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Kinked DNA
Biochimica et Biophysica Acta, 4 7 8 ( 1 9 7 7 ) 9 - - 2 2 © E l s e v i e r / N o r t h - H o l l a n d B i o m e d i c a l Press
BBA 98986
KINKED DNA ENERGETICS AND CONDITIONS F A V O R I N G ITS F O R M A T I O N
G E O R G E R. P A C K a, M A R C A. M U S K A V I T C H b a n d G I L D A L O E W a , .
a Department of Genetics and b Department of Biochemistry, Stanford University Medical Center, Stanford, Calif. 94305 (U.S.A.) (Received March 7th, 1977)
Summary Theoretical calculations demonstrate that the formation of kinks in DNA in the manner proposed b y Crick and Klug produces a conformation which corresponds to a local energy minimum when the phosphate backbone is charged. This conformation becomes the global minimum under certain conditions which neutralize the anionic backbone oxygens. A sequence preference for kink formation is predicted. The possible role of kinking in experimentally observed phenomena and experimental means of demonstrating the existence of kinks are discussed.
Introduction Among the models which have been proposed for the supramolecular organization of eukaryotic chromatin, two are particular attractive. Kornberg [1] explains the "beads on a string" [2] appearance of chromatin from ruptured nuclei as the winding of a continuous DNA helix around successive histone octamers [3]. Finch and Klug [4] have suggested that the thick (250 A) filaments observed in chromatin treated with divalent cations are solenoidal coils of thethin (100 £) filaments obtained in the presence of chelators [5--7]. Despite intense research activity, the detailed molecular structure underlying these proposed superstructures remains unclear. At a finer level of resolution, Crick and Klug [8] have speculated that DNA in chromatin assumes a " k i n k e d " conformation. This departs from B-form DNA at intermittent " k i n k " sites only by a single rotation of approx. 120 ° * To whom all reprint requests should be addressed. Abbreviations: D N A , d e o x y r i b o n u c l e i c acid; dA, deoxyadenosine; dC, d e o x y c y t i d i n e ; dG, deoxyguanosine; dT, thymidine; dX-dY, dX b o n d e d to dY by a 3'- to 5'-phosphodiester linkage.
10 abut the C4'-C5' bond of the exocyclic deoxyribose of the backbone. This is torsion angle e as previously defined [9] (Fig. 1). The rotation results in the loss of a stacking interaction (but no disruption of hydrogen bonding) and in a " k i n k " of a b o u t 90 ° between successive segments of the helix with movement of part of the helix toward the minor groove. This kinking then permits construction of successively higher order structures. First-order kinking could allow DNA to wind around histone octamers; and successive kinks between beads could lead to solenoidal structures. More recently, another plausible kink has been proposed [10]. Based on a kinking of the structures observed in ribodinucleoside monophosphate pairs complexed with an intercalated ethidium molecule, this model can also account from chromatin structure. In this paper we present the results of a study of the energetics of the formation of those kinks arising from rotation a b o u t the C4'-C5' bond. We suggest that this kinked form becomes a low-energy conformation under conditions in which the phosphate oxygens are neutralized and that A + T-rich regions should be preferentially kinked under neutralizing conditions. Methods The method of calculation was the quantum chemical Perturbative Configuration Interaction using Localized Orbitals (PCILO) [11]. Extensive studies on the backbone of nucleic acids [12] and other large molecular systems [13,14] have confirmed the validity of this method. Comparison of local minima in the potential energy hypersurface c o m p u t e d using PCILO with conformations shown to be preferred in crystallographic studies [15] gives remarkably good correspondence. In an a t t e m p t to deal with the sequence specificity of the proposed kink, all sixteen dideoxynucleoside monophosphates were studied. Since the PCILO method considers all valence electrons of a molecule, computation size ranged from 192 electrons for dC-dC to 220 electrons for dG-dG. All computations were performed on the CDC 7600 computer, effectively a double precision machine, to avoid artifacts which might have arisen from the limitations of single precision capability. Geometries of dideoxynucleoside monophosphates were derived from the B-form DNA structure of Arnott and Hukins [16]. A representative structure is shown in Fig. 2a. Hydrogen atoms were placed at standard bond distances of 0.96 A for O--H, 1.04 A for N--H and 1.09 A for C--H. Orientations of hydrogen atoms and lone pair electrons were determined using an interactive molecular-model building c o m p u t e r program to establish optimal placement. The effect of solvent is not explicitly included in the calculation. It is presumed that this effect will vary little with different sites of the kink, leaving the relative energies and hence the preferred sites of kinking unaffected. The agreeement of theory with experiment in studies of DNA structure [12] also m a y be taken to indicate that the solvent may well effect the kinked and unkinked forms equally, and thus be validly neglected in these comparisons of energies. All calculations on the variation of energy with e were performed for single dideoxynucleoside monophosphates. The energy of the molecule was calcu-
11 lated for each balue of e. The lowest energy calculated for the molecule was taken as an arbirary zero, and all other energies were expressed relative to that zero value. A helical segment is defined as the structure consisting of a dideoxynucleoside monophosphate paired with its complementary dideoxynucleoside monophosphate by standard Watson-Crick base pairing. In calculating the energy of a helical segment as a function of conformation two assumptions are made: (i) in accordance with the model of Crick and Klug, hydrogen bonding between complementary base pairs does not change as backbone conformation changes and is n o t a factor in the calculations; (ii) by symmetry, the magnitude and sense of e is the same for both dideoxynucleoside monophosphates in the helical segment. Therefore, the total energy of the segment in a given conformation (defined by a specific value of e) is calculated by adding the energies for the complementary dideoxynucleoside monophosphates, each characterized b y the same balue of e. Results The variation of energy with e calculated for anionic dideoxynucleoside monophosphates is presented in Table I. The shape of the curve (energy vs. e) is similar for the four subfamilies with the same base in a 5' linkage. Fig. 1 gives a representative curve for each category of dinucleoside phosphate. Global minima generally occur at either 56 ° or 66 ° (except for dG-dC) and local minima are found at 146 ° for all species but with varying depth of both minima (Fig. 2c). The anomalous global minimum found for dG-dC can be attributed to the particularly large stacking interaction between guanine and cytosine at this value of e. The interaction between these bases has been calculated to be much greater than between other combinations of bases [ 17]. Those molecules with thymidine in a 5' linkage {dA
12 6 t d A<'I A
a
5 I'-
•
6
dA<~C
5
/° AE
4
•
,...;.,,.? V I
36 °
76 °
ll6 ° E
6b dA~JG
4p
/'~
3,6°
!",, ;" 2
-w I
76 =
I
I
116° E
76 °
tl6 °
I
I
I
156 °
E
,
b
A. /
*
Z "e
AE31-
36 °
156"
I
I
156 e
I
,F-/,,,,,, 36 o
76 °.,
II6 ° E
156 °
F i g . 1. E n e r g y o f r o t a t i o n ( k c a l / m o l ) a b o u t C4'-C5' a x i s ( e ) for n e u t r a l d X - d Y a n i o n i c d i d e o x y n u c l e o t i d e s . (a) d A - d A c u r v e similar f o r all d X - d A . (b) d A - d C c u r v e similar f o r all d X - d C . (c) d A - d G c u r v e similar to all d X ° d G . (d) d A - d T c u r v e similar t o all d X - d T .
little with base composition. Since the PCILO net charge is not greater than those calculated by ab initio methods, it is unlikely the interaction is being overestimated. The next set of calculations dealt with the variation of energy with e for ten possible anionic helical segments. Again, global minima were observed at 56 ° and local minima at 146 °. The global minima at 56 °, though indicating a preferred conformation different from that calculated by Arnott for B-form
a ,-~o 3 (::'3
C'5 H
13
®
)C' 2
6
Z.,~ C'3
/ 04
/ / /
© 03
bo'5 c~, 04
)0 2
~C'3 0'5
/
/ 04
/ /
Fig. 2. T h e g e o m e t r y o f t h e k i n k r o t a t i o n , i l l u s t r a t e d for t h e single s t r a n d d A - d T . T h e p o s i t i o n a n d sense o f t h e r o t a t i o n , e, are i n d i c a t e d b y t h e a r r o w . T h o s e a t o m s o f t h y m i d i n e w h i c h are m o v e d in t h e c h o s e n c o o r d i n a t e s y s t e m are s h a d e d . (a) r e p r e s e n t s t h e D N A - B c o n f o r m a t i o n w i t h t h y m i n e s t a c k e d b e l o w a d e n i n e . (b) illustrates an i n t e r m e d i a t e c o n f o r m a t i o n (e = 66 ° ) w i t h an i n t e r a c t i o n b e t w e e n t h e t h y m i n e m e t h y l g r o u p a n d t h e p h o s p h a t e . T h e final k i n k g e o m e t r y (e = 146 °) is s h o w n in c. D a s h e d lines i n d i c a t e " c l o s e c o n t a c t s " b e t w e e n base a n d b a c k b o n e , p a n d d d e s i g n a t e p r o x i m a l a n d distal o x y g e n a t o m s , respectively.
MONOPHOSPHATES
dA-dA
1.37 0.44 0.0 0.27 1.18 2.18 2.66 2.57 3.39 4.77 3.87 3.49 4.41 5.16
C(° )
36 46 56 66 76 86 96 106 116 126 136 146 156 166
1.01 0.40 0.0 0.22 1.06 2.00 2.40 2.24 3.00 4.34 3.40 2.99 3.86 4.59
dC-dA
0.23 0.15 0.0 0.38 1.37 2.43 2.95 2.89 3.73 5.13 4.25 3.88 4.79 5.54
dG-dA
0.73 0.30 0.0 0.30 1.21 2.20 2.66 2.54 3.35 4.75 3.88 3.48 4.36 5.09
dT-dA
0.45 0.37 0.0 0.34 0.77 1.03 0.90 0.90 2.23 3.18 2.12 1.27 2.20 3.47
dA-dC 0.33 0.37 0.0 0.14 0.46 0.60 0.38 0.30 1.55 2.54 1.34 0.53 1.45 2.69
dC-dC 0.0 1.93 2.42 3.08 3.76 4.19 4.19 4.28 5.67 6.76 5.63 4.89 5.86 7.14
dG-dC 0.48 0.40 0.0 0.13 0.44 0.58 0.37 0.30 1.57 2.66 1.39 0.68 1.55 2.82
dT-dC 0.57 0.19 0.0 0.42 1.49 2.68 3.30 3.24 3.97 5.37 4.47 3.99 4.77 5.35
dA-dG 0.73 0.22 0.0 0.43 1.51 2.69 3.29 3.19 3.86 5.20 4.21 3.62 4.30 4.77
dC-dG 0.62 0.21 0.0 0.45 1.61 2.89 3.58 3.56 4.30 5.70 4.75 4.20 4.91
dG-dG 0.97 0.27 0.0 0.42 1.52 2.72 3.34 3.27 3.97 5.33 4.34 3.76 4.45 4.93
dT-dG 3.66 2.30 0.50 0.0 1.87 3.26 2.58 2.01 3.70 4.73 2.58 2.38 4.00 5.57
dA-dT
3.56 2.16 0.47 0.0 1.85 3.19 2.45 1.82 3.44 4.43 2.25 2.02 3.60 5.15
dC-dT
e c o r r e s p o n d s to t h e angle o f r o t a t i o n a b o u t t h e C 4 ' - C 5 ' b o n d o f t h e e x o c y c l i c d e o x y r i b o s u g a r as d e f i n e d in ref. 9. E n e r g y in k c a l / m o l .
POTENTIAL ENERGY VARIATION WITH e FOR ALL DIDEOXYNUCLEOSIDE
TABLE I
2.51 1.96 0.37 0.0 1.99 3.47 2.86 2.35 4.08 5.14 3.01 2.83 4.46 6.04
dG-dT
3.94 2.32 0.51 0.00 1.84 3.17 2.43 1.82 3.46 4.45 2.27 2.04 3.64 5.19
dT-dT
15 TABLE
II
VARIATION OF DISTANCE WITH e BETWEEN CARBON THE BACKBONE PHOSPHATE G R O U P IN dA-dT
ATOMS
OF THYMINE
AND
OXYGENS
OF
R[Cm....O 2 ] represents separation of the methyl carbon and phosphate oxygen. R[C6....O 4] represents separation of C 6 and phosphate oxygen. The angle of the C6-H....O bond is included parenthetically.For the numbering of atoms see Fig. 2. e(°)
R [ C m ...02] (A)
R [ C 6 ...04] (A)
36 46 56 66 76 86 96 106 116 126 136 146 156 166
4.02 3.52 3.08 2.72 2.49 2.45 2.59 2.90 3.31 3.78 4.29 4.80 5.30 5.79
3.05(141.9) 2.87(137.7) 2.73(132.1) 2.63(125.4) 2.58(118.5) 2.59(112.2) 2.66(107.2) 2.79(103.6) 2.95(101.3) 3.15(100.1) 3.36( 99.8) 3.59(100.2) 3.82(101.1) 4.04(102.5)
DNA (36 °), are in good agreement with the values of e tabulated by Rosenberg et al. [20] and Sundaralingam [21] from the crystal structures of numerous nucleic acids. This agreement establishes confidence in the efficacy of the PCILO m e t h o d as applied to conformational stt~dies of nucleic acids. The local minima at 146 ° corresponds very well to the value of e (156 °) predicted b y Crick and Klug for the structure of kinked DNA. The existence of local minima near the angle corresponding to the kinked conformation suggests the kinked form could become energetically favored under appropriate conditions. The energy of the kinked form of each possible helical segment relative to the minimum energy calculated for the segment along with the statistical probability of finding a kink at a specific sequence are given in Table III. There is some sequence-related variation of the energy of the kinked state b u t all segments exhibit a positive relative energy for kink formation. It is apparent that the preferred conformation of the segments in anionic form will be witho u t significant contribution from the kinked form. A number of considerations then led us to determine the effect of changing the state of the backbone on the energetics of conformational change of helical segments. First, it is conceivable that the base-backbone electrostatic interaction can significantly affect the stability of a given conformation (see above). Second, it has been noted that the positive charge available from histones, calculated from the molar ratios of DNA to histone generally found in chromatin, is sufficient to neutralize approximately half the negative charge of the associated DNA [22]. This electrostatic interaction between anionic and cationic sites is likely to be a major c o m p o n e n t of the total interaction of DNA with histones. Third, the addition of divalent cations to uncondensed chromatin can result in the conversion to a condensed state [4--7]. We therefore decided to study the effects of neutralization of the phosphate oxygens on the
16 TABLE IlI ENERGIES
AND PROBABILITIES
FOR KINK FORMATION
BY ANIONIC HELICAL
SEGMENTS
A r r o w i n d i c a t e s 3'- to 5 ' - p h o s p h o d i e s t e r l i n k a g e . E n e r g y o f k i n k f o r m a t i o n for all ten p o s s i b l e a n i o n i c helical s e g m e n t s ( d e f i n e d in M e t h o d s ) given relative t o m i n i m u m e n e r g y c a l c u l a t e d for e a c h s e g m e n t . F r e q u e n c y -1 d e n o t e s n u m b e r o f helical s e g m e n t s in w h i c h o n e k i n k is e x p e c t e d at 2 5 ° C c a l c u l a t e d f r o m an e x p o n e n t i a l d i s t r i b u t i o n using B o l t z m a n n statistics. Segment
Energy (kcal/mol)
Frequency- 1
dA-dT dT-dA
4.76
3.1 • 103
dA-dA dT-dT
5.54
1.1 " 1 0 4
dA-dC dT-dG
4.10
1.0 • 103
dA-dG dT-dC
3.29
2.6 - 102
dG-dC dC-dG
4.73
3.0 " 103
riG-riG dC-dC
7.24
2.0 ' 10 s
dG-dA
4.56
2.2 " 103
dT-dA dA-dT
6.96
1.3 " 10 $
dC-dA
6.75
9.0 ' 104
9.78
1.7 " 107
dC-dT
dG-dT
dG-dC dC-dG
energetics of conformational changes of dideoxynucleoside monophosphates and hence the kinking of helical segments. The proton was chosen to act as the cation involved in neutralization of the phosphate charge. As a model for the interaction of positively charged histone residues and the D N A backbone, molecular orbital studies on the interaction of the a m m o n i u m cation (NH4 ÷) and monoanionic phosphate (H2PO4-) indicate the most stable complex .could involve a linear hydrogen bond with migration of the proton [23] from nitrogen to oxygen. The protonation of one of the
17
non-esterified phosphate oxygens was therefore taken as a reasonable model of backbone charge neutralization. Calculations were performed on dA-dT with an associated proton at either of two positions to determine whether one of the non-esterified oxygens would be preferentially protonated, as well as the effect of protonation on the variation of energy with conformation. Variation of energy with e for the two protonated forms and a form in which NH4* is shared by the two non-esterified oxygens is given in Table IV. When the oxygen distal to the bases is protonated the conformation corresponding to a kink (156 °) is neither a local nor global minimum. When the proximal oxygen is protonated, the conformation corresponding to a kink becomes the global minimum. Comparison of the global minima for both forms indicates that the minimum for the proximally protonated form is lower in energy by 4.7 kcal/mol, indicating protonation at the proximal oxygen will be preferred. As a result of the neutralization of this oxygen, the kinked conformation of the dideoxynucleoside monophosphate is energetically favored (Fig. 3). Assignment of a third geometry in which the NH4 + is shared equally between the two non-esterified oxygens also yields an indication that the kinked conformation will be energetically favored. Thus, more than one geometry in which the backbone phosphate is neutralized will result in a preference for the kinked conformation. Using the l~rotonation of the proximal oxygen as a model geometry, the variation of energy with conformation was calculated for the remaining 15
T A B L E IV V A R I A T I O N O F T H E P O T E N T I A L E N E R G Y O F d A - d T W I T H e AS A F U N C T I O N O F T H E G E O M E T R Y OF P R O T O N A T I O N OF T H E BACKBONE P H O S P H A T E Edistal is d e f i n e d as t h e e n e r g y f o r a m o l e c u l e in w h i c h o n l y t h e n o n - e s t e r i f i e d o x y g e n distal to t h e b a s e s is p r o t o n a t e d . E p r o x i m a l r e p r e s e n t s t h e e n e r g y w i t h o n l y the p r o x i m a l n o n - e s t e r i f i e d o x y g e n p r o t o n a t e d . Distal and p r o x i m a l o x y g e n s are d e s i g n a t e d in Fig. 2. Eshared is d e f i n e d as t h e e n e r g y w h e n a m m o n i u m is shared e q u a l l y b y t h e t w o n o n - e s t e r i f i e d o x y g e n s . T h e e x t r e m e l y high barrier for Eshared results f r o m i n t e r a c t i o n b e t w e e n the t h y m i n e m e t h y l group and the N H 4 + in w h i c h van der Waal radii are grossly viol a t e d . This is n o t m e a n t to suggest t h a t a barrier t o r o t a t i o n o f this m a g n i t u d e w o u l d actually e x i s t since t h e N H 4 + p o s i t i o n c o u l d easily adjust t o a l l o w a freer r o t a t i o n . T h e c a l c u l a t i o n s w e r e d o n e f o r R N _ P = 3 A, w i t h t h e h y d r o g e n a t o m s d i r e c t e d at t h e n o n - e s t e r i f i e d o x y g e n a t o m s .
e(°)
Edistal (kcal/mol)
36 46 56 66 76 86 96 106 116 126 136 146 156 166 176 186
1.21 0.80 0.00 0.27 2.84 4.79 4.43 4.62 7.08 8.93 6.67 3.86 2.36 2.01 2.11 2.38
Eproximal (kcal/mol) 3.73 3.41 3.27 6.87 19.15 26.10 10.38 3.05 4.51 4.65 1.01 0.0 1.12 2.25 2.94
Eshared (keal/mol) 3.00 2.47 1.82 3.70 13.5 67.2 367.0 1492.0 1688.0 40.3 0.49 0.0 1.15
18
7, f 6
5:
II 36 °
/j
dA~ dT. H
/ ,\J,
, , 76 o
116°
,
156 °
Fig. 3. E n e r g y o f r o t a t i o n ( k c a l / m o l ) a b o u t C4'-C5' axis (e) for n e u t r a l d A - d T . E f f e c t o f P h o s p h a t e neut r a l i z a t i o n on e n e r g e t i e s o f k i n k i n g ,
dideoxynucleoside monophosphates. The results of these calculations are listed in Table V. The relative energy of the kinked form of the neutral molecule is lower than that of the anionic molecule for all dideoxynucleoside monophosphates. In particular, a preference for the conformation corresponding to the kinked form (e = 146 °) is apparent for those molecules having a 5'-linked thymidine. Sequence specificity of the preference for kinked conformation stems from two disparate sources. First, stabilization energy associated with base stacking is lost. The variation of this energy with sequence has been discussed in several theoretical studies [ 17,24,25]. Second, the contribution to stabilization b y the base-backbone interaction varies depending on the base involved. In particular, loss of the close association between 04 of the backbone and hydrogen b o n d e d to either C6 of pyrimidines of Cs of purines may be significant. Although long noted by crystallographers [26] and observed in nuclear magnetic resonance spectra [27], its importance has been questioned [28] and its magnitude undetermined. Stacking effects are probably involved in the preferences of dG-dC and dG-dA for a conformation in which e is equal to 36 °. The preference of neutral dideoxynucleoside monophosphates with 5'-linked thymidine for the kinked conformation could be due to the relative destabilization of the conformation for which e is equal to 56 ° C. Such destabilization would result from loss of the
TABLE V V A R I A T I O N OF P O T E N T I A L E N E R G Y WITH e FOR N E U T R A L D I D E O X Y N U C L E O S I D E MONOPHOSPHATES c(~) )
36 56 146
36 56 146
E (kcal/mol) dA-dA
dC-dA
dG-dA
dT-dA
dA-dC
dC-dC
dG-dC
dT-dC
0.84 0.0 0.62
0.53 0.0 0.67
0.0 0.12 0.98
0.30 0.0 0.48
1.24 2.00 0.0
1.97 2.79 0.0
0.0 3.46 2.52
1.98 2.66 0.0
dA-dG
dC-dG
dG-dG
dT-dG
dA-dT
dC-dT
dG-dT
dT-dT
0.24 0.0 1.20
0.52 0.52 0.0
0.58 0.0 1.50
0.77 0.0 1.22
3.73 3.27 0.0
4.06 3.67 0.0
2.38 2.81 0.0
4.45 3.66 0.0
19 T A B L E VI ENERGIES FOR KINK FORMATION
BY P R O T O N A T E D
HELICAL sEGMENTS
E n e r g y o f k i n k f o r m a t i o n f o r all t e n p o s s i b l e h e l i c a l s e g m e n t s , given relative t o t h e e n e r g y m i n i m u m c a l c u l a t e d f o r t h e B - f o r m s t r u c t u r e o f e a c h s e g m e n t . S y m b o l s h a v e t h e s a m e m e a n i n g as in T a b l e l I l . N e g a t i v e v a l u e f o r e n e r g y i n d i c a t e s t h e k i n k e d f o r m is m o r e s t a b l e t h a t t h e B - f o r m . N u m b e r s in p a r e n t h e ses axe t h e e n e r g y o f k i n k i n g if o n l y o n e p h o s p h a t e g r o u p o f t h e h e l i c a l s e g m e n t ( t h e o n e l e a d i n g t o m o r e f a v o r a b l e k i n k i n g ) is n e u t r a l i z e d . Segment
Energy (kcal/mol)
Segment
Energy (keal/mol)
dA-dT dT..d A
--6.54(--2.45)
dC..dG dG..dC
--1.04(+3.10)
dA-dC dT-dG
--3.62(--1.54)
dG-dA dC-dT
--1.00(+1.54)
dA-dA dT-dT
--3.04(--2.33)
dT-dA dA-dT
+0.96(+3.96)
dA-dG dT-dC
--2.47(+0.32)
dC-dA dG-
+1.89(+4.20)
--,
__>
dC-dC dG-dG
--1.05(+2.03)
dG-dC dC-dG
+5.04(7.41)
electrostatic interaction between thymidine and the anionic backbone (Table II). A similar effect is possible in those molecules having 5'-linked deoxycytidine. The magnitude and specificity of potential destabilization for pyrimidines is demonstrated by calculations currently in progress in this laboratory which show the base-anionic backbone interaction is approx. 9.1 kcal for dT and 4.3 kcal for dA. The fact that previous studies [18] of the effect of phosphate oxygen neutralization on backbone conformation indicated no significant changes in conformation is probably due to failure to consider specific base-backbone interactions. The energy of the kinked form for the ten neutral helical segments, relative to the energy minimum calculated for the B t y p e structure, is given in Table VI. One is struck by the fact that the kinked form is n o w energetically favored for seven of the ten segments. The variation in energy indicates a sequencespecific ordering of the preference for assumption of a kinked conformation. For example, when phosphate oxygens are neutralized one would expect dA-dT • dA-dT to kink much more readily than dG-dC • dG-dC. Neutralization of half the phosphates as might occur if DNA lies on the outside of the histone core leads to less kinking as indicated also in Table VI. Discussion
Although calculations suggest DNA would not frequently assume a kinked conformation when backbone phosphates are negatively charged, the kinked
20
,
form is preferred in some helical segments when the b a c k b o n e is neutralized. It should be emphasized that the protonated structures employed represent one of many possible model systems and might overestimate the neutralization of phosphate oxygens. The calculations also support a sequence specificity of preference for kink formation. While the order in Table VI may not be strictly correct, A + T-rich sequences should kink preferentially relative to G + C-rich sequences. Experimentally, the digestion of native [29] or reconstituted chromatin [3] with DNAase I, followed b y analysis of the products of denaturing gels, reveals multiples of a ten base repeating unit ranging from 30 to 220 bases. Noll [29] has suggested this repeating unit could arise from kinking of the DNA helix a b o u t the nucleosome or could reflect the pitch of the helix and backbone accessibility. This ten base repeat is still observed following DNAase I digestion of chromatin subjected to treatments which prevent appearance of the 180 base pair repeat [31], believed to reflect the amount of DNA protected by the intact nucleosome [32,33 ] on non-denaturing gels. If the ten base repeat is indeed a reflection of the kinked structure of DNA resulting from histoneDNA interactions, these interactions would suffice to form kinks in the absence of intact nucleosomal structure. Kinking also helps explain chromatin condensation. After first-order kinking of DNA around the histone octamers as the result of histone-DNA interactions, second-order kinking of DNA helical regions between nucleosomes as a result of cationic neutralization of the backbone could lead to the observed condensation. The efficacy of a given cation could depend on its hydration sphere which would, in turn, affect its ability to approach and neutralize backbone anionic oxygens. Two ions of the same charge but different hydration geometry could therefore differ in effectiveness, leading to ionic specificity for condensation. The molar ratio of cations to backbone oxygens could also be critical. In light of the results in Table VI, the model for kinking of the lac operator proposed by Crick and Klug [8] may be reexamined (Fig. 4). Comparison of their intuitive predictions and our calculations reveal a remarkable correspondence between the kinking sites. Three of the four sites they designate are identical with or adjacent to the sequence which we calculated as having the largest negative energy for kink formation (dA-dT • dA-dT). Calculations show the fourth site they designated also has a negative energy for kink formation, and is the most easily kinked anionic site (Table III). The existence of kinks has not, as yet, been demonstrated experimentally. We suggest only a few of many possible approaches to determining whether they do exist. Condensation of DNA in the presence of simple polyamines has been reported [34] and circular dichroism spectra are said to indicate that the helical form of T7 DNA condensed in the presence o f spermidine differs negligibly 5'AA~
TTGTGAGCGGA
T T A* ACACT÷
~TAACAA
CGCCT÷
ATTGT÷
~TT T A A 5'
Fig. 4. Comparison of the predicted kinking of the lac operator sequence. Solid arrows indicate sites with maximum negative energy for kink formation as calculated in this Study (when backbone phosphate neutral). Broken arrows indicate potential kink sites noted by Crick and Klug [8].
21 from the B-form. It would appear the condensation is achieved by a structural modification t h a t leaves the vast majority of helical structure unchanged, such as periodic kinking. If DNA condensation is mediated by kinking, a study of defined polymers such as poly(dA-dT) • poly(dA-dT), poly(dG
22
References 1 Kornberg, R.D. (1974) Science 184, 868--871 2 0 l i n s , A . L . a n d Olins, D . E . ( 1 9 7 4 ) S c i e n c e 1 8 3 , 3 3 0 - - 3 3 2 3 Kornberg, R.D. and Thomas, J,O. (1974) Science 184, 865--868 4 F i n c h , J . T . a n d K l u g , A. ( 1 9 7 6 ) P r o c . N a t l . A c a d . Sci. U.S. 73, 1 8 9 7 - - 1 9 0 1 5 Ris, H. a n d K u b a i , D . F . ( 1 9 7 0 ) A n n . R e v . G e n e t . 44 2 6 3 - - 2 9 4 6 P o o l e y , A.S., P a r d o n , J . F . a n d R i c h a r d s , B,M. ( 1 9 7 4 ) J. Mol. Biol. 8 5 , 5 3 3 - - 5 4 9 7 Jaeobs, G.A., Smith, J,A., Watt, R.A. and Barry, J.H. (1976) Biochim. Biophys. Aeta 442, 109--115 8 C r i c k , F . H . C . a n d K l u g , A. ( 1 9 7 5 ) N a t u r e 2 5 5 , 5 3 0 - - 5 3 3 9 S e e m a a , N.C., R o s e n b e r g , J . M . , S u d d a t h , F , L . , K i m , J . J . P . a n d R i c h , A. ( 1 9 7 6 ) J. Mol. Biol. 1 0 4 , 109--144 1 0 S o b e l l , H.M., Tsai, C., G i l b e r t , S . G . , J a i n , S.C. a n d S a k o r e , T.D. ( 1 9 7 6 ) P r o c . Natl. A c a d . Sci. U.S. 73, 3068--3072 11 D i n e r , S., M a l r i e u , J . P . , J o r d a n , F. a n d G i l b e r t , M. ( 1 9 6 9 ) T h e o r . C h i m . A e t a 15, 1 0 0 - - 1 1 0 1 2 P u l l m a n , B. a n d S a r a n , A. ( 1 9 7 6 ) P r o g . N u c l e i c A c i d Res. Mol. Biol. 18, 2 1 5 - - 3 3 2 a n d r e f e r e n c e s therein 13 L o e w , G . H . , W e i n s t e i n , H., S r e b r e n i k , S. a n d B e r k o w i t z , D. ( 1 9 7 4 ) in M o l e c u l a r a n d Q u a n t u m P h a r m a c o l o g y , D. R e i d e l P u b l . Co., D o r d r e c h t , H o l l a n d 1 4 P u l l m a n , B., M a i g r e t , B. a n d P e r a h i a , D. ( 1 9 7 0 ) T h e o r . C h i m . A c t a 18, 4 4 - - 5 6 1 5 P e r a h i a , D. a n d P u l l m a n , B. ( 1 9 7 6 ) B i o c h i m . B i o p h y s . A c t a 4 3 5 , 2 8 2 - - 2 8 9 16 A r n o t t , S. a n d H u k i n s , D.W.L. ( 1 9 7 2 ) B i o c h e m . B i o p h y s . Res. C o m m u n . 4 7 , 1 5 0 4 - - 1 5 0 9 17 P u l l m a n , B. ( 1 9 6 8 ) in M o l e c u l a r A s s o c i a t i o n s in B i o l o g y ( P u l l m a n , B., e d . ) , N e w Y o r k 1 8 P e r a h i a , D., P u l l m a n , A. a n d B e r t h o d , H. ( 1 9 7 5 ) T h e o r . C h i m . A c t a 4 0 , 4 7 - - 6 0 1 9 P u l l m a n , A., B e r t h o d , H. a n d G r e s h , N. ( 1 9 7 5 ) C h e m . P h y s . L e t t . 3 3 , 1 1 - - 1 4 2 0 R o s e n b e r g , J.M., S e e m a n , N.C., D a y , R . O . a n d R i c h , A. ( 1 9 7 6 ) J. Mol. Biol. 1 0 4 , 1 4 5 - - 1 6 7 21 S u n d a r a l i n g a m , M. ( 1 9 6 9 ) B i o p o l y m e r s 7, 8 2 1 - - 8 6 0 2 2 F r e d e r i c q , E. ( 1 9 7 1 ) in H i s t o r i e s a n d N u c l e o h i s t o n e s (Phillips, D.M.P., e d . ) , P l e n u m Press, L o n d o n 2 3 B e r k o w i t z , D.S. a n d L o e w , G. ( 1 9 7 6 ) O p i a t e s a n d E n d o g e n o u s O p i o i d P e p t i d e s , E l s e v i e r / N o r t h H o l l a n d B i o m e d i c a l Press, A m s t e r d a m , T h e N e t h e r l a n d s 2 4 R e i n , R., Claverie, P. a n d P o l l a k , M. ( 1 9 6 8 ) I n t . J. Q u a n t . C h e m . 2, 1 2 9 - - 1 4 4 2 5 F u j i t a , H., I m a m u r a , A. a n d N a g a t a , C. ( 1 9 7 4 ) J. T h e o r . Biol. 4 5 , 4 1 1 - - 4 3 3 2 6 S u t o r , D.J. ( 1 9 6 3 ) J. A m . C h e m . Soc. 8 5 , 1 1 0 5 - - 1 1 1 0 2 7 T s ' o , P.O.P., K o n d o , N.S., S e h w e i z e r , M. a n d Hollis, D.P. ( 1 9 6 9 ) B i o c h e m i s t r y 8 , 9 9 7 - - 1 0 2 9 2 8 D o n o h u e , J. ( 1 9 6 8 ) in S t r u c t u r a l C h e m i s t r y a n d M o l e c u l a r B i o l o g y ( R i c h , A. a n d D a v i d s o n , N., eds.), Freeman, San Francisco 2 9 Noll, M. ( 1 9 7 4 ) N u c l e i c A c i d s . Res. 1, 1 5 7 3 - - 1 5 7 8 3 0 C a m e r i n i - O t e r o , R . D . , S o l l n e r - W e b b , B. a n d F e l s e n f e l d , G. ( 1 9 7 6 ) Cell 8, 3 3 3 - - 3 4 7 31 Y a n e v a , M. a n d Desser, G. ( 1 9 7 6 ) N u c l e i c A c i d s Res. 3, 1 7 6 1 - - 1 7 6 7 3 2 N o l l , M. ( 1 9 7 4 ) N a t u r e 2 5 1 , 2 4 9 - - 2 5 1 3 3 N o l l , M., T h o m a s , J . O . a n d K o r n b e r g , R . D . ( 1 9 7 5 ) S c i e n c e 1 8 7 , 1 2 0 3 - - 1 2 0 6 3 4 Gosvli, L.C. a n d S e h e l l m a n , J . A . ( 1 9 7 6 ) N a t u r e 2 5 9 , 3 3 3 - - 3 3 5
BBA 98986
KINKED DNA ENERGETICS AND CONDITIONS F A V O R I N G ITS F O R M A T I O N
G E O R G E R. P A C K a, M A R C A. M U S K A V I T C H b a n d G I L D A L O E W a , .
a Department of Genetics and b Department of Biochemistry, Stanford University Medical Center, Stanford, Calif. 94305 (U.S.A.) (Received March 7th, 1977)
Summary Theoretical calculations demonstrate that the formation of kinks in DNA in the manner proposed b y Crick and Klug produces a conformation which corresponds to a local energy minimum when the phosphate backbone is charged. This conformation becomes the global minimum under certain conditions which neutralize the anionic backbone oxygens. A sequence preference for kink formation is predicted. The possible role of kinking in experimentally observed phenomena and experimental means of demonstrating the existence of kinks are discussed.
Introduction Among the models which have been proposed for the supramolecular organization of eukaryotic chromatin, two are particular attractive. Kornberg [1] explains the "beads on a string" [2] appearance of chromatin from ruptured nuclei as the winding of a continuous DNA helix around successive histone octamers [3]. Finch and Klug [4] have suggested that the thick (250 A) filaments observed in chromatin treated with divalent cations are solenoidal coils of thethin (100 £) filaments obtained in the presence of chelators [5--7]. Despite intense research activity, the detailed molecular structure underlying these proposed superstructures remains unclear. At a finer level of resolution, Crick and Klug [8] have speculated that DNA in chromatin assumes a " k i n k e d " conformation. This departs from B-form DNA at intermittent " k i n k " sites only by a single rotation of approx. 120 ° * To whom all reprint requests should be addressed. Abbreviations: D N A , d e o x y r i b o n u c l e i c acid; dA, deoxyadenosine; dC, d e o x y c y t i d i n e ; dG, deoxyguanosine; dT, thymidine; dX-dY, dX b o n d e d to dY by a 3'- to 5'-phosphodiester linkage.
10 abut the C4'-C5' bond of the exocyclic deoxyribose of the backbone. This is torsion angle e as previously defined [9] (Fig. 1). The rotation results in the loss of a stacking interaction (but no disruption of hydrogen bonding) and in a " k i n k " of a b o u t 90 ° between successive segments of the helix with movement of part of the helix toward the minor groove. This kinking then permits construction of successively higher order structures. First-order kinking could allow DNA to wind around histone octamers; and successive kinks between beads could lead to solenoidal structures. More recently, another plausible kink has been proposed [10]. Based on a kinking of the structures observed in ribodinucleoside monophosphate pairs complexed with an intercalated ethidium molecule, this model can also account from chromatin structure. In this paper we present the results of a study of the energetics of the formation of those kinks arising from rotation a b o u t the C4'-C5' bond. We suggest that this kinked form becomes a low-energy conformation under conditions in which the phosphate oxygens are neutralized and that A + T-rich regions should be preferentially kinked under neutralizing conditions. Methods The method of calculation was the quantum chemical Perturbative Configuration Interaction using Localized Orbitals (PCILO) [11]. Extensive studies on the backbone of nucleic acids [12] and other large molecular systems [13,14] have confirmed the validity of this method. Comparison of local minima in the potential energy hypersurface c o m p u t e d using PCILO with conformations shown to be preferred in crystallographic studies [15] gives remarkably good correspondence. In an a t t e m p t to deal with the sequence specificity of the proposed kink, all sixteen dideoxynucleoside monophosphates were studied. Since the PCILO method considers all valence electrons of a molecule, computation size ranged from 192 electrons for dC-dC to 220 electrons for dG-dG. All computations were performed on the CDC 7600 computer, effectively a double precision machine, to avoid artifacts which might have arisen from the limitations of single precision capability. Geometries of dideoxynucleoside monophosphates were derived from the B-form DNA structure of Arnott and Hukins [16]. A representative structure is shown in Fig. 2a. Hydrogen atoms were placed at standard bond distances of 0.96 A for O--H, 1.04 A for N--H and 1.09 A for C--H. Orientations of hydrogen atoms and lone pair electrons were determined using an interactive molecular-model building c o m p u t e r program to establish optimal placement. The effect of solvent is not explicitly included in the calculation. It is presumed that this effect will vary little with different sites of the kink, leaving the relative energies and hence the preferred sites of kinking unaffected. The agreeement of theory with experiment in studies of DNA structure [12] also m a y be taken to indicate that the solvent may well effect the kinked and unkinked forms equally, and thus be validly neglected in these comparisons of energies. All calculations on the variation of energy with e were performed for single dideoxynucleoside monophosphates. The energy of the molecule was calcu-
11 lated for each balue of e. The lowest energy calculated for the molecule was taken as an arbirary zero, and all other energies were expressed relative to that zero value. A helical segment is defined as the structure consisting of a dideoxynucleoside monophosphate paired with its complementary dideoxynucleoside monophosphate by standard Watson-Crick base pairing. In calculating the energy of a helical segment as a function of conformation two assumptions are made: (i) in accordance with the model of Crick and Klug, hydrogen bonding between complementary base pairs does not change as backbone conformation changes and is n o t a factor in the calculations; (ii) by symmetry, the magnitude and sense of e is the same for both dideoxynucleoside monophosphates in the helical segment. Therefore, the total energy of the segment in a given conformation (defined by a specific value of e) is calculated by adding the energies for the complementary dideoxynucleoside monophosphates, each characterized b y the same balue of e. Results The variation of energy with e calculated for anionic dideoxynucleoside monophosphates is presented in Table I. The shape of the curve (energy vs. e) is similar for the four subfamilies with the same base in a 5' linkage. Fig. 1 gives a representative curve for each category of dinucleoside phosphate. Global minima generally occur at either 56 ° or 66 ° (except for dG-dC) and local minima are found at 146 ° for all species but with varying depth of both minima (Fig. 2c). The anomalous global minimum found for dG-dC can be attributed to the particularly large stacking interaction between guanine and cytosine at this value of e. The interaction between these bases has been calculated to be much greater than between other combinations of bases [ 17]. Those molecules with thymidine in a 5' linkage {dA
12 6 t d A<'I A
a
5 I'-
•
6
dA<~C
5
/° AE
4
•
,...;.,,.? V I
36 °
76 °
ll6 ° E
6b dA~JG
4p
/'~
3,6°
!",, ;" 2
-w I
76 =
I
I
116° E
76 °
tl6 °
I
I
I
156 °
E
,
b
A. /
*
Z "e
AE31-
36 °
156"
I
I
156 e
I
,F-/,,,,,, 36 o
76 °.,
II6 ° E
156 °
F i g . 1. E n e r g y o f r o t a t i o n ( k c a l / m o l ) a b o u t C4'-C5' a x i s ( e ) for n e u t r a l d X - d Y a n i o n i c d i d e o x y n u c l e o t i d e s . (a) d A - d A c u r v e similar f o r all d X - d A . (b) d A - d C c u r v e similar f o r all d X - d C . (c) d A - d G c u r v e similar to all d X ° d G . (d) d A - d T c u r v e similar t o all d X - d T .
little with base composition. Since the PCILO net charge is not greater than those calculated by ab initio methods, it is unlikely the interaction is being overestimated. The next set of calculations dealt with the variation of energy with e for ten possible anionic helical segments. Again, global minima were observed at 56 ° and local minima at 146 °. The global minima at 56 °, though indicating a preferred conformation different from that calculated by Arnott for B-form
a ,-~o 3 (::'3
C'5 H
13
®
)C' 2
6
Z.,~ C'3
/ 04
/ / /
© 03
bo'5 c~, 04
)0 2
~C'3 0'5
/
/ 04
/ /
Fig. 2. T h e g e o m e t r y o f t h e k i n k r o t a t i o n , i l l u s t r a t e d for t h e single s t r a n d d A - d T . T h e p o s i t i o n a n d sense o f t h e r o t a t i o n , e, are i n d i c a t e d b y t h e a r r o w . T h o s e a t o m s o f t h y m i d i n e w h i c h are m o v e d in t h e c h o s e n c o o r d i n a t e s y s t e m are s h a d e d . (a) r e p r e s e n t s t h e D N A - B c o n f o r m a t i o n w i t h t h y m i n e s t a c k e d b e l o w a d e n i n e . (b) illustrates an i n t e r m e d i a t e c o n f o r m a t i o n (e = 66 ° ) w i t h an i n t e r a c t i o n b e t w e e n t h e t h y m i n e m e t h y l g r o u p a n d t h e p h o s p h a t e . T h e final k i n k g e o m e t r y (e = 146 °) is s h o w n in c. D a s h e d lines i n d i c a t e " c l o s e c o n t a c t s " b e t w e e n base a n d b a c k b o n e , p a n d d d e s i g n a t e p r o x i m a l a n d distal o x y g e n a t o m s , respectively.
MONOPHOSPHATES
dA-dA
1.37 0.44 0.0 0.27 1.18 2.18 2.66 2.57 3.39 4.77 3.87 3.49 4.41 5.16
C(° )
36 46 56 66 76 86 96 106 116 126 136 146 156 166
1.01 0.40 0.0 0.22 1.06 2.00 2.40 2.24 3.00 4.34 3.40 2.99 3.86 4.59
dC-dA
0.23 0.15 0.0 0.38 1.37 2.43 2.95 2.89 3.73 5.13 4.25 3.88 4.79 5.54
dG-dA
0.73 0.30 0.0 0.30 1.21 2.20 2.66 2.54 3.35 4.75 3.88 3.48 4.36 5.09
dT-dA
0.45 0.37 0.0 0.34 0.77 1.03 0.90 0.90 2.23 3.18 2.12 1.27 2.20 3.47
dA-dC 0.33 0.37 0.0 0.14 0.46 0.60 0.38 0.30 1.55 2.54 1.34 0.53 1.45 2.69
dC-dC 0.0 1.93 2.42 3.08 3.76 4.19 4.19 4.28 5.67 6.76 5.63 4.89 5.86 7.14
dG-dC 0.48 0.40 0.0 0.13 0.44 0.58 0.37 0.30 1.57 2.66 1.39 0.68 1.55 2.82
dT-dC 0.57 0.19 0.0 0.42 1.49 2.68 3.30 3.24 3.97 5.37 4.47 3.99 4.77 5.35
dA-dG 0.73 0.22 0.0 0.43 1.51 2.69 3.29 3.19 3.86 5.20 4.21 3.62 4.30 4.77
dC-dG 0.62 0.21 0.0 0.45 1.61 2.89 3.58 3.56 4.30 5.70 4.75 4.20 4.91
dG-dG 0.97 0.27 0.0 0.42 1.52 2.72 3.34 3.27 3.97 5.33 4.34 3.76 4.45 4.93
dT-dG 3.66 2.30 0.50 0.0 1.87 3.26 2.58 2.01 3.70 4.73 2.58 2.38 4.00 5.57
dA-dT
3.56 2.16 0.47 0.0 1.85 3.19 2.45 1.82 3.44 4.43 2.25 2.02 3.60 5.15
dC-dT
e c o r r e s p o n d s to t h e angle o f r o t a t i o n a b o u t t h e C 4 ' - C 5 ' b o n d o f t h e e x o c y c l i c d e o x y r i b o s u g a r as d e f i n e d in ref. 9. E n e r g y in k c a l / m o l .
POTENTIAL ENERGY VARIATION WITH e FOR ALL DIDEOXYNUCLEOSIDE
TABLE I
2.51 1.96 0.37 0.0 1.99 3.47 2.86 2.35 4.08 5.14 3.01 2.83 4.46 6.04
dG-dT
3.94 2.32 0.51 0.00 1.84 3.17 2.43 1.82 3.46 4.45 2.27 2.04 3.64 5.19
dT-dT
15 TABLE
II
VARIATION OF DISTANCE WITH e BETWEEN CARBON THE BACKBONE PHOSPHATE G R O U P IN dA-dT
ATOMS
OF THYMINE
AND
OXYGENS
OF
R[Cm....O 2 ] represents separation of the methyl carbon and phosphate oxygen. R[C6....O 4] represents separation of C 6 and phosphate oxygen. The angle of the C6-H....O bond is included parenthetically.For the numbering of atoms see Fig. 2. e(°)
R [ C m ...02] (A)
R [ C 6 ...04] (A)
36 46 56 66 76 86 96 106 116 126 136 146 156 166
4.02 3.52 3.08 2.72 2.49 2.45 2.59 2.90 3.31 3.78 4.29 4.80 5.30 5.79
3.05(141.9) 2.87(137.7) 2.73(132.1) 2.63(125.4) 2.58(118.5) 2.59(112.2) 2.66(107.2) 2.79(103.6) 2.95(101.3) 3.15(100.1) 3.36( 99.8) 3.59(100.2) 3.82(101.1) 4.04(102.5)
DNA (36 °), are in good agreement with the values of e tabulated by Rosenberg et al. [20] and Sundaralingam [21] from the crystal structures of numerous nucleic acids. This agreement establishes confidence in the efficacy of the PCILO m e t h o d as applied to conformational stt~dies of nucleic acids. The local minima at 146 ° corresponds very well to the value of e (156 °) predicted b y Crick and Klug for the structure of kinked DNA. The existence of local minima near the angle corresponding to the kinked conformation suggests the kinked form could become energetically favored under appropriate conditions. The energy of the kinked form of each possible helical segment relative to the minimum energy calculated for the segment along with the statistical probability of finding a kink at a specific sequence are given in Table III. There is some sequence-related variation of the energy of the kinked state b u t all segments exhibit a positive relative energy for kink formation. It is apparent that the preferred conformation of the segments in anionic form will be witho u t significant contribution from the kinked form. A number of considerations then led us to determine the effect of changing the state of the backbone on the energetics of conformational change of helical segments. First, it is conceivable that the base-backbone electrostatic interaction can significantly affect the stability of a given conformation (see above). Second, it has been noted that the positive charge available from histones, calculated from the molar ratios of DNA to histone generally found in chromatin, is sufficient to neutralize approximately half the negative charge of the associated DNA [22]. This electrostatic interaction between anionic and cationic sites is likely to be a major c o m p o n e n t of the total interaction of DNA with histones. Third, the addition of divalent cations to uncondensed chromatin can result in the conversion to a condensed state [4--7]. We therefore decided to study the effects of neutralization of the phosphate oxygens on the
16 TABLE IlI ENERGIES
AND PROBABILITIES
FOR KINK FORMATION
BY ANIONIC HELICAL
SEGMENTS
A r r o w i n d i c a t e s 3'- to 5 ' - p h o s p h o d i e s t e r l i n k a g e . E n e r g y o f k i n k f o r m a t i o n for all ten p o s s i b l e a n i o n i c helical s e g m e n t s ( d e f i n e d in M e t h o d s ) given relative t o m i n i m u m e n e r g y c a l c u l a t e d for e a c h s e g m e n t . F r e q u e n c y -1 d e n o t e s n u m b e r o f helical s e g m e n t s in w h i c h o n e k i n k is e x p e c t e d at 2 5 ° C c a l c u l a t e d f r o m an e x p o n e n t i a l d i s t r i b u t i o n using B o l t z m a n n statistics. Segment
Energy (kcal/mol)
Frequency- 1
dA-dT dT-dA
4.76
3.1 • 103
dA-dA dT-dT
5.54
1.1 " 1 0 4
dA-dC dT-dG
4.10
1.0 • 103
dA-dG dT-dC
3.29
2.6 - 102
dG-dC dC-dG
4.73
3.0 " 103
riG-riG dC-dC
7.24
2.0 ' 10 s
dG-dA
4.56
2.2 " 103
dT-dA dA-dT
6.96
1.3 " 10 $
dC-dA
6.75
9.0 ' 104
9.78
1.7 " 107
dC-dT
dG-dT
dG-dC dC-dG
energetics of conformational changes of dideoxynucleoside monophosphates and hence the kinking of helical segments. The proton was chosen to act as the cation involved in neutralization of the phosphate charge. As a model for the interaction of positively charged histone residues and the D N A backbone, molecular orbital studies on the interaction of the a m m o n i u m cation (NH4 ÷) and monoanionic phosphate (H2PO4-) indicate the most stable complex .could involve a linear hydrogen bond with migration of the proton [23] from nitrogen to oxygen. The protonation of one of the
17
non-esterified phosphate oxygens was therefore taken as a reasonable model of backbone charge neutralization. Calculations were performed on dA-dT with an associated proton at either of two positions to determine whether one of the non-esterified oxygens would be preferentially protonated, as well as the effect of protonation on the variation of energy with conformation. Variation of energy with e for the two protonated forms and a form in which NH4* is shared by the two non-esterified oxygens is given in Table IV. When the oxygen distal to the bases is protonated the conformation corresponding to a kink (156 °) is neither a local nor global minimum. When the proximal oxygen is protonated, the conformation corresponding to a kink becomes the global minimum. Comparison of the global minima for both forms indicates that the minimum for the proximally protonated form is lower in energy by 4.7 kcal/mol, indicating protonation at the proximal oxygen will be preferred. As a result of the neutralization of this oxygen, the kinked conformation of the dideoxynucleoside monophosphate is energetically favored (Fig. 3). Assignment of a third geometry in which the NH4 + is shared equally between the two non-esterified oxygens also yields an indication that the kinked conformation will be energetically favored. Thus, more than one geometry in which the backbone phosphate is neutralized will result in a preference for the kinked conformation. Using the l~rotonation of the proximal oxygen as a model geometry, the variation of energy with conformation was calculated for the remaining 15
T A B L E IV V A R I A T I O N O F T H E P O T E N T I A L E N E R G Y O F d A - d T W I T H e AS A F U N C T I O N O F T H E G E O M E T R Y OF P R O T O N A T I O N OF T H E BACKBONE P H O S P H A T E Edistal is d e f i n e d as t h e e n e r g y f o r a m o l e c u l e in w h i c h o n l y t h e n o n - e s t e r i f i e d o x y g e n distal to t h e b a s e s is p r o t o n a t e d . E p r o x i m a l r e p r e s e n t s t h e e n e r g y w i t h o n l y the p r o x i m a l n o n - e s t e r i f i e d o x y g e n p r o t o n a t e d . Distal and p r o x i m a l o x y g e n s are d e s i g n a t e d in Fig. 2. Eshared is d e f i n e d as t h e e n e r g y w h e n a m m o n i u m is shared e q u a l l y b y t h e t w o n o n - e s t e r i f i e d o x y g e n s . T h e e x t r e m e l y high barrier for Eshared results f r o m i n t e r a c t i o n b e t w e e n the t h y m i n e m e t h y l group and the N H 4 + in w h i c h van der Waal radii are grossly viol a t e d . This is n o t m e a n t to suggest t h a t a barrier t o r o t a t i o n o f this m a g n i t u d e w o u l d actually e x i s t since t h e N H 4 + p o s i t i o n c o u l d easily adjust t o a l l o w a freer r o t a t i o n . T h e c a l c u l a t i o n s w e r e d o n e f o r R N _ P = 3 A, w i t h t h e h y d r o g e n a t o m s d i r e c t e d at t h e n o n - e s t e r i f i e d o x y g e n a t o m s .
e(°)
Edistal (kcal/mol)
36 46 56 66 76 86 96 106 116 126 136 146 156 166 176 186
1.21 0.80 0.00 0.27 2.84 4.79 4.43 4.62 7.08 8.93 6.67 3.86 2.36 2.01 2.11 2.38
Eproximal (kcal/mol) 3.73 3.41 3.27 6.87 19.15 26.10 10.38 3.05 4.51 4.65 1.01 0.0 1.12 2.25 2.94
Eshared (keal/mol) 3.00 2.47 1.82 3.70 13.5 67.2 367.0 1492.0 1688.0 40.3 0.49 0.0 1.15
18
7, f 6
5:
II 36 °
/j
dA~ dT. H
/ ,\J,
, , 76 o
116°
,
156 °
Fig. 3. E n e r g y o f r o t a t i o n ( k c a l / m o l ) a b o u t C4'-C5' axis (e) for n e u t r a l d A - d T . E f f e c t o f P h o s p h a t e neut r a l i z a t i o n on e n e r g e t i e s o f k i n k i n g ,
dideoxynucleoside monophosphates. The results of these calculations are listed in Table V. The relative energy of the kinked form of the neutral molecule is lower than that of the anionic molecule for all dideoxynucleoside monophosphates. In particular, a preference for the conformation corresponding to the kinked form (e = 146 °) is apparent for those molecules having a 5'-linked thymidine. Sequence specificity of the preference for kinked conformation stems from two disparate sources. First, stabilization energy associated with base stacking is lost. The variation of this energy with sequence has been discussed in several theoretical studies [ 17,24,25]. Second, the contribution to stabilization b y the base-backbone interaction varies depending on the base involved. In particular, loss of the close association between 04 of the backbone and hydrogen b o n d e d to either C6 of pyrimidines of Cs of purines may be significant. Although long noted by crystallographers [26] and observed in nuclear magnetic resonance spectra [27], its importance has been questioned [28] and its magnitude undetermined. Stacking effects are probably involved in the preferences of dG-dC and dG-dA for a conformation in which e is equal to 36 °. The preference of neutral dideoxynucleoside monophosphates with 5'-linked thymidine for the kinked conformation could be due to the relative destabilization of the conformation for which e is equal to 56 ° C. Such destabilization would result from loss of the
TABLE V V A R I A T I O N OF P O T E N T I A L E N E R G Y WITH e FOR N E U T R A L D I D E O X Y N U C L E O S I D E MONOPHOSPHATES c(~) )
36 56 146
36 56 146
E (kcal/mol) dA-dA
dC-dA
dG-dA
dT-dA
dA-dC
dC-dC
dG-dC
dT-dC
0.84 0.0 0.62
0.53 0.0 0.67
0.0 0.12 0.98
0.30 0.0 0.48
1.24 2.00 0.0
1.97 2.79 0.0
0.0 3.46 2.52
1.98 2.66 0.0
dA-dG
dC-dG
dG-dG
dT-dG
dA-dT
dC-dT
dG-dT
dT-dT
0.24 0.0 1.20
0.52 0.52 0.0
0.58 0.0 1.50
0.77 0.0 1.22
3.73 3.27 0.0
4.06 3.67 0.0
2.38 2.81 0.0
4.45 3.66 0.0
19 T A B L E VI ENERGIES FOR KINK FORMATION
BY P R O T O N A T E D
HELICAL sEGMENTS
E n e r g y o f k i n k f o r m a t i o n f o r all t e n p o s s i b l e h e l i c a l s e g m e n t s , given relative t o t h e e n e r g y m i n i m u m c a l c u l a t e d f o r t h e B - f o r m s t r u c t u r e o f e a c h s e g m e n t . S y m b o l s h a v e t h e s a m e m e a n i n g as in T a b l e l I l . N e g a t i v e v a l u e f o r e n e r g y i n d i c a t e s t h e k i n k e d f o r m is m o r e s t a b l e t h a t t h e B - f o r m . N u m b e r s in p a r e n t h e ses axe t h e e n e r g y o f k i n k i n g if o n l y o n e p h o s p h a t e g r o u p o f t h e h e l i c a l s e g m e n t ( t h e o n e l e a d i n g t o m o r e f a v o r a b l e k i n k i n g ) is n e u t r a l i z e d . Segment
Energy (kcal/mol)
Segment
Energy (keal/mol)
dA-dT dT..d A
--6.54(--2.45)
dC..dG dG..dC
--1.04(+3.10)
dA-dC dT-dG
--3.62(--1.54)
dG-dA dC-dT
--1.00(+1.54)
dA-dA dT-dT
--3.04(--2.33)
dT-dA dA-dT
+0.96(+3.96)
dA-dG dT-dC
--2.47(+0.32)
dC-dA dG-
+1.89(+4.20)
--,
__>
dC-dC dG-dG
--1.05(+2.03)
dG-dC dC-dG
+5.04(7.41)
electrostatic interaction between thymidine and the anionic backbone (Table II). A similar effect is possible in those molecules having 5'-linked deoxycytidine. The magnitude and specificity of potential destabilization for pyrimidines is demonstrated by calculations currently in progress in this laboratory which show the base-anionic backbone interaction is approx. 9.1 kcal for dT and 4.3 kcal for dA. The fact that previous studies [18] of the effect of phosphate oxygen neutralization on backbone conformation indicated no significant changes in conformation is probably due to failure to consider specific base-backbone interactions. The energy of the kinked form for the ten neutral helical segments, relative to the energy minimum calculated for the B t y p e structure, is given in Table VI. One is struck by the fact that the kinked form is n o w energetically favored for seven of the ten segments. The variation in energy indicates a sequencespecific ordering of the preference for assumption of a kinked conformation. For example, when phosphate oxygens are neutralized one would expect dA-dT • dA-dT to kink much more readily than dG-dC • dG-dC. Neutralization of half the phosphates as might occur if DNA lies on the outside of the histone core leads to less kinking as indicated also in Table VI. Discussion
Although calculations suggest DNA would not frequently assume a kinked conformation when backbone phosphates are negatively charged, the kinked
20
,
form is preferred in some helical segments when the b a c k b o n e is neutralized. It should be emphasized that the protonated structures employed represent one of many possible model systems and might overestimate the neutralization of phosphate oxygens. The calculations also support a sequence specificity of preference for kink formation. While the order in Table VI may not be strictly correct, A + T-rich sequences should kink preferentially relative to G + C-rich sequences. Experimentally, the digestion of native [29] or reconstituted chromatin [3] with DNAase I, followed b y analysis of the products of denaturing gels, reveals multiples of a ten base repeating unit ranging from 30 to 220 bases. Noll [29] has suggested this repeating unit could arise from kinking of the DNA helix a b o u t the nucleosome or could reflect the pitch of the helix and backbone accessibility. This ten base repeat is still observed following DNAase I digestion of chromatin subjected to treatments which prevent appearance of the 180 base pair repeat [31], believed to reflect the amount of DNA protected by the intact nucleosome [32,33 ] on non-denaturing gels. If the ten base repeat is indeed a reflection of the kinked structure of DNA resulting from histoneDNA interactions, these interactions would suffice to form kinks in the absence of intact nucleosomal structure. Kinking also helps explain chromatin condensation. After first-order kinking of DNA around the histone octamers as the result of histone-DNA interactions, second-order kinking of DNA helical regions between nucleosomes as a result of cationic neutralization of the backbone could lead to the observed condensation. The efficacy of a given cation could depend on its hydration sphere which would, in turn, affect its ability to approach and neutralize backbone anionic oxygens. Two ions of the same charge but different hydration geometry could therefore differ in effectiveness, leading to ionic specificity for condensation. The molar ratio of cations to backbone oxygens could also be critical. In light of the results in Table VI, the model for kinking of the lac operator proposed by Crick and Klug [8] may be reexamined (Fig. 4). Comparison of their intuitive predictions and our calculations reveal a remarkable correspondence between the kinking sites. Three of the four sites they designate are identical with or adjacent to the sequence which we calculated as having the largest negative energy for kink formation (dA-dT • dA-dT). Calculations show the fourth site they designated also has a negative energy for kink formation, and is the most easily kinked anionic site (Table III). The existence of kinks has not, as yet, been demonstrated experimentally. We suggest only a few of many possible approaches to determining whether they do exist. Condensation of DNA in the presence of simple polyamines has been reported [34] and circular dichroism spectra are said to indicate that the helical form of T7 DNA condensed in the presence o f spermidine differs negligibly 5'AA~
TTGTGAGCGGA
T T A* ACACT÷
~TAACAA
CGCCT÷
ATTGT÷
~TT T A A 5'
Fig. 4. Comparison of the predicted kinking of the lac operator sequence. Solid arrows indicate sites with maximum negative energy for kink formation as calculated in this Study (when backbone phosphate neutral). Broken arrows indicate potential kink sites noted by Crick and Klug [8].
21 from the B-form. It would appear the condensation is achieved by a structural modification t h a t leaves the vast majority of helical structure unchanged, such as periodic kinking. If DNA condensation is mediated by kinking, a study of defined polymers such as poly(dA-dT) • poly(dA-dT), poly(dG
22
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