a continuum method for determining membrane protein insertion energies and the problem of charged residues

ARTICLE A Continuum Method for Determining Membrane Protein Insertion Energies and the Problem of Charged Residues Seungho Choe,'' Karen A Hecht/ and Michael Grabe^'^ ^ Department of Bioiogical Sciences and ^Department of Computational Biology in the School of Medicine, University of Pittsburgh Pittsburgh, PA 15260 Continuum electrostatic approaches have been extremely successful at describing the charged nature of soluble proteins and how thfy iiitrraci with bindinj^ parlners However, il is unclear whether ((nilinnuni mctliods can be used lo quaniitativt'ly undt'istand tht- t-ncrgctics of mcinbrant' protein insertion and siabiliiy Rcct-ni iranslaiion expt rinuMU-s su^gt-st that thf eiierg)- required to insert charged pcptides into membranes is much smaller tliau predicted b\ present c = c^/kuT is the reduced electrostatic potential and is the electrostatic potential; K is the DebyeHuckel screening paratneter, which accounts for ionic shielding; e is the dielectric constant for each ofthe dis566 Modeling Membrane Insertion Energies tinct microscopic regimes in lhe system; atid p is the density of charge witliin the protein moiety For a given 3D structure, we tised the PARSE parameter set to assign the atomic partial chatges, p and the van der Waals radii to each atom Following the PARSE protocol, we assigned e - 2.0 to protein and e = 80.0 to water As can be seen in the Fig A for a flat bilayer, we started by treating the entiie length of the bilayer as a low-dielectric environment with s = 2.0 For a specific protein configitration and dielecttic environment can be calculated and the- unal electrosuitic c-nerg) determined as GHIT = Z 't(ri)p(ri), where the sum rtttis over all charges in the system There is a large driving force for nonpolar solutes to sequester themselves from water This phenomenon is associated with the hydrophobic collapse of protein cores during protein folding, atid it is a tnajor consideration for membrane protein insertion into the hydrophobic bilayei Traditionally, the hydrophobic ity of an apolar solute is described in terms of the entropy loss and the enthalpy gaiti associated with the formation of rigid networks of water molecules around the solute Theoretical treatments of the nonpolar energy- generally assume that tlie transfer free energy from vacuum to water scales linearly with the SASA (Ben-Tal et al., 1996) However, detailed computational studies of small alkane molecules liave shown that for cyclic alkanes the SASA is only weakly elated with the total free energy of solvation This is due to cyclic alkanes having a more favorable solute-solvent interaction enetg)', per unit surface area, as compared with linear alkanes (GalHcchio et al 2000) Recently, it was shown that continuum methods can correctly describe these effects if they incorporate solvent accessible volume terms and dispersive sokile-solvent intetactions in addition to the SASA tettiis (Wagoner and Baker, 2006) Fortunately, helices and chain-like molecules have volumes and surface areas that are nearly proportional, and a pioper parameterization of the prefactor multiplying the SASA term can effectively account for the voltime dependence Therefore, following the work of Sitkofl and coworkers, we calculated AG,,,, as the difference between the SASA ofthe TM helix embedded in the niembrane, Am^,,,, and tbe value in solution A^,,,: AG,,p = a-(An,em ~ A^oi) + b, where the values a = 0.028 kcal/moI-A^ and b = -1.7 kcal/mol were obtained by using the equation for AG,,,, to Ht the experinientally determined transfer ft ee energies of several alkanes between water and liquid alkane phases (Sitkoff et al., 1996) Next, we wanted to use Eq together with calculations like those shown in Fig A to address the appat ent free energy of insertion for amino acids as determined by the translocon experiments (Hessa et al., 2005a) We used MOLDA to create ideal poly-alanine/leucine a helices with tbe central position chosen to be one ofthe 20 natural amino acids, excluding proline (Yoshida and Interestingly, the PARSE parameter set was developed U) qitantitatively reproduce the solitbilities of side-chain analogues (SitkofTet al., 1994), yet when we extend this work to describe tbe results ftoni the translocon scale, the computational and experimental values lack quantitative agieenient Most not;tbly the ttiuislocon scale predicts a very small apparent ftee energ)' difTerence between incorporating charged lesidues and polar residues, while our continuum electrostatic calculations predict that charged residues require 30-35 kcal/mol more eni-igy to itisert into the membrane (Fig B) While it is possible that the energetics of the translocon experiment.s are skewed by tbe close proximity ofthe extruded seguienl to the membrane, atnong olher possibilities, part ofthe discrepancy surely lies in our simplified treatment ol the membrane Elasticity Theory Determines the Membrane Shape and Strain Energy Moleculai- simulations highlight two features that are missing in our continuutn model First, the membrane is not a slab of pure hydrocarbon, but rather the lipid head gtoups are quite polar and interact intimately with charged moieties on the protein; and second, lipids adjacent to the helix bend to allow significant water penetration into the plane of the membrane (Freites et al., 2005; Dorairaj and Allen, 2007) Both of these features can potentially reduce the energy required to inset l charged tesidues into the membrane Phospholipid head groups are polar and mobile, making their electrostatic natttre much tnoie like water than livdiocarbon A ^e\\x Matsitura 1997) Subsequently, we optimized tlie sidechain rotatner confonnations with SCCOMP (Eyal et a!., 2004) The ftee energ\' difference of the helical segment in solutioti versus the membrane, AG,,,, was calculated, and the insertion propensity of the central amino acid was determined by correcting for the backgrottnd alanine-leucine helix (see Materials and methods) Next, we ordered the amino acid insertion energies along the x-axis according to the findings of Hessa et al (2005a) in wliich the far left residue inserts the most favotably and the insertion energetics increase monoionically going to the right (Fig B) It can be seen that the flanking residues are in qualitative agreement; our theoretical calculations show that isoleucine is one of the most favorably inserted amino acids and aspartic acid is the least favorable Our scale is not strictly monotonic, but it does exhibit a similar trend of increasing insertion energy from left to right The most obvious deviation from this trend occurs for tlie polar residues, which decrease in energ)' from N to Q Also, while our calculations predict that glycine is among the least favorahlv inserted nonpolar residues, Hessa et al found that glycine is clustered with the polar residues, which produces a noticeable dip in the bar graph between Y and S (Fig B) |u,/2 n th(r,e) upper leaflet lower leaflet increasing r upper contact curve B maximum — minimum lower contact curve TM helix Figure System geometiy corresponding to electrostatic and elasticity calculations (A) Cross section of the deformed membrane showing the flat lower leaflet and cur^'ed upper leaflet (solid red) Liiis theeqtiilibritnn membrane width aud h is the hciKhlof the tipper leaflei The inidplane is assigned / = tt (dashed black) The radius ol tlie "I'M lielix is i,, and only half Of" tlu' helix is pictured (B) The idealized helix is shown and ilie contact cur\'es of the tipper and lower membrane leaflets are shown in red The lower curve is Hat; however, the upper curve dips down wilh a minimum value at lhe position where ihe central residue resides on the full molecular helix when present For dipahnitoylphosphatidylcholine (DFPC) bilayers the width of the head grotLp region is between and A based on synchrotron studies (Hehn et al., 1987), and MD simulations estimate thai the corresponding dielectric value for this i egion is higlier than bulk water (Stern and Fellei; 2003) This additional level of complexity is easily accounted for by adding an 8-A-wide iniermediate dielectric region, wbich we assigned lo GhR = 80, on each side of the inetnbtane core It is also known that membrane siiTJiems exliibil an interior electrical potential ranging from +300 to +600 iiiV that is thought to arise from dipole charges at the itpper and lower leaflets (Jordan, 1983) While the exact nature of this potential is not known, it is thought that interfacial watei, ester linkages, and head gtotip charges may play a role Following the work of Jordan and Coalson, we have adopted a physical tnodel of the membrane dipole potential in which a thin layer of dipole charge is added to the upper and the lower leaflet between the head group region and hydrocarbon core (Jordan, 1983; Cardenas et al., 2000) The strength of the dipoles was acljusted so that the v-aliie of the polenlial was +300 mV at lhe center of lhe bilayer far from the TM helix While this additional energy could be considered part of AG,.],., we chose to call it ACi,ij[«,i,., and we amended Eq as follows: Choe et al 567 site of helix minimum compression maximum compression -20 20 lower leaflet o B 20 •t-l D) CD X -20 50 Radial Position [A] [kcal/mo X-axis [A] E 0) E (3 '^ 10 20 Leaflet Thickness [A] Tlie much more difficult lask is lo detciTnine how lo model membrane defects at the continuum level We chose to use elasticity tlieoiy which treats ihe membrane surface as an elastic sheet characterized by material properties that describe its resistance to distortions such as benditig (Hclfrich, 1973) This method has been successfully applied to tnemhnine mediated protein-protein interactions (Kim et al., 1998; Grabe et al., 2003) and membrane sorting based on height mismatcli between tiie hydrophobic length of tlie protein and the membrane (Nielsen et al., 1998; Nielsen and \ndersen, 2000) These later models are often termed "mattress models" since diey allow the membrane to compress vertically much like a mattiess hed does when sat upon Simtilations indicate that the membrane undergoes significant compression around huried charged groups, so we closely followed the formulation of the mattress models in oui" present work The membrane deft^nnation etiergy is written in terms of die compression, bending, and stretch of the membrane as foUows: (4) AG ^ compression dii, bending slretch where K^ is the bilayer compression modulus, K^- is the bilayer bending nKJdnlus, a is the surface tension, and u is the deviation of the leaflet height, h, from its equilibrium value, u ^ h — Lo/2 The total energy is given by the double integral of the deformation energ\' densit)^ over the plane of the membrane A cartoon cross section of the membrane bending around an embedded TM helix illustrates the geometiy in Fig 568 Modeling Membrane Insertion Energies Figure4 Sliapi'(i[ tlifnicmbraiif from claslitity tlieory (A) The solution to Eq was computed to detennine the height of the upper leaflet of the membrane given a deformiilion near the ori^n The metiihrane-water interfaces of the upper and lower leaflets are represented as two surfaces We only show the surfaces within a 20 A radius of the origin The centers of the surfaces are missing since we assumed that the membrane terminates on a cylindrical helix witli a radius of 7.5 A; full molecular delail is noi incorporated at this point C:a!culations were perfbiincd with parameters found in Table I (B) The membrane profile for the solution in A is shown along the axis of largest deformation The cylinder representing tlie TM segment is shown at the origin (solid hlack lines), and the surface of the membrane is shown in red The equilibrium height of Uie upper leaflet is also picliited (dashetl black Hue) to show that a significant amouul of water peuetration (blue shatle) accompanies membrane bending (C) The membrane deibruiation energy increases as the leaflet bends with the deformation reaching a maximmn of~.5 kcal/mol, The energy tninitna of Eq cotrespond to stable membrane configurations The equation for these equilibrium shapes is determined via standard functional differentiation of Eq with respect to u: (5) where - a/K and P = 2K«/(L,Mi,) We solved Eq to determine the shape of the membrane, but before doing this we had to specify ihe values of ihe membrane height and slope both far from the helix and where it meets the helix We assumed that the membrane asymptotically approaches its ttnstressed eqtulibi ium height, u = 0, far from the TM helix Unfonunately, we not know the height of the membrane as it contacts the helix We started by positing the shape of the contact curve based on visual inspection of MD simulations, but later in the manuscript we will describe a systematic method for determining the true membrane-protein contact curve, which requites no a priori knowledge In the unstressed case, as in Fig A, we assumed that AG,,n.,,, is zero and that the metnbrane meets ihe helix without bending From the MD work of Dorairaj and Allen, we observed that the ttpper leaflet bends to contact charged residues embedded in llie outer half of the metnbrane {Dorairaj and Allen, 2007) The membrane appears to contact the helix at the height of the chaiged residue, while remaining unpertiubed on the backside of the helix and along ihe entirety of the lower leaflet Therefore, for the present set of calculations we only concerned otirselves with deformations in the tipper leallet and the enei^ in Eq was ^vritten to reflect tliis assumption (see online supplemental material, available at litlp:// www.jgp.org/cgi/content/full/jgp.200809959/DCl) dipole layer dipole layer dipole layer dipole layer 10 20 Arginine Positron [A] We constrained the contact ciirvt- of the upper leaflet to form a sinusoidal cttrve against the helix with the mininuiin \A\UV being the height of the C,, atom of ihe (barged residue and the tiiaxintum\aluc' being ihe heigiit of the unstressed bilayer as shown in Fig B As the dt'|)lh ()( the charged residue changed, we adjttsted the niiiiiniuni value of the cime to reflect this chatige We solved Eq numerically as detailed in the Materials aud methods ttsitig a Finite difTerence scheme in polar coordinates witli tlie standard bilayer parameter values provided in Tahle I and taken frotn Huang (1986) and Nielsen etal (1998) The shape of the membrane when the charged residue is located at its center can be seen in Fig A As discussed above, only the upper leaflet is deformed, and the helix is not explicitly represented at tliis slage, ratlier the membrane originates from a cylinder with a radius approximately the size of the TM segtnent (7.5 A) The metnbiaue-water interface along the radial line corresponding lo the point of largest deformation is depi* ted in Fig B By comparing the flashed hlack lines to llie ted line, it is clear thai a sigttificant atiiotitu of water penetration from the extracellular space accompatiies tliis deformation, solvating residtte.s at the helix center However, this deformation comes at a cost; tlie compression and curvature introduced to the tnembiane tesiilts in a strain energy The magnittide of the sttain energ)', AGn,f,,,, is plotted in Fig C; where the far Figure Helix insertion energy' of a model polyieuciTif helix with a cenUiii arginiiK", As ihc iirginiiie enItrs the nicinbrane, ihe upper leallet Ix-iids to allow water penetration At tlie upper leaflet, the arginine height is 21 A, and it is A at the center (A) The total elecnosliilic energy remains nearly constant upon insertion (B) The nonpolar energy increases linearly to 18 kcal/mol as tlie membiane bending exposes buried TM residues lo water (tl) The membrane delniinalion energy icdrawii from Fig C (D) The total helix insertion energy is the sum of A-f^ plus ACiipoi.- which is not shown (solid red line) Correcting tor the optimal membrane deformation at a given arginine depth, as shown in Fig B, produces a noticeably smaller inserlion eneig)' (dashed red line) Onr continuum computatiiinal model matches well wilh results from fully ;itomistic MD simulations on ihe same syslem (dianioiuls taken Ironi Doraiiaj and Allen 1^0(17) The result trom a classical continuum calculation is shown for reference (solid blue line) (E) System geometry when the arginitie (green) is positioned at the upper leaflet This configiiraiion represents the tar right posilion ()n A-D Gray surfaces repiesem ihe lipid head grou|>-water interface, purple suifaces lepreseni the lipifl head grt)up-liydi()earboii core intei face The membrane is not deformed in this instance (F) System geometry when the arginine is the center of ihe membrane This configuration represents the far left position on A-D The shape of the upper membrane-water iriierface (gray) was determined by solving Eq left corresponds to a compression of half the bilayer width, as shown in Fig A, and the far right corresponds to no compression at all hnportantly the strain energy for the most drastic tU foriiiatitm is only ^ kcal/mol, and the energy falls off faster than linear as the upper leaflet height at the helix is increased to its eqttilibrittm valtie Localizing the penetialion to one side of the membrane and one side of the heiix dramatically reduces the strain energy, which is essential for this to be a viable mechanism for reducing the insertion energedcs of charged residues while minimizing memhiane defoitnation The Electrostatics of Charge Insertion Is Minimal Next, we used the metiibtane shape predicted ftom our elastostatic calctilations to revisit the electrostatic calculations with an arginine at the central position We asstitiied that the deformation of the tipper leaflet does not alter the width of the high-dielectric region corresponding to the polar head groups The helix was positioned such that the C,, atom of arginine was at the tnetiibi^atie-waler interface (21 A, Fig E), and then it was ti~anslated down until the Q, atom reached a height of A at the center of the membrane For each ( onfiguralion, the membrane leaflet was deformed iis in Fig B so that it contacted the Cu, atom, resulting in an everiticieiLsitig tiienihriuie deformation as the arginine leached die bilayer core The final geometiy is pictured in Fig F Choe et al 569 10 15 20 Leaflet Thickness [A] Figure Delennining lhe optimal nicmbranf shape for a fixed charge in the core of ihe inemhrane (A) Starling with the arginine at the center of the membrane as in Fig F, the helix was held fixed, and the point of contact of the upper membranewater interface with the helix was varied from a height of A to its equilibrium uidth of 21 A The electrostatic ctierg)' decreases by 35 kcal/mol as the arginine residue gains access to the polar head groups and extracellular water The majority of lhe decrease in electrostatic energy occurs from 21 to A, and there is pronounced flattening in the curve between and A (B) The total insertion energy exhibits a well-defined energy minimum at a contact membrane height of A Dtiring peptide insertion, we calculated each lemi of tlie free energy in Eq Remarkably, the electrostatic component ofthe energy is essentially flat when the membrane is allowed to bend (Fig A) This result is not obvious, and it highlights the importance of the local geometry with regard to the solvation energ\' of"charged proteins This restth will have important consequences for the mechanistic workings of membrane proteins that move charged residues in the membrane electric field as part of their normal ftinction Nonetheless, defbrming the membrane exposes the surface ofthe protein to water; and therefore, it incurs a significant nonpolar energy, AGn,,, that is proportional to the change in the exposed surface area (Fig B) Additionally, AG,,,,,,,, increases as discussed above (Fig C) Adding together panels A-(' and AGrfjp,,!^, we obtain the contintitini approximation to the potential of mean force (PMF) for inserting an arginine-containing helix into a membrane (Fig D, solid red curve) Continuum Calculations Match MD Simulations Our peptide sysiem is the one exploied by Dorairaj and Allen, which allowed us to directly compare our continuum PMF with their PMF (diamonds in Fig 5D adapted from Dorairaj and Allen, 2007) The shapes of both 570 Modeling Membrane Insertion Energies curves and their dependence on the arginine depth in the membrane are incredibly similar, despite our results (solid red line) being 3-5 kcal/moI higher than the MD simulations Redoing the continuum cakulatit)n without allowing the membrane to bend, and neglecting the polarity of the head gnmps, results in the classical calctilation shown in solid blue For this model, the insertion energetics quickly rise once the charged residue penetrates the memhrane-water interface, and then the energy plateaus to a valtie ^15 kcal/mol larger than vaiues predicted by the membrane-bending model or MD simttlations Allowing for niembrane bending and the proper treatment ofthe polar head grtnip region, firings the qualitative shape of the continiuim calctiiations much more in-line with the MD simulations, suggesting that otu" calctilations are capturing the correct physics of charged residue insertion into the bilayer Additionally, we calculated the pK,, of the arginine side chain as described in the online sttpplemental matei ial and found il to be close to at the center ofthe membritne, wliicb is in excellent agreement with the MD simulations of Li etal (2008) The most tnisatisfying aspect of otir ctu rent approach is that we have to first posit the contact curve of the membrane height against the protein, hi realitv; the membrane will adopt a shape that minimizes the system's total energy A priori we have no way of knowing what that shape is, nor we know if the shapes shown in Fig (E and F) are stahle for the given arginine positions We circumvented this shortcoming by canning out a set of calculations in which the helix remained fixed with the arginine at the membrane center, hut we varied the degree of leaflet compression As the leaflet compresses from its eqtnlibritnn value, the electrostatic component of the helix transfer energ\^ chops by 35 kcal/mol (see Fig A), again highlighting lhe importance of water penetration and lipid head grotip bending Over 90% of tbis energ)' is gained by compressing the metnbrane down to a height of A, and vei7 little further electrostatic stabilization is gained by compressing farther The reason for this can be seen from F'ig F in which the arginine "snorkels" up toward the extracellular space Therefore, once the membrane height comes down to ^ A, the charged gtianidinium group is completely engulfed in a high-dielectric environment When the nonpolar, lipid deformation, and membrane dipole energies are added, lhe energy profile produces a noticeable free energy minimum at A (Fig B) Thus, by extending our simulation protocol we have shown that these strtictures with deformed membranes are mechanically stable, and we have removed the uncertainty regarding the proper placement of the membrane at the protein interface Initially, we expected the curve in Fig B to exhibit a sharp jump in energy as the positively charged arginine side chain moved across the dipole charge layer interface between the membrane core and the lipid head group I lowever, the depth of the residue and the shape of the l)fiiding ineiiihraiif snuxilhes out the transition and resulls in a 5-6 kcal/mol stabilization as the charge exits the interior of the core rather than the full kcal/mol corn'spondiiif^- to a charge in a +300 mV potential Inipoi latitly, when the arginine is at the center of the membrane, the free energy is kcal/mol lower if the mtMTihranc only conipicsscs down to A rather than compressing the lull halt-width ol the membratie (Fig B) Ihis realization shows that the original helix insertion cnci^rv' (Fijif D, red r u n e ) is wrong—it is too high For each vertical posiLion of Uie helix, we then performed a set of calculations in which we swept throtigh all values of the leaflet thickness from to 21 A to determine the optimal compression of the membrane These coiTected tiKig)' values were tised to detennine the PMF of arginine helix insertion into tlie memhrane (Fig D, red dashed curve) The results of the MD simulations and our contintiuni approach are now in excellent agreement, and even at the center of the bilayer the two approaches give values that differ by ' of alanine lo zero (1.97 kcal/mol green, -O.I I kcal/mol red 2.02 kcal/mol blue) Tlie insertion energy' of cliarged residues is ledured by 2530 ktal/niol \>\ penniiting membiane bending Calcnlalions similar [n rhose in Fig (i li indicale llial only (haiged residues result ill distorted mcmbi-.mes (li) he energy' diffeieiue between veiy polar amino acids and charged amhio acids is quite small; 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