pubs.acs.org/Langmuir © 2009 American Chemical Society
Influence of Lipid-Bilayer-Associated Molecules on Lipid-Vesicle Adsorption Kristian Dimitrievski* Department of Applied Physics, Chalmers University of Technology, S-412 96 G€ oteborg, Sweden Received October 8, 2009. Revised Manuscript Received November 10, 2009 Supported lipid bilayers (SLBs) containing different types of bilayer-associated molecules (membrane-bound molecules) where one part of the molecule resides inside the lipid bilayer and another part of the molecule sticks out of the bilayer (e.g., membrane proteins) are important biophysical model systems. SLBs are commonly formed via lipid vesicle adsorption on certain surfaces (e.g., SiO2). However, vesicles doped with different types of (bio)molecules often do not form an SLB on the surface, and the reasons for this are not clear. Using a newly developed model of a lipid bilayer, simulations were performed to clarify the influence of the bilayer-associated molecules on vesicle adsorption and rupture. It is shown that by increasing the concentration of membrane-bound molecules in the vesicles the tendency for vesicle rupture decreases markedly and for a certain concentration rupture does not happen. The reason for this is that vesicles containing significant concentrations of such molecules tend to deform less on the surface (lower vesicle strain), especially for a significantly corrugated bilayer-surface potential. After vesicle rupture, membrane-bound molecules face either the surface or the solution in the resulting bilayer patch on the surface, depending on whether the molecules point outward or inward in the original vesicle, respectively. Vesicle surface diffusion is also studied for weak and strong surface corrugation, where vesicles are found to be almost immobile in the latter case.
1. Introduction Supported lipid bilayers (SLBs) are model systems for cell and organelle membranes and are interesting for future biotechnology applications (e.g., biosensors, biochips, diagnostics, drug screening devices, and controlling stem cell proliferation) and also for academic reasons. Incorporating different types of (bio)molecules into an SLB is an important developmental step. SLBs are commonly formed via lipid vesicle adsorption on certain surfaces.1-5 However, using vesicles that contain membrane-bound molecules that stick out of the bilayer membrane, such as certain membrane proteins6 or specially functionalized lipids,7 often hampers SLB formation on the solid support. Experimental observations show that the formation of an SLB depends not only on the type of membrane-bound molecule that is being incorporated into the bulk vesicles but also on the concentration of these molecules.6,7 In general, a low concentration of such molecules does not inhibit SLB formation, but larger concentrations make vesicles stay intact on the surface and no SLB is formed. The work presented here is intended to clarify the circumstances that are likely to lead to SLB formation or to intact vesicle adsorption. The quantities that are varied in the simulations are the concentration of bilayer-associated molecules, the vesiclesurface interaction strength, and the magnitude of the corrugation of the vesicle-surface potential. The experimental development of SLB research has been fast, but theoretical modeling is lagging behind. This is because the interface between a bilayer and its support is complicated (on the *Tel: þ46 317726114. Fax: þ46 317723134. E-mail: kristian.dimitrievski@ chalmers.se.
(1) Keller, C. A.; Kasemo, B. Biophys. J. 1998, 75, 1397. (2) Reimhult, E.; H€oo€k, F.; Kasemo, B. Langmuir 2003, 19, 1681. (3) Richter, R.; Mukhopadhyay, A.; Brisson, A. Biophys. J. 2003, 85, 3035. (4) Richter, R. P.; Brisson, A. R. Biophys. J. 2005, 88, 3422. (5) Reviakine, I.; Rossetti, F. F.; Morozov, A. N.; Textor, M. J. Chem. Phys. 2005, 122, 204711. (6) Graneli, A.; Rydstr€om, J.; Kasemo, B.; H€oo€k, F. Langmuir 2003, 19, 842. (7) Svedhem, S.; Dahlborg, D.; Ekeroth, J.; Kelly, J.; H€oo€k, F.; Gold, J. Langmuir 2003, 19, 6730.
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molecular scale and the nanoscale). Atomistic resolution of this interface is today limited in theory to a few tens of nanometers in size, and molecular dynamics simulations are typically limited to a few tens of nanoseconds for such systems,8,9 which is many orders of magnitude shorter than the timescale of adsorption and the rupture of a single vesicle on a surface (which takes seconds to minutes). Coarse-grained models for vesicles and substrates are therefore needed as a complement to study this physical region theoretically.
2. Model A lipid bilayer is modeled via beads, with each bead representing a small bilayer fragment (Figure 1). A 2D version of the model is used here, and a string of beads (that are oriented properly) represents an extended bilayer (Figure 2e). A closed bead chain represents a lipid vesicle (Figure 2f). An orientation vector is associated with each bead, which indicates the orientation of the bilayer fragment such that the vector is normal to the bilayer surface (Figure 1). This orientation vector is referred to as the bead’s normal. A bead-bead interaction potential is constructed, including a hard-core repulsion term, a term describing attraction between two beads, and a term that takes into account the relative orientation between two beads. The orientation-dependent term favors a parallel alignment of adjacent normal vectors and also takes into account the relative positions of the beads such that the normal vectors prefer to be orthogonal to the relative position vector between the beads. The energy of the bead arrangement (in the absence of a surface and bilayer-associated molecules) is given by Eb ¼
N -1 X
N X
i ¼1 j ¼i þ 1
e
-Rðrij -σÞ
ASij -B þ 1 þ eRðrij -βσÞ
ð1Þ
(8) Roark, M.; Feller, S. E. Langmuir 2008, 24, 12469. (9) Fortunelli, A.; Monti, S. Langmuir 2008, 24, 10145.
Published on Web 12/07/2009
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bead-surface potential irrespective of the value of C, and the height of the surface diffusion barrier is always 2C. A simple phenomenological two-bead model for bilayer-associated molecules is constructed where one bead represents the hydrophobic part of the molecule (labeled h) that preferably sits inside the lipid bilayer membrane (i.e., surrounded by the hydrophobic tails of lipid molecules) and where the other bead represents the hydrophilic/polar part of the molecule (labeled p) that sticks out of the lipid bilayer membrane. The energy of the arrangement of bilayer-associated molecules is given by Em ¼ Emi þ Emm þ Emb þ Ems Figure 1. Schematic illustration of two bilayer fragments that are
where
represented by beads. The orientation of each bilayer fragment is indicated by a normal vector on the associated bead.
where N is the number of beads, σ represents the radius of the beads, rij is the distance between bead i and bead j, B is a parameter controlling the attraction between two beads, A is a parameter controlling the energy penalty caused by the nonoptini 3 r^ij)2 þ (^ nj 3 r^ij)2 mal orientation of beads, Sij is defined as Sij = (^ where n^i, n^j, and r^ij are unit vectors (Figure 1), and R and β control the steepness and the range of the potential, respectively. One can regard the above potential as a coarse-grained representation of the hydrophobic interaction that drives the system toward membrane formation, where the hydrophobic lipid-tail regions of the bilayer fragments join in order to maximize entropy (in reality, via the rearrangement of water molecules surrounding the bilayer fragments). Using β > 1 makes the potential longranged, which was required to obtain stable and properly oriented bead chains. In reality, the shape of a bilayer fragment is not rigid but changes constantly because of the fluid nature of a lipid bilayer. Therefore, one bead represents a multitude of bilayer-fragment shapes, including different arrangements of lipids at the edge of the bilayer fragment. A bilayer fragment is thus not as rigid as indicated in Figure 1, and the normal vector defining the orientation of a bilayer fragment may be considered to be the average normal vector to the curved bilayerfragment surface. The bead-surface potential is represented by a Lennard-Jones potential together with a surface corrugation potential (which is similar but not identical to the one used by Zhdanov and Kasemo10) Es ¼
N X
Uðyi , EÞ Vðxi , EÞ
ð2Þ
i ¼1
Emi ¼ D
Nm X
ðsi - σÞ2 =2
ð6Þ
i ¼1
is the “intrinsic” elastic stretching energy between h and p beads belonging to a molecule, where Nm is the number of molecules and si is the separation between the h and p beads in molecule i, Emm ¼
NX m -1
X
Nm X
exp½ -Rðrkl ij -σÞ
ð7Þ
k, l∈fp, hg i ¼1 j ¼i þ 1
is the hard core molecule-molecule potential (indices k and l indicate the bead type, p or h, of molecules i and j, respectively), p h þ Emb Emb ¼ Emb
ð8Þ
is the molecule-bilayer potential where h ¼ Emb
Nm X N X i ¼1
-G 1 þ eRðrij -γσÞ j ¼1
ð9Þ
is the potential between the hydrophobic part of the molecule and bilayer beads and γ is selected such that molecules diffuse into the bilayer, p ¼ Emb
Nm X N X
exp½ -Rðrij - σÞ
ð10Þ
i ¼1 j ¼1
is the hard core potential between the hydrophilic/polar part of the molecule and the bilayer beads, h p þ Ems Ems ¼ Ems
where
ð5Þ
ð11Þ
is the molecule-surface potential where 12
6
Uðy, EÞ ¼ 4E½ðσ=yÞ - ðσ=yÞ
ð3Þ h Ems ¼
and
Nm X
exp½ -Rðyi - σÞ
ð12Þ
i ¼1
C Vðx, EÞ ¼ 1 þ ½sinð2πx=aÞ -1 E
ð4Þ
where yi is the (vertical) distance between bead i and the surface, ɛ is the depth of the potential, and C and a are the corrugation amplitude and periodicity, respectively. (Note that V(x, ɛ) is defined as V(x, ɛ) = 1 for y < σ). The form of V(x, ɛ) is such that the parameter ɛ always represents the deepest point in the (10) Zhdanov, V. P.; Kasemo, B. Langmuir 2000, 16, 4416.
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is the hard core molecule-surface potential for h beads, and p Ems ¼
Nm X
Uðyi , Em ÞVðxi , Em Þ
ð13Þ
i ¼1
is the molecule-surface potential for p beads where U and V are defined in eqs 3 and 4, respectively. Different Lennard-Jones potential-depth parameters ɛ and ɛm are introduced for bilayer beads and p beads of bilayer-associated molecules (eqs 2 and 13) DOI: 10.1021/la903814k
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Figure 2. Self-assembly of an extended bilayer from a random distribution of bilayer beads. The snapshots in a-e are taken at t = 0, 1.5 105, 9.0 105, 3.1 106, and 1.7 107 MCS, respectively, and the box size is 60 60 lu2. Spontaneous membrane formation happens independently of the box size (if the box is not too small) because as soon as beads come close enough to other beads via their random walk they will approach and stick together if the orientation of the beads is favorable. By initializing the bilayer beads to lie on a circle, we get a model vesicle (panel f) that is stable for a very long run up to 108 MCS.
because the polar part of the bilayer-associated molecules may have different surface adsorption affinities than the lipid headgroups, depending on what type of bilayer-associated molecules are being simulated. The total energy of the system is given by E ¼ Eb þ Es þ Em
ð14Þ
The algorithm of the simulations was performed as follows. Initially, a circularly shaped vesicle (with rij = σ between neighboring beads and with each bead having an orientation that is perpendicular to the circle) is placed above the surface at a distance of 5σ. At this distance, the bead-surface interaction is negligible and the vesicle shape equilibrates before adsorbing to the surface. Occasionally, however, the vesicle simply diffuses away from the surface, but these cases are not taken into account. (The 5σ distance is relatively far from the surface because the bead-surface interaction becomes relevant only at about 3σ.) Bilayer-associated molecules are put randomly into the vesicle, with the h beads located on the circular line of bilayer beads and with the p beads located at the vesicle exterior (with si = σ). Time starts to run in units of Monte Carlo steps (MCS), where 1 MCS is defined as the following steps: (i) A bilayer bead is selected at random. One attempt to move and reorient the selected bilayer bead is performed according to the Metropolis rule (see text below). (ii) A trial to move a bilayer-associated molecule is performed, provided that ξ < P, where ξ is a random 5708 DOI: 10.1021/la903814k
number between 0 and 1, and where P = 2Nm/N. If the trial is accepted, then a bilayer-associated molecule is selected at random, one of its two beads is selected at random, and one attempt to move the selected bead is performed according to the Metropolis rule. (iii) Steps i and ii are repeated N times. The new bead coordinates and orientation (orientation only for bilayer beads) are selected randomly in the range xi ( δx, yi ( δy, and φi ( δφ, where (xi, yi) is the initial position of the bead and φi is the initial orientation of the (bilayer) bead. The bead move is realized with probability P = 1 if ΔE e 0 and with probability P = exp(-ΔE/kBT) if ΔE > 0 (i.e., according to the Metropolis rule), where ΔE is the energy difference between the final and initial states of the system. In 1 MCS there are N bilayerbead move trials (including reorientation) and 2Nm bilayerassociated-molecule-bead move trials on average. That is, in 1 MCS, each bead in the system has made one move trial on average. Fixed and governing model parameters are outlined in Table 1. A maximum time, tmax, was defined in order to terminate simulation runs and was chosen to be tmax = 107 MCS. The length scale is expressed in length units (lu) and is defined by σ = 1.
3. Results To illustrate how the bilayer model works, we omit both the surface and any bilayer-associated molecules and consider only bilayer beads (eq 1). One of the merits of the bead model presented here is that an extended chain of beads is formed spontaneously Langmuir 2010, 26(8), 5706–5714
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Table 1. Fixed and Governing Model Parametersa fixed
governing
A = 200 G = 30 ɛ B = 100 γ = 0.5 ɛm R = 20 δx = 0.1 C β = 1.5 δy = 0.1 Nm σ = 1.0 δφ = π/20 a = 1.0 N = 50 D = 100 kBT = 1.0 a (Top to Bottom) The left column includes the following fixed parameters: the orientational penalty factor, the bead-bead attraction, the steepness of the potential, the range of the potential, the hard-core repulsion distance for bilayer beads (which is also the equilibrium bead-bead distance within a membrane-bound molecule), the periodicity of the surface corrugation, and the elastic stretching prefactor for membrane-bound molecules. The middle column includes the following fixed parameters: the factor for the hydrophobic interaction and the range of the interaction between bilayer beads and the hydrophobic part of membrane-bound molecules, the coordinate sampling in the x, y, and φ directions, the number of beads in the vesicle, and the definition of temperature. The right column includes the governing parameters, namely, the strength of the attraction between bilayer beads and the surface, the strength of the attraction between the polar part of membrane-bound molecules and the surface, the amplitude of the surface diffusion barrier, and the number of membrane-bound molecules present in the vesicle.
from an initially random distribution of beads (Figure 2a-e). Eventually, the free ends of the bead chain join, and the final structure is a closed bead chain that represents a lipid vesicle (Figure 2f). The vesicle is stable, and its shape fluctuates around the circular one. The model is robust in the sense that the values of parameters R, β, A, and B can be varied and still give rise to spontaneous membrane formation and stable vesicles; however, taking A to be too large compared to B will make vesicles unstable because then the bead chain becomes too rigid, and taking B to be too large compared to A makes the whole bead chain collapse because then bead-bead attraction overrules the orientation dependence. Another merit of the model is that it is directly extendable to three dimensions, however, with lower values of parameters A and B because there are more nearest neighbors in 3D than in 2D. Introducing a surface (eq 2) and allowing the vesicle to adsorb results in either an intact vesicle on the surface (Figure 3a) or a bilayer patch on the surface resulting from spontaneous vesicle rupture (Figure 3b-d). The fate of an adsorbing vesicle depends on the bilayer-surface interaction strength, which depends primarily on the type of substrate used and the lipid composition of the vesicle.1-5,11,12 For moderate bilayer-surface attraction (e.g., a POPC vesicle on SiO2), the vesicle stays intact on the surface,3,13 whereas for strong bilayer-surface attraction (e.g., a DOTAP or POEPC vesicle on SiO2), the vesicle ruptures spontaneously and forms a bilayer patch on the surface.3,14 3.1. Vesicle Surface Diffusion. It is still an open question as to why adsorbed vesicles on SiO2 and mica do not diffuse, although a possible mechanism for the nondiffusivity was proposed recently.15 It was proposed that transient (i.e., temporary) electrostatic pinning of lipid headgroups to surface charges might be the reason for the nondiffusivity. Here, another mechanism is probed, where the beads face a significantly corrugated surface potential simulating the case where lipid headgroups are relatively strongly (11) Dimitrievski, K.; Kasemo, B. Langmuir 2008, 24, 4077. (12) Dimitrievski, K.; Kasemo, B. Langmuir 2009, 25, 8865. (13) Keller, C. A.; Glasmastar, K.; Zhdanov, V. P.; Kasemo, B. Phys. Rev. Lett. 2000, 84, 5443. (14) Wikstr€om, A.; Svedhem, S.; Sivignon, M.; Kasemo, B. J. Phys. Chem. B 2008, 112, 14069. (15) Klacar, S.; Dimitrievski, K.; Kasemo, B. J. Phys. Chem. B 2009, 113, 5681.
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Figure 3. Snapshots of (a) an adsorbed vesicle that stays intact on the surface and (b-d) a vesicle that ruptures upon adsorption to form a bilayer patch on the surface. In panel a, the bilayer-surface interaction is intermediate (ɛ = 40), but in panels b-d, the interaction is strong (ɛ = 80). (The rupture and unfolding of the vesicle to a bilayer patch are independent of the surface diffusion barrier and depend only on the bilayer-surface interaction strength. C = 20.)
Figure 4. Vesicle surface diffusion data for zero, low, and high diffusion barriers (C = 0, 0.3, and 20, respectively). The data points show the mean squared displacement of the center of mass of the vesicle (in the x direction). The diffusion coefficients are indicated; they are calculated via the 1D diffusion equation. Filled circles show data for the flat surface (C = 0), filled squares show data for a surface with a low diffusion barrier (C = 0.3), and open circles show data for a surface with a high diffusion barrier (C = 20). The straight lines are least-squares fits to the diffusion data.
attached to surface charges but are not pinned. Figure 4 shows diffusion data for three values of the corrugation parameter, C = 0, 0.3, and 20. The surface diffusion barrier is, respectively, 0, 0.6kBT, and 40kBT. The surface diffusion coefficient is larger by almost a factor of 3 on the flat surface (C = 0) than on the DOI: 10.1021/la903814k
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Dimitrievski Table 2. Summary of Resultsa
bil-surf int:
intermediate (ɛ = 40)
strong (ɛ = 80)
surf diff barr:
Nm = 0 Nm = 2 Nm = 4 Nm = 6 Nm = 8 Nm = 10
low (C = 0.3) R/tot
def
0/50 0/5 0/5 0/5 0/5 0/5
0.28 ( 0.00 0.29 ( 0.00 0.29 ( 0.01 0.28 ( 0.01 0.33 ( 0.07 0.38 ( 0.10
R/tot
def
def(R)
R/tot 5/5 5/5 4/5 4/5 2/5 1/5
surf diff barr:
def
def(R)
0.30 ( 0.02 0.29 ( 0.02 0.40 ( 0.09 0.40 ( 0.06
0.36 ( 0.16 0.36 ( 0.19 0.28 ( 0.11 0.19 ( 0.08 0.15 ( 0.05 0.11 ( 0.0
def
def(R)
high (C = 20) def(R)
R/tot
0/50 0.29 ( 0.00 5/5 0.23 ( 0.02 Nm = 0 0/5 0.31 ( 0.04 4/5 0.36 ( 0.02 0.38 ( 0.20 Nm = 2 0/5 0.65 ( 0.24 3/5 0.64 ( 0.03 0.57 ( 0.23 Nm = 4 0/5 0.68 ( 0.32 2/5 0.71 ( 0.25 0.27 ( 0.02 Nm = 6 0/5 0.71 ( 0.09 1/5 0.60 ( 0.08 0.24 ( 0.0 Nm = 8 0/5 0.61 ( 0.06 0/5 0.59 ( 0.13 -; Nm = 10 a The tendency for vesicle rupture and the deformation of adsorbed vesicles, as a function of the concentration of bilayer-associated molecules in a vesicle, are shown. The data is shown for intermediate and strong bilayer-surface interactions (ε = 40 and 80, respectively), with either a low (upper section) or high (lower section) surface diffusion barrier (C = 0.3 or 20). The “R/tot” column shows in how many simulation runs a vesicle ruptured compared to the total number of runs performed (50 runs were performed for Nm = 0 and ε = 40 in order to calculate the surface diffusion coefficient). The “def” column shows the average deformation (aspect ratio) of adsorbed vesicles that stay intact on the surface (height-to-width ratio). The “def(R)” column shows the average deformation at the moment of vesicle rupture.
significantly corrugated surface (C = 20). It is not clear whether vesicles should be considered to be immobile for C=20. A rough estimation of the vesicle movement in this case is [Æ(Δx)2æ]1/2 ≈ (2Dtmax)1/2=[(2)(8.5)(10-7)(107)]1/2=4 lu. If each bead represents roughly seven lipids (in each leaflet), then 1 lu represents roughly 5 nm (because one lipid headgroup occupies about 0.7 nm in a bilayer). Thus, 4 lu translates to about 20 nm. To estimate what tmax means in real units is more difficult, but if one defines that 1 MCS corresponds roughly to 1000 place exchanges of adjacent lipid molecules in a bilayer leaflet (lipid place exchange within a leaflet occurs roughly in 10-7 s), then tmax = 107 MCS corresponds to about (1000)(10-7)(107) = 1000 s, which is about 17 min. In other words, a vesicle would have moved about 20 nm in 20 min. The radius of the model vesicle is about 40 nm, so the vesicle would have moved half of its radius in 20 min. AFM measurements of adsorbed vesicles on SiO2 have been made where about 20 and up to about 50 adsorbed vesicles were imaged repeatedly for up to 60 min with no indication of any vesicle movement on the surface (unpublished results by Michael Z€ach). In 60 min, the model vesicle would have moved about one, or one and a half, vesicle diameters, which would have been detectable with AFM. Even if the surface diffusion coefficient obtained is somewhat large and the model vesicles cannot be considered to be really immobile, the vesicles are at least close to immobile and we cannot rule out that the mechanism of nondiffusion of adsorbed real vesicles is the relatively strong attachment of lipid headgroups to surface charges. The significant difference from the pinning case is that, for the mechanism discussed here, there should be less water trapped between the lipids and the surface. For the pinning case, there is more room for water molecules between the bilayer and the surface because on average there is a significant population of lipids that are not attached to surface charges, and in these regions a few monolayers of water separate the bilayer and the substrate (i.e., the local hydration shells of lipid headgroups and surface charges are intact15). 3.2. Vesicle Deformation and Summary of Results. An SLB that covers the whole surface is commonly formed by
continuous vesicle adsorption from the bulk solution.2-4,13,16 Even if vesicles do not rupture spontaneously on the surface, vesicle rupture may occur as a consequence of other vesicles adsorbing close by that touch and push on the original vesicle. (Note that lipid vesicles are not rigid structures but are rather soft and flexible and exhibit thermal shape fluctuations.) Vesicles are immobile on SiO2 and mica, which means that, upon adsorption close by, vesicle-vesicle “pushing” between neighboring vesicles takes place, if not constantly then at least during an equilibration time during which neighboring vesicles have pushed themselves away from each other.15 This interaction between adjacent vesicles probably lowers the barrier for vesicle rupture. Both the degree of deformation of adsorbed vesicles and the number of neighbors are likely to influence the probability of vesicle rupture. If the deformation is large enough (but not so large that a single vesicle ruptures spontaneously), then a critical number of neighbors should be sufficient to initiate rupture. When this happens, we talk about a critical coverage of vesicles on the surface, and an SLB is eventually formed as more vesicles adsorb on the surface from the bulk liquid in standard experiments.1,17 SLB formation proceeds quickly as soon as the critical coverage is reached because bilayer patches from ruptured vesicles induce rupture in nearby vesicles via the bilayer edge, which is a relatively fast process and accelerates SLB formation.3,18 However, if the deformation of adsorbed vesicles is moderate, then it does not matter how many vesicles are adsorbed to the surface;vesicle rupture will not be initiated, and we will end up with a supported vesicular layer (SVL) on the surface.2,5 In the work presented here, only one vesicle is simulated at a time and the degree of deformation of an adsorbed vesicle will be used as a qualitative measure of the tendency to form an SLB. There are reports stating that formation of an SLB is hampered and even suppressed when the vesicles contain a certain type and number of membrane-associated molecules.6,7 The general observation is that low concentrations of membrane-associated molecules in the vesicles do not inhibit SLB formation, while at and
(16) Zhdanov, V. P.; Keller, C. A.; Glasmastar, K.; Kasemo, B. J. Chem. Phys. 2000, 112, 900.
(17) Reimhult, E.; Z€ach, M.; H€oo€k, F.; Kasemo, B. Langmuir 2006, 22, 3313. (18) Dimitrievski, K.; Reimhult, E.; Kasemo, B.; Zhdanov, V. P. Colloids Surf., B 2004, 39, 77.
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above some critical concentration an SLB is not formed. In the latter case, adsorbing vesicles stay intact on the surface and vesicle rupture is never initiated. The size of the membrane-bound molecules most likely also influences the tendency for vesicle rupture, where larger molecules presumably result in larger hampering of vesicle rupture. Here, the size of the molecules is kept constant and simulation results are presented where the number of membrane-associated molecules in a vesicle is varied and where the surface properties are also varied. For simplicity, the polar part of membrane-associated molecules (the part that sticks out of the bilayer) is taken to have the same interaction with the surface as the bilayer beads (i.e., ɛm = ɛ (eqs 2 and 13)). The effect of differences in interaction strength with the surface between membraneassociated molecules and bilayer beads is omitted here but can 6 ɛ if the desire occurs. be studied by taking ɛm ¼ Table 2 shows a summary of the simulation results. The middle and right columns show data for intermediate (ɛ = 40) and strong (ɛ = 80) attractive bilayer-surface interactions, respectively. The upper and lower parts of the Table show data for low (C = 0.3) and high (C = 20) surface diffusion barriers, respectively. A noncorrugated surface was also simulated by taking C = 0 (data not shown), with almost identical results to the case with C = 0.3. The columns labeled R/tot, def, and def(R) show the number of runs in which a vesicle ruptured compared to the total number of runs performed, the average deformation of intact vesicles (height-to-width ratio), and the average deformation at the moment of vesicle rupture, respectively. 3.3. Intermediate Bilayer-Surface Interaction. Looking at the data for intermediate (attractive) bilayer-surface interaction and low surface diffusion barrier (Table 2), we see that vesicles never rupture and that the deformation decreases slightly (larger aspect ratio) as more membrane-bound molecules are present. Snapshots of the final configuration of a vesicle is shown in Figure 5a for two of these cases: Nm = 6 and 10. The final vesicle shape is similar to that in the upper image in Figure 5a in almost all cases (i.e., vesicles deform in most cases as if there were no membrane-bound molecules present). This is because the surface diffusion barrier is too low for the molecules to stay where they originally adsorbed on the surface. The molecules are pushed toward the rim of the adsorbed portion of the bilayer as more bilayer beads adsorb on the surface. However, if there are many molecules already adsorbed at the rim, as in the lower image of Figure 5a, then this configuration is relatively stable and the molecules cannot easily be pushed further sideways. Note that simulations were also performed with membranebound molecules pointing inward (i.e., with the polar part of the molecules residing in the interior of the vesicle), but there was no effect at all on vesicle adsorption for these cases ranging from Nm = 2 to 10 (for each combination of ɛ and C). However, for spontaneous vesicle rupture there is a significant effect, namely, that the molecules are pointing upward (i.e., away from the surface) facing the bulk solution when the bilayer island has formed (see text below). Now turn to the case with intermediate (attractive) bilayer-surface interaction but with a high surface diffusion barrier (Table 2). Vesicles are clearly much less deformed in this case compared to the case with a low surface diffusion barrier (i.e., vesicles are less strained and the tendency for SLB formation is therefore lower). Snapshots of vesicle shapes are shown in Figure 5b for Nm = 6 and in Figure 5c for Nm = 10. For Nm = 4, one run out of five has the same final vesicle shape as the one in the upper image of Figure 5a, whereas the remaining four runs have shapes similar to those in the lower image of Figure 5b. For Nm = 6, also one run out of five looks similar to the one in the Langmuir 2010, 26(8), 5706–5714
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Figure 5. Vesicle configurations at the end of simulation runs (at t = tmax = 107 MCS) for intermediate bilayer-surface interaction strength (ɛ = 40). A membrane-bound molecule is indicated by black (hydrophobic part, h) and gray (hydrophilic/polar part, p) beads. Panel a shows two examples of final configurations for C = 0.3. All final configurations for Nm = 6 are similar, but for Nm = 10, two out of five runs have final configurations with a lower deformation (larger aspect ratio) than the rest of the runs (which look similar to the runs with Nm = 6). Panel b shows two final configurations for C = 20 and Nm = 6. Final configurations are diverse for Nm = 6 (main text). In one of five runs, the final configuration looks similar to the upper one in panel a. Panel c shows two final configurations for C = 20 and Nm = 10. In one run, no bilayer beads adsorbed. In two runs, not all molecules adsorbed to the surface. Note that vesicles are more deformed here compared to the case in panel b because more molecules are present that adsorb and force the vesicles to flatten more. Typically, a relatively small fraction of the bilayer is adsorbed.
upper image of Figure 5a, whereas in the other four runs the shapes vary from practically circular to an aspect ratio of about 0.5. (Note that the standard deviation of the average deformation is large for Nm = 6.) By observing the vesicles live as the simulations proceed (which is made possible via the graphics DOI: 10.1021/la903814k
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interface provided by OpenGL programming code), it is clear that the molecules rarely diffuse on the surface and instead stay put where they land (i.e., for the case with C = 20). The different final vesicle shapes (e.g., for Nm = 6) were clearly observed to be a consequence of the particular distribution of molecules within the vesicle at the beginning of vesicle adsorption. For example, as soon as the vesicle adsorbs to the surface with bilayer beads, the adsorption of adjacent bilayer beads proceeds quickly until a molecule is encountered that adsorbs to the surface. When this happens, the adsorption of the molecule inhibits any further adsorption of bilayer beads. There are two important timescales involved here that influence the final configuration of the vesicle. One timescale is for the propagation of bilayer adsorption on the surface, and the other timescale is for the diffusion of membrane-bound molecules within the bilayer. Because the propagation of bilayer adsorption is much faster than the diffusion of membrane-bound molecules within the bilayer, the final vesicle configurations are diverse for intermediate concentrations of membrane-bound molecules (for the case with a high surface diffusion barrier). For high concentrations of such molecules, the probability that a molecule happens to be in the vicinity just where the vesicle starts to adsorb results in fewer bilayer beads adsorbed in total in the final vesicle configuration (Figure 5c, upper image) and may result even in only molecules adsorbing with no bilayer adsorbed at all (Figure 5c, lower image). If instead the diffusion of membranebound molecules within the bilayer was much faster than the propagation of bilayer adsorption, then only a very small fraction of the bilayer would be adsorbed in each run, if at all. Experimentally, a significant concentration of maleimide-functionalized lipids is needed to suppress SLB formation on SiO2,7 which suggests that the propagation of bilayer adsorption is faster than the diffusion of lipids within a leaflet of the bilayer. Therefore, the diffusion of membrane proteins should be even slower, and thus the condition in the simulations regarding the two timescales is correct. 3.4. Strong Bilayer-Surface Interaction. To show more explicitly that membrane-bound molecules indeed hamper the tendency for vesicle rupture, simulations were performed using a strong (attractive) bilayer-surface interaction (ɛ = 80). For this strong interaction, vesicles always rupture spontaneously when there are no membrane-bound molecules (Table 2). Interestingly, the probability of vesicle rupture decreases with increasing concentration of membrane-bound molecules, and this effect is especially pronounced for the case with a high surface diffusion barrier (Table 2). Not only is the probability of vesicle rupture lower, but also the deformation is markedly lower for the case with a high surface diffusion barrier compared to the case with a low surface diffusion barrier. This means that the probability of critical-coverage-induced rupture is lower for the case with a high surface diffusion barrier compared to the case with a low surface diffusion barrier (which is the same tendency as for the case with the intermediate bilayer-surface interaction discussed above). Snapshots of vesicle configurations at the moment of rupture and final configurations when vesicles stay intact are shown in Figure 6. Panel a shows two different vesicle shapes at rupture for the case with a low surface diffusion barrier and Nm = 2. Note that the average deformation at rupture is relatively low (with a relatively high aspect ratio) for Nm = 0 and 2 and C = 0.3 and that the standard deviation is relatively large. This is because rupture occurs early and late, respectively, during the adsorption process, as seen in the lower and upper images of Figure 6a. (This feature was observed by Dimitrievski and Kasemo11 as well and is discussed there in detail.) However, the corresponding data for 5712 DOI: 10.1021/la903814k
Dimitrievski
Figure 6. Vesicle configurations at the end of simulation runs (at t = tmax = 107 MCS) or at the moment of vesicle rupture for strong (attractive) bilayer-surface interaction (ɛ = 80). Panels a and b shows configurations for C = 0.3, and panel c shows the configuration for C = 20. Panel a shows examples of vesicle shapes for late and early rupture during the adsorption process (upper and lower images, respectively) for Nm = 2. Panel b (upper image) shows an example of vesicle rupture, although membrane-bound molecules are adsorbed at the rim of the adsorbed portion of the bilayer. Panel b (middle image) shows an example of a stable configuration where the vesicle has ruptured at both ends. Panel b (lower image) shows a vesicle that stayed intact on the surface and where a membrane-bound molecule has been detached from the bilayer membrane. Panel c (upper image) shows an example where a vesicle ruptures, although there are many membrane-bound molecules present. Panel c (middle and lower images) show examples of intact vesicles.
the high surface diffusion barrier and Nm = 0 does not indicate a relatively low deformation on average at rupture. There is no reason that this should be the case. There should also be instances where vesicles rupture early during the adsorption process. Additional runs were therefore performed for C = 20 and Nm = 0 to check the vesicle configurations at rupture for this case. Indeed, early vesicle rupture also occurs, but this feature Langmuir 2010, 26(8), 5706–5714
Dimitrievski
Article
membrane. Because the bilayer-surface interaction (and thus also the molecule-surface interaction) is relatively strong here, adsorbed membrane-bound molecules are occasionally pulled out of the bilayer membrane. In this case (i.e., in the lower image), the vesicle was first adsorbed more to the left, but when nonadsorbed membrane-bound molecules started to adsorb on the right side of the vesicle, the whole vesicle was eventually pulled to the right side as more and more molecules adsorbed on the right side. (This was seen explicitly via the graphics interface that was mentioned above.) As a result, one of the adsorbed molecules on the left side was pulled out of the membrane. Figure 6c shows some vesicle configurations for a high surface diffusion barrier. In the upper image, the vesicle ruptured because a large part of the bilayer was not occupied by membrane-bound molecules, which then happened to adsorb to the surface. Thus, the distribution of molecules was responsible for the rupture in this case. (Only in one run out of five did a vesicle rupture for C = 20 and Nm = 8.) The middle and lower images show stable vesicles. The lower image shows a situation where a vesicle first adsorbed with a small part of the bilayer (left part of the adsorbed bilayer) and stayed adsorbed with a very circular shape for a while (upper image in Figure 5b). Then, some nonadsorbed molecules diffused to the right side of the vesicle and (as the vesicle shape fluctuated) eventually were adsorbed and shaped the final vesicle configuration. Finally, Figure 7 shows a sequence of snapshots of a vesicle that adsorbs and then ruptures. The snapshots show the vesicle configuration at different time steps (indicated in the Figure). The final structure is a bilayer patch with the membrane-bound molecules facing the surface.
Figure 7. Snapshots at different times during the adsorption process of a vesicle with Nm = 6 for C = 20 and ɛ = 80. The vesicle eventually ruptures, and the final configuration is a bilayer patch on the surface with the membrane-bound molecules facing the surface.
escaped the original five runs. The statistics for early rupture during the adsorption process are as follows: for C = 0.3 and Nm = 0, 2, 4, 6, 8, 10, early rupture occurred in 3, 2, 1, 0, 0, 0 runs out of five runs, respectively. For C = 20 and Nm = 0, 2, 4, 6, 8, early rupture occurred in 0, 2, 3, 0, 0 runs out of five runs, respectively. Panel b of Figure 6 shows additional examples of vesicle configurations for a low surface diffusion barrier. The upper image shows an example where a vesicle ruptures, although membrane-bound molecules occupy the rim of the adsorbed portion of the bilayer. Even though the bilayer-surface interaction is strong, the molecules are pushed sideways during the adsorption process because of the low surface diffusion barrier. The middle image shows a vesicle that ruptured at both ends and where the final stable configuration is a bilayer “arc” under which there is a small bilayer patch. This configuration might also be stable in a real system because the active bilayer edge is neutralized by membrane-bound molecules that stick out just at the bilayer edge (such that the bilayer edge cannot induce further rupture of the adjacent bilayer membrane). The lower image shows a vesicle that stayed intact on the surface and where one membrane-bound molecule was detached from the bilayer Langmuir 2010, 26(8), 5706–5714
4. Conclusions A new phenomenological, coarse-grained (bead) model of a lipid bilayer was presented (here used in 2D), with the following attributes: (i) an extended membrane is formed spontaneously from an initially random distribution of beads, which eventually closes and forms a coarse-grained representation of a vesicle; (ii) the model is directly extendable to 3D (with a few adjustments of parameter values); (iii) vesicle rupture occurs naturally and can be studied without introducing a critical bending angle (defining such an angle was needed in previous coarse-grained models); (iv) it might be possible to study patch-induced vesicle rupture (not done here but will be attempted); and (v) the critical coverage pathway to SLB formation might be studied more explicitly by adsorbing vesicles adjacently and looking for conditions when one of the vesicles ruptures, followed by patch-induced vesicle rupture in the remaining nonruptured vesicles (not done here but will be attempted). A surface was introduced on which a vesicle was allowed to adsorb. The properties of the bilayer-surface interaction were varied in order to simulate different real situations. The interaction was taken to be intermediately attractive or strongly attractive, for which vesicles were shown to stay intact on the surface and rupture spontaneously, respectively. The (sinusoidal) surface corrugation was also varied from a flat surface (i.e., without corrugation) to a highly corrugated surface. Vesicle surface diffusion was studied for three different surface corrugations in an attempt to clarify the reasons for the immobility of adsorbed real vesicles on SiO2 and mica (which is still an open question, although a suggestion for a mechanism for the immobility was proposed recently15). The highly corrugated bilayer-surface interaction studied here simulates the case for which lipid headgroups attach relatively strongly to surface charges. However, the DOI: 10.1021/la903814k
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surface diffusion coefficient that was obtained turned out to be slightly larger than what is expected for immobile vesicles. At the moment, therefore, the best candidate for the explanation of the nondiffusivity of vesicles is the transient pinning mechanism.15 A simple model to account for membrane-bound molecules (e.g., membrane proteins) located in the bilayer of a vesicle was also presented. A membrane-bound molecule was represented by two beads, one hydrophobic and one hydrophilic. The former bead is located in the vesicle bilayer, and the latter sticks out of the bilayer. The model allows membrane-bound molecules to diffuse inside the vesicle bilayer. In this study, the polar part of the membrane-bound molecules and the bilayer beads was set to have the same interaction with the surface; however, the model allows for having different bilayer-surface and molecule-surface interactions (e.g., the latter can be repulsive and the former can be attractive). By using vesicles with different concentrations of membranebound molecules, it was shown that the surface corrugation played a central role in the final shape of an adsorbed vesicle. For weak surface corrugation (and intermediate and attractive bilayer-surface interactions), vesicles deform on the surface almost as if there were no membrane-bound molecules present. In this case, it was shown that membrane-bound molecules are pushed toward the sides of the vesicle during the adsorption process. However, if the surface corrugation is strong, then vesicles deform much less when a significant number of membrane-bound molecules are present. This is because the strong surface corrugation prohibits sideways pushing of the membranebound molecules during vesicle adsorption and the vesicle therefore obtains a less strained adsorbed configuration. It was discussed that the degree of vesicle deformation probably reflects the tendency for vesicle rupture and thereby SLB formation. It was therefore concluded that for significant surface corrugation, SLB formation is hampered for vesicles containing a significant number of membrane-bound molecules (which is in line with experimental results).
5714 DOI: 10.1021/la903814k
Dimitrievski
To show explicitly that significant concentrations of membrane-bound molecules indeed hamper the tendency for vesicle rupture, a strongly attractive bilayer-surface interaction was used as well. For this strong interaction, vesicles always ruptured spontaneously when no (or a small number of) membrane-bound molecules were present. However, for larger concentrations of membrane-bound molecules in the vesicles, the probability of rupture decreases strongly and for a critical number of such molecules the vesicles always stay intact on the surface. The simulation results shown were for vesicles that contain membrane-bound molecules that stick out of the vesicle bilayer on the outside of the vesicle. Simulations were also performed (data not shown) with the molecules sticking out into the interior of the vesicle, but for this arrangement, there were no differences from the case with no membrane-bound molecules present in the vesicle. Thus, the molecules that point outward, toward the exterior of the vesicle, are responsible for the decreasing vesicle deformation and decreasing rupture tendency as the concentration of molecules increases. Furthermore, it was shown (for outward-pointing molecules) that membrane-bound molecules end up facing the substrate after vesicle rupture had occurred and the bilayer unfolded to form a bilayer patch on the surface. For the case with inward-pointing molecules (not shown) and strong bilayer-substrate interaction, the molecules face the bulk solution after vesicle rupture. For the mixed case (with both inward- and outward-pointing molecules), there are thus regions where molecules face the substrate and other regions where molecules face the bulk solution (not shown). Acknowledgment. I thank Bengt Kasemo and Vladimir P. Zhdanov for valuable discussions. Financial support was obtained from the Swedish Research Council (contract nos. 16254111 and 16254099).
Langmuir 2010, 26(8), 5706–5714
