Interaction of Wedge-Shaped Proteins in Flat Bilayer Membranes T. Sintes and A. Baumgaertner* Forum Modellierung, Forschungszentrum, 52425 Ju ¨ lich, Germany ReceiVed: January 8, 1998; In Final Form: March 12, 1998 We present extensively Monte-Carlo simulations of two conically-shaped proteins in parallel and antiparallel relative orientation, embedded in a flat lipid bilayer membrane with zero bending elasticity. We found two protein attractive regimes. The first one, in the range r s < σ L , where σ L is the lipid diameter and r s the distance between the surfaces of the two proteins, is due to depletion effects. The second one, in the range 1 < r s /σ L < 6, originates from the density and orientational fluctuations of the lipids around each protein. It is found that the attractive force decays exponentially with a correlation length /σ L ≈ 3.2 independent of the shape and the size of the proteins. I. Introduction Cell membranes are a highly heterogeneous mixture of lipids and inhomogeneities like proteins and cholesterols. In many biological membranes, proteins may cover almost 50% of the surface area, so that proteins are separated by a few layers of lipids and tend to pack even in the absence of cytoskeleton interactions. Lipid-protein interactions play therefore a crucial role in the clustering process and thus, in the control of membrane functionality 1,2 and structure. It may modulate the activity of membrane-bound enzymes 3 or lateral distribution of proteins on the membrane surface. 4 Several mechanisms have been proposed to explain the aggregation process. Direct interactions between inclusions due to Van der Waals and electromagnetic forces are well under- stood. 5 They are important, for example, at temperature driven phase separations among lipids and proteins 6 or between dipoles on pairs of antiparallel R-helices. 7 Indirect interactions that are membrane-induced by imposed perturbations on the bilayer structure, have been also largely considered. Local curvature effects and membrane undulations are predicted to lead to long- range interactions of 1/R 4 type. 8-13 At short distances, of the order of a few lipid layers between two proteins, a nonspecific lipid-mediated attraction may exist 14-17 that is shown to decay exponentially. In addition, the aggregation of proteins can also be related to the presence of asymmetric proteins or to asymmetric properties of curved membranes. 18 In general, amphiphilic monolayers have a spontaneous curvature. In bilayers, the tendency to curve is balanced and it adopts, locally, a flat configuration. However, the presence of inclusions is shown in one-dimension 19 to decouple the two monolayers. As a consequence, the spontaneous curvature may dominate the perturbation profile and the interaction between inclusions depends on the magnitude of the spontaneous curvature and the inclusion boundary condition. For symmetric inclusions the force is found to be attractive, but for inclusions that are asymmetric under reflection in the plane of the membrane the character of the force may depend on the temperature and bending energies. 9-11 A different situation corresponds to a bilayer composed of amphiphiles with zero spontaneous curvature or when the stretching dominates the bending energy in the limit of infinite rigidity. Under such conditions one expects that the presence of conical inclusions may affect the local fluctuation of lipids and, thus, the range and sign of the interaction at short distances. Here we present a detailed Monte Carlo simulation of two conically shaped proteins embedded in a lipid bilayer membrane. We have estimated the forces and the range of interaction for proteins being in a parallel or antiparallel relative orientation. In both cases we found two types of lipid-mediated attractive forces. The first one, limited to the depletion zone around the proteins, r < σ L , where σ L is the thickness of the lipid molecule, can be described in terms of the Asakura-Oosawa approach. 20 The second type is induced by density and orientational fluctuations of the lipids around a protein. The range of this fluctuation-induced attraction seems to decay exponentially, although the range of attraction is rather large and in the order of 1.5 < r/σ L < 6. The result in this regime has been compared with previous studies 21 with cylindrical type inclusions and different diameter sizes obtaining the same behavior. II. Model Membrane We have used Monte Carlo methodes to investigate a model lipid-bilayer membrane at air-water interface 23 containing two conically shaped model proteins. Two cases have been considered: the proteins being in a parallel or antiparallel orientation with respect to each other (see Figure 1). In both cases, we have introduced an assembly of lipids per layer such that we have an equal density in each layer. Periodic boundary conditions in the x-y plane have been applied. The total number of lipids in both layers is N L ≈ 1000. The actual number of lipids in each layer, however, depends slightly on the shapes and the mutual orientation of the conical proteins. A lipid molecule has been modelled by a flexible chain of M ) 5 effective monomers of diameter σ L ) 4 Å. The proteins, whose axes are oriented perpendicularly to the x-y plane, have a maximum diameter of σ P ) 16 Å and a minimum of σ L (Figure 1). The size of the cell is chosen to be L 2 ) 22500 Å 2 . Finite size effects for the equilibrium properties of the membrane are negligible. In this coarse-grained representation of the lipid molecule, each monomer represents a group of about 3 or 4 successive chemical monomers (CH 2 groups) of a real lipid molecule. 24 * To whom correspondence should be addressed. Forum Modellierung (MOD), Forschungszentrum Juelich, 52425 Juelich, Germany. www: http:/ www.kfa-juelich.de/mod. 7050 J. Phys. Chem. B 1998, 102, 7050-7057 S1089-5647(98)00726-3 CCC: $15.00 © 1998 American Chemical Society Published on Web 08/19/1998