J . Phys. Chem. 1992, 96, 6045-6055
6045
Absorption Spectroscopy and Dynamic and Static Light-Scattering Studies of Ethidium Bromide Binding to Calf Thymus DNA: Implications for Outside Binding and Intercalation Eckhard Nordmeier* Department of Physical Chemistry, FB 5, University of Osnabrkk, Germany (Received: December 11, 1991)
By combining absorption and light-scattering spectroscopy,including photon correlation and angular distribution of absolute scattered intensity, we have studied the modes of ethidium bromide binding to calf thymus DNA at constant temperature and pH. It is found that the fraction of total bound dye molecules per nucleotide, T8D, is dependent on the counterion concentration, Cs T 8 D decreases slightly as C, is raised. Furthermore, the data indicate two modes of dye binding: intercalation and outside binding. The analysis of the Scatchard plots by Manning's polyelectrolyte theory of site-bindingequilibria suggests ( I ) '8D, the fraction of intercalated dye molecules per nucleotide, increases continually with T 8 D , (2) over the experimental accessible range of T8D, intercalation is the stronger mode of binding, and (3) dye binding appears to be saturated when ' 8 D = T 8 D . The light-scatteringmeasurements gave useful data for the DNA radius of gyration, ( S ) z ,the DNA radius of hydration, Rh,the second virial coefficient, A2, and the DNA translational diffusion coefficient, Dz*o.These data were analyzed in terms of the wormlike chain and the sliding rod model. It is found that each intercalated EBr molecule adds a length of 0.27 nm to the total contour length of CT-DNA. Interestingly, the DNA persistence length of bending, I,, is smaller in the presence than in the absence of EBr. This indicates that dye binding reduces the DNA rigidity due to a neutralization of phosphate groups. Finally, it was shown that the angular dependence of the apparent diffusion coefficient, D (q2),is well simulated by the Rouse-Zimm polymer model comprised of a number of subchains and an apparent subchain that scales as TIT. In particular, it is found that the Rouse-Zimm subchain extension, RZbs,is d8usion coefficient DPIat twice the effective persistence length, which is the weighted sum of the persistence length due to bending, twisting, and contraction/extension. A further result is that the ionic strength dependence of I, can be well described by Manning's theory of territorial counterion binding and that a process such as spontaneous transient opening of DNA base pairs becomes important, if at all, when the ionic strength tends to zero.
Introduction
It is very important in biophysical chemistry to know how the molecular structure and the biological function of a nucleic acid are interrelated under different conditions. Recently,'-3 two areas in DNA research have received considerable attention, the interactions of DNA with cations from simple salts and the interactions of DNA with drugs such as ethidium bromide or proflavine. These ligands can bind to a DNA molecule in two ways: by territorial binding and by site binding. In territorial binding, the ligands (cations) interact by their Coulombic forces with the DNA phosphate groups but they are not associated with any one site or group of sites, Le., they move free in a volume Vp around the DNA skeleton. In site binding, the ligands associate with one or more sites on the DNA. In particular, if the ligand is a dye, two modes of site binding can be distinguished. The primary and generally stronger mode of binding has been interpreted as intercalationM where a part of the dye ions sandwiches between adjacent base pairs. The second mode of site binding is most evident at low salt and high dye concentration. The mode is thought to be an association between the dye molecules and the phosphate groups at the DNA surface. It is often called outside binding.' The object of this report concerns the interrelations between site and territorial binding in a system that contains DNA, salt, and dye molecules. In particular, we determine the fractions of intercalated and outside bound dye molecules per DNA nucleotide, and we compare the results with the predictions of present polyelectrolyte theories. These are Manning's counterion condensation theorf and Manning's theory of site-binding eq~ilibria.~ The dye used is ethidium bromide (EBr), and the salt is KC1. As a drug, EBr has trypanocidal, antibacterial, and antiviral activities.10 EBr inhibits DNA polymerase and in vitro it binds to both RNA and DNA."-I2 The intercalation hypothesis is supported by spectral shifts in the 480-nm absorption band together with a decrease in the viscosity of DNA upon the addition Correspondence should be addressed to the author at Platanenallee 9,
4515 Bad Essen I , Germany.
of the drug.13 The interaction of a drug with superhelical closed circular DNA is also a good means of determining if a dye intercalate~.'~ Interestingly, dye binding is not significantly influenced by base composition or by denaturation of DNA.l2J5 It is, on the other hand, very sensitive to increases in the salt concentration, particularly when divalent cations are added.I6 Readers interested in this topic are referred to the work of Wilson et al.,''-l9 who have elegantly analyzed the mechanism of intercalation, Le., the ionic effects on the kinetic constants for the interaction of EBr with DNA. From the spectroscopic point of view, the intercalated and the outside-bound EBr molecules display the same characteristic, i.e., a visible absorption band red shifted and hypochromic relative to that of the free dye. A determination of the proportions of EBr molecules bound by the two modes of site binding is thus possible only if an absorption method is combined with a hydrodynamic one. Here we utilize static and dynamic light scattering as the hydrodynamic methods. SLS2021delivers the weight average molar mass, M,, the z-average radius of gyration, (S),, and the second virial coefficient,A2. DLS2*is sensitive to temporal fluctuations in the polarizabilityof the sample under study. It is the standard method for obtaining the center of mass translational diffusion coefficient,D,, and the hydrodynamic radius, Rh. Under certain circumstance^,^^^^^ DLS gives also useful information about the dynamics of intramolecular deformations such as bending and twisting motions of polymer segments. In this report, the dynamics of CT-DNA are analyzed by three theories. They are the models of a wormlike a sliding rod,%and the Rouse-Zm theory?' The best experimental molar mass range to study a DNA via light-scattering is between 1 and 15 X IO6 Da. At the lower end of the scale, it is difficult to derive an accurate value for the DNA persistence length, Ip. At the higher end of the scale, it becomes increasingly difficult to obtain accurate experimental data at low enough scattering angles so that an unambiguous determination is no longer possible. The present experiments of M , and (S), were therefore performed with calf thymus DNA, which falls in the middle of this optimum empirical molar mass range (Mw,CT.DNA = 8.6 X IO6 Da).
0022-3654/92/2096-6045%03.00/00 1992 American Chemical Society
Nordmeier
6046 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992
Experimental Section Materials and Sample Preparation. Calf thymus DNA (CTDNA) was purchased from Aldrich and was purified as described by Muller and C r o t h e r ~ . It ~ ~was then dissolved at 0.01-0.8 mg/mL in a 0.01 M Tris-HC1 buffer adjusted to pH = 7.2 containing 0.002-0.2 M KC1 and 0.001 M EDTA. Glass-double-distilled water was used throughout. After that each DNAsample was fdtered through a 0.22-pm Millipore fdter and directly filled into a cleaned dust-free dialysis cell. The temperature of the cell was controlled to be constant at T = 20 f 0.05 OC. The dialysis itself was performed against 500 mL of several times filtered buffer containing 0.001 M EDTA, KC1, and 0-4.6 lo4 M ethidium bromide (Sigma). The purity of the dye was determined using the method described by K r e i ~ h m a n .A~ ~small amount of impurity (-4%) was removed by recrystallization of the dye from methanol. After reaching the dialysis equilibrium, which was checked spectrophotometrically,the DNA samples were filled directly into the UV absorbance and light-scattering cells, respectively. Each cell was previously thoroughly cleaned and rinsed with dust-free buffer. The UV cells were immediately used to determine the exact DNA concentration, CDNA, by using an extinction coefficient of 6600 M-l at X = 260 nm, based on nucleotide phosphate. The amount of EBr added to a DNA solution was determined from the optical density at the isobestic point (A = 510 nm) of the free and bound dye using e = 41 10 M-I. Details will be given later. The light scattering cells were stored at 5 OC in a dark room and used always within 1 week. No significant changes in the DNA dye properties were observed within this relatively long time. spectrophotometricMeam"& The absorption spectra were recorded on a Perkin-Elmer and a Hitachi spectrophotometerin a 1-cm cell, with the temperature regulated at T = 20 OC. Readings on the absorbance of solutions containing DNA and dye were made with reference to a blank containing only DNA of the same concentration. This cancels out the effect of light scattering due to the macromolecular phase. Solutions of free ethidium bromide were found to follow Beer's law over the whole range of concentrations used (up to 4.6 X lo-" M), and there was no evidence of any adsorption of the dye or its complexes with the DNA onto the surfaces of the UV and light-scattering cells. At 480 and 510 nm the molar extinction coefficients of free EBr were found to be 5600 and 41 10 M-l. Light Scattering Apparatus. The static and dynamic measurements were simultaneously performed with an ALV-3000 spectrophotometer. Two different laser light sources (both Spectra-Physics) were employed, a He-Ne laser operating at 632.8 nm and an argon laser operating at 363.8 nm. Together these gave access to a range of q2 values extending from 0.12 X 1Oloto 20 X 1OO ' where q2 is the square of the wave vector. It should be pointed out that an interference filter, calibrated for the wavelength of the incident beam, was placed in front of the photomultiplier for both lasers. This makes sure that all undesired light, such as room and fluorescence light, rised from the illumination of EBr with 363.8 nm, was filtered out. The efficiency of the filtering was nearly 100% because (1) EBr fluoresces at substantially larger wavelengths than the 363.8-nm exciting light and (2) the intensity of the fluorescent light induced at this wavelength is rather small. For X = 632.8 nm, there is no detectable fluorescence at all. The correlator (1024 channels plus optional delay) was the same as described previou~ly.~ The dust discrimination level was always set to several times the mean count rate to prevent biasing the data. To obtain refractive index matching and temperature control, the scattering cell (2" selica tube) was placed in a temperature-controlled Decalin bath. The measurements were performed at T = 20 f 0.02 OC, and the angular positions were changed in the range 15-150°. Static Light Scattering. First, the time-averaged scattering intensity, I(q), corrected for the scattering from the pure buffer + dye (if present), was measured as a function of the scattering angle, 8,at five different DNA-concentrations for each ionic
TABLE I: Refractive Index Incrementa for CT-DNA from Our Experiments and the Literature dnldcl, in L/g at Cvrr/M
0.002 0.02 0.20
0.20 0.20
author this work this work this work Eisenberg*O Kra~na'~
various wavelengths, X 546.lhm 632.8/nm 0.182 0.168 0.165 0.180 0.168 0.164 0.178 0.166 0.164 0.165-0.168 0.164 0.166
363.81nm
strength. Second, the Rayleigh ratio, R(q), was calculated from I ( q ) , which for unpolarized incident light is given by where q = (4xn&) sin (6/2), V the scattering volume, r the distance from that volume to the detector, and Io the intensity of the incident beam. n,, is the index of refraction of the solvent (buffer added dye), and X, the wavelength of the laser in vacuum. Third, the scattering data were analyzed on a Peacock/AT computer. Since DNA molecules are polyelectrolytes, this analysis cannot be performed in the conventional way by using a Zimm plot.31 Instead, we have to use a more general scattering formula, which was recently proposed by G r e ~ c h n e r .That ~ ~ is
+
(3A3C2) - ... (2) with (3) Here M, is the weight average molar mass, (S2), is the mean square-radius of gyration, and A2 and A3 are the second and third osmotic virial coefficients, respectively. rl and r2are parameters that characterize the molecular structure, N A is Avogadro's number, C is the DNA concentration in g/cm3, and dn/dcl, is the refractive index increment at constant chemical potential, p . We must point out that eq 2 is derived for a two-component system. According to ref 33 it is, however, still valid when a salt and a dye are present, provided the sample solution is dialyzed to equilibrium with the solvent containing salt and dye and the quantity dn/dc is determined between these dialyzed solutions. Here, this requirement is fulfilled. Let us also say some words about the molar mass, M,. M, is very sensitive to the refractive index increment, dn/dcl,, as well as to the values used for the polymer concentration, C. In particular, the determination of M, is a problem when dye is added to a solution. To obtain the right molar mass, which is the sum of the DNA skeleton molar mass plus the mass of the side-bound dye molecules, we have to calculate C as the sum C D N =~ CDN + Here, CDNA is the DNA skeleton concentration, and is the concentration of the total bound dye at CDNA, both in g/cm3. CDNA is known from the solution preparation and 'c", from the dye binding experiments (Scatchard plots). Additionally, we have to calculate the refractive index increment in a way that
'G.
'&
where nDNA,D and &ffer,D are the refractive indexes of the DNA/dye and the buffer/dye solutions when these are dialyzed to equilibrium. That is, in the presence of dye we get one dn/dcl, value for each DNA and salt concentration, while in the absence of dye dn/dcl, is independent of CDNA but dependent on C,. Values of dn/dc(, obtained in the absence of dye at various wavelengths, A, and salt concentrations, C,, are listed in Table I. The corresponding refractive indexes were measured at T = 20 f 0.1 OC in a Brice-Phoenix differential refractometer. The reproducibility in nDNA,D was not very good, but for dnldcl,, the error was within 5%. Table I contains also some literature data of dnldcl,. The agreement with our data is quite well, which
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 6047
Calf Thymus DNA
.?
encourages belief that the accuracy of dn/dcl, is also high enough for the DNA/dye systems. D y ~ m i cLight Scattering. The quantity measured was the intensity-intensity correlation function Gz(T ) . This is given by
+ Blg1(T)I2)
G2(7) = A(l
I
-
5.2
I
0C,
=0.002M
@ Cs
=0.10 M
::
(5)
w
where A is the baseline, B a constant which is a function of the detecting optics, and 1, the sampling time, T = t,, 24, ..., 10242,. lgl(r)l is the normalized electric field autocorrelation function. It is related to the normalized distribution function, G(I'), of the relaxation time constant, I' = DaPpq2, by
2.8 Ig'(r)l = JmG(I') exp(-d') d r
(6)
where Dappis the apparent translational diffusion coefficient at the wave vector q. lg'(T)1 can be expanded in a Taylor series: Ig'(T)l
= exp[(-PT)(l
Figure 1. Determination of At for binding of ethidium bromide to CT-
+ (r - F ) 2 ~ ~ / 2+! ...)I
DNA.
and a polynominal expansion of In lgl(T)l leads to
TABLE II: Equilibrium Binding Parameters for a - D N A with EBr CSIM
(7) At/(103 M-I) fcpPp/(l@ M-I)
with
nD
The zeroth-order moment, f', is related to the z-average value of Dappby = ( 0 , , ) ~ and ~ p2 to the variance by u = p 2 / r 2 . Equation 7 is called the cumulant fit,35which is found to fit the experimental data adequate in the region q(S), I1.0. In the region, q(S), > 1, the correlation function becomes increasingly nonexponential due to contributions from intramolecular DNA motions. Therefore, higher order cumulant fits or other methods of analysis must be used to obtain (O,PP)z.For our experiments in the region q ( S ) , > 1, the multiexponential sampling technique was applied. In this method, G(r) is approximated by a set of logarithmically spaced discrete singleexponentials G(r) = x,P&(I? Fi), where P,are the weighting factors of the 6 functions with x i p i = 1 and I',/l'i-l = constant. We follow then the procedure of Ostrowsky et a1.,36 who have sampled G2(r)in a series of exponentially spaced sample times, i.e., T, exp(r/w,,,)T, e x p ( 2 ~ / ~ , , ) ~ , , Then the Nyquist sampling theorem can be applied along with an interpolation procedure3' to fully reconstruct the correlation function at all values of T , limited only by the band limit w,. Finally, a linear least-squares procedure is used where
r
0.002 3.62 128 0.224
0.01 3.56 102 0.215
0.02 3.60 76.8 0.203
0.10 3.58 41.9 0.192
0.20 3.60 18.6 0.180
which is applicable when the total molar concentration of DNA nucleotides, TCDNA, is in excess over dye. Kappis the apparent dye binding constant, and TnDis the saturation number of dye molecules bound per nucleotide. Typical plots of l / ( F ~ D tnpp) vs 1/ T C ~ N Ashows Figure 1. Since these plots are linear for all ionic strengths at constant pH, linear regression is used to calculate ABand Tn&,pp. The values obtained for Ac are listed in Table 11. They agree well with those previously obtained by Yielding et al.39 Third, KBpp and TnDwere determined from the Scatchard" equation
T8D/FCD = Ka~p(~nD - T8D) (10) where T 8 D is the ratio of bound dye to total nucleotide concentration, i.e., = 'CD/~CDNA, and FCDis the free dye concentration, Le., FCD= TCD- BC,. According to this treatment, a plot of T8D/FCD vs T 8 D should yield a straight line of gradient K, , with the intercept on the T81,axis equal to TnD. This is, however, correct only if the binding process involves no more than a single type of DNA site, or binding at one site does not affect the interaction at neighboring sites. A view on Figure 2, on the other hand, shows at least two different modes M N of binding at each K+ concentration. Furthermore, there is a significant decrease of 'nD with ionic strength, indicating a strong C(G2(7)- Cui exp(-I'ir))z (8) i 1- I competition between dye and cation binding. In the following, we use therefore only those K, and TnDvalues that are obtained is minimized. The values of I' ((0, }J obtained from the above from the nearly linear region each isotherm. These values are analysis were compared to the resuK obtained from the secondsummarized in Table 11. They are in moderately good agreement and third-order cumulant fits. It was found that all Dappvalues with t h w of Yielding,39who obtained Kapp= 18.7 X 104 M-'and were within 2 4 %of each other for q(Sz)I1.0, but for q(S,) TnD = 0.19 under conditions pH = 7.5, I = 0.20 M , and T = 20 > 1 the agreement was only within 10%where the multiexpoOC. nential analysis gives a much better fit to the experimental data It should be noted that we have also performed some temof G2(r) than the cumulant analysis. perature experiments. That is, we have raised stepwise the temResults and Discussion perature from 20 to 40 O C . The result is that the values of TnD are essentially the same for each K+ concentration as those deEBr Binding. The binding studies of ethidium bromide were termined for T = 20 "C, while the values of Kappdecreases with done as follows. First, the absorbances of free dye and DNA T. This indicates that the ionic strength has a more profound dye solutions were measured at T = 20 OC. This gives the difinfluence on the competition between dye and cation binding than ference in absorbance between free and bound dye solutions, AA, and the apparent molar extinction coefficient e,,,,, = ADNA+D/~CD, temperature. Static Light-Scattering Results. Table III contains the weight where ADNA+D is the DNA + dye solution absorbance and 'CD average molecular masses, M,,the z-average radius of gyration, the total dye concentration. Second, the molar concentration of ( S ) z and , the second virial coefficient, Az, of calf thymus DNA the dye bound to DNA, BCD,is calculated from BCD= AA/At, both with and without EBr for various KCl concentrations at T where Ac = FtD - be^ and FtDand B~~ are the molar extinction = 20 "C. In the absence of EBr, the average value of M, is M, coeMicients of free and bound dye. To determine At, we have used 6.0 X lo6 Da. This M, value is somewhat smaller than that the given by the supplier, which is M, = 8.9 X lo6 Da. Likely, the 1 / ( F e ~- %pp) = 1/At + 1 /(Tn&appAtTcDNA) (9) high molecular mass fractions of the DNA sample are separated
-
...
3
+
-
6048 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992
Nordmeier
TABLE III: Physicochemical Quantities Obtained by Static Light Scattering CT-DNA
-
CT-DNA
A Y in41 La2 L",
C,/M 0.002 0.01 0.02 0.10 0.20
M, X 10"/Da
(S),/nm
5.8 6.0 5.9 6.2 6.0
358 312 286 240 218
X lo4
M. b T C=~ 2.0
OTC~ = 0.5
(cm3 mol/g2) 24.8 14.0 12.2 6.7 5.6
X
lo4 M. c T C=~3.3
M, X 10d/Da 7.0 6.9 6.8 6.6 6.5 X
lo4 M. dTCD = 4.6
142 135 122 115
1.51 1.58 1.75 1.86
a T C=~0.5 X lo4 M. "CD
2.0
X
565 485 246 189
lo4 M. "CD = 3.3
CT-DNA
1.41 1.49 1.67 1.80 X
lo4 M. dTCD = 4.6
17.6" 11.5 9.4 6.0 4.8
152 144 128 119 X
14.9b 10.2 8.3 5.5 4.5
13.Y 9.3 7.8 5.1 4.2
12.3d 8.8 7.3 4.9 3.9
lo4 M.
TABLE I V Physicochemical Quantities Obtained by Dymmic Light Scattering CT-DNA
0.01 0.02 0.10 0.20
A2 X l@/(Cm3 mol/g2)
(S),/nm 365 318 292 246 222 X
+ EBr
+ EBr
464 382 22 1 162
412 354 203 148
374 330 188 139
353 306 180 127
lo4 M.
I 3o
-t
26 a
.
,o 2 2
-
c an 18
1L
10
I
0 ' 0.5
1.5
2.5
6 Figure 3. Plots of KCDNA+D/RI,,O versus centrations, TCD.
2 0.02 0.06 0.10 0.14 0.18 0.22
% Figure 2. Scatchard plots of EBr binding to CT-DNA at T = 20 OC.
out during the purification (filtration) procedure. This hypothesis is supported by viscosity measurements at C, = 0.02 M,which gave an intrinsic viscosity of [ q ] = 36.2cm3/g. According to Spatz and Crothers:' who have found that M,/Da = 3.82 X 104([v]/(cm3/g))'.4 (11) the following results:
M, = 5.6
lo6 Da In the presence of EBr, M, decreases with increasing salt concentration. This is clear because we have just before found that the maximum number of bound dye molecules per nucleotide, T?tD, is highest when C, is smallest. It should be noted that M, and (S),refer to infiite DNA dye dilution. Both quantities depend therefore not on the dye concentration used and the ratio (Mw,DNA+D - M w , D N A ) / ( N D N A M w , D ) is within the experimental error identical with the saturation value TnD. The second virial coefficient, A*, is, on the other hand, given by half the slope of the K C D N A + D / R vs CDNA+D curve (see Figure 3) at zero wave vector. It describes the intermolecular thermodynamic interactions between two segments of different DNA molecules, and A2 depends therefore very sensibly both on the solvent properties, e.g., ionic strength, pH value, and viscosity, and on the actual physical state of the segments, Le., whether these are charged or uncharged.
+
X
I
I
1
3.5 L.5 5.5 x 1 0 4 /(g/cm3 1 at various dye con-
From Table I11 it is seen that A2 decreases with both C, and TCD. This is probably due to charge-shieldingeffects, which become larger at higher ionic strength. A quantitative understanding of A? is complicated by coupled charge and intercalation effects; we defer detailed analysis to a later paper. Dynamic Iigbt-Scatteriug ResulQ. The translational diffusion coefficients, Dz,o, extrapolated to CDNA+D = 0 g/L, the corresponding hydrodynamic Stokes radii, Rh,and the second hydrodynamic virial coefficients, kD, obtained for calf thymus DNA by dynamic light scattering are listed in Table IV. The results are consistent with thwe discussed just before. According to eq 14, DZpis inverse proportional to the DNA contour length, L. This increases with increasing degree of intercalation and thus Dz,o decreases as EBr is added. However, L is defined as L = ( M D N A + D / m a r where M is the average effective molar mass and the average length of a DNA subunit after intercalation. In detail, the following holds: if = W+ + WDI~ W = w B p M B p + w&D with = (NDNAMBP)/MDNA+D WD = ( ' ~ D N D N A M D ) / M D N A + D That is, L is proportional to M D N A + D and Dr,Ois inversely proportional to the DNA molar mass. This implies that the decrease of D,,o with TCDcan be attributed both to the increase in the DNA length and alternatively to the rise in MDNA+D. However, it is also seen that D,,o and Rhremain unaffected by the actual dye concentration, TCD. The reason is that Dr,Oand WBP
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 6049
Calf Thymus DNA
TABLE M: Dependewe of the Number of Interdated EBr Molecules per Nucleotide, Inm 011 the Salt Coaccatrrtioa, C,
TABLE V: Dependence of the Persistence kngth, I , rad the Contour h g t h , LDNA+m on the Salt Concenhrtion, C, CT-DNA CT-DNA + EBr
Cs/M
l;/nm
0.002 0.01 0.02 0.10 0.20
l,b/nm
LDNA+D/nm
1,lnm
136 98 82 59 50
3646 3602 3583 3538 3522
121 91 76 54 44
142 104 86 59 48
Cs/M
I nDSR
where kf,, is the frictional coefficient at 0 conditions, N A is Avogadro's number, and Vh and 3 are the hydrodynamic and the partial specific volumes of the DNA in solution. In most cases, B is by orders of magnitude smaller than 2A2Mwand may be therefore neglected. That is, kD is proportional to A2, and it is thus not astonishing that kD behaves physically like A2, e.g., that kDdepends on TCD.Some values of keo and Vhwill be discussed later in this paper. Indiatiam of DNA Elongation. The conformation of a DNA molecule in solution can be well characterized by the Kratkypersistence length, 1, which was related in straightforward fashion to the elastic properties of a stiff coil, or a bending rod, subject to Brownian motion. A rather considerabledependence of I , on the ionic strength has been claimed in the past. We therefore would like to investigate the extent to which dye binding, or intercalation, produces additional stiffening. To obtain numerical values for I,, we use the equations
6L
~2
1: +2--
(1 - exp(-L/l,))
~4121;
~3
(13)
first derived by Benoit and Dotyts, and
(i)+
D,,o = %[In
0.1666(
6) + (311 -1
(14)
first derived by H e a r ~ t , ~on9the ~ ~assumption that both equations describe the same wormlike chain model. L is the contour length of the polymer, a the monomer length, and d the monomer diameter. For a DNA duplex, one has u = 0.34 nm, d = 2 nm, and L = NDNAu, where N D N A is the average number of DNA monomers in a chain of length L. In the absence of EBr, N D N A is identical with NDNA = Mw,DNA/MBp, where MBpis the average molar mass of a base pair. If we adopt MBp= 660 Da, one has NDNA 9090 and L 3090 nm. That is, all parameters of eqs 13 and 14 are known except l,, which can be easily calculated by bisection. The results are summarized in Table V. It is seen that the 1, values derived by eq 13 are nearly identical with those calculated by eq 14, suggesting that the above-stated hypothesis of model consistence is reasonable. In the presence of EBr, the DNA chain is elongated due to intercalation and L is no longer known. That is, now we have two fit parameters, L and 1,. They are obtained by solving eqs 13 and 14 simultaneously. A summary of the results contains Table V. Two effects are seen: (1) LDNA+D, the contour length with dye, is always larger than LDNA, the contour length without dye; (2) LDNA+D increases as C, is decreased. This may be explained as follows. The intercalation of one EBr molecule elongates the DNA contour length about a certain length 11, while L is not changed at all if the EBr molecule binds peripheral to the DNA skeleton. The average number of intercalated dye molecules per nucleotide, InD, is thus given by
-
-
InD
=
[LDNA+D
b
SRfi/%b
'II
~2
I
wfi/%b
Rh refer like Mw and (S),to the saturation state of dye binding, while kD does not. Irreversible thermodynamic shows, that the virial coefficients, kD and A2, are related bf2
1:
"
21%" nD
"Equation 13. bEquation 14.
-( =~ -2- -) ~21,
I
- LDNAIIC,/(NDNAII)
0.002 0.226 100 0.180 80 0.210 94
(15)
=:
0.01 0.209 97 0.166 77 0.182 85
0.02 0.201 99 0.159 78 0.165 81
0.10 0.182 95 0.146 76 0.141 73
0.20 0.176 98 0.140 78 0.112 62
0.27 nm. bll = 0.34 nm.
Hogan4 et al. have found by transient electric dichroism that EBr lengthens DNA by lI * 0.27 nm upon intercalation. However, a lengthening by one base-pair length (1, = 0.34 nm) is also discussed?' We think therefore that it is the best to work with both l1values. A summary of the results thus obtained gives Table VI. If we adopt l1= 0.27 nm, we find that InD is nearly identical with TnD,Le., the procentual fraction of intercalated EBr molecules, fr, is in the order of 100%. For lI = 0.34 nm, fr becomes significantly smaller, i.e.,fr = 80%. That is, fr is independent on C, and larger than 50% in both cases. This indicates that intercalation is the stronger mode of dye binding. However, it should be pointed out that InD refers to saturation and that besides this statefr may take on much smaller values. Next, we consider the persistence length, I,. Table V shows that 1, becomes smaller as C, is raised. This is clear due to a stronger charge shielding between neighbored DNA-segments at high ionic strength's. Surprisingly, is smaller in the presence than in the absence of dye, suggestmg that dye binding or intercalation lowers the intrinsic resistance of CT-DNA against bending motions. This may be explained as follows: Dye binding by intercalation involves a chain lengthening and raises the nonelectrostatic stress. Both intercalated and side-bound dyes neutralize, on the other hand, a certain part of the DNA charge. This reduces the electrostatic stress and it also lowers the concentration stress by causing the release of territorially bound cations (K+ and dye) into the bulk solution. Now it seems, that the stress reduction by neutralization is somewhat stronger than the stress increase caused by intercalation. However, it is not expected that this holds at general. Near the 0 state, i.e., at salt concentrations in the order of 2-5 M, electrostatic interactions are negligible and nonelectrostatic interactions should become dominant for chain stiffing in a way that lp,DNA+D is larger than lp,DNA, provided intercalation takes place at such high ionic strengths. We defer this problem to a later paper. Madog's Persistence Length and the Sliding Rod Model. The wormlike chain is a useful and fruitful model to characterize the conformational properties of semiflexible DNA molecules. However, it should be noted that there are a number of other interesting models which may be applied alternatively. Two of them, the sliding rod modelz6and Manning's persistence length model: shall be inspected in some detail here. According to the sliding rod model, a polymer chain consists of SRNbonds, each of length SRu,so that its contour length is L = SRNsRu. Chain sequences of up to SRn bonds (base pairs) behave as rigid rods, and larger sequences follow Gaussian statistics. That is, when SRn = SRN,the polymer is a rod, and when SRnis very small, it is a Gaussian coil. The mean-square radius of gyration, (Sz),, of a sliding rod is given by
!,
(sq, = (~2/12)(2j-- 2j-3
+j-4)
(16)
and the translational diffusion coefficient at infinite dilution by 4.0
=
(k~T/3?rV&) In
(
f6 - f + (8/3~)'/~(2f-'/~ -3
)
( L ) (17) f i s SRn/SRN with the limits SRN' S f S 1, where at the limitf
6050 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992
-.1L
TABLE VII: Parameters Tlut Refer to the Sliding Rod Model CT-DNA CT-DNA + EBr CSIM '"f SRb.lnma SRL/nm SRn SRb.lnma
0.002 0.081 737 251 12 3740 630 0.01 0.061 558 190 3654 489 16 0.02 0.052 468 159 19 3600 418 0.10 0.036 329 112 28 3526 303 0.20 0.030 272 92 33 3436 248 = X 0.34 nm. bsRN= TNDNa(l+ b$R)/SRn.
214 166 142 103 84
Nordmeier u)
N
18
22 25 34 40
. 1
5 -.
0
E
C T - DNA
12
X
a m
0" 10
El80
-a
1LO
8 10 0
60 6 20
0.7
0.8
0.9 1.0
1.1 1.2 X In"
mC, = 0.002M
L
0 C, = 0.01 M
Figure 4. Plots of lpversus X in the presence and in the absence of dye.
A
C, = 0.02 M C, = 0.10 M c, = a20 M
= 1, eq 17 converts to the familiar formula for a rigid rod. That is, we have again a system of two equations with two unknown parameters, L andf. These can be easily determined by iteration. If we adopt that SRais 0.34 nm, we obtain the data listed in Table VII. It is seen that SRLDNA+o and are of the same order as LDNA+D and InD,estimated by the wormlike chain model. However, sRfidecreases continually from 94 to 62%,while wfi is a constant over the whole range of C, = 0.002-0.20 M. Thus,fi depends on the model used and further analysis is necessary to decide which model is the best one. A second interesting theory is that derived by Manning for the persistence length, I,. The central formula of this theorys is
11, 16 18 20 q2 / (lolo cm-* 1 Figure 5. Rouse-Zimm plots for CT-DNAat T = 20 O C .
I, = + ( I 2 / l 2 6 ) ~ ' [ 2-t 1 + In ( ~ w / C s+) In ( ~ b ) ](18) Here Ip,o is the contribution to I originating from the nonelectrostatic free energy Ago of ben&ng through the small angle a, Le., = Ag021/(RTa2). 5 is the charge density parameter. It is given by t = e2/4mokBTb,where e is the electronic charge, c the dielectric constant of the solvent (H20), and b the average spacing between neighbored DNA skeleton charges. d," is the local salt concentration at the DNA surface. For a 1:l salt of small concentration, approximately it holds that Gw 24.3. (tb3)-'/NA.The central parameter of eq 18 is 1. It describes the lowest length possible of a DNA segment that retains rigid mechanical rodlike properties over the whole range of ionic strengths. To prove the existence of such a parameter I, we introduce the quantity X = ('/126t)[2t- 1 + In (CW/Cs)+ In ( K b ) ] . Equation 18 can then be rewritten as I, = I PX,where a plot of I, versus X should give a straight line of%ope I*, provided I exists. Figure 4 shows the results obtained. In the absence of dye, the least-squares fit gives I = -303.9 nm and 1 = 19.3 nm, where for I, the average of NP I, oand SRIp was used. These data agree sufficiently good with those of Manning, who has found that = -317.1 nm and I = 20.4 nm. In the presence of dye, b and also t and CF depend on the actual degree of intercalation and thus on C,. Taking into account that (1) one DNA base pair contains two phosphate groups and (2) one intercalated EBr molecule neutralizes one DNA phosphate charge, one has b = LDNA+D/ - ' n f l ~ ~ ~For ) . the wormlike chain this gives = -205.9 nm and I = 18.4 nm, while in the case of the sliding rod model IPp = -356 nm and I = 22.5 nm. The most probable values of and I are obtained by averaging over both models. -This gives the dashetline of Figure 4, which corresponds with = -245.9 nm and I = 19.5 nm. That is, 1 is independent whether
dye is present or not, while-fp,o is significantly larger when dye is present. In other words, I is a universal constant, while is not. To see whether the numerical values of are physically reasonable, let us translate them into an equivalent free energy, Ag,,. At T = 20 OC and with f with 19.5 nm, we have Ago = -4.6 kcal without dye and Ago = -3.7 kcal with dye for an angle a of 1 rad. Since a segment of length 1 contains nearly 57 base pairs, these free energies correspond to more -81 or -65 cal/mol of base pair. An increased entropy of base motion when the DNA is locally bent may be therefore easily imagined as a possible source of these free energies. Now it seems, that the local base pair motions (base breathing) are lower dominant in the intercalated DNA state. This is probably due to the lower intrinsic stiffness when dye molecules are stacked between the base pairs. That is, in summary we can state (1) 18 and the experiment are consistent and (2) our results for land are physically reasonable. A;llgclbu Jkpedme of D , The apparent diffusion coefficient, Dapp,Le., the reduced first cumulant I'/q2, shows a significant dependence on the scattering angle, 8.With respect to u = ( S ) A four regions can be distinguished,48i.e., (1) u 1, and (4) u >> 1. We remember that q = (4~n&) sin (0/2) and (S), is the radius of gyration. In the limit of very small wave vectors q (u 0.04,fi is found to be always larger than 0.5. This suggests that except for the small region near c"pBL = 0, intercalation is the dominant type of EBr binding to CTDNA. Second, at the saturation state, which is given by = ylnf,,fi takes on values which lie between 0.9 and 1. This indicates that 11, the length by which a single EBr molecule lengthens a CT-DNA molecule due to intercalation, is significantly smaller than lBp,the length of a DNA base pair. That is, a value of lI in the order of 0.27 nm seems to be more reasonable than II = 0.34 nm. Third, it is seen that at a given value of "@,,A incream as C, is raised. A high salt concentration is therefore hindering for outside binding and promoting for intercalation. An explanation for this effect cannot be given yet. The probable reason is a competition between outside bound dye molecules and territorial bound counterions. Both types of ligands interact by Coulombic forces with the DNA phosphate groups, where the attraction of a K+ion may be somewhat stronger due to its smaller size and its higher mobility than that of a EBr molecule.
Conclusions On the basis of absorption and light-scattering experiments we have shown that the dye, ethidium bromide, binds to calf thymus DNA. The binding seemsto be saturated when one dye molecule is bound for every four or five nucleotides. At constant temperature and pH the degree of binding decreases as the salt concentration is raised. The binding isotherms and the changes in the light-scattering results indicate two modes of dye-DNA interactions. The weaker mode probably represents electrostatic outside binding between the dye cation and the ionized DNA phosphate groups. The stronger mode leading an increase of the DNA contour length can be interpreted as intercalation. The degree of intercalated dye molecules per nucleotide depends, however, sensitive on the model used for its calculation. Values in the order of 60-100% of the degree of totally bound dye molecules per nucleotide are found. With slight modifications, the effects of added salt on dye binding, including both intercalation and outside binding can be analyzed by the polyelectrolyte theory, as elegantly described by Manning et al.7-9 The results are (1) each intercalated EBr molecule lengthens the DNA about 0.27 nm, and (2) outside binding becomes dominant (if at all) at low salt concentrations. In any case, there are a number of open questions such as: ( 1) How well (tightly, rapidly) does a dye bind? (2) Once bound, how efficiently and by what mechanism does it influence DNA structure and function? Much more work on the theory and experiment of ligand binding to large molecules like CT-DNA is needed. It is therefore hoped that the ideas and methods used here will be further developed and applied to other systems of more complicated composition.
Here y and Y are scaling parameters which have a positive sign. The analysis is then as follows: Since the process of dye binding is a superposition of intercalation and outside binding, the weighted sum of eqs 29 and 30 should give a good fit for WeL/[L] vs WL. In detail, we have to weight eq 30 byfi and eq 29 by [l -A]. To make sure that = leL,aoOL,a,additionally we have to replace *eL in eq 30 byf,cxPBLand OeLin eq 29 by [l -fileXPeL. Equation 32 contains then only two adjustable parameters, 7 and Y, which can be easily determined by a least-squares method. In a first fit, we found that v is in the order of 0.33 f 5% for and a second fit was all C,. We have therefore set Y = performed to give the best value for y. The results thus obtained for y are summarized in Table XII. A plot of the best-fit curve "PeL/[L] vs "PBL is shown in Figure 8. Over the whole range of the theoretical curve fits the experimental data in a fantastically good manner, suggesting that our analysis is indeed quite successful. This holds for all C, used Acknowledgment. I thank Prof. M. D. Lechner for provision here, where the agreement between theory and experiment beof excellent facilities and Dip1.-Chem. W. Bare for performing comes slightly better with increasing C,. which is shown in Figure some of the absorption measurements included in Figures 1 and Instructive is also a plot offi vs 2. This research was supported in part by the Fonds der Chem9. Three observations are made. First, in the experimentally
+
J. Phys. Chem. 1992, 96,6055-6061 ischen Industrie and in part by the BMFT. Registry No. EBr, 1239-45-8.
References a d Notes (1) Porumb, H. Prog. Biophys. Mol. Biol. 1978, 34, 175. (2) Record, M. T.; Anderson, C. F.; Lohman, T. M. Q. Rev. Biophys. 1978, 11, 103. (3) Langley, K. H.; Patel, M. R.; Fournier, M. J. Loser Light Scattering Studies of DNA-Bleomycin Binding, Elsevier Biomedical Res: Amsterdam, 1982; p 37. (4) Waring, M. J. Biochim. Biophys. Acta 1966, 114, 234. (5) Krugh, T. R.; Wittlin, F. N.; Cramer, S . P. Biopolymers 1975,14, 197. (6) Winkle, S.A.; Rostnberg, L. S.;Krugh,T. R. Nucleic Acids Res. 1982, 10, 8211. (7) Manning, G. S . J. Phys. Chem. 1981, 85, 870. (8) Manning, G. S. Q.Rev. Biophys. 1978, 11, 179. (9) Friedman, R. A. G.; Manning, G. S . Biopolymers 1984, 23, 2671. (10) Tomchick, R.; Mandel, H. G. J . Gen. Microbiol. 1964. 36. 225. (11) Elliott. W. H. Biochem. J . 1963. 86. 652. ,--, --(12) Waring, M;J.J. Mol. Biol. 1965, 13, 269. (13) Le Pecq, H. B.; Paoletti, C. J . Mol. Biol. 1967, 27, 87. (14) Crawford, L. V.; Waring, M. J. J . Mol. Biol. 1967, 25, 23. (15) Le P m . J. B.: Yot. P.: Paoletti. C. Comor. Rend. 1964.. 259.. 1786. (l6j Strauss:'U. P.i Siegel,'A. J. Phjs. Chem. 1963, 67, 2683. (17) Wilson, W. D.; Lopp, I. G. Biopolymers 1979, 18, 3025. (18) Wilson, W. D.; Krishnamoorthy, C. R.; Wang, Y. H.; Smith, J. C. Biopolymers 1985, 24, 1941. (19) Chandrasekaran, S.;Jones, R. L.; Wilson, W. D. Biopolymers 1985, 24, 1963. (20) Borochov, N.; Eisenberg, H. Biopolymers 1984,23, 1757. (21) Nordmeier, E.; Dauwe, W. Polym. J . 1991, 23, 1297. (22) Pecora, R. Annu. Rev. Biophys. Bioeng. 1972,1, 257. (23) Maeda. T.; Fujime, S . Macromolecules 1985, 18, 2430. (24) Fujime, S.;Takasaki-Ohsita, M.; Maeda, T. Macromolecules 1987, 20, 1292. (25) Benoit, H.; Doty. P. J . Phys. Chem. 1953, 57, 958. (26) Benmouna, M.; Akcasu, 2.;Doud, M. Macromolecules 1980, 13, 1703. (27) Lin, S.C.; Schurr, J. M. Biopolymers 1978, 17, 425. (28) Muller, W.; Crothers, D. M. Eur. J . Biochem. 1975, 54, 267. (29) Kreishman, G. P.; Chan, S. L.; Bauer, W. J. Mol. Biol. 1971,61,45.
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(30) Nordmeier, E.; Lechner, M. D. Polym. J . 1989, 21, 623. (31) Zimm, B. H. J . Chem. Phys. 1948, 16, 1099. (32) Greschner, G. Maxwellgleichungen, Hilthig & Wepf Heidelberg, 1981; Band 2. (33) Nagasawa, M.; Takahashi, A. Light Scattering from Polymer Solutions; H u g h , M., Ed.; Academic Press: New York, 1972. (34) Krasna, A. I. Biopolymers 1970, 9, 1029. (35) Koppel, D. E. J . Chem. Phys. 1972, 57, 4814. (36) Ostrowsky, N.; Sornetle, D.; Parker, P.; Pike, E. R. Opt. Acta 1981, 28, 1059. (37) McWhinter, J. G.; Pike, E. R. J. Phys. A: Math Gen. 1978, 11, 1729. (38) Li, H.; Crothers, D. M. J . Mol. Biol. 1969, 39, 461. (39) Yielding, L. W.; Yielding, K. L.; Donoghue, J. E. Biopolymers 1984, 23, 83. (40) Scatchard, G. Ann. N.Y. Acad. Sei. 1949, 51, 660. (41) Spatz, H. Ch.; Crothers, D. M. J . Mol. Biol. 1969, 42, 191. (42) Yamakawa, H. Modern Theory of Polymer Solutions, Harper and Row: New York, 1971. (43) Kratky, 0.;P o d , G. Recl. Trav. Chim. Puys-Bas 1949,68, 1106. (44) Hearst, J. E.; Stockmayer, W. H. J . Chem. Phys. 1962, 37, 1425. (45) Hearst, J. E. J . Chem. Phys. 1963, 38, 1062. (46) Hogan, M. E.; Dattagupta, N.; Crothers, D. M. Biochemistry 1979, 18, 280. (47) Bustamante, C.; Stigter, D. Biopolymers 1984, 23, 629. (48) Burchard, W.; Patterson, G. D. Adv. Polym. Sci. 1983, 48, 1. (49) Rouse, P. E. J . Chem. Phys. 1953, 21, 1272. (50) Zimm, B. H. J . Chem. Phys. 1956, 24, 269. (51) Burchard, W.; Schmidt, M.; Stockmayer, W. H. Macromolecules 1980, 13, 580. (52) Wilcoxon, J.; Schurr, J. M. Biopolymers 1983, 22, 849. (53) Schurr, J. M. J . Chem. Phys. 1981, 74, 1428. (54) Schurr, J. M. Biopolymers 1983, 22, 3007. (55) Wilcoxon, J. H.; Schurr, J. M. In Biochemical Applications of Loser Light Scattering, Elsevier Biomedical Press: Amsterdam, 1982; pp 21-36. (56) Horowitz, D. S.;Wang, J. C. J. Mol. Biol. 1984, 173, 75. (57) Wilcoxon, J.; Schurr, J. M. Biopolymers 1983, 22, 2273. (58) Manning, G. M. Biopolymers 1988, 27, 1529. (59) Nordmeier, E. J . Phys. Chem. 1992, 96, 1493. (60) Burchard, W. Macromolecules 1978, 11, 455. (61) Pecora, R. Dynamic Light Scattering, Plenum Press: New York, 1985. (62) Pyun, C. W.; Fixman, M. J. Chem. Phys. 1964, 41, 937.
Quantum Yields of the Photochromic Equilibrium between Bacteriorhodopsin and Its Bathointermediate K. Femto- and Nanosecond Optoacoustic Spectroscopy M. Rohr? W. Glrtner,* G. Schweitzer, A. R. Holzwarth, and S. E. Braslavsky Max-Planck-Institut f i r Strahlenchemie, Stiftstrasse 34-36, 0-4330 Miilheim a.d. Ruhr, Germany (Received: August 29, 1991; In Final Form: March 25, 1992)
The primary photochemistry of bacteriorhodopsin (BR) was investigated by laser-induced optoacoustic spectroscopy. Excitation of light adapted BR by femtosecond flashes of 585 nm (OS) for the quantum yield of the BR photochemistry which in the literature was controversially discussed as being 0.3 or 0.6.
-
-
Introduction
The intrinsic membrane protein bacteriorhodopsin (BR, ,A, = 570 nm) of Halobacterium halobium converts the energy of absorbed light into electrochemical energy, which is stored in form 'This publication is part of the Ph.D. Thesis of M.Rohr, Heinrich Heine Universitit Dbseldorf and MPI for Strahlenchemie.
of a proton gradient across the cell membrane.' This function of BR as a "light-driven proton pump" represents an alternative energy source and allows phototrophic growth of the bacterium under conditions of low oxygen Essential for this process is the retinal chromophore of BR which is covalently bound to the polypeptide via a protonated Schiffs base formed with lysine residue 216.
0022-3654/92/2096-6055$03.00/00 1992 American Chemical Society
