Comment pubs.acs.org/Langmuir
Comment on “Structural Properties of POPC Monolayers under Lateral Compression: Computer Simulations Analysis”
I
n a recent article, Huynh et al.1 carried out simulations of POPC monolayers at the water−air interface using the GAFF force field for lipids and the TIP3P model for water. We argue that (1) the apparent agreement between the simulated and measured surface pressure−area isotherms is coincidential and due to a cancellation of errors. Furthermore, we claim that (2) some of the simulations are stuck in a metastable state and thus do not represent the underlying model’s true predictions. Finally, we point out that simply shifting the surface pressure− area isotherms to match the experimental surface tension of water ignores microscopic interactions at the surface. This implies that (3) any force field used to simulate monolayers at the water−air interface must, in principle, produce the experimental surface tension of water. The simulations of ref 1 employed the NPγT ensemble, where γ relates to the surface pressure by the equation Π = γ0 − γ. The surface tension of the pure interface, γ0, was assigned the experimental value of 71.8 mN/m. However, according to our computations using the simulation parameters of ref 1, the surface tension of TIP3P is 51 mN/m. This is the value that should be used instead since the surface pressure is, by definition, the reduction of interfacial tension due to surfactant adsorption. It then follows that the reported surface pressures are some 20 mN/m larger than the true surface pressures present in the
simulations. Observing that GAFF underestimates the surface pressure of each leaflet of a bilayer roughly by 20 mN/m,2 one finds an error in the opposite direction. These errors thus cancel each other out and this leads to the seeming agreement between simulations and experiments, which is our claim (1). When the reported surface pressure is below 20 mN/m, the interfacial tension is higher than the tension of the pure interface (γ > 51 mN/m). This means that the surface pressure in the simulations is actually negative. This is not possible in thermodynamical equilibrium, but rather it implies metastability.3 Put another way, ref 1 predicts that the addition of lipids increases interfacial tension for large areas per lipid. This is nonphysical, for the entire point of surfactants is to lower the tension. This again can be understood in terms of metastability: the small system size and the careful preparation of initial conditions in ref 1 enforces a metastable uniform state enabling the system to reach a negative surface pressure. However, the minimum free energy state would actually see the monolayer phase separate into regions rich and poor in lipids, which would take the interfacial tension close to that of the pure interface. Our results in Figure 1 demonstrate how this equilibriation would manifest itself in molecular simulations. As a more general statement, monolayers with negative surface pressures can be simulated by carefully setting up the initial configurations, but
Figure 1. Final structures of simulations with (a) 66 and (b) 33 lipids per monolayer at the water−air interface with the model of the original publication.1 The red square denotes the size of the periodic box. Both simulations (NVT ensemble, area per lipid of 0.80 nm2) initially had the lipids uniformly distributed. During the 50 ns simulation, the smaller system remained uniform (b), resulting in an average interfacial tension of 61 mN/m, in agreement with ref 1. However, the monolayers in the larger system, less encumbered by finite size effects, spontaneously perforated, i.e., phase separated (a), and the interfacial tension dropped considerably to 53 mN/m and thus into a lower free energy state. Received: July 1, 2014 Published: September 26, 2014 © 2014 American Chemical Society
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dx.doi.org/10.1021/la5025845 | Langmuir 2015, 31, 886−887
Langmuir
Comment
this leads to a metastable state not seen in large scale experiments. This is analogous to the van der Waals equation of state, where producing supercooled configurations is certainly possible with delicate sample preparation, but the true equilibrium is dictated by the Maxwell equal area construction. This completes our claim (2). Next, we turn to the more general question of whether microscopic properties of monolayers can be studied with a model whose surface tension of water is wrong, i.e., our claim (3). One could argue that the incorrect surface tension simply shifts the simulated isotherm with a constant and that the properties of the monolayer as a function of surface pressure remain unchanged. However, the Langmuir adsorption model, and models related to it, suggest that changes in molecular interactions result in a nonlinear shift to the isotherm.4 Accordingly, one of us has recently shown for a lipid system that a change in the interfacial tension induced by a modification in the force field can indeed lead to a prominently nonlinear shift.5 This was argued to be due to a change in the microscopic composition of the interface. In conclusion, a constant shift of the isotherm is without a solid theoretical basis. The exact magnitude of the nonlinear correction, however, remains an open question.
Antti Lamberg† O. H. Samuli Ollila*,‡ †
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Department of Chemical Engineering, Kyoto University, Kyoto 615−8510, Japan ‡ Helsinki Biophysics and Biomembrane Group, Department of Biomedical Engineering and Computational Science, Aalto University, Espoo, Finland
AUTHOR INFORMATION
Corresponding Author
*E-mail: samuli.ollila@aalto.fi. Notes
The authors declare no competing financial interest.
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REFERENCES
(1) Huynh, L.; Perrot, N.; Beswick, V.; Rosilio, V.; Curmi, P. A.; Sanson, A.; Jamin, N. Structural Properties of POPC Monolayers under Lateral Compression: Computer Simulations Analysis. Langmuir 2014, 30, 564−573. (2) Siu, S. W. I.; Vacha, R.; Jungwirth, P.; Bockmann, R. A. Biomolecular Simulations of Membranes: Physical Properties from Different Force Fields. J. Chem. Phys. 2008, 128, 125103. (3) Landau, L. D.; Lifshitz, E. M. Statistical Physics, 3rd ed.; Butterworth-Heinemann: Oxford, U.K., 1996. (4) Hill, T. L. An Introduction to Statistical Thermodynamics; Dover Publications: Mineola, NY, 1986. (5) Lamberg, A.; Taniguchi, T. Coarse-Grained Computational Studies of Supported Bilayers: Current Problems and Their Root Causes. J. Phys. Chem. B 2014, 118, 10643−10652.
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