SHRINKAGE IN RIBONUCLEASE FIBERS
April 5 , 1961
than half that found by the first method and a ridiculous ao. Also, it is not possible to find a single J that will make the theoretical and experimental curves coincide over any range of concentration. Permutations and combinations of the above do not give anything much better in the way of a fit. A viscosity correction does not give enough aid and the simple association correction would push the Ar curve up instead of down. At the present time, we can only hope that further work on this type salt and particularly mixed solvent work will help our interpretive problem. To illustrate the difficulties involved in adding these “corrective” terms to the original limiting law, Table IV gives the relative size of the terms in the CuBDS and LaNTS extended equations a t a few concentrations. To say that we are straining the theory in these cases is certainly an understatement. Approximations of no import for a 1-1 may become very important for a 3-3. We hope to shed more light on these unsettled questions by the extensive experimental program we have in progress. At present we are exploring both the low-field and high-field conductance of the BDS- salts of the other stable divalent ions as well as other lanthanide NTS’ salts. We also have prepared salts of benzenetrisulfonic acid and 4,4‘-
[CONTRIBUTION FROM
THE
1573
TABLE IV Salt
cx
CuBDS
LaNTS
104
1 10 50
1 10 50
AO
SC’/~
~ ~ i co g
114.64 4 . 5 2 - 1.29 114.54 14.25 - 9.70 114.54 31.95 - 37.20 140.5 140.6 140.5
14.1 44.6 99.6
-
23.5 -176.3 -676.6
JC
A
0 . 8 4 109.57 8 . 3 5 98.94 41.75 87.14 15.8 158.0 790.0
118.7 77.7 154.3
diphenyldisulfonic acid and are doing preliminary work with them. I n addition, we are collaborating with workers a t other universities in the exploration of the activity coefficients and transference numbers of these salts. It is hoped that this paper will stimulate more interest in the properties of this intriguing new class of strong electrolytes. Finally, one must say that the success of the extended Fuoss-Onsager theory in treating these high charge type salts is a striking demonstration of the essential correctness of the theory. The authors wish to thank Professor R. W. Parry for the loan of the conductance equipment and the National Science Foundation for partial support of the work. C. J. H. acknowledges the aid of a fellowship from the Horace Rackham School of Graduate Studies.
DEPARTMENT O F CHEMISTRY, CORNELL UNIVERSITY, ITHACA, NEW YORK]
Thermodynamic Study of Shrinkage and of Phase Equilibrium under Stress in Films Made from Ribonuclease182 BY AKIONAKAJIMA3AND HAROLD A. SCHERAGA RECEIVEDAUGUST25, 1960 Ribonuclease films were used for studies of shrinkage and phase equilibrium under stress. The films were prepared by coagulating ribonuclease with formaldehyde, compacting the clot to a thin film, partially cross-linking with p-benzoquinone, stretching in hot urea solution and further cross-linking to obtain a partially oriented, partially crystalline material. The film is considered to consist of two regions, ;.e., amorphous zones which crystallize on stretching and separate zones which contain crystallites in equilibrium with the surrounding amorphous zone. With these films, investigations were carried out on the dependence of the helix-random coil transition temperature on the pH of the medium, using measurements of retractive force. The change in force with temperature was reversible in the presence of 2 M KC1 a t low pH where no side-chain hydrogen bonding is present. The pH-dependence of the transition temperature was adequately accounted for by means of a reasonable model and a recent theory of reversible protein denaturation, in which side-chain hydrogen bonds play a dominant role. The heat and entropy change per peptide residue, accompanying the helix-random coil transition, were obtained from similar experiments on the dependence of the transition temperature on the concentration of urea. The crystalline unit in the assumed model consisted of two helical portions of 12 amino acid residues each, connected a t both ends by cross-links, Force-temperature curves as a function of relative length, as well as data on swelling and its dependence on ionic strength, also were obtained, the data being subjected to a thermodynamic analysis from the point of view of phase equilibrium under stress. It was thus possible to obtain estimates of the contributions of the heat of solution, heat of rupture of a backbone hydrogen bond and the heat change accompanying the change of composition of the fiber induced by a change in its length. The model and the results are compatible with known structural features of ribonuclease and the elastic behavior of other fibrous proteins.
Introduction The effect of side-chain hydrogen bonds on the elastic properties of protein fibers and on the configurations of proteins in solution recently has been treated theoretically4 on the basis of earlier work (1) This investigation was supported b y Research Grant E-1473 from the National Institute of Allergy and Infectious Diseases of the National Institutes of Health, U. S. Public Health Service. (2) Presented before t h e Division of Biological Chemistry a t the 138th Meeting of the American Chemical Society, New York, N. Y.. September, 1960. (3) Visiting Research Fellow (1958-1960) from the Department of Textile Chemistry, Kyoto University, Kyoto, Japan. (4) H. A. Scheraga, J . Phrs. Chem., 64, 1917 (1960).
on elastic mechanisms in proteins5 and on the stability of side-chain hydrogen bonds6 The purpose of this paper is to provide experimental evidence for the earlier theoretical considerations4 and to obtain further information about the role of side-chain hydrogen bonds in the mechanism of shrinkage. Ribonuclease was chosen for this study since the amino acid sequence7and disulfide bridge positions8 are known, and some information is (5) P. J. Flory, J . A m . Chem. SOC.,78, 5222 (1956). (6) M. Laskowski, Jr., and H. A. Scheraga, i b i d . , 76, 6305 (1954). ( 7 ) C. H. W. Hirs, S. Moore and W. H. Stein, J . Bid. Chem., 236, 633 (1960). (8) D. H. Spackman, W.H. Stein and S. Moore, ibid., 235, G48 (1960).
available about its secondary and tertiary struct ~ r e .Films ~ were prepared from ribonuclease and cross-linked with p-benzoquinoiie. The chain configuration in such filnis need not be the same as in native ribonuclease. The point of view adopted in this work is that of Flory,s viz., that the shrinkage of fibrous proteins involves a crystalline-to-amorpl!ous phase transition, the sound~iessof this approach !laving been :I inply deirionstrat e J . 'o--lo I t is further assumed here that the c r y s t a l l h furni is an a-heiix and the aniorphous form is a random coi! so that the process may be regarded 2s a hclix-to-random coil transition. Several workers have considered tliis transition (denaturation j , and t h e effect of temperature, @H,and concentration of chemical denaturants thereon, from both a thermodynamical and statistical niechanical I>oiilt of It sheuld be noted that the theory is essentially the saiiic, indepcndent of mhether the transitions occur in singly dispersed nm!ecu!es in dilute so!ution or i n the (swollen) solid phase of a fiber. Experimental Preparation of Filins.--Arnioiir
and 0.43 Af in 2;a reagent mas prep
:w%inc ri1x)nuclease (Lot StcJCk solutions of C ! L . 1017 tng. of t21c (1.I 111 in piiospliatc I-rnaltlehyde clotting %j solution with pH rratioii of 2 . 5 g./lnO
T o clot the ribonucicnse, 1.5 11.~1. of !he rlilutc form:tltiehyde solution was adtlcd t:, an eqti.al volume of the protein solutiou with rapid s or? ge1,itioii began, t!ie solution was poured ont i: in an area surr-oundetl Clotting w i ~ s:dloweri b y a glass cylinder o l 3 . 5 c i n . to proceed for 20 min. !in ~ 1 1 tc? after which the clot was transfex.ret1 t o ii with another piece of n:usii!i anti a fib I
(9) H. A. Scheraca, J . A m C h e m . .Soc., S2, 35.17 (1960). (10) P.J. Flory. S i e u c r , 124, 57 (19Zfj). (11) J. F. M. Otli, R. T. Uumitru, 0 . K. Spurr, Jr., and 1'. J Flory, J . A m . Chem. Soc., 75, 3288 (1957). (12) P. J. Flory, J . Cell. n?;d Comp. PhyiioZ.. 49, Sug:~l. 1. 175 (1957).
(13) J. I.". IvI. 0 t h and P. 1. Flory, J . .4m. C h z m . S o i . , 80, 1297 (1958). (14) C . A . J. Iloeve and P. 5. Flory, i b i d . . SO, G523 (1958). (15) L. Mandelkern. D. E. Roberts, A. F. Diorio and A. :i. Posiier. i b i d . , 81, 4148 (1959). (16) L. hlandelkern, A. S. Posner. A . .:1 Ijiorio and K. Laki, Pvoc. N a l l . Acad. Sci.. U.S . , 46, 814 (1958). (17) E. T. Dumitru, PI1 I>. Thesis, Cornell Uuiversity. SepL., 1957. (18) 0. K.Sp!irr. Jr., 1'ti.I). Thesis, Cornell University, Sept., 195s. (19) G. I. Loeb. Ph.D. Thesis, Cornell Uuiversi!y, June, 1900. 230 (1955). (21) T.I.. 11111,1.P o i y + ~ oSiz., 23, 548 (13.77). (22) J A. Schdln-an, J . P h y s . Chef%.,62, 1483 (1958). (23) B. H . Ziiritn arid J. K . lka&?$;.J Cheps. PAyr.. 28, 124G (1958); 31, 5261 il9,59). (24) J. is, Cilibs a n d 6.A ilikfarzio, ibid., 28, 1217 (l95S), 3 0 , 271 (1959). ( 2 5 ) I,. Peller, J . P h y s . Cl;i.m., 63, 1194, 1199 (1959). (26) S. A . Rice and A. IVada, Atistracts of the 131th meeting of the Amer. Chem. SOC.,Chicago, 111.. Srpt., 1958, p. 4 1 3 . (27) T h e gH was chosrn as 9 5 t o obtain a witable reactiou rate in t h e subsequent clottins with formalriehyde. At higher pH ( e x . $13 11j the clotting reaction was too fast, bring almost instantaneous; a t l o w e r p H ( e . g . 013 5.R) the reaction was too slow (about 2 4 h r . ) : ut gl-1 9 R gelation occurred in about 2 min. These observations are in accord with t h e notion t h a t formaldehyde reacts with tincharged amino pronps. T h e SaCl was ailded to reduce electrostatic repulsions between protein molecules during gc1atiri:i
with a wiglit of 700 g. for 1 hr. The resulting film then was washrd with water. I n order to partially cross-link the film, it was immersed in a 1 % solution of p-benzoquinone (buffered with pH 9.5 phosphate) a t rnom temperature for 1 hr. and then washed with water. The cross-linked film was cut into strips of 1 mm. width and stored in water a t 4'. Films prepared in this manner probably have their chains preferentially oriented in the plane of the film. I n order t o obtain an oriented film, the strips were stretched 3 0 7 ~ OF their length in a 4 IM urea solution28 a t G5' oii a metal stretching frame and t!ien re-immersed in the htfierrd p-beiizoqiiiiione solution at rooIr1 temperature for 1 lir. under stress t o fix the oriented configuration with more cress-links. After cross-linking, the stress relaxed in the stretched state, indicating that the oriented configuration was maintained in the absence of external stress. The oriented films were washed with water and stored in distilled mater a t 4'. Such films were stable for a t least a month, using thcir unchanged force-temperature characteristics as a criterion of stability. The cross-linking witli formaldehyde and p-benzoquinone probably involves the basic amino acid residues, primarily lysine e-amino g r o ~ p s , of ~ ~which - ~ ~there are 10 in ribonuc l e e ~ e . ~The cross-linking reactions between amino groups and formaldehyde and p-benzoquinone, respectively, have been disciissed by Mihalyi and Lorand.32 Under the conditions used here, the degree of cross-linking with formaldehyde is very low.32 Furthermore, when such cross-links are in?roc!uced into collagen, they tend t o disappear upon storage in \vatCr.lR Tlierefore, after the initial preparation of the film; o-benzoquinone was used t o obtain more permanent cross-links. Since p-benzoquinone darkens 011 standing at pFI 9.5 clue to polymeriz;ttion, fresh solutions of this reagent i i l w ~ y swere used. Force Measurement.-The dynamometer for the measurement of force was essentially the same as that of 0 t h and Florp13; the sample !ength was 1to 2 cm., and the sample !vas iininerscti in a b:iffer whose pH and temperature could he controlled during the measurement of the force. The strain gaii,oe was a rnndel G7A-1-2500 (Statham Instrunient Co., Puerto Rico) with a capacity of 1 ounce (28 g.) and itiaxiniiiin excitation voltage of 36 volts. The input voltage w:is obtained from 3 Mallorp mercury batteries of 9 volts each, arrangrd in series with a variable resistor t o control the input voltage. T!ie sensitivity of the gauge was 3354 niicrovolts per i n p u t vnlt per ounce. The output voltage was fed into a General Electric model 8CE5CP19A recording potentionieter having a sensitivity adjustable from 0.2 to 500 tnillivolts full-scale in 11 steps and two chart speeds of 6 in./hr. anti 6 in./niin., respectively. The system was calibrated by hanging known weights or the strain gauge and noting the deflection of the recorder pen. I n experiments of lung duration, the calibration was carried out before and after t h e run. 'The lengths of the samples were measured simultaneously with the force b y means of a cathetometer with a precision of i 0 . 0 0 1 m i .
Results and Discussion a film is heated to induce a transition, the length will decrease a t constant force, or the force exerted by the film will increase a t constant length. If the transition is R reversible one, then a therniodynaniic analysis can be carried out. In such an analysis it is helpful if one can demonstrate experimentally that the initial and final states are indeed helical and randomly coiled, respectively. For such purpose, X-ray diffraction photographs were taken of ribonuclease films a t 5094 extension in the presence of bit$er. However, the photographs were not of State of Film.--If helix-randon: coil
(28) Urea a t G 5 O was used t o unfold the molecule since the deuatiiration r,T rilmnticlease with urea i s reversible.'B ( 2 0 ) 1%'. P. Harrington and J. A. Schellman, Compt. r e n d . ~ Y U Y .Zub. CQf'!-s6Pt'K,S P Y , Chill.. 30, 21 (1950). (30) K. H Gustavsori. Koll. Z . . 103, 4 3 (1943). (31) H Nitschniann and H. Hadron, Helv. Chi?%. Acla, 26, 1084 (1943).
(32! E. hlilialyi and I,. l.orand, I I f i n g . Acto Physiol., 1, 218 (1918).
SHRINKAGE IN RIBONUCLEASE FIBEKS
April 5, 1061
1577
cGc 05-
04 -
0
+ 1 0
20
30
Temperature,
40
50
"c
Fig. 1.-Change in contractile force with temperature in a buffer solution at p H 2.36 containing 2 M KC1: 0, ascending; e, descending temperature in the first run; A, ascending temperature in the second run; Tt, = 23.5'.
sufficient clarity, because of the low degree of extension and high degree of swelling, to enable us to decide whether oriented crystallites were present in the film a t low temperature. Higher extensions could not be induced because the films would then rupture. We shall, therefore, have to assume that the sample in its initial state contains (partially oriented) crystalline regions distributed among amorphous regions.33 This assumption is compatible with the results of studies of dilute solutions of ribonuclease in water,29j36,37 from which the presence of a-helices is inferred.9.29~36~37 Similarly, it will be assumed that the chains are in the randomly coiled configuration above the transition temperature. Force-Temperature Behavior.-Since our primary concern here is to assess the influence of sidechain hydrogen bonding on the helix-random coil transition" (and, therefore, on the elastic properties), 2 M KCI was used to minimize electrostatic contributions to the free energy of the transformation. As will be shown below, the degree of swelling is essentially independent of pH in 2 M KCI. The first set of experiments was designed to examine the reversibility of the heat-induced transition. The sample was mounted between two (33) We have been more successful in demonstrating crystallinity by X-ray diffraction with other fibers (fibrin84 and insulinB5) in buffer with or without stretching. If a fibrin fiber, made in a n analogous way as the ribonuclease film, is extended about 300% a n a-keratin X-ray pattern is obtained, even in buffer; with the insulin fiber we observed a transformation from a non-oriented crystalline pattern t o a n amorphous one as t h e temperature was increased in t h e presence of buffer. However, the degree of swelling of fibrin a n d insulin fibers was less than t h a t of t h e ribonuclease film. If t h e degree of swelling is large, i t is very difficult t o detect crystallinity by X-ray diffraction. (34) A. Nakajima, G. I . Loeb and H. A. Scheraga, unpublished observations. (35) A. Nakajima a n d H. A. Scheraga, J . A m . Chem. Soc., 85, 158.5 (1961). ( 3 6 ) R. E. Weber and C . Tanford, i b i d . , 81, 3255 (1959). (37) J. Hertnans, Jr., and H . A. Scheraga, { b i d . , submitted.
20
30
40
50
60
70
Temperature, "C
Fig. 2.-Change in contractile force with temperature in a buffer solution a t PH 6.53 containing 2 M KC1: 0, ascenddescending temperature; Tt, = 49'. ing; .,
clamps in a buffer a t a constant temperature until equilibrium was attained and the length adjusted to take up the slack a t zero force a t that temperature. The temperature then was raised a t a rate of about l"C./lO min. After denaturation the sample was cooled slowly to the starting temperature and then reheated a t the original rate. Fig. 1 shows the relation between the contractile force, in a buffer solution a t pH 2.35 containing 2 M KCI, and temperature a t constant length. The behavior in a buffer solution a t pH 6.53 containing 2 M KCI is shown in Fig. 2. The transformation is reversible a t pH 2.35 but hysteresis is observed a t fiH 6.53. As will be discussed below, there is a maximum degree of side-chain hydrogen bonding a t p H 6.53 but essentially none a t p H 2.35. I t seems that the helix can re-form readily a t pH 2.35. At pH 6.53, where the recrystallization requires the formation of the side-chain hydrogen bonds as well as the backbone ones, the process is slower, giving rise to the observed hysteresis. In dilute solution, the heatinduced denaturation is r e v e r ~ i b l e ~ ~inq ~the ' pH range of 1 to 7. Presumably, the constraints in the crystalline cross-linked fiber are somewhat different from those in the native molecule in dilute solution. The transition temperature, Tt,, is taken as the inflection point obtained in a run of increasing temperature starting from essentially zero force. Model for Elastic Behavior.-According to a recently proposed model for native ribonuclease in water,g about 60% of the molecule is helical and divided into several short helical portions. Since our films were obtained by cross-linking with formaldehyde and p-benzoquinone, it is likely that the introduction of cross-links reduces the helical content. We shall therefore assume that the crystalline portions are representable by units of the type shown in Fig. 3. The assumption of a higher degree of crystallinity of the same type would not alter the
1578
-4KIO NAK.4 JIM-4 A N D
HAROLD A. SCIIERAG.~
Vol. 83
-
0.4
t
t
v)
$,
0.3-
0;
2
Fig. 3.-A
model for the assumed helical portion of ribonuclease in the cross-linked film.
thermodynamic argument. This crystalline unit is composed of 2 0-helices, each containing 13 residues and cross-linked a t both ends as shown. The remainder is considered to be in the amorphous region. The free energy change, A F o o b s d , for converting the helical portions of the unit to random coils may be computed from the equation of Schellman,20 applied to the backbone helix, and the equation of Floryj for the effect of the cross-links. For the present, we are considering the behavior a t very low pH where no side-chain hydrogen bonds are formed.
9
0.2-
0.1-
h
IO
20
30 Temperature, "C
40
Fig. 4.-Typical force-temperature curves in urea solution (PH 2.63, 2 ,If KC1); the urea. concentration is indicated on the curves.
c is the concentration of urea in moles/liter. The value of K for the association of urea monomers to dimers was found38to be 0.041 a t 25'. However, this value cannot be used in eq. 4 since the value AF'obsd = 2 { ( n - 4)AH'res - (a 0.041 applies to urea dimers which are mixtures of l)TASo,,s) - TASoX (1) two forms containing one and two hydrogen bonds, where n is the number of amino acid residues in the respectively. However, from Schellman's treatchain, and AHo,,, and AS',,, are the enthalpy and ment of the heat of association of urea,3a it can entropy changes, respectively, per residue, for the be estimated that 60% of the dimers have only one unfolding of an infinitely long helix to an unstressed, hydrogen bond. We shall, therefore, take K as ;.e., isotropic, random coil. As in aprevious theory,6 60% of 0.041 or 0.025. Since c is in the range of the free energy of mixing of amorphous polymer 0 to 1, in the experiments to be described, Kc < 1 with diluent has been omitted. This omission and eqn. 4 may be approximated by could reflect itself in somewhat different values for AFooomb = -48RTKc (5) AHo,,, and Asores in eq. 1. Since our measurements were made a t very low force, we can assume The temperature dependence of K may be obtained the random coil to be isotropic. The quantity from AS0, is the molar entropy decrease of the random coil due to the introduction of cross-links in the crystalline form and is given by the expression6 where AH, is the heat of formation of the comASO, = - ( 3 R v / 4 ) [In n' 31 (2) plex between urea and the peptide CO or NH where v is the number of cross-linked helices and group. n' is the number of statistical elements (assumed If the value of AFocomt of eq. 5 is added t o the here equal to n) between cross-links. I n our use of right hand side of eq. 3 and A F o o b s d set equal to eq. 2 it is assumed that it is valid for short chains. z&o a t the transition-temperature, we obtatn With n = 12 and v = 2 , eq. 1 becomes
+
AFoobsd.
+
16A.Hore.- 22TASoreB 16.5T
(3)
Before A F o o b s d can be evaluated it is necessary to know the magnitude of AH',,, and ASOres. These values can be obtained from measurements of the transition temperature in the presence of urea.*O Such experiments were carried out a t pH 2.63 in the presence of 2 M KC1 to eliminate side-chain hydrogen bonding and charge effects, respectively. ACcording to Schellman,20the free energy of combination, A F o c o m b , of the extended chain with urea is given by eq. 4 (valid for p > 20). AF'eomb
=
- 2 p R T In ( 1
+ KC)
(4)
where p is the number of amino acid residues which may react with urea when the helix is unfolded and is equal to 24 in our model. The quantity K is the equilibrium constant for the binding of a urea molecule to a C=O or N-H group of a peptide unit, and
3E e+AHu/RTz5 e - A H u / R T t r
(7)
AHores
Thus, if K is known as a function of temperature, a plot of l / T t , against c e - A H u / R T t r should give a straight line, the slope and intercept of whic,h will give AHo,,, and ASOres, Figure 4 shows some typical measurements of the force-temperature behavior in urea. The transition temperatures are plotted, according to eqn. 7, for AH, = -3, -6 and -9 kcal./mole, respectively, in Fig. 5 . From the initial slopes of these curves we obtain Mores = 1800, 1750, and 1700 cal./mole for AH, = -3, -6 and - 9 kcal./mole, respectively. These values are in good agreement with estimates of Schellman.2o (38) J. A. Schellman, Comfit. v e n d . i ~ a vlab. , Carlsbrrg, S e r . Chiin., 29, 223 (1955).
SHRINKAGE IN RIBONUCLEASE FIBERS
April 5, 1961
1579
i I . ".Q
-------0
I x IO2
3 28 0
2 x 102 I
I
I
*
~
0
1x104
2x104
I
I
0
2x106
4 0 6
2
*
Fig. 5.-Relation between 1/Tt, and urea concentration, in a buffer solution of PH 2.63 containing 2 M KCl; the symbols 0, 0 , and 0 correspond to A H , = -3, -6, -9 kcal./mole, respectively.
I n a previous paper39i t has been shown that
I < I AffuI
(8)
where AH'ij is the heat of formation of a side-chain hydrogen bond between an ithdonor andjfhacceptor. Since we are taking6 AH'ij = -6 kcal./mole for the side-chain hydrogen bond, we shall take AH'res = 1700 cal./mole (corresponding to AH, = -9 kcal./mole). Since the value of AH're, is not very sensitive to the choice of AH,, we are not committing any significant error in our essentially arbitrary choice of A H u . Therefore, no significance should be attached to the value AH, = -9 kcal./mole selected here. By the above criterion, i t could have been zero without affecting our calculated value of AH',,, very much. With the value of AHo,,, = 1'700 cal./mole, we obtain A s o r e s = 4.83 e.u. from the intercept of the appropriate curve in Fig. 5. These values of AHo,,, and AS',,, may be substituted in eq. 3. However, before doing so, we shall first consider the effect of side-chain hydrogen bonding in the next section. pH Dependence of Ttr.-Equation 3 does not yet contain the pH-dependent contribution to AFoob,d. However, if the p H is varied, then AFo,b,d (and consequently Ttr) depends on This p H dependence has been treated4 by introducing an additive, pH-dependent term, AF'H, to the right hand side of eq. 3; the term AFOH arises from sidechain hydrogen bonds between ionizable groups.6 For heterologous, single hydrogen bonds A P H = -RTZ In (1 X" "
-
1
+
Kij
Kij
- xij)
+ KI/[H"] + L " ] / K t
6
8
IO
12
PH
c ' exp (- $)
I
4
(9)
(10)
where Kij is the equilibrium constants for the formation of a side-chain hydrogen bond between a n ith donor and j l h acceptor, xi, is the fraction of the molecules having this hydrogen bond, K1 and (39) hl. Laskowski, Jr.. and H. A. Scheraga, J . Am. Chem. Soc., 83, 2GG (1961).
Fig. 6.-Experimental (solid line) and calculated (broken lines) results for PH dependence of transition temperature, Tt,. Experimental values in 0.07 M buffer solutions, 0; in the same buffer with added 2 M KC1, 0 . Calculated curves were obtained with the numerical values listed in Table I, assuming 1 tyrosyl-carboxylate and 1 histidplcarboxylate hydrogen bond.
K z are the ionization constants of the donor and acceptor groups, respectively, in the absence of the hydrogen bond, and [H+] is the hydrogen ion activity. I n using these equations the temperature dependence of K1, Kz and Kij must be taken into account. With the aid of eq. 9, eq. 3 becomes Apobsd = 1 6 A H L - 22ThS'rea
+ 16.5T -
RTZln (1 - xij)
(11)
where the sum is taken over all the side-chain hydrogen bonds between the helices illustrated in Fig. 3. The transition temperature is obtained as a function of p H from eqn. 11 by setting A F o o b s d . equal to zero. Details of such calculations have been described previously. As in the case of eq. 1, the omission of the mixing term should be noted. However, it will be shown below that the degree of swelling of ribonuclease films in 2M KC1 is independent of pH. Therefore, this mixing term will not contribute to the pH-dependence of A F o o b s d . Experimental data for the pH-dependence of Tir are shown in Fig. 6. These were obtained from force-temperature measurements a t various p H values. It should be noted that the same experimental curve (solid line in Fig. 6) is obtained both in the presence and absence of 2 M KC1. The two dashed curves in Fig. 6 are theoretical ones, calculated from eq. 11; using the values of M o r e s and ASOres obtained in the previous section from experiments in urea solutions and assuming two sidechain hydrogen bonds per helical unit given in Fig. 3 to be contributing to the sum in eqn. 11. The two side-chain bonds are assumed to be 1 tyrosylcarboxylate ion and 1 hystidyl-carboxylate ion hydrogen bond with parameters given in Table I. These parameters were chosen on the basis of previously published data.6,40 The slightly higher value of Ki,=. 10 was used to take into account an increased stability due to electrostatic interactions. (40) G. I. Loeb and H. A. Scheraga,
J. Phyr. Chem., 60,1633 (1956).
Lysyl groups were not considered 2s donors since Above the transition temperature] the swollen they are used up in the cross-linking reaction. phase can be treated as an amorphous network. At This is demonstrated by the fact that the p H of the swelling cquilibrium equation (13) holds for the water around a film (isoionic) is 6.5, as compared amorphous, isotropic state, neglecting any non-ranwith that of native ribonuclease in dilute solution doni cross-linking which may occur in that part of the ($H 9.6). The theoretical curves fit the experi- amorphous network which arose from melted crysmental data fairly well, especially in the region of tallites 4 1 maximum stability and a t low pH. The discrep- - j l n ( 1 + PI2 + X , Q ] = ancy a t high p H may be due to electrostatic interactions which were neglected here or, of course, t , ) inadequacies of the model. Effect of Swelling.-Since measurements of where the volume fraction of protein in the swollen shrinkage and elasticity are usually carried out in phase. ~ ' 2 ,is related t o q (or Q) by the equation 1 the presence of solvent, it is necessary to consider yJ, = .the effect of pH, temperature and force on the P degree of swelling. Since our experiments on the is the molar volume of the solvent, x1 is a free pH-dependence of Ttr were carried out a t a force as energy parameter for the polymer-solvent interclose to zero as possible, we shall examine here the action and M c is the molecular weight per crosseffects of swelling at zero force. linked unit. The differential heat of dilution, Afl;Tl, is given by TABLE I the expression42 ASSUMEDVALUESAT 25" FOR MODELCALCULATION^ i j 2 )
Tyrosyl carboxylate Curve A Curve 13
Histidyl-carboxylate Curve A Curve I3
10-6.0 10-8.6 10-6.6 K , (donor) 10-8.S 10-4.0 10-4.6 10-4.6 10-4.0 Kf (acceptor) AHLO,kcal./rnole 6 7 AHz0, kcal./rnole 0 0 4 10 K,j AHo,j,kcal./mole -6 -6 AHo,,. = 1700 cal./mole. Asores = 4.83 e x .
The degree of swelling, Q, was computed as the ratio of the weight of the wet film, W , to that of the dry film, TV0. The films were allowed to come to equilibrium with solvent for 3 days at constant temperature. The solvent on the surface of the film was removed with a piece of filter paper. The swollen film was weighed and then washed with water, dried i n vacuo a t 100' and then re-weighed. Table I1 shows the data obtained. The weight ratio, Q, is related to the volume ratio, q, by
where fj is the partial specific volume of the protein and p1 is the density of the solvent. TriE
TABLE II DEGREEO F SWnLLING WITIr PI< AND TEMPERATURE AT DIFFERENT IOSIC STREXGTII~
CHANCES O F THE
(A) I n 0.07 Af buffer solution Q = ?V/W'o pH 2.35 3.09 4 . 9 3 5.87 6 . 9 1 7.48 8 . 3 5 9 . 5 3 30" 10.77 5.03 4.43 4 . 6 5 6.39 7 . 2 1 7.79 8 . 3 4 45" 9.96 4.80 4.23 4.36 6 . 2 1 6 . 9 0 8.00 8 . 5 9 60" 9 . 7 3 4 . 3 4 3 . 9 2 4.13 6.00 7.17 8.22 8.84 2 M KCI (B) In 0.0; A[ buffer solution Q = W/Wo pH 2.35 2.84 4.41 6.53 7.36 8.73 4.71 4.98 4.68 4.56 4.44 4.35 30" 4.80 4.34 4.28 4.25 4.15 4.10 45' 3.80 4.57 4.10 3.85 3.64 3.71 60" a Some of these data apply t o mixed crystalline and amorphous phases, some to completely amorphous material, depending on tlie trnnsition temperature nt tlie givcn PH and ionic strength.
+
=
RT R ~ Z Q
(15)
where K~ is the heat parameter for the polyniersolvent pair and is related to x1 by the e q ~ a t i o n ~ ~ ? ~ ~
Therefore, the integral heat of solution per mole of peptide units, AHsol, is obtained by integrating eq. 15 from nl = 0 to nl a t constant polymer volume, b and M u n i t ; this leads to eq. 17. 0
AHSO] = V , M u n i t RT
KI(
1-
212)
(17
-
where M u n i t is the rnolccular weight per peptide unit ( i e . IOOl. We are justified in applying the above theory to our swelling data a t pH 2.5 since Tu is lower than 30" at this pH, i e . , the protein is in the randomly coiled condition. Since v2 is known from g (eq. 14) ( 4 being obtainable from the Q-data of Table I1 using eq. 12) and T'1 is known, i t is possible to conipute x1 from eq. 13 if Mc is known. Assuming that the randomly coiled units have 20-30 residues between cross-links, the value of M c would be 20003000. The ~ ~ - v a l u e scalculated , from the p H 2.84 data of Table IIB are plotted against temperature in Fig. 7 (see also Table 111). The resulting values of 0.4-0.5 seem r e a ~ o n a b l e . ~The ~ values of K ~ computed , from the slopes in Fig. 7 , and AHsol from eq. 17, are shown in Table ITI. The values of A H , o ~will be used in the discussion in the next section. The pH-dependence of the degree of swelling, @, at two different ionic strengths and tenlperatures is plotted in Fig. 8. The degrec of swelling is independent of pH in the presence of 2 1 11 KCl but markedly dependent on PH a t low and high pH in the absence of the KC1. Even in the absence of KCI, the degree of swelling is independent of pH in the intermediate p H range where the crystalline form is most stable (see Fig. 6). The presence of 2 (41) versity (42) (43) (14)
P. J Flory, "Principles of Polymer Chemistry," Cornell UniPress, Ithaca, N Y.,1953, P. 878. Ref 41, p. 523. Ref. 41, p. 510. Spurrls obtained 0 59 fur collagen it1 3 M K C S S s o l i ~ t i o na t Coo
April 5, 1961
SIiRINKAGE I N
I
I
0.52 -
I
048 O.
/
0.36
1 Mc7 M c = 2 0 0 0' 0
x,
/
/ N O
O
i
t5 1 40
30
50
60
Temperature, " C
I
Fig. 7 -XI calculated from swelling data, assuming M , equal to 2,000 and 3,000, respectively, plotted against temperature; pH 2.84, 0.07 M buffer solution containing 2 M KC1.
11.1 KC1 seems to suppress electrostatic effects and render Q independent of PH. Therefore, we may conclude that our discussion of the pH-dependence of T, is not influenced by pH-dependent swelling. This adds validity to our assumption that side-chain hydrogen bonding plays an important role in the stabilization of the crystalline form. K,
TABLE I11 AND AH,,i OBTAINED FROM SWELLING DATA,AT pH 2.84 IN 0.07 M BUFFERCONTAINING 2 M KCl
I (assumed) pi (measured)
M O = 2000 M , = 3000 M , = 2000 j M , = 3ono A H d (=I.)
1581
1
I
O
044 040 -
I
RIBONUCLEASE FIBERS
= 2000 3ooo A4:
30' 0.7 1.08619 18.0787 0.392
-
-843 -723
,450 .42 .36
.46G .44
-
-910
- 765
.37
0.7 1.07237 18.3068 0.435 .4 84 .47
-
- 995 - 847
.40
Thermodynamics of Phase Equilibrium under Stress.-When a protein film, composed of amorphous and crystalline phases, is immersed in a diluent, phase equilibrium can be established.6 We shall assume that solvent can mix with the amorphous regions; we shall further assume that the constraints of the system prevent the crystalline phase from swelling but that the solvent can make contact with the side-chains so that the latter can equilibrate with hydrogen ions of the solvent, ie., the pure crystalline phase is defined by the $H and melts t o an amorphous phase which is in equilibrium with diluent. We shall thus describe the phase equilibria as crystalline phase
amorphous phase
I
I
I
Fig. 8.--pH dependence of degree of swelling a t two different ionic strengths: 0.07 M buffer solution, 30°, 0; 2 il.1KCl, 30'. 0 ; BO", GOo, A ; 0.07 M buffer solution A.
+
her man^^^ and K ~ h n , the ~ ' film should be considered as an open system since the number of moles of diluent in the amorphous protein phase may change with a change in length due to the presence of the surrounding diluent phase. 48 According to (19) applies to such an open K a t ~ h a l s k yequation ,~~ system, where the diluent contains only one component
GO'
450
0.7 1.07929 18.1774 0.411
-
1
I
diluent phase (18)
When a uniform force, f, is applied along the axis of the film strip, these equilibria will be affected.s As pointed out by F l ~ r yK, ~a t ~ h a l s k yPrins , ~ ~ and ( 4 5 ) A. Katchalsky, Conference on Contractibility, hIelion Institute, Pittsburgh, Pa., Jan. 27-30, 1960, p. 22.
where T is the absolute temperature, P the pressure, L the length of the sample, H the enthalpy, ml the partial molar heat of dilution and nl and n.? are the number of moles of diluent and protein, respectively. Now, representing the changes in enthalpy and length in bringing the sample from the crystalline to the amorphous state in a closed system by AI$ and A I , respectively, we obtain the equation a t the transition temperature, Ttr
(2)
P .Ttr ni
AB1
(20)
If we apply this relation a t p H 2.73, where the contributions of the side-chain hydrogen bonds vanish, we may write AH of eq. 20 as Munit AH
wo
= AH.,I
4- AHOrao
(21)
where A H s o l is given by eq. 17, and the other terms have been defined. The second term on the right hand side of eq. 20 may be expressed in terms of the temperature dependence of q and L , since W66 nl = - (9 VI
(46) (47) (48) IIoeve
- 1)
(22)
W. Prins and J. J. Hermans, ibid., p . 26. W . Kuhn, ibid., p. 14. We are indebted to Drs. P. J. Florp, L. Mandelkern, C. A . and A. Katchalsky for helpful discussions of this problem.
AKIONAKAJIMA AND HAROLD A. SCHERAGA
1582
VOl. 83
9
:3: 2
Relative Length,
a'
Fig. 10.-Relation between force, f,and relative length, in 0.07 M buffer solutions containing 2 M KCl. Results shown by ( R ) were obtained directly from force-relative length measurements a t 11". Other results were obtained from Fig. 9: pH = 2.73; LO = 1.603 cm. a t 11'; cross sectional area of dried sample = 0.0023 CY',
IO
20
30
40
Temperature,
50
"C
eq. 23. It should be noted that the correction term (last term on :he right hand side of eq. 23) is only a n approximation since our diluent contains more than one component, and we have introduced an inconsistency by keeping L and ;.6i independent of temperature in our treatment of swelling. Fig. 9 shows some experimental results of forcetemperature measurements in pH 2.73 buffer containing 2 M KC1 a t different relative length, a', where a' is the ratio of the length, Lf, a t temperature T under the force f , to the length, Lo, a t a given temperature (here 11") under zero force, i.e., a' = Lf/Lo. These data were obtained directly by heating the sample a t fixed length. The data of Fig. 9 are re-plotted in Fig. 10 a s f 2's. a' at several temperatures. Also shown in Fig. 10 (solid squares) are the results of a direct set of measurements of the stress-strain curve (i.c. f US. a') a t 11'. The direct measurements agree with those obtained from Fig. 9, demonstrating again the r e ~ e r s i b i l i t y ~ ~ of the equilibria involved. Some data characterizing the curves of Fig. 9 Temperature, "C are shown in Table IV. It can be seen that T t r is Fig. 9.-Temperature dependence of contractile force, j, independent of a' up to 157' extension; however, a t different relative lengths, a', in 0.07 M buffer solutions a t higher extensions Ttr is inclined to increase, probcontaining2 M K C l ; pH = 2.73; Lo = 1.603 cm. a t 11'. ably due to a change in the state of the amorphous inaterial above the transition temperature (i.e., the and, a t constant temperature (49) Fig. 11 is another demonstration of the reversibility a t condnl =
wo.Tiozl dq
Using the values of ij and VI a t Ttr, we obtain eq. 23 from eq. 20, 21 and 22.
The left hand side of eq. 23 is obtainable from experiment and we can deduce therefrom information about the enthalpy terms on the right hand side of
s t a n t temperature a t p H 2.79, 2 M KCI. T h e length of t h e sample a t zero force a t 1 l 0 was La = 1.1246 cm. T h e sample was extended t o L = 1.1377 cm. and brought t o equilibrium a t this temperature for about 3 hr. This was taken as "zero time" in Fig. 11. T h e relative length a t this stage was 1.0116. T h e force remained constant a t about 0.42 g . for 1.25 hr.; after obtaining point no. 1, t h e sample was extended 0,005 cm. and t h e force determined (points no. 2 and 3 ) . T h e force decayed toward no. 3 . After obtaining point no. 3 the length was reduced t o its original value and t h e force determined After 2 hr. a t equi(points no. 4 , 5 and subsequent one4 a t 0.426.). librium, point no. G was obtained and then the sample shortened 0.010 cm. I t can be seen t h a t the force then rises (points no. 7 and 8) t o its equilibrium value. After obtaining point no. 8, the length mas increased t o i t s original value a n d points no. 9, 10, etc., were obtained. T h e decrease in force after points no, 2 and 9 in Fig. 11 is considered t o be due t o a tendency t o crystallize and the increase in force after puints no '1 and 7 to a ti.ndrncy to melt.
April 5 , 1961
SHRINKAGE IN
RIBONUCLEASE FIBERS
1583
TABLE IV TRANSITION TEMPERATURE AT DIFFERENT R E L A r I V E LENGTHS a', I N BUFFERSOLUTIOKS O F pH 2.73 CONTAINING 2 ~\f KCl 1,176 1.060 1.130 1.040 1.004 1.019 01' 25 28 25 25 25 25 Ttr, ' C . 5.80 2.05 3.18 1.57 0.35 0.91 j , g., a t Ttr -0.081 -0.035 -0.043 -0.031 AL, cm." -0.023 -0.026 -3.2 -1.7 -2.1 -1.5 -1.0 -1.3 (dL/bT)r x 103at ~ t , b From Fig. 12. a This is the total change in L in the transition a t constant force (see Fig. 12).
transition temperature for the crystalline-amorphous transformation increases as the tension on the amorphous form increases due to a decrease in the entropy of the amorphous form on stretching). Fig. 10 shows the relation hetween f and a'. Within a relatively small range of low a' values, the retractive force f was proportional to a'. After the initial linear region the slopes of the curves decrease and then increase again a t high a'. I n an ideal homogeneous fibril, lo melting should take place a t a sharply defined temperature. Starting from a completely amorphous state a t f = 0, the force f should first increase linearly with a' until the critical force for crystallization is reached; then i t should be constant and independent of a', since there is coexistence of amorphous and crystalline regions, until it is totally crystalline; thenf should increase sharply. However, if the sample contains partially crystalline regions in the initial stages a t f = 0 in an ideal fibril, f should be zero until the fibril is totally crystalline and increase sharply with a'. The curves shown in Fig. 10 are not ideal but correspond to a schematic curve which Flory'O gave for an inhomogeneous fibril. Presumably the whole curve a t a temperature below the transition point (-J 25') in Fig. 10 corresponds to the coexistence situation of amorphous and crystalline phases. That is, with increasing a' crystallization is taking place while there is coexistence of both phases. FlorylO pointed out that such diffuse melting may be due to variations in chemical structure along the fiber axis or to non-uniformities in the crosssectional area The last rather steep slope portion of the curve in Fig. 10 is presumed to be due to the stress-strain behavior of a material rich in crystalline regions. The data of Fig. 10 may also be considered in the following way. A vertical line ( i e . , increase in temperature a t constant a') corresponds to an increase inf due to melting a t any particular value of a'. An isothermal increase in a' leads to an increase in f due to an increasing amount of crystallization. Because of the diffuseness cited above, the coexistence region is not as sharply defined as it would be in the case of an ideal fibril. Above some critical temperature (greater than 40°), the system would be totally amorphous a t all a'. The data of Fig. 10 are re-plotted in Fig. 12 as L vs. T a t constant f. From these curves i t can also be seen that the low-temperature, partially crystalline material undergoes a helix-random coil transition around 25'. Further, we can obtain AL a t constant force from these curves as the difference in L at high and low temperatures. The slope a t Tt, gives (dL/bT)r. AH1 can be calculated from eq. 15 and is about -10 cal./mole for ~1 = -0.44 at G o ;the measured value of b q/bT is about -0.02,
both quantities a t zero force. Since q was not obtained as a function of L, we cannot evaluate the third term on the right hand side of eq. 23. However, we can make a rough estimate using the 0.7
I
0.11
0
R2
I
I
I
I
I
I
I
I
I
I
2
3
4
5
Time, hrs. Fig. 11.-Establishment of equilibrium force at 11' in a buffer solution of @H2.79 containing 2 M KCl, L = 1.1377 cm.
values obtained from the f vs. L function in place of the q us. L function. From the values at zero force in the f us. L curve we obtain50
-16 t o -18 cal./peptide unit
(24)
Comparing this value to that of AHs01= -765 to -910 cal./peptide unit (Table 111),we see that the contribution of the term in eq. 24 is about 2% of the first term on the right hand side of eqn. 23. While we have thus justified its neglect here, i t is still important that future experiments be carried out t o determine ( b n l / d L ) p , T , n 2 , as Katchnlsky has emphasized. If we neglect the third term on the right hand side of eqn. 23, we can evaluate the second term since we know the first term and also the left hand side of the equation. In Fig. 13 [f- T(hf/bT)P,L] is plotted against temperature using numerical values obtained from Fig. 9. First of all, it should be 45p48
(50) As can be seen f r o m Table 11, the degree of swelling is large and makes a significant contribution tof in this system. We have assumed t h a t the change in force with length is due t o a change in swelling at the transition temperature. Since A L is small (see Table IV) we have used the value of ( b p / b T ) ~ ,a, t~f = 0 for ( ~ P / ~ T ) L . P .The ~ ~ .term
(
~ ) F ~ , I . , of Z
eq. 23 can be replaced by (aL/bT)p.q,nZ a t Tt,, i.e.,
constancy of nl and nz implies constancy of q . Again, attributing the change in farce with length to a change i n swelling a t Tt,, (bL/aT)p,,,,, was replaced by ( . 3 L / . 3 T ) ~ , f , " ~ .
AKIO NAKAJIMA AND HAROLD A. SCIIIZK~GA
1584
Vol. s3
j
L' i-
154 I62
i
Y
I-.
Y1
1
'\
i_-_: . -_! . --- ."! . -L
!O
20
Zr/
I 46
50
,
l&o~---'------.l
30
40
Fig. 13.-Rclation betaecn [f - T ( d f / b T ) p , ~and ] tema' = 1.0i3 X , perature; data from Fig. 9: a' = 1.004 a' = 1.040,A; a' 1.0600, a' = 1.1300,CY' = 1.176,A.
+,
50
Temperature, "C Fig. l2.-Change
Ii
I i
--s
f = IO
U IO 20
..
in length with temperature a t constant force; data from Fig. 10.
noticed that these curves are independent of CY'. The minimum occurs a t the transition temperature. Neglecting the second term on the right hand side of eq. 20, we can obtain AH a t the transition ternperature from the minimum value of the ordinate in Fig. 13. Using AMs01from Table 111, we can then calculate A J l o r e s from eq. 21. These values are listed in Table V. It can be seen that A H ( M u n i t / W,) is essentially zero. Therefore, AHs0i -A €Pres if we neglect the third term of eq. 23; ;.e., the contribution of the heat of solution is just compensating the contribution of the heat of dissociation of the hydrogen bond. Thus the calculated values of U$Q,,, are $765 to $910 cal./peptide unit (about 40-5070 of the value of 1700 obtained from the urea experiments). This means that the degree of crystallinity of the film is about 40-50%.
-
In conclusion, the helical units shown in Fig. 3 are distributed in a partially oriented fashion in the film, occupying about 40-50% of the film. The remaining parts (iiO-50~o'o)are in the amorphous regions. The assumed presence of ( n e tyrosyl-carboxylate and one histid:J1-cnrboxylate sidechain hydrogen bond per fielicnl unit gives fnirly good agreement with the experinicntnl results. 'rA\nLE
v
ESTIMATIOX~ OF E x n x . \ L p I E S 1s cAL./I'E:PTIDR vxr.r = 0.0024 g.: M , , , t = 100 AH (ill,"it/TVo) 0.25 /Os ' r to -910 (from Table 111) A ~ ~ ~ " , AH",,. (calcd.) 4-7'65 t o +910 - lij to -11s Eq. 24
w,
_-
Acknowledgments.-'i'he auiliors wish to thank Mrs. Miriam Taylor for able assistance in the experimental work and n r . George Loeb for many helpful discussions.
