1 Biointerphases (2012) 7:57 DOI /s ARTICLE Computer Simulation of Water-Meiate Ahesion Between Phospholipi Bilayer an Soli Support Functionalize with Self-Assemble Monolayers Alexaner Pertsin Michael Grunze Receive: 17 May 2012 / Accepte: 16 August 2012 / Publishe online: 28 August 2012 The Author(s) This article is publishe with open access at Springerlink.com Abstract An attempt is mae to estimate, via computer simulation of the force istance relation, the free energy of ahesion between a phosphatiylethanolamine bilayer an an alkanethiolate self-assemble monolayer (SAM) in aqueous meium. The simulations are performe using the gran canonical Monte Carlo technique an atomistic force fiels. The bilayer ahesion free energy is preicte to be -22 ± 3 mj/m 2 ( 1.4 ± 0.2 kcal/mol) on a hyrophilic carboxyl-terminate SAM an -1 ± 1 mj/m 2 ( 0.06 ± 0.06 kcal/mol) on a hyrophobic methyl-terminate SAM. In the last two ecaes, the water-meiate interaction of lipi bilayers with various surfaces has receive much attention . This is explaine, in particular, by everincreasing practical interest in planar bilayer membranes supporte on soli substrates. For biologists an biophysicists, the supporte lipi bilayers (SLBs) provie a goo moel system for stuying the membrane structure an properties because of a better stability of SLBs with respect to chemical manipulation an estructive effects of surface-sensitive characterization techniques. For physicists an physicochemists, SLBs are of interest mainly as a means for biofunctionalization of inorganic solis an polymeric materials. A practical outcome of the associate research is the evelopment of new biosensors, which combine the small thickness an high electrical resistivity of SLBs with their ability to serve as a matrix for incorporating receptors an, simultaneously, to suppress nonspecific ligan bining . A. Pertsin (&) M. Grunze Angewante Physikalische Chemie, Universität Heielberg, Im Neuenheimer Fel 253, Heielberg, Germany A critical parameter that governs the stability an other properties of SLBs is the free energy of ahesion between the bilayer an substrate, W. In a general case, W can be represente as the sum of two basic components. One component is ue to irect bilayer substrate interactions, while the other arises from so-calle hyration forces. These latter are associate with a thin aqueous film that is usually present between the bilayer an substrate. (It is this film that maintains the lateral fluiity of the bilayer.) In principle, W can be etermine experimentally by the surface force apparatus (SFA) or atomic force microscopy (AFM) an relate techniques. A thorough inspection of the literature has however reveale only one relevant stuy, as recently reporte by Anerson et al.  from the Israelachvili group for zwitterionic phospholipi bilayers (DMPC) supporte on silica glass substrates. The lack of experimental ata on the bilayer-substrate ahesion energy attracts attention to computer simulations as a potential means of aequately moeling SFA experiments base on realistic force fiels. An avantage of computer simulations is the possibility of partitioning W into iniviual physical components corresponing to the iniviual components of the intermolecular interaction energy. The knowlege of the physical components of W offers a clearer insight into the mechanism of the bilayer substrate ahesion. By now, the number of computer simulations of SLBs is very limite. Of the eight publishe simulation stuies [3 10], only three [3 5] were base on a realistic atomistic escription. The others were concerne with oversimplifie coarse-graine [6 8] an highly coarse-graine [9, 10] moels, which are harly capable of quantitatively escribing water-meiate bilayer substrate interactions. Of particular interest is the atomistic simulation stuy by Heine et al.  who mae a first attempt to quantify the
2 Page 2 of 6 Biointerphases (2012) 7:57 ahesion energy between a lipi bilayer an a-quartz substrate in aqueous meia. Although the simulation correctly preicte the equilibrium separation between the bilayer an substrate, the calculate ahesion energies prove to be about two orers of magnitue higher than the experimental values measure by Anerson et al.  ( mj/m 2, epening on the metho of bilayer preparation). It is worth noting that the above-cite computer simulations of SLBs were all performe using the molecular ynamics (MD) technique an close statistical ensembles (NVT an NP N T), where the number of particles in the confine system remaine constant. By contrast, a real SLB stuie in an SFA experiment represents an open confine system, where water sanwiche between the bilayer an substrate is allowe to exchange molecules with a surrouning bulk water reservoir. The relevant statistical escription is provie by the gran canonical (lvt) or isostress (lp N T) ensembles. In our previous simulations of the water-meiate interaction between two ientical phospholipi bilayers [11, 12], the problem of moeling an open system was solve by resorting to a gran canonical Monte Carlo (GCMC) technique involving special expeients for enhancing sampling efficiency . The aim was to unerstan the physical nature of forces responsible for the short-range interbilayer repulsion. In the present work, our GCMC simulations are extene to asymmetric systems, where one bilayer is replace by a soli substrate. Unlike the previous stuies [11, 12], now the interest is concentrate on separations where one can expect bilayer substrate attraction responsible for ahesion. The specific lipi consiere in the present work is ilauroylphosphatiylethanolamine (DLPE) stuie in our previous simulations [11, 12]. As a substrate, we use a gol support functionalize by carboxyl- an methyl-terminate alkanethiolate self-assemble monolayers (hereafter, O-SAM an C-SAM) of the general formula X(CH 2 ) n S (X = COOH an CH 3, n = 12 an 13, respectively). This choice is natural as far as aqueous meium is concerne, where the water affinity of the substrate may play a ecisive role in the bilayer substrate ahesion. As a preliminary stage of this work, we have recently simulate water-meiate ahesion between the O- an C-SAMs both in symmetric an asymmetric combinations (i.e., between like SAMs an between unlike SAMs, respectively) . The calculate free energies of ahesion prove to be in acceptable agreement with the available experimental ata extracte from AFM measurements of force istance relations. The behavior of the two symmetric an one asymmetric systems with increasing confinement was quite ifferent. The symmetric system boune by the hyrophilic O-SAMs kept confine water at all separations trie, incluing separations in the region of repulsive pressures. The system confine by two hyrophobic C-SAMs showe a capillary evaporation occurring at a fairly large separation in the attractive region. As a consequence, the ahesion energy was mainly etermine by the irect interaction of bare SAMs. A capillary evaporation was also observe in the asymmetric O-SAM/water/C-SAM system. In this case, however, the evaporation was incomplete. The remaining water molecules were all asorbe on the hyrophilic O-SAM, while the hyrophobic C-SAM was separate from the rest of the system by a thin vapor layer. These observations have provie a goo basis for a comparative analysis of the behavior of DLPE/water/SAM systems. The moel system use in the present simulations reflects the configuration of an SFA experiment, as schematically epicte in Fig. 1. The system elements shown in black are explicitly present in the system, while those shown in gray are simulate implicitly. As in our previous stuies [11, 12] the outer (upper) phospholipi monolayer was represente in a mean-fiel manner as a flat structureless surface interacting with the carbon atoms of the lower monolayer through a (3 9) inverse power potential. The position of this surface correspons to the mi-plane of the bilayer, as shown by the ashe line in Fig. 1. The parameters of the (3 9) potential were calibrate so as to fit atomistic force fiel results for the interaction energy of two DLPE monolayers facing each other with their hyrophobic sies. The inter- an intramolecular energies of DLPE were calculate using the AMBER-base force fiel refine by Smonyrew an Berkowitz . The methyl an methylene groups were treate in the unite-atom approximation, while the hyrogen atoms of the amino group were treate explicitly. The DLPE molecules were regare as flexible but subject to bon-length constraints. These latter were Fig. 1 Configuration of the simulation moel. The parts simulate explicitly an implicitly are shown in black an gray, respectively
3 Biointerphases (2012) 7:57 Page 3 of 6 implemente using the rotational isplacement proceure suggeste in our early paper . The gol support was represente by a two-imensional hexagonal lattice of force sites corresponing to the (111) plane of the gol monocrystal. The interaction of gol with water was neglecte. The alkane chains were escribe with an all-atom moel, with the atom atom potentials calibrate by Williams  by fitting the equilibrium structure an lattice energy of hyrocarbon crystals to the relevant experimental ata. The potential parameters of sulfur were the same as use by Mar an Klein  in their MD simulations of an alkanethiolate SAM, while the interactions involving the COOH group were treate using the respective potentials from the OPLS-AA force fiel . As with DLPE, the conformation of the SAM molecules was subject to bon-length constraints. In calculations of the intermolecular interaction energy, each molecule bearing Coulombic charges was represente as a set of electrically neutral groups. At short separations between the group centers, the electrostatic interaction energy was calculate irectly as the sum of charge charge interactions, while at large separations the ipole ipole group group approximation was use. The cutoff istances for the charge charge an ipole ipole contributions were 20 an 100 Å, respectively. The Lennar Jones potentials escribing the exchange repulsion an ispersion interactions were cut off at a istance of 15 Å. The bulk water reservoir surrouning the SLB in Fig. 1 was treate implicitly by equating the chemical potential of confine water to that of bulk water [20, 21], as etermine in separate GCMC simulations of the latter. The fluctuations of the number of confine water molecules were simulate through repeate attempts to create or estruct a water molecule in the confine region. The water water interactions were escribe with the TIP4P force fiel , while the mixe water DLPE an water SAM interaction parameters were calculate using geometric mean combination rules. The substrate (SAM) sie of the simulation box was constructe base on an orthorhombic unit cell with two symmetrically istinct alkanethiolate molecules an perios a = 3c, b = c 3 where c = 4.08 Å is the lattice pffiffi constant of gol. The starting arrangement of the molecules in the unit cell was taken the same as foun in our early work  by global energy minimization. The simulation box was compose of 18 unit cells (3 unit cells along x axis an 6 unit cells along y), so that the number of alkanethiolate molecules in the substrate sie of the simulation box was 36 an the lateral imensions of the simulation box were L x = 3a = Å, L y = 6b = 42.4 Å. The starting configuration of the lipi sie of the simulation box was built up proceeing from the crystal-state bilayer configuration, as observe in the DLPE acetic aci crystal . To make the lipi an substrate sies of the system commensurable, the crystal-state bilayer configuration was slightly stretche along the x axis an compresse along the y axis so as to fit the lateral imensions of the simulation box. The area per lipi molecule in the resulting configuration prove to be 48.7 Å 2, which is close to a semi-empirical estimate of 51.2 Å 2 reporte by Nagle an Wiener  for flui-phase DLPE bilayers at 308 K. The GCMC simulation proceure use was iscusse in etail elsewhere [11, 12]. In brief, the simulations were performe with a fixe number of the bilayer an substrate molecules, so that the system was actually treate as a semi-gran canonical ensemble. A total of five types of ranom moves were attempte: insertion, eletion, an translational-rotational (hereafter isplacement) moves of water plus conformational an isplacement moves of DLPE an SAM molecules. To improve the acceptance probability of insertion an eletion moves, the Swensen Wang filtering  an an orientational bias proceure  were use. The former rejecte an improbable insertion or eletion of a ranomly selecte water molecule base on its position an a computationally cheep preictor of the associate energy. The latter i the same with respect to molecular orientation. The attempts to insert a water molecule were mae over the whole volume treate explicitly. The key quantity evaluate in our GCMC simulations was the normal pressure, p. It was calculate in the force form (as oppose to the virial form ) by summation of the z-components of the forces exerte on the DLPE bilayer by the SAM substrate an water. The total pressure p was represente as the sum two components, p ¼ p þ p h, where p was associate with irect bilayer substrate interactions an p h was the so-calle hyration (solvation) pressure  ue to the forces exerte on the bilayer by water molecules. (It is worth noting in this context that the hyration pressure p h is frequently use to mean the total pressure p operating between the substrates. Here we prefer to follow the efinition given by Evans an Markoni , where p h is just a component of p.) The irect pressure p was further partitione into contributions from electrostatic, ispersion, an exchange repulsion (steric) forces, p ¼ p elst þ p isp þ p rep, by collecting the forces associate with the respective terms of the intermolecular interaction potentials. The ahesion free energy was calculate by integrating the pressure-separation relation p(h) from the equilibrium separation, h 0, as efine by the conition ph ð 0 Þ ¼ 0, to the largest separation trie, h max, where the magnitue of p was within the respective statistical error. All the simulations were performe at a temperature of 308 K.
4 Page 4 of 6 Biointerphases (2012) 7:57 Consiering a fairly slow convergence of pressure , we ha to use very long GCMC runs an to check the reproucibility of the calculate values of pressure by comparing the results of inepenent runs iffering in the initial structure an/or the sequence of ranom numbers. The length of a GCMC run was passes, each comprising N 0 moves, where N 0 is the initial number of water molecules in a given pass. The first half of the run serve to equilibrate the system, while the ensemble averages were calculate in the secon half. For each particular separation h, 5 7 inepenent GCMC runs were performe an the calculate quantities were average out. The calculation error was estimate as the average absolute eviation from the mean. Typical curves emonstrating the convergence of pressure in the course of five inepenent GCMC runs are presente in Fig. 2. We first consier the case of the hyrophilic O-SAM substrate. The calculations of the pressure-separation relation p(h) were performe in orer of increasing confinement starting from h max = 43.5 Å, where the magnitue of p i not excee the respective average eviation, D p. The highest confinement trie for at h = 33 Å, which correspone to strongly repulsive bilayer substrate interaction. The calculate p(h) is shown in Fig. 3a, where positive an negative pressures correspon to repulsion an attraction, respectively. The curve shows a well efine minimum at h = 36 Å with a epth of about 0.7 kbar. The equilibrium separation is at h 0 & 34.3 Å. The hyration egree at the separation nearest to h 0 (h = 34.5 Å) is 6.6. The integration of p(h) from 34.3 to 43.5 Å results in the ahesion free energy W =-2.2 ± 0.3 kbar Å = - 22 ± 3 mj/m 2, which is close to the values calculate for the O-SAM/water/O-SAM an O-SAM/water/C-SAM systems (-26 ± 4 an -25 ± 3 mj/m 2, respectively) . The istribution of pressure over its iniviual components at the separation of strongest attraction (36 Å) is Fig. 2 Convergence of pressure in the course of five inepenent GCMC runs. The ata refer to the DLPE/water/O-SAM system at h = 36 Å Fig. 3 Pressure-separation relations for DLPE bilayer supporte on O-SAM (a) an C-SAM (b) shown in Fig. 4a. It can be seen that the factor responsible for ahesive attraction is the irect bilayer substrate interaction p, which is in turn etermine by the interplay between the attractive p elst strongly repulsive p rep an p isp, on one han, an, on the other. It is worth noting that the force fiel use in our simulations involves no explicit terms responsible for hyrogen boning. The latter is escribe by the electrostatic interaction of proton-onor an proton-acceptor groups, an hence the contribution to p ue to formation of hyrogen bons between the bilayer an substrate enters into p elst, while the contribution to pressure from hyrogen bons forme by water with the bilayer an substrate is a part of p h. As seen from Fig. 4a, the hyration forces play an important role in the total force balance: Being comparable in magnitue with p, the repulsive p h substantially weakens the water-meiate ahesion between the bilayer an substrate. The replacement of the hyrophilic O-SAM substrate by the hyrophobic C-SAM reuces the ahesive strength to values comparable with the calculation error (Fig. 3b). The minimum of the p(h) curve occurs somewhere between 37 an 38 Å an has a epth of about 0.1 ± 0.1 kbar. The equilibrium separation h 0 is at h = 36.8 Å. The hyration egree at the separation nearest to h 0 (h = 37 Å) is 7.2. The istribution of pressure over its components (Fig. 4b) is qualitatively similar to that foun in the DLPE/water/ O-SAM system, except for the lack of p elst because of the absence of electrostatic terms in the Williams potentials . The ahesion free energy W calculate from the p(h) curve in Fig. 3b is -1 ± 1 mj/m 2. The corresponing
5 Biointerphases (2012) 7:57 Fig. 4 Distribution of pressure over its physical components for DLPE supporte on O-SAM (a) an C-SAM (b) at separations corresponing to the minimum of the pressure-separation curve. Note that the pressure scales in a an b are ifferent experimental value of W is not available because the attempts to prepare an SLB by asorption of small unilamellar vesicles (SUV) onto C-SAM faile [28, 29]: The SUV asorption le to formation of a supporte lipi monolayer (SLM) with the hyrophobic tails irecte towar the hyrophobic SAM substrate. The associate ahesion energy has not been measure experimentally but it harly iffers significantly from the value of -88 ± 35 mj/m2 foun in AFM experiments with the C-SAM/water/C-SAM system . That is, the contact of the hyrophobic C-SAM substrate with the hyrophobic lipi tails is 1 2 orers of magnitue more favorable in ahesion energy compare to the contact with the hyrophilic lipi heas, as moele by our simulation of the DLPE/water/C-SAM system. It is very likely therefore that the ifference in ahesion energy is the main factor that etermines the preference of SLM over SLB on eposition of SUVs on C-SAM. As the confinement was increase, both of the DLPE/ water/sam systems showe a monotonous ecrease in the ensemble-average number of water molecules, hn i. In this respect, they were similar to the symmetric O-SAM/ water/o-sam system but iffere from the asymmetric O-SAM/water/C-SAM an symmetric C-SAM/water/CSAM ones, where the function hn i(h) showe a iscontinuity associate with capillary evaporation . The lack of capillary evaporation in the DLPE/water/SAM systems is not surprising in view of a high water affinity of the DLPE bilayer ue to an easy accessibility of its proton-acceptor an proton-onor groups to water molecules. A eep penetration of water into bilayer can be Page 5 of 6 Fig. 5 Snapshot of the DLPE/water/O-SAM system at h = 36 A. O, N, an P atoms of DLPE are shown in re, blue, an purple, respectively; S an O atoms of SAM are shown in green an re; water O atoms are shown in turquoise Fig. 6 Snapshot of the DLPE/water/C-SAM system at h = 37 A appreciate from snapshots of the DLPE/water/SAM systems in Figs. 5 an 6. In conclusion, this work represents a first attempt to simulate an SLB as an open system, where confine water is allowe to exchange molecules with surrouning bulk water so as to sustain the chemical equilibrium with the latter. Compare to the previous GCMC simulations concerne with the short-range repulsion between phospholipi bilayers [11, 12] similar simulations of SLBs in the region responsible for ahesion are more emaning an inexact because of much smaller magnitues of attractive pressure. This is particularly true of systems where the bilayer substrate ahesion energy is less than 1 mj/m2.
6 Page 6 of 6 Biointerphases (2012) 7:57 Unfortunately, the experimental ata on the ahesion forces operating in SLBs are limite by single systems [2, 31] so that our simulation results cannot be irectly compare with experiment. Nevertheless, the acceptable agreement of our previous results for the SAM/water/SAM systems  with the experimental ahesion energies provies a reason to hope that the approach suggeste in this an previous  works will be useful in preicting an interpreting the bilayer substrate ahesion strength. Acknowlegment This work was supporte by the Deutsche Forschungsgemeinschaft through grant GR 625/60-1. Open Access This article is istribute uner the terms of the Creative Commons Attribution License which permits any use, istribution, an reprouction in any meium, provie the original author(s) an the source are creite. References 1. Sackmann ES (1996) Science 271: Anerson TH, Min Y, Weirich KL, Zeng H, Fygenson D, Israelachvili JN (2009) Langmuir 25: Heine DR, Rammohan AR, Balakrishnan J (2007) Molec Simul 33: Tarek M, Tu K, Klein ML, Tobias DJ (1999) Biophys J 77: Roark M, Feller SE (2008) Langmuir 24: Xing C, Faller R (2008) J Phys Chem B 112: Xing C, Faller R (2009) J Chem Phys 131: Xing C, Ollila OHS, Vattulainen I, Faller R (2009) Soft Matter 5: Hoopes MI, Deserno M, Longo ML, Faller R (2008) J Chem Phys 129: Ró_zycki B, Weikl TR, Lipowsky R (2008) Phys Rev Lett 100: Pertsin A, Platonov D, Grunze M (2005) J Chem Phys 122: Pertsin A, Grunze M (2011) Curr Opin Colloi Interface Sci 16: Shelley JC, Patey GN (1994) J Chem Phys 100: Pertsin A, Grunze M (2012) J Chem Phys 137: Smonyrev AM, Berkowitz ML (1999) J Comput Chem 20: Pertsin AJ, Hahn J, Grossmann H-P (1994) J Comput Chem 15: Williams DE (1967) J Chem Phys 47: Mar W, Klein ML (1994) Langmuir 10: Jorgensen WL, Maxwell DS, Tirao-Rives J (1996) J Am Chem Soc 118: Frenkel D, Smit B (2002) Unerstaning molecular simulation: from algorithms to applications, 2n en. Acaemic Press, San Diego 21. Allen MP, Tilesley DJ (1987) Computer Simulation of Liquis. Clarenon Press, Oxfor 22. Jorgensen WL, Chanrasekhar J, Maura JD, Impey RW, Klein ML (1983) J Chem Phys 79: Pertsin AJ, Grunze M (1994) Langmuir 10: Nagle JF, Wiener MC (1988) Biochim Biophys Acta 942: Swensen RH, Wang J-S (1987) Phys Rev Lett 58: Shelley JC, Patey GN (1995) J Chem Phys 102: Evans R, Marconi UMB (1987) J Chem Phys 86: Lingler S, Rubinstein I, Knoll W, Offenhäusser A (1997) Langmuir 13: Keller CA, Kasemo B (1998) Biophys J 75: Clear SC, Nealey PF (1999) J Colloi Interface Sci 213: Valtiner M, Donalson SH Jr, Gebbie MA, Israelachvili JN (2012) J Am Chem Soc 134: