biological membranes 
 are indispensable and multifunctional components 
 of all living cells and serve as a dynamic platform for a wide range 
 of vital cellular processes , including signaling and transport . cellular membranes are a complex environment 
 characterized by high leaflet asymmetry and heterogeneous composition , where more than 25% of the surface area is occupied by proteins . far from the initial perception of serving as 
 a passive enclosure , cellular membranes regulate numerous membrane - associated 
 proteins via the mechanical and electrical properties 
 of the lipid bilayer . the importance of the membrane to life can not 
 be overstated , as nearly a third of the 34  000 identified human 
 proteins are thought to function only in their membrane - bound forms 
 and depend on membranes for proper function . experimental biophysical and biochemical studies have contributed 
 significantly to our understanding of membrane  protein interactions . such interactions are particularly key to peripheral membrane proteins , in which case the binding 
 and activity of the protein are strongly coupled to the lipid composition 
 of the bilayer . a number of membrane anchoring domains are now structurally 
 resolved and display a wide range of diversity in structural motifs 
 and modes of interaction with the membrane including varying insertion 
 depth , requirement for a particular ion or lipid for proper membrane 
 binding , post - translational modifications to enhance membrane binding , 
 and the need for dimerization . although interactions 
 of peripheral proteins with the membrane are thought to be mediated 
 by both lipid - specific interactions and response 
 to bulk electrical and mechanical properties of the lipid bilayer , challenges to and limitations of experimental 
 approaches have prevented detailed atomic characterization of the 
 membrane binding process and associated phenomena for most peripheral 
 membrane proteins . molecular dynamics ( md ) is a valuable tool 
 for an atomistic description 
 of protein  membrane interactions , as it offers temporal and 
 spatial resolutions needed to study molecular events at an unparalleled 
 level of detail . indeed , combining experimental 
 approaches and computational methodologies in a number of peripheral 
 proteins has proven very effective in understanding how atomic - level 
 phenomena affect cellular - level events . however , relatively 
 slow lateral lipid dynamics and limits to time scales achievable have 
 made capturing spontaneous binding and insertion of peripheral proteins 
 into a membrane challenging to computational studies . these challenges 
 led us to develop a novel membrane model , termed the highly mobile 
 membrane mimetic ( hmmm ) , which expedites computational studies of 
 membrane - associated phenomena by enhancing lipid dynamics . the hmmm is based on the conceptually 
 simple idea of representing 
 a large part of the membrane hydrophobic core by a more fluid representation , 
 while using short - tailed lipids to maintain an atomistic description 
 of the head groups . the hmmm accelerates lipid dynamics without compromising 
 accurate description of the lipid head groups , which are key to the 
 interactions of peripheral proteins with membranes . the model has 
 been successfully applied to capture the spontaneous membrane binding 
 and insertion of individual phospholipids , various membrane anchoring domains , as well as 
 individual transmembrane helices . a number 
 of other applications of the model are now in progress in our laboratory . despite its utility in accelerating insertion events , concerns remain as to the degree to which the in silico changes 
 to the membrane perturb the energetic cost of partitioning a protein 
 into the membrane . to characterize the energetics of the hmmm model 
 and gain a better understanding of protein  membrane interactions 
 in the model , we report the potentials of mean force ( pmf ) of side 
 chain insertion into a hmmm membrane . these pmfs are compared to reported 
 experimental , computational all - atom 
 ( full - aa ) , and coarse - grained ( full - cg ) free energies . reconstructed pmfs analyzed on 
 the basis of four regions within the membrane demonstrate that the hmmm model accurately reproduces the free energy 
 of side chain partitioning at the membrane interface , an essential 
 feature needed for a proper description of protein  lipid interactions 
 in peripheral proteins . on the other hand , the hmmm in its present 
 form has difficulty describing membrane core energetics for all side 
 chains due to the fluid and slightly polar nature of the core solvent , 
 currently limiting the model s use to peripheral proteins and 
 single - pass transmembrane proteins . we also compare the results to 
 previously reported hydrophobicity scales based on the free energy 
 of side chain insertion into lipid membranes . as the hmmm model was 
 designed to describe the interactions of peripheral proteins with 
 the membrane , we devote particular attention to the interactions of 
 the side chains with the interfacial regions of the membrane . in order to assess the accuracy of the hmmm model in describing 
 the partitioning of proteins into membranes and isolate the impact 
 of individual residues on the overall protein membrane interaction , 
 we prepared simple side chain analogues of 10 amino acids and calculated 
 the pmf for their insertion into a hmmm membrane . the analogues were 
 constructed by removing both the amino and carboxylate moieties of 
 each side chain and replacing the -carbon by a hydrogen . the 
 new hydrogen was assigned a partial charge of + 0.09 , typical for an 
 aliphatic hydrogen in charmm , and the charge on the 
 -carbon was adjusted by 0.09 to maintain the net charge 
 of the side chain . the partitioning of the constructed side chain 
 analogues was investigated for 10 residues that span four major classes , 
 namely , ( 1 ) hydrophobic / aliphatic residues ala ( methane ) and ile ( n - butane ) ; ( 2 ) aromatic residues trp ( 3-methylindole ) , phe 
 ( toluene ) , and tyr ( p - cresol ) ; ( 3 ) polar residues 
 asn ( acetamide ) , cys ( methanethiol ) , and ser ( methanol ) ; and ( 4 ) charged 
 residues asp ( acetate ) and arg ( n - propylguanidinium ) . the choices of amino acid analogues are identical to those used in 
 previous experimental and computational studies , which will be our primary basis for comparison . wherever 
 possible , our methodology was identical to those of the reference 
 studies which used a conventional bilayer . each system 
 was constructed by placing two copies of a protein side chain analogue , 
 offset by 32.5  in the z - direction , in a pre - equilibrated 
 hmmm membrane containing phosphatidylcholine ( pc ) short - tailed lipids 
 ( st - lipids ) along with water and ions . the total charge of the system 
 was neutralized by adding two na ions for the system with 
 asp and two cl ions to the system with arg ( one 
 counterion for each copy of the analogue ) . the hmmm membrane used 
 in this study was made of 72 st - lipids ( 36 pc lipids per leaflet ) 
 with an area per lipid of 68  , matching the experimentally 
 determined value for dioleoylphosphatidylcholine ( dopc ) . 1,1-dichloroethane ( dcle ) was used as the liquid 
 solvent representation of the hydrophobic core of the bilayer . each system , slightly varying depending on the 
 side chain size , contained approximately 21  300 atoms , including 
 nearly 4300 water molecules . simulations were performed 
 using namd2.8 with the charmm36 force 
 field parameter set for lipids and small molecules , the charmm27 parameter set for the side chains , and the tip3p model for water in the 
 npnat ( constant normal pressure , area , and temperature ) 
 ensemble . hoover 
 method were employed to maintain the temperature 
 at 298 k and pressure at 1.0 atm . the long - range electrostatic forces 
 were calculated using the particle mesh ewald ( pme ) method with a grid density of 1  . the cutoff for van der waals interaction was set at 13.5  
 with a smoothing function applied after 10  . an integration 
 time step of 2 fs was used . in order to prevent artificially large , 
 out - of - plane fluctuations of the st - lipids and their occasional partitioning 
 into bulk water , we applied a weak harmonic constraint ( 0.05 kcal / mol ) to the z - position to the carbonyl carbon 
 atoms of each st - lipid . the choice of the weak force constant allowed 
 for fluctuations of 3.5  along the z - axis , 
 consistent with membrane fluctuations seen in a conventional bilayer . no restraints were applied in the xy - plane , allowing 
 for rapid lateral lipid diffusion . the umbrella sampling method was 
 used to calculate the pmfs for inserting the side chain analogues 
 into a hmmm membrane . using the membrane normal ( z - axis ) as the reaction coordinate , the space to be sampled was divided 
 into 36 windows with neighboring windows separated by 1  . since 
 each system contains two copies of the side chain analogue and each 
 copy is offset by 32.5  along the normal , the effective window 
 spacing is 0.5  . the first 500 ps 
 was considered equilibration time and not included in the analysis . 
 in aggregate , these simulations encompass more than 3.7 s of 
 simulated trajectories . the free energy profiles were reconstructed 
 using the weighted histogram analysis method ( wham ) . the wham calculations and error estimates were carried out using 
 the g_wham program in the gromacs package . all data within 35  of the membrane center were used for the 
 wham calculation . solvation free 
 energies were calculated using alchemical free - energy perturbation 
 ( fep ) . in fep calculations , side chain 
 analogues were alchemically solvated in a liquid of interest , namely , 
 dcle , water , or dodecane . growth of the side chain into solution was 
 controlled by the parameter  , ranging from 0 to 1 , which couples 
 the side chain to the hamiltonian of the rest of the system . a scaled - shifted soft - core potential was used for van der waals interactions to reduce 
 occurrences of singularities for small values of . each simulation 
 was run in both directions : forward ( solvation ,  from 0 to 
 1 ) and backward ( desolvation ,  from 1 to 0 ) . the calculations 
 were divided into 25 windows , where  increased linearly by 
 0.04 between windows . each window consisted of 10 ps of equilibration 
 and 250 ps of data collection , for a total of 13 ns for each side 
 chain analogue / solvent combination . analysis of fep results was performed 
 using the bennett acceptance ratio as 
 implemented in the parsefep plugin of 
 vmd . the pmfs resulting from the umbrella sampling calculations were 
 analyzed on the basis of four distinct regions of the modeled membranes 
 ( figure 1 ) . these regions correspond to the 
 changing properties of the membrane , and also allow direct comparison 
 to previous computational and experimental reports , which made 
 use of this regional analysis scheme . the original definition of the 
 regions was based on the free volume accessible to spherical particles . here , region i ( ri - core ) is defined to be |z|  10  ( with z = 0 representing 
 the midpoint of the membrane ) , where liquid dcle , representing the 
 hydrophobic core of the hmmm membrane , predominates . region ii ( rii - tails ) , 
 10  < |z|  17.5  , 
 is the region encompassing the acyl chains of the short lipid tails . 
 this region is predominantly composed of the acyl tails , and resembles 
 a soft polymer that introduces restrictions on rotational and translational 
 degrees of freedom of penetrants . region iii ( riii - heads ) , 17.5  
 < |z|  25  , is the lipid headgroup 
 region which also contains water molecules and ions that are strongly 
 bound to the head groups . the riii - heads region contains most of the 
 phosphate atomic density and is the interfacial region of the membrane . region iv ( riv - water ) includes all atoms with |z| 
 > 25  and contains primarily bulk water . the hmmm model was developed to facilitate studies of peripheral protein interactions 
 with membranes ; therefore , special attention in the following analyses 
 is devoted to rii - tails and riii - heads regions , where most of the 
 membrane - anchoring protein domains appear to interact with lipids . for ease of understanding , we use descriptive abbreviated names 
 ( e.g. , ri - core ) throughout the text . ( top ) a snapshot of the system used to 
 calculate the pmfs of membrane 
 insertion of the 10 side chain analogues . in the hmmm membrane , dcle 
 is shown in green , bulk water in blue , and the short - tailed pc lipids 
 as sticks with carbon in gray , oxygen in red , nitrogen in blue , and 
 phosphorus in gold . the ala analogue , methane , is included to demonstrate 
 the initial positioning of the two copies in the system . ( bottom ) 
 the atomic density of various chemical groups in the hmmm system . the dashed lines show the demarcation between the different regions 
 used in the analysis of pmf plots . region i , ri - core , is defined to 
 be the area in the center of the membrane with |z|  10  and is composed mostly of liquid dcle . region 
 ii , rii - tails , occupies the area 10  < |z|  17.5  and encompasses the tails of the st - lipids 
 as well as the glycerol moiety and some phosphate density . |z| 
  25  and contains the majority of the phosphate density 
 as well as all of the choline density and associated water molecules 
 and ions . region iv , riv - water , is |z| > 25  
 and is comprised of bulk aqueous solution . the main goal of this report is to quantitatively assess 
 the accuracy 
 of the hmmm model membrane in describing protein side chain insertion 
 into distinct regions of a membrane and , in doing so , to facilitate 
 further development and application of model membranes . we compare 
 our calculations to the previously reported computational studies 
 of full - tail membrane models described with all - atom opls ( full - aa ) and coarse - grained martini ( full - cg ) force fields . additionally , we compare our results 
 to the free energy values reported on the basis of experiments by 
 wimley and white ( ww ) , hessa et al . , aliphatic protein side chains 
 are critical in the binding and insertion of peripheral proteins into 
 the membrane . the calculated pmfs for insertion of representative 
 aliphatic side chains , ala and ile , into the hmmm membrane show excellent 
 agreement , both in the shape and in the absolute values , when compared 
 to the full - aa and full - cg calculations ( figure 2 ) . the pmfs display a small ( 1 kcal / mol or 1.5 kt ) barrier 
 at the interface between water and the membrane , the riii - heads region , 
 followed by an attractive basin that reflects the hydrophobic nature 
 of the side chains . the free energy steeply decreases from the riii - heads 
 and rii - tails regions into the ri - core region as the side chains move 
 into a less dense and more nonpolar environment . the liquid core of 
 the hmmm reproduces the free energy of transfer from water to a full - tail 
 membrane core for both the linear ile side chain ( n - butane ) and for the nearly spherical ala ( methane ) . the absolute 
 values of the transfer free energies of ala and ile from water into 
 the center of the membrane ( ri - core region ) agree very well with the 
 values reported from early experiments of radzicka and wolfenden on partitioning of the same side chain analogues 
 between water and cyclohexane : ala , 2.0 kcal / mol ( hmmm ) vs 
 1.8 kcal / mol ( rw ) and ile , 4.7 
 kcal / mol ( hmmm ) vs 4.9 kcal / mol ( rw ) . pmfs for representative aliphatic side chain analogues , ala ( left ) 
 and ile ( right ) . data are presented for the hmmm membrane ( blue ) , 
 full - aa ( black ) , and full - cg ( purple ) . all pmfs 
 are presented by setting the free energy to zero in aqueous solution . free energy of ile transfer from water into the 
 center of the rii - tails 
 region ( 3.0 kcal / mol at z = 13.75  ) 
 is in closer agreement with the experimental measurements by wimley 
 and white of the partitioning of specifically designed peptides from 
 water to the popc membrane interface ( 4.5 kcal / mol ) than the calculated value for the transfer from 
 water into the center of the riii - heads region ( 0.75 kcal / mol at z = 21.25  ) . this suggests that the interfacial interactions 
 between membrane and peptides reported by wimley and white were likely reflecting localization of the side 
 chain at the beginning of the lipid tails , just below the lipid head 
 groups , which agrees well with computational results for similar systems . the small differences in the absolute values 
 between the hmmm and experimental measures can be attributed to the 
 absence of the protein backbone in our calculations . aromatic side chains studied here 
 ( tyr , trp , phe ) display a more complex behavior due to variations 
 in shape , hydrogen bonding capacity , and dipole moments . the free energies of aromatic side chain insertion into all regions 
 of hmmm agree well with full - aa and full - cg pmfs , except in ri - core where insertion into 
 the liquid dcle is more favorable than it is in full - aa or full - cg 
 membranes , and will be discussed at length below ( figure 3 ) . tyr and trp are nearly twice as overstabilized 
 as phe in the ri - core region of the hmmm membranes as compared to 
 full - tailed membranes ( full - aa and full - cg ) . pmfs for aromatic side chain analogues , phe 
 ( top ) , tyr ( middle ) , 
 and trp ( bottom ) . data are presented for the hmmm membrane ( blue ) , 
 full - aa ( black ) , and full - cg ( purple ) . all pmfs are presented by setting the free energy 
 to zero in aqueous solution . headgroup 
 interface , displays stabilization relative to the solution in the 
 calculated pmfs ( figure 3 ) . trp and tyr are 
 especially known for their abundance in the  interfacial belt  
 of membrane proteins and for their role in anchoring transmembrane 
 helices . indeed , we observe the deepest minimum in the pmf 
 of trp ( 5.0 kcal / mol ) , followed by slightly shallower minima 
 for tyr ( 3.5 kcal / mol ) and phe ( 4.1 kcal / mol ) ( figure 3 ) . while preserving the general form of the pmfs , 
 the free energies within the rii - tails region deviate slightly but 
 are in good agreement with previous computational and experimental data ( adjusted to the value for ala ) on interfacial 
 free energies : trp , 2.85 kcal 
 ( hmmm ) vs 3.7 kcal / mol ( full - aa ) vs 2.0 kcal / mol ( ww ) ; tyr , 
 2.15 kcal / mol ( hmmm ) vs 2.0 kcal / mol ( full - aa ) vs 
 1.1 kcal / mol ( ww ) ; and phe , 2.25 kcal ( hmmm ) vs 1.8 
 kcal / mol ( full - aa ) vs 1.3 kcal / mol ( ww ) . the ri - core 
 region of the hmmm membrane shows the largest free 
 energy deviation from the full - aa and 
 full - cg data for aromatic side chains 
 ( figure 3 ) . insertion free energies of aromatic 
 side chains to the center of the membrane are more favorable in the 
 liquid core of hmmm than in the center of full - aa membranes by 4 kcal / mol for tyr and trp versus 2 kcal / mol 
 for phe . these differences can be partially attributed to additional 
 translational and rotational freedom offered by the liquid dcle as 
 compared to the lipid tails in the center of the full - aa and full - cg 
 membranes . in ri - core of the hmmm , bulky side chains are free to rotate , 
 and are not constrained laterally by lengthy acyl tails . this 
 is supported by the distribution of the orientation of tyr 
 in the different regions of the hmmm ( figure 4 ) . the orientation of tyr in ri - core of the hmmm is random , similar 
 to riv - water , demonstrating that tyr is not constrained in orientation 
 in the membrane interior . in rii - tails , where tyr primarily interacts 
 with acyl tails , tyr preferentially orients itself along the membrane 
 normal in both hmmm and full - aa systems . since the interior of a hmmm membrane is liquid , we expect all larger 
 side chains to freely sample orientational space , lowering the free 
 energy in ri - core relative to full - aa values by at least 5/2 kt , with 
 3 rotational and 2 translational additional degrees of freedom that 
 can be populated . distribution of the orientation of tyr at different regions 
 in 
 the hmmm membrane : ri - core ( top ) , rii - tails ( middle ) , and riv - water 
 ( bottom ) . the distribution of orientations in ri - core and riv - water 
 is fairly unbiased , whereas the orientation in rii - tails shows a dramatic 
 skew toward remaining parallel to the membrane normal . the orientation 
 is determined by measuring the angle between the membrane normal and 
 the long axis of tyr ( i.e. , the vector from the carbon at the para position to the phenol oxygen atom ) . the polar nature of dcle also contributes to discrepancies 
 in ri - core 
 between hmmm and full - aa pmfs . dcle has been shown to efficiently 
 orient its dipole around neighboring polar groups in order to reduce 
 the energy penalty for burying these species . thus , the hmmm and full - aa pmfs in ri - core for trp and tyr are more 
 greatly separated than the phe pmfs , due to their polar functional 
 groups that orient surrounding dcle . this can also be seen from the 
 solvation free energies for solvating tyr and phe in dcle , water , 
 and dodecane ( table 1 ) . dcle - watertyr > dcle - waterphe suggests that dcle 
 has 
 water - like interactions with the hydroxyl of tyr , as the two values 
 should be the same when considering the solvation of the phenyl ring . this hypothesis is also supported by the fact that dcle - dodecanetyr < dcle - dodecanephe , suggesting that 
 there are additional stabilizing interactions when solvating tyr into 
 dcle relative to solvating phe . the solvation free 
 energy differences for tyr and phe in water 
 relative to dcle for tyr and phe calculated using fep ( 2.04 
 and 4.28 kcal / mol , respectively ) agree closely with the free 
 energy difference between riv - water and ri - core recovered using umbrella 
 sampling ( figure 3 ) . we believe the differences 
 in the free energy of insertion into the ri - core region are due to 
 an increased entropic stabilization of these bulky groups and the 
 polar nature of dcle . as the hmmm model is designed primarily for 
 studies of peripheral proteins interacting with the membrane , the 
 variances in the free energy of insertion into the membrane center 
 are unlikely to be of a major concern for specific systems of interest . representative polar 
 side chains , ser ( methanol ) and asn ( acetamide ) , show good agreement 
 with the full - aa and full - cg pmfs in the riii - heads and riv - water regions 
 ( figure 5 ) , while the minima in the rii - tails 
 region appear to be more shallow in the hmmm membrane . the full - cg pmf calculated with the martini coarse - grained force field similarly failed to capture the minimum in rii - tails 
 for asn ( figure 5 ) . we believe that dipole 
 interactions are essential to capturing the correct depth of the minima 
 in polar groups , which may have arisen due to favorable interactions 
 between the polar moieties and the acyl tail carbonyl . these interactions 
 would be perturbed in a coarse - grain representation by an inaccurate 
 dipole representation , and are perturbed by dcle occasionally intercalating 
 into the acyl tail region . similar to 
 the aromatic amino acids , the pmfs for polar amino acids in the hmmm 
 show overstabilization in the ri - core region compared to full - aa and 
 full - cg . dipole interactions 
 between the side chains and dcle , and their tumbling within the solvent . pmfs for 
 representative polar side chain analogues , asn ( top ) , 
 ser ( middle ) , and cys ( bottom ) . data are presented for the hmmm membrane 
 ( blue ) , full - aa ( black ) , and full - cg 
 ( purple ) . all pmfs are presented by setting 
 the free energy to zero in aqueous solution . the calculated pmf for cys is in good agreement with the 
 full - aa 
 pmf in regions ii iv ( figure 5 ) , particularly the slope of the free energy from 
 the riii - heads to the rii - tails regions , which is mainly due to the 
 amphipathic nature of the side chain . once again , interactions between 
 the side chain and dcle solvent lead to a low calculated free energy 
 within ri - core of the hmmm relative to comparison membranes . calculated pmfs of representative charged side chains , asp ( acetate ) and arg ( n - propylguanidinium ) , 
 show good agreement with both types of full - tail lipid calculations , 
 full - aa and full - cg , in the regions riii - heads and riv - water ( figure 6 ) . negatively charged asp displays a continuous 
 increase in free energy as it moves from bulk water to the membrane 
 center . for a charged species like asp , it is unsurprising that dipole 
 interactions between the carboxylate of asp and dcle result in a stabilization 
 of asp in ri - core relative to comparison membranes . the flat profile 
 for asp within the interior of ri - core reflects the position at which 
 asp is fully immersed in dcle , and the further insertion results in 
 no free energy change . pmfs for representative charged side chain analogues , 
 asp ( left ) 
 and arg ( right ) . data are presented for the hmmm membrane ( blue ) , 
 full - aa ( black ) , and full - cg ( purple ) . all pmfs are presented by setting the free energy 
 to zero in aqueous solution . since arg is amphipathic , our 
 simulations , as well as the full - aa and 
 full - cg simulations 
 that use an identical protocol ( figure 6 ) , 
 show a sizable free energy well across rii - tails and riii - heads . the 
 wide minimum can be attributed to the interaction of arg s 
 charged guanadinium group with the polar region of up to three lipids 
 ( figure 7 ) simultaneous to partitioning of 
 its alkyl chain into the membrane core , creating a significantly favorable 
 environment and lowering the free energy in these regions . indeed , 
 this orientation is so favorable that it has been proposed to facilitate 
 membrane penetration by arginine - rich peptides , such as antimicrobial peptides . when the guanadinium starts 
 to be buried in the hydrophobic region ( ri - core ) , however , the energetic 
 penalty rapidly rises , as is expected for burying naked charge in 
 a membrane . these high energy penalties arise from the deformation of the membrane 
 to hydrate the charge ( figure 8) , which accounts 
 for a significant portion of the energy penalty , which may be reduced in vivo by the surrounding 
 protein environment . snapshot of the system 
 with an arg side chain analogue ( spheres ) 
 in the interfacial region ( riii - heads ) of the hmmm membrane . oxygen 
 atoms ( red ) of pc lipid head groups ( sticks ) interact with hydrogen 
 atoms ( white ) of the guanidinium group of arg . other atoms shown are 
 carbon ( gray ) , nitrogen ( blue ) , and phosphorus ( gold ) . snapshots of systems with polar and charged residues that 
 display 
 formation of the water defects when amino acids are positioned : at 
 the membrane center - charged arg ( a ) and near the membrane center 
 - polar asn ( b ) . partitioning of polar 
 and charged side chains into the membrane 
 has been shown to be accompanied by the formation of stable water - filled 
 membrane defects . additionally , johansson and lindahl 
 have shown correlation between the hydration level of transmembrane 
 helices and hydrophobicity scales . during 
 our simulations , we observed formation of a stable water - filled defect 
 when charged side chains , arg or asp , are positioned in the center 
 of hmmm membrane ( figure 8) . the water - filled 
 defect was the widest at the base on the membrane interface and was 
 narrowed down to a few water molecules surrounding the side chain 
 in the center of the membrane . in the case of a polar side chain , 
 asn , a water - filled defect is only present when asn is positioned 
 closer to the ends of the tails and not when the residue is near the 
 center of the membrane ( figure 8) . through analysis 
 of the calculated free energy profiles at particular points along 
 the hmmm normal , we can compare the transfer free energy from solution 
 to a specific region of the hmmm with developed hydrophobicity scales . these scales 
 are based on different experimental measurements , including partitioning 
 of side chain analogues from water to cyclohexane , partitioning of specifically designed pentapeptides from 
 water to the interface of the membrane , membrane protein insertion into a membrane via the sec translocon , and equilibrium between folded and unfolded 
 states of a membrane protein . naturally , 
 these different experiments are measuring the energetic difference 
 between the aqueous solution and different regions of a membrane . 
 as the hmmm model is designed to capture partitioning into the membrane 
 interface , the wimley white hydrophobicity scale based on partitioning of pentapeptides to the 
 membrane interface is of particular importance for this study . comparing 
 the insertion free energy of the hmmm to any experimental scale is 
 not intended to reproduce exact free energy differences . due to the 
 differences in protocols between each scale , the uncertainty 
 in exactly which region the peptides partition , and the fact that 
 the simulation system used here does not replicate any of these protocols , 
 there will necessarily be differences in insertion free energies between 
 the hmmm and experimental studies . computational agreement with experimental 
 free energy scales the purpose of this 
 discussion is merely to compare trends in free energy differences 
 for individual amino acids between hydrophobicity scales to gain a 
 better understanding of where the amino acids might partition in experimental 
 studies . first , we compare hmmm free energies to the computational 
 full - aa data reported for a full - tail membrane for different regions from the center of the membrane to 
 lipid head groups ( figure 9 ) . the correlation 
 between all regions studied ( figure 9 ) suggests 
 that the overall energetic trends for side chain  membrane interactions 
 are preserved in the hmmm in all four regions . the slopes of the trend 
 lines for all four membrane regions are also near unity ( figure 9 ) , suggesting that the conversion of a full - tail 
 membrane to the hmmm preserves population - based interaction statistics 
 in all four regions of membrane . notably , though , the riv - water  
 ri - core trend line ( figure 9 ) has the largest 
 vertical shift of + 2.52 kcal / mol with respect to the full - aa data , a systematic shift in the free energy profiles 
 as a result of the increased entropic contribution due to the liquidity 
 of the dcle and the larger dipole of dcle relative to acyl tails that 
 promotes stronger interaction between amino acids with polar groups 
 and the membrane core which replace the membrane core in the hmmm . 
 in regions rii - tail  riv - water , where dcle is less prevalent , 
 we expect and observe native - like membrane interactions and forces 
 in the hmmm system . the preservation of contacts and interaction patterns 
 upon membrane conversion has been observed in studies on peripheral 
 proteins , specifically coagulation factor binding domains and cytochrome 
 p450 . comparison of the transfer free energy of the 
 side chains from 
 solution ( riv - water ) to the regions within the membrane . the points 
 for rii - tails and riii - heads were taken at the midpoint of the region 
 ( z = 13.75  and z = 21.25 
  , respectively ) , while the ri - core position was taken to be 
 the bilayer center . an additional measurement was taken at the interface 
 between rii - tails and riii - heads ( rii / riii , at z = 
 17.5  ) . the positions of points along the x - axis are determined by the hmmm free energy values , while the y - axis values were computed for a full - tail membrane . the dotted lines represent the linear fit of 
 the points , and essential fit information is reported . comparisons of transfer free energies calculated 
 with the hmmm 
 model to experimental hydrophobicity scales show good agreement for most side chains where the 
 hmmm design matches experimental conditions , such as in rii - tails 
 and riii - heads . in particular , comparison of free energy values for 
 riv - water  rii - tails transfer in the hmmm membrane to these 
 scales ( figure 10 ) agrees best with the hydrophobicity 
 scale proposed by wimley and white , where a designed pentapeptide 
 interacts with the membrane interface . the ww hydrophobicity scale is most similar to the conditions in 
 rii - tails , as the peptide explores the region corresponding to the 
 free energy wells for hydrophobic and aromatic side chains ( figures 2 and 3 ) . the behavior in 
 the hmmm for arg is much more different than that of most experiments . 
 due to the favorable interactions arg can form in our simulation system 
 ( figure 7 ) while keeping its long tail buried 
 in the membrane , our simulations show arg insertion to be more favorable 
 than the consensus of experimental findings , where such configurations 
 for arg are not possible . comparison of hydrophobicity scales to the 
 riv - water  rii - tails 
 transfer free energy of the hmmm . published hydrophobicity scales 
 from wimley and white , hessa et al . , radzicka and wolfenden , and moon and fleming were compared 
 against the transfer free energy from riv - water to the midpoint of 
 rii - tails in the hmmm model . the dotted lines represent the linear 
 fit of the points , and essential fit information is reported . a comparison of free energy for 
 riv - water  ri - core transfer 
 in the hmmm membrane to the same scales ( figure 11 ) shows good agreement with the cyclohexane water scale 
 proposed by radzicka and wolfenden and 
 modest agreement with scales based on a transfer of side chains within 
 larger transmembrane proteins . water 
 scale ( figure s1 , supporting information ) , is based on the use of an organic 
 solvent - rich ri - core in the hmmm . the low slopes of the trendline 
 that compares the two experimental studies employing membrane proteins to the hmmm transfer free energies ( figure 11 ) might be a result of the complexity of the environment surrounding 
 the side chains . rather than proceeding from a fully solvated to a 
 fully inserted side chain , as in the case of side chain analogues , 
 in the presence of a protein , interactions between neighboring residues 
 lower the energetic cost for membrane entry by providing favorable 
 interactions for buried side chains . comparison 
 to the computational and experimental hydrophobicity scales indicates 
 the relative accuracy of the hmmm model membranes in capturing the 
 energetics of the membrane interface . comparison of hydrophobicity 
 scales to the riv - water  ri - core 
 transfer free energy of the hmmm . published hydrophobicity scales 
 from wimley and white , hessa et al . , radzicka and wolfenden , and moon and fleming were compared 
 against the transfer free energy from riv - water to the midpoint of 
 the membrane ( within ri - core ) in the hmmm model . the dotted lines 
 represent the linear fit of the points , and essential fit information 
 is reported . the 
 energetic characterization of the highly mobile membrane mimetic 
 ( hmmm ) representation has been presented . the strength of the hmmm model is in its accelerated lipid dynamics , 
 which expedites the formation of optimal protein  lipid interactions , 
 while maintaining an atomistic description of the lipid head groups . a potential drawback of the use of the liquid organic solvent to represent 
 the bilayer core is the introduction of additional fluidity of the 
 core of the membrane and additional polarity , as dcle is not as hydrophobic as the lipid tails in a conventional full - tail 
 membrane . nevertheless , this report shows that the hmmm model captures 
 the interaction energetics of side chains along the membrane interface , 
 a feature that is essential for studying peripheral proteins . we demonstrate that the energetics of insertion into the interfacial 
 membrane regions for representatives of all classes of protein side 
 chains are generally in good agreement with previously reported computation- 
 and experiment - based values . on the other hand , we observe overstabilization 
 of aromatic , polar , and charged side chains in the center of the hmmm 
 membrane due to the more liquid and polar nature of the organic solvent 
 currently used in hmmm ( dcle ) compared to acyl lipid tails . these 
 variations do not appear to interfere with the phenomena at the membrane 
 interface , for which hmmm was specifically developed and is currently 
 used . in particular , it is of value that the hmmm model 
 is capable of capturing the energetic cost of trp and tyr insertion 
 into the membrane interface . these amino acids are known to serve 
 as anchors of the transmembrane helices , especially 
 in single - pass membrane proteins where they ensure proper positioning 
 and tilting within the membrane bilayer . we expect that the hmmm will 
 perform well with single - pass transmembrane helices where aliphatic 
 residues in the core and aromatic side chains at the interface are 
 the most important determinants of the depth of insertion and tilting . further development to address inaccuracies in the membrane core and 
 to extend the applicability of the model to larger transmembrane systems 
 is currently underway .
energetics 
 of protein side chain partitioning between aqueous solution 
 and cellular membranes is of fundamental importance for correctly 
 capturing the membrane binding and specific protein 
 lipid interactions 
 of peripheral membrane proteins . 
 we recently reported a highly mobile 
 membrane mimetic ( hmmm ) model that accelerates lipid dynamics by modeling 
 the membrane interior partially as a fluid organic solvent while retaining 
 a literal description of the lipid head groups and the beginning of 
 the tails . 
 while the hmmm has been successfully applied to study spontaneous 
 insertion of a number of peripheral proteins into membranes , a quantitative 
 characterization of the energetics of membrane  protein interactions 
 in hmmm membranes has not been performed . 
 we report here the free 
 energy profiles for partitioning of 10 protein side chain analogues 
 into a hmmm membrane . in the interfacial and headgroup regions of 
 the membrane , the side chain 
 free energy profiles show excellent agreement 
 with profiles previously reported for conventional membranes with 
 full - tail lipids . in regions where the organic solvent is prevalent 
 , 
 the increased dipole and fluidity of the solvent generally result 
 in a less accurate description , most notably overstabilization of 
 aromatic and polar amino acids . as an additional measure of the ability 
 of the hmmm model to describe membrane  protein interactions , 
 the water - to - membrane interface transfer energies were analyzed and 
 found to be in agreement with the previously reported experimental 
 and computational hydrophobicity scales . 
 we discuss strengths and 
 weaknesses of hmmm in describing protein 
 membrane interactions 
 as well as further development of model membranes .