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Studies of the temperature-dependent conformation and phase separation of polyriboadenylic acid solutions at neutral pH
J. Mol. Biol. (1967) 30, 1737
Studies of the Temperature-dependent Phase Separation of Polyriboadenylic Neutral pH HENRYK
EmmmRot
Conformation and Acid Solutions at
AND GARY FELSENFELD
National Institute of Arthritis and Metabolic Diseases National Institutes of Health Bethesda, Maryland, 20014, U.S.A. (Received 12 June 1967) The conformation of polyriboadenylic acid (poly A) in aqueous solutions at 8 solvent conditions, as a neutral pH has been investigated under “ideal”, function of temperature. The studies were carried out on fractions of well-defined molecular weight obtained by reversible phase separation of the polymer in sodmm chloride solutions more concentrated than 1 M. Under such conditions, poly A is soluble at low and high temperatures, but only partially miscible in a range centered on 35 to 40°C. The extent of the range varies with molecular weight, and polymer and salt concentrations. The upper and lower 0 temperatures for solvents in the range of sodium chloride concentrations from 1 to 1.33 M were derived from the phase diagrams. Light-scattering experiments yielded the molecular weights, radii of gyration and second virial coefficients (AZ) of several fractions at various salt concentratlons. in the temperature range - 2 to 62~4°C. At a fixed salt concentration, d, xranished at two temperatures, the upper and lower 0 temperatures for that solvent. In this way it was possible to obtain values of the radius of gyration at various B temperatures which were unperturbed by solvent effects, thus separatmg long-range solvent-dependent influences on molecular conformation from the influences of short-range interactions due to base stacking. The sedimentation velocity and viscosity behavior of poly A as a function of salt concentration and temperature were also studied. In 1 M-NaCl, both the sedimentation coefiiclent and intrinsic viscosity vary as &P5 at a temperat,ure quite close to the 0 temI”“‘atLlW. The results show that poly A forms a highly extended structure at low temperature but that this structure is rapidly disrupted as the fraction of bases in stacks falls below unity. The observations are consistent with t,he existence of a ~tructllre formed by a non-co-operative process.
1. Introduction The study of preferred conformations and structural transitions in synthetic polo-1111c~lwtit1esis important for a better understanding of the structures and interactions in nat,ura’lly occurring nucleic acids. Polyriboadenylic acid (poly A) has been shown to exist in several characteristic forms in aqueous solutions. Thus, at acid pH, a double-stranded helical form prevails (Fresco & Doty, 1957; Rich, Davies, Crick & Il’atson, l%l), whereas at neutral pH poly A is single stranded and uncl~rgt~~~ a c~lm~acterkt ic temperature-dependent, transition which has been studied in detail by t Permanent address: Weizmann Institute of Science, Rehovoth, Israel 17
2
18
H. EISENBERG
AND
G. FELSENFELD
absorption spectroscopy, circular dichroism and optical rotation (Holcomb & Tinoco, 1965 ; Leng & Felsenfeld, 1966; Brahms, Michelson & Van Holde, 1966 ; Poland, Vournakis & Scheraga, 1966; Applequist & Damle, 1966). Light-scattering, viscosity and sedimentation-velocity studies of poly A at room temperature are consistent with a random coil model (Fresco $ Doty, 1957; Steiner $ Beers, 1957). On the basis of the studies cited above, it is now generally believed that the temperature-dependent optical properties of poly A arise from the tendency of the bases of poly A to “stack” with their planes parallel to one another. The extent of stacking is temperature dependent, but the stacked structure is formed by a non-co-operative process, so that even when a relatively large fraction of the bases is stacked, there are very few long sequences of uninterrupted stacks. The main purpose of this investigation was the study of the conformation of poly A at neutral pH, as a function of temperature, in an effort to relate the temperature dependence of the conformation to the changes in base stacking described above. We expect that poly A will be a flexible macromolecule, even if we assume a fairly high degree of base stacking. The flexibility arises from bond-angle rotations along the macromolecular chain, particularly involving bonds in repeating units with nonstacked bases. A primary consequence, well documented in conformational studies of coiling macromolecules (Flory, 1953), is that over-all polymer dimensions will depend on polymer-solvent interactions as well as local structure and rotations of hindered bonds; in “good” solvents, polymer dimensions are expanded beyond socalled unperturbed dimensions, whereas in “poor” solvents they are compressed below the unperturbed dimensions. The unperturbed dimensions are related to polymer structure and short-range interactions, whereas long-range interactions with solvent procluce either expansion or compression of the macromolecular coils. Excluaeavolume theory (Flory, 1953) states that “ideal” 0 conditions, obtained by suitable choice of solvent or temperature, can be realized in which long-range interactions are effectively compensated. At the Flory 0 temperature, the second virial coefficient A, (in osmotic pressure and light-scattering experiments) vanishes, and molecular dimensions obtained under these conditions represent the required unperturbed dimensions. Excluded-volume theory, originally developed for non-ionic polymers, is generally also applicable to multicomponent polyelectrolyte solutions (Eisenberg & Woodside, 1962). It thus appeared feasible to seek suitable solvent and temperature systems for poly A such that the unperturbed dimensions could be studied as a function of temperature. The most direct method of obtaining information about the distribution of mass in a macromolecular structure is the study of the angular dependence of scattered light, which permits determination of the radius of gyration. If the particles are identical with respect to size and shape, and furthermore of suitable size, then the analysis is straightforward. Not all of these requirements are met in the case of poly A. The material synt’hesizecl by the use of polynucleotide phosphorylase has a broad spectrum of chain lengths. It is thus necessary to obtain a series of fractions with well-defined and sharp chain-length distributions. Our first efforts were therefore directed to the development of fractionation procedures. The discovery reported here of molecular weight-dependent phase transitions in poly A solutions at NaCl concentrations Furthermore, greater than 14 M provides an effective method of fractionation. the phase transition behavior is closely related to the existence of 0 solvent conditions, and can be used to determine them.
CONFORMATION
OF POLYRIBOADENYLIC
ACID
I!)
As it is known (Leng & Felsenfeld, 1966) that the hypochromism of poly A at a given temperature is almost invariant to changes in NaCl concentrat’ion above 0.01 31, it was decided to seek 0 conditions by varying the NaCl concentration, on the reasonable assumption that the extent of stacking would not be affected by this variation provided the temperature was held constant. In this way we have found 0 solvent conditions at several temperatures. Using 0 solvents, we have measured the temperature dependence of the unperturbed radius of gyration of poly A. We have also >t udicd the temperature- and molecular weight-dependence of the intrinsic viscosit> and sedimentation velocity of poly A fractions. We find t,hat in 1 nr-NaCl at the 0 t,empcrature, these parameters vary as MO.‘, as expected for random coils under 0 conditions. These results open the way to a rigorous analysis of conformat8ional behavior of polynucleotides with precise theoretical tools. Our results show that poly A does form a highly extended structure at low t’emperature, where most of the bases are in the stacked conformation. Only a small increase in temperature is necessary to disrupt the structure despite the fact that this involves small changes in the extent of stacking. It will be shown that this behavior is consistent with a non-co-operative model of poly A structure formabion. Our results represent the first direct evidence for a temperature-dependent configurational change in the structure of poly A which can be correlated with its optical properties.
2. Experimental Procedure (a) Ma&i.als
and solutions
Polyadenylic acid (poly A) was a commercial preparation supplied by the Miles Chemical Company, and purified by extraction with water-saturated phenol and dialysis, first against 1.0 M-Nacl, 0.01 a6-sodium phosphate buffer (pH = 7.5), 10d4 M-EDT& then against the same buffer without EDTA. Concentrations were determined spectrophotometrically at room temperature, assuming a molar extinction value of 10,100 at 257mp. as reported by Stevens & Felsenfeld (1964). To transform concentrations C, (equiv./l.) to c (g/ml.), it is necessary to multiply by 0.351 (351 is the equivalent weight of the monomer repeating unit in the Na form). The weight average degree of polymerization 2, of the starting material was 1375, as determined by light scattering, and its median sedimentation coefficient szO measured at 20°C was 11.3 Svedberg units in 1.0 M-NaCl, O.Ol-Msodium phosphate buffer (pH 7.6). The corresponding value of szO,Wwas 12.8. For a typical fractionation procedure, we added (at 0%) 10 ml. 5 M-NaCl with continuous stirring to 200 ml. poly A solution (25 mg/ml., 1.0 M-NaCl, 0.01 M-phosphate buffer. pH 7.5). The solution (~1.2 aa-NaCl) was transferred to a pear-shaped flask immersed in a thermostatic bath accurate to O.l”C. The temperature was raised slowly, with gentle stirring, until the first turbidity appeared. It was further increased slowly by 0.2% and the first fraction was allowed to settle overnight at 15.4%. The supernatant fraction was quickly decanted into a similar cooled flask and re-immersed in the thermostat. The precipitated fraction was dissolved in a small amount of water and dialyzed against repeated changes of 1 M-N&~, 0.01 M-sodium phosphate buffer (pH 7.5). The first fracr IOII contained about 170 mg poly A in 32 ml. solution. Further fractions were collected at 17.1; and 24.O’C (150 and 90 mg, respectively). Finally, 25 ml. 5 M-N&~ were added to the remaining solution and the last fraction (80 mg) collect,ed at 26°C. All solvents and poly A solutions used in this procedure were filtered through HA (0.45 p) Millipore filters before use. Fractions prepared in this fashion were stable in the refrigerator over many months, as established by unchanged light-scattering and sedimentation behavior, although no special precautions were taken to assure the sterility of the solutions. Exposure to temperatures up to 63°C in light-scattering cells, for periods up to 1 hr, did not affect the stability of the solutions.
20
H.
EISENBERG
AND
(b) Phase separation
G. FELSENFELD experiments
For these experiments 1.0 ml. of a poly A solution in 1.0 M-NaCl was introduced into a small test tube sealed with a thermometer with ground-glass joint, such that the thermometer bulb was completely immersed in the liquid. The solution was warmed to the lower precipitation temperature, which was recorded, and then it was further warmed until the upper, dissolution, temperature was reached. The sample was now cooled and the precipitation and dissolution temperatures recorded upon lowering of the temperature. With provision of good shaking, the phase-separation behavior was reversible and the characteristic temperatures were reproducible to within 0+2”C. The onset and disappearance of turbidity were determined visually from the blurring of a background scale. Next the concentration of NaCl was raised by careful repeated addition of 30 ~1. of 5 Ma-NaCl solution, and observation of the appearance of turbidity at each NaCl concentration. Such experiments were repeated on different poly A fractions, at different poly A concentrations. At high salt concentrations (above 1.3 M-NaCl), some irreversible behavior was observed for the lower precipitation temperature. A poly A sample (2, = 7 14) at a concentration of 7.5 X 10T3 equiv./l., in 1.33 M-NaCl, was turbid at - 12°C; uponslow warming, the solution became clear at +2 to 3°C. No precipitation now occurred upon cooling to - 12°C. Upon warming the solution, precipitation now occurred at $9”C, which was taken as the incipient phase-separation temperature. This process could now be repeated indefinitely, provided the precipitate was cooled below 0°C and then slowly warmed to +2 t? 3°C to obtain a clear solution. In all cases in which irreversible or time-dependent phenomena occurred, the incipient separation of the clear solution was taken as the phase-transition point. No such irreversible phenomena were observed at salt concentrations below 1.3 M-NaCl. (c) Light
scattering
eqerirnents
Light-scattering experiments with unpolarized light were performed in the temperature interval from -2°C to 62*4”C, at angles of observation 0 ranging from 30” to 150°, at a wavelength X = 546 mp, with a light-scattering photometer (Wippler & Scheibling, 1954) manufactured by Sofica, Paris. For the evaluation of the light-scattering results the quantity KC,/ARe is required. Here C, is the concentration in equiv./l., AR0 is the reduced intensity of scattering (corrected for solvent contribution) at angle 0 with the incident beam, and K is equal to index increment at constant (an/aC,); 2000 a2n~/h4N,, where (an/aC,), is the refractive chemical potential p of diffusible solutest, no is the refractive index of the medium, h is the wavelength in vacua and N, is Avogadro’s number. We obtain : AR, = (AI,/I,,,,)R,(n,/n,)2
sine/(1
+ cos20)
from the ratio of light scattered at angle t? in excess of solvent, (AI0 = (I-I&) over the [by the absolute Rayleigh ratio light scattered by benzene at 0 = 90” (1s,90) multiplied for benzene, R, = 15.8 x 10u6 cm-l (Coumou, 1960) at 23”C, and correction factors (no/ns)” due to the ratio of refractive indices of medium and calibrating liquid, sin B due to the change in scattering volume with angle, and (1 + cos2 0) due to the use of unpolarized incident light. The final working equation is :
and (2000 n2 ni/PN, RB) = 523 at 23°C. We use as secondary standard a clear glass cylinder calibrated against benzene at 23”C, the scattering of which is not affected by temperature in the range of our investigation. For further details on the experimental procedure, we refer to a recent publication (Cohen & Eisenberg, 1965). t Strictly speaking the refractive increment should be determined at constant pressure P and constant chemical potentials of all diffusible solutes, except the main solvent, water. In practice, for one measures (&L/X’,),, which specifies constant +,zo as well, but relaxes the requirement constant P. The two increments are identical for all practical purposes (Casassa & Eisenberg. 1964).
CONFORMATION
OF POLYRIBOADENYLIC
ACID
21
Buffer dialyzate and poly A solutions were freed of dust by direct filtration under gravit,y into clean dry cylindrical cells (28 mm diam.) through HA Millipore filters (0.45~ pore size). Solutions of poly A of various concentrations were made up by weight, from tht, stock solutions, by diluting with the dialyzate buffers. Concentrations were checked bJ for each ,p~‘t.t rophotometric analysis after light scattering. About 17 ml. were required solut*ion. (d) Refractive ir&x irr( 1‘6t/1111f.9 Refractive index increments were determined interferomet,rically at A = 546 mp at 25°C In an Ammco model B electrophoresis instrument fitted with a special cell (Svensson & Odengrim, 1952) ; (an/&), was found to be 0.164 ml./g, which corresponds to ! ?rt: r-f ‘,, I,. = 0.0576 l./equiv. This result was obtained in the concentration range 7 to 18 mg/ml.. on an unfractionated poly A sample dialyzed extensively against 1.0 M-NaCl, 0.01 RIsodium phosphate buffer (pH 7.5); for both these and the density-increment measurements (see below), final dialysis of the poly A solutions was carried out for 3 to 4 hr at room temperature. sp(-f2ji(-volumes (e) Partial Densities required 2.’ C’ in capillary-neck used m refractive-index M-sodium phosphate increment I f-p: cc 16,= by I c r-‘:CL I+, = 1-$*p)
in the determination of partial specific volumes were determined at, pycnometers of about 7.5 ml. capacity, on the same solutions as increment measurement. The density of the 1.0 M-NaCl, 0.01 buffer (pH 7.5), was found to be 1.03838 g/ml. and the densit) 0.433 ; from this we calculate an apparent partial volume ?* (defined equal to 0.546. (f)
Viscosity measurements
Vincos;lt 1’ measurements were made in the temperature range from 0 to 37% in CannonUbbelohde viscometers with flow times for water of about 300 set at 25’C. No dependence on shear was found in the extreme case of the highest fraction (2, = 1740) at OT, with the use of a Cannon multibulb Ubbelohde shear viscometer, over a tenfold variation in the rate of shear. (g) Sedimentation
velocity measurements
Sedimentation velocity measurements in the Spinco model E ultracentrifuge were undertaken at 7.8, 20 and 32”C, in 1.0 M-NaCl, 0.01 M-sodium phosphate buffer (pH 7.5), at 44.770 rev./min. The instrument was equipped with ultraviolet optics with film recording. Poly A concentrations were of the order of 5 x 10e5 equiv./l. No dependence on concentration of the sedimentation coefficients was observed at these low concentrations. Exposure and development procedures were chosen to give linear dependence of film density upon optical absorbance of the sample in the range of concentrations used. Measurements of film density were made with the Joyce-Loebl microdensitomet,er. Analysis of the integral distribution of sedimentation coefficients at intervals of 10% of the total concentration was carried out after correction for radial dilution. Analysis of photographs showed that the variation in the apparent sedimentation coefficient distribut,ion with time was small even for the smallest molecular weight fraction studied. The + ft’rrt, of diffusion upon the results was therefore considered negligible. Calculations wercb Iberformed using a Honeywell 800 computer and a program written by us. Fitt,mg of the sedimentation coefficient distribution to the average molecular weight, cletermined by light scattering was carried out making use of the equation :
~rh+rt’ a, is the exponent
in s, = K’ Z,‘s,
g, is the fraction, problem value of
weight fraction and s, the sedimentation coefficient of component i in a given and 2, is the weight average degree of polymerization of this fraction. The was solved on the Honeywell 800 computer by fixing l/a,, and calculating the K which gave the least squares best fit value of the calculated values of 2, for
22
H.
EISENBERG
AND
G. FELSENFELD
all four fractions studied. The coefficient l/as was then changed by a fixed increment, and the calculation repeated. The value of l/a* which gave the smallest deviations for the calculated values of 2, was retained. Using this exponent and the appropriate value of K’, the average degrees of polymerization given in Table 1 were computed from the sedimentation coefficient distribution.
3. Results and Discussion (a) Phase separation behavior The phase separation behavior of four poly A fractions, at various salt concentrations, as a function of poly A concentration, is shown in Fig. 1. It is seen that, for each salt concentration, precipitation occurs when the temperature is raised from low temperatures. The precipitates dissolve again when the upper branch of the precipitation curve is reached. Samples of higher molecular weight precipitate at lower temperatures in the lower precipitation branch and dissolve at higher temperatures in the upper branch. From the maxima in the separation temperature concentration plots, it is possible to obtain the critical temperature t,, for phase separation. For a discussion of critical temperatures and their relationship to 8 temperatures, the reader is referred to the book by Flory (1953). Unfortunately, in most of the cases shown in Fig. 1, it was not possible to reach the critical concentration range required for the evaluation of the critical temperatures, because of
100
I
I
I
I
I
I
I
I
(b)
(a)
6
80 -$.EE6Cl
--.--
/40x‘. i!!
m-.-m
--. --Sz+-’
20-g;&o*
2 0 P x E 80e 60-
0
I
I
I
I
I
I
I
I
I 8
I 12
I 16
Cd)
(cl .a/ pos&J d +.+-
I 4
+-*
I 8
o-o-/a *x/o 0-O
--
I 12
I I6
Concentration
0
I 4 (equlv./C
20
x IO31
FIG. 1. Temperatures of phase separation against concentration of poly A; regions of limited miscibility are between upper and lower curves corresponding to same salt concentration. (d) 2,=379. 0, 1.00 M-N&~; +, 1.116 M-NaCl; (a) Z,= 1740; (b) Z,== 1123; (c) 2,=714; 0, 1.226 M-N&~; x, 1.266 M-NaCl; 0, 1.33 M-N&I.
CONFORMATION
cI)
OF POLYRIBOADENYLIC
ACID
2.3
3,2-
0 x 7 l-2
..
2.61
0
15
I 30
I
45
60
z;“*X 102 FIG. 2. Estimated upper and lower critical convolute temper&urea plotted as Tc-l against Cw-1:2; salt concentrations as in Fig. 1.
T, (in degrees Kelvin).
lack of sufficient amounts of the rather expensive fractions. As the curves in Fig. 1 become rather shallow at higher poly A concentrations, critical temperatures were estimated, in most cases in rather arbitrary fashion, to establish the general pattern of the poly A phase diagram. The estimated upper and lower critical consolute temperatures T, (in degrees Kelvin) have been plotted in the usual fashion (Flory, 1953) in Fig. 2, as T,-l against Z,- Ii2 ; they yield linear plots, the intercepts of which, in the limit Z,-+m define the upper and lower 0 temperatures, 0, and O,, for each system. In Fig. 3 we show the estimated values t, (in degrees centigrade) for the various fractions, against NaCl concentration; 0, and 0, are also given in Fig. 3. It is seen that 0, increases and 0, decreases with NaCl concentration. Below a NaCl concentration of O-9 to 0.95 M, phase separation does not occur and 0 conditions cannot be achieved. Above thin NaCl concentration we find two 0 temperat,ures for each system, which enables us in principle to study the behavior of poly A over almost the whole rang” of temperatures accessible in aqueous solutions under 0 conditions. It will be seen below that 0, = 60°C at, 1.0 M-NaCl coincides well with the value obtained from the vanishing of A,; on the other hand, 0, = 22°C at 1.0 M-NaCl and 0, = 5’C at 1.3 M-NaCl are somewhat lower than the corresponding values (26 and 10°C) found from light scattering. This may be due to the difficulty of correct’ly estimating t, for the lower precipitation branch with the limited amount of data available, to the irreversible phenomena observed at high xalt concentrations in the lower branch (see Experimental Procedure), or to the fact that whereas the upper precipitation branch represents a normal amorphous polymersolvent phase transition, the lower branch occurs at a temperature where the polymer
24
H.
EISENBERG
AND
G. FELSENFELD
Fro. 3. Estimated upper and lower critical consolute temperatures againstNaClconcentration; q ,&=379; X, 2,=714; 0, 2,=1123; and lower theta temperatures 8, and eL, from intercepts in Fig. 2.
t,, in degrees centigrade, +, 2,=1740; 0, upper
is fairly highly ordered, leading to a more complex phase-transition behavior. The quantitative aspects of this problem will not be pursued further in view of the limited data available. (b) Light-z;ca/ftri,rg results Light-scattering
data were evaluated in terms of the two equations: W’,/WI
co = 27,-l + 2A, C, + . . .
(1)
[l + (167~%z/3h2) (S2), sin2 (O/2) + . ..]
(2)
and (Zimm, 1948): (KC,JdR),U=,
= 2,-l
where the concentration C, is expressed in equivalents of nucleotides (or moles of phosphorus) per liter, and 2, is the weight average degree of polymerization in units of nucleotides (or moles of phosphorus) per macromolecule; (S2) = Sg is the lightscattering average of the mean square radius of gyration S2, derived independent of any assumption of the shape of the macromolecules, from the ratio of the slope to intercept of equation (2) : &n, s = initial’slope, at C, = 0, of (KC,/AR), versus sin2 (O/2) l/2 intercept, at fl = 0, of (KC,JAR)o=, at C, = 0 1 . 2/3x B [
(3)
For values of this ratio smaller than unity, plots of (KCJAR), against sin2 (8/Z) should be linear, independent of the shape of particles or the distribution of their size,
CONFORMATION
0
OF POLYRIBOADENYLIC
0.2
0.6
0.4
26
ACID
0.8
IO
sin2(tT/2) FIG. 4. A typical result showing the angular dependence of reciprocal scattering function K (?,j AR0 of poly A (2, = 1740) in 1.0 M-Nacl, 0.01 M-sodium phosphate buffer (pH 7.5) at various temperatures.
The concentration
of polymer
is 2.5 x 10y3 equiv./l.
Such plots are shown in Fig. 4 for a single poly A concentrat,ion (2, = 1740) in 1.0 M-Nacl, 0.01 M-sodium phosphate buffer (pH 7.5), at various temperatures, from -2 to 62.4”C. Both slopes and intercepts decrease in value with increasing temperature, hut above 30 to 40°C the values of the intercepts begin to rise. Figure 5 shows the reciprocal scattering function (KC,/ AR) 0= o, plotted against concentration, for the same fraction, at a number of temperatures. The linear plots extrapolate to the same intercept, within experimental error, which indicates that no molecular aggregation OWX~Sat low temperatures. The second virial coefficients, A,, are plotted as a function of temperature, for two fractions 2, = 1740 and 2, = 1462, 1.0 M-N&~, in Fig. 6. It is seen that the As's vanish at two temperature?, which correspond to 0, = 26°C and 0, = 61”C, respectively. The values of A, for t’he two molecular weight fractions arp indistinguishable within experimental error. Fraction 2, = 1740 has also been in\-e>t.igat,ed in l-3 M-NaCl; it is seen that A, is much lower and vanishes at about 0, = 10°C. The radii of gyration S, in 1.0 &I-NaCl for two poly A fractions are given in Fig. 7. It is seen that the values of S, at fixed salt concentration decrease steeply with increasing temperature, reach a minimum in a region between 0, and O,, and again increase, albeit to a much smaller extent at higher temperatures, In Fig. 8, t#ht
26
H.
EISENBERG I
AND
G. FELSENFELD
I
I
I
t (“0
I.O-
0
0.44 0
1
2 Concentration
FIG 5. Reciprocal various
temperatures;
6. Second virial
(equiv
0.x
5
103)
scz&xing function KC,/A &(atB=O) against concentration of poly A, at I;,= 1740; 1.0 m-N&l, 0.01 M-sodium phosphate buffer (pH 7.5).
Temperature FICA
4
3
(“cl
coefficients A2 (from light scattering) ofpoly A, as a function of temperature; 0, 2, = 1462, 1.0 M-NaCl; 0, Z,= 1740, 1.3 M-Nacl.
+, Zw= 1740, 1.0 M-N&~;
CONFORMATION
OF POLYRIBOADENYLIC
6OOr
ACID
2i
I
I
r Temperature
(“C)
FIG. 7. Radii of gyration 8, (from light scattering) of poly A in 1-O M-NaCl, 0.01 M-sodium phosphate buffer (pH 7.5); +, Z,= 1740; 0, Z,= 1462. 60C l-
I
I
I
I
500 -
4oc I2 “, v) 30( )-
20( II
1
I
I
0
20
40
60
Temperature
(“Cl
Fro. 8. Unperturbed radii of gyration 8: (solid line) from light Sc&tering measurements at “ideal” 8 temperatures, as a function of temperature. Upper and lower dotted curves correspond to values of Sz at I.0 and 1.3 x-NaCl, respectively.
upper dotted line is identical with the upper curve in Fig. 7 and represents the variat,ion ofs, with temperature for 1.0 M-NaCI, 2, = 1740. The lower dotted line in Fig. 8 pertains to the values of S, of the same fraction, but in I.3 M-NaCl. The circles correspond to three values of the unperturbed radius of gyration S& under 0 temperature conditions. The solid line, although connecting only three experimental points, represents the change of unperturbed dimensions of poly A as a function of temperature. The values of 1.5’:decrease with increasing temperature. In relation to what is
28
H.
EISENBERG
AND
G. FELSENFELD
known from the optical behavior of poly A at neutral pH with change in temperature, we may conclude that as bases unstack with increase in temperature, the unperturbed dimensions tend to decrease in parallel fashion. It is now possible, in principle, to carry out a theoretical analysis that permits derivation of the dimensions of poly A coils from the degree of base stacking and the rotation about angles in non-stacked repeating units. Such an analysis will be attempted below. The pronounced minimum is due to the fact that between in the values of S, at fixed salt concentration (1 M-N&) the two 0 temperatures the molecular coils are compressed because of unfavorable polymer-solvent interactions, whereas below 0, and above 0, expansion of the coils occurs. I
I
I
26 / (/y 24 /
$ 2.2 I
1
20,
25
27
29
3.1
3.3
Ioil zw FIG. 9. Double logarithmic plot of radius of gyration 8, against Zw, for fractions 1.0 M-Nacl, 0.01 M-sodium phosphate buffer (pH 7.5) at 2O’c.
of poly A in
In Fig. 9 we have plotted S, in 1-OM-NE&l at 20°C against Z,,,, in a double logarithmic plot. The relationship between S and Z is:
S = K, ZaS.
(4)
However, this holds true rigorously only for monodisperse systems, and does not apply strictly to average values of 8, and S, such as those displayed in Fig. 9. Fortunately, we can make use of the molecular weight distributions determined by sedimentation velocity experiments (see below, Table 1). The light-scattering experiments yield the light scattering average of S2 (Tanford, 1961), 2 ah s: (S2)2 =zzg Y i 1 where g, is the weight fraction of component i. By substituting equation (4) into this equation, a simple relationship between (X2),, KS and a, is obtained. Using the radius of gyration and molecular weight distribution data for all four poly A fractions, it is possible to minimize the mean square deviation of calculated and observed values of (S2),. The computational method is similar to that described for treatment of sedimentation data (see Experimental Procedures). We find that at 2O”C, in 1 M-NaCl, a, = 0.56 and KS = 4.873, if S is expressed in Angstrom units. These values hold for monodisperse systems. For Gaussian coils, at the 0 temperature (26” in this instance), a, should equal 0.5, and at lower temperatures, corresponding to better solvent power, a, should, as is observed here, increase above 0.5.
CONFORMATION 1001
OF POLYRIBOADENYLIC
, +\
0
I
1----
I IO
I 20
ACID
“9
__--~
I 30
I 40
Temperature (“C)
. 10. Intrinsic viscosity [q] (I./e quiv.) of poly A solutions in 1-O M-N&I, 0.01 M-sodium phosphate buffer (pH 7.5) as a function of temperature; +, Z,= 1740; O,Z,= 1462; 0, Z,= 1123; x, Z,= 714; 0, Z,= 379; ‘J, Z,= 1740; 1.30 M-N&~, 0.01 M-sodium phosphate buffer (pH 7.5). FIG.
J
3
4
6
8 IO z, x 10-2
20
30
FIG. 11. Intrinsic viscosity, [T], plotted against Z, for fractions nr-sodium phosphate buffer (pH 7.5), at four temperatures.
of poly A in 1.0 M-N&I,
0.01
The intrinsic viscosities of poly A fractions in 1.0 M-K&l as a function of temperature are shown in Fig. 10. The temperature range is not as extensive as in the case of t’he light-scattering experiments and covers mainly 0” to 30°C. Some low temperature values of [T] for fraction 2, = 1740 in 1.3 &I-NaCl are also given. The intrinsic viscosities are shown to ‘decrease sharply with increase in temperature, and also with NaCl concentration, in exact analogy to the behavior of S,. Figure 11 is a double logarithmic plot of [y] against Z,, in 1 M-Nacl at a number of temperatures. The equation which relates [y] and 2 is:
[y]= Kg?
(5)
30
H.
EISENBERU
AND
G. FELSENFELD
In a heterogeneous system, the average value of [T] which is measured is :
Using computational techniques similar to equation (4), and again using the known fractions, we find, for K,, and a,, respectively, at 7*8”C, 0,533 and 0.569 at 2O”C, 0.641 and l./equiv. Figure 12 shows that a,, interpolates
0
5
I IO
those described for the parameters in molecular weight distributions of the O-483and 0.713 at O”C, 0446 and 0.680 0.467 at 30°C. The dimensions of [T] are to the value 0.5 at 27*O”C, which is quite
1 20
15
Temperature
FIG. 12. Dependence
of exponents
a4 (equation
25
I 30
(“C)
(5)) and a, (equation
(6)) on temperature.
close to the 0 temperature as found from the light-scattering experiments. Thus another requirement of excluded volume theory, namely, that a,, (for non-draining Gaussian coils) be equal to 0.5 at the 0 temperature, is accurately obeyed. This conclusion should be accepted with some caution, as it is known that a relationship with a,, = 0.5 often persists far below the range in which non-draining Gaussian coil behavior should be expected.
FIG. 13. Sedimentation coefficient 8, at vanishing polymer concentration, plotted against Zw, for fractions of poly A in 1.0 M-NaCl, 0.01 M-sodium phosphate buffer (pH 7.5) at three ternperatures.
(d) Xedimentation velocity The median sedimentation velocity values szOat vanishing
polymer concentration
CONFORMATION
OF POLYRIBOADENYLIC
31
ACID
in 1-O M-NaCl, 0.01 M-sodium phosphate buffer, (pH 75), are summarized in Fig. 13, for each of the four fractions studied at each of three temperatures. The data have been corrected to 20°C in 1 Icl-NaCl, i.e. the temperature dependence of the solvent viscosity and density have been taken into account. (Talues of s~~,,~may be obtainetl 1)~ multiplying the values given by 1.135.) It is obvious from the resulbs shown t Lent t’he frictional coefficient of each poly A fraction increases with &creasing temperat urt., as might be expected for a molecule showing increasing viscosity and radius of gyration. From an analysis of the distribution of sedimentation coefficients (see Experimental Procedures), the distributions were fitted to the measured values of 2,. The ~~-lrn. meters K, and a, in the equation S = K,Za”
(6) are O-337 and O-437 at 7*8”C, O-405 and 0.467 at 20°C and 0.420 and 0.521 at 32*5”C, if s is (Ispressed in Svedberg unit’s. These values are uncorrected for solvent %cositJ. and temperature and represent the measured sedimentation coefficients at the respective temperatures. Equation (6) relates Z, the degree of polymerization of a ho~nogcnt~~~~~ sample, to its sedimentation coefficient. Given t’he “best fit” values of K, and a, at any temperature, it is possible to compute the molecular weight distribut’ion of each fraction from the distribution of scclimentntion coefficients, and from this any desired degree of polymerizat’ion average may he computed. The values given in Table 1 were obtained by determining the molecular 1
TABLE
‘-1WI 171y
. . tJc~I’c~.s of polymerzzataon of poly coeflcient didritutions
1740 Calculated Z,, Cnlcu1ntw.l 2, Ctilculatwl 2, z,,:z,:z,
1360 5 75 1770 f 85 2190*150 1: 1.29: 1.60
A fractions computed from at three fcnl1,frutt(res
1123 930 f 1120 f 1210 + 1: 1.15:
714 30 30 40 1.30
665 l 40 740 f 20 815 f 10 1: 1.11: 1.22
.~td;rl,,-lllnI/‘o,,
37!) 324 _t 10 380 f 10 440 f 20 1: 1.17: 1.35
weight distribution of each fraction at each temperature (two separate sedimentation runs of each fraction were performed at 2O”C, and one each at 7.8”C and 32*5”C). The values of Z,, Z, and Z, given in Table 1 are the average for all these determinations (with their mean deviations). The results show that the fractions are reasonably homogeneous. The exponents a, are plotted in Fig. 12 as a function of temperature. They are seen t,o increase with increase in temperature, and furthermore u, equals 0.5 at nearly the identical temperature (26.6’C) at which a,, equals 0.5 (27.0%). This againis inexcellent agreement with the general requirement of excluded volume theory and further confirms the essent,ial correctmss of our attempt to analyze the structure transition with temperature in t’he poly A solutions, under conditions (at 0 temperatures) postulatcsrl to be comparable from excluded volume theory. The dotted line representsing the variation of a, with temperature has been calculated from the experimental curve of a7 ,‘I ,‘.‘I/(A t, hy use of the classical relationship (Flory, 1053) a,g - 0.5 = ~(O..S --- n ).
32
H.
EISENBERG
AND
G. FELSENFELD
(e) Model for poly A umtacliing The results given in Fig. 8 are consistent with the existence of an extended, ordered poly A structure at low temperature. They are also consistent with a nonco-operative thermal denaturation process of the kind proposed for poly A by a number of workers (Leng & Felsenfeld, 1966; Poland, Vournakis & Scheraga, 1966; Brahms, Michelson & van Holde, 1966; Applequist & Damle, 1966). (It should be emphasized that the presence of stacking, and of the relatively large stacking energy observed for poly A, is not inconsistent with a non-co-operative stacking process. In the case of single-strand stacking, the formation of the first interaction in a region of otherwise unstacked bases is accompanied by a change of free energy which is not much different from the change which occurs when a base is added at the end of an already existing stacked sequence. Only when this difference is large will marked cooperativeness exist.) In Fig. 14 is given the temperature dependence of poly A stacking calculated from
I
0
IO
I
I
I
I
/
I
20
30
40
50
60
70
Temperature
FIQ. 14. F, the fractional
(“(3
amount of stacking interaction,
calculated from the data of Leng & Felsenfeld number of interactions.)
as a function of temperature, as (1966). (F = 0.5 corresponds to half of the maximum
the data of Leng & Felsenfeld. Comparison with Fig. 8 shows that there is little change in the radius of gyration in going from 30% of bases stacked to 60% stacked. The sharp increase in S, occurs in the region where >SO% of the bases are stacked. Such behavior is qualitatively reasonable if there are no long stretches of uninterrupted ordered structure present at T,,, (50% stacking), i.e. if the process of formation of such structures is not very co-operative. In order to place the analysis of these data on a somewhat more quantitative basis, we have made a preliminary analysis of a simple model of poly A configurations. We have assumed that the elements of the polymer may be replaced by virtual bond vectors connecting the phosphorus atoms. The ordered form of poly A is assumed to have a conformation rather like that of one of the two strands of DNA (Luzzati, Mathis, Masson t Witz, 1964; Witz & Luzzati, 1965) with virtual bond lengths corresponding to the inter-phosphorus distance in DNA, which is 6.5 A (Langridge et al., 1960). This conformation can be specified by two angles : IV,, the complement of the angle between successive bond vectors, and $u, the angle between the planes defined by pairsof bond vectors (Zi, Z,, 1) and (Z,, 1, Zi+J, respectively. The coil form is assumed to have the same virtual bond length, and to be defined by a single complementary angle Bo between successive vectors. Rotation about the interplanar angle +o is
CONFORMATION
OF POLYRIBOADENYLIC
33
ACID
assumed to be free. It is clear that this is a drastic simplification of the coil structure, since there are actually five backbone bonds per monomer unit that’ are capable of relatively free rotation. However, it has been pointed out by Scl~il~klnut & Lifson (1965) that the mutual repulsions of the charges on the phosphate groups will tend to make those configurations energetically unfavorable in which the intrrpho~phat~~ distance is much smaller than the maximum possible. Following these authors, we assume that the interphosphate distance in the coil form is t’hat of a nearly fully extended backbone (and the same as that found in the helical DNS structure). At any intermediate temperature, poly A may be treated formally as a random distribution of the two kinds of elements described above. The assumption of randomness in the sequence of individual helical and coil elements is of course equivalent to an assumption of completely non-co-operative helix format’ion. FOII IIKY W~IItig~u.:~til ml problems of this kind have been discussed at length by a number of inve~tig:,ltor-. (Lifson, 1958; Volkenstein, 1958) and in particular the soluCon to the problem of a random distribution of two kinds of elements has been given in matrix form by Miller. &ant & Flory (1967), who find that, for very long polymer chains : 9
= {(ES)
(E -)-l},,.
where is the mean square end-to-end distance, n is the number of virtua’l I~OIK~ of length 1, E is the identity matrix of dimensions 3 x 3, and T is the appropriate transformation matrix. The local co-ordinates of each virtual bond vector are defined so that the x axis is coincident with the vector; the subscript refers to the 1,l element, of the matrix product. In a homopolymer, T is the rotation matrix which transforms the vector Z,, 1, expressed in its own co-ordinate system, into the co-ordinat’e system for bond i. The poly A “helix” which we use as a model can be defined by such a matrix, T,. The random coil form of poly A is defined by a similar matrix,
Studies of the Temperature-dependent Phase Separation of Polyriboadenylic Neutral pH HENRYK
EmmmRot
Conformation and Acid Solutions at
AND GARY FELSENFELD
National Institute of Arthritis and Metabolic Diseases National Institutes of Health Bethesda, Maryland, 20014, U.S.A. (Received 12 June 1967) The conformation of polyriboadenylic acid (poly A) in aqueous solutions at 8 solvent conditions, as a neutral pH has been investigated under “ideal”, function of temperature. The studies were carried out on fractions of well-defined molecular weight obtained by reversible phase separation of the polymer in sodmm chloride solutions more concentrated than 1 M. Under such conditions, poly A is soluble at low and high temperatures, but only partially miscible in a range centered on 35 to 40°C. The extent of the range varies with molecular weight, and polymer and salt concentrations. The upper and lower 0 temperatures for solvents in the range of sodium chloride concentrations from 1 to 1.33 M were derived from the phase diagrams. Light-scattering experiments yielded the molecular weights, radii of gyration and second virial coefficients (AZ) of several fractions at various salt concentratlons. in the temperature range - 2 to 62~4°C. At a fixed salt concentration, d, xranished at two temperatures, the upper and lower 0 temperatures for that solvent. In this way it was possible to obtain values of the radius of gyration at various B temperatures which were unperturbed by solvent effects, thus separatmg long-range solvent-dependent influences on molecular conformation from the influences of short-range interactions due to base stacking. The sedimentation velocity and viscosity behavior of poly A as a function of salt concentration and temperature were also studied. In 1 M-NaCl, both the sedimentation coefiiclent and intrinsic viscosity vary as &P5 at a temperat,ure quite close to the 0 temI”“‘atLlW. The results show that poly A forms a highly extended structure at low temperature but that this structure is rapidly disrupted as the fraction of bases in stacks falls below unity. The observations are consistent with t,he existence of a ~tructllre formed by a non-co-operative process.
1. Introduction The study of preferred conformations and structural transitions in synthetic polo-1111c~lwtit1esis important for a better understanding of the structures and interactions in nat,ura’lly occurring nucleic acids. Polyriboadenylic acid (poly A) has been shown to exist in several characteristic forms in aqueous solutions. Thus, at acid pH, a double-stranded helical form prevails (Fresco & Doty, 1957; Rich, Davies, Crick & Il’atson, l%l), whereas at neutral pH poly A is single stranded and uncl~rgt~~~ a c~lm~acterkt ic temperature-dependent, transition which has been studied in detail by t Permanent address: Weizmann Institute of Science, Rehovoth, Israel 17
2
18
H. EISENBERG
AND
G. FELSENFELD
absorption spectroscopy, circular dichroism and optical rotation (Holcomb & Tinoco, 1965 ; Leng & Felsenfeld, 1966; Brahms, Michelson & Van Holde, 1966 ; Poland, Vournakis & Scheraga, 1966; Applequist & Damle, 1966). Light-scattering, viscosity and sedimentation-velocity studies of poly A at room temperature are consistent with a random coil model (Fresco $ Doty, 1957; Steiner $ Beers, 1957). On the basis of the studies cited above, it is now generally believed that the temperature-dependent optical properties of poly A arise from the tendency of the bases of poly A to “stack” with their planes parallel to one another. The extent of stacking is temperature dependent, but the stacked structure is formed by a non-co-operative process, so that even when a relatively large fraction of the bases is stacked, there are very few long sequences of uninterrupted stacks. The main purpose of this investigation was the study of the conformation of poly A at neutral pH, as a function of temperature, in an effort to relate the temperature dependence of the conformation to the changes in base stacking described above. We expect that poly A will be a flexible macromolecule, even if we assume a fairly high degree of base stacking. The flexibility arises from bond-angle rotations along the macromolecular chain, particularly involving bonds in repeating units with nonstacked bases. A primary consequence, well documented in conformational studies of coiling macromolecules (Flory, 1953), is that over-all polymer dimensions will depend on polymer-solvent interactions as well as local structure and rotations of hindered bonds; in “good” solvents, polymer dimensions are expanded beyond socalled unperturbed dimensions, whereas in “poor” solvents they are compressed below the unperturbed dimensions. The unperturbed dimensions are related to polymer structure and short-range interactions, whereas long-range interactions with solvent procluce either expansion or compression of the macromolecular coils. Excluaeavolume theory (Flory, 1953) states that “ideal” 0 conditions, obtained by suitable choice of solvent or temperature, can be realized in which long-range interactions are effectively compensated. At the Flory 0 temperature, the second virial coefficient A, (in osmotic pressure and light-scattering experiments) vanishes, and molecular dimensions obtained under these conditions represent the required unperturbed dimensions. Excluded-volume theory, originally developed for non-ionic polymers, is generally also applicable to multicomponent polyelectrolyte solutions (Eisenberg & Woodside, 1962). It thus appeared feasible to seek suitable solvent and temperature systems for poly A such that the unperturbed dimensions could be studied as a function of temperature. The most direct method of obtaining information about the distribution of mass in a macromolecular structure is the study of the angular dependence of scattered light, which permits determination of the radius of gyration. If the particles are identical with respect to size and shape, and furthermore of suitable size, then the analysis is straightforward. Not all of these requirements are met in the case of poly A. The material synt’hesizecl by the use of polynucleotide phosphorylase has a broad spectrum of chain lengths. It is thus necessary to obtain a series of fractions with well-defined and sharp chain-length distributions. Our first efforts were therefore directed to the development of fractionation procedures. The discovery reported here of molecular weight-dependent phase transitions in poly A solutions at NaCl concentrations Furthermore, greater than 14 M provides an effective method of fractionation. the phase transition behavior is closely related to the existence of 0 solvent conditions, and can be used to determine them.
CONFORMATION
OF POLYRIBOADENYLIC
ACID
I!)
As it is known (Leng & Felsenfeld, 1966) that the hypochromism of poly A at a given temperature is almost invariant to changes in NaCl concentrat’ion above 0.01 31, it was decided to seek 0 conditions by varying the NaCl concentration, on the reasonable assumption that the extent of stacking would not be affected by this variation provided the temperature was held constant. In this way we have found 0 solvent conditions at several temperatures. Using 0 solvents, we have measured the temperature dependence of the unperturbed radius of gyration of poly A. We have also >t udicd the temperature- and molecular weight-dependence of the intrinsic viscosit> and sedimentation velocity of poly A fractions. We find t,hat in 1 nr-NaCl at the 0 t,empcrature, these parameters vary as MO.‘, as expected for random coils under 0 conditions. These results open the way to a rigorous analysis of conformat8ional behavior of polynucleotides with precise theoretical tools. Our results show that poly A does form a highly extended structure at low t’emperature, where most of the bases are in the stacked conformation. Only a small increase in temperature is necessary to disrupt the structure despite the fact that this involves small changes in the extent of stacking. It will be shown that this behavior is consistent with a non-co-operative model of poly A structure formabion. Our results represent the first direct evidence for a temperature-dependent configurational change in the structure of poly A which can be correlated with its optical properties.
2. Experimental Procedure (a) Ma&i.als
and solutions
Polyadenylic acid (poly A) was a commercial preparation supplied by the Miles Chemical Company, and purified by extraction with water-saturated phenol and dialysis, first against 1.0 M-Nacl, 0.01 a6-sodium phosphate buffer (pH = 7.5), 10d4 M-EDT& then against the same buffer without EDTA. Concentrations were determined spectrophotometrically at room temperature, assuming a molar extinction value of 10,100 at 257mp. as reported by Stevens & Felsenfeld (1964). To transform concentrations C, (equiv./l.) to c (g/ml.), it is necessary to multiply by 0.351 (351 is the equivalent weight of the monomer repeating unit in the Na form). The weight average degree of polymerization 2, of the starting material was 1375, as determined by light scattering, and its median sedimentation coefficient szO measured at 20°C was 11.3 Svedberg units in 1.0 M-NaCl, O.Ol-Msodium phosphate buffer (pH 7.6). The corresponding value of szO,Wwas 12.8. For a typical fractionation procedure, we added (at 0%) 10 ml. 5 M-NaCl with continuous stirring to 200 ml. poly A solution (25 mg/ml., 1.0 M-NaCl, 0.01 M-phosphate buffer. pH 7.5). The solution (~1.2 aa-NaCl) was transferred to a pear-shaped flask immersed in a thermostatic bath accurate to O.l”C. The temperature was raised slowly, with gentle stirring, until the first turbidity appeared. It was further increased slowly by 0.2% and the first fraction was allowed to settle overnight at 15.4%. The supernatant fraction was quickly decanted into a similar cooled flask and re-immersed in the thermostat. The precipitated fraction was dissolved in a small amount of water and dialyzed against repeated changes of 1 M-N&~, 0.01 M-sodium phosphate buffer (pH 7.5). The first fracr IOII contained about 170 mg poly A in 32 ml. solution. Further fractions were collected at 17.1; and 24.O’C (150 and 90 mg, respectively). Finally, 25 ml. 5 M-N&~ were added to the remaining solution and the last fraction (80 mg) collect,ed at 26°C. All solvents and poly A solutions used in this procedure were filtered through HA (0.45 p) Millipore filters before use. Fractions prepared in this fashion were stable in the refrigerator over many months, as established by unchanged light-scattering and sedimentation behavior, although no special precautions were taken to assure the sterility of the solutions. Exposure to temperatures up to 63°C in light-scattering cells, for periods up to 1 hr, did not affect the stability of the solutions.
20
H.
EISENBERG
AND
(b) Phase separation
G. FELSENFELD experiments
For these experiments 1.0 ml. of a poly A solution in 1.0 M-NaCl was introduced into a small test tube sealed with a thermometer with ground-glass joint, such that the thermometer bulb was completely immersed in the liquid. The solution was warmed to the lower precipitation temperature, which was recorded, and then it was further warmed until the upper, dissolution, temperature was reached. The sample was now cooled and the precipitation and dissolution temperatures recorded upon lowering of the temperature. With provision of good shaking, the phase-separation behavior was reversible and the characteristic temperatures were reproducible to within 0+2”C. The onset and disappearance of turbidity were determined visually from the blurring of a background scale. Next the concentration of NaCl was raised by careful repeated addition of 30 ~1. of 5 Ma-NaCl solution, and observation of the appearance of turbidity at each NaCl concentration. Such experiments were repeated on different poly A fractions, at different poly A concentrations. At high salt concentrations (above 1.3 M-NaCl), some irreversible behavior was observed for the lower precipitation temperature. A poly A sample (2, = 7 14) at a concentration of 7.5 X 10T3 equiv./l., in 1.33 M-NaCl, was turbid at - 12°C; uponslow warming, the solution became clear at +2 to 3°C. No precipitation now occurred upon cooling to - 12°C. Upon warming the solution, precipitation now occurred at $9”C, which was taken as the incipient phase-separation temperature. This process could now be repeated indefinitely, provided the precipitate was cooled below 0°C and then slowly warmed to +2 t? 3°C to obtain a clear solution. In all cases in which irreversible or time-dependent phenomena occurred, the incipient separation of the clear solution was taken as the phase-transition point. No such irreversible phenomena were observed at salt concentrations below 1.3 M-NaCl. (c) Light
scattering
eqerirnents
Light-scattering experiments with unpolarized light were performed in the temperature interval from -2°C to 62*4”C, at angles of observation 0 ranging from 30” to 150°, at a wavelength X = 546 mp, with a light-scattering photometer (Wippler & Scheibling, 1954) manufactured by Sofica, Paris. For the evaluation of the light-scattering results the quantity KC,/ARe is required. Here C, is the concentration in equiv./l., AR0 is the reduced intensity of scattering (corrected for solvent contribution) at angle 0 with the incident beam, and K is equal to index increment at constant (an/aC,); 2000 a2n~/h4N,, where (an/aC,), is the refractive chemical potential p of diffusible solutest, no is the refractive index of the medium, h is the wavelength in vacua and N, is Avogadro’s number. We obtain : AR, = (AI,/I,,,,)R,(n,/n,)2
sine/(1
+ cos20)
from the ratio of light scattered at angle t? in excess of solvent, (AI0 = (I-I&) over the [by the absolute Rayleigh ratio light scattered by benzene at 0 = 90” (1s,90) multiplied for benzene, R, = 15.8 x 10u6 cm-l (Coumou, 1960) at 23”C, and correction factors (no/ns)” due to the ratio of refractive indices of medium and calibrating liquid, sin B due to the change in scattering volume with angle, and (1 + cos2 0) due to the use of unpolarized incident light. The final working equation is :
and (2000 n2 ni/PN, RB) = 523 at 23°C. We use as secondary standard a clear glass cylinder calibrated against benzene at 23”C, the scattering of which is not affected by temperature in the range of our investigation. For further details on the experimental procedure, we refer to a recent publication (Cohen & Eisenberg, 1965). t Strictly speaking the refractive increment should be determined at constant pressure P and constant chemical potentials of all diffusible solutes, except the main solvent, water. In practice, for one measures (&L/X’,),, which specifies constant +,zo as well, but relaxes the requirement constant P. The two increments are identical for all practical purposes (Casassa & Eisenberg. 1964).
CONFORMATION
OF POLYRIBOADENYLIC
ACID
21
Buffer dialyzate and poly A solutions were freed of dust by direct filtration under gravit,y into clean dry cylindrical cells (28 mm diam.) through HA Millipore filters (0.45~ pore size). Solutions of poly A of various concentrations were made up by weight, from tht, stock solutions, by diluting with the dialyzate buffers. Concentrations were checked bJ for each ,p~‘t.t rophotometric analysis after light scattering. About 17 ml. were required solut*ion. (d) Refractive ir&x irr( 1‘6t/1111f.9 Refractive index increments were determined interferomet,rically at A = 546 mp at 25°C In an Ammco model B electrophoresis instrument fitted with a special cell (Svensson & Odengrim, 1952) ; (an/&), was found to be 0.164 ml./g, which corresponds to ! ?rt: r-f ‘,, I,. = 0.0576 l./equiv. This result was obtained in the concentration range 7 to 18 mg/ml.. on an unfractionated poly A sample dialyzed extensively against 1.0 M-NaCl, 0.01 RIsodium phosphate buffer (pH 7.5); for both these and the density-increment measurements (see below), final dialysis of the poly A solutions was carried out for 3 to 4 hr at room temperature. sp(-f2ji(-volumes (e) Partial Densities required 2.’ C’ in capillary-neck used m refractive-index M-sodium phosphate increment I f-p: cc 16,= by I c r-‘:CL I+, = 1-$*p)
in the determination of partial specific volumes were determined at, pycnometers of about 7.5 ml. capacity, on the same solutions as increment measurement. The density of the 1.0 M-NaCl, 0.01 buffer (pH 7.5), was found to be 1.03838 g/ml. and the densit) 0.433 ; from this we calculate an apparent partial volume ?* (defined equal to 0.546. (f)
Viscosity measurements
Vincos;lt 1’ measurements were made in the temperature range from 0 to 37% in CannonUbbelohde viscometers with flow times for water of about 300 set at 25’C. No dependence on shear was found in the extreme case of the highest fraction (2, = 1740) at OT, with the use of a Cannon multibulb Ubbelohde shear viscometer, over a tenfold variation in the rate of shear. (g) Sedimentation
velocity measurements
Sedimentation velocity measurements in the Spinco model E ultracentrifuge were undertaken at 7.8, 20 and 32”C, in 1.0 M-NaCl, 0.01 M-sodium phosphate buffer (pH 7.5), at 44.770 rev./min. The instrument was equipped with ultraviolet optics with film recording. Poly A concentrations were of the order of 5 x 10e5 equiv./l. No dependence on concentration of the sedimentation coefficients was observed at these low concentrations. Exposure and development procedures were chosen to give linear dependence of film density upon optical absorbance of the sample in the range of concentrations used. Measurements of film density were made with the Joyce-Loebl microdensitomet,er. Analysis of the integral distribution of sedimentation coefficients at intervals of 10% of the total concentration was carried out after correction for radial dilution. Analysis of photographs showed that the variation in the apparent sedimentation coefficient distribut,ion with time was small even for the smallest molecular weight fraction studied. The + ft’rrt, of diffusion upon the results was therefore considered negligible. Calculations wercb Iberformed using a Honeywell 800 computer and a program written by us. Fitt,mg of the sedimentation coefficient distribution to the average molecular weight, cletermined by light scattering was carried out making use of the equation :
~rh+rt’ a, is the exponent
in s, = K’ Z,‘s,
g, is the fraction, problem value of
weight fraction and s, the sedimentation coefficient of component i in a given and 2, is the weight average degree of polymerization of this fraction. The was solved on the Honeywell 800 computer by fixing l/a,, and calculating the K which gave the least squares best fit value of the calculated values of 2, for
22
H.
EISENBERG
AND
G. FELSENFELD
all four fractions studied. The coefficient l/as was then changed by a fixed increment, and the calculation repeated. The value of l/a* which gave the smallest deviations for the calculated values of 2, was retained. Using this exponent and the appropriate value of K’, the average degrees of polymerization given in Table 1 were computed from the sedimentation coefficient distribution.
3. Results and Discussion (a) Phase separation behavior The phase separation behavior of four poly A fractions, at various salt concentrations, as a function of poly A concentration, is shown in Fig. 1. It is seen that, for each salt concentration, precipitation occurs when the temperature is raised from low temperatures. The precipitates dissolve again when the upper branch of the precipitation curve is reached. Samples of higher molecular weight precipitate at lower temperatures in the lower precipitation branch and dissolve at higher temperatures in the upper branch. From the maxima in the separation temperature concentration plots, it is possible to obtain the critical temperature t,, for phase separation. For a discussion of critical temperatures and their relationship to 8 temperatures, the reader is referred to the book by Flory (1953). Unfortunately, in most of the cases shown in Fig. 1, it was not possible to reach the critical concentration range required for the evaluation of the critical temperatures, because of
100
I
I
I
I
I
I
I
I
(b)
(a)
6
80 -$.EE6Cl
--.--
/40x‘. i!!
m-.-m
--. --Sz+-’
20-g;&o*
2 0 P x E 80e 60-
0
I
I
I
I
I
I
I
I
I 8
I 12
I 16
Cd)
(cl .a/ pos&J d +.+-
I 4
+-*
I 8
o-o-/a *x/o 0-O
--
I 12
I I6
Concentration
0
I 4 (equlv./C
20
x IO31
FIG. 1. Temperatures of phase separation against concentration of poly A; regions of limited miscibility are between upper and lower curves corresponding to same salt concentration. (d) 2,=379. 0, 1.00 M-N&~; +, 1.116 M-NaCl; (a) Z,= 1740; (b) Z,== 1123; (c) 2,=714; 0, 1.226 M-N&~; x, 1.266 M-NaCl; 0, 1.33 M-N&I.
CONFORMATION
cI)
OF POLYRIBOADENYLIC
ACID
2.3
3,2-
0 x 7 l-2
..
2.61
0
15
I 30
I
45
60
z;“*X 102 FIG. 2. Estimated upper and lower critical convolute temper&urea plotted as Tc-l against Cw-1:2; salt concentrations as in Fig. 1.
T, (in degrees Kelvin).
lack of sufficient amounts of the rather expensive fractions. As the curves in Fig. 1 become rather shallow at higher poly A concentrations, critical temperatures were estimated, in most cases in rather arbitrary fashion, to establish the general pattern of the poly A phase diagram. The estimated upper and lower critical consolute temperatures T, (in degrees Kelvin) have been plotted in the usual fashion (Flory, 1953) in Fig. 2, as T,-l against Z,- Ii2 ; they yield linear plots, the intercepts of which, in the limit Z,-+m define the upper and lower 0 temperatures, 0, and O,, for each system. In Fig. 3 we show the estimated values t, (in degrees centigrade) for the various fractions, against NaCl concentration; 0, and 0, are also given in Fig. 3. It is seen that 0, increases and 0, decreases with NaCl concentration. Below a NaCl concentration of O-9 to 0.95 M, phase separation does not occur and 0 conditions cannot be achieved. Above thin NaCl concentration we find two 0 temperat,ures for each system, which enables us in principle to study the behavior of poly A over almost the whole rang” of temperatures accessible in aqueous solutions under 0 conditions. It will be seen below that 0, = 60°C at, 1.0 M-NaCl coincides well with the value obtained from the vanishing of A,; on the other hand, 0, = 22°C at 1.0 M-NaCl and 0, = 5’C at 1.3 M-NaCl are somewhat lower than the corresponding values (26 and 10°C) found from light scattering. This may be due to the difficulty of correct’ly estimating t, for the lower precipitation branch with the limited amount of data available, to the irreversible phenomena observed at high xalt concentrations in the lower branch (see Experimental Procedure), or to the fact that whereas the upper precipitation branch represents a normal amorphous polymersolvent phase transition, the lower branch occurs at a temperature where the polymer
24
H.
EISENBERG
AND
G. FELSENFELD
Fro. 3. Estimated upper and lower critical consolute temperatures againstNaClconcentration; q ,&=379; X, 2,=714; 0, 2,=1123; and lower theta temperatures 8, and eL, from intercepts in Fig. 2.
t,, in degrees centigrade, +, 2,=1740; 0, upper
is fairly highly ordered, leading to a more complex phase-transition behavior. The quantitative aspects of this problem will not be pursued further in view of the limited data available. (b) Light-z;ca/ftri,rg results Light-scattering
data were evaluated in terms of the two equations: W’,/WI
co = 27,-l + 2A, C, + . . .
(1)
[l + (167~%z/3h2) (S2), sin2 (O/2) + . ..]
(2)
and (Zimm, 1948): (KC,JdR),U=,
= 2,-l
where the concentration C, is expressed in equivalents of nucleotides (or moles of phosphorus) per liter, and 2, is the weight average degree of polymerization in units of nucleotides (or moles of phosphorus) per macromolecule; (S2) = Sg is the lightscattering average of the mean square radius of gyration S2, derived independent of any assumption of the shape of the macromolecules, from the ratio of the slope to intercept of equation (2) : &n, s = initial’slope, at C, = 0, of (KC,/AR), versus sin2 (O/2) l/2 intercept, at fl = 0, of (KC,JAR)o=, at C, = 0 1 . 2/3x B [
(3)
For values of this ratio smaller than unity, plots of (KCJAR), against sin2 (8/Z) should be linear, independent of the shape of particles or the distribution of their size,
CONFORMATION
0
OF POLYRIBOADENYLIC
0.2
0.6
0.4
26
ACID
0.8
IO
sin2(tT/2) FIG. 4. A typical result showing the angular dependence of reciprocal scattering function K (?,j AR0 of poly A (2, = 1740) in 1.0 M-Nacl, 0.01 M-sodium phosphate buffer (pH 7.5) at various temperatures.
The concentration
of polymer
is 2.5 x 10y3 equiv./l.
Such plots are shown in Fig. 4 for a single poly A concentrat,ion (2, = 1740) in 1.0 M-Nacl, 0.01 M-sodium phosphate buffer (pH 7.5), at various temperatures, from -2 to 62.4”C. Both slopes and intercepts decrease in value with increasing temperature, hut above 30 to 40°C the values of the intercepts begin to rise. Figure 5 shows the reciprocal scattering function (KC,/ AR) 0= o, plotted against concentration, for the same fraction, at a number of temperatures. The linear plots extrapolate to the same intercept, within experimental error, which indicates that no molecular aggregation OWX~Sat low temperatures. The second virial coefficients, A,, are plotted as a function of temperature, for two fractions 2, = 1740 and 2, = 1462, 1.0 M-N&~, in Fig. 6. It is seen that the As's vanish at two temperature?, which correspond to 0, = 26°C and 0, = 61”C, respectively. The values of A, for t’he two molecular weight fractions arp indistinguishable within experimental error. Fraction 2, = 1740 has also been in\-e>t.igat,ed in l-3 M-NaCl; it is seen that A, is much lower and vanishes at about 0, = 10°C. The radii of gyration S, in 1.0 &I-NaCl for two poly A fractions are given in Fig. 7. It is seen that the values of S, at fixed salt concentration decrease steeply with increasing temperature, reach a minimum in a region between 0, and O,, and again increase, albeit to a much smaller extent at higher temperatures, In Fig. 8, t#ht
26
H.
EISENBERG I
AND
G. FELSENFELD
I
I
I
t (“0
I.O-
0
0.44 0
1
2 Concentration
FIG 5. Reciprocal various
temperatures;
6. Second virial
(equiv
0.x
5
103)
scz&xing function KC,/A &(atB=O) against concentration of poly A, at I;,= 1740; 1.0 m-N&l, 0.01 M-sodium phosphate buffer (pH 7.5).
Temperature FICA
4
3
(“cl
coefficients A2 (from light scattering) ofpoly A, as a function of temperature; 0, 2, = 1462, 1.0 M-NaCl; 0, Z,= 1740, 1.3 M-Nacl.
+, Zw= 1740, 1.0 M-N&~;
CONFORMATION
OF POLYRIBOADENYLIC
6OOr
ACID
2i
I
I
r Temperature
(“C)
FIG. 7. Radii of gyration 8, (from light scattering) of poly A in 1-O M-NaCl, 0.01 M-sodium phosphate buffer (pH 7.5); +, Z,= 1740; 0, Z,= 1462. 60C l-
I
I
I
I
500 -
4oc I2 “, v) 30( )-
20( II
1
I
I
0
20
40
60
Temperature
(“Cl
Fro. 8. Unperturbed radii of gyration 8: (solid line) from light Sc&tering measurements at “ideal” 8 temperatures, as a function of temperature. Upper and lower dotted curves correspond to values of Sz at I.0 and 1.3 x-NaCl, respectively.
upper dotted line is identical with the upper curve in Fig. 7 and represents the variat,ion ofs, with temperature for 1.0 M-NaCI, 2, = 1740. The lower dotted line in Fig. 8 pertains to the values of S, of the same fraction, but in I.3 M-NaCl. The circles correspond to three values of the unperturbed radius of gyration S& under 0 temperature conditions. The solid line, although connecting only three experimental points, represents the change of unperturbed dimensions of poly A as a function of temperature. The values of 1.5’:decrease with increasing temperature. In relation to what is
28
H.
EISENBERG
AND
G. FELSENFELD
known from the optical behavior of poly A at neutral pH with change in temperature, we may conclude that as bases unstack with increase in temperature, the unperturbed dimensions tend to decrease in parallel fashion. It is now possible, in principle, to carry out a theoretical analysis that permits derivation of the dimensions of poly A coils from the degree of base stacking and the rotation about angles in non-stacked repeating units. Such an analysis will be attempted below. The pronounced minimum is due to the fact that between in the values of S, at fixed salt concentration (1 M-N&) the two 0 temperatures the molecular coils are compressed because of unfavorable polymer-solvent interactions, whereas below 0, and above 0, expansion of the coils occurs. I
I
I
26 / (/y 24 /
$ 2.2 I
1
20,
25
27
29
3.1
3.3
Ioil zw FIG. 9. Double logarithmic plot of radius of gyration 8, against Zw, for fractions 1.0 M-Nacl, 0.01 M-sodium phosphate buffer (pH 7.5) at 2O’c.
of poly A in
In Fig. 9 we have plotted S, in 1-OM-NE&l at 20°C against Z,,,, in a double logarithmic plot. The relationship between S and Z is:
S = K, ZaS.
(4)
However, this holds true rigorously only for monodisperse systems, and does not apply strictly to average values of 8, and S, such as those displayed in Fig. 9. Fortunately, we can make use of the molecular weight distributions determined by sedimentation velocity experiments (see below, Table 1). The light-scattering experiments yield the light scattering average of S2 (Tanford, 1961), 2 ah s: (S2)2 =zzg Y i 1 where g, is the weight fraction of component i. By substituting equation (4) into this equation, a simple relationship between (X2),, KS and a, is obtained. Using the radius of gyration and molecular weight distribution data for all four poly A fractions, it is possible to minimize the mean square deviation of calculated and observed values of (S2),. The computational method is similar to that described for treatment of sedimentation data (see Experimental Procedures). We find that at 2O”C, in 1 M-NaCl, a, = 0.56 and KS = 4.873, if S is expressed in Angstrom units. These values hold for monodisperse systems. For Gaussian coils, at the 0 temperature (26” in this instance), a, should equal 0.5, and at lower temperatures, corresponding to better solvent power, a, should, as is observed here, increase above 0.5.
CONFORMATION 1001
OF POLYRIBOADENYLIC
, +\
0
I
1----
I IO
I 20
ACID
“9
__--~
I 30
I 40
Temperature (“C)
. 10. Intrinsic viscosity [q] (I./e quiv.) of poly A solutions in 1-O M-N&I, 0.01 M-sodium phosphate buffer (pH 7.5) as a function of temperature; +, Z,= 1740; O,Z,= 1462; 0, Z,= 1123; x, Z,= 714; 0, Z,= 379; ‘J, Z,= 1740; 1.30 M-N&~, 0.01 M-sodium phosphate buffer (pH 7.5). FIG.
J
3
4
6
8 IO z, x 10-2
20
30
FIG. 11. Intrinsic viscosity, [T], plotted against Z, for fractions nr-sodium phosphate buffer (pH 7.5), at four temperatures.
of poly A in 1.0 M-N&I,
0.01
The intrinsic viscosities of poly A fractions in 1.0 M-K&l as a function of temperature are shown in Fig. 10. The temperature range is not as extensive as in the case of t’he light-scattering experiments and covers mainly 0” to 30°C. Some low temperature values of [T] for fraction 2, = 1740 in 1.3 &I-NaCl are also given. The intrinsic viscosities are shown to ‘decrease sharply with increase in temperature, and also with NaCl concentration, in exact analogy to the behavior of S,. Figure 11 is a double logarithmic plot of [y] against Z,, in 1 M-Nacl at a number of temperatures. The equation which relates [y] and 2 is:
[y]= Kg?
(5)
30
H.
EISENBERU
AND
G. FELSENFELD
In a heterogeneous system, the average value of [T] which is measured is :
Using computational techniques similar to equation (4), and again using the known fractions, we find, for K,, and a,, respectively, at 7*8”C, 0,533 and 0.569 at 2O”C, 0.641 and l./equiv. Figure 12 shows that a,, interpolates
0
5
I IO
those described for the parameters in molecular weight distributions of the O-483and 0.713 at O”C, 0446 and 0.680 0.467 at 30°C. The dimensions of [T] are to the value 0.5 at 27*O”C, which is quite
1 20
15
Temperature
FIG. 12. Dependence
of exponents
a4 (equation
25
I 30
(“C)
(5)) and a, (equation
(6)) on temperature.
close to the 0 temperature as found from the light-scattering experiments. Thus another requirement of excluded volume theory, namely, that a,, (for non-draining Gaussian coils) be equal to 0.5 at the 0 temperature, is accurately obeyed. This conclusion should be accepted with some caution, as it is known that a relationship with a,, = 0.5 often persists far below the range in which non-draining Gaussian coil behavior should be expected.
FIG. 13. Sedimentation coefficient 8, at vanishing polymer concentration, plotted against Zw, for fractions of poly A in 1.0 M-NaCl, 0.01 M-sodium phosphate buffer (pH 7.5) at three ternperatures.
(d) Xedimentation velocity The median sedimentation velocity values szOat vanishing
polymer concentration
CONFORMATION
OF POLYRIBOADENYLIC
31
ACID
in 1-O M-NaCl, 0.01 M-sodium phosphate buffer, (pH 75), are summarized in Fig. 13, for each of the four fractions studied at each of three temperatures. The data have been corrected to 20°C in 1 Icl-NaCl, i.e. the temperature dependence of the solvent viscosity and density have been taken into account. (Talues of s~~,,~may be obtainetl 1)~ multiplying the values given by 1.135.) It is obvious from the resulbs shown t Lent t’he frictional coefficient of each poly A fraction increases with &creasing temperat urt., as might be expected for a molecule showing increasing viscosity and radius of gyration. From an analysis of the distribution of sedimentation coefficients (see Experimental Procedures), the distributions were fitted to the measured values of 2,. The ~~-lrn. meters K, and a, in the equation S = K,Za”
(6) are O-337 and O-437 at 7*8”C, O-405 and 0.467 at 20°C and 0.420 and 0.521 at 32*5”C, if s is (Ispressed in Svedberg unit’s. These values are uncorrected for solvent %cositJ. and temperature and represent the measured sedimentation coefficients at the respective temperatures. Equation (6) relates Z, the degree of polymerization of a ho~nogcnt~~~~~ sample, to its sedimentation coefficient. Given t’he “best fit” values of K, and a, at any temperature, it is possible to compute the molecular weight distribut’ion of each fraction from the distribution of scclimentntion coefficients, and from this any desired degree of polymerizat’ion average may he computed. The values given in Table 1 were obtained by determining the molecular 1
TABLE
‘-1WI 171y
. . tJc~I’c~.s of polymerzzataon of poly coeflcient didritutions
1740 Calculated Z,, Cnlcu1ntw.l 2, Ctilculatwl 2, z,,:z,:z,
1360 5 75 1770 f 85 2190*150 1: 1.29: 1.60
A fractions computed from at three fcnl1,frutt(res
1123 930 f 1120 f 1210 + 1: 1.15:
714 30 30 40 1.30
665 l 40 740 f 20 815 f 10 1: 1.11: 1.22
.~td;rl,,-lllnI/‘o,,
37!) 324 _t 10 380 f 10 440 f 20 1: 1.17: 1.35
weight distribution of each fraction at each temperature (two separate sedimentation runs of each fraction were performed at 2O”C, and one each at 7.8”C and 32*5”C). The values of Z,, Z, and Z, given in Table 1 are the average for all these determinations (with their mean deviations). The results show that the fractions are reasonably homogeneous. The exponents a, are plotted in Fig. 12 as a function of temperature. They are seen t,o increase with increase in temperature, and furthermore u, equals 0.5 at nearly the identical temperature (26.6’C) at which a,, equals 0.5 (27.0%). This againis inexcellent agreement with the general requirement of excluded volume theory and further confirms the essent,ial correctmss of our attempt to analyze the structure transition with temperature in t’he poly A solutions, under conditions (at 0 temperatures) postulatcsrl to be comparable from excluded volume theory. The dotted line representsing the variation of a, with temperature has been calculated from the experimental curve of a7 ,‘I ,‘.‘I/(A t, hy use of the classical relationship (Flory, 1053) a,g - 0.5 = ~(O..S --- n ).
32
H.
EISENBERG
AND
G. FELSENFELD
(e) Model for poly A umtacliing The results given in Fig. 8 are consistent with the existence of an extended, ordered poly A structure at low temperature. They are also consistent with a nonco-operative thermal denaturation process of the kind proposed for poly A by a number of workers (Leng & Felsenfeld, 1966; Poland, Vournakis & Scheraga, 1966; Brahms, Michelson & van Holde, 1966; Applequist & Damle, 1966). (It should be emphasized that the presence of stacking, and of the relatively large stacking energy observed for poly A, is not inconsistent with a non-co-operative stacking process. In the case of single-strand stacking, the formation of the first interaction in a region of otherwise unstacked bases is accompanied by a change of free energy which is not much different from the change which occurs when a base is added at the end of an already existing stacked sequence. Only when this difference is large will marked cooperativeness exist.) In Fig. 14 is given the temperature dependence of poly A stacking calculated from
I
0
IO
I
I
I
I
/
I
20
30
40
50
60
70
Temperature
FIQ. 14. F, the fractional
(“(3
amount of stacking interaction,
calculated from the data of Leng & Felsenfeld number of interactions.)
as a function of temperature, as (1966). (F = 0.5 corresponds to half of the maximum
the data of Leng & Felsenfeld. Comparison with Fig. 8 shows that there is little change in the radius of gyration in going from 30% of bases stacked to 60% stacked. The sharp increase in S, occurs in the region where >SO% of the bases are stacked. Such behavior is qualitatively reasonable if there are no long stretches of uninterrupted ordered structure present at T,,, (50% stacking), i.e. if the process of formation of such structures is not very co-operative. In order to place the analysis of these data on a somewhat more quantitative basis, we have made a preliminary analysis of a simple model of poly A configurations. We have assumed that the elements of the polymer may be replaced by virtual bond vectors connecting the phosphorus atoms. The ordered form of poly A is assumed to have a conformation rather like that of one of the two strands of DNA (Luzzati, Mathis, Masson t Witz, 1964; Witz & Luzzati, 1965) with virtual bond lengths corresponding to the inter-phosphorus distance in DNA, which is 6.5 A (Langridge et al., 1960). This conformation can be specified by two angles : IV,, the complement of the angle between successive bond vectors, and $u, the angle between the planes defined by pairsof bond vectors (Zi, Z,, 1) and (Z,, 1, Zi+J, respectively. The coil form is assumed to have the same virtual bond length, and to be defined by a single complementary angle Bo between successive vectors. Rotation about the interplanar angle +o is
CONFORMATION
OF POLYRIBOADENYLIC
33
ACID
assumed to be free. It is clear that this is a drastic simplification of the coil structure, since there are actually five backbone bonds per monomer unit that’ are capable of relatively free rotation. However, it has been pointed out by Scl~il~klnut & Lifson (1965) that the mutual repulsions of the charges on the phosphate groups will tend to make those configurations energetically unfavorable in which the intrrpho~phat~~ distance is much smaller than the maximum possible. Following these authors, we assume that the interphosphate distance in the coil form is t’hat of a nearly fully extended backbone (and the same as that found in the helical DNS structure). At any intermediate temperature, poly A may be treated formally as a random distribution of the two kinds of elements described above. The assumption of randomness in the sequence of individual helical and coil elements is of course equivalent to an assumption of completely non-co-operative helix format’ion. FOII IIKY W~IItig~u.:~til ml problems of this kind have been discussed at length by a number of inve~tig:,ltor-. (Lifson, 1958; Volkenstein, 1958) and in particular the soluCon to the problem of a random distribution of two kinds of elements has been given in matrix form by Miller. &ant & Flory (1967), who find that, for very long polymer chains : 9
= {(ES
(E -
where
is the mean square end-to-end distance, n is the number of virtua’l I~OIK~ of length 1, E is the identity matrix of dimensions 3 x 3, and T is the appropriate transformation matrix. The local co-ordinates of each virtual bond vector are defined so that the x axis is coincident with the vector; the subscript refers to the 1,l element, of the matrix product. In a homopolymer, T is the rotation matrix which transforms the vector Z,, 1, expressed in its own co-ordinate system, into the co-ordinat’e system for bond i. The poly A “helix” which we use as a model can be defined by such a matrix, T,. The random coil form of poly A is defined by a similar matrix, .,
IO,> IO
08
06
04
02
0
Fhelm FIG. 15. Calculations of the dependence of the unperturbed radius of gyration S upon P the fractional amount of stacking interaction, using the simple model discussed in the text. Results for three sets of assumed values of the parameters are shown: ___ p=4(p; e,
= 350;
I&
@a = 18’, (+) 3
=25";
- - - - - - -e,=40.30;
experimentally
observed
e,
=30-70;
values of 8:.
+H =i90;
---,
ec=51~5~;
8,,=30.70:
34
H. EISENBERG
AND
G. FELSENFELD
which is, however, an average over all values of &. If the fraction of stacking interactions is F, then in equation (7) is given (Miller, Brant & Flory, 1967) by:
= ET, + (l-F)<&>.
The evaluation of equation (7) is straightforward. The values of F are taken from Fig. 14. Results are shown in Fig. 15, for a number of sets of values of &, 8n and &. Values of these parameters which seem “reasonable” (i.e. en and +n close to the values for DNA) lead to predicted change of the radius of gyration with temperature in fairly good agreement with observation. An interesting prediction derived from this model is that the radius of gyration might rise again at high temperatures, a result which will not be surprising if it is realized that short stretches of the coil form ma,y actually be somewhat more extended than short stretches of the helix form. A similar result has been predicted (Nagai, 1961; Saito, Go & Ochiai, 1966) for the conformation of polypeptides in the helix-coil transition region. In any event, we consider that detailed comparisons with experiment are probably not justified within the framework of our simple model. Nonetheless, it seems reasonable to suppose that a somewhat more elaborate model would be capable of accounting for the observed behavior quite exactly. It has recently been proposed (R. C. Davis 6 I. Tinoco, Jr.,personal communication) that the temperature-dependent optical properties of poly A might be explicable not in terms of a two-state (“stacked” versus “unstacked”) model, but rather in terms of a multi-state model, in which every base remained parallel to every other base at all temperatures, but with an increasing tendency to oscillate in a sliding fashion relative to adjacent bases. Decreases in hypochromism and optical rotation with increasing temperature would be accounted for by the increasing excursion of the oscillation. It does not seem likely that such a model in its most extreme form would be consistent with the observed temperature dependence of intrinsic viscosity, sedimentation velocity and radius of gyration which we report here. The requirement that the planes of the bases remain parallel would tend to prevent the collapse of the molecule, over a very small temperature range, which we observe. It is of course not possible to rule out some model in which oscillation and unstacking both have a role. (f) Relationah@ between s, [T] and M The values of s, [v], and M obtained above can be combined to yield the parameter /3 NAS hl 1’3rlo s = Ma/3 (l-v*,,) where N, is Avogadro’s number and rlo is the solvent viscosity. If [v] is expressed in deciliters/gram, /l is usually found to lie in the range 2 to 3 x lo6 (Flory, 1953). Using the values of [T], M and s obtained for each of four poly A fractions, and assuming that v* = O-546 at all temperatures, we find that in 1 M-NaCl, 0.01 M-phosphate, (pH 75), /3 x low6 has the values 2.80 f 0.02 at 7*8”C, 2.77 5 0.05 at 20°C and 2.55 f 0.05 at 32.5”C. It is clear that /3 is not a temperature-independent constant; quite possibly, it also varies with salt concentration. The common procedure of using an assumed fixed value of /l, in combination with measurements of s and [v], to determine molecular weights is therefore questionable.
CONFORMATION
OF POLYRIBOADENYLIC
(g) Radii of gyration, intrinsic
35
ACID
viscosities and molecular weight
The intrinsic viscosity of coiling macromolecules may be related to the root-meansquare end-to-end distance (h2)@ by (B’lory, 1953) :
where [T], in agreement with common practice, is expressed in units of deciliters/gram and is assumed to have the value 6 X2, applicable to Gaussian coils. (When [q] is expressed in units of literlequiv., the right-hand side of equation (8) is equal to 10 @ 3’2/Z.) @ is a constant; its accurate evaluation from experimental data is difXcult because the calculation involves cubing the radius of gyration; any errors in the latter quantity are thus considerably magnified. The theoretical value for @ at the 0 temperature is now believed to be 2.8 x 1021 (Kirkwood, Zwanzig & Plock, 1955) but experimental values, in particular for polyelectrolyte By&ems, are often found to be much lower. We have, in Table 2, assembled values of 0 derived ii-om our measurements, under a number of experimental conditions. These values refer to results for TABLE 2
Universal constant @ derived from equation (8) s, x 106, (cm)
({ t = 20”C, 1.0 1740 1462 1123 714 379
Es) (w4
@x 10-21
M-N&~
3.66 3.26 2.67 2.11 1.38
1.026 0*906 O-809 0.627 0.427
0.869
t”C (b) 2 = 1740, 1-O an-N&l 0 7.8 20.0 30.0
5.69 4.94 3.66 2.63
2.721 1.966 1.026 0.584
0.648 0.678 0.869 1.334
(c) I; = 1740, 1.3 0 7.8
~-N&cl
2.42 1.65
2.422 1.652
0.729
(d) 2 = 1462, 1.0
M-N&I
4.87 4.36 3.26 2.16
2.382 1.680 0.906 0.390
0.720 0.708 0.912 l-37
1
7.5 20 37
0.912 1.14 1.14 1.49
0.817
CT], S, and Z, experimentally derived, without taking into account the chain length distribution of the individual fractions. The values of @in the last column of Table 2 show t,hat it is not constant but increases somewhat with decrease in Z, at fixed temperature (20°C) and also increases with increase in temperature (in the range from 0” to 37°C) at fixed value of Z,. That @ increases as Z decreases is also apparent from the detailed statistical analysis we have presented for the variation of [q] and S with Z, taking into account the
36
H.
EISENBERG
AND
G. FELSENFELD
complete chain length distribution, as derived from a detailed analysis of the sedimentation coefficients s. We have shown that, at 20°C [v] (liters/equiv.) = 0633 2°‘56g and S (A) = 4.873 Z”.56, for polymer homogeneous with respect to chain length. Use of equation (8) now shows that @ should vary with Z-o,111, which is in qualitative agreement with the data in Table 2. In conclusion to this section we would like to state that, whereas we feel that our experiments indicate in rather clear-cut fashion the general relationship between macromolecular conformation, temperature, solvent interaction and backbone structure (base stacking), rather more precise data for S, will have to be provided for a quantitative analysis in terms of excluded volume theory and a more sophisticated model of “frozen” and “hindered” backbone bond rotations.
4. Conclusion We have shown that it is possible to find 0 solvents for poly A, to fractionate the polymer making use of the properties of such solvents, and to study the viscosity, sedimentation, and light-scattering behavior of the fractions, as a function of temperature, under conditions close to “ideal”. The importance of examining the polymer conformation in 0 solvents lies in the fact that only in such solvents is the conformation determined entirely by short-range interactions. Under other conditions, contributions from interaction with solvent, or long-range interactions within the polymer will also have a role in determining the conformation. Since a principal aim of this work is to relate the temperature-dependence of the conformation to the temperatmedependence of formation of local stacking interactions detected by optical methods, it is essential that the effect of all but short-range interactions be eliminated. On the other hand, at low values of the ionic strength, far from 0 conditions, solvent interactions or electrostatic forces are likely to have a more important role than local base-stacking interactions in determining conformation. No statements with respect to the relationship between base stacking and chain conformation can therefore be made under the latter conditions. Our results show, for the first time, that the formation of stacking interactions in single-stranded poly A (as detected by changes in hypochromism, circular dichroism or optical rotation) is accompanied by an increase in the degree of extension of the molecule, as measured by an increase in the unperturbed radius of gyration. The temperature dependence of the radius of gyration is consistent with a model in which the regions of order are non-co-operatively formed, but quite rigid. We thank Drs R. C. Davis and I. Tinoco, Jr. for the opportunity manuscript before publication. REFERENCES Applequist, J. & Damle, V. (1966). J. Amer. Chem. Sot. 88, 3896. Brahms, J., Michelson, A. M. & Van Holde, K. E. (1966). J. Mol. Biol. Casassa, E. F. & Eisenberg, H. (1964). Adwanc. Protein Chern. 19, 287. Cohen, G. & Eisenherg, H. (1965). J. Chem. Phys. 43, 3881 Coumou,
D. J. (1960).
J. CoLbid.
of reading their
15, 467.
Sci 15, 408.
Eisenberg, H. & Woodside, D. (1962). J. Chem. Whys. 36, 1844. Flory, P. J. (1953). Principles of Polywr Chemistry, Ithaca: Cornell University Fresco, J. R. & Doty, P. (1967). J. Amer. Chem. SOC. 79, 3928. Holcomb, D. N. t Tinoco, I., Jr. (1966). Biopolymm, 3, 121.
Press.
CONFORMATION
OF POLYRIBOADENYLIC
ACID
37
Kirkwood, J. G., Znanzig, R. W. & Plock, R. J. (1955). J. ,‘tll r~. Phya. 16, 565. Langrdge, R., Marvin, D. A., Seeds, W. E., Wilson, H. R., Hooper, C. W., Wilkins, M. H. F. & Hamilton, L. D. (1960). J. fiIo2. Biol. 2, 38. Leng. M. 8r. Felsenfeld, G. (1966). J. iKoZ. Biol. 15, 455. Lifson, S. (1958). J. C’hg ~1. Phya. 29, 80. Luzzati, V., Mathis, A., Masson, F. & Witz, J. (1964). J. iUoZ. Biol. 10, 28. Miller, \V. G., Brant, D. A. 85 Flory, P. J. (1967). J. Mol. BioZ. 23, 67. Nagal, B. (1961). J. C’hern. Phya. 34, 887. Poland, D., Vournakls, J. N. & Scheraga, H. A. (1966). Biopolymcra, 4, 223. Rich, A., Davies, D. R., Crick, F. H. C. & Watson, J. D. (1961). J. Mol. BioZ. 3. 71. Saito, N., Go, M. & Ochiai, M. (1966). J. Polymer Sci. C15, 303. Schildkraut, C. & Lifson, S. (1965). Biopolymera, 3, 195. Steiner, R. F. & Beers, R. F. (1957). Biochim. biophya. Acta, 26, 336. Stevens, C. & Felsenfeld, G. (1964). Biopolymera, 2, 293. Svensson, H. & Odengrim, H. (1952). Acta Chim. &and. 6, 720. Tanford, C’. (196 1). Ph yaical C’hr ~1;srr,lt of Macromolecules. New York : John Wiley & Sons, Inc. Volkenstein. M. V. (1958). J. Polymer 81%. 29, 441. Wippler, C. & Scllelbllnp. G. (1954). J. Chim. Phya. 51, 201. Wltz, J. & Luzzati, V. (1965). J. Mol. BioZ. 11, 620. Zimm, B. H. (1948). J. Chem. Phya. 16, 1093.
IO,> IO
08
06
04
02
0
Fhelm FIG. 15. Calculations of the dependence of the unperturbed radius of gyration S upon P the fractional amount of stacking interaction, using the simple model discussed in the text. Results for three sets of assumed values of the parameters are shown: ___ p=4(p; e,
= 350;
I&
@a = 18’, (+) 3
=25";
- - - - - - -e,=40.30;
experimentally
observed
e,
=30-70;
values of 8:.
+H =i90;
---,
ec=51~5~;
8,,=30.70:
34
H. EISENBERG
AND
G. FELSENFELD
which is, however, an average over all values of &. If the fraction of stacking interactions is F, then
= ET, + (l-F)<&>.
The evaluation of equation (7) is straightforward. The values of F are taken from Fig. 14. Results are shown in Fig. 15, for a number of sets of values of &, 8n and &. Values of these parameters which seem “reasonable” (i.e. en and +n close to the values for DNA) lead to predicted change of the radius of gyration with temperature in fairly good agreement with observation. An interesting prediction derived from this model is that the radius of gyration might rise again at high temperatures, a result which will not be surprising if it is realized that short stretches of the coil form ma,y actually be somewhat more extended than short stretches of the helix form. A similar result has been predicted (Nagai, 1961; Saito, Go & Ochiai, 1966) for the conformation of polypeptides in the helix-coil transition region. In any event, we consider that detailed comparisons with experiment are probably not justified within the framework of our simple model. Nonetheless, it seems reasonable to suppose that a somewhat more elaborate model would be capable of accounting for the observed behavior quite exactly. It has recently been proposed (R. C. Davis 6 I. Tinoco, Jr.,personal communication) that the temperature-dependent optical properties of poly A might be explicable not in terms of a two-state (“stacked” versus “unstacked”) model, but rather in terms of a multi-state model, in which every base remained parallel to every other base at all temperatures, but with an increasing tendency to oscillate in a sliding fashion relative to adjacent bases. Decreases in hypochromism and optical rotation with increasing temperature would be accounted for by the increasing excursion of the oscillation. It does not seem likely that such a model in its most extreme form would be consistent with the observed temperature dependence of intrinsic viscosity, sedimentation velocity and radius of gyration which we report here. The requirement that the planes of the bases remain parallel would tend to prevent the collapse of the molecule, over a very small temperature range, which we observe. It is of course not possible to rule out some model in which oscillation and unstacking both have a role. (f) Relationah@ between s, [T] and M The values of s, [v], and M obtained above can be combined to yield the parameter /3 NAS hl 1’3rlo s = Ma/3 (l-v*,,) where N, is Avogadro’s number and rlo is the solvent viscosity. If [v] is expressed in deciliters/gram, /l is usually found to lie in the range 2 to 3 x lo6 (Flory, 1953). Using the values of [T], M and s obtained for each of four poly A fractions, and assuming that v* = O-546 at all temperatures, we find that in 1 M-NaCl, 0.01 M-phosphate, (pH 75), /3 x low6 has the values 2.80 f 0.02 at 7*8”C, 2.77 5 0.05 at 20°C and 2.55 f 0.05 at 32.5”C. It is clear that /3 is not a temperature-independent constant; quite possibly, it also varies with salt concentration. The common procedure of using an assumed fixed value of /l, in combination with measurements of s and [v], to determine molecular weights is therefore questionable.
CONFORMATION
OF POLYRIBOADENYLIC
(g) Radii of gyration, intrinsic
35
ACID
viscosities and molecular weight
The intrinsic viscosity of coiling macromolecules may be related to the root-meansquare end-to-end distance (h2)@ by (B’lory, 1953) :
where [T], in agreement with common practice, is expressed in units of deciliters/gram and
is assumed to have the value 6 X2, applicable to Gaussian coils. (When [q] is expressed in units of literlequiv., the right-hand side of equation (8) is equal to 10 @ 3’2/Z.) @ is a constant; its accurate evaluation from experimental data is difXcult because the calculation involves cubing the radius of gyration; any errors in the latter quantity are thus considerably magnified. The theoretical value for @ at the 0 temperature is now believed to be 2.8 x 1021 (Kirkwood, Zwanzig & Plock, 1955) but experimental values, in particular for polyelectrolyte By&ems, are often found to be much lower. We have, in Table 2, assembled values of 0 derived ii-om our measurements, under a number of experimental conditions. These values refer to results for TABLE 2
Universal constant @ derived from equation (8) s, x 106, (cm)
({ t = 20”C, 1.0 1740 1462 1123 714 379
Es) (w4
@x 10-21
M-N&~
3.66 3.26 2.67 2.11 1.38
1.026 0*906 O-809 0.627 0.427
0.869
t”C (b) 2 = 1740, 1-O an-N&l 0 7.8 20.0 30.0
5.69 4.94 3.66 2.63
2.721 1.966 1.026 0.584
0.648 0.678 0.869 1.334
(c) I; = 1740, 1.3 0 7.8
~-N&cl
2.42 1.65
2.422 1.652
0.729
(d) 2 = 1462, 1.0
M-N&I
4.87 4.36 3.26 2.16
2.382 1.680 0.906 0.390
0.720 0.708 0.912 l-37
1
7.5 20 37
0.912 1.14 1.14 1.49
0.817
CT], S, and Z, experimentally derived, without taking into account the chain length distribution of the individual fractions. The values of @in the last column of Table 2 show t,hat it is not constant but increases somewhat with decrease in Z, at fixed temperature (20°C) and also increases with increase in temperature (in the range from 0” to 37°C) at fixed value of Z,. That @ increases as Z decreases is also apparent from the detailed statistical analysis we have presented for the variation of [q] and S with Z, taking into account the
36
H.
EISENBERG
AND
G. FELSENFELD
complete chain length distribution, as derived from a detailed analysis of the sedimentation coefficients s. We have shown that, at 20°C [v] (liters/equiv.) = 0633 2°‘56g and S (A) = 4.873 Z”.56, for polymer homogeneous with respect to chain length. Use of equation (8) now shows that @ should vary with Z-o,111, which is in qualitative agreement with the data in Table 2. In conclusion to this section we would like to state that, whereas we feel that our experiments indicate in rather clear-cut fashion the general relationship between macromolecular conformation, temperature, solvent interaction and backbone structure (base stacking), rather more precise data for S, will have to be provided for a quantitative analysis in terms of excluded volume theory and a more sophisticated model of “frozen” and “hindered” backbone bond rotations.
4. Conclusion We have shown that it is possible to find 0 solvents for poly A, to fractionate the polymer making use of the properties of such solvents, and to study the viscosity, sedimentation, and light-scattering behavior of the fractions, as a function of temperature, under conditions close to “ideal”. The importance of examining the polymer conformation in 0 solvents lies in the fact that only in such solvents is the conformation determined entirely by short-range interactions. Under other conditions, contributions from interaction with solvent, or long-range interactions within the polymer will also have a role in determining the conformation. Since a principal aim of this work is to relate the temperature-dependence of the conformation to the temperatmedependence of formation of local stacking interactions detected by optical methods, it is essential that the effect of all but short-range interactions be eliminated. On the other hand, at low values of the ionic strength, far from 0 conditions, solvent interactions or electrostatic forces are likely to have a more important role than local base-stacking interactions in determining conformation. No statements with respect to the relationship between base stacking and chain conformation can therefore be made under the latter conditions. Our results show, for the first time, that the formation of stacking interactions in single-stranded poly A (as detected by changes in hypochromism, circular dichroism or optical rotation) is accompanied by an increase in the degree of extension of the molecule, as measured by an increase in the unperturbed radius of gyration. The temperature dependence of the radius of gyration is consistent with a model in which the regions of order are non-co-operatively formed, but quite rigid. We thank Drs R. C. Davis and I. Tinoco, Jr. for the opportunity manuscript before publication. REFERENCES Applequist, J. & Damle, V. (1966). J. Amer. Chem. Sot. 88, 3896. Brahms, J., Michelson, A. M. & Van Holde, K. E. (1966). J. Mol. Biol. Casassa, E. F. & Eisenberg, H. (1964). Adwanc. Protein Chern. 19, 287. Cohen, G. & Eisenherg, H. (1965). J. Chem. Phys. 43, 3881 Coumou,
D. J. (1960).
J. CoLbid.
of reading their
15, 467.
Sci 15, 408.
Eisenberg, H. & Woodside, D. (1962). J. Chem. Whys. 36, 1844. Flory, P. J. (1953). Principles of Polywr Chemistry, Ithaca: Cornell University Fresco, J. R. & Doty, P. (1967). J. Amer. Chem. SOC. 79, 3928. Holcomb, D. N. t Tinoco, I., Jr. (1966). Biopolymm, 3, 121.
Press.
CONFORMATION
OF POLYRIBOADENYLIC
ACID
37
Kirkwood, J. G., Znanzig, R. W. & Plock, R. J. (1955). J. ,‘tll r~. Phya. 16, 565. Langrdge, R., Marvin, D. A., Seeds, W. E., Wilson, H. R., Hooper, C. W., Wilkins, M. H. F. & Hamilton, L. D. (1960). J. fiIo2. Biol. 2, 38. Leng. M. 8r. Felsenfeld, G. (1966). J. iKoZ. Biol. 15, 455. Lifson, S. (1958). J. C’hg ~1. Phya. 29, 80. Luzzati, V., Mathis, A., Masson, F. & Witz, J. (1964). J. iUoZ. Biol. 10, 28. Miller, \V. G., Brant, D. A. 85 Flory, P. J. (1967). J. Mol. BioZ. 23, 67. Nagal, B. (1961). J. C’hern. Phya. 34, 887. Poland, D., Vournakls, J. N. & Scheraga, H. A. (1966). Biopolymcra, 4, 223. Rich, A., Davies, D. R., Crick, F. H. C. & Watson, J. D. (1961). J. Mol. BioZ. 3. 71. Saito, N., Go, M. & Ochiai, M. (1966). J. Polymer Sci. C15, 303. Schildkraut, C. & Lifson, S. (1965). Biopolymera, 3, 195. Steiner, R. F. & Beers, R. F. (1957). Biochim. biophya. Acta, 26, 336. Stevens, C. & Felsenfeld, G. (1964). Biopolymera, 2, 293. Svensson, H. & Odengrim, H. (1952). Acta Chim. &and. 6, 720. Tanford, C’. (196 1). Ph yaical C’hr ~1;srr,lt of Macromolecules. New York : John Wiley & Sons, Inc. Volkenstein. M. V. (1958). J. Polymer 81%. 29, 441. Wippler, C. & Scllelbllnp. G. (1954). J. Chim. Phya. 51, 201. Wltz, J. & Luzzati, V. (1965). J. Mol. BioZ. 11, 620. Zimm, B. H. (1948). J. Chem. Phya. 16, 1093.
Universal constant @ derived from equation (8) s, x 106, (cm)
({ t = 20”C, 1.0 1740 1462 1123 714 379
Es) (w4
@x 10-21
M-N&~
3.66 3.26 2.67 2.11 1.38
1.026 0*906 O-809 0.627 0.427
0.869
t”C (b) 2 = 1740, 1-O an-N&l 0 7.8 20.0 30.0
5.69 4.94 3.66 2.63
2.721 1.966 1.026 0.584
0.648 0.678 0.869 1.334
(c) I; = 1740, 1.3 0 7.8
~-N&cl
2.42 1.65
2.422 1.652
0.729
(d) 2 = 1462, 1.0
M-N&I
4.87 4.36 3.26 2.16
2.382 1.680 0.906 0.390
0.720 0.708 0.912 l-37
1
7.5 20 37
0.912 1.14 1.14 1.49
0.817
CT], S, and Z, experimentally derived, without taking into account the chain length distribution of the individual fractions. The values of @in the last column of Table 2 show t,hat it is not constant but increases somewhat with decrease in Z, at fixed temperature (20°C) and also increases with increase in temperature (in the range from 0” to 37°C) at fixed value of Z,. That @ increases as Z decreases is also apparent from the detailed statistical analysis we have presented for the variation of [q] and S with Z, taking into account the
36
H.
EISENBERG
AND
G. FELSENFELD
complete chain length distribution, as derived from a detailed analysis of the sedimentation coefficients s. We have shown that, at 20°C [v] (liters/equiv.) = 0633 2°‘56g and S (A) = 4.873 Z”.56, for polymer homogeneous with respect to chain length. Use of equation (8) now shows that @ should vary with Z-o,111, which is in qualitative agreement with the data in Table 2. In conclusion to this section we would like to state that, whereas we feel that our experiments indicate in rather clear-cut fashion the general relationship between macromolecular conformation, temperature, solvent interaction and backbone structure (base stacking), rather more precise data for S, will have to be provided for a quantitative analysis in terms of excluded volume theory and a more sophisticated model of “frozen” and “hindered” backbone bond rotations.
4. Conclusion We have shown that it is possible to find 0 solvents for poly A, to fractionate the polymer making use of the properties of such solvents, and to study the viscosity, sedimentation, and light-scattering behavior of the fractions, as a function of temperature, under conditions close to “ideal”. The importance of examining the polymer conformation in 0 solvents lies in the fact that only in such solvents is the conformation determined entirely by short-range interactions. Under other conditions, contributions from interaction with solvent, or long-range interactions within the polymer will also have a role in determining the conformation. Since a principal aim of this work is to relate the temperature-dependence of the conformation to the temperatmedependence of formation of local stacking interactions detected by optical methods, it is essential that the effect of all but short-range interactions be eliminated. On the other hand, at low values of the ionic strength, far from 0 conditions, solvent interactions or electrostatic forces are likely to have a more important role than local base-stacking interactions in determining conformation. No statements with respect to the relationship between base stacking and chain conformation can therefore be made under the latter conditions. Our results show, for the first time, that the formation of stacking interactions in single-stranded poly A (as detected by changes in hypochromism, circular dichroism or optical rotation) is accompanied by an increase in the degree of extension of the molecule, as measured by an increase in the unperturbed radius of gyration. The temperature dependence of the radius of gyration is consistent with a model in which the regions of order are non-co-operatively formed, but quite rigid. We thank Drs R. C. Davis and I. Tinoco, Jr. for the opportunity manuscript before publication. REFERENCES Applequist, J. & Damle, V. (1966). J. Amer. Chem. Sot. 88, 3896. Brahms, J., Michelson, A. M. & Van Holde, K. E. (1966). J. Mol. Biol. Casassa, E. F. & Eisenberg, H. (1964). Adwanc. Protein Chern. 19, 287. Cohen, G. & Eisenherg, H. (1965). J. Chem. Phys. 43, 3881 Coumou,
D. J. (1960).
J. CoLbid.
of reading their
15, 467.
Sci 15, 408.
Eisenberg, H. & Woodside, D. (1962). J. Chem. Whys. 36, 1844. Flory, P. J. (1953). Principles of Polywr Chemistry, Ithaca: Cornell University Fresco, J. R. & Doty, P. (1967). J. Amer. Chem. SOC. 79, 3928. Holcomb, D. N. t Tinoco, I., Jr. (1966). Biopolymm, 3, 121.
Press.
CONFORMATION
OF POLYRIBOADENYLIC
ACID
37
Kirkwood, J. G., Znanzig, R. W. & Plock, R. J. (1955). J. ,‘tll r~. Phya. 16, 565. Langrdge, R., Marvin, D. A., Seeds, W. E., Wilson, H. R., Hooper, C. W., Wilkins, M. H. F. & Hamilton, L. D. (1960). J. fiIo2. Biol. 2, 38. Leng. M. 8r. Felsenfeld, G. (1966). J. iKoZ. Biol. 15, 455. Lifson, S. (1958). J. C’hg ~1. Phya. 29, 80. Luzzati, V., Mathis, A., Masson, F. & Witz, J. (1964). J. iUoZ. Biol. 10, 28. Miller, \V. G., Brant, D. A. 85 Flory, P. J. (1967). J. Mol. BioZ. 23, 67. Nagal, B. (1961). J. C’hern. Phya. 34, 887. Poland, D., Vournakls, J. N. & Scheraga, H. A. (1966). Biopolymcra, 4, 223. Rich, A., Davies, D. R., Crick, F. H. C. & Watson, J. D. (1961). J. Mol. BioZ. 3. 71. Saito, N., Go, M. & Ochiai, M. (1966). J. Polymer Sci. C15, 303. Schildkraut, C. & Lifson, S. (1965). Biopolymera, 3, 195. Steiner, R. F. & Beers, R. F. (1957). Biochim. biophya. Acta, 26, 336. Stevens, C. & Felsenfeld, G. (1964). Biopolymera, 2, 293. Svensson, H. & Odengrim, H. (1952). Acta Chim. &and. 6, 720. Tanford, C’. (196 1). Ph yaical C’hr ~1;srr,lt of Macromolecules. New York : John Wiley & Sons, Inc. Volkenstein. M. V. (1958). J. Polymer 81%. 29, 441. Wippler, C. & Scllelbllnp. G. (1954). J. Chim. Phya. 51, 201. Wltz, J. & Luzzati, V. (1965). J. Mol. BioZ. 11, 620. Zimm, B. H. (1948). J. Chem. Phya. 16, 1093.