A. YOUNGMOON,DOUGLAS C. POLAND, AND HAROLD A. SCHERAGA
2960
Thermodynamic Data from Fluorescence Spectra. I. The System Phenol-Acetatel
by A. Young Moon, Douglas C. Poland, and Harold A. Scheraga Department of Chemistry, Cornell University, Ithaca, New York
(Received February $6,1965)
This paper demonstrates how fluorescence measurements may be used to determine association constants, KasBOo, for weak complexes, involving hydrogen and/or hydrophobic bonds. If one member of the complex fluoresces, when free, and the other member quenches the fluorescence, upon formation of the complex, then the technique of concentration quenching of fluorescence will provide a value of K,,,,, from a quantitative measurement of the deviations from ideal or Stern-Volmer quenching behavior. Data are given for the system phenol-acetate, with the results that K,,,,, is approximately 0.5 M-' and its variation with temperature over the range 10 to 40" gives a temperature-independent enthalpy of association, AH, of about -400 f 400 cal./mole. Independent measurement of K,,,,, using the technique of ultraviolet difference spectra gives essentially the same results. From a consideration of AH, it is suggested that it is composed of two compensating contributions, a negative one from the intermolecular hydrogen bond and a positive one from an intermolecular hydrophobic bond in the formation of the complex. Further interpretation must await the results of experiments on the quenching of phenol fluorescence by the other members of the series of carboxylic acids. The magnitude of K,,,,, suggests that analogous tyrosyl-carboxylate ion interactions (together with hydrophobic bonding) are potentially important in stabilizing protein structure. Discussion and quantitative interpretation are given of literature data on analogous studies of polyamino acid copolymers.
Introduction Noncovalent bonds play an important role in maintaining the three-dimensional folding of a protein molecule. Nevertheless, even for model systems, it has been difficult to obtain reliable thermodynamic parameters for these noncovalent interactions over a range of temperatures. Schellman2 interpreted data on the osmotic pressure and heat of dilution of aqueous urea solutions (assuming that the departure from ideality could be attributed to intermolecular hydrogen bonding), obtaining a value for AH, the heat of formation of the urea-urea hydrogen bond, of -1.5 kcal./ mole at 25'. These calculations were recently extended to several temperaturesla with the result that AH varies very little, becoming slightly more positive with increasing temperature. Klotz and Franzen, * using the technique of near-infrared spectrophotometry, obtained a value close to zero for the heat of formation of the N-methylacetamide dimer; however, this value The Journal of Physical Chemistry
may be the resultant of both hydrogen and hydrophobic bonding.5 Based on titration data for formic acid in aqueous 3 M NaC1, Schrier, et aZ.,6 computed a value of 0 f 1kcal./mole for the heat of formation of the formic acid dimer; these workers used this value, together with literature data for dimer formation in higher homologs, to obtain values of the free energy of formation of hydrophobic bonds between the nonpolar ~
(1)
~~~~
This work was supported by a research grant (HE-01662) from
the National Heart Institute, National Institutes of Health, Public Health Service, and by a research grant (GB-2238) from the N a tional Science Foundation. (2) J. A. Schellman, Compt. rend. trav. lab. Carisberg, 29, 223 (1955). (3) G. C. Kresheck and H. A. Scheraga, J . Phys. Chem., 69, 1704 (1965). (4) I. M. Klotz and J. S. Franzen, J . A m . Chem. Soc., 84, 3461 (1962). (5) G. NBmethy and H. A. Scheraga, J . Phys. Chem., 66,1773 (1962). (6) E. E. Schrier, M. Pottle, and H. A. Scheraga, J . A m . Chem. SOC., 86, 3444 (1964).
THERMODYNAMIC DATAFROM FLUORESCENCE SPECTRA
portions of these dimers, with good agreement with theoretical values.6 Derivation of thermodynamic data for water from a statistical mechanical theory led to the value of - 1.32 kcal./mole for the heat of formation of the water-water hydrogen bond in the liquid.’ An even higher value was obtained for the internal hydrogen bond in salicylic acid based on ultraviolet difference spectra data.8 The above examples illustrate the divergence in values reported for the heat of formation of the hydrogen bond. These differences between various systems may be real. On the other hand, they may arise because of the following difficulties inherent in the methods used to determine AH. (1) Since hydrogen and hydrophobic bonds are relatively weak (AH being of the order of 1 kcal./mole) and association is accompanied by a large loss of translational entropy, high concentrations (of the order of 2 M ) are required to produce a measurable degree of association; at such high concentrations the assumption that activity coefficients are unity is a very poor one. (2) Since the hydrogen bond is weak, it produces only a small perturbation in the system; e.g., it leads to only a very small change in the absorption coefficient of the bonded chromophore or in the infrared stretching frequency. Thus, in obtaining thermodynamic data for hydrogen bond formation from ultraviolet absorption, infrared absorption, or titration curves, one is utilizing these techniques close to the limit of their accuracy. This paper will describe a method for obtaining equilibrium constants for association as a function of temperature in the phenol-acetate system; it is based on the measurement of the intensity of fluorescence. While not overcoming all the difficulties mentioned above, this method appears able to provide results which approach the precision necessary for testing the validity of presently employed concepts of protein structure.
2961
In an extensive study of the fluorescence of the aromatic amino acids that occur in proteins and of the simple analogs of these chromophores, Whitelo found that the fluorescence of phenol (an analog of tyrosine) is quenched by various small molecules; in particular, carboxylate ion is a very strong quencher. White reported that the fluorescence of the phenol-carboxylate ion system obeyed eq. 1; i.e., the decrease in the intensity of phenol fluorescence upon an increase in the concentration of carboxylate ion was adequately explained by collisional quenching. However, many systems do not obey the SternVolmer relation. Boaz and Rollefson” were able to explain deviations from the Stern-Volmer equation for inorganic systems by postulating either the association of quencher with chromophore or the self-association of the quenchers. If current concepts of noncovalent bonds are correct, there should be an association of the carboxylate ion with phenol but no selfassociation of carboxylate ions or phenol since, in the first case, both monomers are negatively charged and, in the second case, the concentration is very small. Using an argument completely analogous to that of Boaz and Rollefson, we can obtain a modified Stern-Volmer relation and thus have a basis for testing quantitatively the aforementioned prediction. If the chromophore and quencher do associate by the reaction
F + Q G F - - * Q then the appropriate association constant would be
(3)
In eq. 3, we have used concentrations to replace activities for the following reasons. (1) The concentration of F is very small, of the order of M. (2) The concentration of Q is less than 0.4 M . If Fluorescence of Associating Systems Q is charged, then F Q will also be charged, and the Suppose a chromophore has an intensity of fluoreselectrostatic part of the activity coefficients will cence IO, in the absence of d d e d Wencher. Then, if largely cancel. (3) The only source of nonideality is the quenching action is by colhional Processes, the thus attributable to association, which we are conintensity of fluorescence, I , in the presence of quencher sidering here explicitly. concentration [&I, is given by the S ~ ~ n - V o l m e r ~ If F and Q are associated, then the F molecules in relation the complex are always in a position to be quenched
-
I-O - 1 I
=
kqlQ]
(‘)
where k , is the quenching constant and is equal to the product of the mean radiative lifetime of the excited state in the absence of the particular quenching process and the bimolecular rate constant for collisional quenching.
(7) G.Nbmethy and H. A. Scheraga, J. Chem. Phys., 36,3382 (1962). (8) J. Hermans, Jr., S. J. Leach, and H. A. Scheraga, J . Am. Chem. SOC., 85,1390 (1963). (9) 0.Stern and M. Volmer, Physik. Z., 20, 183 (1919). (10) A. White, Bwchem. J., 71, 217 (1959); Ph.D. Thesis, University of Sheffield, 1960. and (11)H. K. Rollefson, J , Aln, Chem. sot., ,2, 3435 (1950).
Volum 69,Number 9 September 1966
A. YOUNG MOON,DOUGLAS C. POLAND, AND HAROLD A. SCHERAGA
2962
immediately. Hence, the association constant corresponds to the association of quencher and groundstate chromophore. Using eq. 3, we may express the fraction of chromophore that is free by
)
probability of a chromophore being free
(4)
I n the absence of association, the intensity of fluorescence, I, is given by eq. 1 in the following form (involving only collisional quenching)
I
=
probability of a free = Io chromophore not being quenched by collision
1
Io
)
(
(5)
When both association and collision are possible, then the intensity of fluorescence is
I
=
Io
probability of a chromophore being free>
(
x
1
probability of a free chromophore not being quenched by collision
(
(6)
which, upon substitution of the expressions in eq. 4 and 5 , gives
Upon rearrangement, eq. 7 becomes T
-- 1
10
I- -
[Q1
-
(kq
+
Kaaaoc)
+ (kqKassoo)[&I
(8)
The [ Q ] in eq. 8 represents the concentration of free quencher. If [ Q ]>> [F],as is the case in the experiments to be reported here, then [Q] may be identified with the total concentration of quencher. Hence, if one measures the fluorescence of a chromophore (e.g., phenol) as a function of the concentration of quencher (e.g., carboxylate ion) and plots the data according to eq. 8, one should obtain a straight line with a slope of kqKsasocand an intercept of ( k , KassOc), thereby determining both k , and K,,,,,. A plot according to eq. 8 is a more sensitive test of deviations from the Stern-Volmer relation than is one according to eq. 1. If the experiments are carried out a t several temperatures, it is possible to evaluate the enthalpy of association and obtain all the thermodynamic parameters for the association process as well as the activation energy for collisional quenching.
+
The Journal of Physical Chemistry
Experimental work was carried out to test the validity of eq. 8, which is based on hydrogen bond formation between compounds such as phenol and acetate, the analog of the tyrosyl-carboxyl hydrogen bond which may be involved in protein molecules. For comparison purposes, ultraviolet difference spectra measurements were made on the same system, in order to verify that the fluorescence method does indeed lead to a correct association constant.
Experimental Material and Solutions. All materials used were Mallinckrodt reagent grade. Anhydrous sodium acetate was dried a t 110' overnight in an oven before use, and its purity was found to be 99.6% by potentiometric titration of a 0.02 M solution from pH 1.7 to 11.0. Stock solutions of phenol and sodium acetate were prepared by weighing out crystalline phenol into a 1000-ml. volumetric flask for fluorescence measurements and into a 100-ml. volumetric flask for ultraviolet difference spectra measurements, and anhydrous sodium acetate into a 100-ml. volumetric flask, and by dissolving them with deionized water to volume to give concentrations of 8 X lo-* M , 6.4 X M, and 2.0 M , respectively. For the fluorescence experiments the phenol conM , which lies within the centration was 2 X range in which there is a linear dependence of fluorescence intensity on the concentration. The sample solution was prepared by pipetting 25 ml. of the 8 X M phenol stock solution into a 100-ml. volumetric flask, adding the desired amount of quencher with a pipette, and bringing the solution to volume with deionized water. The reference solution was prepared similarly, but without quencher. The solutions were kept approximately neutral by previous adjustment of the pH of the stock solution of acetate to pH 7.0 with 1 N HC1, using a Beckman pH meter, and the ionic strength a t 0.4 M by addition of the appropriate amount of sodium chloride. The prepared solutions were thermally equilibrated to the desired temperature before each run. For ultraviolet difference spectra measurements the sample solution was prepared by pipetting 1 ml. of the M phenol stock solution into a 10-ml. 6.4 X volumetric flask, adding the desired amount of sodium acetate solution, previously adjusted to pH 7.0 with 1 N HC1, using a Beckman pH meter, and bringing the solution to volume with deionized water. I n order to avoid discrepancies in concentration, the same pipet and volumetric flask were used in the preparation of all of the solutions.
THERMODYNAMIC DATAFROM FLUORESCENCE SPECTRA
Fluorescence Measurements. The measurements of fluorescence intensity were made with an AmincoKeir (Model No. 4-8201) spectrofluorimeter, having two grating monochromators which permitted the selection of excitation and emission wave lengths; spectra were recorded by means of an XY recorder (Model No. 1011-518). Since we are interested in the relative fluorescence intensities from solutions of phenol and phenol-plus-quencher, there was no need to determine an absolute value of the quantum yield; hence, the fluorescence intensity was read from the transistorized photometer (Catalog No. A1-63165) directly in terms of per cent transmittance. Since the instrument is a single-beam one, the fluorescence intensity from the phenol solution was measured before and after each measurement on the solution containing phenolplus-quencher, in order to minimize errors arising from possible fluctuations in the light intensity. The maximum excitation and emission wave lengths (270 and 310 mp, respectively12) were used in all experiments. The cell compartment was encased in a copper block, through which water from a constanttemperature bath was circulated, to control the temperature within .t0.lo. Below room temperature, the cell compartment was flushed with nitrogen gas to prevent fogging of the windows. Ultraviolet Difference Spectra Measurements. The measurements of difference spectra were made with a Cary Model 14 spectrophotometer, using an expanded scale. Here, too, the cell compartment was thermostated, and nitrogen gas was used for flushing a t low temperature. Tandem cells (described by Herskovits and Laskowski13) were used for the measurements. The sample cell contained phenol, sodium acetate, and sodium chloride in the front compartment and water in the rear; the reference cell contained phenol plus sodium chloride in the front compartment and sodium acetate solution in the rear.
Results Fluorescence Measurements. There is no shift in wave length of the fluorescence spectrum of phenol upon addition of quencher, as shown in Figure 1. Hence, all measurements were made a t 310 mp, the maximum of the fluorescence curve. Positive deviations from the Stern-Volmer equation were obtained when (Io/I - l)/[Ac-] was plotted against [Ac-1, as suggested by eq. 8, where [Ac-] is the total concentration of acetate. An example of such a plot is shown in Figure 2. Since a plot according to eq. 8 is more sensitive to deviations from the Stern-Volmer relation than is one according to eq. 1, this may explain why Whitelo did not observe the association
2963
I
d
Figure 1. Fluorescence spectra of 4 x 10-4 M phenol with various concentrations of sodium acetate: A, 0; B, 0.15; C, 0.2; D , 0 . 3 5 M .
4.5
I
I
I
I
phenomenon in the phenol-carboxylate system. As indicated in eq. 8, the association and the quenching constants a t a given temperature may be calculated from the slope and intercept of a straight line of the type shown in Figure 2. Table I shows the association and the quenching constants obtained at various temperatures. In the temperature range studied, the plot of (1 log K,,,,) vs. 1/T (Figure 3) indicates that the enthalpy of association is -400 f 400 cal./ mole, independent of temperature. This value is in good agreement with the value of -100 f 100 cal./ mole, obtained by Kresheck in this laboratory, using a calorimetric method at 25O, together with the assumption that K,,,, = 0.47 at this temperature. The
+
(12) The wave length scale of the instrument w w calibrated with these values given in Luminescence Data Sheet No. 2392-4, Aminco Instrument Co.,Inc., 8030 Georgia Ave., Silver Spring, Md. (13) T. T. Herskovits and M. Laskowski, Jr., J. BWZ. Chem., 235, PC 56 (1960); 237, 2481 (1962).
Volume 69,Number 9 September 1QBS
A. YOUNGMOON,DOUGLAS C. POLAND, AND HAROLD A. SCHERAGA
2964
value of k, = 5.36 f 0.21 a t 25' is in good agreement with the value of k, = 6.4 f 3y0 obtained by Feitels o d 4 for the tyrosine-acetate system. A plot of log k, vs. 1/T gives an activation energy of 2.71 f 0.12 kcal./mole. This value falls in the range characteristic of diffusion-controlled processes.16 Additional evidence that the collisional quenching is a diffusion-controlled process is obtained from the magnitude of the quenching rate constant (8.5 X lo8 M-' see.-') in the tyrosine-acetate system.14 Since the k, values of the phenol-acetate and tyrosine-acetate systems are similar, we may take the values of kbimolm as similar, by assuming comparable values of T., the mean radiative lifetime of the excited state. ~~
~
I
I
N::K V T X 103
Figure 3. Temperature dependence of log K,,.,,.
0
a 0.1
~
Table I: Temperature Dependence of the Association and Quenching Constants from Fluorescence Intensity t, oc.
10 15 18 25 35 40
Kwtwc, M-'
0.52 f 0.02 0.51 f 0.05 0.47 It 0.00 0.47 f 0.03 0.48 f. 0.04 0.47 f 0.03
kq, M-1
4.08 f 0.02 4.37 f 0.15 4.79 f 0.03 5.36 f 0.21 6.00 f 0.12 6.22 f 0.16
Ultraviolet Digereme Spectra Measurements. I n order to obtain an independent measurement of the association constants and thereby establish that the interpretation of the fluorescence data according to eq. 8 is correct, ultraviolet difference spectra were used to study the same association. WetlaufeP and La+ kowski17 previously observed that the maxima in the absorption spectra of phenol and N-acetyltyrosine ethyl ester are shifted to longer wave lengths when sodium acetate is added. These shifts were attributed to phenol-carboxylate ion and tyrosinecarboxylate ion hydrogen bonds, respectively, from considerations of analogous shifts in proteins such as insulinl8 and ribonuclease. l9 Neither of these workers reported association constants in these particuIar studies; the impossibility of distinguishing complex formation from what may be a medium effect was mentioned by Wetlaufer. Wetlaufer, however, found K.,,, for the phenol-acetate system to be no greater than 0.10 from studies on phenol solubilities upon addition of acetate. l6 Joesten and Dragom have used the method of difference spectra to study complexes of phenol and various compounds in CCL; our use of the method of difference spectra is similar to theirs. Figure 4 shows two examples of the difference The Journal of Phyakal Chemistry
270 200 290
270 280 290
Wavelength (mlc)
Figure 4. Ultraviolet difference spectra of 6.4 X 10-4 M phenol at pH -7.0, loo, ionic strength 1 M ; a, 1 M sodium acetate; b, 0.5 M sodium acetate.
spectra with peaks at 272 and 280 mb. Assuming that the difference spectra arise from the production of a complex, according to the equilibrium of eq. 2, then it can be shownwthat
where concentrations are equated to activities for reasons cited in connection with eq. 3 and where AD is the observed difference in optical density. ADm, is the value of hD when all the phenol is in the form of the complex. In the experiments reported here, AD/AD,,, is of the order of 0.25 (at 10' in 1.0 M sodium acetate), [Q]is in the range of 0.4 to 1.0 M , and [F] is 6.4 X M . Hence, [&I >> [F]AD/ AD,,; this relation has been used in obtaining eq. 9. A plot of l/AD us. l/[Ac-]yields a straight line, as in Figure 5, and the slope and intercept give both K.,,o, and AD,,, which are shown in Table 11. (14) J. Feitelson, J . Phya. C h a . , 68, 391 (1964). (15) M. Eigen and L. De Maeyer in "Technique of Organic Chemistry," Vol. VIII, Part 11, S. L. Friess, E. S. Lewis, and A. Weissberger, Ed., Interscience PubIishers, Inc., New York, N. Y.,1963, p. 1033. (16) D. B. Wetlaufer, Compt. rend. trav. lab. Carlaberg, 30, 135 (1956). (17) M. Laskowski, Jr., Abstracts, 131st National Meeting of the American Chemical Society, Miami, Fla., April 1957,p. 47C. (18) M. Laskowski, Jr., J. M. Widom, M. L. McFadden, and H.A, Scheraga, Bwchim. Bwphys. Acta, 19, 581 (1956). (19) R,A. Scheraga, ibid,, 25, 196 (1957). (20) M. D.Joesten and R. S. Drago, J . Am. C h . Soc., 84, 2037, 2696,3817 (1962).
2965
THERMODYNAMIC DATAFROM FLUORESCENCE SPECTRA
existence of a large negative contribution to the free energy of association. If the corresponding groups (ie., tyrosine, instead of phenol, and glutamic acid, instead of acetate) were attached to a macromolecule, then there would be no loss of translational entropy upon association; there would be some loss of entropy of internal rotation of the associating groups in the macromolecule, but this entropy loss would probably I I 1 I I I I 0 0.5 1.0 1.5 2.0 2.5 3.0 be smaller than that arising when independent parI m ticles associate. Hence, the postulated negative contribution to the free energy of association (to give as Figure 5. Plot of l/AD vs. l/[Ac-], according would make the tyrosyllarge a value as 0.5 to KaBBOO) to eq. 9, at loo, pH -7.0, ionic strength 1.0 M , phenol concentration 6.4 X 10-4 M . glutamate interaction a strong one in proteins. Since AHwm is very small (-400 cal./mole) and since it is reasonable to expect a contribution of apTable II: Temperature Dependence of the Association proximately 1000 cal./mole from the hydrogen bond, Constants from Ultraviolet Difference Spectra" there is most probably a partially compensating positive enthalpy contribution from some other process. To offset the loss of translational entropy _ " there must 10 0.36 f 0.12 0.10 f 0.03 be a corresponding entropy gain from this other 18 0.32 f 0.10 0.10 f 0.03 process. These two conditions, a gain in enthalpy 25 0.35 f 0.11 0.10 f0.03 and in entropy, are characteristic of the formation of 35 0.32 f 0.18 0.10 0.05 hydrophobic bonds. We thus suggest that, in addition " It is possible to improve the precision in the values of Lam to the formationof the intermolecular hydrogen bond, and ADmr. However, the precision obtained here is good a hydrophobic bond is formed between the methyl enough to demonstrate that the same values of K,.,, are obgroup of the acetate and the benzene ring of the phenol. tained by both the absorption and fluorescence techniauea. Courtauld's space-filling molecular models indicate that this is possible. When the thermodynamics of association are known for the system phenol-formate, Discussion then the contribution of the hydrogen bond may be We have shown that it is possible to measure associsubtracted from the values for acetate and higher ation constants for weakly associating systems with homologs to ascertain the contribution of hydrophobic some degree of precision using the technique of conbonds to the thermodynamics of such associations. centration quenching of fluorescence. The numerical Such experiments are now in progress; when they are values of Kmsmthus obtained are in fair agreement with completed, a more detailed discussion of these results those obtained from ultraviolet difference spectra. It should be noted that the data from fluorescence will be possible. Experiments on the association of neutral carboxylic acids and amides (both of which we are more precise and the experiments employ lower find do quench phenol fluorescence) are also possible. concentrations (e.g., a maximum of 0.4 M Ac- as I n these cases, one must consider the association of compared with the 1 M Ac- for ultraviolet difference quencher with quencher as well as quencher with spectra). The results for the phenol-acetate system fluorescer. may be summarized as follows in the temperature range of 0 to 40° (see Table I) Application of These Concepts to Polyamino Acids
-
*
-
KssBm 0.5
AHmm
f
10% M-l
-400 i 400 cal./mole
Since the association of two m a l l molecules in aqueous solution would be expected to involve a large loss of translational entropy, without much of an accompanying decrease in enthalpy upon formation to be of the hydrogen bond, we would expect K,,Bsoo much less than 0.5. In order to account for the large experimental value of K.880c,we must postulate the
We have shown that eq. 8 gives a possible interpretation of the fluorescence of the system phenolacetate. It is of interest that this relation also can linearize the data on the fluorescence of a copolymer of glutamic acid (analog of carboxylate) and tyrosine (analog of phenol). Specifically, Fasman, et aZ,21922 (21) G.D.Faaman, I(.Norland, and A;Pesoe, Biopolymers, Sump., 1, 325 (1964). (22) A. Pesee, G. Bodenheimer, K. Norland, and G. D. Fasman, J. Am, Chem. SOC.,86,6669 (1964).
Volume 89,Number 9 September 1986
A. YOUNG MOON,DOUGLAS C. POLAND, AND HAROLD A. SCHERAGA
2966
(where references to earlier work can be found), have recently published data on the fluorescence as a function of per cent ionization for the copolymer L-G~u: L-T~ (95:5), obtaining a sigmoidal curve. If we assume that the “concentration” of quenchers in the copolymer is proportional to the per cent ionization
[Q] = a[% ionization]
(10)
then eq. 8 becomes
-1
[% ionization] a@,
-
+ K,,,,,) + az(JcqKassoo) 1% ionization]
I
Figure 6 (curve A) is a plot of the data of Fasman, et al., according to eq. 11. Fasman, et al., have argued that their data do not imply any tyrosine-carboxylate association since “then the quenching of fluorescence should fall off sharply at the beginning (during the first 20% ionization), especially in the DL-L polymer where the tyrosines are easily accessible to carboxylate ions, however it does not.” If there were no association, curve B (Le,, K,,,,, = 0 ) would result. I n fact, just the opposite difficulty ensues; i.e., the intensity of fluorescence falls off too rapidly with per cent ionization and, as a result, K,,,, of eq. 11 can be shown to be imaginary, independent of a. It should not be expected that tyrosine-carboxylate interactions would be very probable in the random coil form.2a However, this does not argue that the same interactions are unlikely in a globular protein. Since an equation of the form of eq. 11 can linearize the sigmoidal curve found by Fasman, et aZ., it is of interest to see how this equation could arise without involving association. We assume that ionized carboxyl groups are present only in the random-coil form, or rather that ionization forces those portions of the molecule (in which the ionized carboxyl groups are situated) to be in a random coil form. At low pH (ie., low degrees of ionization) these random-coil portions will be small, and few in number, but will increase as the pH increases. Thus, the accessibility of carboxyl groups to tyrosyl groups will increase as the pH increases, owing to the increased flexibility of the chain; in other words, each carboxylate ion group becomes a better quencher as the pH increases. This effect would be manifested by an increase in the quenching constant with pH. Assuming that this increase in k, is linear in [% ionization], we may write
k,
= k,(O)
+ p [ % ionization]
(12)
where k,(O) is the value of k , when [% ionization] = The Journal of Physical Chemistry
I
0.25
0
(11)
0.502,
8
0.75
L
1.c
[“coo 1
Figure 6. Replot of data of Fasman, et aLJzlaccording to eq. 11. Curve A: experimental data; curve B: expected behavior if only collisional quenching is operative, Le., if no tyrosineglutamate hydrogen bonds form.
0, and p is a constant equal to
’
=
bk, ionization]
Thus, eq. 1becomes
‘-, 01 1
[% ionization]
= akq(0)
+ ab[% ionization]
(14)
which has the same form as eq. 11 and fits the data equally well, with a slope a@ and an intercept ak,(O). Although none of the parameters can be evaluated, for the slope and intercept offer only two equations with three unknowns, this mechanism of increased flexibility provides a quantitative explanation of the data of Fasman, et aZ., on the L copolymer. One difficulty with this interpretation is that the DL copolymer, which is a random coil even at low pH, should have a quenching constant at zero concentration of quencher (zero per cent ionization) very much larger than that of the L copolymer. However, Fasman, et aZ., report, but do not show, that the dependence of fluorescence on pH in both systems is nearly identical. One further note is that Fasman, et al., attribute the higher intensity found in the L (helical) over the DL (random-coil) copolymer to be due to environmental effects of being in a helix; since carboxylic acids (uncharged) also quench phenol fluorescence, the abovementioned collisional interaction in the DL random coil is a “first-order-eff ect” explanation of the lower fluorescence in that system. (23) D. C. Poland and H. A. Scheraga, BwpoEymers, 3, 283 (1965).
