J. MOE. Biol.
(1979) 132, 411434
Solvent-accessible Surfaces of Nucleic Acids CHARLES J. ALDEN
AND SUNG-H•
U KIM?
Department of Biochemistry Duke University Medical Center Durham, N. C. 27710, U.S.A. (Received 15 January
1979)
Static solvent-accessible surface areas were calculated for DNA and RNA double helices of varied conformation, composition and sequence, for the single helix of poly(rC), and for a transfer RNA. The results show that for DNA and RNA double helices, two thirds of the water-accessible surface area become buried on double helix formation; phosphate oxygens retain near maximal exposure while the bases are 80% buried. Transfer RNA exposes slightly less surface per residue than does double-helical RNA, despite the presence of several additional “modified” groups, a,11of which are exposed significantly. When a probe corresponding to a single water molecule is used, both the total and atom type exposures are very similar for A-DNA and B-DNA, although marked differences appear in the major and minor groove exposures between the two conformations. For a given base-pair, the accessible surface area buried upon double-helical stacking is nearly constant (within 5%) for different sequences of neighboring base-pairs. For probes larger than single water molecules, there exist considerable diffctrences in the total and atom type exposures of A-DNA and B-DNA. Conformational transitions between the A-DNA and B-DNA helical forms can thus be related to differences in the accessible areas for “structured” water, or a secondary hydration shell, rather than to interactions with individual water molecules of the primary hydration shell. The base-composition dependence of DNA helical conformation can be explained in terms of the opposing effects of thymine methyl groups of A.T base-pairs and the amino groups of 0.C base-pairs upon the solvent within the grooves. The area calculations show that primarily the major groove of B-DNA and the minor groove of A-DNA have sufficient accessible surface area to be recognized by a probe size corresponding to the side-chains of amino acids.
1. Introduction The folding of a biological macromolecule into a stable, functional conformation is mediated principally by interactions with the aqueous environment: variations of ionic concentration, pH, organic solvents or water activity will in general result in conformational changes and, at extreme levels, denaturation of the polymer. Indeed, the relative strengths of the intramolecular forces considered to be the primary stabilizing factors for secondary and tertiary structures (hydrogen bonding, base forces) depend strongly upon the nature of the surstacking, and “hydrophobic” t Present address: Department University of California, Berkeley,
of Chemistry and Laboratory California 94720, U.S.A.
of Chemical
Biodynamics,
411
0022-2836/79/230411-24 $02.00/O
0 1979 Academic
Press Inc. (London)
Ltd.
412
C.
J.
ALDEN
AND
d:.R.
Klbl
rounding liquid. X-ray cryst,allographic studies of‘ maeromolecuiar structures allow ready identification of intramolecular interactions from the proximity and orientation of the constituent residues; however, solvent influences are less amenable tzo such direct visualization, partly because the solvent is seldom completely ordered about the surface of the molecule and also because the solvent effect,s are most influential in the dynamic events leading to chain folding and aggregation, For proteins, which incorporate a wide spectrum of polar, aliphatic and aromatic: side groups and which exhibit a variety of secondary structures, the question of solvent effects as a driving force in chain folding has long been discussed (Kauzmann, 1959; Tanford, 1962). The concept of accessible surface area has been introduced to estimate the relative changes in solvent-accessible surface upon folding polymers from random coils to compact forms and also to assess the surface exposures of different classes of atoms within folded polypeptides (Lee & Richards, 1971; Shrake & Rupley, 1973; Finney: 1975; Chothia, 1975; Richards, 1977). For nucleic acids, by contrast, the concept of relative surface exposure has not been explored extensively. Thus we have examined the solvent-accessible surfaces of a variety of polynucleotides, (1) to evaluate the extent of surface burial on folding, (2) to compare relative exposures between hydrophobic and hydrophilic atoms, (3) to identify the most’ accessible atoms for intermolecular interactions, and (4) to relat,e helical conformational t’r ansitions to environmental changes.
2. Calculation
of Accessible Surface Areas
(a) kfethod
of calculation
The methodology employed in this study is very similar to t)bat described by Lee & Richards (1971) in their calculation of polypeptide surface areas. We imagine a spherical “probe” or solvent molecule of radius Y, free just to touch but not penetrate the van der Waals surface of the examined molecule. The closed surface defined by
Fig. 1. Schematic diagram of accessible surface areas. Around the examined molecule (shaded) is constructed an envelope defining the loci of points for the center of a spherical probe which may just touch the molecule. This construction is sliced by a set of parallel planes, and the perimeter (A) of the surface envelope is calculated for each atom. In the Figure 2 separate envelopes, correspending to different probe sizes, are shown. Note that as the probe radius increa,ses, the accrsaibilities to it for atoms within a concavity decrease.
ACCESSIBLE
SURFACES
OF
NUCLEIC
ACIDS
413
all possible loci for the center of the probe is defined as the accessible surface of the molecule, and those portions of the surface for which the probe touches only one atom comprise the accessible surface of that atom (Fig. 1). Throughout, we use the terms and “accessibility” synonymously, always in “accessible surface area”, “exposure”, AZ. Note that these surface areas involve contacts with only one probe molecule; interaction of the probe with other (bound) solvent molecules is not considered in the calculations. A computer program was written to calculate accessible surface areas in the following manner. Each atom is assigned a characteristic van der Waals radius rv, and Cartesian co-ordinates for each atom are supplied as input data. A sphere of radius rv + rw is constructed about each atom, and the ensemble is sliced by a set of parallel planes of uniform separation h; the intersection of each plane with the ensemble is a set of circles. For each circle, the fraction of the perimeter not enclosed within any other circle is calculated as f,, and the accessible surface area for that atom within that slice is given by A = 27ilfph(r, + r,). For the special case where the slice is at the end of a sphere (i.e. an adjacent plane does not intersect that sphere), this segment of area is corrected to A = 2xfP(rV + r,)(r,+r,+~h-lZ,-Z8,1),whereZ,andZ, are the 2 co-ordinates (perpendicular to the slicing planes) of the atom center and terminal slicing plane, respectively. The partial areas thus calculated are summed for each atom, for each atom type, and for the total ensemble to yield the accessible surfaces for the molecule. While the formulae for surface area are exact for isolated spheres, slight inaccuracies arise when the spheres overlap, since f, does not account for the curvature of the spherical intersections. Hence, the calculation is an approximate integration, for which the precision will increase as h decreases. In general the calculation is repeated several times, with slicings at different orientations, both to test the reproducibility of the calculations and to achieve a credible average value for each surface. The accuracy of these calculations depends only upon the values chosen for the van det Waals and probe radii (r, and rw), and of course upon the accuracy of the inpur co-ordinates. (b) Determination
of van der Waals radii
Preliminary tests showed that individual and total calculated surface areas are quite dependent upon the choice of atomic radii, so it was necessary first to determine physically justifiable values for these parameters. The assumption of spherical atoms implicit in these calculations may not be absolutely correct in all cases (e.g. for carbonyl oxygens); however, what are most significant in these calculations are the relative changes in accessibilities for different conformations, so this slight deviation from ideality should not affect general conclusions. To determine best values for van der Waals radii, we used the intermolecular contact and volume survey of Bondi (1964) for carbon, phosphorus, aromatic nitrogen and ester oxygen radii. Values for presumed spherical carbonyl oxygen, amino and methyl groups were derived from the volume decrements for each group, cited in the same survey, by the use of a computer program which calculates volumes in an approximate integral fashion, analogous to the surface accessibility program. The eight non-hydrogen atom types used for nucleic acid calculations and the van der Waals radii used are listed in Table 1.
414
Symbol
Group type
ALC ARC sox
Aliphatic carbon Aromatic carbon Sugar oxygen (ring and ester) Carbonyl oxygen Phosphate oxygen Aromatic ring nitrogen Amino nitrogen Phosphorus Aromatic ring hydrogen Aliphatic hydrogen Amino hydrogen Water
BOX POX ARN AMN PHO ARH ALH AMH WAT
Ratlius (A) hydrogen Including explicitly atoms
Including at,oms
1.70 1.77 140
2.00 1.77 140
1.64 1.64 1.55 1.72 1.80 1.01 1.17 I.17 1.40
1.64 1.64 1.55 I.751 1~80 1.40
t Values for aromatic carbon and nitrogen, sugar oxygen, and phosphorus from Bondi (1964). Values for other atoms were calculated from the volume the same survey, as described in the text. $ 1.86 d is suggested as more appropriate.
(c) Reproducibility
hydrogen implicitly
are taken decrements
directly cited in
of the calculations
Since t*he precision of these calculations, as well as their expense, depends upon the slicing int’erval h, it was useful to gauge the reproducibility of surface accessibility estimates as a function of h. The results of this test upon the model syst,em deoxyadenosine are shown in Figure 2. The spread of total surface areas calculated at differentf slicing orientations ranges from less than 0.4% at h = 0.05 A to about 40/6 at h = 0.6 A. For large molecules, such as transfer RNA, averaging three separate calculations at a slicing width of 0.5 d was deemed suitable t,o yield a total surface
!
1
0-I
0.2
0.3
0.4
0.5
0.6
h (81 Fig. 2. Reproducibility of surface accessibliity calculations as a function of separation between slices. The total accessible surface area for deoxyadenosine was calculated using different slicing separations h; for each value of h, the calculation was performed with the slicing planes oriented differently with respect to the molecule. Ash increases, the spread ofcalculatcd values also increases. At h = 0.5 11, the average of any 3 calculations is within 1 o/0 of the mean surface area.
ACCESSIBLE
SURFACES
OF
NUCLEIC
-4CIDS
415
area reproducible to within 1 o/O.Given the uncertainties in true van der Waals radii and atomic co-ordinates, this is an adequate margin of error. For DNA helix calculations, where only small surface exposure changes might be expected, areas were calculated at a slicing separation of 0.1 A. (d) Effect of explicit
inclusio?t
of hydrogen
atoms
Since a large fraction of nucleic acid atoms consists of hydrogen, we also calculated accessible surface areas for nucleotides with hydrogen atoms included explicitly. Hydrogen atom co-ordinates were generated using the bonded geometries of the atoms t’o which they are joined and the covalent bond lengths compiled by Kennard (1974). Values for their van der Waals radii were those of Bondi (1964) or, for methyl and amino hydrogens, were calibrated as above from the group volume decrements. Values used in this study are also listed in Table 1. Treatment of aliphatic carbons as simple spheres, with larger radii to simulate the effect of hydrogen atoms, yields slightly different results than inclusion of hydrogen atoms explicitly in the co-ordinate lists (Table 2). For example, the accessible surface TABLE
Effect of including
hydrogen atoms explicitly With
2 in surface calculations
H
Without
(b2) A. Adenosine
5’-monophosphate Total ALC + ALH sox ARC + ARN + ARH POX + PHO AMN + AMH
B. poly(dA)3.poly(dT), Total ALC + x0x POX + BOX ARC + AMN +
491.3 108.8 83.6 135.0 92.3 X1.6
for H
(87
ALC sox ARC + ARN POX + PHO AMN
I,
= I.4 ip Difference (AZ)
(%)
484.6 113.7 74.9 130.9 93.5 71.6
6.7 -4.9 8.7 4.1 -1.2 0.0
1.4 -4.5 10.4 3.0 -1.3 0.0
1528.3 556.6 176.9 481.3 76.7 176.6 60.2
19.1 -22.8 31.1 -0.5 0.8 1.8 7.7
1.2 -4.3 15.0 -0.1 1.0 1.0 11.3
B-DNA ALH PHO ARN AMH
+ ARH
1547.4 533.8 208.0 481.8 71.5 178.4 67.9
ALC sox POX + PHO BOX ARC + ARN AMN
areas for deoxyadenosine (5’)-phosphate were calculated both with and without hydrogen atoms, using a probe radius rw = 1.4 A corresponding to the average radius of a water molecule. The total accessible surface in the former case was slightly greater (6.7 AZ, or about 1.5% of the total), with the primary difference being due to an enhanced exposure (by about 11%) of the sugar oxygens when hydrogens were attached on the neighboring carbons. Similarly, when the accessible surface for (dA)a . (dT), in the B-conformation is calculated both ways, the total area was again slightly greater with the hydrogens included. The enhancement of sugar oxygen surface was even more pronounced in this case, being about one sixth again as large for the hydrogen as for the non-hydrogen case, and the aliphatic surface was again diminished by about 5%. In addition, the apparent exposure of an amino group treated as a single sphere of radius 175 A is about 10% less than with hydrogens
116
included. A value valent to that in these calculations application of any similar results.
C. J. ALDEN
4EU
S.-H.
KTJI
of 146 A for the spherical amino radius yields an exposure equithe case with hydrogens included. Since QUT primary interest in changes in exposure lan.der different condit,ion.s, is in relative set of reasonable, self-consistent8 values should yield qualitatively
To gauge the change in surface exposure upon folding a molecule, it, is necessary first to determine the maximum possible surface exposure of the components of that molecule, corresponding to the unfolded stat!e. For polypeptides, this exposure has usually been determined by calculating t)he surface exposure of the middle residue of with all conformation angles terns (Lee & Richards, 1971). For model tripeptides polynucleotides, however, it is unclear that) an, analogous procedure is a,ppropriate: with several variable torsion angles per residue, the all-tra7a.s conformation may not correspond. to the one (of - 50) most exposed conformation; in addition, it is known that two adjacent phosphoester bond torsion angles are reluctant simultaneously to adopt’ trans values (Kim et aZ., 1973). Figure 3 illustrates the accessible surface ex-
360
240
0 5
m
180
0
60
120
180
240
300
360
Alpha
Fig. 3. Accessible surface exposure of phosphate oxygens in dimethyl phosphate. The exposure of the phosphate oxygens was calculated for different conformations about the 2 ester bonds. Broken lines represent contours of equa7 exposure; triangles represmt the corresponding conformations in t>he backbone of the observed crystal structure of yeast phenylalanine transfer RN4 (Sussman et al., 1978). The reluctance of nucleotide backbones to adopt an all-traw conformation may be due in part to the burial of charged phosphate oxygens that such conformations entail.
posure of the phosphate oxygens for the model case of dimethyl phosphate as a function of the conformat,ion angles about the two ester bonds; included also are indicat*ors for the corresponding conformat,ion angles about. the est,er bonds observed in the struct’urc of transfer RNA (91.ussman eE gl., 1978). We note t,hat t,he all-trans conformation, avoided by pol~ynuclootide phosphat~ea, corresponds t,o a minimal
ACCESSIBLE
Fig. 4. Division of a nucleotide imal surface exposure. Accessible shown to estimate the maximum thus obtained for the following region B; C-4’, C-3’ from region
SURFACES
OF
NUCLEIC
ACIDS
417
backbone into covalently linked groups for estimation of maxsurface areas were calculated for each of the 4 molecular fragments possible exposure for each atom. The maximal exposures were atoms: O-3’, O-5’, P, 0-1P and 0-2P from region A; C-5’ from C; O-l’, C-l’, C-2’ and all base atoms from region D.
exposure for the charged phosphate oxygens. In addition the repulsive lone-pair interactions of the ester oxygens are believed to discourage adoption of this conformation in polymers (Sundaralingam, 1969; Newton, 1973). Hence a more elaborate construction was invoked to determine maximal exposures for the individual atoms. Figure 4 illustrates the division of a nucleotide backbone into four regions, which were used to determine the maximum exposure of the nucleotide atoms limited only by their covalently bonded neighbors, i.e. invariant with respect to conformation. Maximal exposures for the deoxyribose atoms were calculated for both the C-3’-endo and C-3’-exo puckered forms, and the total maximum exposures for the carbon and oxygen atoms were seen to be very similar, although the exposure of individual atoms was different for the two forms. Maximal exposures of the nucleoside bases were calculated for the bases assuming the normal anti conformation observed in polynucleotides. Table 3 lists the maximal surface exposures for the DNA components (calculated with hydrogen atoms) and for the RNA components (without hydrogens). While it is quite possible that not all of the atoms in a nucleotide may simultaneously achieve their maximal exposure, this list gives a fair estimate of the relative degree of exposure for the various nucleotide atom types for the unfolded state. Thus we note that the average maximal accessible surface area for an unfolded DNA chain is approximately 490 A” per nucleotide, with the bases accounting for nearly half (44%) of this total. 15
DNA C-3’-em sugms
C-3’-end0
sugars
______~~~~ P Q-3’ o-IP o-2P O-1’ C-5’ C-5’H-I C-5/H-2 c-4 C-4’H C-3’ C-3’H C-2’ C-2’H-1 C-2’H-2 C-l’ C-1’H O-5’ Total
B. Maximum
Total
0.95 9.65 52.40 48.36 14.56 6.18 22.92 22.56 0.93 19.75 1.10 19.31 2.37 21.86 9.00 0.07
14.96 10.87
10.31 12.00
275.01
274.28
P O-3’ O-II? o-2P O-l’ C-5’
19.03
7.43 28.40 18.36 24.79 7.89 17.09 30.86 15.03 15.02 7.99
cm-1
CC-6 CC-6H cc-5 CC-BH CN-4 CN-4H- 1 CN-4H-2 cc-4 CN-3 co-2 cc-2
213.66
p TME, methyl
46.18
7.96 59.38
C-4’
16.97
C-3’
18.74
C-2’ O-2’
25.68 30.10
C-l'
19.78
O-5'
7.72 258.93
bases in C-3’-exo
Guanine
Cytosine 0.17 17.96 3.64
O”95 ti.4Q 48.98
accessible surface areas (in kf”) for DNA nucleosides for I‘, = I.4 A
Adenine AN-Q AC-8 AC-8H AN-7 AC-5 AN-6 AN-6H-1 AN-6H-2 AC-6 AN-l AC-2 AC-2H AN-3 AC-4
I.00 14.16 48.75 53.05 IO.80 6.00 23.01 22.74 0.47 18.55 0.33 11.12 1.29 20.43 16.14 1.34
RNA
0.17 8.67 1.15 20.54 12.44 27.08 22.51 25.07 7.81 14.50 45.92 9.98
GN-9 GC-8 GC-AH GN-7 GC-5 GO-6 GC-6 GN-1 ON-IH GN-2 GN-2H-1 GN 2H-2 GC-2 GN-3 GC-4
195.84
Thymine O”19 18.33 3.84 22.23 7.59 54.02 9.39 5.84 12.20 27.15 23.60 24.63 9.92 9.72 8.08
236.76
TN-1 TC-6 TC-6H TMET T;MEH- 1 TMEH-2 TMEH-3 TC-5 TO-4 TC-4 TN3 TN-3H TO-2 TC-2
0.16 6.53 0.49 13.68 24.24 15.33 12.91 5.76 47.05 9.40 5.83 16.10 44.87 IO.32 212.67
carbon of thymine.
(f) Polarity
of exposed
atoms
One difficulty in describing the relative exposures of polar and non-polar groups is the assignment for the aromatic nikogen atoms, which are quite polar an.d frequently form hydrogen bonds within the plane of the base, yet which contribute to the TT orbitals of the ring and act as aromatic molecules when approached normal to the
ACCESSIBLE
SURFACES
OF NUCLEIC
ACIDS
419
plane of the base. Arbitrarily dividing the contribution from such atoms equally among the polar and non-polar classifications, we note that in the unfolded state polar atoms comprise slightly over half (54%) of the exposed surface of DNA, with approximately equal contributions from the bases and the backbone. For the backbone there is an almost equal exposure of hydrocarbon and oxygen atoms, while for the bases 42% of the atoms may be classed as non-polar. For the individual nucleoside bases, however, there is a pronounced range of maximal polar group exposure: 69% for G, 61 y0 for C, 52% for T and 45% for A.
3. Results (a) Surfaces of DNA
double helices
Accessible surface areas for double-helical DNAs were calculated by summing the individual atomic exposures of the middle base-paired residues in various doubleHelices examined were A- and B-DNA stranded, complementary trinucleotides. (Arnott & Hukins, 1972) C-DNA (Arnott & Selsing, 1975) and D-DNA (Arnott et al., 1974). For each of these helices hydrogen atoms were included in the input co-ordinates, and areas were calculated with a slicing separation of 0.1 A. In all cases except D-DNA, several different base sequences were examined, to test for sequence and composition dependence of surface accessibility. Values for A + T- and G + C-rich polymers were taken as the averages of the four distinct trinucleotide sequences consisting of one type of base-pair. The results of these averagings are summarized in Tables 4 and 5. Overall, the folding of a long DNA molecule into a double helix results in the burial of approximately two thirds of its maximally exposed surface, a value quite similar to the result for globular proteins (Lee & Richards, 1971). A comparison of the relative surface exposures of B-DNA with the unfolded molecules is shown in Figure 5. For most atom types, the reduction of accessible surface upon folding is close to their TABLE
Atomic
exposures (in d”) of DNA
4
double helices for r, = 1.4 A
A. Backbone Atom P O-3’ o-1P o-2P O-5’ C-5’ C-5’H-1 C-5’H-2 O-l’ C-4’ C-4’H C-3’ C-3’H C-2’ C-2’H-1 C-2/H-2 C-l’ C-I’H
A-DNA 0.48 5.34 41.67 31.27 0.00 2.39 8.91 9.73 5.94 0.50 18.50 0.00 0.34 0.00 4.60 0.00 0.35 12.56
B-DNA 0.18 5.12 44.40 32.72 0.00 1.98 12.12 4.76 4.01 0.68 19.52 0.50 8.35 0.03 0.28 4.46 0.00 0.00
C-DNA 0.07 4.76 29.82 47.46 0.00 1.99 12.47 4.19 3.85 0.86 21.00 0.70 9.90 0.01 5.00 0.18 0.00 0.00
420 TABLE
Stem AS-Q AC-S AC-SH AN-7 AC-5 AN-6 AN-GHAN-OH-2 AC-6 AN-1
4 (corztimed)
A -DNB
1
AC-2 AC-PH AN-3 AC-4
0.00 1.07 0.00 5.06 0.00 1.40 7.98 0.00 0.00 0.00 2.86 5.02 6.32 0.00
B-DIVA -~__ 0.00
C-DNAAI 0.00
3.95 0.00 7.06 0.00
3.55 0.00 &TO 0.00 1 .BS 11.28 0.00 0.00 0.00 0.59 2.35 2.29 0.00
1.91 11,23 o-00 0.00 0.00 2.06 0.29 140 a.00
CN- 1 CC-G CC-6H cc-5 CC-AH CN-4 CN-4H-I CN-4H-2 CN-3 CO-2 cc.2 cc-4
0.00 0.30 0.00 4.40 3.1G 2.48 12.32 0.00 0.00 6.56 0.00 0.02
0.00 1.91 0.00 5.69 5.70 2.63 16.17 0.00 0.00 0.00 0.57 0.00
0.00 1.81 0.00 5.36 4.8s 2.51 17.29 0.00 0.00 0.32 0.00 0.00
GN-9 GC-8 GC-YH GN-7 GC-5 GO-6 GC-6 GN- 1 GN-11-I GN-2 GN-2HGN-2H-2 GC-2 GN-3 GC-4
0.00 1.60 0.00 7.02 0.00 5.80 0.00 0.00 0.00 3-87 O-03 IS.45 0.00 2.26 0.00
0.00 4.73 0.00 8.85 0.00 8.61 0.00 0.00 0.00 0.62 0.00 9.16 0.00 0.03 0.00
0.00 4.11 0.00 9.01 0.00 8.86 0.00 0.00 0.00 0.17 0.00 6.52 0.00 0.03 0.00
0.00 0.26 WOO 1.00 12.55 0.00 1.82 0.58 6.20 0.00 o-00 0.00 11.28 0.00
0.00 1.06 0.00 5.51 20.66 0.02 4.16 0.22 8.08 0.00 o,oo 0.00 3.82 0.00
0.00 0.72 0.00 10.27 12.44 7.20 2.02 0.12 6.87 0.00 o-00 0.00 3.34 0.00
TN-I TC-6 TC-6H TME TXEH-1 TMEH-2 TMEH-3 TC-5 TO-4 TC-4 TN-3 TN-3H TO-2 TC-2
I
ACCESSIBLE
SURFACES
OF
NUCLEIC
ACIDS
421
TABLE 5 Group type exposures (in A”) for DNA A-DNA A.
A + T-rich
B-DNA
double he&es for two residues C-DNA
D-DNA
polymers
ALC ARC sox POX BOX ARN AMN PHO ARH ALH AMH
7.50 4.77 23.12 143.92 17.45 11.38 1.40 0.96 5.02 126.47 7.98
11.87 5.41 21.34 152.52 1 I.90 8.99 1.58 0.36 2.35 122.70 11.28
17.39 4.50 20.24 152.06 10.21 9.12 1.91 0.14 1.40 125.64 11.23
26.31 3.96 22.41 128.12 8.44 7.20 2.34 0.30 0.00 129.17 11.67
Total
350.00
350.30
353.84
339.92
POS NEUT NEG
20.76 143.76 185.48
21.85 142.33 186.12
22.26 148.93 182.65
21.21 159.44 159.27
B.
G + C-rich
polymers
4LC ARC sox POX BOX ARN AMN PHO ARH ALH AMH
6.46 6.32 22.00 150.34 12.36 9.28 6.35 0.96 3.16 106.48 30.80
6.36 12.33 14.96 155.84 9.18 8.88 3.25 0.36 5.70 100.78 25.33
7.12 11.28 14.10 157.06 9.18 9.04 2.68 0.14 4.88 106.98 23.51
Total
354.51
342.97
346.27
POS NEUT NEG
46.43 122.42 185.66
37.46 125.17 180.34
35.53 130.26 lSO.48
POS = ARN + AMN + AMH NEUT = ALC + ARC + ARH NEG = SOX + POX + BOX
+ ALH + PHO
proportion of the total maximal surface area, with base atoms being buried relatively more than sugar atoms. The sole and striking contrast to this pattern occurs for the phosphate oxygens, whose exposure is reduced only slightly upon transition from the extended to the helical form. Thus the accessible surface in DNA double helices is more polar than for the random coils, with the phosphate oxygens alone accounting for nearly 45% of the total accessible surface area. The contribution from the bases now accounts for only about a fifth of the total surface in the double-stranded helices, while the sugars account for over a third of the surface. Considering the observed effect of solvent upon DNA helix conformation, and the pronounced difference in gross shapes of the different forms, the similarities of their
422
6.
J.
ALDEN
AND Unfolded
S.-N.
KIM
DNA
Total =490*5
x2
B-DNA Buried POX
Total-3172
8’
(b) Fig. 5. Group type exposures in unfolded and helical B-DNA. Solvent-accessible surface areas were calculated using a 1.4 d probe radius for maximally unfolded DNA (a) and B-DNA (b) of average base sequence. The accessible surface buried in folding the extended chain into a double helix, i.e. the difference between (a) and (b), is also shown. In folding of the polymer, the bases become mostly buried while the phosphate oxygens remain nearly fully exposed.
total exposures was somewhat surprising. Hence we calculated the surface accessibilities for A- and B-DNA over a wide range of probe radii (1.0 t,o 50 A), to determine if larger probes, such as hydrated metal ions or structured water aggregates, could discriminate between the different DNA shapes. The results of this test are shown in Figure 6. We note that as r,,, increases, the total surface accessibility of B-DNA increases more rapidly than does that of A-DNA. Moreover, this difference is attributable almost entirely to a greater exposure of the phosphate oxygens in B-DNA, as the aliphatic carbon exposure becomes relatively greater for A-DNA. Curiously, the point at which the A- and B-DNA accessibility curves intersect is just at the yW corresponding to the radius of a single water molecule. For larger values of rW: corresponding to bulky side groups of proteins, structured water, or hydrated metal ions, the accessibility of the major groove of A-DNA decrea,ses abruptly, as does the minor groove exposure of B-DNA (see Fig. 7).
ACCESSIBLE
SURFACES
OF
NUCLEIC
423
ACIDS A-T
I.0
I.4
2.0
3.0 4.0
t
50
I.0
2.0 3.0
4-o
5.0
I.4 (a)
(b)
Fig. 6. Accessible surface areas for 2 base-paired residues of (a) poly(dG).poly(dC) and (b) poly. (dA).poly(dT) in the A- and B-helical forms, calculated varying the probe radius rW. For both polymers, the B-DNA form entails relatively greater total exposure, and particularly a greater exposure of phosphate oxygens, for large probe radii. This result is consistent with the experimentally observed result that high water activity encourages adoption of the B-DNA conformation(-----) A-DNA; ( 1.4 A) can provide clues about, the willingness of the environment to allow or enforce a particular DNA conformation. For A.T basepairs, the greatest exposure is exhibited by thymine methyl groups, and here only in the B conformation (over 80% of the total base exposure for rw > 4.0 A). Since methyl groups are hydrophobic, their exposure in the major groove would tend to encourage water-water aggregation in the major groove and thus exert pressure on the major groove to remain wide. For G.C pairs the most exposed groups are the amino groups of guanine on the minor groove (over 80yb of the total base exposure in the A form, no exposure in the B form, for yw = 4.0 A) or cytosine on the major groove (over 70% of the total base exposure in B-DNA at rw > 4-O A). Both groups are hydrophilic; therefore, extended water-DNA base interactions would result in either the A- or B-helical forms. Thus for G $- C-rich DKA, the availability or lack of excess water will dictate the DNA conformation: under high water activity the major groove will fill and the phosphates will form more extensive hydration complexes; under low water activity, the major groove will collapse and the phosphate oxygens will become more buried. (d) Major
groove of B-DNA and minor groove of A-DNA recognition surfaces for proteins
as primary
As can be seen from Figure 7, when the radius of the probe becomes 3 A or greater, the dominant base exposures occur in the major groove of B-DNA and the minor groove of A-DNA. Specifically, the methyl group of thymine and amino group of eytosine provide most of the accessible area on the major groove in B-DP\TA, and the
ACCESSIBLE
SURFACES
OF NUCLEIC
ACIDS
433
amino group of guanine does so on the minor groove of A-DNA (see Table 4). Since most of the side-chains of amino acids are considerably larger than single water molecules the above observation can be considered as suggesting that the primary recognition surface of B-DNA is the major groove and that of A-DNA is the minor groove. This is consistent with the observation that protein-DNA contacts occur predominantly in the major groove of DNA in the Escherichia coli RNA polymeraselac promoter complex (Johnsrud; 1978) and in the Zac repressor-Zac operator complex (Gilbert et al., 1976), if one interprets protection as well a.s enhancement of methylation as due to close contact of grooves with proteins. This work was supported
by grants from the National Institutes
and K04-CA-00352) and the National Science Foundation authors (C. J. A.) is a National Institutes of Health research The atomic co-ordinates
of tRNA
used in this work are available
of Health (CA-15802
(PCM76-04248). fellow.
One of the
from S.-H. Kim on request.
REFERENCES Amott, S. (1976). In Organization and Expression of Chromosomes (Allfrey, V. G., Bautz, E. K. F., McCarthy, B. J., Schimke, R. T. & Tissieres, A., eds), pp. 209-222, Dahlem Konferenzen, Berlin. Amott, S. & Hukins, D. W. L. (1972). Biochem. Bioplzys. Res. Commun. 47, 150441509. Arnott, 8. & Selsing, E. (1975). J. Mol. Biol. 98, 265-269. Arnott, S., Hukins, D. W. L. & Dover, S. D. (1972). Biochem. Biophys. Res. Commun. 48, 1392-1399. Arnott, S., Chandrasekaran, R., H&ins, D. W. L., Smith, P. J. C. & Watts, L. (1974). J. Mol. Biol. 88, 523-533. Arnott, S., Chandrasekaran, R. & Leslie, A. G. W. (1976). J. Mol. Bid. 106, 735-748. Bondi, A. (1964). J. Phys. Chem. 68, 441-451. Borer, P. N., Dengler, B., Tinoco, I., Jr & Uhlenbeck, 0. C. (1974). J. Mol. Bid. 86, 8433853. Brahms, J., Pilet, J., Tran, T. P. L. 85 Hill, L. R. (1973). Proc. Nat. Acad. Xci., U.S.A. 70,3352-3355. Chothia, C. (1974). Nature (London), 248, 338-339. Chothia, C. (1975). Nature (London), 254, 3044308. Edelhoch, H. & Osborne, J. C., Jr (1976). Advan. Protein Clzem. 30, 183-756. Erfurth, S. C., Bond, P. J. & Peticolas, W. I. (1975). Biopolymers, 14, 1245-1257. Falk, M., Hartman, K. A., Jr & Lord, R. C. (1962). J. Amer. Chem. Sot. 84, 3843-3846. Falk, M., Hartman, K. A., Jr & Lord, R. C. (1963). J. Amer. Chem. Sot. 85: 387-391. Finney, J. L. (1975). J. Mol. Biol. 96, 721-732. Gilbert, W., Maxam, A. & Mirzabekov, A. (1976). In Control of Ribosome Synthesis (Kjeldgaard & Maaloe, eds), pp. 139-148, Academic Press, New York. Goldblum, A., Perahia, D. & Pullman, A. (1978). FEBS Letters, 91, 213-215. Hearst, J. R. (1965). Biopolymers, 3, 57-68. Hingerty, B. & Broyde, 8. (1978). Nucl. Acids Res. 5, 127-137. Johnsrud, L. (1978). Proc. Nat. Acad. Sci., U.S.A. 75, 5314-5318. Kauzmann, W. (1959). Adwan. Protein Ch.em. 14, l-63. Crydallography, vol. 3, Kynoch Kennard, 0. (1974). In International Tablea for X-say Press, Birmingham. Kim, S. H. (1978). Advan. Ewymol. 46, 2799315. Kim, S. H., Berman, H. M., Seeman, N. C. & Newton, M. D. (1973). Acta Crystdogr. sect. B, 29, 7033710. Lee, B. & Richards, F. M. (1971). J. Mol. Biol. 55, 379-400. Lewin, S. J. (1967). J. Theoret. Biol. 17, 181-212. Newton, M. D. (1973). J. Amer. Chem. Sot. 95, 256-258. Pilet, J. & Brahms, J. (1973). Biopolymers, 12, 387-403. Privalov, P. L. & Filimonov, V. V. (1978). J-. Mol. Biol. 122, 447-464.
434
c. J. ALDEN
asu
S.-M.
KlM
P*‘iva10v, P’. L. &i, Mreclishvili, G. M. (1967). Biq~&Ycu, 1.2, Sk--d9. Richards, F. M. (1977). Anw,t,. Rev. Biophya. Bioeng. 6, LSI--176. Shrake, A. & Rupley, J. A. (1973). J. Mol. Bid. 79, 351-371.. Sundaralingam, M. (1969). Biopolywzers, 7, 821-860. Sussman, J. L., Holbrook, S. R., Warrant, R. W., Church, 0. M. c% Rxm, S.-H. j1978). J. Mol. Biol. 123, 607-630. Tanford, C. (1962). J. Amer. Chem. Sot. 84, 4240-4247. Tunis, M. J. 13. & Hearst, J. E. (1968). Biopolymers, 6, 1345-1353. Wells, RI. D., Burd, J. F., Ghan, H. W., Dodgson, J. B., Jensen, K. F., Ncs, I. F. & ‘Wartell, R. %!I. (1977). CRC Cd. Rev. Biochem. 305-340. Wolf, B. & Hanlon, S. (1975). Biochemistry, 1.4, 1661-1670.
(1979) 132, 411434
Solvent-accessible Surfaces of Nucleic Acids CHARLES J. ALDEN
AND SUNG-H•
U KIM?
Department of Biochemistry Duke University Medical Center Durham, N. C. 27710, U.S.A. (Received 15 January
1979)
Static solvent-accessible surface areas were calculated for DNA and RNA double helices of varied conformation, composition and sequence, for the single helix of poly(rC), and for a transfer RNA. The results show that for DNA and RNA double helices, two thirds of the water-accessible surface area become buried on double helix formation; phosphate oxygens retain near maximal exposure while the bases are 80% buried. Transfer RNA exposes slightly less surface per residue than does double-helical RNA, despite the presence of several additional “modified” groups, a,11of which are exposed significantly. When a probe corresponding to a single water molecule is used, both the total and atom type exposures are very similar for A-DNA and B-DNA, although marked differences appear in the major and minor groove exposures between the two conformations. For a given base-pair, the accessible surface area buried upon double-helical stacking is nearly constant (within 5%) for different sequences of neighboring base-pairs. For probes larger than single water molecules, there exist considerable diffctrences in the total and atom type exposures of A-DNA and B-DNA. Conformational transitions between the A-DNA and B-DNA helical forms can thus be related to differences in the accessible areas for “structured” water, or a secondary hydration shell, rather than to interactions with individual water molecules of the primary hydration shell. The base-composition dependence of DNA helical conformation can be explained in terms of the opposing effects of thymine methyl groups of A.T base-pairs and the amino groups of 0.C base-pairs upon the solvent within the grooves. The area calculations show that primarily the major groove of B-DNA and the minor groove of A-DNA have sufficient accessible surface area to be recognized by a probe size corresponding to the side-chains of amino acids.
1. Introduction The folding of a biological macromolecule into a stable, functional conformation is mediated principally by interactions with the aqueous environment: variations of ionic concentration, pH, organic solvents or water activity will in general result in conformational changes and, at extreme levels, denaturation of the polymer. Indeed, the relative strengths of the intramolecular forces considered to be the primary stabilizing factors for secondary and tertiary structures (hydrogen bonding, base forces) depend strongly upon the nature of the surstacking, and “hydrophobic” t Present address: Department University of California, Berkeley,
of Chemistry and Laboratory California 94720, U.S.A.
of Chemical
Biodynamics,
411
0022-2836/79/230411-24 $02.00/O
0 1979 Academic
Press Inc. (London)
Ltd.
412
C.
J.
ALDEN
AND
d:.R.
Klbl
rounding liquid. X-ray cryst,allographic studies of‘ maeromolecuiar structures allow ready identification of intramolecular interactions from the proximity and orientation of the constituent residues; however, solvent influences are less amenable tzo such direct visualization, partly because the solvent is seldom completely ordered about the surface of the molecule and also because the solvent effect,s are most influential in the dynamic events leading to chain folding and aggregation, For proteins, which incorporate a wide spectrum of polar, aliphatic and aromatic: side groups and which exhibit a variety of secondary structures, the question of solvent effects as a driving force in chain folding has long been discussed (Kauzmann, 1959; Tanford, 1962). The concept of accessible surface area has been introduced to estimate the relative changes in solvent-accessible surface upon folding polymers from random coils to compact forms and also to assess the surface exposures of different classes of atoms within folded polypeptides (Lee & Richards, 1971; Shrake & Rupley, 1973; Finney: 1975; Chothia, 1975; Richards, 1977). For nucleic acids, by contrast, the concept of relative surface exposure has not been explored extensively. Thus we have examined the solvent-accessible surfaces of a variety of polynucleotides, (1) to evaluate the extent of surface burial on folding, (2) to compare relative exposures between hydrophobic and hydrophilic atoms, (3) to identify the most’ accessible atoms for intermolecular interactions, and (4) to relat,e helical conformational t’r ansitions to environmental changes.
2. Calculation
of Accessible Surface Areas
(a) kfethod
of calculation
The methodology employed in this study is very similar to t)bat described by Lee & Richards (1971) in their calculation of polypeptide surface areas. We imagine a spherical “probe” or solvent molecule of radius Y, free just to touch but not penetrate the van der Waals surface of the examined molecule. The closed surface defined by
Fig. 1. Schematic diagram of accessible surface areas. Around the examined molecule (shaded) is constructed an envelope defining the loci of points for the center of a spherical probe which may just touch the molecule. This construction is sliced by a set of parallel planes, and the perimeter (A) of the surface envelope is calculated for each atom. In the Figure 2 separate envelopes, correspending to different probe sizes, are shown. Note that as the probe radius increa,ses, the accrsaibilities to it for atoms within a concavity decrease.
ACCESSIBLE
SURFACES
OF
NUCLEIC
ACIDS
413
all possible loci for the center of the probe is defined as the accessible surface of the molecule, and those portions of the surface for which the probe touches only one atom comprise the accessible surface of that atom (Fig. 1). Throughout, we use the terms and “accessibility” synonymously, always in “accessible surface area”, “exposure”, AZ. Note that these surface areas involve contacts with only one probe molecule; interaction of the probe with other (bound) solvent molecules is not considered in the calculations. A computer program was written to calculate accessible surface areas in the following manner. Each atom is assigned a characteristic van der Waals radius rv, and Cartesian co-ordinates for each atom are supplied as input data. A sphere of radius rv + rw is constructed about each atom, and the ensemble is sliced by a set of parallel planes of uniform separation h; the intersection of each plane with the ensemble is a set of circles. For each circle, the fraction of the perimeter not enclosed within any other circle is calculated as f,, and the accessible surface area for that atom within that slice is given by A = 27ilfph(r, + r,). For the special case where the slice is at the end of a sphere (i.e. an adjacent plane does not intersect that sphere), this segment of area is corrected to A = 2xfP(rV + r,)(r,+r,+~h-lZ,-Z8,1),whereZ,andZ, are the 2 co-ordinates (perpendicular to the slicing planes) of the atom center and terminal slicing plane, respectively. The partial areas thus calculated are summed for each atom, for each atom type, and for the total ensemble to yield the accessible surfaces for the molecule. While the formulae for surface area are exact for isolated spheres, slight inaccuracies arise when the spheres overlap, since f, does not account for the curvature of the spherical intersections. Hence, the calculation is an approximate integration, for which the precision will increase as h decreases. In general the calculation is repeated several times, with slicings at different orientations, both to test the reproducibility of the calculations and to achieve a credible average value for each surface. The accuracy of these calculations depends only upon the values chosen for the van det Waals and probe radii (r, and rw), and of course upon the accuracy of the inpur co-ordinates. (b) Determination
of van der Waals radii
Preliminary tests showed that individual and total calculated surface areas are quite dependent upon the choice of atomic radii, so it was necessary first to determine physically justifiable values for these parameters. The assumption of spherical atoms implicit in these calculations may not be absolutely correct in all cases (e.g. for carbonyl oxygens); however, what are most significant in these calculations are the relative changes in accessibilities for different conformations, so this slight deviation from ideality should not affect general conclusions. To determine best values for van der Waals radii, we used the intermolecular contact and volume survey of Bondi (1964) for carbon, phosphorus, aromatic nitrogen and ester oxygen radii. Values for presumed spherical carbonyl oxygen, amino and methyl groups were derived from the volume decrements for each group, cited in the same survey, by the use of a computer program which calculates volumes in an approximate integral fashion, analogous to the surface accessibility program. The eight non-hydrogen atom types used for nucleic acid calculations and the van der Waals radii used are listed in Table 1.
414
Symbol
Group type
ALC ARC sox
Aliphatic carbon Aromatic carbon Sugar oxygen (ring and ester) Carbonyl oxygen Phosphate oxygen Aromatic ring nitrogen Amino nitrogen Phosphorus Aromatic ring hydrogen Aliphatic hydrogen Amino hydrogen Water
BOX POX ARN AMN PHO ARH ALH AMH WAT
Ratlius (A) hydrogen Including explicitly atoms
Including at,oms
1.70 1.77 140
2.00 1.77 140
1.64 1.64 1.55 1.72 1.80 1.01 1.17 I.17 1.40
1.64 1.64 1.55 I.751 1~80 1.40
t Values for aromatic carbon and nitrogen, sugar oxygen, and phosphorus from Bondi (1964). Values for other atoms were calculated from the volume the same survey, as described in the text. $ 1.86 d is suggested as more appropriate.
(c) Reproducibility
hydrogen implicitly
are taken decrements
directly cited in
of the calculations
Since t*he precision of these calculations, as well as their expense, depends upon the slicing int’erval h, it was useful to gauge the reproducibility of surface accessibility estimates as a function of h. The results of this test upon the model syst,em deoxyadenosine are shown in Figure 2. The spread of total surface areas calculated at differentf slicing orientations ranges from less than 0.4% at h = 0.05 A to about 40/6 at h = 0.6 A. For large molecules, such as transfer RNA, averaging three separate calculations at a slicing width of 0.5 d was deemed suitable t,o yield a total surface
!
1
0-I
0.2
0.3
0.4
0.5
0.6
h (81 Fig. 2. Reproducibility of surface accessibliity calculations as a function of separation between slices. The total accessible surface area for deoxyadenosine was calculated using different slicing separations h; for each value of h, the calculation was performed with the slicing planes oriented differently with respect to the molecule. Ash increases, the spread ofcalculatcd values also increases. At h = 0.5 11, the average of any 3 calculations is within 1 o/0 of the mean surface area.
ACCESSIBLE
SURFACES
OF
NUCLEIC
-4CIDS
415
area reproducible to within 1 o/O.Given the uncertainties in true van der Waals radii and atomic co-ordinates, this is an adequate margin of error. For DNA helix calculations, where only small surface exposure changes might be expected, areas were calculated at a slicing separation of 0.1 A. (d) Effect of explicit
inclusio?t
of hydrogen
atoms
Since a large fraction of nucleic acid atoms consists of hydrogen, we also calculated accessible surface areas for nucleotides with hydrogen atoms included explicitly. Hydrogen atom co-ordinates were generated using the bonded geometries of the atoms t’o which they are joined and the covalent bond lengths compiled by Kennard (1974). Values for their van der Waals radii were those of Bondi (1964) or, for methyl and amino hydrogens, were calibrated as above from the group volume decrements. Values used in this study are also listed in Table 1. Treatment of aliphatic carbons as simple spheres, with larger radii to simulate the effect of hydrogen atoms, yields slightly different results than inclusion of hydrogen atoms explicitly in the co-ordinate lists (Table 2). For example, the accessible surface TABLE
Effect of including
hydrogen atoms explicitly With
2 in surface calculations
H
Without
(b2) A. Adenosine
5’-monophosphate Total ALC + ALH sox ARC + ARN + ARH POX + PHO AMN + AMH
B. poly(dA)3.poly(dT), Total ALC + x0x POX + BOX ARC + AMN +
491.3 108.8 83.6 135.0 92.3 X1.6
for H
(87
ALC sox ARC + ARN POX + PHO AMN
I,
= I.4 ip Difference (AZ)
(%)
484.6 113.7 74.9 130.9 93.5 71.6
6.7 -4.9 8.7 4.1 -1.2 0.0
1.4 -4.5 10.4 3.0 -1.3 0.0
1528.3 556.6 176.9 481.3 76.7 176.6 60.2
19.1 -22.8 31.1 -0.5 0.8 1.8 7.7
1.2 -4.3 15.0 -0.1 1.0 1.0 11.3
B-DNA ALH PHO ARN AMH
+ ARH
1547.4 533.8 208.0 481.8 71.5 178.4 67.9
ALC sox POX + PHO BOX ARC + ARN AMN
areas for deoxyadenosine (5’)-phosphate were calculated both with and without hydrogen atoms, using a probe radius rw = 1.4 A corresponding to the average radius of a water molecule. The total accessible surface in the former case was slightly greater (6.7 AZ, or about 1.5% of the total), with the primary difference being due to an enhanced exposure (by about 11%) of the sugar oxygens when hydrogens were attached on the neighboring carbons. Similarly, when the accessible surface for (dA)a . (dT), in the B-conformation is calculated both ways, the total area was again slightly greater with the hydrogens included. The enhancement of sugar oxygen surface was even more pronounced in this case, being about one sixth again as large for the hydrogen as for the non-hydrogen case, and the aliphatic surface was again diminished by about 5%. In addition, the apparent exposure of an amino group treated as a single sphere of radius 175 A is about 10% less than with hydrogens
116
included. A value valent to that in these calculations application of any similar results.
C. J. ALDEN
4EU
S.-H.
KTJI
of 146 A for the spherical amino radius yields an exposure equithe case with hydrogens included. Since QUT primary interest in changes in exposure lan.der different condit,ion.s, is in relative set of reasonable, self-consistent8 values should yield qualitatively
To gauge the change in surface exposure upon folding a molecule, it, is necessary first to determine the maximum possible surface exposure of the components of that molecule, corresponding to the unfolded stat!e. For polypeptides, this exposure has usually been determined by calculating t)he surface exposure of the middle residue of with all conformation angles terns (Lee & Richards, 1971). For model tripeptides polynucleotides, however, it is unclear that) an, analogous procedure is a,ppropriate: with several variable torsion angles per residue, the all-tra7a.s conformation may not correspond. to the one (of - 50) most exposed conformation; in addition, it is known that two adjacent phosphoester bond torsion angles are reluctant simultaneously to adopt’ trans values (Kim et aZ., 1973). Figure 3 illustrates the accessible surface ex-
360
240
0 5
m
180
0
60
120
180
240
300
360
Alpha
Fig. 3. Accessible surface exposure of phosphate oxygens in dimethyl phosphate. The exposure of the phosphate oxygens was calculated for different conformations about the 2 ester bonds. Broken lines represent contours of equa7 exposure; triangles represmt the corresponding conformations in t>he backbone of the observed crystal structure of yeast phenylalanine transfer RN4 (Sussman et al., 1978). The reluctance of nucleotide backbones to adopt an all-traw conformation may be due in part to the burial of charged phosphate oxygens that such conformations entail.
posure of the phosphate oxygens for the model case of dimethyl phosphate as a function of the conformat,ion angles about the two ester bonds; included also are indicat*ors for the corresponding conformat,ion angles about. the est,er bonds observed in the struct’urc of transfer RNA (91.ussman eE gl., 1978). We note t,hat t,he all-trans conformation, avoided by pol~ynuclootide phosphat~ea, corresponds t,o a minimal
ACCESSIBLE
Fig. 4. Division of a nucleotide imal surface exposure. Accessible shown to estimate the maximum thus obtained for the following region B; C-4’, C-3’ from region
SURFACES
OF
NUCLEIC
ACIDS
417
backbone into covalently linked groups for estimation of maxsurface areas were calculated for each of the 4 molecular fragments possible exposure for each atom. The maximal exposures were atoms: O-3’, O-5’, P, 0-1P and 0-2P from region A; C-5’ from C; O-l’, C-l’, C-2’ and all base atoms from region D.
exposure for the charged phosphate oxygens. In addition the repulsive lone-pair interactions of the ester oxygens are believed to discourage adoption of this conformation in polymers (Sundaralingam, 1969; Newton, 1973). Hence a more elaborate construction was invoked to determine maximal exposures for the individual atoms. Figure 4 illustrates the division of a nucleotide backbone into four regions, which were used to determine the maximum exposure of the nucleotide atoms limited only by their covalently bonded neighbors, i.e. invariant with respect to conformation. Maximal exposures for the deoxyribose atoms were calculated for both the C-3’-endo and C-3’-exo puckered forms, and the total maximum exposures for the carbon and oxygen atoms were seen to be very similar, although the exposure of individual atoms was different for the two forms. Maximal exposures of the nucleoside bases were calculated for the bases assuming the normal anti conformation observed in polynucleotides. Table 3 lists the maximal surface exposures for the DNA components (calculated with hydrogen atoms) and for the RNA components (without hydrogens). While it is quite possible that not all of the atoms in a nucleotide may simultaneously achieve their maximal exposure, this list gives a fair estimate of the relative degree of exposure for the various nucleotide atom types for the unfolded state. Thus we note that the average maximal accessible surface area for an unfolded DNA chain is approximately 490 A” per nucleotide, with the bases accounting for nearly half (44%) of this total. 15
DNA C-3’-em sugms
C-3’-end0
sugars
______~~~~ P Q-3’ o-IP o-2P O-1’ C-5’ C-5’H-I C-5/H-2 c-4 C-4’H C-3’ C-3’H C-2’ C-2’H-1 C-2’H-2 C-l’ C-1’H O-5’ Total
B. Maximum
Total
0.95 9.65 52.40 48.36 14.56 6.18 22.92 22.56 0.93 19.75 1.10 19.31 2.37 21.86 9.00 0.07
14.96 10.87
10.31 12.00
275.01
274.28
P O-3’ O-II? o-2P O-l’ C-5’
19.03
7.43 28.40 18.36 24.79 7.89 17.09 30.86 15.03 15.02 7.99
cm-1
CC-6 CC-6H cc-5 CC-BH CN-4 CN-4H- 1 CN-4H-2 cc-4 CN-3 co-2 cc-2
213.66
p TME, methyl
46.18
7.96 59.38
C-4’
16.97
C-3’
18.74
C-2’ O-2’
25.68 30.10
C-l'
19.78
O-5'
7.72 258.93
bases in C-3’-exo
Guanine
Cytosine 0.17 17.96 3.64
O”95 ti.4Q 48.98
accessible surface areas (in kf”) for DNA nucleosides for I‘, = I.4 A
Adenine AN-Q AC-8 AC-8H AN-7 AC-5 AN-6 AN-6H-1 AN-6H-2 AC-6 AN-l AC-2 AC-2H AN-3 AC-4
I.00 14.16 48.75 53.05 IO.80 6.00 23.01 22.74 0.47 18.55 0.33 11.12 1.29 20.43 16.14 1.34
RNA
0.17 8.67 1.15 20.54 12.44 27.08 22.51 25.07 7.81 14.50 45.92 9.98
GN-9 GC-8 GC-AH GN-7 GC-5 GO-6 GC-6 GN-1 ON-IH GN-2 GN-2H-1 GN 2H-2 GC-2 GN-3 GC-4
195.84
Thymine O”19 18.33 3.84 22.23 7.59 54.02 9.39 5.84 12.20 27.15 23.60 24.63 9.92 9.72 8.08
236.76
TN-1 TC-6 TC-6H TMET T;MEH- 1 TMEH-2 TMEH-3 TC-5 TO-4 TC-4 TN3 TN-3H TO-2 TC-2
0.16 6.53 0.49 13.68 24.24 15.33 12.91 5.76 47.05 9.40 5.83 16.10 44.87 IO.32 212.67
carbon of thymine.
(f) Polarity
of exposed
atoms
One difficulty in describing the relative exposures of polar and non-polar groups is the assignment for the aromatic nikogen atoms, which are quite polar an.d frequently form hydrogen bonds within the plane of the base, yet which contribute to the TT orbitals of the ring and act as aromatic molecules when approached normal to the
ACCESSIBLE
SURFACES
OF NUCLEIC
ACIDS
419
plane of the base. Arbitrarily dividing the contribution from such atoms equally among the polar and non-polar classifications, we note that in the unfolded state polar atoms comprise slightly over half (54%) of the exposed surface of DNA, with approximately equal contributions from the bases and the backbone. For the backbone there is an almost equal exposure of hydrocarbon and oxygen atoms, while for the bases 42% of the atoms may be classed as non-polar. For the individual nucleoside bases, however, there is a pronounced range of maximal polar group exposure: 69% for G, 61 y0 for C, 52% for T and 45% for A.
3. Results (a) Surfaces of DNA
double helices
Accessible surface areas for double-helical DNAs were calculated by summing the individual atomic exposures of the middle base-paired residues in various doubleHelices examined were A- and B-DNA stranded, complementary trinucleotides. (Arnott & Hukins, 1972) C-DNA (Arnott & Selsing, 1975) and D-DNA (Arnott et al., 1974). For each of these helices hydrogen atoms were included in the input co-ordinates, and areas were calculated with a slicing separation of 0.1 A. In all cases except D-DNA, several different base sequences were examined, to test for sequence and composition dependence of surface accessibility. Values for A + T- and G + C-rich polymers were taken as the averages of the four distinct trinucleotide sequences consisting of one type of base-pair. The results of these averagings are summarized in Tables 4 and 5. Overall, the folding of a long DNA molecule into a double helix results in the burial of approximately two thirds of its maximally exposed surface, a value quite similar to the result for globular proteins (Lee & Richards, 1971). A comparison of the relative surface exposures of B-DNA with the unfolded molecules is shown in Figure 5. For most atom types, the reduction of accessible surface upon folding is close to their TABLE
Atomic
exposures (in d”) of DNA
4
double helices for r, = 1.4 A
A. Backbone Atom P O-3’ o-1P o-2P O-5’ C-5’ C-5’H-1 C-5’H-2 O-l’ C-4’ C-4’H C-3’ C-3’H C-2’ C-2’H-1 C-2/H-2 C-l’ C-I’H
A-DNA 0.48 5.34 41.67 31.27 0.00 2.39 8.91 9.73 5.94 0.50 18.50 0.00 0.34 0.00 4.60 0.00 0.35 12.56
B-DNA 0.18 5.12 44.40 32.72 0.00 1.98 12.12 4.76 4.01 0.68 19.52 0.50 8.35 0.03 0.28 4.46 0.00 0.00
C-DNA 0.07 4.76 29.82 47.46 0.00 1.99 12.47 4.19 3.85 0.86 21.00 0.70 9.90 0.01 5.00 0.18 0.00 0.00
420 TABLE
Stem AS-Q AC-S AC-SH AN-7 AC-5 AN-6 AN-GHAN-OH-2 AC-6 AN-1
4 (corztimed)
A -DNB
1
AC-2 AC-PH AN-3 AC-4
0.00 1.07 0.00 5.06 0.00 1.40 7.98 0.00 0.00 0.00 2.86 5.02 6.32 0.00
B-DIVA -~__ 0.00
C-DNAAI 0.00
3.95 0.00 7.06 0.00
3.55 0.00 &TO 0.00 1 .BS 11.28 0.00 0.00 0.00 0.59 2.35 2.29 0.00
1.91 11,23 o-00 0.00 0.00 2.06 0.29 140 a.00
CN- 1 CC-G CC-6H cc-5 CC-AH CN-4 CN-4H-I CN-4H-2 CN-3 CO-2 cc.2 cc-4
0.00 0.30 0.00 4.40 3.1G 2.48 12.32 0.00 0.00 6.56 0.00 0.02
0.00 1.91 0.00 5.69 5.70 2.63 16.17 0.00 0.00 0.00 0.57 0.00
0.00 1.81 0.00 5.36 4.8s 2.51 17.29 0.00 0.00 0.32 0.00 0.00
GN-9 GC-8 GC-YH GN-7 GC-5 GO-6 GC-6 GN- 1 GN-11-I GN-2 GN-2HGN-2H-2 GC-2 GN-3 GC-4
0.00 1.60 0.00 7.02 0.00 5.80 0.00 0.00 0.00 3-87 O-03 IS.45 0.00 2.26 0.00
0.00 4.73 0.00 8.85 0.00 8.61 0.00 0.00 0.00 0.62 0.00 9.16 0.00 0.03 0.00
0.00 4.11 0.00 9.01 0.00 8.86 0.00 0.00 0.00 0.17 0.00 6.52 0.00 0.03 0.00
0.00 0.26 WOO 1.00 12.55 0.00 1.82 0.58 6.20 0.00 o-00 0.00 11.28 0.00
0.00 1.06 0.00 5.51 20.66 0.02 4.16 0.22 8.08 0.00 o,oo 0.00 3.82 0.00
0.00 0.72 0.00 10.27 12.44 7.20 2.02 0.12 6.87 0.00 o-00 0.00 3.34 0.00
TN-I TC-6 TC-6H TME TXEH-1 TMEH-2 TMEH-3 TC-5 TO-4 TC-4 TN-3 TN-3H TO-2 TC-2
I
ACCESSIBLE
SURFACES
OF
NUCLEIC
ACIDS
421
TABLE 5 Group type exposures (in A”) for DNA A-DNA A.
A + T-rich
B-DNA
double he&es for two residues C-DNA
D-DNA
polymers
ALC ARC sox POX BOX ARN AMN PHO ARH ALH AMH
7.50 4.77 23.12 143.92 17.45 11.38 1.40 0.96 5.02 126.47 7.98
11.87 5.41 21.34 152.52 1 I.90 8.99 1.58 0.36 2.35 122.70 11.28
17.39 4.50 20.24 152.06 10.21 9.12 1.91 0.14 1.40 125.64 11.23
26.31 3.96 22.41 128.12 8.44 7.20 2.34 0.30 0.00 129.17 11.67
Total
350.00
350.30
353.84
339.92
POS NEUT NEG
20.76 143.76 185.48
21.85 142.33 186.12
22.26 148.93 182.65
21.21 159.44 159.27
B.
G + C-rich
polymers
4LC ARC sox POX BOX ARN AMN PHO ARH ALH AMH
6.46 6.32 22.00 150.34 12.36 9.28 6.35 0.96 3.16 106.48 30.80
6.36 12.33 14.96 155.84 9.18 8.88 3.25 0.36 5.70 100.78 25.33
7.12 11.28 14.10 157.06 9.18 9.04 2.68 0.14 4.88 106.98 23.51
Total
354.51
342.97
346.27
POS NEUT NEG
46.43 122.42 185.66
37.46 125.17 180.34
35.53 130.26 lSO.48
POS = ARN + AMN + AMH NEUT = ALC + ARC + ARH NEG = SOX + POX + BOX
+ ALH + PHO
proportion of the total maximal surface area, with base atoms being buried relatively more than sugar atoms. The sole and striking contrast to this pattern occurs for the phosphate oxygens, whose exposure is reduced only slightly upon transition from the extended to the helical form. Thus the accessible surface in DNA double helices is more polar than for the random coils, with the phosphate oxygens alone accounting for nearly 45% of the total accessible surface area. The contribution from the bases now accounts for only about a fifth of the total surface in the double-stranded helices, while the sugars account for over a third of the surface. Considering the observed effect of solvent upon DNA helix conformation, and the pronounced difference in gross shapes of the different forms, the similarities of their
422
6.
J.
ALDEN
AND Unfolded
S.-N.
KIM
DNA
Total =490*5
x2
B-DNA Buried POX
Total-3172
8’
(b) Fig. 5. Group type exposures in unfolded and helical B-DNA. Solvent-accessible surface areas were calculated using a 1.4 d probe radius for maximally unfolded DNA (a) and B-DNA (b) of average base sequence. The accessible surface buried in folding the extended chain into a double helix, i.e. the difference between (a) and (b), is also shown. In folding of the polymer, the bases become mostly buried while the phosphate oxygens remain nearly fully exposed.
total exposures was somewhat surprising. Hence we calculated the surface accessibilities for A- and B-DNA over a wide range of probe radii (1.0 t,o 50 A), to determine if larger probes, such as hydrated metal ions or structured water aggregates, could discriminate between the different DNA shapes. The results of this test are shown in Figure 6. We note that as r,,, increases, the total surface accessibility of B-DNA increases more rapidly than does that of A-DNA. Moreover, this difference is attributable almost entirely to a greater exposure of the phosphate oxygens in B-DNA, as the aliphatic carbon exposure becomes relatively greater for A-DNA. Curiously, the point at which the A- and B-DNA accessibility curves intersect is just at the yW corresponding to the radius of a single water molecule. For larger values of rW: corresponding to bulky side groups of proteins, structured water, or hydrated metal ions, the accessibility of the major groove of A-DNA decrea,ses abruptly, as does the minor groove exposure of B-DNA (see Fig. 7).
ACCESSIBLE
SURFACES
OF
NUCLEIC
423
ACIDS A-T
I.0
I.4
2.0
3.0 4.0
t
50
I.0
2.0 3.0
4-o
5.0
I.4 (a)
(b)
Fig. 6. Accessible surface areas for 2 base-paired residues of (a) poly(dG).poly(dC) and (b) poly. (dA).poly(dT) in the A- and B-helical forms, calculated varying the probe radius rW. For both polymers, the B-DNA form entails relatively greater total exposure, and particularly a greater exposure of phosphate oxygens, for large probe radii. This result is consistent with the experimentally observed result that high water activity encourages adoption of the B-DNA conformation(-----) A-DNA; ( 1.4 A) can provide clues about, the willingness of the environment to allow or enforce a particular DNA conformation. For A.T basepairs, the greatest exposure is exhibited by thymine methyl groups, and here only in the B conformation (over 80% of the total base exposure for rw > 4.0 A). Since methyl groups are hydrophobic, their exposure in the major groove would tend to encourage water-water aggregation in the major groove and thus exert pressure on the major groove to remain wide. For G.C pairs the most exposed groups are the amino groups of guanine on the minor groove (over 80yb of the total base exposure in the A form, no exposure in the B form, for yw = 4.0 A) or cytosine on the major groove (over 70% of the total base exposure in B-DNA at rw > 4-O A). Both groups are hydrophilic; therefore, extended water-DNA base interactions would result in either the A- or B-helical forms. Thus for G $- C-rich DKA, the availability or lack of excess water will dictate the DNA conformation: under high water activity the major groove will fill and the phosphates will form more extensive hydration complexes; under low water activity, the major groove will collapse and the phosphate oxygens will become more buried. (d) Major
groove of B-DNA and minor groove of A-DNA recognition surfaces for proteins
as primary
As can be seen from Figure 7, when the radius of the probe becomes 3 A or greater, the dominant base exposures occur in the major groove of B-DNA and the minor groove of A-DNA. Specifically, the methyl group of thymine and amino group of eytosine provide most of the accessible area on the major groove in B-DP\TA, and the
ACCESSIBLE
SURFACES
OF NUCLEIC
ACIDS
433
amino group of guanine does so on the minor groove of A-DNA (see Table 4). Since most of the side-chains of amino acids are considerably larger than single water molecules the above observation can be considered as suggesting that the primary recognition surface of B-DNA is the major groove and that of A-DNA is the minor groove. This is consistent with the observation that protein-DNA contacts occur predominantly in the major groove of DNA in the Escherichia coli RNA polymeraselac promoter complex (Johnsrud; 1978) and in the Zac repressor-Zac operator complex (Gilbert et al., 1976), if one interprets protection as well a.s enhancement of methylation as due to close contact of grooves with proteins. This work was supported
by grants from the National Institutes
and K04-CA-00352) and the National Science Foundation authors (C. J. A.) is a National Institutes of Health research The atomic co-ordinates
of tRNA
used in this work are available
of Health (CA-15802
(PCM76-04248). fellow.
One of the
from S.-H. Kim on request.
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