Simulation of High Density Lipoprotein Behavior on a Few Layer

Article pubs.acs.org/JPCB

Simulation of High Density Lipoprotein Behavior on a Few Layer Graphene Undergoing Non-Uniform Mechanical Load Olga E. Glukhova,*,† Tatiana R. Prytkova,‡ and George V. Savostyanov† †

Saratov State University, Astrakhanskaya 83, 410012, Saratov, Russia Schmid College of Science & Technology, Chapman University, Orange, California 92866, United States

‡

ABSTRACT: Effect of a nonuniform external mechanical load on high density lipoprotein (HDL) in aqueous medium was investigated using course-grained molecular dynamics simulations. The nonuniform load was achieved by a few layer graphene on one side and closed single-walled carbon nanotube (SWNT) (7, 7) on the opposite side of lipoprotein. The tube had a diameter of 1 nm and was oriented perpendicularly to the graphene. HDL was located between them. The tube was approaching to HDL on graphene deforming it. We considered two cases of the tube movement with velocities of 20 and 5 m/s. Coarse-grained (CG) molecular dynamics with application of the MARTINI force field for HDL and coarse-grained model with an all-atom (AA)/CG mapping ratio of 1.5 for carbon nanotube (CNT) (each CG bead was modeled by the 4-site CG benzene) were used. Coarse-grained model of HDL was received by method of self-assembly. HDL was static but not fixed that gave the possibility to compensate its external influence in some way. It was established that in water medium HDL interacted with graphene substrate. It was established that in water HDL interacts with graphene substrate, slightly flattening but retaining its shape of the whole. It was also observed that during the calculations HDL partially dodged nanotube. Lipoprotein belts unfolded on the graphene substrate in the way of the best compensation for the impact of nanotubes. Finally, we observed that the approaching tube has passed through the less dense medium of dipalmitoylphosphatidylcholine (DPPC) and its pressure on the macromolecule decreased. Inhomogeneity of the external exposure deformed HDL at approximately 10−50%. The character of deformation demonstrated that lipoprotein has viscoelastic properties similar to a fluid. The discovered ability of lipoprotein may help to establish mechanism of interaction of lipoproteins with arterial walls and dynamic behavior of lipoproteins in arterial intima.

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INTRODUCTION The exportation of interaction of biomacromolecules with carbon nanostructures (nanotubes and graphene) aroused recent interest because of its possible application in the field of biotechnology.1 Carbon nanostructures can be used at targeted drug delivery,2 they can also facilitate penetration through the blood-brain barrier3 and the delivery of various substances through the membrane cells.4 Experimental studies showed that the lipid bilayer of membrane recovers fully during the passing of the CNT through it.5,6 It was found in a study by Titovet al.7 that interaction between the lipid bilayer and graphene made it possible to create a new composite material of the “sandwich” type. It is established also that graphene promotes the formation of vesicles in a lipid layers.8 Recently it was determined that oxidized graphene can promote selforganization of phospholipids on its surface.9 Also, it was established the mechanism of degradation of the Escherichia coli membrane during the process of penetration of graphene nanosheets into the depth of phospholipids. 10 Recent investigations were carried out both experimentally and by computer simulations. Computer simulations allow us to obtain © XXXX American Chemical Society

molecular understanding of chemical and physical properties of nanoscale systems. Indeed, atomistic molecular dynamics simulations of large nano- and biosystems by means of petaflop supercomputers are beginning to probe human life on molecular-atomic level.11 But the complexity of biomacromolecular systems does not allow to investigate all phenomena on atomic level. To overcame this limitation and begin to study such phenomena as self-assembly in complex biological systems and fluids CG models were applied.12 In particular, recent investigations using the MARTINI CG force field have helped establish biophysics of C60 and single-walled CNT interactions with lipid bilayers.5,13−15 The present article present results of simulations of HDL biomacromolecule under external nonuniform mechanical load applied by a few layer graphene from one side and one-walled carbon nanotube from another side. Modeling of the HDL behavior under external mechanical loads allows us to Received: December 27, 2015 Revised: March 7, 2016

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DOI: 10.1021/acs.jpcb.5b12648 J. Phys. Chem. B XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry B The potential Vbond:

understand mechanism how lipoproteins transform its shape to penetrate through narrow channels such as gaps between endothelial cells of internal surface of vessel. Our results can be used to explain mechanism of the interaction of HDL with carbon nanostructures but also can be used to gain insight into mechanism of passing of the lipoproteins into arterial intima through the narrow gaps between endothelial cells. This problem is very important since lipoproteins carrying cholesterol (lipoproteins of low and very low density) and they are able to penetrate into vessel intima. Accumulation of cholesterol leads to such a dangerous condition as atherosclerosis. Experimental investigations of particular lipoproteins are very difficult. As a result single molecule experiments for lipoproteins are rare and technically challenging and they are mostly made in a bulk.16 Therefore, computer simulation is helpful method to elucidate details how lipoproteins interact with its surroundings. HDL is the specific type of lipoprotein that tends to promote the formation of fatty plaques in the arteries.17,18 Many studies are devoted to the investigation of HDL topology. Many of them use computer simulation to investigate of the HDL formation from phospholipid drop and protein belts.19−22 Different methodologies can be used to obtain initial structures. For example in the article by Shihet al.22 a HDL was composed from two scaffold proteins and 160 randomly scattered DPPC lipids. The scaffold proteins are shaped as halfcircles separated by 40 Å. Then, the protein−lipid system was solvated with water. To neutralize the net electrostatic charge the sodium ions were added. Depending on the initial configuration the time of assembly was varied from 0.5 to 4 μs. The simulations of a CG system were carried out by the modified version of NAMD 2.5. In another study a discoidal model was applied.19 A discoidal apoA-I/HDL all-atom particle was made with the palmitoyloleoylphosphatidylcholine (POPC), unesterified cholesterol (UC) and apoA-I stoichiometry of the DSH model. Their number was correlated as 200:20:2. CGMD simulations were performed on the starting structure using GROMACS 4.0 and the MARTINI force-field 2.1. However, the authors of this work indicated some problems of this model which might incorrectly reproduce the structure of HDL. Although there are several papers considered modeling of the interaction between CNTs and lipid membranes,6,15,23 study of the HDL deformation capacity and its interaction with carbon nanostructures have not been carried yet. It was a motivation to research presented below.

Vbond =

1 Kki(rki − rki0 )2 2

∑ i

(2)

where index i runs numbers of CGPs, with which the particle k is chemically bonded, Kki is the weighting coefficient for interacting atoms k and i, rki is the length of the valence bond, and r0ki is the equilibrium length. The potential Vangle characterizes the valence angles change: Vangle =

∑ Mjki(cos(θjki) − cos(θjki0 ))2 (3)

i≠j

where θjki is the angle with vertex on atom k, formed by three tandem particles j,k,i; θ0jki is the corresponding equilibrium angle; and Mjki is the weighting coefficient. The term Vdihedral describes energy, conditioned by the change in dihedral angle: Vdihedral =

∑ i

1 Φljki(1 + cos(χljki − δljki)) 2

(4)

where Φljki is the force constant, χljki is the linear angle of the dihedral angle between faces with the common bond ki, and indexes l,j determinate two other CGPs, bonded with k; δljki is the corresponding equilibrium angle. The potential of interaction between particles unbounded with particle k, is presented by the Lennard-Jones potential and electrostatic potential: Vnonbond =

⎡⎛

12 ⎛ σ ⎞6 ⎤ σik ⎞ ⎟ − ⎜ ik ⎟ ⎥ + ⎝ rik ⎠ ⎥⎦ ⎣⎝ rik ⎠

∑ 4εik⎢⎢⎜ i≠k

∑ i≠k

qiqk 4πεε0rik (5)

where index i runs system particles chemically unbounded with k, εik is the depth of the potential well, rik is the distance between pairs of CGPs, σik is the distance between CGPs when the interaction energy is equal to zero, qi and qk are the charges of CGPs correspondingly, ε is the medium dielectric constant, and ε0 is the dielectric constant of vacuum. Molecular dynamic approach was used to describe trajectory of coarse-grained particles. We used the KVAZAR program to run calculations.24 For the solution of the Newton’s equations of motion the Nordsieck third-order predictor-corrector algorithm with the step of 4 fs was applied. The time step of modeling was 0.1 ps. Forces acted on coarse-grained particles were calculated as gradient of the particle’s potential energy. The temperature and the pressure were controlled by the Nose−Hoover algorithm at 310 K and 1 atm. All electrostatic interactions were evaluated with a dielectric constant of 80. The cutoff radius (rcutof f = 15 Å) was used in all numerical simulation. Periodic boundary conditions and constant pressure conditions was used in calculations. The solvent was described explicitly using coarse grained model of water.24 CG-Model of HDL. Structure of HDL was built using selfassembly process of the coarse-grained model (CGMD). The central part of the model is a lipid core. It was built in a shape of a lipid disk. The lipid bilayer consisted of 160 phospholipids DPPC. Initial model of the protein composed of two antiparallel amphipathic helical protein platforms of ApoA-1. Each of these platforms contained of 178 amino acid residues rolled in a ribbon around the lipid bilayer. Self-assembly was made in aqueous solvent at temperature 310 K. Self -assembly was mostly finished at 300 ns. Then the structure was

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METHODS In the framework of a coarse-grained model for macromolecule its potential energy is constructed as a sum of energies Uk of all coarse-grained particles (CGPs), where index k runs over all particles in a system. The energy of the particle is represented by a polynomial Uk. Each member represents a specific type of interaction term of virtual atoms. We constructed a polynomial of four energy terms: Uk = Vbond + Vangle + Vdihedral + Vnonbond (1) where the first three terms describe the chemically bonded CGPs: Vbond takes into account the change in the bond lengths between CGPs, Vangle is the change in bond angles, and Vdihedral is the change in dihedral angles. Potential Vnonbond describes the interaction of unbounded CGPs. All potentials have classical form. B


Article

The Journal of Physical Chemistry B

To describe the behavior of HDL under a nonuniform external load the lipoprotein was constrained by a few layer graphene (FLG) from one side and was indented by CNT from another side. The graphene substrate did not allow lipoprotein to move freely and the tube moved with a constant velocity perpendicular to graphene. FLG contained 20 layers and was placed on the SiO2 substrate. Deflection of graphene under the influence of the lipoprotein was not observed. The whole process took place in water medium at 310 K.

equilibrated during next several hundreds of nanoseconds. The overall system size was 206 × 177 × 111 Å with 20 000 CG beads of water. Each CG bead of water was modeled using 4 molecules of water. CGMD simulation of the HDL assembly was performed using the MARTINI force field. Protein belts and phospholipids were built by analogy with the paper by Shih et al.22 To get an equilibrium HDL configuration the modeling has been made during 1 μs. To track conformational changes of HDL at each step the root mean-square deviations (RMSD) of protein were calculated. RMSDs of all protein were measured over the entire trajectory using the structure obtained after the first 300 ps of the MD simulation as a reference. The RMSD of proteins usually calculated at the average position of α-carbons of the protein chain. Within the applied CG-model22 the αcarbons do not exist. These atoms are parts of enlarged particles of the Nda class which form the skeleton of the apoA-I protein belt. We calculated RMSD of a protein belt for the average position of the CG-bean of the Nda class from the last 20% of each trajectory. We used principal moments of inertia to analyze shape of the proteins. The well known formula for the calculation of tensor elements of moment of inertia is Iij =

∫ (δijr 2 − rri j) dm ,

i, j ∈ x, y, z

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RESULTS AND DISCUSSION Snapshots of the self-assembly process at various simulation times presented on Figure 1a. It can be seen that holistic configuration of HDL has been formed by the time of 300 ns. In the figure red ribbons correspond to protein belts apoA-I, green-blue drop correspond to lipid core. Blue color represent “heads” of phospholipids, green color represent “tails”. Molecules of water are not shown on the figure to demonstrate a clear picture of the lipoprotein assembly. The graph of the RMSD for HDL protein belts dependence on simulation time is presented on Figure 1b (curve “HDL free”). The graph shows that by reaching of 500 ns the HDL topology became stable and achieved an equilibrium configuration. The energy was stabilized already at time 300−350 ns. Noticeable changes were observed in the beginning of the assembly process when the macromolecule was forming its structure (Figure 1c, curve “HDL free”). It was observed that during the process of the lipoprotein 3D-topology formation the energy oscillated with an amplitude 0−15 eV. This indicates noticeable configuration changes in the geometry of the macromolecule. These changes are caused by displacement of phospholipids relatively to protein belts and by convergence of belts positions to the equilibrium configuration. In Figure 1d, dependence of principal moments of inertia during the process of the self-assembly is presented. Calculated moments of inertia are presented in the Table 1 (all beads were included in the calculation and all values were averaged over the last 20% of the trajectory). For comparison there are moments of inertia for spheroidal model19 and for the droplet model25 are presented in the table. Minor difference in values or parameters can be explained by different quantities of POPC in models of these papers and in our model. All in all, the coincidence is satisfying and that proves correctness of the built HDL model. HDL on the Graphene. Lipoprotein was placed on the graphene substrate. There is van der Waals Interaction between substrate and HDL. Simulation of the HDL behavior was carried out. Equilibration was monitored by calculation of the HDL energy and RMSD of CG-particles with protein belts of the Nda class. These data are presented in Figure 1, parts b and c (noted as “HDL on FLG”). It can be seen from the figures that potential energy of interaction between HDL and FLG is decreased. The simulation of the HDL behavior on graphene was carried out during several nanoseconds. As the result it was established that HDL lost its spheroidal form by partially flattening on substrate. Protein belts slightly unfolded and lipid layer was slightly spread on the graphene. Shape of the HDL is presented on Figure 2a (the graphene substrate is shown as a black background). The change of the HDL topology was tracked during 2 ns. To do this the tensor of inertia moment, energy and RMSD CG-particle of lipoprotein belt Nda class were calculated at each time point. During the time of calculation the location of the tensor coordinate axis X, Y, Z did

(6)

where ri is the coordinate component of the radius-vector; dm = ρdV, where ρ is density and dV is volume element. The principal moments of inertia (Ixx, Iyy, and Izz) indicate that the shape of the lipid droplet fluctuates strongly during the equilibration period. As a result the form looks like the prolate ellipsoid for which rotation is characterized by three numbers a, b, and c. Moments of inertia were determined by integration26 Ixx =

∫

(y 2 + z 2) dm , Iyy =

dm , Izz =

∫ (x 2 + y 2 ) d m

∫ (x 2 + z 2 ) (7)

Here principal moments of inertia coincide with axis moments of inertia. CG-Model of CNT and Graphene. There are several approaches to the construction of coarse-grained models of carbon nanostructures. One approach saves the hexagonal structure of a nanotube. Such approach was applied in the paper by Wallaceet al.1 for describing behavior of nanotubes in lipid area. In order to preserve the hexagonal symmetry of the CNT lattice authors used the CG model of CNT using an approximate 3:1 mapping for carbon atoms. They used Marrink’s apolar (C) particles as a first approximation to model CNT particles. However, the authors reduced the strength of CNT- lysophosphatidylcholine interaction relative to the strength of LPC (lysophosphatidylcholine) interaction. In order to maintain the preferred geometry of the nanotube the CNT particles in the range of 10 Å were bonded by means of a harmonic potential using a force constant of 25 kJ mol−1 Å−2. In another paper the model with an AA/CG mapping ratio of 1.5 was used to study the effect of carboxylation on CNT aqueous dispersibility.27 It should be noted that today there is no any accepted universal CG-model of carbon nanostructures. In our paper we applied the second model.14 The resulting SWNT within the current investigation is considered as a rigid cylinder. Closed tube (7,7) with the diameter of ∼1 nm was built. Its length of the tube is 11 nm. The similar approach was applied to build the CG-model of graphene. C


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Table 1. Calculated Parameters for Principal Moments of Inertia I (amu nm2/106), a, b, c (nm)

our results, 310 K

Ixx Iyy Izz a b c

1.7 1.5 1.2 4.0 4.5 5.0

comparisons for T = 310 K, refs 20 and 26 2.3,20 1.8,20 1.4,20 3.1,20 3.5,20 4.3,20

1.226 1.226 1.126 426 426 426

Figure 2. Behavior of HDL on graphene: (a) change of HDL for top view; (b) changes in the components of the tensor of moments of inertia. X-component of the tensor of moment of inertia (Ixx) was noted as red curve, Y-component (Iyy) was noted as green curve, and Z-component (Izz) was noted as blue curve (Izz). The graphene substrate is shown as a black background.

increased. At first femtoseconds nondiagonal elements of inertia tensor became nonzero. At the first hundreds of picoseconds, deep changes in 1.5−2 times were observed, but after 1 ns, the lipoprotein’s shape stabilized and moments of inertia stopped changing. Observed low oscillations within 5− 10% correspond to collisions of HDL with graphene. At the same time, its configuration almost did not change, and the 3D structure of the molecule corresponded to the equilibrium configuration. Principle moments of inertia reached following values: Ixx = 0.5; Iyy = 2.0; Izz = 1.6 amu × nm2/106. HDL-Particle Undergoing Compression from Graphene and CNT. Furthermore, we modeled the influence of nonuniform mechanical load on HDL squeezed between graphene and the nanotube. Initially the nanotube was located at a distance of ∼2.4 nm from HDL (from the level of its top atoms). Furthermore, the nanotube was approaching the macromolecule with a constant velocity and returned back with the same velocity. Simulation of this process was carried

Figure 1. Lipoprotein in the process of the self-assembly: (a) formation of the macromolecule in water at T = 310 K; (b) dependence of RMSD on simulation time; (c) dependence of energy on simulation time; (d) dependence of principal moments of inertia on simulation time. In part a, red ribbons correspond to protein belts apoA-I, green-blue drop correspond to lipid core, blue color represent “heads” of phospholipids, green color represent “tails”. In parts b and c, the energy of HDL and RMSD of CG-particles with protein belts are noted as “HDL free”; the energy of HDL on graphene and RMSD of CG-particles with protein belts are noted as “HDL on FLG”. In part d, the X-component of the tensor of moment of inertia (Ixx) was noted as red curve, Y-component (Iyy) was noted as green curve, and the Zcomponent (Izz) was noted as blue curve.

not change significantly. Initially axis X, Y, Z matched the principle axis of inertia as was mentioned above. Changes of the tensor’s components are shown in Figure 2. It is clear that in the result of the macromolecule’s transformation on the substrate the moments of inertia Ixx, Iyy D


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Figure 3. HDL undergoing nonuniform mechanical load in water at T = 310 K. The velocity of CNT is equal to 20 m/s. Upper series of figures from 0 to 350 ps corresponds to direct movement of the tube; lower series corresponds to the reverse movement.

out continuously in the course of time in water at T = 310 K. We considered two cases of the tube’s movement with velocities 5 and 20 m/s. Low velocity corresponds to the average velocity of the blood flow in which HDL moves. We assume that HDL can collide with different objects on internal surface of vessels’ walls with this velocity 5 m/s. The higher velocity of 20 m/s corresponds to the typical speed of an atomic-force microscope tip, in this case we assume that CNT may play role of such a tip. The common pattern of transformations 3D structures of HDL which undergoes interaction with nanotube moving with velocity 20 m/s is presented on Figure 3. The upper series of figures from 0 to 350 ps corresponds to direct movement of the tube, while the lower series corresponds to the reverse movement. Total time of the simulation was 935 ps. On all snapshots orientation of the substrate and the nanotube in surface stays constant during the whole process. The depth of immersion of the tube in HDL equals to 4.6 nm. It is clearly seen from the data that protein belts dodge the tube’s influence by unfolding on the graphene, so that CNT passes through a softer medium. It is significant that HDL followed the tube for some time during reverse movement of CNT as shown on the lower series of the Figure 3. To characterize processes in the HDL molecule quantitatively at each moment of contact between the tube and HDL we calculated: (1) energy of interaction between HDL and its surrounding (except water), (2) pressure on HDL from the side of the tube and from the side of graphene (separately), (3) RMSD of the protein belt, and (4) tensor of the HDL inertia moment. The common fact for all calculated parameters is a mismatch for the forward and return movements. The dependence of energy of interaction between HDL and its surroundings is shown on Figure 4a. The forward stroke corresponds to the continuous curve, the return stroke to the dotted curve (green line correspond to velocity of CNT 5 m/s, orange line correspond to velocity of CNT 20 m/s). It was observed that interaction energy decreased due to the tube’s influence (z-coordinate increases from −2.4 to +4.6 nm). It can be explained by favorable (more negative) van der Waals interaction between lipoprotein and graphene due to smaller

distance between graphene surface and HDL. As a result energy decreases as it is shown in Figure 4. Coordinate Z = 0 corresponds to the moment when the tube and the upper board of HDL came in contact. At the same time during the removal of the tube the HDL topology changed noticeably. Several molecules of phospholipid stick to the tube and left HDL. At the same time the energy of the return tube’s stroke changes little because more time is required for the recovery of the initial topology. Lipoprotein undergoes pressure from the side of the tube. It does not change similarly to the interaction energy change. To make it more evident we calculated the pressure from the side of CNT and from the side of graphene (Figure 4b, the forward stroke corresponds to the continuous line, the return stroke correspond to the dotted line). During the immersion of CNT into lipoprotein the pressure from both sides increases. During the return stroke, the pressure almost does not change (z = −1). It can be explained by the strong deformation of lipoprotein, which does not have time to relax. Furthermore, coordinate z = 0 does not correspond to the upper edge of HDL anymore, as phospholipids follow the tube stretching the phospholipidic drop in this direction. Furthermore, when for the tube z ← 1, the pressure from the tube decreases significantly as it influences just on upper fields of the phospholipid drop. On the other hand, the pressure from the side of graphene increased as lipoprotein started to relax. When lipoprotein started to recover its shape and it moved toward graphene and interacted with it. The pressure from the graphene has decreased when the initial shape of lipoprotein had recovered. Longer simulation time is needed to observe it. The strong deformation of lipoprotein can be observed as abrupt change of RMSD of protein belts during the interaction with the tube. At first RMSD increased and then slightly decreased on the return stroke (Figure 4c). It can be concluded from presented data that dependence of the interaction energy of HDL with its surrounding, pressure and RMSD of protein belts for velocities of 20 and 5 m/s is qualitatively similar. It can be seen also that in the case of a lower velocity HDL topology transformations are more significant because the macromolecule has time to reacts on E


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Figure 4. Parameters of HDL undergoing nonunifrom mechanical load from graphene and a nanotube in water at T = 310 K (orange and red curves−for velocity of CNT 20 m/s, blue and green curve−for velocity of CNT 5 m/s: (a) change of interaction energy of HDL with graphene and CNT; (b) pressure on HLD from CNT (orange and blue curves) and graphene (red and green curves); (c) RMSD of the α-carbons protein belts (the position of CG-bean of class Nda). The forward stroke of CNT corresponds to the continuous curve, the return stroke - to the dotted curve. The inset in part a images the scheme of HDL indentation by nanotube. Coordinate Z = 0 corresponds to the moment when the tube and the upper board of HDL came in contact.

Figure 5. Change of diagonal elements of inertia tensor during the influence of nonuniform mechanical load: (a) for velocities of CNT 5 m/s; (b) for velocities of CNT 20 m/s. The forward stroke of CNT corresponds to the continuous curve, the return stroke to the dotted curve. X-component of the tensor of moment of inertia (Ixx) was noted as red curve,Y-component (Iyy) was noted as green curve, and Zcomponent (Izz) was noted as blue curve (Izz).

the external influence. Also it is shown in Figure 4 that protein belts were rebuilt in a greater extent than in the case of the rapid influence. It is seen that at the same distances between the tube and the macromolecule during the slow approach of the tube, the protein belts have time to respond. We see a sharp increase of RMSD at approaching on 1 nm, then RMSD almost did not change because the belts were able to rebuild in the first few picoseconds. During the reverse stroke of the nanotube from Z = 4.6 to Z = −2.4 nm all parameters almost do not change. Components of inertia tensor are able to report transformation of lipoprotein topology in greater details. Figure 5 shows dependence of diagonal elements of inertia tensor from coordinate z for velocities 5 m/s (a) and 20 m/s (b). This dependence

corresponds to flattening of lipoprotein during the tube’s approaching (Ixx increased and Izz decreased simultaneously). During the tube removal Ixx, Iyy, and Izz values behaved quite differently. Ixx and Iyy decreased up to a certain point. Then during the tube’s removal, the HDL shape change varies for the cases of 5 and 20 m/s velocities. The value of change was determined by degree of the HDL damage. The phospholipids adhered to the tube noticeably change the three-dimensional structure of HDL and moments of inertia. Full recovery of the HDL shape occurred within 1 ns after the nanotube’s removal. At the same time the energy achieved its initial value and the structure of the molecule recovered. F


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(6) Raczyński, P.; Górny, K.; Pabiszczak, M.; Gburski, Z. Nanoindentation of Biomembrane by Carbon Nanotubes − MD Simulation. Comput. Mater. Sci. 2013, 70, 13−18. (7) Titov, A. V.; Král, P.; Pearson, R. Sandwiched GrapheneMembrane Superstructures. ACS Nano 2010, 4, 229−234. (8) Furukawa, K.; Hibino, H. Self-Spreading of Supported Lipid Bilayer on SiO2 Surface Bearing Graphene Oxide. Chem. Lett. 2012, 41, 1259−1261. (9) Liu, S. J.; Wen, Q.; Tang, L. J.; Jiang, J. H. PhospholipidGraphene Nanoassembly as a Fluorescence Biosensor for Sensitive Detection of Phospholipase D Activity. Anal. Chem. 2012, 84, 5944− 5950. (10) Tu, Y.; Lv, M.; Xiu, P.; Huynh, T.; Zhang, M.; Castelli, M.; Liu, Z.; Huang, Q.; Fan, C.; Fang, H.; et al. Destructive Extraction of Phospholipids from Escherichia coli Membranes by Graphene Nanosheets. Nat. Nanotechnol. 2013, 8, 594−601. (11) Miao, L.; Schulten, K. Probing a Structural Model of the Nuclear Pore Complex Channel through Molecular Dynamics. Biophys. J. 2010, 98, 1658−1667. (12) Klein, M. L.; Shinoda, W. Large-Scale Molecular Dynamics Simulations of Self-Assembling Systems. Science 2008, 321, 798−800. (13) D’Rozario, R. S. G.; Wee, C. L.; Wallace, E. J.; Sansom, M. S. P. The Interaction of C60 and Its Derivatives with a Lipid Bilayer via Molecular Dynamics Simulations. Nanotechnology 2009, 20, 115102. (14) Wong-Ekkabut, J.; Baoukina, S.; Triampo, W.; Tang, I. M.; Tieleman, D. P.; Monticelli, L. Computer Simulation Study of Fullerene Translocation through Lipid Membranes. Nat. Nanotechnol. 2008, 3, 363−368. (15) Shi, X. H.; Kong, Y.; Gao, H. J. Coarse Grained Molecular Dynamics and Theoretical Studies of Carbon Nanotubes Entering Cell Membrane. Acta Mech. Sin. 2008, 24, 161−169. (16) Orlova, E. V.; Sherman, M. B.; Chiu, W.; Mowri, H.; Smith, L. C.; Gotto, A. M. Three-Dimensional Structure of Low Density Lipoproteins by Electron Cryomicroscopy. Proc. Natl. Acad. Sci. U. S. A. 1999, 96, 8420−8425. (17) Zeng, D.; Juzkiw, T.; Read, A. T.; Chan, D. W.; Glucksberg, M. R.; Ethier, C. R.; Johnson, M. Young’s Modulus of Elasticity of Schlemm’s Canal Endothelial Cells. Biomech. Model. Mechanobiol. 2010, 9, 19−33. (18) Prassl, R.; Laggner, P. Molecular structure of low density lipoprotein: current status and future challenges. Eur. Biophys. J. 2009, 38, 145−158. (19) Gu, F.; Jones, M. K.; Chen, J.; Patterson, J. C.; Catte, A.; Jerome, W. G.; Li, L.; Segrest, J. P. Structures of Discoidal High Density Lipoproteins: A Combined Computational-Experimental Approach. J. Biol. Chem. 2010, 285, 4652−4665. (20) Catte, A.; Patterson, J. C.; Bashtovyy, D.; Jones, M. K.; Gu, F.; Li, L.; Rampioni, A.; Sengupta, D.; Vuorela, T.; Niemelä, P.; et al. Structure of Spheroidal HDL Particles Revealed by Combined Atomistic and Coarse-Grained Simulations. Biophys. J. 2008, 94, 2306−2319. (21) Jones, M. K.; Zhang, L.; Catte, A.; Li, L.; Oda, M. N.; Ren, G.; Segrest, J. P. Assessment of the Validity of the Double Superhelix Model for Reconstituted High Density Lipoproteins: A Combined Computational-Experimental Approach. J. Biol. Chem. 2010, 285, 41161−41171. (22) Shih, A. Y.; Arkhipov, A.; Freddolino, P. L.; Schulten, K. Coarse Grained Protein−Lipid Model with Application to Lipoprotein Particles. J. Phys. Chem. B 2006, 110, 3674−3684. (23) Hilder, T. A.; Gordon, D.; Chung, S. H. Computational Modeling of Transport in Synthetic Nanotubes. Nanomedicine 2011, 7, 702−709. (24) Glukhova Research Group. http://nanokvazar.ru/ (accessed 20 January, 2015). (25) Hadley, K. R.; McCabe, C. Coarse-Grained Molecular Models of Water: A Review. Mol. Simul. 2012, 38, 671−681. (26) Samuel Ginn College of Engineering, Auburn University. http://www.eng.auburn.edu (accessed 10 February, 2015).

CONCLUSIONS The dynamical behavior of HDL under external nonuniform mechanical load was investigated. The load was made by a few layer graphene and the nanotube. It is revealed that lipoprotein is very elastic and is able to dodge external influence. We observed that deformation of the lipoprotein’s structure reached 50%, and it did not violate its stability. Though the size of the lipoprotein’s change was within the range of 113− 126% and 120−146% in X and Y directions (Figure 3) from the equilibrium value, it remained stable. It can be concluded that the lipoprotein deformed similar to a soft but elastic ball. After the end of the nanotube’s influence, HDL recovered its structure and returned to the stable configuration. It was also determined that during the indentation lipoprotein belts are able to rearrange themself in a structure of HDL in such way that CNT that can be considered as the tip of AFM passes not through them but through phospholipid medium. All above-mentioned suggests that elasticity and high ability of the structure to be rebuilt without any loss of integrity provide lipoprotein a good diffusion ability of passing through interendothelial gaps of the arterial intima. As is known, interendothelial gaps have a complex shape; their dimensions might be narrow and comparable to the size of lipoproteins. On the basis of the results of our calculations, the mechanism of the HDL diffusion can be suggested. We assume that lipoproteins are able to be deformed to pass through narrow gaps. Our studies investigated dynamics of the HDL behavior, as HDLs move with the velocity of the blood flow during the interaction with intercellular gaps of an endothelial layer of internal vessel’s walls.

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AUTHOR INFORMATION

Corresponding Author

*(O.E.G.) Fax: +7 8452 511527. Telephone: +7 8452 514562. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Ministry of Education and Science of the Russian Federation within the framework of the Project of the State Task in the Field of Scientific Work (Project No. 3.1155.2014/K) and by grants of the Russian Scientific Foundation for Basic Research (Project No. 15-2901025).

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Article

The Journal of Physical Chemistry B (27) Koivuniemi, A.; Heikelä, M.; Kovanen, P. T.; Vattulainen, I.; Hyvönen, M. T. Atomistic Simulations of Phosphatidylcholines and Cholesteryl Esters in High-Density Lipoprotein-Sized Lipid Droplet and Trilayer: Clues to Cholesteryl Ester Transport and Storage. Biophys. J. 2009, 96, 4099−4108.

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Simulation of High Density Lipoprotein Behavior on a Few Layer

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