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Analysis of accessible surface of residues in proteins

Centre de Biophysique Moléculaire Numérique (CBMN), Faculté des Sciences Agronomiques de Gembloux (FSAGx), 5030 Gembloux, Belgium

Reprint requests to: Robert Brasseur, CBMN, Passage des Déportés, 2, FSAGx, B-5030 Gembloux, Belgium; e-mail: brasseur.r{at}fsagx.ac.be; fax: 32-8162-2522.

(RECEIVED January 31, 2003; FINAL REVISION April 26, 2003; ACCEPTED April 28, 2003)

Article and publication are at http://www.proteinscience.org/cgi/doi/10.1110/ps.0304803.

	Abstract

TOP Abstract Introduction Results Discussion Materials and methods References

 
We analyzed the total, hydrophobic, and hydrophilic accessible surfaces (ASAs) of residues from a nonredundant bank of 587 3D structure proteins. In an extended fold, residues are classified into three families with respect to their hydrophobicity balance. As expected, residues lose part of their solvent-accessible surface with folding but the three groups remain. The decrease of accessibility is more pronounced for hydrophobic than hydrophilic residues. Amazingly, Lysine is the residue with the largest hydrophobic accessible surface in folded structures. Our analysis points out a clear difference between the mean (other studies) and median (this study) ASA values of hydrophobic residues, which should be taken into consideration for future investigations on a protein-accessible surface, in order to improve predictions requiring ASA values. The different secondary structures correspond to different accessibility of residues. Random coils, turns, and ß-structures (outside ß-sheets) are the most accessible folds, with an average of 30% accessibility. The helical residues are about 20% accessible, and the difference between the hydrophobic and the hydrophilic residues illustrates the amphipathy of many helices. Residues from ß-sheets are the most inaccessible to solvent (10% accessible). Hence, ß-sheets are the most appropriate structures to shield the hydrophobic parts of residues from water. We also show that there is an equal balance between the hydrophobic and the hydrophilic accessible surfaces of the 3D protein surfaces irrespective of the protein size. This results in a patchwork surface of hydrophobic and hydrophilic areas, which could be important for protein interactions and/or activity.

Keywords: Solvent accessibility; Pex files; hydrophobicity; secondary structure; amphipathy

	Introduction

TOP Abstract Introduction Results Discussion Materials and methods References

 
Understanding the folding of proteins remains one of the major scientific challenges. One way to explore this complex problem is to get information from the protein structures themselves. We recently developed an analytical tool, named Pex files, in which numerical data on various structural parameters of proteins are described, such as secondary structures, side chain interactions, H-bonds, and more (Thomas et al. 2001, 2002a,b). Here we introduce a new Pex file that, in addition to the major structural parameters of proteins, lists a series of parameters describing the solvent accessibility.

The folding process of soluble proteins decreases the surface in contact with the solvent. This is related to the secondary structures of proteins. Accurate knowledge of residue accessibility would thus aid the prediction of secondary structures. Different methods of prediction are based on the use of protein structure databases and on multiple sequence alignments. They have various efficiencies, notably depending on the number of relative accessibility states (i.e., exposed, buried, and in-between; Rost and Sander 1994; Rost 1996; Li and Pan 2001; Naderi-Manesh et al. 2001; Yuan et al. 2002).

Further, because active sites of proteins are often located at the surface of the protein, greater insight into residue accessibility would be important in understanding and predicting structure/function relationships.

In the present study, we analyzed 587 proteins from the Protein Data Bank (PDB) using the Pex files. We extracted the total, hydrophobic, and hydrophilic accessible surfaces of residues. The method used to calculate the accessible surface is that of Shrake and Rupley (1973). The 587-protein bank is a nonredundant bank of structures (Liu and Chou 1999).

	Results

TOP Abstract Introduction Results Discussion Materials and methods References

 
Calculation of residue accessible surfaces in extended conformation
To check that the calculation of accessible surfaces in ASA-Pex files is correct, we used a window of three residues along the structure; the surface of the central residue is calculated. This mimics the surface of residues measured in tripeptide by others, such as Gly-X-Gly or Ala-X-Ala (Creighton 1993; Samanta et al. 2002) and corresponds to the residue surface in the unfolded state. A very good correlation is observed between Pex data and previously published values (Table 1). When the residue surface is split into hydrophilic and hydrophobic surfaces (Table 1; Fig. 1), the residues with the highest hydrophobic versus hydrophilic ASA ratio are Phe and Met. Their hydrophobic surface is more than four times higher than the hydrophilic one. Residues with the smallest ratio (3–4 times more hydrophilic than hydrophobic) are Asp and Asn. Plotting the hydrophobic/hydrophilic ratio as a function of the total ASA value clusters the residues into three groups (Fig.1): One group is the hydrophobic amino acids (G<A<V,C,P<I,L<F,M) for which the hydrophobic/hydrophilic ratio is increasing with the surface; the second contains the hydrophilic residues (D,N<E,Q<R) whose ratio is rather independent of the residue surface; and a third group containing S,T,H,K,Y and W, whose ratio varies almost exponentially with the residue surface. This underlines that the aromatic residues with polar atoms (W,Y,H) do not behave like Phenylalanine and are not pure hydrophobic residues. It is worth noting that Lysine, although generally considered as a hydrophilic residue, has a ratio near 1 (Fig.1) and belongs to the third group, unlike Arg. This is due to its long hydrophobic chain holding the polar head.

View larger version (11K): [in this window] [in a new window]   Figure 1. Hydrophobic/hydrophilic accessible surface ratio (corresponding to column 6 of Table 1) as a function of the total accessible surface for each residue (Table 1, column 3) in the unfolded state.

View larger version (39K): [in this window] [in a new window]   Figure 2. Values of median pho (black bars) and phi (gray bars) ASA for each residue in the extended state (A) and in folded proteins (B). Residues are sorted by decreasing total ASA values.

View larger version (14K): [in this window] [in a new window]   Figure 3. Median hydrophilic ASA as a function of median hydrophobic ASA of residues in folded proteins. Residues with similar behavior are grouped. Pro (P) and Lys (K) are left out of this classification.

View larger version (21K): [in this window] [in a new window]   Figure 4. Distribution of the total ASA for (A) Lysine, (B) Glutamine, (C) Isoleucine, and (D) Phenylalanine. Values of the median and mean total ASA are indicated for each of these residues.

For each structural class, the total, hydrophobic, and hydrophilic median ASAs were calculated (Tables 3–7) and compared to the residue ASA in the extended conformation (ASA calculated with a window of 3). The most accessible residues belong to the random coil/turn (C-T) class, whereas the Ba and Bp structures result in the most solvent-inaccessible residues.

It should be noted that the hydrophilic accessible surface of the most hydrophobic residues (i.e., Ile, Val, Leu, Met, Phe) should correspond to the accessibility of their backbone (Table 3).

ß-Strands (B-structures)
The residues are almost as accessible in B-structures as in random coil/turn structures, and the segregation between the hydrophobic and the hydrophilic residues is also observed (Table 4). A noticeable difference lies in how the hydrophobic and hydrophilic accessible surfaces of residues decrease (cf. columns 9, 10 of Tables 3 and 4). Although the hydrophobic and hydrophilic ASAs of hydrophilic residues are similarly reduced, hydrophobic residues show a twofold more pronounced decrease in the hydrophobic surface compared to the hydrophilic surface. This suggests that B-structure is more prone to shield the hydrophobic moiety of hydrophobic amino acids compared to the random coil/turn structure.

For Proline, which is 30% accessible, the opposite is observed; that is, the hydrophilic surface is less accessible than the hydrophobic one (as in the random coil/turn structure).

Further, as for random coil/turn, the hydrophilic accessible surface of the most hydrophobic residues in B-structures should correspond to the accessibility of the backbone.

Parallel and antiparallel sheets
These folds correspond to the less accessible residues: On average, only 10% of the residue surface is accessible (Tables 5,6). This is particularly true for the hydrophobic residues such as Leu, Ile, Val, Met, Cys, and Phe (1%–5% accessibility). In these folds, again, the most accessible residues are Lys and Glu (23%–33% accessibility) and hydrophobic and hydrophilic residues are segregated, Ser and Thr having intermediate values. For almost all residues, the Ba/Bp structures appear to shield their hydrophobic domains from the solvent better than any other structure, as reported by Chothia (1976).

This suggests that a sequence will have a smaller hydrophobic accessible surface as a ß-sheet than in any other conformation. This could be related to the formation of fibrils observed with highly hydrophobic peptides. Indeed, fibrils are made of antiparallel ß-strands, as reported regarding the amyloid aggregates of Alzheimer’s disease (Li et al. 1999; Schladitz et al. 1999).

It is interesting to note that the backbone of hydrophobic residues (corresponding to the phi ASA of those residues) is no more accessible in Ba/Bp structures, in contrast to what happens for random coil/turn and B-conformations.

-Helices
Residues of helical folds have an intermediate solvent accessibility of 20% (Table 7). The difference between the accessibility of hydrophobic and hydrophilic residues is highly marked. For -helices, K, E, R, N, D, Q, S, and T are 45% (Lys) to 19% (Ser) accessible with an average of 35% accessibility, whereas hydrophobic residues are only 1%–5% accessible (except for Trp and Tyr, which are 10% accessible). This is linked to the observation that most -helices of protein 3D structures are amphipathic (Chou et al. 1997). Amphipathic helices have most of the hydrophobic residues oriented toward the protein core, whereas the hydrophilic residues are water-accessible.

It should be noted that the helical structure similarly reduces the hydrophobic and the hydrophilic surfaces of all residues, in contrast to what happens in ß-folds.

In the helical structure, as for ß-sheets, the backbone is not accessible (hydrophilic surfaces of hydrophobic residues are almost null).

The same calculations of surfaces were made by selecting the secondary structures attributed to the CO-side of the residue. The number of residues analyzed for each structural class remains similar, as were the surfaces (data not shown).

Analysis of ASAs in data sets containing only ß- or -proteins
In light of our observation that the ß-fold better shields hydrophobic parts of amino acids from water whereas helical structure better segregates hydrophobic and hydrophilic residues (the latter remaining accessible to the solvent), we wondered whether this would also hold true for two data sets one containing proteins with -structures (no ß-residues) and the other with ß-proteins (no helical folds). These sets were extracted from the 587-protein bank by selecting 26 ß-proteins and 55 -proteins, as described in Materials and Methods.

Table 8 shows that the accessible surfaces of residues in helical conformation of -proteins (corresponding to 6,530 residues) are the same as those determined for the 587 proteins, confirming the amphipathic character of the helical fold.

View larger version (9K): [in this window] [in a new window]   Figure 5. Log of the total ASA as a function of the log of the number of residues for the 587 proteins analyzed. The coefficient of the linear regression is 0.97.

View larger version (13K): [in this window] [in a new window]   Figure 6. Hydrophobic () and hydrophilic () ASA as a function of the total ASA for the 587 proteins analyzed. The coefficient of the linear regression is 0.99 for both curves.

View larger version (51K): [in this window] [in a new window]   Figure 7. (Left panels) Molecular hydrophobicity potentials (MHPs) around three proteins analyzed (one -protein, apolipophorin III, PDB code 1AEP [PDB] ; one ß-protein, human fibronectin, FBR; one /ß-protein, dienelactone hydrolase, 1DIN [PDB] ). MHPs, based on atomic transfer energies, allow the visualization of pho (orange) and phi (green) domains around a protein and are calculated as described in (Brasseur 1991). (Right panels) Ribbon representations of the protein in the same orientation as in the left panels. (A) 1AEP [PDB] , (B) 1FBR [PDB] , (C) 1DIN [PDB] .

	Discussion

TOP Abstract Introduction Results Discussion Materials and methods References

Three groups of amino acids can be distinguished based on the relationships between their hydrophobic and hydrophilic accessible surfaces, either in the extended state or in the folded proteins. One group is made of the hydrophobic residues (I,L,V,F,M,A,G), another contains the hydrophilic residues (D,N,E,Q,R), and the third shows intermediate behavior (H,Y,W,S,T). Proline and Lysine are apart. Among the hydrophilic residues, Lysine is peculiar: It is often looked at as a hydrophilic residue but in the unfolded state, it has almost equal hydrophobic and hydrophilic accessible surfaces. Moreover, in the folded state, it has the highest hydrophobic ASA of all residues. Proline also has special features, as it has the highest hydrophobic accessible surface among the hydrophobic residues. This is related to its preferential location in accessible turns of proteins.

The classification of amino acids into three amino acid "families" following their hydrophobic/hydrophilic accessible surface should be important in terms of the prediction of conservative mutations.

The different types of secondary structure correspond to different accessible surfaces. Random coils, turns, and ß-strands that are either not H-bound or are H-bound to a structure that is not a strand are the most accessible folds, with an average of 30% of residue accessibility. In these structures, the backbone of the most hydrophobic residues (I,V,L,M,F) is quite accessible, with 10%–15% accessibility.

The ß-sheets (parallel and antiparallel strands) are the most solvent-inaccessible structures (with about 10% of residue accessibility), whereas the helical conformation has an intermediate value, with about 20% of the residue surface accessible.

Both helical and ß-sheet conformations shield the backbone of the most hydrophobic residues from water, in contrast to what happens for the "unordered" structures.

In all folds, there is a noticeable difference between the hydrophobic and hydrophilic residues, the latter being always more solvent-accessible. The greatest difference is observed in -helices related to their amphipathic character. When the protein folds, the hydrophobic side of the helix is buried in the protein core, and the hydrophilic side remains solvent-accessible. The ß-sheets are the most appropriate structures to shield the hydrophobicity of residues. This is likely important in the formation of fibrils in pathological and nonpathological phenomena.

Note that Lysine and Glutamic acid are the most accessible residues, whereas Leucine, Isoleucine, and Valine are the most inaccessible, irrespective of secondary structures.

As described earlier by Chothia (1976) regarding 12 proteins, there is a simple relationship between the total accessible surface of folded proteins and their size. We also show that there is a balance between the hydrophobic and the hydrophilic surfaces of the 3D protein surface. This balance is maintained irrespective of the protein size, resulting in a patchwork surface of hydrophobic and hydrophilic areas. Size and accessibility of the patches should be important for protein-protein interaction sites and/or for activity, as suggested by others (Eisenhaber and Argos 1996; Jones and Thornton 1997).

	Materials and methods

TOP Abstract Introduction Results Discussion Materials and methods References

 
Proteins
The PDB files of the 587 proteins were transformed into ASA Pex files, giving a total of 156,215 residues that were analyzed. These structures were issued from the nonredundant bank described by Liu and Chou (1999) containing 593 entries. Five proteins were discarded, their format being incompatible with their transformation into Pex files. The PDB codes are listed below; the experimental resolution is between 1.2 and 2.9 Å. ASA Pex files are accessible on the CBMN Web site (http://www.fsagx.ac.be/bp/) or can be obtained from author R. Brasseur.

153l 1bec 1chd 1daa 1ecl 1ftp 1gtr 1aa8 1ber 1chk 1dar 1ecp 1fua 1gym 1aaf 1bgw 1chm 1dbq 1ede 1fup 1han 1abr 1bhs 1cid 1ddt 1edg 1gad 1har 1ade 1bia 1ciy 1dea 1edh 1gai 1hav 1aep 1bmf 1cks 1def 1efn 1gal 1hbq 1aer 1bmt 1clc 1dek 1efu 1gar 1hce 1afb 1bnc 1cmb 1dhp 1eny 1gca 1hcn 1alo 1bnd 1cns 1dhr 1eri 1gcb 1hcp 1amm 1bp2 1cnt 1din 1erw 1gdo 1hcz 1amp 1bpl 1cof 1dja 1esc 1gdy 1hfh 1anv 1bri 1col 1dkz 1esf 1gen 1hge 1aoc 1bro 1cpc 1dlh 1esl 1ghr 1hgx 1aor 1buc 1cpo 1dnp 1etp 1gky 1hjr 1aoz 1bur 1cpq 1doi 1eur 1glc 1hlb 1apy 1bvp 1cpt 1dor 1ext 1gln 1hmy 1arb 1bw4 1crl 1dpe 1fba 1gnd 1hng 1ars 1byb 1csh 1dpg 1fbr 1gof 1hqa 1arv 1cau 1csm 1drw 1fc2 1got 1hrd 1ash 1ccr 1csn 1dsb 1fcd 1gp1 1hsl 1atl 1cdo 1ctn 1dsn 1fib 1gpb 1htm 1axn 1cdq 1ctt 1dsu 1fie 1gpc 1htp 1ayl 1cdy 1cur 1dts 1fil 1gph 1htt 1bam 1cea 1cus 1dup 1fim 1gpl 1huc 1bbh 1cel 1cvl 1dyn 1fjm 1gpm 1huw 1bbp 1cem 1cxs 1dyr 1fkj 1gpr 1hxn 1bbt 1ceo 1cyd 1eaf 1fkx 1grj 1hxp 1bcf 1cew 1cyg 1eal 1fnc 1grx 1i1b 1bco 1cfb 1cyv 1eca 1fnf 1gsa 1iae 1bdm 1cfr 1cyw 1ece 1frp 1gtq 1ice 1icn 1lba 1mka 1npo 1pii 1rci 1snc 1ign 1lbd 1mla 1oac 1pkm 1rec 1spg 1ihf 1lbi 1mld 1obp 1pkp 1reg 1sra 1ilk 1lbu 1m1s 1occ 1pls 1req 1sri 1ino 1lci 1mml 1oct 1pmi 1rfb 1std 1inp 1lck 1mol 1ofg 1pmy 1rgs 1stm 1iow 1lcl 1mpp 1omp 1pnk 1rhg 1svb 1irk 1lcp 1mrj 1onc 1poc 1rie 1svp 1irl 1ldm 1msa 1onr 1pot 1rnl 1svr 1isc 1leh 1msc 1ord 1pox 1rpa 1tag 1iso 1len 1msf 1oro 1rrg 1tal 1itg 1lfa 1msk 1osp 1pre 1rsy 1taq 1ivd 1lgr 1msp 1otg 1prs 1rtp 1tbr 1jap 1lis 1mty 1oun 1prt 1rva 1tca tjcv 1lit 1mup 1ova 1psd 1sac 1tcr 1jon 1lki 1mut 1oxa 1ptv 1sat 1tfe 1jud 1lnh 1nal 1oxy 1ptx 1sbp 1tfr 1jvr 1lrv 1nar 1oyc 1pue 1sch 1tgx 1kaz 1ltd 1nba 1pbe 1put 1scm 1thj 1kcw 1lts 1ndh 1pbg 1pvc 1scu 1tht 1knb 1luc 1nfa 1pbn 1pvd 1sei 1thv 1kny 1lxa 1nfk 1pbw 1pxt 1ses 1thx 1kob 1lyl 1nfn 1pco 1pya 1sfe 1tii 1kpb 1mas 1nfp 1pdg 1qap 1sft 1tiv 1kpt 1mat 1nhk 1pdn 1qas 1slt 1tlk 1kuh 1maz 1nhp 1pea 1qba 1slu 1tml 1kve 1mda 1nif 1pfk 1qor 1sly 1tnr 1kxu 1mey 1nip 1pgs 1qpg 1smd 1tpg 1l48 1mhc 1nox 1phg 1rbu 1sme 1tpl 1lau 1mhl 1noy 1phr 1rcb 1smn 1trk 1tsp 1xjo 2bpa 2hts 2sil 4mt2 2aza 1ttb 1xnb 2btf 2hvm 2stv 4rhv 2bbv 1tul 1xrb 2cae 2ihl 2tbd 4sbv 2bgu 1tup 1xsm 2cas 2kau 2tct 4ts1 2blt 1tys 1xva 2cba 2lbp 2tgi 4xia 2bnh 1uby 1xyz 2cbp 2lfb 2tmd 5p21 2bop 1ucy 1ydr 2ccy 2mev 2tmv 5rub 2hft 1ulp 1yha 2cpl 2mnr 2tys 5tim 2hhm 1uxy 1ypp 2ctc 2mpr 2vil 6fab 2hmx 1vdc 1ytb 2cyp 2mta 3chy 7rsa 2hmz 1vhh 1ytw 2dkb 2nac 3cla 8abp 2hpd 1vhi 1yua 2dld 2olb 3cox 8acn 2hpe 1vhr 1znb 2dri 2omf 3dfr 8atc 2psp 1vid 1zqa 2ebn 2ora 3dni 8fab 2reb 1vin 2aaa 2end 2pcd 3fru 8tln 2rsi 1vls 2aakent 2eng 2pec 3geo 9pap 2rsp 1vmo 2abd 2er7 2pgd 3grs 9rnt 2sas 1vnc 2abh 2fal 2phy 3hhr 9wga 2scp 1vol 2abk 2fcr 2pia 3kin 1wba 3sdh 1vorm 2acq 2fd2 2pii 3min 1wdc 4aah 1vpt 2adm 2gmf 2pld 3pga 1whi 4bcl 1vsd 2ak3 2gsq 2pol 3pgm 1wht 4enl 1vsg 2amg 2gst 2por 3pmg 1xel 4fgf 1wad 2ayh 2hbg 2prk 3pte 1xik 4kbp

For the ß-only proteins data set, 26 files were extracted with the criterion that the proteins do not contain -helical structure; for the -only proteins, 54 files were extracted with the criterion that they do neither contain Ba- or Bp-structured residues.

The -bank corresponds to the following files:

1aep,1arv,1ash,1axn,1bbh,1bcf,1ccr,1cem,1cns,1cnt,1col,1cpq, 1eca [PDB] ,1etp,1hlb,1huw, 1ign [PDB] ,1ilk,1jvr,1kxu,1lis,1lki,1lrv,1maz,1mey, 1mls [PDB] ,1msf,1nfn,1oct,1pbw,1poc,1rci,1rfb,1rhg,1spg,1sra,1uby, 1vin [PDB] ,1vls,1xsm,2abd,2abk,2ccy,2cyp,2end,2fal,2hbg,2hmz,2lfb, 2tct [PDB] ,2tmv,3sdh,6fab,9wga.

The ß-bank corresponds to the following files:

1cea,1cur,1fbr,1fnf,1hce,1i1b,1knb,1lcl,1msa,1msp,1nfa,1npo, 1pco [PDB] ,pdg,1ptx,1svp,1tgx,1tpg,1tul,1ulp,1vmo,1wba,1yha,2mpr, 2pii [PDB] ,4fgf.

ASA-Pex files
Each Pex file originates from the PDB file of a protein. Each line of the Pex corresponds to a residue in the order of the sequence, and each column is a parameter calculated in the 3D structure as described by Thomas (Thomas et al. 2001). In the ASA-Pex file, calculation of accessible surface areas (ASAs) of the whole residue (lateral chain and backbone) was achieved using the method of Shrake and Rupley (1973). In brief, the spherical surface of each atom is covered by a net of 642 points (the initial method used 92 points), and the points that lie within other expanded atoms are determined. The SERF algorithm where this method is implemented was used (Flower 1997).

Determination of the hydrophobic and hydrophilic accessible surfaces of residues
The method of Shrake and Rupley (1973) was also used to calculate the hydrophobic and hydrophilic ASAs. With this method, the hydrophobic and hydrophilic ASAs correspond to the sum of the surface of hydrophobic or hydrophilic atoms of the residue, respectively. Atoms are considered hydrophobic or hydrophilic depending on their transfer energy, as described (Brasseur 1991).

Median values of total, hydrophobic, and hydrophilic accessible surfaces were calculated using Excel software (Microsoft).

Determination of the secondary structure of the residues
In the PDB files, no protein has a complete description of secondary structures. We therefore established our definition of secondary structures based on the (phi/psi) values and on the occurrence of main chain H-bonds (O..H distance less than 3.5 Å), as described in Thomas et al (2001). Two different structures were attributed to the same residue according to the fact that that residue can be involved in two H-bonds, one on its NH side, the other on its CO side. Both secondary structures are listed in the Pex. In the present study, the NH secondary structure was considered.

Definition of the different secondary structures
Helices
Helical residues have a main chain H-bond and / within a circle of 45° around the couple = -57° and = -47°. The main chain H-bond has an O . . . H distance less than 3 Å. The helix is (Ha) when the n and the n ± 4 residues are H-bound.

ß-Structures
Residues are in ß when the / are within a circle of 90° around the = -129° and = 123° . When two strands are H-bound, they are either antiparallel (Ba) or parallel (Bp) sheets. The sheets are parallel when the vectors between the C of the residues n and n + 1 of each strand draw an angle of -90° to +90°. They are antiparallel when the same vector angles are between 90° and 180° or -90° and -180° apart. B is for ß-strands that are either not H-bound or are H-bound to a structure that is not a strand.

Random coils/turns
The / values of the different turns are from Srinivasan and Rose (1995). The presence of an H-bond is not mandatory.

The / of random coils span a large range of values, including the left helices that were not individualized in this study. Random coils also account for right helices and ß-residues when the H-acceptor (the O=C residue, n + i) and the NH-donor (n) are too far away in the sequence for a helix (i > 6) or too close for a ß-sheet (i < 3).

Molecular hydrophobicity potential (MHP) calculations
MHP is a three-dimensional plot of the hydrophobicity potential of a molecule created to visualize its amphipathy. The hydrophobicity of a molecule is calculated using its partition coefficient between water and octanol.

We postulate that the hydrophobicity induced by an atom i and measured at a point M of space decreases exponentially with the distance between this point M and the surface of an atom i according to the equation (Brasseur 1991):

where N is all atoms of the molecule, E_tri is the transfer energy of atom i, r_i is the radius of the atom i, and d_i is the distance between atom i and the point M. E_tri is the energy required to transfer an atom i from a hydrophobic to a hydrophilic medium. Atomic E_tri values were calculated from the molecular transfer energies compiled by Tanford (1973), assuming that molecular E_tr are the sum of their atomic E_tr. Atomic E_tr values were derived for seven different atom types (Brasseur 1991).

The hydrophobic and hydrophilic isopotential surfaces were calculated by a cross-sectional computational method. A 1-Å mesh-grid plane was set to sweep across the molecule by steps of 1 Å. At each step, the sum of the hydrophobicity and hydrophilicity values at all grid nodes was calculated. The hydrophobic and hydrophilic MHP surfaces were then drawn by joining the isopotential values.

All calculations were performed on Pentium III processors, using Z-TAMMO and Z-PEX software. Molecular graphs were drawn using WinMGM (Ab Initio).

	Acknowledgments

 
R.B. and L.L. are Research Director and Research Associate, respectively, at the Belgian Funds for Scientific Research (FNRS). A.T. is Research Director at the French National Institute for Medical Research (INSERM). This work was supported by Region Wallone (Grants 114.830 and 14.540 to R.B.) and the Belgian Fonds de la Recherche Scientifique Médicale (grant 3.4568.03 to L.L.). We thank Dr. D.R. Flower for kindly providing the SERF algorithm.

The publication costs of this article were defrayed in part by payment of page charges. This article must therefore be hereby marked " advertisement" in accordance with 18 USC section 1734 solely to indicate this fact.

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TOP Abstract Introduction Results Discussion Materials and methods References

 
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