the production rate. If the outward flux is only through one side of the square, the partition coefficient k should be smaller than 7 × 10-3 (= 104 / (1.4 × 107)). In other words, if the fence is leaky to PIP2 above this value, the fence would not be an effective barrier to maintain the PIP2 pool. This impermeability calculation for an effective protein fence is in good agreement with our simulation results, which predicts virtually complete blockade from U CORE or U CORE + q PIP2ϕ PHIX barrier (Figures 6d and 7).
Langevin dynamics simulations of PIP2 on a membrane surface with rod-like steric and electrostatic as well as all-atom protein fence models were carried out to determine the general conditions for fencing PIP2 and the specific fencing ability of actin, human septin, and yeast septin. Simulations on the model systems indicate that even a small gap leads to ineffective blocking. Likewise, electrostatic blockage is only effective at very high charge density, and is unlikely to play a major role in blockage of PIP2 diffusion.
These observations place significant limitations on the abilities of individual proteins to form effective fences. In fact, single filaments of actin, human septin, and yeast septin provided little blockage when placed on the membrane surface. Even burial to 15 Å did not yield significant blocking by actin, as could be anticipated by its pronounced arch-like shape. However, the two septins did provide blockage consistent with experiment when the human septin is buried 9 Å and the yeast septin 12 Å below the membrane surface. Implicit membrane-solvent models indicate that burial to 10 Å can be achieved, though further penetration requires protein conformational changes. All-atom simulations with fully flexible proteins and explicit membrane and solvent will undoubtedly yield further insight to the mechanism of blockage.
Though not simulated here, a fence could be made more effective by adding more rows or more components. For example, if each of three rows provides 80% blockage and the rows are independent, the array leads to more than 99% blockage. Similarly, a small gap in a single row could be filled by a membrane-associated peptide. In closing, it was not the purpose of this study to determine the molecular level mechanism of corralling of PIP2 on the cell surface by protein fences. Rather, it was to elucidate some of the molecular level considerations that must be applied to models for fencing, and to stimulate more detailed simulation studies.
KIL carried out the Langevin dynamics simulations and data analysis, and drafted the manuscript. WI and RWP conceived of the study, and participated in its design and coordination. WI and RWP also participated in the data analysis and preparation of the manuscript. The authors read and approved the final manuscript.
We gratefully acknowledge Stuart McLaughlin for motivating the present study, and for helpful comments on the manuscript. This work was supported by the National Science Foundation (NSF MCB-1157677 to WI), XSEDE Resources (TG-MCB070009 to WI), and the Intramural Research Program of the NIH, National Heart, Lung, and Blood Institute (to RWP).
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