ELECTRIC DICHROISM OF NUCLEOSOMES
17,
VOL.
NO.
2 1 , 1978
4525
Transient Electric Dichroism Studies of Nucleosomal Particles? D. M. Crothers,* N. Dattagupta, M. Hogan, L. Klevan, and K. S. Lee
ABSTRACT: We report transient electric dichroism experiments on nucleosomal core particles containing 140 and 175 base pairs of DNA, and on spacerless dinucleosomes. The results indicate that all particles possess a permanent dipole moment. The orientation time of 140 base pair nucleosomes implies an estimated maximum dimension of a = 130 A ( a must be at least 11 1 A), consistent +Ah the disk model. The maximum dimension of the spacerless ainucleosome is estimated to be about 290 %, (at least 180 A), ruling out a structure in which two disks are stacked directly on top of each other.
The reduced dichroism amplitude indicates that the D N A superhelix axis in nucleosomes aligns perpendicular to the electric field, as expected for a dipole moment directed along a C2 symmetry axis across the disk diameter. Nucleosomes containing 175 base pairs of DNA show a substantially larger dichroism amplitude than do 140 base pair nucleosomes. In the context of the disk model, this result is shown to be consistent with 100 base pairs of DNA per superhelical turn, but not with 80 base pairs per turn.
T h e size and shape of nucleosomes, and their arrangement in chromatin, are problems of intense current interest. The model of nucleosomal core particle structure that has emerged from X-ray diffraction (Finch et at., 1977), electron microscopy (Langmore & Wooley, 1975), and neutron scattering studies (Hjelm et al., 1977; Pardon et at., 1975; Suau et a]., 1977) is a disk-like object about 1 10 A across and 57 A thick, with histones H2A, H2B, H3, and H4 at the core and DNA wrapped in a superhelix around the circumference. Structural problems still unsolved are the spacial relationship between successive H 1-containing nucleosomes in chromatin, and between H l -depleted nucleosomes in the spacerless interaction mode, for which the dimer was isolated and characterized by Klevan & Crothers (1 977). Electric dichroism is a technique of considerable potential utility for addressing such questions because it is highly sensitive not only to the size and shape of a macromolecular species, but also to the angular disposition of the nucleic acid bases relative to the macromolecular orientation axis in the electric field. We describe here electric dichroism measurements on both nucleosomal core particles containing different lengths of DNA, and on spacerless dinucleosomes. In each case analysis of the time required for the particle to orient in the field gives information about the particle’s size and shape. The magnitude of the dichroism, when extrapolated to perfect molecular orientation at infinite field, reveals the mean square projection of the UV transition moments of the bases on the axis of orientation in the field. A preliminary account of these results has been communicated (Klevan et al., 1977). Conversion of dichroism amplitudes to structural parameters such as the superhelix pitch angle requires some extension of existing theory, specifically (a) to treat particles which align with their superhelical axes in a direction other than parallel to the field, and (b) to allow for superhelices that have a nonintegral number of half turns and therefore cannot be considered to possess cylindrical optical symmetry about the superhelix axis. Furthermore, in interpreting dichroism amplitudes, one must recognize the potential for loss of cylindrical optical symmetry of the DNA double helix because of its periodic distortion by bending and by contacts with the histone
proteins. In the theoretical section that follows some standard results (Fredericq & Houssier, 1973; Ding et al., 1972; Allen & Van Holde, 1971; Maestre & Kilkson, 1965; Rill, 1972) are rederived briefly in order to provide a coherent basis for our extension of the theory.
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~-
From the Department of Chemistry, Yale University, New Haven, Connecticut 06520. Received April 21, 1978. Supported by Grant CA 15583 from the National Cancer Insitute.
0006-2960/78/0417-4525$01 .OO/O
Theory Extinction Coefficients. Recall that the extinction coefficient t of an absorbance transition moment oriented at an angle 8 to the direction of the polarization of the electric field vector is proportional to the squared projection of the transition moment on the polarization direction, or t
= to cos2 8
(1)
in which EO is the extinction coefficient when the transition moment is parallel to the electric vector. We define the reduced extinction coefficient F as -
t
t = - = t0
cos2 8
(2)
so that Z depends only on geometric factors. Because of the Pythagorean theorem, the sum of the squared projections of the reduced (unity) transition moment on the rectangular coordinate axes must be unity: Zx
+ Fy + Zz = I
(3) For a set of identical transition moments oriented randomly, the sum of the average squared projections ( Zx ), etc., also must be unity. Furthermore, because random orientation implies ( tx ) = ( Fy ) = ( tz ), the reduced average extinction coefficient trfor a randomly oriented chromophore is 1 ( Zx ) = Zr = (4) 3 Application of an electric field produces orientation of a molecular axis, taken to be the z axis, along the field direction, but permits free rotation about the z axis. Let t2be the reduced extinction coefficient for light polarized parallel to the z molecular axis, and Zx and Cy be the corresponding quantities for arbitrarily chosen perpendicular axes (Figure 1). The reduced extinction coefficient t for light polarized parallel to the orientation direction is
-
€11 =
€2
0 1978 American Chemical Society
4526
B ~ O H C E M IS T R Y
C R O T H E R S ET A L X
L
Ey
Y--
1
F I G L R E 1 : Calculation of the reduced extinction coefficient for light polarized parallel and perpendicular to the z molecular axis, assuming free rotation about z . Arbitrarily chosen perpendicular molecular axes x and y rotate freely in the perpendicular plane. The squared projection due to C, on the perpendicular polarization direction is t Xcos2 p, and the squared projection due to 7, is S,. sin2 p. The reduced extinction in the equatorial plane is the sum of these components averaged over all values of 8, or 7 = (7, + 7) ) / 2 .
FIGURE 3: Contribution of the axial 7(); and perpendicular (7,’(2)) reduced extinction along the x direction in an incomplete superhelix. The view is taken along the superhelix axis, normal to the x-y plane. The squared projection due to 7,’ on the x-y plane is C,’ sin2 p, so the squared projection on x is 7,’ sin2 p sin2 0. The squared projection due to Fe’(2) on x is 7’(2) cos2 0. Referring to Figure 2b shows that the squared projection due toZl(1) tangent to thesuperhelix and in the x-y plane is Z,( 1) sin2 ( ~ / 2 - 4). Therefore the squared projection due to Fe’( 1) along x is 7,l( I ) sin2 ( ~ /2 p) sin2 8. Addition of these three components yields eq I O .
component Ea is made up of contributions from t,’ directed along the D N A axis, and 7; perpendicular to the D N A axis (Figure 2b), or 7, = Fa‘ cos* p
a) F I G U R E 2: Calculation of the axial (Sa) and equatorial (te)reduced extinction components of a superhelix from the axial 7)(; and equatorial 7(); reduced extinction components of the D N A molecule. (a) View of the superhelix showing 7, directed along the superhelix axis, and Se in the equatorial plane. (b) Reduced extinction coefficients in an element of the superhelix. Fa’ is tangent to the superhelix, and forms an angle p with the superhelix axis. T,’(2) is perpendicular to the D N A helix and to the supis also erhelix axis (perpendicular to the plane of the drawing). 7:(1) perpendicular to the D N A helix and perpendicular to 7;(2), lying in the plane of the drawing. T h e axial reduced extinction component 7, along the superhelix axis is the sum of the components contributed by Fa’ and - I ce ( I ) , or = 7,’ cos2 /3 7,’ cos2 ( n / 2 - 6). It is assumed that ;,’(I) = 7,(2) = because of rotational averaging of the D Y A extinction.
in which 0 is the superhelix pitch angle, tan /3 = (superhelix circumference/pitch). Insertion of eq 7a and 7b and use of trigonometric identities yield -
1 = - [I
+
- ( cos? cy ) cos* (3 (cos* a ) - I ) ] (9a) 2 a result equivalent to that obtained earlier by Rill (1 972). The rotationally averaged equatorial extinction coefficient of a superhelix is, by eq 6 t,
+
Assuming free rotation about the z axis, the extinction coefficient f L for light polarized perpendicular to the orientation direction is (Figure 1 )
Using eq 3, Fl can also be expressed as
The reduced extinction coefficient of a helical array of transition moments, such as provided by the bases in a DNA molecule, can be expressed in terms of the reduced extinction coefficient t,’ directed along the helix axis, and the average reduced extinction 7,‘ in the equatorial plane, assuming rotational averaging about the helix axis. If cy is the angle between a transition moment and the helix axis, eq 1 and 6 yield Fa’ = (cos2 c y )
- =1 - t,’ 1 -- - ( 1
te
1-t, =-
2
A slightly more difficult problem is provided by the case in which the molecule does not have cylindrical optical symmetry; an example is a fractional superhelical turn under orientation conditions that do not allow rotational averaging about the superhelical axis. Figure 3 shows a projection of such an object in a plane perpendicular to the superhelix axis. The axial extinction C, of an incomplete superhelix is given by eq 9a, but the equatorial extinction coefficient must be calculated separately for the x (re,) and y (C,)) molecular axes, rather than computed from T , as in eq 9b. The reduced extinction coefficient along the x direction contains components due to the squared projection on the x axis of the axial (&’) and equatorial (ee’( 1) and ~ ~ ’ ( 2 )DNA ) reduced extinction components. Consideration of Figures 2b and 3 shows that the contribution dZ,, to the average extinction given by the DNA contained in d8 is dt,, = [ta’sin2 8 sin* /3dO
(7a)
- (cos2cu)) (7b) 2 2 The extinction components of a DNA molecule coiled into a superhelix are readily calculated (Figure 2). Let 7, and Ze be respectively the reduced extinction coefficients along the superhelix axis and in the perpendicular equatorial plane, the latter averaged for rotation about the superhelix axis. The axial
+ te‘ cos2 (;- - /3 )
+ t k ( 1) sin2 8 sin2 ( 2 - p )d8 + te/(2) cos2 8d8]/JdO ( I O )
Because the D N A is assumed to have cylindrical optical symmetry, t l ( 1 ) = F((2). Insertion of eq 7b and use of trigonometric identities give 1
- [(32,’
dtex =
2
- 1) sin* 8 sin2 J-dO
+ 1 - ta’]d8 ( 1 1)
ELECTRIC DICHROISM
VOL.
OF NUCLEOSOMES
Integration of eq 11 over 8 = 0 to 27r (6 = 0) yields the value of 7, given by eq.9a and 9b, as expected when the number of turns in the superhelix is integral. When the number of turns in the superhelix is less than 1, 6 # 0, and 0 varies from 6 to 2 x - 8. Hence Ees is given by
+ 1 -2,’ldB
(12)
6e.x
=
(3(cos2 a ) - 1) sin26 (1 + B ) 4
a) + 1 - (cos2 2
+
Use of eq 9b and 14 yields for the (perpendicular) dichroism p1
Similarly =
(3(cos2 a ) - I)sin2 @ (1 - B ) 4
a) + 1 - (cos2 2
(13c)
Dichroism. The results so far obtained allow us to calculate the dichroism of superhelices oriented parallel or perpendicular to a polarization direction, with rotational freedom about the orientation axis. The equations derived apply to perfect molecular orientation. The reduced linear dichroism p is defined (Fredericq & Houssier, 1973) as the ratio P=
All - A 1 A
in which A 11 is the absorbance for light polarized parallel to the orientation direction, and A 1 is the absorbance for the perpendicular polarization direction. A is the absorbance in absence of orientation. Note that A,l = qCI, A 1 = clC1, and A = &I, in which C i s the concentration and 1 the path length. BY eq 4 fr = €02~ = €0/3 and p can be expressed
3 = - (1 - 32,) 4 3 =--(3c0s2@8 - 1
--
(18a) 1)(3(C0s2cu) - 1 )
(18b)
p
( 18c)
Two limiting cases of this equation are (a) a linear DNA, with a = 90’ and p = O’, aligned perpendicular to the field, for which p l = 3/4, and (b) a D N A circle (CY= 90°, /3 = 90’) whose diameter parallels the field, for which pi1 = -3/~. Case 3. Incomplete superhelix with axis parallel to orientation direction. I n this case, rotation is allowed about the superhelix axis, thus conferring cylindrical optical symmetry on the molecule, and the dichroism is that predicted for case 1. Case 4 . Fractional superhelix with superhelical axis perpendicular to the orientation direction. In this case we assume orientation along the C2 symmetry axis, the x axis in Figure 3. Therefore €li =
-
(1 9a)
tex
Ze
+ ta
