Estimating the Lipophobic Contributions in Model Membranes - The

Subscriber access provided by UNIVERSITY OF SOUTH CAROLINA LIBRARIES

Article

Estimating the Lipophobic Contributions in Model Membranes Vikas Dubey, Xavier Prasanna, and Durba Sengupta J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.6b09863 • Publication Date (Web): 10 Feb 2017 Downloaded from http://pubs.acs.org on February 12, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

The Journal of Physical Chemistry B is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Estimating the Lipophobic Contributions in Model Membranes Vikas Dubey, Xavier Prasanna, and Durba Sengupta∗ Physical Chemistry Division, National Chemical Laboratory, Pune 411008, India E-mail: [email protected] Phone: +91 20 2590 2408

1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract The insertion and association of membrane proteins is critical in several cellular processes. These processes were thought to be protein-driven, but increasing evidence points towards an important role of the lipid bilayer. The lipid-mediated contribution has been shown to be important in the association of membrane peptides, but the corresponding “lipophobic” component has not been directly estimated. Here, we calculate the free energy of insertion for transmembrane peptides and estimate the lipophobic component from the cost of cavity formation. The free energy calculations were performed using the coarse-grain Martini force-field, that has been successful in predicting membrane protein interactions. As expected, the charged moieties have the least favorable free energy of insertion, and the highest cost of cavity formation. A length-dependence was observed in polyalanine peptides with the lipid-mediated component increasing non-linearly with peptide length. Membrane fluidity was tested by varying temperature and opposing effects were observed for short and long peptides. The dependence of the lipid-mediated effects on peptide length and temperature was not uniform, and gives valuable insight into the anisotropic nature of the membrane. The results are an important step in estimating membrane effects in protein insertion and association.

2


Page 2 of 28

Page 3 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Introduction Membrane proteins are key players in several cellular processes, and their interactions determine the efficacy and specificity of function. 1 The insertion of these proteins into the membrane is thought to be facilitated by their “hydrophobicity”, and hydrophobicity scales based on the experimental partitioning of membrane peptides have been proposed. 2,3 The free energy of amino acid residues partitioning into model membranes has been estimated computationally and exhibits a high correlation to experimental values. 4–8 Additionally, a biological scale has been calculated from the insertion of membrane proteins via the translocon system. 9 Studies decomposing the residue-wise free energy of membrane insertion have focused on the unfavorable protein-water interactions (hydrophobic effect) and the favorable protein-lipid interactions. Most of these studies neglected the lipid-lipid energetics since it had been suggested that it does not contribute significantly to the overall free energy of insertion. 10 However, recent studies indicate that protein-lipid interactions, although favorable, could be lower in magnitude to lipid-lipid interactions. Consequently, it was reported that the association of membrane proteins is dependent on lipid-mediated forces, and not just protein-protein contacts. 11,12 For instance, experimental studies on model membranes demonstrated that the association of transmembrane proteins is dependent on membrane thickness, fluidity 13 and composition. 14,15 Importantly, free energy calculations using coarsegrain simulations identified that lipid energetics plays a large role in driving membrane protein association. 16–21 In general, these effects that appear to tune membrane protein association have been termed as the “lipophobic” effect, but its molecular determinants and magnitude are unclear. 22 Several mechanisms have been proposed regarding the origin of the lipophobic effect, including packing mismatch, hydrophobic mismatch, fluctuation-induced and curvatureinduced effects. 23 On the one hand, the lipophobic effect has been attributed to be enthalpic

3



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

in nature based on experimental studies on the association of poly-alanine-leucine peptides in model membranes. 15 On the other hand, White and Wimley suggested that the lipid effects can be accounted for by the difference in acyl chain order around the protein compared to the bulk lipid. 24 Computational 25 and theoretical 10 studies have supported the important role of lipid packing at the protein surface in model membranes. Another view of the lipophobic effect is that it is analogous to the “hydrophobic” effect, with a large contribution from lipid entropy. 26 Fluctuation-induced (Casimir-like) and curvature-elastic (ground-state) induced models have also been formulated. 27,28 Interestingly, it has been suggested that although the elastic theory provides a good description of membrane fluctuation spectra of pure bilayers, the Landau-de Gennes theory explains protein assembly better, implying that the lipophobic effect could arise from the differences in acyl chain order. 23 No direct estimates of the lipophobic effect have been reported, but several theoretical estimates have been given, as an indirect measure of the lipophobic contribution. In a few studies, the lipophobic effect was theoretically modeled from the differences in acyl chain order in model membranes and was suggested to be quite small. 10,29 Estimates based on the local curvature (hydrophobic mismatch) also reported values of the order of kT. 30,31 Roux and coworkers reported a contribution of the order of 2kT from membrane perturbations observed around a protein surface in atomistic simulations. 32 An indirect estimate can be made from the cost of cavity formation in hexane, and atomistic simulations have reported a value of 20 kJ/mol for a sphere of 0.2 nm radius. 33 Here, we use coarse-grain molecular dynamics simulations to characterize the lipophobic effect. We have used the Martini force-field since it has been successful in predicting lipophobic contribution in transmembrane protein association. 16–19 Additionally, the “orderophobic” nature of this effect was suggested based on simulations using this force-field. 25 As a first step, we have calculated the free energy of insertion and the cost of cavity formation to characterize the lipophobic contribution to membrane protein insertion. We have analyzed 4


Page 4 of 28

Page 5 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


individual beads that comprise the force-field, to study the effect of different chemical moieties. We then compute the energetics of model peptides comprising of a single representative bead-type. Finally, the energetics of polyalanine peptides of increasing length was estimated at varying temperatures. Our results point towards a significant anisotropic lipophobic effect for membrane peptides.

Methods Coarse-grain molecular dynamics simulations were performed to analyze the energetics of the insertion of transmembrane peptides in the bilayers. The Martini force-field 34–36 (version 2.2) was used to represent the protein, lipids and water.

System setup Each system comprised of 160 DPPC (1,2-dipalmitoyl-sn-glycero-3-phosphocholine) lipids and 1600 water beads (with 10% antifreeze particles), together with the appropriate protein model. Martini Beads:

A single Martini bead was placed at the center of a pre-equilibrated

DPPC bilayer. The main bead types- Q, P, N and C were considered. C5-bead model peptide Model α-helical peptides comprising of C5 beads were constructed with increasing number of residues (1-30). The apolar C5 bead type was considered since it represents a single alanine residue at the center of a transmembrane helix. Each peptide was inserted into the bilayer and equilibrated for 2μs. Polyalanine peptide Polyalanine peptides of increasing length (1-30 residues) were built using the standard Martini residue types. The terminal residues were considered to be charged (Qa, Qd), the flanking residues of type P4 and N0, and the core residues of type C5 (see Supplementary Table 1). All peptides were considered to be α-helical. The systems 5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

were built with the recently developed Insane tool for Martini simulations. 37,38

Simulation protocol Simulations were performed using the GROMACS software package (version 4.5.5) 39,40 with the scheme developed for Martini coarse-grain simulations, under periodic boundary conditions. 34–36 Stochastic dynamics integrator was used for the free energy calculations. Simulations were performed at temperature T = 300 K. Additional simulations were performed at T=200 K and 373 K to test the effect of temperature. Pressure was coupled using a Berendsen barostat 41 with semiisotropic type pressure coupling scheme, in which the lateral and perpendicular pressures were coupled independently to an external pressure of 1 bar. Free energy of insertion The free energy of insertion, ΔGinsertion , i.e. the free energy of solvation into the membrane environment from vacuum, was calculated using Bennett’s acceptance ratio method with a coupling parameter λ similar to the protocol described in Ref. 42,43 For each system, the values reported are the averages of the lipidation (coupling non-bonded interactions) and delipidation (decoupling the non-bonded interactions) to test for convergence and minimize errors. For each free energy calculation, 21 equispaced windows were considered with λ = 0 1, with an increment, δλ = 0.05. The initial conformation for the decoupling step was taken from the equilibrated output of the Insane tool, 37,38 and equilibrated for each subsequent λ. For the lipidation step, the first conformation was taken from a completely decoupled system and each subsequent λ window was equilibrated. The helicity of the polyalanine peptides is imposed by bonded interactions, and is thus not affected during the decoupling or coupling steps. The distance between the center of mass of the peptide (or bead) and the center of the bilayer was kept close to zero, by means of a harmonic position restraint along the bilayer normal (force constant 1000 kJ mol−1 nm−2 ). A soft-core potential was used for 6


Page 6 of 28

Page 7 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


the nonbonded Lennard-Jones interactions with potential height α = 1.3, λ-power = 1, and interaction range σ = 0.47 nm, similar to the protocol described in previous studies. 42,43 The systems were minimized using the steepest descent algorithm, followed by Broyden Fletcher Goldfarb Shanno (BFGS) algorithm at each λ. The systems were equilibrated using a NVT and NPT ensemble at each λ for 200 ps. The production run at each λ was performed for 100 ns, totaling to 2.1 μs for each free energy calculation. Lipophobic contribution The ΔGinsertion term can be decomposed into the electrostatic and the Lennard Jones components; that can be further written as the sum of the dispersion and the cavity term.

VLJ =

4σ 12 4σ 6 − 6 r12 r

(1)

C12 C6 − 6 r12 r

(2)

or VLJ =

By setting the dispersion term (C6 ) to zero, the cost of cavity formation (ΔGc ) can be estimated. To estimate ΔGc , the attractive contribution (C6 ) to the Lennard Jones interactions was removed, and free energy calculations were performed using the same parameters as before. Only the protein-lipid and protein-water dispersion terms were set to zero. These calculations provide the free energy cost of creating a soft repulsive van der Waals cavity near the peptide. The approach used is similar to the work of Hajari et al. 44 In the Martini model, the beads are not assigned partial charges, such that only the charged bead types Qd/a are assigned a +/-1 charge. As a result, the lipophobic contribution is directly related to ΔGc . We have also included a second term ΔG∗c that includes the electrostatic term together with ΔGc . The charged particles cause large perturbations in the bilayer leading to differences in the cavity formed and are accounted for by this term. 7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Results Membrane Insertion of Martini Beads: Free Energy and Lipophobic Contribution We estimated the ΔGinsertion for inserting each of the Martini bead types into the center of the bilayer, by performing a series of free energy calculations. An average of the free energy of lipidation (vacuum to membrane) and delipidation (membrane to vacuum) is plotted in Fig. 1a. As expected, ΔGinsertion is the most unfavorable for the charged bead types (Qa, Qd, Qda), followed by the polar bead-types (P1 to P5 ). The free energy of insertion of the N-type (neutral, intermediate) and C-type (apolar) beads was found to be favorable. The values calculated compare well to the previous estimates of the free energy of insertion into hexadecane. 35 In the next step, the lipophobic contributions arising from the cost of cavity formation, ΔGc was calculated for each of the Martini beads (Fig. 1b). The values were calculated from the repulsive term in the Lennard Jones potential, similar to the work of Hajari et al. 44 As in the case of ΔGinsertion , values were calculated from the average of the lipidation (decoupling) and delipidation (coupling) calculations. The lipophobic contribution for the polar, neutral and apolar was similar, between +55 and +65 kJ/mol. In contrast, the value of the lipophobic contribution for the charged beads was ≈ +145 kJ/mol. In the case of the charged beads, the electrostatic interactions have also been accounted for, and can be considered to be a lipid-mediated effect, ΔG∗c . Neglecting the electrostatic component (and setting the charges to zero), ΔGc reduces to ≈ +135 kJ/mol. At the center of the membrane, there are few direct interactions between the charged beads and the charged lipid head-group beads. The difference between the charged and uncharged bead therefore arises from the bilayer perturbations due to the charged bead. As a comparison, the cost of cavity formation for alanine (side chain) in water (using an atomistic force-field) has been

8


Page 8 of 28

Page 9 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


reported to be +34.6 kJ/mol, and that of leucine (side chain) was +66.8 kJ/mol. 44 The values reported here are large in comparison, suggesting that the contribution of ΔGc at the center of the bilayer will be significant for all amino acid residues. Length-dependent Energetics of Martini C5-Bead Model Peptide In order to analyze the energetics of model peptides in lipid bilayers, we considered a simple C5-bead model peptide. The C5 beads were chosen since they correspond to the representation of an alanine residue at the center of an α-helix in the Martini model. In the first step, ΔGinsertion was calculated for peptides of increasing length (Fig. 2a). As expected, ΔGinsertion is favorable for all peptides and decreases with peptide length. The dependence of the free energy of insertion appears to be linear. In the second step, the lipophobic contribution was calculated as described above (Fig. 2b). A significant cost of cavity formation is observed in all peptides. A steep increase is observed for peptides up to 10 residues, followed by a lower slope. The shorter peptides until Ala-10 lie completely in the core of the bilayer and it appears that ΔGc is higher for the bilayer core, than the head-group region. Length-dependent Energetics of Polyalanine Peptides To analyze the effect of transmembrane helices on the membrane, we chose a polyalanine helix as represented in the Martini model. We would like to point out that the shorter polyalanine peptides (1-10) are comprised of charged and polar bead types. The longer peptides (Ala-12 onwards) are comprised of central C5 beads to account for the hydrogen bonding within the α-helix. A detailed description of the peptide composition is given in Table S1. Figure 3a represents the ΔGinsertion for polyalanine peptides of increasing length. ΔGinsertion is unfavorable up to 4 residues, not surprising since the peptides comprise of mainly charged and polar residues. The free energies for polyalanine peptides of 6 residues or longer are negative, favoring their insertion into the bilayer. In the next step, the lipid-mediated contribution of polyalanine peptides was calculated 9



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

as described above (Fig. 3b). We would like to point out that this includes the cost of cavity formation, together with the electrostatic interactions of the peptide termini with the lipid head-group beads. The ΔG∗c profile is non-uniform, reflecting the anisotropic nature of the bilayer. With increasing number of residues in the core of the bilayer, ΔG∗c increases till Ala-10. A sharp decrease is observed at Ala-12 when the first C5 bead is considered in the Martini model. The lipophobic contribution remains constant till about 22 residues and then increases again. In order to decompose the free energy into the electrostatic and the van der Waal’s components, we set the charges on the peptide termini to zero and calculated ΔGinsertion and ΔGc (Fig. 4). The free energy profile of the uncharged peptide is similar to that of the peptide with charged termini, but less favorable. This suggests that the electrostatic contribution to ΔGinsertion is favorable and systematic. Interestingly, the ΔGc profile of uncharged polyalanine peptides differs significantly from that of the peptides with charged termini (Fig. 4b). It is interesting that such a significant difference is observed, with only two charges at the termini, since no partial charges are considered in the Martini model. A linear dependence, similar to the C5-bead model peptide was observed. ΔGc for a single residue is ≈ 50 kJ/mol, increasing to ≈ 400 kJ/mol for Ala-30. In the case of Ala-10, the electrostatic contribution to ΔGc (difference between charged and uncharged peptide) is ≈ 100 kJ/mol, and the sharp rise seen in the charged peptide is absent. Correspondingly, no decrease in ΔGc is observed at Ala-12, and the van der Waal’s component increases with increasing number of residues. It appears that the charged termini help in “stabilizing” the peptide in the vicinity of the head-group region. ΔGc for Ala-30 (uncharged) is close to 400 kJ/mol, compared to 250 kJ/mol for the charged peptide. Despite the relatively apolar nature of the bilayer, the electrostatic contribution to ΔGc is high, and counters the cost of cavity formation for the longer membrane peptides. To analyze the spike observed in the ΔG∗c profile for the Ala-10 peptide (Fig. 3b), we 10


Page 10 of 28

Page 11 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


analyzed the peptide and membrane dynamics. The orientation of the peptide switches for Ala-8- and Ala-10 to an orientation that is parallel to the membrane normal (see Fig. S1). In this orientation, the charged termini of Ala-10 lie at the interface of the bilayer core and head-group region. The head-group beads are perturbed and move inwards to interact with the peptide terminal residues. The bilayer perturbations cause a decrease in the lipid acyl chain order parameters (Fig. S2). However, these perturbations do not persist at the boundary of the simulation box (see Fig. S3). For the Ala-10 peptide, the perturbations in the head-group of the bilayer are large and appear to increase the cavity term significantly. In contrast, the bilayer perturbations are lower in Ala-8 as it is too short, and Ala-12 as it is longer than the core-head group interface region. These bilayer perturbations together with the fluidity changes lead to a difference in the bilayer structure itself, and consequently the cavity term is significantly larger for the Ala-10 peptide compared to Ala-8 and Ala-12. The lipophobic effect reported here therefore accounts for the cavity formation, together with the membrane perturbation and fluidity changes. Effect of Membrane Fluidity Previous work has suggested that the main contribution to lipophobic effect is from the acyl chain order, 10 and the effect has been termed as “orderophobic” by Chandler and co workers. 25 To test this, we calculated the free energy and lipophobic contribution at 200 K and 373 K, above and below the transition temperature of DPPC (Fig. 5). ΔGinsertion becomes less favorable with increasing temperature. A possible explanation is that the increased dynamics of the acyl chains reduces the interactions with the polyalanine peptides, suggesting the effect could be due to the entropic component. However, due to the coarsegrain nature of the force-field, it is difficult to decompose the free energy into the entropic and enthalpic components. Interestingly, the dependence of ΔG∗c on temperature is not uniform. The profile at 200 K is similar to that at 300 K, but differs considerably at 373 K. The initial increase till 11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Ala-8 peptides is observed at all temperatures. This is surprising since these peptides are positioned in the core of the bilayer. The sharp peak and fall at the Ala-10 peptide is more prominent at 200 K and absent at 373 K. Interestingly, for the Ala-10 peptide the free energy is the most favorable at 200 K, while the lipophobic contribution is the least favorable. The gradual increase in ΔG∗c for peptides longer than 20 residues, shows a similar trend at all temperatures. For the longer peptides, both ΔGinsertion and ΔG∗c are less favorable at higher temperatures. The data suggests that the cost of cavity formation is favorable at higher temperatures when the peptide length is shorter or similar to the thickness of the bilayer core, and is less favorable when the peptide is longer than the bilayer core. The bilayer perturbations are highest at 200 K, when it is in the gel phase (see Fig. S4), and the least at 373 K when it is fluid in nature. The decreased acyl chain order at 373 K requires a lower cost for perturbing the bilayer in the case of the Ala-10 peptide and the spike observed for Ala-10 at 300 K is observed to be absent. The effect of the peptides with uncharged termini followed the same trend to that at 300 K (Fig. S5). Taken together, the data suggests that the lipophobic effect is complex and related to the anisotropic nature of the bilayer.

Discussion The lipid bilayer is a complex anisotropic environment in which membrane proteins are embedded. The physico-chemical properties of membranes have been relatively well studied, but several aspects are only now beginning to emerge. An important question that remains is how lipids interact with membrane proteins, especially compared to lipid-lipid interactions. Here, we have calculated the cost of cavity formation in bilayers in order to analyze the lipid-mediated contributions to membrane protein insertion. Previously, the lipophobic contribution has been indirectly estimated from the association of membrane proteins, and the current study is one of the first direct estimates from membrane protein insertion. By an-

12


Page 12 of 28

Page 13 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


alyzing peptides of varying lengths, we incorporate the membrane perturbation effects from both changes in acyl chain order at the protein surface and the local membrane thickness (hydrophobic mismatch). However, long range fluctuations and curvature are not considered due to the limited system size. We would like to point out though that the long range effects have been suggested to not contribute significantly. 23 One of the main outcomes of our work is that the lipid-mediated contributions are significant. A cost of 55 - 65 kJ/mol was calculated for an uncharged bead of radius 0.47 nm at the center of the bilayer. The value increases to 140 kJ/mol for the charged beads at the center of the bilayer. As expected, for the simple peptide models, the free energy decreases, but the lipid-mediated ΔGc term increases with peptide length. When considering a more realistic peptide, such as polyalanine peptide with charged and polar termini, a similar decrease in free energy is observed, but not in ΔGc . A non-monotonic relationship is observed, with a sharp maximum for the Ala-10 peptide The main determinant appears to be the electrostatic contributions that cause large perturbations in the bilayer, since setting the charges to zero establishes a uniform increase. With increasing temperature, ΔGinsertion is less favorable, following an opposite trend to that of water. At the same time, ΔGc follows a more complex trend - decreasing for shorter peptides and increasing for the longer peptides. The “orderophobic” effect predicted for peptides, 25 appears to hold only for the shorter peptides embedded in the core of the bilayer. Further work analyzing more complex proteins is needed to resolve the issue. In this study, we have estimated both the free energy and the corresponding cost of cavity formation using coarse-grain simulations. The free energy of insertion of the side chain analogue of alanine into cyclohexane or membrane core has been previously estimated to be 8 kJ/mol. 6,45,46 The values are of the same order of magnitude calculated for the apolar (C1-5) beads in this study. For the longer peptides, the reported free energy of membrane insertion for WALP peptides (650 kJ/mol to 900 kJ/mol) is in the same range as calculated 13



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

here. 42 Interestingly, the absence of charged termini 47 and explicit membranes 48 reduces the free energy by an order of magnitude. In addition, several studies have reported the free-energy of partitioning between water and membrane, 5 or from the surface-aligned to membrane inserted conformations. 49 There have been no previous reports of cost of cavity formation in membranes. Here we estimate ΔGc to be 55 - 65 kJ/mol for an uncharged bead of radius 0.47 nm at the center of the bilayer. This in good agreement with the cost of forming a cavity of radii of 0.2 nm in hexane that was reported to be 20 kJ/mol. 33,50 Importantly, the values calculated by using the repulsive potential (similar to the method used here) and the test particle insertion method 33,50 were similar, increasing the confidence in the current study. Several studies have highlighted the importance of sampling and membrane perturbations in correctly estimating free energy profiles. 51–53 The bilayer considered in this study is less than 50 nm2 in area. Although the bilayer perturbations do not appear to propagate over the periodic images (Fig. S3 and S4), the small bilayer considered could lead to an over estimation of ΔGc . Another important limitation of the current study is the handling of electrostatics in the coarse-grain model. Several corrections have been proposed in the free energy calculations of charged moieties, such as from periodic boundary conditions 54 and finite size effects. 55 We have not considered these corrections in the current work that could refine the energy values. The estimates from our coarse-grain study is an important first step. In the future, detailed atomistic studies would be required to quantitatively address these issues. However, it is important to keep in mind is that force-field dependence is observed in the protein-ligand electrostatic binding free energies. 56 Additionally, conformational changes in the polyalanine backbone have not been considered in this work, and secondary structural restraints in the coarse-grain model have been maintained. Determining conformational free energies are one of the most challenging problems in free energy calculations even with atomistic force-fields. 57 In the case of deca-alanine, the free energy difference between the 14


Page 14 of 28

Page 15 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


α-helical and the π and 310 helical states have been estimated to be of the order of kT. 58,59 In conclusion, the work presented here estimates the lipid-mediated contributions to membrane protein insertion, which have been suggested to modulate association of membrane proteins. In this respect, it will be important to consider these effects during de novo design of membrane proteins. 60 It was found that the values of cavity formation in membranes is significant and does not depend linearly on peptide length for polyalanine peptides. The work is an important step in our understanding of the energetics of membrane protein association and folding.

Supporting Information The Supporting Information is available free of charge on the ACS Publications website at DOI: . This includes sequence of the polyalanine peptides (Table 1), peptide orientations (Supplementary-Figure 1), membrane properties (Supplementary-Figure 2-4) and energetics (Supplementary-Figure 5), together with a longer discussion on the free energy and cavity formation calculations.

Acknowledgement The authors thank Arnab Mukherjee and Aiswarya Pawar for discussions and proof-reading. DS gratefully acknowledges the Ramalingaswami Fellowship (DBT) for funding, and VD acknowledges IISER, Pune for support. The authors thank MSM (CSC0129, CSIR) and 4PI institute for computational time.

15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

References (1) Ng, D. P.; Poulsen, B. E.; Deber, C. M. Membrane protein misassembly in disease. Biochim. Biophys. Acta 2012, 1818, 1115–1122. (2) Wimley, W. C.; White, S. H. Experimentally determined hydrophobicity scale for proteins at membrane interfaces. Nat. Struc. Mol. Biol. 1996, 3, 842–848. (3) Moon, C. P.; Fleming, K. G. Side-chain hydrophobicity scale derived from transmembrane protein folding into lipid bilayers. Proc. Natl. Acad. Sci. U.S.A 2011, 108, 10174–10177. (4) Ben-Tal, N.; Ben-Shaul, A.; Nicholls, A.; Honig, B. Free-energy determinants of alpha-helix insertion into lipid bilayers. Biophys. J. 1996, 70, 1803. (5) MacCallum, J. L.; Bennett, W. D.; Tieleman, D. P. Partitioning of amino acid side chains into lipid bilayers: results from computer simulations and comparison to experiment. J. Gen. Physiol. 2007, 129, 371–377. (6) Sengupta, D.; Smith, J. C.; Ullmann, G. M. Partitioning of amino-acid analogues in a five-slab membrane model. Biochim. Biophys. Acta 2008, 1778, 2234–2243. (7) MacCallum, J. L.; Bennett, W. F. D.; Tieleman, D. P. Distribution of amino acids in a lipid bilayer from computer simulations. Biophys. J. 2008, 94, 3393–3404. (8) Fleming, P. J.; Freites, J. A.; Moon, C. P.; Tobias, D. J.; Fleming, K. G. Outer membrane phospholipase A in phospholipid bilayers: a model system for concerted computational and experimental investigations of amino acid side chain partitioning into lipid bilayers. Biochim. Biophys. Acta 2012, 1818, 126–134. (9) Hessa, T.; Kim, H.; Bihlmaier, K.; Lundin, C.; Boekel, J.; Andersson, H.; Nilsson, I.; White, S. H.; von Heijne, G. Recognition of transmembrane helices by the endoplasmic reticulum translocon. Nature 2005, 433, 377–381.

16


Page 16 of 28

Page 17 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(10) Jähnig, F. Thermodynamics and kinetics of protein incorporation into membranes. Proc. Natl. Acad. Sci. U.S.A 1983, 80, 3691–3695. (11) Li, E.; Wimley, W. C.; Hristova, K. Transmembrane helix dimerization: Beyond the search for sequence motifs. Biochim. Biophys. Acta 2012, 1818, 183–193. (12) Rath, A.; Deber, C. M. Protein structure in membrane domains. Annu. Rev. Biophys. 2012, 41, 135–155. (13) Anbazhagan, V.; Munz, C.; Tome, L.; Schneider, D. Fluidizing the membrane by a local anesthetic: phenylethanol affects membrane protein oligomerization. J. Mol. Biol. 2010, 404, 773–777. (14) Hong, H.; Bowie, J. U. Dramatic destabilization of transmembrane helix interactions by features of natural membrane environments. J. Am. Chem. Soc. 2011, 133, 11389–11398. (15) Yano, Y.; Yamamoto, A.; Ogura, M.; Matsuzaki, K. Thermodynamics of insertion and selfassociation of a transmembrane helix: A lipophobic interaction by phosphatidylethanolamine. Biochemistry 2011, 50, 6806–6814. (16) Sengupta, D.; Marrink, S. J. Lipid-mediated interactions tune the association of glycophorin A helix and its disruptive mutants in membranes. Phys. Chem. Chem. Phys. 2010, 12, 12987– 12996. (17) Prasanna, X.; Praveen, P. J.; Sengupta, D. Sequence dependent lipid-mediated effects modulate the dimerization of ErbB2 and its associative mutants. Phys. Chem. Chem. Phys. 2013, 15, 19031–19041. (18) Castillo, N.; Monticelli, L.; Barnoud, J.; Tieleman, D. P. Free energy of WALP23 dimer association in DMPC, DPPC, and DOPC bilayers. Chem. Phys. Lipids 2013, 169, 95–105. (19) Janosi, L.; Prakash, A.; Doxastakis, M. Lipid-modulated sequence-specific association of glycophorin A in membranes. Biophys. J. 2010, 99, 284–292.

17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(20) de Meyer, F. J. M.; Venturoli, M.; Smit, B. Molecular simulations of lipid-mediated proteinprotein interactions. Biophys. J. 2008, 95, 1851–1865. (21) Duneau, J.-P.; Sturgis, J. N. Lateral organization of biological membranes: Role of long-range interactions. Eur. Biophys. J. 2012, 42, 843–50. (22) Duneau, J.-P.; Khao, J.; Sturgis, J. N. Lipid perturbation by membrane proteins and the lipophobic effect. Biochim. Biophys. Acta 2016, 1859, 126–134. (23) West, B.; Brown, F. L. H.; Schmid, F. Membrane-protein interactions in a generic coarsegrained model for lipid bilayers. Biophys. J. 2009, 96, 101–115. (24) White, S. H.; Wimley, W. C. Membrane protein folding and stability: Physical principles. Annu. Rev. Biophys. Biomol. Struct. 1999, 28, 319–336. (25) Katira, S.; Mandadapu, K. K.; Vaikuntanathan, S.; Smit, B.; Chandler, D. Pre-transition effects mediate forces of assembly between transmembrane proteins. eLife 2016, 5, e13150. (26) Helms, V. Attraction within the membrane: Forces behind transmembrane protein folding and supramolecular complex assembly. EMBO Rep 2002, 3, 1133–1138. (27) Yolcu, C.; Deserno, M. Membrane-mediated interactions between rigid inclusions: An effective field theory. Phys. Rev. E 2012, 86 . (28) Sintes, T.; Baumgärtner, A. Protein attraction in membranes induced by lipid fluctuations. Biophys. J. 1997, 73, 2251–2259. (29) Owicki, J. C.; McConnell, H. M. Theory of protein-lipid and protein-protein interactions in bilayer membranes. Proc. Natl. Acad. Sci. U.S.A 1979, 76, 4750–4754. (30) Chou, T.; Kim, K. S.; Oster, G. Statistical thermodynamics of membrane bending-mediated protein-protein attractions. Biophys. J. 2001, 80, 1075–1087.

18


Page 18 of 28

Page 19 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(31) Ben-Shaul, A.; Ben-Tal, N.; Honig, B. Statistical thermodynamic analysis of peptide and protein insertion into lipid membranes. Biophys. J. 1996, 71, 130–137. (32) Lag¨ ue, P.; Zuckermann, M. J.; Roux, B. Lipid-mediated interactions between intrinsic membrane proteins: a theoretical study based on integral equations. Biophys. J. 2000, 79, 2867– 2879. (33) Prévost, M.; Oliveira, I. T.; Kocher, J.-P.; Wodak, S. J. Free energy of cavity formation in liquid water and hexane. J. Phys. Chem. 1996, 100, 2738–2743. (34) de Jong, D. H.; Singh, G.; Bennett, D. W. F.; Arnarez, C.; Wassenaar, T.; Sch¨ afer, L.; Periole, X.; Tieleman, D.; Marrink, S. J. Improved parameters for the Martini coarse-grained protein force field. J. Chem. Theory Comput. 2013, 9, 687–697. (35) Marrink, S. J.; Risselada, H. J.; Yefimov, S.; Tieleman, D. P.; de Vries, A. H. The MARTINI Force Field: Coarse grained model for biomolecular simulations. J. Phys. Chem. B 2007, 11, 7812–7824. (36) Monticelli, L.; Kandasamy, S. K.; Periole, X.; Larson, R. G.; Tieleman, D. P.; Marrink, S. J. The MARTINI coarse grained forcefield: Extension to proteins. J. Chem. Theory Comput. 2008, 4, 819–834. (37) Wassenaar, T. A.; Pluhackova, K.; Moussatova, A.; Sengupta, D.; Marrink, S. J.; Tieleman, D. P.; B¨ ockmann, R. A. High-throughput simulations of dimer and trimer assembly of membrane proteins. The DAFT approach. J. Chem. Theory Comput. 2015, 11, 2278–2291. (38) Wassenaar, T. A.; Ingólfsson, H. I.; Böckmann, R. A.; Tieleman, D. P.; Marrink, S. J. Computational lipidomics with insane: A versatile tool for generating custom membranes for molecular simulations. J. Chem. Theory Comput. 2015, 11, 2144–2155. (39) Van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. GROMACS: Fast, flexible, and free. J. Comput. Chem. 2005, 26, 1701–1718.

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(40) Pronk, S.; P´ all, S.; Schulz, R.; Larsson, P.; Bjelkmar, P.; Apostolov, R.; Shirts, M. R.; Smith, J. C.; Kasson, P. M.; Van Der Spoel, D. et al. GROMACS 4.5: A high-throughput and highly parallel open source molecular simulation toolkit. Bioinformatics 2013, 29, 845–854. (41) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.; Nola, A. D.; Haak, J. R. Molecular dynamics with coupling to an external bath. J. Chem. Phys. 1984, 81, 3684–3690. (42) Schäfer, L. V.; de Jong, D. H.; Holt, A.; Rzepiela, A. J.; de Vries, A. H.; Poolman, B.; Killian, J. A.; Marrink, S. J. Lipid packing drives the segregation of transmembrane helices into disordered lipid domains in model membranes. Proc. Natl. Acad. Sci. U.S.A 2011, 108, 1343–1348. (43) Sengupta, D. Cholesterol modulates the structure, binding modes and energetics of caveolinmembrane interactions. J. Phys. Chem. B 2012, 116, 14556–14564. (44) Hajari, T.; Van Der Vegt, N. F. A. Solvation thermodynamics of amino acid side chains on a short peptide backbone. J. Chem. Phys. 2015, 142, 144502. (45) Chang, J.; Lenhoff, A. M.; Sandler, S. I. Solvation free energy of amino acids and side-chain analogues. J. Phys. Chem. B 2007, 111, 2098–2106. (46) MacCallum, J. L.; Tieleman, D. P. Calculation of the water-cyclohexane transfer free energies of neutral amino acid side-chain analogs using the OPLS all-atom force field. J. Comput. Chem. 2003, 24, 1930–1935. (47) Gumbart, J.; Chipot, C.; Schulten, K. Free-energy cost for translocon-assisted insertion of membrane proteins. Proc. Natl. Acad. Sci. U.S.A 2011, 108, 3596–3601. (48) Sengupta, D.; Meinhold, L.; Langosch, D.; Ullmann, G. M.; Smith, J. C. Understanding the energetics of helical peptide orientation in membranes. Proteins 2005, 58, 913–922. (49) Ulmschneider, J. P.; Smith, J. C.; White, S. H.; Ulmschneider, M. B. In silico partitioning

20


Page 20 of 28

Page 21 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


and transmembrane insertion of hydrophobic peptides under equilibrium conditions. J. Am. Chem. Soc. 2011, 133, 15487–15495. (50) Tomas-Oliveira, I.; Wodak, S. J. Thermodynamics of cavity formation in water and n-hexane using the Widom particle insertion method. J. Chem. Phys. 1999, 111, 8576–8587. (51) Jämbeck, J. P.; Lyubartsev, A. P. Exploring the free energy landscape of solutes embedded in lipid bilayers. J. Phys. Chem. Lett. 2013, 4, 1781–1787. (52) Filipe, H. A.; Moreno, M. J.; Rog, T.; Vattulainen, I.; Loura, L. M. How to tackle the issues in free energy simulations of long amphiphiles interacting with lipid membranes: convergence and local membrane deformations. J. Phys. Chem. B 2014, 118, 3572–3581. (53) Neale, C.; Pomès, R. Sampling errors in free energy simulations of small molecules in lipid bilayers. Biochim. Biophys. Acta 2016, 1858, 2539–2548. (54) Lin, Y.-L.; Aleksandrov, A.; Simonson, T.; Roux, B. An overview of electrostatic free energy computations for solutions and proteins. J. Chem. Theory Comput. 2014, 10, 2690–2709. (55) Rocklin, G. J.; Mobley, D. L.; Dill, K. A.; H¨ unenberger, P. H. Calculating the binding free energies of charged species based on explicit-solvent simulations employing lattice-sum methods: An accurate correction scheme for electrostatic finite-size effects. J. Chem. Phys. 2013, 139, 184103. (56) Izadi, S.; Aguilar, B.; Onufriev, A. V. Protein-ligand electrostatic binding free energies from explicit and implicit solvation. J. Chem. Theory Comput. 2015, 11, 4450–4459. (57) Hansen, N.; van Gunsteren, W. F. Practical aspects of free-energy calculations: A review. J. Chem. Theory Comput. 2014, 10, 2632–2647. (58) Hansen, H. S.; H¨ unenberger, P. H. Ball-and-stick local elevation umbrella sampling: Molecular simulations involving enhanced sampling within conformational or alchemical subspaces of

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

low internal dimensionalities, minimal irrelevant volumes, and problem-adapted geometries. J. Chem. Theory Comput. 2010, 6, 2622–2646. (59) Lin, Z.; Liu, H.; Riniker, S.; van Gunsteren, W. F. On the use of enveloping distribution sampling (EDS) to compute free enthalpy differences between different conformational states of molecules: Application to 310 -, α-, and π-helices. J. Chem. Theory Comput. 2011, 7, 3884–3897. (60) Nash, A.; Notman, R.; Dixon, A. M. De novo design of transmembrane helix-helix interactions and measurement of stability in a biological membrane. Biochim. Biophys. Acta 2015, 1848, 1248–1257.

22


Page 22 of 28

Page 23 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


A:

B:

Figure 1: Energetics of individual Martini beads (A) The free energy of membrane insertion (B) The lipophobic contribution to the free energy of membrane insertion. The values were calculated from the average of the lipidation and the reverse delipidation process.

23



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

A:

B:

Figure 2: Energetics of C5-bead model peptide with increasing lengths (A) The free energy of membrane insertion (B) The lipophobic contribution to the free energy of membrane insertion. The values were calculated from the average of the lipidation and the reverse delipidation process. The black lines represent the fit to the calculated values of free energy and lipophobic contribution.

24


Page 24 of 28

Page 25 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


A:

B:

Figure 3: Energetics of polyalanine peptide of varying lengths (A) The free energy of membrane insertion (B) The lipophobic contribution to the free energy of membrane insertion. The values were calculated from the average of the lipidation and the reverse delipidation process. The black line represents the fit to the calculated values of free energy.

25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

A:

B:

Figure 4: Decomposition of the energetics of polyalanine peptide of varying lengths (A) The Lennard Jones component of the free energy of membrane insertion (B) The Lennard Jones component of the lipophobic contribution to the free energy of membrane insertion. The values were calculated from the average of the lipidation and the reverse delipidation process. The black lines represent the fit to the calculated values of free energy and lipophobic contribution.

26


Page 26 of 28

Page 27 of 28

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


A:

B:

Figure 5: Energetics of polyalanine peptide of varying lengths at varying temperatures (A) The free energy of membrane insertion (B) The lipophobic contribution to the free energy of membrane insertion. The values were calculated from the average of the lipidation and the reverse delipidation process.

27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

28


Page 28 of 28

Estimating the Lipophobic Contributions in Model Membranes - The

Recommend Documents