Pre-transition effects mediate forces of assembly between transmembrane proteins.

We present a mechanism for a generic, powerful force of assembly and mobility for transmembrane proteins in lipid bilayers. This force is a pre-transition (or pre-melting) effect for the first-order transition between ordered and disordered phases in the membrane. Using large-scale molecular simulation, we show that a protein with hydrophobic thickness equal to that of the disordered phase embedded in an ordered bilayer stabilizes a microscopic order-disorder interface. The stiffness of that interface is finite. When two such proteins approach each other, they assemble because assembly reduces the net interfacial energy. Analogous to the hydrophobic effect, we refer to this phenomenon as the 'orderphobic effect'. The effect is mediated by proximity to the order-disorder phase transition and the size and hydrophobic mismatch of the protein. The strength and range of forces arising from this effect are significantly larger than those that could arise from membrane elasticity for the membranes considered.

Introduction

This paper presents implications of first-order order–disorder phase transitions in lipid bilayers. The fluid mosaic model (Singer and Nicolson, 1972) and the lipid raft hypothesis (Simons and Ikonen, 1997; Munro, 2003) have guided intuition on how proteins diffuse and assemble in biological membranes—ordered clusters floating in an otherwise disordered fluid membrane (Simons and Toomre, 2000; Lingwood and Simons, 2010). However, recent advances show that a significant proportion of the membrane is liquid-ordered (Swamy et al., 2006; Owen et al., 2012; Polozov et al., 2008), with coexistence between the liquid-ordered and disordered phases. This coexistence suggests that effects of an order–disorder transition might be at play in the assembly of proteins. This possibility is studied here by examining the effects mediated by the simplest related order–disorder transition, that between solid-ordered and liquid-disordered phases.

Specifically, with molecular simulation, we study a coarse-grained model of a hydrated one-component bilayer and proteins that are added to the membrane. The model membrane exhibits two distinct phases—a solid-ordered phase and a liquid-disordered phase—and a first-order transition between them. We find that a transmembrane protein in the ordered bilayer can induce effects that resemble pre-melting (Lipowsky, 1982; 1984; Limmer and Chandler, 2014). In particular, within the otherwise ordered membrane phase, mesoscopic disordered domains surround proteins that favor disordered states. Importantly, the boundary of the domains resembles a stable, fluctuating order–disorder interface. The dynamic equilibrium established at the boundary allows the protein and its surrounding domain to diffuse. Moreover, because the interface has a finite stiffness, neighboring proteins can experience a membrane-induced force of adhesion, an attractive force that is distinctly stronger and can act over significantly larger lengths than those that can arise from simple elastic deformations of the membrane (Dan et al., 1993; Goulian et al., 1993; Phillips et al., 2009; Kim et al., 1998; Haselwandter and Phillips, 2013).

This force between transmembrane proteins is analogous to forces of interaction between hydrated hydrophobic objects. In particular, extended hydrophobic surfaces in water can nucleate vapor–liquid-like interfaces. In the presence of such interfaces, hydrophobic objects cluster to reduce the net interfacial free energy. This microscopic pre-transition effect manifesting the liquid–vapor phase transition can occur at ambient conditions (Chandler, 2005; Lum et al., 1999; Willard and Chandler, 2008; Stillinger, 1973; ten Wolde and Chandler, 2002; Mittal and Hummer, 2008; Patel et al., 2011; 2012). In the transmembrane case, we show here that a protein favoring the disordered phase creates a similar pre-transition effect. In this case it manifests the order–disorder transition of a lipid bilayer. Like the raft hypothesis, therefore, clusters do indeed form, but the mechanism for their assembly and mobility emerge as consequences of order–disorder interfaces in an otherwise ordered phase. We refer to this phenomenon as the 'orderphobic effect'.

While considering the effect with one specific order–disorder transition, one should bear in mind its generic nature. The orderphobic effect should be a general consequence of a first-order transition, whether the transition is between solid-ordered and liquid-disordered phases as considered explicitly herein, or between liquid-ordered and liquid-disordered phases as in multicomponent membrane systems. More is said on this point in the Implications section of this paper.

The order–disorder transition is a first-order phase transition

We choose the MARTINI model of hydrated dipalmitoyl phosphatidylcholine (DPPC) lipid bilayers (Marrink et al., 2007) to illustrate the orderphobic effect. See Materials and methods. This membrane model exhibits an ordered phase and a disordered phase. Figure 1A contrasts configurations from the two phases, and it shows our estimated phase boundary between the two phases. The ordered phase has regular tail packing compared to the disorganized tail arrangement of the disordered phase. A consequence of the regular tail packing is that hydrophobic thickness of the ordered phase, is larger than that of the disordered phase, . Correspondingly, the area per lipid in the ordered phase is smaller than that in the disordered phase.

Figure 1.

First-order phase transition in a model lipid bilayer.

(A) Order–disorder phase diagram in the tension–temperature, , plane. The lateral pressure across the membrane is . Points are estimated from 10 independent heating runs like those illustrated in Appendix 1–figure 1 for a periodic system with 128 lipids. Insets are cross sections showing configurations of a bilayer with 3200 lipids in the ordered and disordered phases. The heads are colored gray while the tails are colored pink. Water particles are omitted for clarity. The hydrophobic thicknesses, and , are the average vertical distances from the first tail particle of the upper monolayer to that of the lower monolayer. A macroscopic membrane buckles for all . Snapshots of the last tail beads in one monolayer of each phase are shown to illustrate the difference in packing. (B) Snapshot of a system showing coexistence between the ordered and disordered phases. The gray contour line indicates the location of the interface separating the ordered and disordered regions. The snapshot is a top view of the bilayer showing the tail-end particles of each lipid in one monolayer. is the distance of the instantaneous interface from a reference horizontal axis. (C) Fourier spectrum of . The line is the small- capillarity-theory behavior with  pN.

DOI: http://dx.doi.org/10.7554/eLife.13150.003

Appendix 1—figure 1.

Structural measures of different phases as a function of temperature, .

(A) Variation in area per lipid with temperature during heating and cooling shows finite jumps and hysteresis. (B) Average local orientational order, , also shows finite jumps as a function of temperature while heating and cooling. Magnitudes of heating and cooling rates are 3 K/µs.

DOI: http://dx.doi.org/10.7554/eLife.13150.010

Rendering the end particles of all the lipid chains in one of the two monolayers provides a convenient visual representation that distinguishes the two phases. These tail-end particles appear hexagonally-packed in the ordered phase and randomly arranged in the disordered phase. Regions that appear empty in this rendering are in fact typically filled by non tail-end particles or by tail-end particles from the other lipid monolayer.

To quantify the distinctions between the two phases, we consider a local rotational-invariant (Nelson, 2002; Halperin and Nelson, 1978; Frenkel et al., 1980), , where is the angle between an arbitrary axis and a vector connecting tail-end particle to tail-end particle , and the summation is over the six nearest neighbors of particle . The equilibrium average, , is 1 for a perfect hexagonal packing, and it is 1/6 or smaller in the absence of bond-orientation correlations. Small periodically replicated samples of the hydrated DPPC membrane exhibit hysteretic changes in area per lipid and in during heating and cooling. See Appendix, and Marrink et al. (2005) and Rodgers et al. (2012). To establish whether the first-order-like behavior persists to large scales and thus actually manifests a phase transition, we consider larger systems and the behavior of the interface that separates the ordered and disordered phases.

Figure 1B shows coexistence for a system size of N = 3900 lipids with an interface between the two phases. To analyze interfacial fluctuations, we first identify the location of the interface at each instant. This location is found with a two-dimensional version of the three-dimensional constructions described in Limmer and Chandler (2014) and Willard and Chandler (2010). Specifically, and as discussed in Materials and methods, the interface is the line in the plane of the bilayer with an intermediate coarse-grained value of the orientational-order density,

where is the position of the th tail-end particle projected onto a plane parallel to that of the bilayer, is a two-dimensional vector specifying a position in that plane, and is Dirac’s delta function. We focus on this field rather than the tail-end number density, , because the difference between the two phases is larger for typical orientational-order than for typical tail-end density.

A director density field, , could also be used to distinguish disordered regions from ordered regions. would specify the degree to which the hydrophobic chain of lipid is perpendicular to the average plane of the membrane. A field of this form would be useful for systems where liquid-ordered behavior occurs in the absence of solid-ordered behavior. Multicomponent membranes, for example, can exist in solid-ordered, liquid-ordered, and liquid-disordered states. For constructing the order–disorder interface of the simple one-component membrane considered here, however, offers little more information than .

Figure 1C shows the Fourier spectrum of the height fluctuations of this interface, . Two different system sizes are studied, with the larger system having approximately double the interface length of the smaller system. The Fourier component is related to the height fluctuation as where is a point along the horizontal in Figure 1B. Here, , and is the box length. With periodic boundary conditions, , . According to capillarity theory for crystal–liquid interfaces (Nozières, 1992; Fisher et al., 1982),  for small , with being Boltzmann’s constant.

Given the proportionality with at small (i.e., wavelengths larger than 10 nm), comparison of the proportionality constants from simulation and capillarity theory determines the interfacial stiffness (Camley et al., 2010), yielding  pN. This value is significantly larger than the prior estimate of interfacial stiffness for this model,  pN (Marrink et al., 2005). That prior estimate was obtained from simulations of coarsening of the ordered phase.

Because the ordered phase has a hexagonal packing, the interfacial stiffness depends on the angle between the interface and the lattice of the ordered phase. For a hexagonal lattice, there are three symmetric orientations for which the interfacial stiffnesses are equal. We will see that for the model we have simulated there appears to be only little angle dependence. Irrespective of that angle dependence, the stability of the interface and the quantitative consistency with capillary scaling provide our evidence for the order–disorder transition being a first-order transition in the model we have simulated.

The system sizes we have considered contain up to 107 particles, allowing for membranes with N ≈ 104 lipids, and requiring 10 μs to equilibrate. As such, our straightforward simulations are unable to determine whether the ordered phase is hexatic or crystal because correlation functions that would distinguish one from the other (Nelson et al., 1982) require equilibrating systems at least 10 times larger (Bernard and Krauth, 2011). Similarly, we are unable to determine the range of conditions for which the membranes organize with ripples and with tilted lipids (Sirota et al., 1988; Smith et al., 1990). Presumably, the ordered domain of the phase diagram in Figure 1A partitions into several subdomains coinciding with one or more of these possibilities. With advanced sampling techniques (Frenkel and Smit, 2001), free energy functions of characteristic order parameters can be computed to estimate the positions of boundaries between these various ordered behaviors. Here, we do not pursue this additional level of detail in the phase diagram because the additional boundaries refer to continuous transitions (Sirota et al., 1988). It is only the first-order transition, with its discontinuous change between ordered and disordered phases, that supports coexistence with a finite interfacial stiffness, and it is this stiffness that results in the orderphobic effect, which we turn to now.

Transmembrane proteins can disfavor the ordered membrane

A disordering (i.e., orderphobic) transmembrane protein is one that solvates more favorably in the disordered phase than in the ordered phase. The disordering effect of the protein could be produced by specific side chain structures. See Appendix. Here, in the main text, we consider a simpler mechanism. In particular, we have chosen to focus on the size of the protein’s hydrophobic thickness and the extent to which that thickness matches the thickness of the membrane’s hydrophobic layer (Killian, 1998; Sharpe et al., 2010). See Figure 2.

Figure 2.

Model proteins in the bilayer.

(A) Idealized cylindrical protein-like solutes with radius and hydrophobic thickness (magenta). The hydrophilic caps of the protein are shown in white. (B) Cross section of the lipid bilayer in the ordered phase containing a model protein of radius 2.7 nm with a hydrophobic thickness  nm . (C) The radial variation of the order parameters (right axis) and (left axis) show disorder in the vicinity of the protein of radius 1.9 nm. (D) Comparison of the radial order parameter variation for three different proteins shows an increase in the extent of the induced disorder region with protein radius.

DOI: http://dx.doi.org/10.7554/eLife.13150.004

The membrane’s hydrophobic layer is thicker in the ordered state than in the disordered state. For instance, at zero lateral pressure and 294 K in the model DPPC membrane, we find that the average thicknesses of the hydrophobic layers in the ordered and disordered states are  nm and  nm, respectively. A transmembrane protein with hydrophobic thickness of size  nm will therefore favor the structure of the disordered phase. If the protein is large enough, it can melt the ordered phase near the protein and result in the formation of an order–disorder interface.

Spatial variation of the order parameter field characterizes the spatial extent of the pre-melting layer

To evaluate whether a model protein is nucleating a disordered domain in its vicinity, we calculate the average of the orientational-order density field as a function of , (right axis of Figure 2C). It exhibits oscillations manifesting the atomistic granularity of the system. Dividing by the mean density largely removes these oscillations.

A profile of this ratio in the vicinity of the protein is depicted in Figure 2C (left axis). It changes approximately sigmoidally, connecting its values of 0.15 and 0.45 in the disordered and ordered phases, respectively. The shape of the profile suggests the formation of an order–disorder interface (Rowlinson and Widom, 1982). Further, the increase in the spatial extent of the disordered region with the increasing size of the protein, Figure 2D, is indicative of length scale dependent broadening effects brought about by capillary fluctuations. These impressions can be quantified by analyzing fluctuations of the instantaneous interface, which we turn to now.

An orderphobic protein nucleates a fluctuating order–disorder interface

Figure 3A shows a configuration of the instantaneous interface that forms around the orderphobic protein shown in Figure 2B. The interface is identified as described above. A video of its dynamics is provided as Video 1. As is common in crystal–liquid interfaces, the interface nucleated by an orderphobic protein may exhibit hexagonal faceting (Nozières, 1992), remnants of which can be observed in Figure 3A.

Figure 3.

Soft order–disorder interface.

(A) Arrangement of the tail-end particles of the top monolayer corresponding to the protein in Figure 2B. Far away from the protein, the tail-end particles show hexagonal-like packing and are in the ordered state. Proximal to the protein, it can be seen that the tail-end particles are randomly arranged, and resemble the disordered phase. The line connected by the black points denotes the instantaneous order–disorder interface. (B) The fluctuations in the radius of the order–disorder interface are consistent with the fluctuations of a free order–disorder interface at coexistence. is the mean radius of the order–disorder interface surrounding a model protein of radius .

DOI: http://dx.doi.org/10.7554/eLife.13150.005

Video 1.

Instantaneous interface around an orderphobic protein.

Also uploaded to https://goo.gl/NBQJP9.

DOI: http://dx.doi.org/10.7554/eLife.13150.006

The mean interface is a circle of radius . Fourier analysis of fluctuations about that circle yields a spectrum of components. To the extent that these fluctuations obey statistics of capillary wave theory for a circular interface, the mean-square fluctuation for the th component is , where and , , and is the order–disorder interfacial stiffness, neglecting the dependence on the angle between the interface and the lattice. The discrete values of reflect periodic boundary conditions going full circle around the model protein.

In Figure 3B, we use the interfacial stiffness from the free interface ( pN) separating coexisting ordered and disordered phases with the capillary theory expression, and its corresponding spectrum, to compare with the spectrum of the protein-induced interface. The agreement between the theory, the free interface and the protein-induced interface is good, and it improves as the radius of the orderphobic protein increases and the wave vector decreases. This agreement indicates that the orderphobic protein does indeed nucleate an interface manifesting the order–disorder transition. The deviations of the fluctuations of the free interface from capillary wave theory occur for  nm−1, corresponding to wavelengths  nm, and a mean interface radius  nm. Indeed, Figure 2 suggests that even a small protein of radius 0.5 nm, which supports an interface of radius  nm, is sufficient to induce an order–disorder interface with fluctuations consistent with capillary theory.

The orderphobic effect generates forces of assembly and facilitates protein mobility

Figure 4 shows three snapshots from a typical trajectory initiated with two orderphobic proteins of radius 1.5 nm separated by a distance of 14 nm. Each induces a disordered region in its vicinity, with soft interfaces separating the ordered and disordered regions. The free energy of the separated state is approximately , where is the perimeter of the order–disorder interface around protein . On average, . After a few hundred nanoseconds, a fluctuation occurs where the two interfaces combine. While the single large interface remains intact, the finite tension of the interface pulls the two proteins together. Eventually, the tension pulls the two proteins together with a final perimeter, , that is typically much smaller than . A video of its dynamics is provided as Video 2.

Figure 4.

Demonstration of the orderphobic force: two proteins separated by a center-to-center distance of 14 nm are simulated at 309 K. 

Snapshots at various times reveal the process of assembly in which the two order–disorder interfaces merge into a single interface.

DOI: http://dx.doi.org/10.7554/eLife.13150.007

Video 2.

Assembly of two orderphobic proteins.

Also uploaded to https://goo.gl/HXS0j7.

DOI: http://dx.doi.org/10.7554/eLife.13150.008

After the separated interfaces join, the assembly process occurs on the time scale of microseconds. This time is required for the proteins to push away lipids that lie in the path of the assembling proteins. Given this time scale, a reversible work calculation of the binding free energy would best control both the distance and the number of lipids between the proteins. Moreover, the evident role of interfacial fluctuations indicates that the transition state ensemble for assembly must involve an interplay between inter-protein separations and lipid ordering as well as lipid concentration.

While we leave the study of reversible work surfaces and transition state ensembles to future work, it seems already clear that the net driving force for assembly is large compared to thermal energies. For example, with a model orderphobic protein radius of 1.5 nm, we find . The range over which the force acts is given by the average radius of the two interfaces, . This range is further amplified by the width of the interface, which is of for one-dimensional interfaces in two-dimensional systems (Kardar, 2007). The typical range is ≈10 to 30 nm. In comparison, given the elastic moduli of the membranes we consider, elastic responses will generate attractive forces between transmembrane proteins that are much smaller in strength and range, typically and 1 nm, respectively (Haselwandter and Phillips, 2013; de Meyer et al., 2008). Moreover, similarly weak and short ranged forces are found from solvation theory that accounts for linear response in microscopic detail while not accounting for the possibility of an underlying phase transition (Lagüe et al., 1998).

As in the hydrophobic effect (Chandler, 2005), the strength and range of the orderphobic force leverages the power of a phase transition, depending in this case on the ability of the orderphobic protein to induce a disordered layer in its vicinity. This ability depends upon the proximity to the membrane’s phase transition, and, for the simple protein models considered in this paper, it depends upon the protein’s radius and hydrophobic mismatch with the membrane. The spatial extent of the disordered region increases with proximity to phase coexistence as shown in Figure 5A.

Figure 5.

Strength of the orderphobic force.

(A) Radial variation of the order parameter showing the extent of the disordered region as a function of temperature, for a protein of radius 1.9 nm and hydrophobic thickness 2.3 nm. The extent of the disordered region increases as the melting temperature is approached, at zero surface tension. (B) Comparison of the radial variation of the order parameter for different hydrophobic mismatches. Proteins with no mismatch do not create any disordered region. (C) Arrangement of lipids around a protein with negative mismatch. (D) Arrangement of lipids around a protein with zero mismatch.

DOI: http://dx.doi.org/10.7554/eLife.13150.009

Furthermore, Figure 5B shows that the strength of the effect is maximal for a hydrophobic thickness equal to that of the disordered phase, and it decreases as the hydrophobic thickness approaches that of the ordered phase. In the case of zero mismatch (i.e., ) the value of the order parameter in the vicinity of the protein is consistent with that of a pure bilayer in the ordered state. Therefore, the model proteins with zero mismatch do not induce a disordered region, and the orderphobic effect vanishes. See Figure 5B and D.

Figure 4 also shows that the orderphobic effect produces excess mobility, by proteins melting order in a surrounding microscopic layer and by facilitating the motions of neighboring proteins. This finding explains how protein mobility and reorganization can be relatively facile in the so-called 'gel' phases of membranes. Further information on this phenomenon is provided in Appendix. Our prediction of enhanced lipid mobility surrounding orderphobic proteins may be amenable to experimental tests by single molecule tracking techniques (Eggeling et al., 2009).

Implications of the orderphobic effect and related phenomena in biological membranes

Biological membranes and transmembrane proteins are far more complicated than the models considered in this paper. Part of the complexity is associated with multiple components, which allow for more than one order–disorder transition. For example, with a membrane composed of three components, coexistence can be established between liquid-ordered and liquid-disordered phases (Veatch and Keller, 2005), and both of these phases exist in bio-membranes (Swamy et al., 2006; Owen et al., 2012; Polozov et al., 2008). The fact that liquid-ordered and liquid-disordered phases can coexist with finite line tension (Veatch and Keller, 2005) implies the existence of a first-order transition between them (Chandler, 1987) and thus the relevance of the orderphobic effect. This effect is much wider in applicability than the Casimir effect (Machta et al., 2012), which applies only within the much smaller range of conditions where the first-order transition reaches its limiting case of criticality. A director density for hydrophobic chains serves as the order parameter distinguishing liquid-ordered and liquid-disordered phases. The strength and range of orderphobic effects that will arise from this order–disorder transition merit future investigation. Modeling might build from recent numerical work on the liquid-ordered phase (Risselada and Marrink, 2008).

Bear in mind that the strength and range of the orderphobic effect depends upon the proximity of the order–disorder transition. This proximity can be changed by changing temperature, as illustrated in Figure 5A. With many components in play, the proximity can also be changed by varying membrane composition. One can therefore anticipate that the strength and range of orderphobic effects will depend upon, for example, cholesterol concentrations. It will also depend upon the presence of additional proteins, and the domains formed with those proteins themselves depend upon the orderphobic effect.

Another source of complexity is the side-chain structure of transmembrane proteins. These side chains can affect the packing of lipid chains. To the extent that lipid packing is disrupted, even small -helix proteins can be orderphobic. Evidence for this assessment is provided in Appendix. Thus, the orderphobic effect can lead to clustering of transmembrane -helices. Moreover, just as the strength and range of the orderphobic effect can be modified by changing the radius and mismatch of our model proteins, the strength and range of the orderphobic effect will also be affected by the structure of protein side chains. Further, an obvious consequence of the orderphobic effect is the existence of a driving force that will move orderphobic proteins from an ordered phase to a disordered phase, and the creation of large disordered domains as a result of clustering orderphobic proteins. Both of these effects have been noted in simulations of disordering -helix proteins in a membrane exhibiting coexisting liquid-ordered and liquid disordered domains (Schäfer et al., 2011; Domański et al., 1818).

Further, there is a dual to the orderphobic effect: a transmembrane protein in the disordered phase that favors the ordered phase can nucleate an ordered region and order–disorder interface. For example, one of our model proteins with a positive mismatch () would induce order in its vicinity. This effect is illustrated in the Appendix. Interfaces separating the ordered and disordered regions will again provide a force for assembly. This case corresponds to the situation of lipid rafts (Simons and Ikonen, 1997), which consists of ordered domains floating in otherwise disordered membranes. The stable interface separating domains then serves as a concrete geometrical definition of the raft. This orderphilic effect will depend upon the extent to which the surface of the transmembrane protein is commensurate with the ordered phase structure. Hydrophobic mismatch is but one possibility. -sheets that align neighboring lipids are others. The fact that the orderphilic effect is a pre-transition effect for the first-order transition between ordered and disordered phases implies it should occur in disordered membranes that are thermodynamically close to coexistence between liquid-ordered and liquid-disordered phases.

The orderphobic effect may also be of direct relevance in understanding the behavior of lung-surfactant monolayers. The primary component of these monolayers is the lipid DPPC, with melting temperature higher than physiological temperature (41°C), and a small proportion of cholesterol, and proteins. These monolayers undergo cyclic surface tension mediated phase transitions between the ordered and disordered phases (Nag et al., 1998). The results of this paper are also applicable to lipid monolayers and could govern the diffusion and assembly of proteins embedded within the relatively rigid ordered phases.

Finally, we speculate that the orderphobic effect plays important roles in membrane fusion, budding, and cell signaling (Fratti et al., 2004; Zick et al., 2014; Qi et al., 2001; James and Vale, 2012; Różycki et al., 2012). In the case of fusion, it would appear that one important role is to promote fluctuations in an otherwise stable membrane. Otherwise, it is difficult to conceive of a mechanism by which thermal agitation would be sufficient to destabilize microscopic sections of membranes. Such destabilization seems necessary for initiating and facilitating membrane fusion. Many proteins are involved in such processes (Fratti et al., 2004; Fasshauer et al., 1998; Wickner and Schekman, 2008), but it may not be a coincidence that the hydrophobic thicknesses of SNARE proteins are 25% smaller than that of the ordered membrane states (Milovanovic et al., 2015; Stein et al., 2015).

Materials and methods

Molecular simulations

We simulate the MARTINI coarse-grained force field using the GROMACS molecular dynamics package (Marrink et al., 2007; Pronk et al., 2013). ‘Antifreeze’ particles are added to the solvent to ensure that the solvent does not freeze over the temperature range considered in the simulations as in Marrink et al. (2007). Thermostats and barostats control temperature and pressure, and checks were performed to assure that different thermostats and barostats yielded similar results (Frenkel and Smit, 2001). The hydrophobic cores of our idealized proteins are constructed using the same coarse-grained beads as the lipid tails (particle C1 in the MARTINI topology Marrink et al. (2007)). Similarly, the hydrophilic caps are constructed using the first bead of the DPPC head group (Q0, in the MARTINI topology). The protein beads also have bonded interactions where the bond length is 0.45 nm and the bond angle is set to 180°. The associated harmonic force constants for the bond lengths and angles are 1250 kJmol−1nm−2 and 25 kJmol−1rad−2. Based on the hydrophobic mismatch with the bilayers, the proteins are classified into three categories: (i) positive mismatch () (ii) negative mismatch () and (iii) no mismatch (). To create different mismatches, we alter the number of beads in the protein core. These idealized proteins do not contain charges.

Proteins are embedded in the equilibrated bilayer at 279 K. The resulting system is then heated to the required temperature and equilibrated for another 1.2 µs. All the subsequent averages are performed using 10 independent trajectories each 600 ns long. The assembly of proteins is also performed using the same DPPC bilayer system with 3200 lipids and 50000 water beads. In this case, two proteins are inserted in this bilayer with centers at a distance of 14 nm and the simulation is carried out at 309 K.

The flat interface is stabilized by juxtaposing an ordered bilayer equilibrated at 285 K and zero lateral pressure with a disordered bilayer equilibrated at the same conditions corresponding to the cooling and heating curves of the hysteresis loop in Appendix 1—figure 1, respectively. The system thus constructed is equilibrated in the ensemble with fixed temperature, volume, and numbers of particles. This ensemble allows for maintaining an area per lipid intermediate between the two phases, thus stabilizing the interface.

Instantaneous interface

For the purpose of obtaining a smooth and continuous interface, is coarse grained by replacing Dirac’s delta function with a finite-width Gaussian, . The replacement changes to . The coarse-graining width, , is chosen to be the average separation between tail-end particles and when in the ordered phase is 1/10. This choice yields a value of  nm. The instantaneous order–disorder interface is the set of points satisfying . Here, and are evaluated in the disordered and ordered phases, respectively. At zero lateral pressure and 294 K, we find nm−2 and  nm−2. For numerics, a square lattice tiles the average plane of the bilayer, and the coarse-grained field is evaluated at each lattice node. Values between are determined by interpolation. For convenience, the Gaussian function is truncated and shifted to zero at 3. Any value of within the range, 1 nm 2 nm gives nearly identical . Outside that range, larger values obscure detail by excessive smoothing, and smaller values obscure detail by capturing a high density of short-lived bubbles of disorder.

In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.

Thank you for submitting your work entitled "Pre-transition effects mediate forces of assembly between transmembrane proteins" for consideration by eLife. Your article has been reviewed by 3 peer reviewers, one of whom is a member of our Board of Reviewing Editors, and the evaluation has been overseen by a Reviewing Editor and Richard Aldrich as the Senior Editor. Two of the three reviewers, Gerhard Hummer and Siewert-Jan Marrink, have agreed to share their identity. The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

This work introduces a new concept to understand membrane protein associations. It suggests that clustering of membrane proteins may not be a consequence of inter-protein or protein-lipid "mismatches" (e.g., membrane thickness as suggested by Milovanovic et al. Hydrophobic mismatch sorts SNARE proteins into distinct membrane domains. Nat Commun 6:5984. doi: 10.1038/ncomms6984, 2015), but rather by the differences in membrane thickness in difference "phases" of a membrane. If transmembrane domains are shorter than the thickness of a particular phase, they would then prefer to be in a phase that matches the length of the transmembrane domains, hence clustering in these areas. Thus, clustering of certain membrane proteins (such as SNAREs) may be a consequence of this "order-phobic" (but see comment 6 below) effect.

More specifically, in this work, simulations of coarse-grained lipid membrane models and of membrane/protein models show that (1) transmembrane proteins can induce a local order/disorder transition in a lipid membrane at conditions close to phase coexistence, and (2) that such local phase separation can drive protein association by a reduction of the interfacial free energy between the ordered and disordered lipid phases. These effects should be general in lipid membranes at conditions close to an order/disorder transition. By using orientational order parameters, the phase boundary in the membrane could be clearly resolved, enabling a characterization of its properties. In particular, the fluctuations of the length and shape of the boundary are shown to follow a capillary wave model down to almost molecular length scales. The observation of nanoscale phase separation induced by transmembrane proteins perturbing the local structure should be of interest not only to the physico-chemical community but also to bioscientists. In particular, it may play a role in lipid-mediated assembly of integral membrane protein complexes and supercomplexes.

While the reviewers and editors found this work interesting, concerns were raised as outlined below that need to be addressed in a revised version before a decision can be made. In particular, the authors are asked to respond to the concern about the biological relevance of the particular phase transition. If possible the authors are encouraged to perform a simulation that is more relevant to biology.

1) The authors mention in the Introduction a number of papers (Nishimura et al., 2006; Polozov et al., 2008; Swamy et al., 2006; Munro, 2003; Thewalt and Bloom, 1992; Owen et al., 2012) that supposedly provide evidence for the physiological relevance of gel domains. Either the referenced papers deal with situations in which membranes are being cholesterol depleted or thermally quenched, or they talk about liquid-ordered domains, not gel domains. In fact, in Munro, 2003 it literally states "The solid gel phase is not thought to be of physiological relevance". Please change the Introduction accordingly.

2) The demonstration of the attraction between proteins in this manuscript concentrates on proteins that induce local disorder in an otherwise ordered phase. In biological membranes the disordered phase is expected to dominate, to ensure fluidity and facile transport. The authors may thus want to discuss the reversed situation in a bit more detail (which should be quite symmetric). Ideally, the authors are encouraged to consider a simulation that is more relevant for the biological situation.

3) The authors may want to discuss in more depth the relation to the lipid raft model. Lingwood and Simons (Lingwood and Simons, 2010) argue that proteins segregate into domains of preferred lipid phase, ordered or disordered. Once such segregation has occurred, would the association force described in this paper effectively disappear? Can the two processes, segregation into domains of preferred phases (at coexistence), and attraction between proteins within mismatched phases, be reconciled (or are they the equivalent)? Could the effect presented here be a driver for raft formation? In such a process, "mismatched" proteins in a membrane close to phase separation would aggregate into clusters, and entropic effects would then push the phase boundary out.

4) Molecular determinants. What would make a protein orderphilic, beyond having low hydrophobic mismatch with the ordered phase? Are there ways to modulate the strength and the range of the interaction?

5) Membrane remodeling. The authors briefly discuss a possible role in membrane fusion. Interestingly, lipid phase separation has been suggested to play a central role in ESCRT-protein induced coat-free vesicle budding (Rozycki et al., PLoS Comp Biol 8, e1002736, 2012).

6) It would be instructive to include the definition of in Figure 1B.

7) The use of the word 'ordered' in both the Abstract and Introduction is misleading in the context of biomembranes. What the authors probably mean is solid-ordered, or gel, and not liquid-ordered. This distinction should be made from the beginning to avoid misunderstanding.

8) The final paragraph on the possible importance of the "order-phobic" force should be revised in light of the above comments.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Thank you for resubmitting your work entitled "Pre-transition effects mediate forces of assembly between transmembrane proteins" for further consideration at eLife. Your revised article has been favorably evaluated by Richard Aldrich (Senior editor), a Reviewing editor, and two reviewers. The manuscript has been improved but there are some minor remaining issues that need to be addressed before acceptance, as outlined below.

Reviewer #2:

The authors have largely addressed my concerns. Introduction Introduction and sections establish the biological relevance more clearly, without hiding the simplifications of the simulation model compared to biological membranes. Even if the new simulations of orderphilic proteins in a liquid-disordered membrane are only at a preliminary stage, the observed behavior clearly mirrors that of orderphobic proteins in a solid-ordered membrane, as would be expected. In my opinion, the new data strengthen the paper considerably, and I thus suggest including them.

Despite the simplifications compared to real biological membranes, the work provides strong evidence that the perturbation of lipid phase behavior by integral membrane proteins can create substantial driving forces for assembly. The paper should attract attention also by the experimental community and stimulate further explorations of the role of phase behavior. I recommend publication in eLife.

Reviewer #3:

My main previous concern, the biological relevance of the findings, is now much more clearly discussed in the revised paper.

There are two remaining aspects that still require some discussion:

1) The authors write "The orderphobic effect should be a general consequence of a first-order transition, whether the transition is between solid-ordered and liquid-disordered phases as considered explicitly herein, or between liquid-ordered and liquid-disordered phases as in multicomponent membrane systems". I strongly doubt that the transition between liquid-ordered and liquid-disordered phases is a first order transition. The experimental work of Veatch, Keller and co-workers (e.g. Veatch et al., ACS Chem Biol, 2008; Honerkamp-Smith et al., BBA Biomem, 2009), clearly shows that, upon cooling of a lipid extract (either from real plasma membranes or model membranes), the system shows critical behavior. I urge the authors to cite this work and discuss the implications thereof.

2) The authors should discuss the connection between their work and the work of Schäfer et al. (Shäfer et al., 2011) in more detail. The simulation studies of Schafer et al., based on the same (Martini) model that is used here, demonstrate that proteins are expelled from liquid-ordered domains as a result of 'orderphobicity'. Although the term orderphobic is not used, the driving forces for the partitioning of proteins into disordered domains are shown to be a direct consequence of the protein-induced perturbation of order in the liquid-ordered domains. In a subsequent study (Domanski et al., BBA Biomem, 2012), it is actually shown that these driving forces can lead to protein-induced domain formation. In the context of the biological significance of the current work, these studies should be properly discussed.

The primary concern of the reviewers appears to be the biological relevance of the solid-ordered phase used to demonstrate the orderphobic effect. We agree with the reviewers that the solid ordered phase has not been directly observed in most biological membranes (except lung surfactants). And we agree that our writing was inaccurate on this issue. Our revision emphasizes that biological membranes exhibit order–disorder phenomena in that significant portions exist in the liquid-ordered state, and these parts coexist with the liquid-disordered state. The liquid-ordered state is multicomponent and much more complicated than the one-component membrane considered in the current work. Nevertheless, our one-component system also exhibits an order–disorder transition between a solid-ordered phase and a liquid-disordered phase, which allows us to demonstrate the generic role of order–disorder in organizing proteins in what we think is the simplest possible context.

1) The authors mention in the Introduction a number of papers (Nishimura et al., 2006; Polozov et al., 2008; Swamy et al., 2006; Munro, 2003; Thewalt and Bloom, 1992; Owen et al., 2012) that supposedly provide evidence for the physiological relevance of gel domains. Either the referenced papers deal with situations in which membranes are being cholesterol depleted or thermally quenched, or they talk about liquid-ordered domains, not gel domains. In fact, in Munro, 2003 it literally states "The solid gel phase is not thought to be of physiological relevance". Please change the Introduction accordingly.

We agree that the original references (Nishimura et al., 2006; Polozov et al., 2008; Swamy et al., 2006; Munro, 2003; Thewalt and Bloom, 1992; Owen et al., 2012) did not provide evidence for the physiological relevance of solid domains and that the Introduction and Implications sections required revision. The comment is correct in that some references (Nishimura et al., 2006; Polozov et al., 2008; Swamy et al., 2006; Munro, 2003; Thewalt and Bloom, 1992; Owen et al., 2012) in our initial submission were about membrane temperature changes and cholesterol depletion. Nevertheless, those references are not irrelevant because such experiments provide important clues to understanding the final state of biological membranes at physiologically relevant temperatures and compositions. That said, the original reference (Munro, 2003) was improperly placed, and we have changed its position now to be a reference for the lipid raft hypothesis.

We revised our Introduction to make our motivation clear as to why we studied the transition between solid-ordered and liquid-disordered phases to facilitate the simplest possible illustration of the generic orderphobic effect. The importance of studying the ordered phase and the orderphobic effect is further elaborated in the revised Implications section. Studying the ordered phases and the effects of order–disorder transitions are also of direct relevance in understanding the behavior of lung-surfactant monolayers. The implications of the orderphobic effect to monolayers is now added in our revised Implications section.

2) The demonstration of the attraction between proteins in this manuscript concentrates on proteins that induce local disorder in an otherwise ordered phase. In biological membranes the disordered phase is expected to dominate, to ensure fluidity and facile transport. The authors may thus want to discuss the reversed situation in a bit more detail (which should be quite symmetric). Ideally, the authors are encouraged to consider a simulation that is more relevant for the biological situation.

First, we direct the reviewers to our revised Introduction and Implications sections that discuss the importance of liquid-ordered phases in biological membranes, in addition to the disordered phase.

Second, concerning the dual to the orderphobic effect, the orderphilic effect, we have followed up on the suggestion of reviewers by reversing the roles of solid-ordered and liquid-disordered phases. Preliminary results of these calculations are shown in Appendix 1—figures 4,5. Bear in mind that without the additional components needed to produce a liquid-ordered phase, these results are no more or less relevant than those already studied for the orderphobic effect.

Appendix 1—figure 4.

Radial profile of the average director density surrounding orderphobic ( nm) and orderphilic ( nm) model proteins in the disordered membrane phase.

DOI: http://dx.doi.org/10.7554/eLife.13150.013

Appendix 1—figure 5.

Configurations of the disordered membrane in the presence of a model orderphilic protein, nm.

The rendered particles are the ‘C2’ tail particles of the lipids, and the gray line marks the boundary between ordered and disordered domains by rendering the contour of the instantaneous interface for the director field, .

DOI: http://dx.doi.org/10.7554/eLife.13150.014

In particular, with the disordered bilayer, we embedded a model protein with a hydrophobic thickness approximately equal to that of the ordered phase, nm. This embedding illustrates the orderphilic case. As a control, we also embedded a model protein with a hydrophobic thickness approximately equal to that of the disordered phase, nm. For both cases, we then calculated the average of the bond orientational order density <)>, and the number density as defined in the main text. We have also computed the director density, , where, with = (3/2) cos. Here, is the angle between the membrane normal and the lth chain’s orientation. Further, with the procedure described in the text, we have computed the instantaneous interfaces from the coarse graining of each of these three fields , and . In the orderphilic case, interfaces are apparent for all three fields. The director field provides the clearest pictures, which are illustrated in Appendix 1–figures 4,5. In the control case, interfaces do not appear.

Distinctions between interfaces for each of the fields are interesting microscopic effects worthy of future study. For the bulk interface between the ordered and disordered phases, the distinction disappears because there is only one order–disorder transition for the membrane model we have considered. In more complicated membrane models, those with mixtures of components exhibiting both liquid-ordered and solid-ordered phases, the different fields offer different information for both large and small length scales, as now mentioned in the Implications section and elsewhere.

3) The authors may want to discuss in more depth the relation to the lipid raft model. Lingwood and Simons (Lingwood and Simons, 2010) argue that proteins segregate into domains of preferred lipid phase, ordered or disordered. Once such segregation has occurred, would the association force described in this paper effectively disappear? Can the two processes, segregation into domains of preferred phases (at coexistence), and attraction between proteins within mismatched phases, be reconciled (or are they the equivalent)? Could the effect presented here be a driver for raft formation? In such a process, "mismatched" proteins in a membrane close to phase separation would aggregate into clusters, and entropic effects would then push the phase boundary out.

The comment raises interesting questions, but answering those questions is beyond the scope of what we have thus far done. We have considered the effects of one or two proteins in a one-component membrane, while understanding lipid rafts and the like requires studies of the collective phase behavior of the mixtures of lipids and proteins including the orderphobic and orderphilic effects. Appropriate modeling is possible, as the revised manuscript indicates, but it will involve extensive new work. The revised manuscript foreshadows studies of these questions in the Implications section.

4) Molecular determinants. What would make a protein orderphilic, beyond having low hydrophobic mismatch with the ordered phase? Are there ways to modulate the strength and the range of the interaction?

As already discussed in the earlier version of our paper, the strength and range of the interaction can be modulated by (a) proximity to the order–disorder transition (in temperature as well as surface pressure), (b) radial size of the solute, and (c) relative interactions between the lipid tail groups and the hydrophilic ‘caps’ of the protein. See the subsection “The orderphobic effect generates forces of assembly and facilitates protein Mobility” of the revised version. An additional factor is that changing components of the membrane change the proximity to the order–disorder transition, thus also affecting the strength and range of the effect. This last aspect is added to the Implications section of the revised manuscript.

Note also that the Appendix shows how a model α-helix is orderphobic even though the chosen peptide has low hydrophobic mismatch with the ordered phase. This finding demonstrates that side-chains of a protein are sufficient to perturb the ordered structure of the membrane, making α-helices orderphobic. Similarly, it should be possible to make a protein less orderphobic by altering its side-chain chemistry, or secondary structure (e.g., β-sheet). A detailed characterization of how proteins of different hydrophobic mismatches, secondary structures, and side-chain chemistries modulate the orderphobic effect is left to future work. This possibility is noted in the Implications section.

5) Membrane remodeling. The authors briefly discuss a possible role in membrane fusion. Interestingly, lipid phase separation has been suggested to play a central role in ESCRT-protein induced coat-free vesicle budding (Rozycki et al., PLoS Comp Biol 8, e1002736, 2012).

We have changed the manuscript to include this reference.

6) It would be instructive to include the definition of

We have modified Figure 1B to include an illustration of .

7) The use of the word 'ordered' in both the Abstract and Introduction is misleading in the context of biomembranes. What the authors probably mean is solid-ordered, or gel, and not liquid-ordered. This distinction should be made from the beginning to avoid misunderstanding.

We have revised the Introduction accordingly.

8) The final paragraph on the possible importance of the 'orderphobic' force should be revised in light of the above comments.

We have revised the Introduction and Implications sections.

[Editors' note: further revisions were requested prior to acceptance, as described below.]

Reviewer #2: The authors have largely addressed my concerns. Introduction and Implications sections establish the biological relevance more clearly, without hiding the simplifications of the simulation model compared to biological membranes. Even if the new simulations of orderphilic proteins in a liquid-disordered membrane are only at a preliminary stage, the observed behavior clearly mirrors that of orderphobic proteins in a solid-ordered membrane, as would be expected. In my opinion, the new data strengthen the paper considerably, and I thus suggest including them. Despite the simplifications compared to real biological membranes, the work provides strong evidence that the perturbation of lipid phase behavior by integral membrane proteins can create substantial driving forces for assembly. The paper should attract attention also by the experimental community and stimulate further explorations of the role of phase behavior. I recommend publication in eLife.

We are pleased with the reviewer’s assessment. We have followed his/her advice and added a section to the Appendix in which we show preliminary results for the orderphilic case. Also, in the Implications section, we have added a few more words both to point to the Appendix and to explain the relevance to lipid rafts.

Reviewer #3: My main previous concern, the biological relevance of the findings, is now much more clearly discussed in the revised paper. There are two remaining aspects that still require some discussion: 1) The authors write "The orderphobic effect should be a general consequence of a first-order transition, whether the transition is between solid-ordered and liquid-disordered phases as considered explicitly herein, or between liquid-ordered and liquid-disordered phases as in multicomponent membrane systems". I strongly doubt that the transition between liquid-ordered and liquid-disordered phases is a first order transition. The experimental work of Veatch, Keller and co-workers (e.g. Veatch et al., ACS Chem Biol, 2008; Honerkamp-Smith et al., BBA Biomem, 2009), clearly shows that, upon cooling of a lipid extract (either from real plasma membranes or model membranes), the system shows critical behavior. I urge the authors to cite this work and discuss the implications thereof.

We appreciate the reviewer’s thoughts on this issue, but with all due respect, we disagree with his/her impression that the first-order transition is not present in these systems. It is true that, for a fixed cholesterol concentration, there is a critical temperature associated with the transition, as located by Veatch and Keller, but below that temperature, there is two-phase coexistence, and the transition at those lower temperatures is first-order. (The same is true for a liquid–vapor transition: below its critical temperature, there is two-phase coexistence, and at such temperatures the transition between those phases is first order.) It is a general principle that at the conditions where two phases with different order-parameter values coexist, the transition between the phases is first order. The reference to Veatch and Keller that we do supply in the Implications section of the paper establishes the region of two-phase coexistence between liquid-ordered and liquid-disordered phases. The temperatures and lipid concentrations for which this coexistence occurs depends upon additional parameters, such as cholesterol concentrations and membrane surface tension.

Because there is some confusion over this point, we have added further explanation concerning first-order and coexistence to the Implications section. We have also added a sentence that contrasts the orderphobic and orderphilic effects, which occur broadly for any membrane close to order–disorder coexistence, with the Casimir effect, which occurs over the much narrower conditions of order–disorder criticality.

2) The authors should discuss the connection between their work and the work of Schäfer et al. (Shäfer et al. 2011) in more detail. The simulation studies of Schafer et al., based on the same (Martini) model that is used here, demonstrate that proteins are expelled from liquid-ordered domains as a result of 'orderphobicity'. Although the term orderphobic is not used, the driving forces for the partitioning of proteins into disordered domains are shown to be a direct consequence of the protein-induced perturbation of order in the liquid-ordered domains. In a subsequent study (Domanski et al., BBA Biomem, 2012), it is actually shown that these driving forces can lead to protein-induced domain formation. In the context of the biological significance of the current work, these studies should be properly discussed.

In the Implications section, we have added discussion of the results that the reviewer points us to.