Thermodynamic stability of the bacteriorhodopsin lattice as measured by lipid dilution

To determine the strength of noncovalent interactions that stabilize a membrane protein complex, we have developed an in vitro method for quantifying the dissociation of the bacteriorhodopsin (BR) lattice, a naturally occurring two-dimensional crystal. A lattice suspension was titrated with a short- and long-chain phosphatidylcholine mixture to dilute BR within the lipid bilayer. The fraction of BR in the lattice form as a function of added lipid was determined by visible circular dichroism spectroscopy and fit with a cooperative self-assembly model to obtain a critical concentration for lattice assembly. Critical concentration values of wild-type and mutant proteins were used to calculate the change in lattice stability upon mutation (DeltaDeltaG). By using this method, a series of mutant proteins was examined in which residues at the BR-BR interface were replaced with smaller amino acids, either Ala or Gly. Most of the mutant lattices were destabilized, with DeltaDeltaG values of 0.2-1.1 kcal/mol at 30 degrees C, consistent with favorable packing of apolar residues in the membrane. One mutant, I45A, was stabilized by approximately 1.0 kcal/mol, possibly due to increased lipid entropy. The DeltaDeltaG values agreed well with previous in vivo measurements, except in the case of I45A. The ability to measure the change in stability of mutant protein complexes in a lipid bilayer may provide a means of determining the contributions of specific protein-protein and protein-lipid interactions to membrane protein structure.     

Substitution rates in α-helical transmembrane proteins

It has been shown previously that some membrane proteins have a conserved core of amino acid residues. This idea not only serves to orient helices during model building exercises but may also provide insight into the structural role of residues mediating helix-helix interactions. Using experimentally determined high-resolution structures of alpha-helical transmembrane proteins we show that, of the residues within the hydrophobic transmembrane spans, the residues at lipid and subunit interfaces are more evolutionarily variable than those within the lipid-inaccessible core of a polypeptide's transmembrane domain. This supports the idea that helix-helix interactions within the same polypeptide chain and those at the interface between different polypeptide chains may arise in distinct ways. To show this, we use a new method to estimate the substitution rate of an amino acid residue given an alignment and phylogenetic tree of closely related proteins. This method gives better sensitivity in the otherwise-conserved transmembrane domains than a conventional similarity analysis and is relatively insensitive to the sequences used.     

Sequence dependence of BNIP3 transmembrane domain dimerization implicates side-chain hydrogen bonding and a tandem GxxxG motif in specific helix-helix interactions

The transmembrane domain of the pro-apoptotic protein BNIP3 self-associates strongly in membranes and in detergents. We have used site-directed mutagenesis to analyze the sequence dependence of BNIP3 transmembrane domain dimerization, from which we infer the physical basis for strong and specific helix-helix interactions in this system. Hydrophobic substitutions identify six residues as critical to dimerization, and the pattern of sensitive residues suggests that the BNIP3 helices interact at a right-handed crossing angle. Based on the dimerization propensities of single point mutants, we propose that: polar residues His173 and Ser172 make inter-monomer hydrogen bonds to one another through their side-chains; Ala176, Gly180, and Gly184 form a tandem GxxxG motif that allows close approach of the helices; and Ile183 makes inter-monomer van der Waals contacts. Since neither the tandem GxxxG motif nor the hydrogen bonding pair is sufficient to drive dimerization, our results demonstrate the importance of sequence context for either hydrogen bonding or GxxxG motif involvement in BNIP3 transmembrane helix-helix interactions. In this study, hydrophobic substitutions away from the six interfacial positions have almost no effect on dimerization, confirming the expectation that hydrophobic replacements affect helix-helix interactions only if they interfere with packing or hydrogen bonding by interfacial residues. However, changes to slightly polar residues are somewhat disruptive even when located away from the interface, and the degree of disruption correlates with the decrease in hydrophobicity. Changing the hydrophobicity of the BNIP3 transmembrane domain alters its helicity and protection of its backbone amides. We suggest that polar substitutions decrease the fraction of dimer by stabilizing an unfolded monomeric state of the transmembrane span, rather than by affecting helix-helix interactions. This result has broad implications for interpreting the sequence dependence of membrane protein stability in detergents.     

Role of the F1 region in the Escherichia coli aerotaxis receptor Aer

In Escherichia coli, the aerotaxis receptor Aer is an atypical receptor because it senses intracellular redox potential. The Aer sensor is a cytoplasmic, N-terminal PAS domain that is tethered to the membrane by a 47-residue F1 linker. Here we investigated the function, topology, and orientation of F1 by employing random mutagenesis, cysteine scanning, and disulfide cross-linking. No native residue was obligatory for function, most deleterious substitutions had radically different side chain properties, and all F1 mutants but one were functionally rescued by the chemoreceptor Tar. Cross-linking studies were consistent with the predicted α-helical structure in the N-terminal F1 region and demonstrated trigonal interactions among the F1 linkers from three Aer monomers, presumably within trimer-of-dimer units, as well as binary interactions between subunits. Using heterodimer analyses, we also demonstrated the importance of arginine residues near the membrane interface, which may properly anchor the Aer protein in the membrane. By incorporating these data into a homology model of Aer, we developed a model for the orientation of the Aer F1 and PAS regions in an Aer lattice that is compatible with the known dimensions of the chemoreceptor lattice. We propose that the F1 region facilitates the orientation of PAS and HAMP domains during folding and thereby promotes the stability of the PAS and HAMP domains in Aer.     

Characterizing molecular interactions in different bacteriorhodopsin assemblies by single-molecule force spectroscopy

Using single-molecule force spectroscopy we characterized inter- and intramolecular interactions stabilizing structural segments of individual bacteriorhodopsin (BR) molecules assembled into trimers and dimers, and monomers. While the assembly of BR did not vary the location of these structural segments, their intrinsic stability could change up to 70% increasing from monomer to dimer to trimer. Since each stable structural segment established one unfolding barrier, we conclude that the locations of unfolding barriers were determined by intramolecular interactions but that their strengths were strongly influenced by intermolecular interactions. Subtracting the unfolding forces of the BR trimer from that of monomer allowed us to calculate the contribution of inter- and intramolecular interactions to the membrane protein stabilization. Statistical analyses showed that the unfolding pathways of differently assembled BR molecules did not differ in their appearance but in their population. This suggests that in our experiments the membrane protein assembly does not necessarily change the location of unfolding barriers within the protein, but certainly their strengths, and thus alters the probability of a protein to choose certain unfolding pathways.     

Sequence specificity in the dimerization of transmembrane alpha-helices.

While several reports have suggested a role for helix-helix interactions in membrane protein oligomerization, there are few direct biochemical data bearing on this subject. Here, using mutational analysis, we show that dimerization of the transmembrane alpha-helix of glycophorin A in a detergent environment is spontaneous and highly specific. Very subtle changes in the side-chain structure at certain sensitive positions disrupt the helix-helix association. These sensitive positions occur at approximately every 3.9 residues along the helix, consistent with their comprising the interface of a closely fit transmembranous supercoil of alpha-helices. By contrast with other reported cases of interactions between transmembrane helices, the set of interfacial residues in this case contains no highly polar groups. Amino acids with aliphatic side chains define much of the interface, indicating that precise packing interactions between the helices may provide much of the energy for association. These data highlight the potential general importance of specific interactions between the hydrophobic anchors of integral membrane proteins.     

The position of the Gly-xxx-Gly motif in transmembrane segments modulates dimer affinity.

Although the intrinsic low solubility of membrane proteins presents challenges to their high-resolution structure determination, insight into the amino acid sequence features and forces that stabilize their folds has been provided through study of sequence-dependent helix-helix interactions between single transmembrane (TM) helices. While the stability of helix-helix partnerships mediated by the Gly-xxx-Gly (GG4) motif is known to be generally modulated by distal interfacial residues, it has not been established whether the position of this motif, with respect to the ends of a given TM segment, affects dimer affinity. Here we examine the relationship between motif position and affinity in the homodimers of 2 single-spanning membrane protein TM sequences: glycophorin A (GpA) and bacteriophage M13 coat protein (MCP). Using the TOXCAT assay for dimer affinity on a series of GpA and MCP TM segments that have been modified with either 4 Leu residues at each end or with 8 Leu residues at the N-terminal end, we show that in each protein, centrally located GG4 motifs are capable of stronger helix-helix interactions than those proximal to TM helix ends, even when surrounding interfacial residues are maintained. The relative importance of GG4 motifs in stabilizing helix-helix interactions therefore must be considered not only in its specific residue context but also in terms of the location of the interactive surface relative to the N and C termini of alpha-helical TM segments.     

Helical integrity and microsolvation of transmembrane domains from Flaviviridae envelope glycoproteins

Charged and polar amino acids in the transmembrane domains of integral membrane proteins can be crucial for protein function and also promote helix-helix association or protein oligomerization. Yet, our current understanding is still limited on how these hydrophilic amino acids are efficiently translocated from the Sec61/SecY translocon into the cell membrane during the biogenesis of membrane proteins. In hepatitis C virus, the putative transmembrane segments of envelope glycoproteins E1 and E2 were suggested to heterodimerize via a Lys-Asp ion-pair in the host endoplasmic reticulum. Therefore in this work, we carried out molecular dynamic simulations in explicit lipid bilayer and solvent environment to explore the stability of all possible bridging ion-pairs using the model of H-segment helix dimers. We observed that, frequently, several water molecules penetrated from the interface into the membrane core to stabilize the charged and polar pairs. The hydration time and amount of water molecules in the membrane core depended on the position of the charged residues as well as on the type of ion-pairs. Similar microsolvation events were observed in simulations of the putative E1-E2 transmembrane helix dimers. Simulations of helix monomers from other members of the Flaviviridae family suggest that these systems show similar behaviors. Thus this study illustrates the important contribution of water microsolvation to overcome the unfavorable energetic cost of burying charged and polar amino acids in membrane lipid bilayers. Also, it emphasizes the novel role of bridging charged or polar interactions stabilized by water molecules in the hydrophobic lipid bilayer core that has an important biological function for helix dimerization in several envelope glycoproteins from the family of Flaviviridae viruses.     

Engineered oligomerization state of OmpF protein through computational design decouples oligomer dissociation from unfolding

Biogenesis of β-barrel membrane proteins is a complex, multistep, and as yet incompletely characterized process. The bacterial porin family is perhaps the best-studied protein family among β-barrel membrane proteins that allows diffusion of small solutes across the bacterial outer membrane. In this study, we have identified residues that contribute significantly to the protein-protein interaction (PPI) interface between the chains of outer membrane protein F (OmpF), a trimeric porin, using an empirical energy function in conjunction with an evolutionary analysis. By replacing these residues through site-directed mutagenesis either with energetically favorable residues or substitutions that do not occur in natural bacterial outer membrane proteins, we succeeded in engineering OmpF mutants with dimeric and monomeric oligomerization states instead of a trimeric oligomerization state. Moreover, our results suggest that the oligomerization of OmpF proceeds through a series of interactions involving two distinct regions of the extensive PPI interface: two monomers interact to form a dimer through the PPI interface near G19. This dimer then interacts with another monomer through the PPI interface near G135 to form a trimer. We have found that perturbing the PPI interface near G19 results in the formation of the monomeric OmpF only. Thermal denaturation of the designed dimeric OmpF mutant suggests that oligomer dissociation can be separated from the process of protein unfolding. Furthermore, the conserved site near G57 and G59 is important for the PPI interface and might provide the essential scaffold for PPIs.     

Forces involved in the assembly and stabilization of membrane proteins.

Hydrophobic organization: Determination of the structure of the bacterial photosynthetic reaction center, bacterial porins, and bacteriorhodopsin allows a comparison of the basic structural features of integral membrane proteins. Structure parameters of membrane- and water-soluble proteins are surprisingly similar, given the different dielectric environments, except for the polarity of residues on the protein surface. Hydrophobic and electrostatic forces: 1) Intramembrane helix-helix interactions that are sensitive to small structure changes can dictate assembly of membrane proteins, as indicated by reconstitution of bacteriorhodopsin from proteolytic fragments and specific dimer formation of the human erythrocyte sialoglycoprotein glycophorin A. 2) Electrostatic interactions have an important role in determining the trans-membrane orientation of integral membrane proteins of the bacterial inner membrane, as expressed by the "positive-inside" rule for the distribution of basic residues on the cis relative to the trans side of the membrane-spanning alpha-helices. The use of this charge asymmetry rule, in conjunction with a hydrophobicity algorithm for prediction of membrane-spanning domains, allows accurate prediction of the folding patterns of such polypeptides across the membrane. A role of electrostatic interactions in assembly and maintenance of the structure of oligomeric integral membrane protein complexes is also implied by the separation and extrusion from the membrane, at high pH, of the major hydrophobic subunits of the cytochrome b6f complex from the chloroplast thylakoid membrane. It is inferred that the hydrophobic helix-helix interactions between the subunits of this complex, whose function is electron transfer and proton translocation, are relatively weak compared to those in bacteriorhodopsin.     

Assembly of a transmembrane b-type cytochrome is mainly driven by transmembrane helix interactions

Folding, assembly and stability of alpha-helical membrane proteins is still not very well understood. Several of these membrane proteins contain cofactors, which are essential for their function and which can be involved in protein assembly and/or stabilization. The effect of heme binding on the assembly and stability of the transmembrane b-type cytochrome b'559 was studied by fluorescence resonance energy transfer. Cytochrome b'559 consists of two monomers of a 44 amino acid long polypeptide, which contains one transmembrane domain. The synthesis of two variants of the b'559 monomer, each carrying a specific fluorescent dye, allowed monitoring helix-helix interactions in micelles by resonance energy transfer. The measurements demonstrate that the transmembrane peptides dimerize in detergent in the absence and presence of the heme cofactor. Cofactor binding only marginally enhances dimerization and, apparently, the redox state of the heme group has no effect on dimerization.     

Membrane-bound structure and energetics of alpha-synuclein

Aggregation and fibrillation of alpha-synuclein bound to membranes are believed to be involved in Parkinson's and other neurodegenerative diseases. On SDS micelles, the N-terminus of alpha-synuclein forms two curved helices linked by a short loop. However, its structure on lipid bilayers has not been experimentally resolved. Using MD simulations with an implicit membrane model we show here that, on a planar mixed membrane, the truncated alpha-synuclein (residues 1-95) forms a bent helix. Bending of the helix is not due to the protein sequence or membrane binding, but to collective motions of the long helix. The backbone of the helix is approximately 2.5 A above the membrane surface, with some residues partially inserted in the membrane core. The helix periodicity is 11/3 (11 residues complete three full turns) as opposed to 18/5 periodicity of an ideal alpha-helix, with hydrophobic residues towards the membrane, negatively charged residues towards the solvent and lysines on the polar/nonpolar interface. A series of threonines, which are characteristic for alpha-synuclein and perhaps a phosphorylation site, is also located at the hydrophobic/hydrophilic interface with their side chain often hydrogen bonded to the main-chain atom. The calculations show that the energy penalty for change in periodicity from the 18/5 to 11/3 on the anionic membrane is overcome by favorable solvation energy. The binding of truncated alpha-synuclein to membranes is weak. It prefers anionic membranes but it also binds marginally to a neutral membrane, via its C-terminus. Dimerization of helical monomers on the mixed membrane is energetically favorable. However, it slightly interferes with membrane binding. This might promote lateral diffusion of the protein on the membrane surface and facilitate assembly of oligomers that precede fibrillation.     

Core side-chain packing and backbone conformation in Lpp-56 coiled-coil mutants

Native proteins exhibit precise geometric packing of atoms in their hydrophobic interiors. Nonetheless, controversy remains about the role of core side-chain packing in specifying and stabilizing the folded structures of proteins. Here we investigate the role of core packing in determining the conformation and stability of the Lpp-56 trimerization domain. The X-ray crystal structures of Lpp-56 mutants with alanine substitutions at two and four interior core positions reveal trimeric coiled coils in which the twist of individual helices and the helix-helix spacing vary significantly to achieve the most favored superhelical packing arrangement. Introduction of each alanine "layer" into the hydrophobic core destabilizes the superhelix by 1.4 kcal mol(-1). Although the methyl groups of the alanine residues pack at their optimum van der Waals contacts in the coiled-coil trimer, they provide a smaller component of hydrophobic interactions than bulky hydrophobic side-chains to the thermodynamic stability. Thus, specific side-chain packing in the hydrophobic core of coiled coils are important determinants of protein main-chain conformation and stability.     

The stability of transmembrane helix interactions measured in a biological membrane

Despite some promising progress in the understanding of membrane protein folding and assembly, there is little experimental information regarding the thermodynamic stability of transmembrane helix interactions and even less on the stability of transmembrane helix-helix interactions in a biological membrane. Here we describe an approach that allows quantitative measurement of transmembrane helix interactions in a biological membrane, and calculation of changes in the interaction free energy resulting from substitution of single amino acids. Dimerization of several variants of the glycophorin A transmembrane domain are characterized and compared to the wild-type (wt) glycophorin A transmembrane helix dimerization. The calculated DeltaDeltaG(app) values are further compared with values found in the literature. In addition, we compare interactions between the wt glycophorin A transmembrane domain and helices in which critical glycine residues are replaced by alanine or serine, respectively. The data demonstrate that replacement of the glycine residues by serine is less destabilizing than replacement by alanine with a DeltaDeltaG(app) value of about 0.4 kcal/mol. Our study comprises the first measurement of a transmembrane helix interaction in a biological membrane, and we are optimistic that it can be further developed and applied.     

Comparison of helix interactions in membrane and soluble alpha-bundle proteins

Helix-helix interactions are important for the folding, stability, and function of membrane proteins. Here, two independent and complementary methods are used to investigate the nature and distribution of amino acids that mediate helix-helix interactions in membrane and soluble alpha-bundle proteins. The first method characterizes the packing density of individual amino acids in helical proteins based on the van der Waals surface area occluded by surrounding atoms. We have recently used this method to show that transmembrane helices pack more tightly, on average, than helices in soluble proteins. These studies are extended here to characterize the packing of interfacial and noninterfacial amino acids and the packing of amino acids in the interfaces of helices that have either right- or left-handed crossing angles, and either parallel or antiparallel orientations. We show that the most abundant tightly packed interfacial residues in membrane proteins are Gly, Ala, and Ser, and that helices with left-handed crossing angles are more tightly packed on average than helices with right-handed crossing angles. The second method used to characterize helix-helix interactions involves the use of helix contact plots. We find that helices in membrane proteins exhibit a broader distribution of interhelical contacts than helices in soluble proteins. Both helical membrane and soluble proteins make use of a general motif for helix interactions that relies mainly on four residues (Leu, Ala, Ile, Val) to mediate helix interactions in a fashion characteristic of left-handed helical coiled coils. However, a second motif for mediating helix interactions is revealed by the high occurrence and high average packing values of small and polar residues (Ala, Gly, Ser, Thr) in the helix interfaces of membrane proteins. Finally, we show that there is a strong linear correlation between the occurrence of residues in helix-helix interfaces and their packing values, and discuss these results with respect to membrane protein structure prediction and membrane protein stability.     

Mutational Analysis of the Class IIa Bacteriocin Curvacin A and Its Orientation in Target Cell Membranes

To analyze the orientation in target cell membranes of the pediocin-like bacteriocin (antimicrobial peptide) curvacin A, 55 variants were generated by site-directed mutagenesis and their potencies against four different target cells determined. The result suggest that the somewhat hydrophilic short central helix (residues 19 to 24), along with the N-terminal β-sheet-like structure (residues 1 to 16), inserts in the interface region of the target cell membrane, with Ala22 close to the hydrophobic core of the membrane. The following hinge region, with Gly28 as an important residue, may then form a turn wherein Gly28 becomes positioned near the border between the interface and the hydrophobic regions, thus permitting the longer and more-hydrophobic C-terminal helix (residues 29 to 41) to insert into the hydrophobic core of the membrane. This helix contains three glycine residues (G33, G37, and G40) that form a putative helix-helix-interacting GxxxGxxG motif. The replacement of any of these glycines with a larger residue was very detrimental, suggesting their possible involvement in helix-helix interactions with a membrane-embedded receptor protein.     

The energetics of consensus promoter opening by T7 RNA polymerase

The 50-residue major coat protein (MCP) of Ff bacteriophage exists as a single-spanning membrane protein in the Escherichia coli host inner membrane prior to assembly into lipid-free virions. Here, the molecular bases for the specificity and stoichiometry that govern the protein-protein interactions of MCP in the host membrane are investigated in detergent micelles. To address these structural issues, as well as to circumvent viability requirements in mutants of the intact protein, peptides corresponding to the effective alpha-helical TM segment of wild-type and mutant bacteriophage MCPs were synthesized. Fluorescence resonance energy transfer (FRET) experiments on the dansyl and dabcyl-labeled MCP TM domain peptides in detergent micelles demonstrated that the peptides specifically associate into non-covalent homodimers, as postulated for the biologically relevant membrane-embedded MCP oligomer. MCP peptides labeled with short-range pyrene fluorophores at the N terminus displayed excimer fluorescence consistent with homodimerization occurring in a parallel fashion. Variant peptides synthesized with single substitutions at helix-interactive positions displayed a wide range of dimer/monomer ratios on SDS-PAGE gels, which are interpreted in terms of steric volume, presence or absence of beta-branching, and the effect of polar substituents. The overall results indicate discrete roles for helix-helix interfacial residues as packing recognition elements in the membrane-inserted state, and suggest a possible correlation between phage viability and efficacy of MCP TM-TM interactions.     

The effect of interactions involving ionizable residues flanking membrane-inserted hydrophobic helices upon helix-helix interaction

We examined the effect of ionizable residues at positions flanking the hydrophobic core of helix-forming polyLeu peptides upon helix-helix interactions within model membrane vesicles composed of dioleoylphosphatidylcholine. The peptides studied were flanked on both the N and C termini either by two Lys (K(2)-flanked peptide), one Lys plus one Asp (DK-flanked peptide), or one Lys plus three Asp (KD(3)-flanked peptide). The fluorescence of a Trp residue positioned at the center of the hydrophobic sequence was used to evaluate peptide behavior. As judged by the concentration dependence of the maximum wavelength of Trp emission, there was significant oligomerization of the KD(3)- and DK-flanked peptides, but not the K(2)-flanked peptide, at neutral pH. At neutral pH mixtures of K(2)- and KD(3)-flanked peptides associated with each other, but mixtures of the K(2)- and DK-flanked peptides did not. Oligomerization by the DK- and KD(3)-flanked peptides decreased under low pH conditions in which the Asp residues were protonated. Additional experiments showed that at neutral pH the KD(3)-flanked peptide showed an increased tendency to oligomerize when as little as 10-15 mol % of an anionic lipid, phosphatidylglycerol, was present. The behavior of the other peptides was not strongly influenced by phosphatidylglycerol. These results can largely be explained by modulation of helix-helix interactions via electrostatic interactions involving the helix-flanking ionizable residues. Such interactions may influence membrane protein folding. The self-association of anionic KD(3)-flanked peptides suggests that additional interactions involving charged residues also can modulate helix-helix association.     

Fluidizing the membrane by a local anesthetic: phenylethanol affects membrane protein oligomerization

The exact mechanism of action of anesthetics is still an open question. While some observations suggest specific anesthetic-protein interactions, nonspecific perturbation of the lipid bilayer has also been suggested. Perturbations of bilayer properties could subsequently affect the structure and function of membrane proteins. Addition of the local anesthetic phenylethanol (PEtOH) to model membranes and intact Escherichia coli cells not only affected membrane fluidity but also severely altered the defined helix-helix interaction within the membrane. This experimental observation suggests that certain anesthetics modulate membrane physical properties and thereby indirectly affect transmembrane (TM) helix-helix interactions, which are not only involved in membrane protein folding and assembly but also important for TM signaling.     

Tryptophan 243 affects interprotein contacts, cofactor binding and stability in D-amino acid oxidase from Rhodotorula gracilis

The flavoenzyme d-amino acid oxidase from Rhodotorula gracilis is a homodimeric protein whose dimeric state has been proposed to occur as a result of (a) the electrostatic interactions between positively charged residues of the betaF5-betaF6 loop of one monomer and negatively charged residues belonging to the alpha-helices I3' and I3' of the other monomer, and (b) the interaction of residues (e.g. Trp243) belonging to the two monomers at the mixed interface region. The role of Trp243 was investigated by substituting it with either tyrosine or isoleucine: both substitutions were nondisruptive, as confirmed by the absence of significant changes in catalytic activity, but altered the tertiary structure (yielding a looser conformation) and decreased the stability towards temperature and denaturants. The change in conformation interferes both with the interaction of the coenzyme to the apoprotein moiety (although the kinetics of the apoprotein-FAD complex reconstitution process are similar between wild-type and mutant D-amino acid oxidases) and with the interaction between monomers. Our results indicate that, in the folded holoenzyme, Trp243 is situated at a position optimal for increasing the interactions between monomers by maximizing van der Waals interactions and by efficiently excluding solvent.