Protein Engineering vol.2 no.5 pp.329-334, 1989

Polarity as a criterion in protein design

G.Baumann, C.Frommel1'2 and C.Sander1

Central Institute of Molecular Biology, Berlin-Buch, GDR, 'BlOcomputingProgramme, EMBL, Heidelberg, FRG2Permanent address: Institute of Biochemistry, Humboldt University, Berlin,GDR

Hypothetical proteins can be tested computationally bydetermining whether or not the designed sequence-structurepair has the characteristics of a typical globular protein. Wehave developed such a test by deriving quantities withapproximately constant value for all globular proteins, basedon empirical analysis of the exposed and buried surfaces of128 structurally known proteins. The characteristic quantitiesthat best appear to segregate badly designed or deliberatelymisfolded proteins from their properly folded natural relativesare the polar fraction of side chains on the protein surfaceand, independently, in the protein interior. Three of the sevenhypothetical structures tested here can be rejected as havingtoo many polar side-chain groups in the interior or too fewon the protein surface. In addition, a recently designednutritional protein is identified as being very much unlikeglobular proteins. These database-derived characteristicquantities are useful in screening designed proteins prior toexperiment and may be useful in screening experimentallydetermined (X-ray, NMR) protein structures for possibleerrors.Key words: Electrostatics/globular proteins/hydrophobicity/pro-tein data bank/protein engineering

IntroductionWith the tremendous progress in gene synthesis and proteinexpression, design of completely new proteins has become anexperimental reality. Several de novo designs are now in theproduction or testing stage. However, as the protein foldingproblem is as yet essentially unsolved, theoretical designs havea less than optimal chance of leading to successful experimen-tation. In order to avoid unnecessary experiments, more stringentdesign evaluation and improved design methods are needed.

An interesting example of design evaluation is provided bydeliberately misfolded proteins in which the sequence of a proteinknown to have an all-helical 3-D structure is placed into a knownstructure of a completely different type, an antiparallel /3-barrel,and vice versa. For the evaluation of the quality of these clearlyincorrect hypothetical structures, intramolecular energy,calculated in vacuum using standard potentials, was not a sensitivecriterion (Novotny et al., 1984). However, the misfoldedstructures (not the improved versions used in this paper) werereported to have surface areas 15—20% larger than the nativestructures and to have a greater proportion of non-polar side-chain atoms exposed to solvent, using Chothia's (1976) definitionof non-polar and polar surfaces. The work of these authorsindicates that characterization of the distribution of polar atoms

in all known globular protein structures may lead to generallyuseful design criteria.

The key aspect is the development of criteria with sufficientdiscriminatory power. For example, the free energy differencebetween the folded and unfolded state would be an optimalcriterion, but present theories are not capable of calculating freeenergy differences to sufficient accuracy. However, faced withthe lack of an accurate theory of protein folding, empiricalobservations of regularities gleaned from the database of solved3-D protein structures can be very useful, assuming that thecurrent database is sufficiently representative of the range ofpossible structures. It is on such empirical analysis of the databasethat we base our criteria.

Derivation of characteristic quantities by empiricalanalysisThe aim of our analysis is to derive quantities that arecharacteristic of globular proteins in that their distribution in thedatabase can be used to discriminate against non-globularproteins, i.e. against sequences that will not fold up into anyglobular shape or not fold into a given globular shape. Previousanalyses (e.g. Klein et al., 1984) have provided us with a longlist of properties useful for classifying or describing sequences(amino acid composition, number of charged residues, net charge,charge segregation along the chain, number of hydrophobicresidues, hydrophobic periodicity, number of hydrophobicsegments, strength of helix/sheet preferences, etc.) or 3-Dstructures (compactness of shape, total solvent accessible surfacearea, hydrophobic contacts, buried charges, etc.). Our task isto select and invent the quantities that are most discriminating.

In order to arrive at generally useful criteria, the quantitiesused must be properly normalized. To illustrate by a trivialexample, natural proteins have a low number of Trp residues;the appropriate quantity is the relative number of Trp residues,i.e. the absolute number divided by the total number of residues.In general, normalization should be such that the distribution ofvalues in the database is narrow compared to the differencebetween a protein in the database and e.g. a misfolded protein.

Below, we first define and analyse quantities that depend onlyon the amino acid sequence (called sequence-dependentcharacteristics) and then quantities that depend on the 3-Dstructure (called structure-dependent characteristics). We discussthe distribution of these quantities in the database of proteins ofknown 3-D structure (hereafter called database), derive reasonablelower and upper limits for each quantity and apply the resultingcriteria to hypothetical sequences and structures.

Sequence-dependent characteristicsMolecular weight per residueThe simplest sequence-dependent properties reflect the amino acidcomposition. MWRES, the molecular weight per residue, quan-tifies the average size per residue

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MWRES =MW

NRES

where MW is the total molecular weight of the protein in daltonsand NRES is the number of residues in the protein. As thereis a linear relationship between molecular weight and maximalsolvent accessible surface of an extended chain, the latter quantitycould be used equivalently. The range of MWRES values in thedatabase (Table n, in units of daltons/residue) is sufficientlynarrow to identify, e.g. polyalanine (MWRES=71), polytyrosine(MWRES = 163) and collagen (MWRES =90.2) as non-globular,but not keratin (MWRES= 107.1).

In the database of known structures, the porcine hormoneglucagon, a 29-residue helical peptide (1GCN, MWRES = 120)and the bovine eye lens protein y-crystallin (1GCR,MWRES = 120) have the highest values of MWRES. The unusualamino acid composition of 7-crystallin, low in Ala, Thr and Lysresidues (1.1, 2.2, 1.1%) and high in Arg, Phe, Tyr, Trp (11.4,5.1, 8.6, 2.2%), may reflect unusual functional requirements asan eye lens protein. Excluding 1GCN, 1PPT and 1GCR, wedefine as normal the range 97 < MWRES < 118 daltons/residue.Maximum polar fractionAnother simple quantity that depends only on the amino acid

composition is POLFRAC MAX, the polar fraction (definedin physical terms below) in an extended chain conformation, cal-culated as a simple function of single residue values POLSURF(A:)and SURF(fc), taken from Table I. Here, NRES is the totalnumber of residues in the protein and POLFRAC MAX is inunits of e, the electronic charge.

NRES NRES

POLFRAC_MAX= E POLSURF()k)/ E SURF(it)i - l k-i

Polyaspartic acid (POLFRAC_MAX = 0.256) is clearly muchmore polar, keratin (POLFRAC MAX = 0.192) somewhatmore polar and polyvaline (POLFRAC MAX =0.112) muchmore hydrophobic than sequences of typical globular proteins(Table H).

Wheat germ agglutinin (isolectin 2, 3WGA) has an unusuallypolar sequence (POLFRAC_MAX = 0.194). Both the aminoacid composition (25% Gly, 18% Cys—somewhat like metallo-thioneins) and the tertiary structure (dimer, 16 S-S bridgesper monomer, little hydrogen-bonded secondary structure) areatypical of globular proteins. Melittin, 1MLT, a small 26-residueprotein capable of membrane insertion is significantly less polar(0.155 e) than water-soluble globular proteins. Excluding 1MLTand 3WGA, we define as normal the range 0.160 <POLFRAC_MAX < 0.185 e.

A recently designed nutritional protein (Biernat et al., 1987)clearly falls outside the class of globular proteins on sequence-based criteria alone, with a very high average residue size(MWRES = 174.0) and very low polarity (POLFRAC_MAX= 0.138). Note the absence of small residues (AGSC) in itssequence: MVWYL VUCVI RLIRL THKHT LITLR (repeated).The low polarity of the sequence may indicate that the proteinwould not be water soluble in physiological conditions and wouldnot fold into a globular shape.

Structure dependent characteristicsAccessible surface area per molecular weightEvaluation of designs becomes more sensitive when both thedesigned sequence and the corresponding hypothetical structure

330

are known, as is the case with the five proteins designed de novoduring an EMBO course in 1986 (Sander, 1987). For example,the relative compactness of globular proteins can be quantifiedby calculating the solvent accessible surface area, as conceptuallydefined by Lee and Richards (1971): for a given chain lengthan extended conformation has maximal accessible surface, whilea perfectly spherical protein would have minimal accessiblesurface. The actual surface values SURF(MW) for globularproteins are somewhat larger than those for a perfect sphere andare proportional to molecular weight (MW), with an offset ofSURF(0) = 1178 A2 at zero molecular weight (Figure 1). Theappropriate normalized characteristic quantity removes thisdependence

SURFMW = ( SURF(MW) - SURF(0) ) / MW

so that SURFMW is approximately constant over the entire rangeof molecular weights with an average value of 0.403 A2/dalton.Non-globular shapes like a long a-helix clearly have an excess-ively large surface: e.g. SURFMW = 0.661 for residues75 — 126 in data set 1HMG, haemagglutinin, taken in isolation.Application of the corresponding criterion (does the value fora protein fall inside or outside the range of values in the database?)leads to some interesting results.

Unusually large values (Table \S) of external surface permolecular weight in the database are from an immunoglobulin(1PFC, fragment, only 3.1 A resolution), a-bungarotoxin(2ABX, little secondary structure, 10 S-S bridges), wheat germagglutinin (3WGA, see above), ovomucoid inhibitor (1OVO,fragment) and melittin (1MLT, see above). The large SURFMWvalues for the multi-haem cytochrome C3 protein (2CDV),

Table I. Reference surface values for amino acids: maximal accessible surfacearea, SURF, and polar surface area, POLSURF, in an extended structure

Residue Main-chain Side-chain Residue Residue

(X) SURF POLSURF SURF POLSURF SURF POLSURF SURF (#)

AlaArgAsnAspCysCHuGinGlyHisDeLeuLysMetPheProSerThrTrpTyrValCSS

43.640.140.541.141.142.043.483.641.139.740.240.442.140.539.642.641.340.540.539.540.7

13.913.513.813.813.813.814.119.613.813.412.913.513.913.511.414.013.813.513.513.513.5

62.7199.3109.2108.497.4

140.8143.1

0.0141.1131.8123.4160.5151.5160.496.380.7

100.4204.6171.9108.942.0

2.645.528.930.4

1.937.531.00.0

13.83.83.7

15.07.62.21.8

11.39.7

10.714.73.20.9

106.3239.5149.8149.5138.5182.8186.683.6

182.2171.5163.6200.8193.7200.9135.9123.1141.7245.4212.4148.482.7

16.559.042.744.315.751.345.219.627.617.216.728.521.515.713.225.223.524.728.216.714.4

11522516015013519018075

195175170200185210145115140255230155-

These values are needed to calculate maximal and internal surfaces andmaximal and internal polar fractions of a protein structure. SURF is in unitsof A2 and POLSURF in eA2 , as defined in the text. Extended structure fora residue X is defined as a 0-strand-like structure Gry-Gly-X-Gly-Gly. SeeFigure 1 for method of calculation. CSS = CYS in S-S bridges (1/2 cystine).(#) values from Lee and Richards (1971).

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tal

o

ia3a

rnal

o•go

20000 -

10000-

0 -

^ y-1178 + 0.4O3x R-0.98 ~/^~

ffl ^T

20000 40000 60000mol. weight

80000

30000y - 2.262 * xA0.842 R-0.98

Obk

20000 40000mol. weight

60000 80000

Fig. 1. Analysis of the empirical relationship between molecular weight andexternal surface area of globular proteins. Each dotted square ( 0 )represents a protein of known 3-D structure. The linear fit with additiveoffset and exponent 1.0 (A) and the exponential fit with zero offset andexponent 0.84 (B) are equally good with a coefficient of regression r =0.98. For simplicity, we work with the linear fit. The purely linear model isuseful in defining characteristic quantities that are independent of molecularweight. Black diamonds ( • ) in (A) show that designed (Sander, 1987) andmisfolded (Novotny et al., 1984) proteins do not have abnormal values oftotal exposed surface.

Exponential versus linear fit: Surface and weight of geometrical spheres arerelated by an exponent of 2/3 [black diamonds ( • ) in (B)]. For globularproteins this simple geometrical fit breaks down at larger molecular weights.There are several ways to improve the fit. (i) Use the exponent of MW as aparameter but still force the fit to include the origin at MW«0, SURF=0;this yields SURF « MW ° M (B) with an exponent significantly larger thanthe purely geometrical value of 2/3 (Janin, 1976; Teller, 1976) and similarto the exponent found by Miller et al (1987a,b), 0.73 and 0.76. (ii) In anexponential fit, ignore the origin, as it is not a data point and allow a non-zero surface at MW=0; this yields SURF = 1200 + O.537*MW097, withan exponent close to 1.0, (iii) Linear fit: SURF = 1178 + 0.403*MW.The linear fit is the simplest and has the same coefficient of linearregression as the exponential fits (i) and (if). The non-zero offset reflectsthe fact that a small (non-cyclic) peptide cannot fold back onto itself in acompact shape until a minimum length of approximately 10—15 residues isreached. No matter which fit is used, there is at larger molecular weights anapparent excess of protein surface over the geometrical minimum of SURF« MW067. The excess may be interpretable in terms of the roughness ofprotein surfaces, the restricted topology of supersecondary structure, domainorganization and the like (Gates, 1979).

Method of surface calculation: the external surface of an atom, also calledthe solvent accessible surface, is calculated by numerical integration of smallsurface patches over 320 isotropically distributed points (Shrake and Rupley,

1973; Kabsch and Sander, 1983); the points are on the surface of a spherecentred at the atom with radius rttoa> + r ^ j , , where r ^ = 1.55 for O,1.65 for N, 1.80 for C, 1.90 for S and rWJUCT = 1.4 AT A point contributesto the external surface if a water molecule centered at it does not touch anyother protein atom. Hydrogen atoms are included in the heavier atom theyare attached to (united atom approximation), except for the hydrogen of thepeptide NH group. The reference value, the external surface of an unfoldedprotein, is calculated simply as the sum over the surfaces of individualamino acids X embedded in the pentapeptidc Gly-Gly-X-Gly-Gly in anextended conformation (Table I). Surfaces are reported in A2 .

Data base: 64 proteins of known structure:

155C, 156B, 1ABP, 1APR, 1AZU, 1BP2, 1CAC, 1CPV,1ECD, 1EST, 1FAB, 1FDX, 1GPD, 1HIP, 1INS, 1LH1,1LHB, 1LZM, 1MBN, 1MBS, 1OVO, 1P2P, 1PCY, 1PTN,1PYP, 1REI, 1RNS, 1SBT, 1TIM, 2ACT, 2ADK, 2ALP,2APE, 2APP, 2B5C, 2CAB, 2GCH, 2GRS, 2PAB, 2PGK,2RHE, 2SBV, 2SGA, 2SNS, 2SOD, 2SSI, 35IC, 3BP2,3C2C, 3CNA, 3CYT, 3FXC, 3FXN, 3PGK, 3PGM, 3TLN,4ADH, 4ATC, 4DFR, 4LDH, 4PTI, 5CPA, 7LYZ, 8PAP.

with four-letter identifiers from the Protein Data Bank (Bernstein et al.,1977). If the data set contains an oligomer, external and internal surfaceareas are calculated for the oligomer as a whole.

0.589, is due to the large binding crevice and is reduced to anormal value, 0.418, when the haems are taken into account asexcluding solvent (Table BT|. The same is true for a structurallyhomologous multihaem protein, 1CY3 (data not shown).

As Miller et al. (1987a) have pointed out, inaccuracies inatomic positions tend to increase the external surface, e.g. by5% for two lysozyme data sets at 2.4 and 1.7 A resolution. Moredramatically, the protein structure with the largest abnormal valueof external surface (SURFMW=0.616) in the database and thusmost obviously identified as questionable or unusual is a ferredoxinstructure reported in 1981 (data set 2FD1) and recently shownto be incorrect by an independent crystallographic experiment(Stout et al., 1988). Excluding 2FD1, 1OVO, 1MLT, 1PFC,2ABX, 2CDV, 3WGA, 1CY3 and 2FD1, we define as normalthe range 0.320<SURFMW<0.520 A2/dalton. Contrary tothe earlier versions (Novotny et al., 1984), the refined data setsof misfolded proteins have acceptable values of external surface,showing that the CONGEN algorithm (Bruccoleri and Karplus,1987) has 'improved' the external surface of these data sets.

Polar fractionThe most sensitive criteria we have been able to find so far aremotivated by the classical observation that the interior of globularproteins tends to be hydrophobic. From an atomic point of view,it is important to distinguish between side chains, which varyin polarity, and backbone, which has repeating polar NH andCO groups, and to distinguish between different parts of largeside chains, e.g. the non-polar stem of Lys and its polar head.

Although many quantitative measures of hydrophobicity existfor entire residues, there are few on the atomic level. The measurewe use, polar surface or POLSURF, reflects the idea that thecontribution of individual atoms to the polar nature of a surfaceis related to the partial charge of an atom; for amino acid side-chains POLSURF was shown by one of us to correlate well withthe solvation energy of amino acid side chains (Frommel, 1984).POLSURF is qualitatively similar to Chothia's (1976) definitionof polar surface, but different in detail.

POLSURF is defined as the weighted sum over absolute valuesof partial atomic charges, with the magnitude of atomic surfacearea as weight. The polar fraction, POLFRAC, is the corres-ponding normalized quantity.

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Table D. Characteristic quantities of globular proteins. Normal range ofvalues in 128 reference proteins of known 3-D structure

A. Quantities independent of 3-D structure: MWRES, molecular weight perresidue; POLFRAC_MAX, maximum polar fraction

Low Mean High Units

MWRES 97.000 109.000 118.000 dalton/resPOLFRAC_MAX 0.160 0.173 0.185 e

B. Quantities dependent on 3-D structure: SURFMW external, externalsurface per molecular weight; POLFRAC internal, internal polar fraction;POLFRAC external, external polar fraction; POLFRAC SC int, internalpolar fraction for side chains; POLFRAC SC ext, external polar fraction forside chains

Low Mean High Units

SURFMW external 0.320 0.400 0.520 A2/daltonPOLFRAC internal 0.158 0.172 0.194 ePOLFRAC external 0.144 0.172 0.2O4 ePOLFRAC SC__int 0.074 0.098 0.122 ePOLFRAC SC_ext 0.115 0.143 0.183 e

The cut-off limits 'low' and 'high' were chosen intuitively by inspection ofstructures with very large or very small values and identifying them asoutliers if their structures appeared atypical of water-soluble, intact globularproteins. The atypical structures are listed in Table III. The 128 known 3-Dprotein structures available to us from the Protein Data Bank (Bernstein et al.,1977) were:

451C 155C 156B 1ABP 2ABX 2ACT nADH 2ALP 4APE nAPE 2APP nAPRnATC 2AZA 1AZU nBP2 3C2C 2CAB 1CAC nCAT 1CC5 1CCR 2CCY 2CDV2CGA nCHA 1CHG 1CN1 2CNA nCPA 2CPP nCFV 1CRN 1CTF nCTS 1CTX1CY3 1CYC 2CYP nCYT 4DFR 2DHB 2EBX 1ECA 1ECD 1ECN 1ECO nEST1FB4 1FBJ nFC2 2FD1 1FDH 1FDX 1FXI nFXN 2GCH 1GCN 1GCR 2GN5IGP1 nGPD 2GRS 1HBS nHCO 1HDS 2HFL nHHB 1HHO IMP 1HKG 1HMG1HMQ 1K32 nINS 2KAJ nLDH nLDX 2LH1 2LYM nLYZ 1LZI 2LXM ILXTnMBN 1MBO 1MBS 1MCP 1MEV 1MLT 1NTP 1NXB nOVO 1P2P 2PAB nPAD9PAP nPCY 1PFC 1PP2 1PPD 1PPT 3PTB 2PTC nPTI nPTN 1PYP 1RH

Table HI. Characteristic quantities of globular proteins. Unusually high orlow values in crystal and mode

Normal

LowMeanHigh

Crystal

1GCR1GCN3WGA1MLT2FD11OVO1PFC2ABX2CDV2CDVh1PPT1NXB2EBX

1CRN1FX1

MWRES POLFRAC

MAX

1 3-D structures

SURFMW

ext int

range deduced from database of globular

97.0109.0118.0

structures

120.4+120.0+97.5

109.2113.7107.9112.2107.8107.7107.7117.7110.6110.6

102.9106.7

U.lbU0.1730.185

U.JZU0.4000.520

U.1380.1720.194

with unusually high (+) or low

0 1800.1800.194 +0.155-0.1730.1750.1680.1690.1670.1670.1820.1820.182

0.1660.183

Misfolded structuresmisHMmisIG

117.9+107.7

j _ _ . .

Designeu structureBEALBUNDBABATINYFXNI

108.1106.7103.9105 3109.7

0.1690.172

s0.1780.2000.1770.1740.182

0.3560.647 +0.524+0.566+0.616+0.529+0.558 +0.539 +0.589+0.4180.5150.4150.434

0.3820.384

0.4010.465

0.4510.3850.4440.4390.424

0.1740.218 +0.215 +0.1850.1830.1790.1680.1820.1890.1730.195 +0.198 +0.195 +

0.1900.168

0.1890.196+

0.1690.214+0.1730.1700.179

POLFRAC

ext

proteins

0.1440.1720.204

SC_int

0.0740.0980.122

(—) values

0.1950.1640.1670.128-0.1640.1710.1690.1530.142-0.1560.1730.1610.166

0.139-0.213 +

0.132-0.137-

0.1920.1710.1840.1810.188

0.1090.0790.125 +0.0770.1180.1030.0880.1030.1070.0970.0990.129 +0.122

0.0920.092

0.126+0.119

0.0830.152 +0.0880.0890.108

SC_ext

0.1150.1430.183

0.1780.1440.1310.104-0.1220.1280.1370.110-0.104-0.1180.1540.1230.131

0.1000.195

0.100-0.107-

0.1750.1500.1630.1590.161

1RHD 2RHE 2RHV 1RN3 1RNS 1RNT 3RP2 nRSA 1RSM nRXN 1SBT 4SBV2SGA 3SGB 1SOC 1SN3 2SNS 2TAA 1TGB 2TGP 1TGS 1TGT 1TIM nTLN1TON 1TPA 3TPI 1TPO 1UBQ 3WGA 2YHX

where the use of several datasets per protein XXX is indicated by nXXX.

NATOM

POLSURF =

NATOMPOLFRAC =

NATOM

\q{f)\-a(f)]/ E [a(0

where atom / has partial charge q(i) [values for united atoms asin Frommel (1984) and Momany et al. (1974)] and surface areaa(i) [calculated as in Kabsch and Sander (1983)]. Mathematically,the polar fraction is like the expectation value of the absolutevalue of partial charges, if the atomic surfaces a(J) are interpretedas statistical weights. The concept of polar fraction is similar tothat of surface charge density. We use atomic units for partialcharge (e) and A2 for surface area, so POLFRAC is in unitsof e.

Here, the atomic surface area a{i) can either be the external(solvent accessible) area or the internal (buried) surface area. Theinternal surface area reflects the extent to which parts of theprotein cover other parts in the folded conformation of the protein,

+ , unusually high value; —, unusually low value; misHM, misfoldedhaemerythrin (CONGEN improved version); misIG, misfoldedimmunoglobulin (CONGEN improved version); 1GCR, gamma crystallin;1GCN, glucagon; 3WGA, wheat germ agglutinin; 1MLT, melittin; 2FD1,ferredoxin; 1OVO, ovomucoid inhibitor, 1PFC, IG fragment; 2ABX,bungarotoxin; 2CDV, cytochrome C3 ( -4 haems); 2CDVh, cytochrome C3(+4 haems); 1CY3, cytochrome C3; 1PPT, pancreatic polypeptide; 1NXB,neurotoxin; 2EBX, erabutoxin; 1CRN, crambin; 1FX1, flavodoxin.

excluding solvent, and is defined as the difference between theexternal surface area of the extended and of the folded form.The atomic surface area can be averaged over all atoms, or overside-chain atoms and backbone atoms separately. The corres-ponding six characteristic quantities are: external/internal polarfraction for side chains/backbone/all atoms. Four of thesequantities (e.g. the ones in Table II) carry non-redundantinformation.

The actual values of POLFRAC for natural proteins areapproximately independent of molecular weight. This statementis true both for the external and internal polar fraction, averagedover all atoms or over side chains only; the relative fluctuationaround the mean value is larger for smaller molecular weights(e.g. Figure 2B and C). The independence of molecular weightsuggest that the polar fraction approximates a physical invariantof folded globular proteins, possibly related to solubilityrequirements in water. Miller et al. (1987a) have made similarobservations in terms of differently defined quantities.

Interestingly, the protein exterior, the protein interior and amaximally unfolded chain are very similar in polarity on average:

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0 . 1 4 -

0 . 1 2 -

II1_ 0.10-

0.08-

0.0620000 40000 60000 80000

molecular weight

O.iiO-

0.18-

0.16-

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0.12-

0.10-

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Q

Q QD D

BP3B 0 D

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20000 40000 60000 80000

molecular weight

Fig. 2. Testing hypothetical structures by polarity characteristics. A misfolded(Novotny et al., 1984) or designed (Sander, 1987) structure [black diamonds( • ) ] is regarded as questionable if its characteristic values fall outside ofthe cloud of reference values [64 proteins, dotted squares (B)] in then-dimensional space of n characteristic values. In practice, 1- and 2-Dprojections are used, as in (A), (B) and (Q. (A) Values of external polarfraction and internal polar fraction (side-chain plus main-chain atoms) scatteraround their (common!) mean value 0.172 e. Three of the seven [ • ]hypothetical structures are identified as questionable, four others are identifiedas normal. (B) The side-chain (SQ internal polar fraction clearly filters outone inadequate design, BUND, on the basis of an excessively polar interior.(C) The side-chain (SC) external polar fraction clearly identifies the twomisfolded proteins (Novotny et at, 1984) on the basis of an insufficientlypolar external surface. For definition of polar fraction see text. The misfoldedproteins are: the sequence of hacmerythrin, a four-helix bundle protein, placed

into the three dimensional structure of the x-chain of the mouseimmunoglobulin variable domain, a structure with two four-stranded (3-sheets;and vice versa (Novotny et al., 1984); the data sets were refined using theCONGEN algorithm for generating conformations (Bruccoleri and Karplus,1987). The designed (de now) proteins are from the September 1986 EMBOcourse Protein Design on Computers (Sander, 1987): bundle (BUND),betaalphacin (BEAL), babarellin (BABA), tiny urn (TINY), and idealizedflavodoxin (FXNI). A detailed description of the design exercises is availableon request from the BlOcomputing Secretary, EMBL, 6900 Heidelberg, FRG.The coordinates are available on electronic mail from the bitnet file serverNETSERV@EMBL. Send an email message containing the string 'help' orthe string 'SEND $PDB:xxxx.BRK_MOD', where xxxx = BUND etc. isthe four-letter protein identifier, PDB stands for Protein Data Bank, BRK forBrookhaven and MOD for model.

the mean values of the polar fraction (averaged over all atomsand all proteins) is 0.172 e for all three, with a scatter of about±10% for the internal and ±20% for the external polarfraction ( Figure 2A). To the extent that this statement is truefor individual proteins, there is no net fractionation of polarity(as quantified here) in the folding process. A literally interpretedoil-drop model of proteins appears not be valid: the. proteininterior is approximately as polar as the exterior, due to theconsiderable concentration of polar peptide units not accessibleto solvent in helices and sheets (see also Lee and Richards, 1971;Chothia, 1976; Richards, 1977; Rose et al., 1985; Miller et al.,1987a). However, the classical notion of a non-polar proteininterior is reflected in the side-chain averages: the protein exteriorhas a much larger (0.143 e) average side-chain polar fractionthan does the interior (0.098 e) (Table H). Interestingly, Milleret al. (1987a) in addition have pointed out that the protein interioris particularly strongly depleted in charged side chains.

In the database of known structures we find several unusuallyhigh and low values of polar fraction (last four columns of TableIH): a flavodoxin (data set 1FX1, original authors explicitly statethat the structure was manually built and not regularized norrefined), melittin (1MLT, see above), crambin (1CRN, small46-residue plant seed protein with three S-S bridges), a-bungarotoxin (2ABX, see above), sea snake erabutoxin (1NXBand 2EBX, four S-S bridges in 62 residues), avian pancreaticpolypeptide (1PPT, small 36-residue helix-loop peptide), multi-haem cytochrome C3 (2CDV, see above) and wheat germ ag-glutinin (3WGA, see above). Excluding these proteins, we defineas normal the ranges of the four types of polar fraction valuesgiven in Table II.

Evaluation of hypothetical structures by polarity criteriaIdeally, characteristic quantities not only have a clear physicalmeaning but are also useful in practice. The available testingground consists of deliberately misfolded proteins (Novotnyet al., 1984), which are clearly wrong, and of proteins designedde novo (Sander, 1987), which may or may not be wrong.

When the polarity values were calculated for these hypotheticalproteins, the misfolded proteins have too few polar side-chainatoms exposed on the surface, with a side-chain external polarfraction of 0.100— 0.107 e, compared to the average of 0.143 eand a lower bound in the database of 0.115 e (Figure 2C). Themisfolded haemerythrin has too many polar side-chain atoms inthe interior, with a side-chain internal polar fraction of 0.126e, compared to the average of 0.098 e and an upper bound inthe database of 0.122 e (Figure 2B).

As a realistic test of the usefulness of the polarity criteriaapplied to new protein designs, consider five protein sequence-structure pairs designed de novo as an exercise during an EMBOcourse in 1986 (Sander, 1987). These designs looked reasonable

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from many points of view (visual examination, secondarystructure preferences, energy minimization, etc.)- However,applying our criteria, one of them can be rejected because ofan excessively high internal polar fraction of side chains:POLFRAC (side chains, internal) = 0.152 e compared to theaverage of about 0.098 e and an upper limit in the database of0.122 e (Figure 2B). Clearly, the designed sequence has verylittle chance of leading to successful experimentation, unlessmodified.

These results show that our criteria are a first step towardtheoretical screening of sequence-structure designs, of 3-Dstructures model-built by homology and even of experimentalstructures. However, as the approach here is based on empiricaland statistical analysis of the database, which may not be fullyrepresentative of the range of physically permissible structures,we are only able to identify a hypothetical structure asquestionable and not yet able to definitively prove or disprovethe validity of a design.

Other recent attempts to evaluate misfolded proteins are basedon the notion of hydrophobicity. Eisenberg and McLachlan (1986)use the relationship between accessible surface area and energyof transfer from water or organic solvent to estimate thehydrophobic stabilization of proteins. They obtain lower thannormal hydrophobic stabilization energy for the misfoldedproteins (refined data sets) of Novotny et al. (1984) comparedto their natural counterparts, but provide no systematic criterionapplicable to protein design. Bryant and Amzel (1987) counthydrophobic neighbour contacts in protein structures.Hydrophobic contact counts are approximately invariant fordifferent proteins, but the criterion based on them is lessdiscriminating than the one used here and cannot easily beextrapolated to higher molecular weights.

ConclusionOur conclusion is that characteristic quantities with sufficientlynarrow scatter around their canonical value can be used toimprove protein design. The normal range of values can be us-ed as a filter, identifying hypothetical protein structures asquestionable when their value of the characteristic quantity fallsoutside of the range of values in the database of referenceproteins. The mean value of the characteristic quantity can beused as a constructive criterion: bringing a protein closer to themean value improves the chances of a successful design.

We expect continued progress in the search for physicallydiverse and more refined criteria and further quantitative andqualitative improvement in the database of known structures. Acomputer program, POL DIAGNOSTICS 88, capable ofapplying the current set of criteria to a data set of proteincoordinates (all atoms), is available on request (academic or otherlicense agreement).

AcknowledgementsWe thank R.E.Bruccoleri and J.Novotny for their refined (using the CONGENalgorithm by Bruccoleri and Karplus, 1987) data sets of two misfolded proteinsand Arthur Lesk for making us aware of the new ferredoxin structure (Stout et al.,1988). We are deeply grateful to the crystallographers who have made proteincoordinates available through the Protein Data Bank.

Note added in proofJ.Novotny, A.A.Rashin and R.E.Bruccoleri [Proteins, 4, 19-30 (1988)] reportsuccessful discrimination between misfolded and native structures using thefollowing criteria: (i) solvent-exposed side-chain non-polar surface, (ii) numberof buried kmizable groups and (iii) empirical free-energy functions that incorporatesolvent effects.

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Received on September 20, 1988; revised on November 9, 1988

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