Method of Determining the Relative Stability of DifferentCon formational States of Biopolymer MoleculesBY 0. B. PTITSYNInstitute of Protein Research, the USSR Academy of Sciences, Poustchino, MoscowRegion, USSRReceived 27th February, 1970A method for estimating the relative stability of conformational states of biopolymer moleculesfrom the degree of sharpness of the transition between them has been suggested. The method isapplied to the estimation of stability of the DNA helical structure under physiological conditions aswell as to the estimation of stability of the a-helical structure of polypeptide chains in differentsolvents. The stability of an or-helical structure of polypeptide chains is relatively low not only inaqueous media but also in water-organic mixtures and even in inert organic solvents in which theenergy of intramolecular hydrogen bonds is essentially higher than in aqueous medium.This isan evidence that the formation of the helical structure in organic solvents must be accompanied bya noticeably greater decrease in the conformational free energy of monomer units than in water.This conclusion is confirmed by independent experimental data on free energies of initiation of helicalregions of polypeptide chains. For the explanation of this effect an assumption is made on the roleof dipole-dipole interactions of peptide groups of the backbone.PRINCIPLES OF THE METHODDepending on external conditions, biopolymer molecules exist in differentconformations, and cooperative transitions between them can occur.The study ofthe relative stability of such conformations is of interest, but under the conditionswhen one of the conformational states is considerably more favourable than the other,a direct measurement of the free energy difference of them is impossible. In thesecases it is necessary to change one of the parameters of the external medium so as tolevel the free energies of both conformational states. If this external parameter isdenoted as X , the free energy difference of the macroniolecule under the conditionsconsidered, X = X,, is equal towhereA@(Xo) CD2(X0)-@1(Xo) = -(&D2-6@1), (1)6% = @ I ~ ~ t ~ - - ~ ~ ~ ~ O ~ ~ (2)6% = @2(Xt) -@2(&),and X , is the value of X corresponding to the condition of A@(X,) = 0, i.e., to themidpoint of the conformational transition between the two states.Consequently,it is possible to determine A@(Xo), if the energies of transfer 6@ of the macromoleculebeing in two conformational states from X = Xo into X = X, conditions are known.The method suggested by Tanford of estimating the stability of the native structureof globular proteins by their denaturation with urea ( X is the urea concentration)and the method suggested both by Zimm and Rice and by Nagasawa and Holtzerof estimating the stability of the helical state of uncharged polypeptide moleules bythe helix-coil transition during their ionization ( X 3 -2.3 pH is the chemicalpotential of protons in solution) are based on this principle. In the first case, the70.B . PTITSYN 71energies of transfer are estimated on the basis of data on separate amino acid residuesand the spatial structure of a protein molecule ; in the second case they are deter-mined by the curves of potentiometric titration.2*suggested a methodof estimating A@(Xo) for those cases where a direct determintion of free energies oftransfer is not possible. The method is based on determining the X derivative ofA@ in the transition region and on estimating A@(Xo) by the equationRecently the author in collaboration with T. M. Birshtein 4*using physical considerations as to the type of dependence of the derivative aA@/sXon X. If, e.g., X is a chemical potential ,u of the " transforming agent ", i.e., asolvent component in different ways interacting with the macromolecule in twoconformational states, thenwhere An(p) is the difference of the number of the transforming agent molecules whichare bound with the macromolecule in the two conformational states; Consequently,amlax = am(p)/ap = -An@), (4)atA@(po) = [ PtAn(p)dp = [ An(a)da/a, ( 5 )J PO J a0where A@ and ,u are expressed in kT units, and a = e p is the transforming agentactivity.The An@*) value in the transition region can be either measured directly (whenthe transforming agent is hydrogen or metal ions), or obtained from calorimetricdata with the help of thermodynamic equality 4* :where AH(T,) is the heat of conformational transition and Tt is the transition tempera-ture, or, finally, determined from the degree of sharpness of the conformationaltransition according to eq~ation,~.where @,(X) and O,(X) are portions of molecules in the two conformational statesin the region of conformational transition. @,(X) and @,(X) values are easilydetermined experimentally when the transition occurs on the " all or none " principle,while in the general case their determination from experimental values requiresknowledge of the dimensions of the " cooperative region ", i.e., of the part of themacromolecule which accomplishes the transition as a whole.After An(a,) has been determined, the value of A@(Xo) can be estimated by theeqn (3) when the type of An(a) dependence is known.If, e.g., An is proportional toa (as in the binding of urea by proteins), thenIf, on the contrary, the molecule in both conformational states binds the maximumaccessible for it number of molecules of the transforming agent (as in the binding ofmetal ions by DNA molecules) then A n(a) = const.andIn @,(X)/@,(X) = -An@J(p--Pt) = -A.n(at) In (ala,), (7)AQ0 = An(a,)(a, - a,)/a,. (8)AB0 = An(a,) In (ar/ao). (9)THE STABILITY OF DNA DOUBLE HELIXWe made use of the above method for the determination of the DNA doublehelix stability in physiological conditiom6 Taking as a basis the microcalorimetri72 RELATIVE STABILITY OF CONFORMATIONAL STATESdata by Privalov on DNA denaturation heats in solution with different NaClconcentrations and using eqn (6) it was found that AnNaCI E -4NaCI mol/mol ofnucleotide pairs and that it practically does not depend on the NaCl concentrationin solution. Substituting this value of An into eqn (9), we find that under the physio-logical conditions (37"C, pH 7 and NaCl concentration -0.2 mol/l) the differenceof free energies of the denatured and native states of DNA Amo 12: 1.2 kcal/mol ofnucleotide pairs, i.e., almost an order of magnitude lower than that of the denatura-tion heat equal to -9.6 kcal/mol at pH 7 and ionic strength 0.2 moI/L7THE STABILITY OF THE CC-HELIX I N POLYPEPTIDE CHAINSLet us consider in more details the application of this method to the estimation ofa-helix stabilities of synthetic polypeptides in different solvents.For polypeptidescontaining ionizable groups and undergoing the helix-coil transition during theirionization, our method is reduced to the method by Nagasawa and H ~ l t z e r , ~ asin this case p = -2.3 pH, An(p) = NAcr(p) and consequently,In eqn (lo), N is the number of ionizable groups in the macromolecule, and Acr(pH)is the difference of degrees of the coil and helix ionization at given pH, which can bedetermined from the curve of potentiometric titration by the extrapolation of thoseparts of this curve which correspond to the titration of the helix and coil (see ref.(3)).We made use of this method in determining the stability of the helical state ofpoly-L-glutamic acid (PGA) molecules in 0.2 M NaCl aqueous solution and itsmixtures with dioxane at different temperatures. The results are given in table 1.TABLE 1THE STABILITY OF CI-HELICES A& (IN CAL~MOL) OF THE UNCHARGED POLY-L-GLUTAMIC ACIDIN WATER AND ITS MIXTURES WITH DIOXANEsolvent 0.2 M NaCl+dioxanetemp.*C 0.2 M NaCl 3 : 1 vol/vol 2 : 1 vol/vol9 240 460 (at 10°C) 49022 150 340 43040 100 280 36050 60 220 250- 245 60- 30 130 --In accordance with the data of other authors, (see, ref. (9)-(I 1)) table 1 showsthat the stability of a helical state of the uncharged poly-L-glutamic acid is lowand decreases rapidly with the increase of temperature. The temperature dependenceof values of A#,-, in aqueous medium given in table 1 leads to the values AH = 1.2kcal/mol and A S = 3.8 cal/mol deg. for the differences of the coil and helix enthalpiesand entropies. By addition of dioxane the stability of the helical state is increasedtwice or threefold remaining, however, comparatively low.The temperaturedependence of the stability also increases (AH = 1.9 kcal/mol, A S = 5.2 cal/mol deg.).These results seem unexpected as the energy of intramolecular hydrogen bondsin the mixtures of water with dioxane must be considerably higher than in water.Therefore, it is of interest to estimate the stability of the helical state of polypeptidechains in the inert organic solvents (e.g., dichloroethane), where the helix-coi0. B . PTITSYN 73The value An(a,) in this case transition can be caused by adding dichloroacetic acid.can be determined from the transition steepness by eqn (7).From the theory of helix-coil transitions it follows thatIn (O,/O,) = N/v (28- l)[O(l -O)]-*,where N is the number of monomers in the chain, v the number of monomers in thecooperative region, and 8 is the degree of helicity.From eqn (7) and (1 1) we obtain(20 - l)[8( 1 - @)I-+ = - vA,n(a,) In (ala,),where a is the activity of DCA, and An is the difference of numbers of DCA moleculesbound with one polypeptide nionomer unit in the random coil and helical states.We applied eqn. (12) to our experimental data 12* l3 on coil-helix transitions forfour polypeptides in the mixture of dichloroethane with DCA, substituting DCAactivity a by its volume fraction v. The values v, corresponding to the midpointof the transition, and the slopes of experimental curves vAn(vr) are given in the 2ndand 3rd columns of table 2. v values for these polypeptides are given in the 4thcolumn and the values of An(v,) obtained in the 5th column.TABLE 2.-AnDcA(ut) FOR SOME POLYPEPTIDES1 2 2 4 5polypeptide ut vAn(ut) V An(ut1poly-y -benzyl-L-glutamate 0.72 5 33 7014 0.47pol y-y -methyl-L-glutamate 0.70 32 -7012 -0.46poly- y -ethyl-L-glutamate 0.56 22 -701’ -0.31poly-E-carbobenzoxy-L-lysine 0.36 22 8315 0.26From table 2 it follows that An(vt) are approximately proportional to vr, which isalso confirmed by the data on transition of the p-structure-coil into poly-S-carbo-benzoxymethyl-L-cystein on addition of DCA to dichloroethane.The steepnessof transition in this polypeptide where 21, = 0.Og5 is considerably less than in theothers (vAn(vr) = 8.5). Since the cooperative region for the P-structure-coil transitioncannot be small, this means that at low ZJ, the value of An(vt) is also low.As DCAmust be bound mainly through NH and CO groups of the backbone, then it can beexpected that for every given polypeptide An will also be approximately proportionalto the DCA concentration. Taking this into account, from eqn (5) we obtain A&values in dichloroethane for all the polypeptides indicated which do not exceed 400callmol. Though this estimation is approximate it clearly shows the comparativelylow stability of the helix state of the polypeptide chain not only in waterforganicmixtures but also in a purely organic solvent.The free energy difference between random coil and helical states of the polypeptidechain can be represented asA40 = A#conf. +A4int., (1 3)where A#conf.( < 0) is the free energy decrease of monomer units due to their leavingthe helical conformation, and A&,t.(>O) is the free energy increase of monomerunits on account of the decrease of interaction between them (in the first place, dueto the rupture of hydrogen bonds). Since must be considerably greater ininert organic solvents than in water, then the comparative closeness of A& valuesin these two types of solvents can denote only a decrease of A$conf, (in absolute value)during the transition from water to organic solvents.This conclusion can be verified by independent experiments as the Acjconf, valu74 RELATIVE STABILITY OF CONFORMATIONAL STATESis closely connected with the cooperativity of transition (the free energy of initiationof the helical region is approximately equal to -2A4conf.17~ Is), so thatThus, it can be expected that the cooperative region of polypeptides will increase forthe transition from water to water + organic mixtures and organic solvents. Tocheck this assumption we determined the values v for PGA in 0.2 M NaCl aqueoussolutions and its mixture with dioxane (2 : 1, vol/vol) at different temperatures from8 to 50°C.The values of v were determined from the dependence of intrinsic viscosityof PGA on its helix degree by the method suggested by the author and A. M.Skvortsov 17* 1 9 9 2o taking into account the influence of Iong-range interactions onthe intrinsic viscosity. It was found that in an aqueous medium v 21 20 (in accordancewith the results of other authors 21) and practically does not depend on temperature.At the same time v increases in the mixture on water with dioxane from -20 to-40 with a decrease in temperature from 50 to 8°C.Thus, at low temperatures weobserve distinct increase of cooperative region during transition from water to water +organic mixtures. In purely organic solvents the cooperative region is still greater(see 4th column, table 2).Data on the temperature dependence of A&, and A+conf. permit us to understandthe nature of stability of the PGA helical state in aqueous medium. We found thatin this case A+o depends greatly on temperature (AH 21 1.2 kcal/mol, A S E 3.8cal/moldeg.). At the same time the v dependence on temperature denotes thatA&onf.is proportional to the absolute temperature T(AHconf. N 0, ASconf. 2: 6.2cal/mol deg.). This means that the helix-coil transition in aqueous medium is notaccompanied by a change of the conformational energy of monomer units but isconnected with a considerable increase in their conformational entropy. For changesof interaction of monomer units we obtain:AH,,,. = AH-AHConf. = 1.2 kcal/mol andASint, = AS-ASconf. = -2.4 cal/mol deg.The enthalpy increase of 1.2 Kcal/mol for the helix-coil transition is very close to thechange of enthalpy for the rupture of hydrogen bonds NH . . . CO in aqueous mediumaccording to Schellman’s estimation ( N 1.4 kcal/mo1)22. The decrease of entropyduring the rupture of intramolecular hydrogen bonds is evidently a result of the forma-tion of hydrogen bonds between peptide groups and water molecules.Thus, thedecrease of energy during the helix-coil transition for PGA in aqueous medium ispractically wholly a result of the rupture of intramolecular hydrogen bonds, and theincrease of entropy is the difference between the increase of conformational entropyof polymer units and the decrease of entropy of a solvent (water) during its binding withpeptide groups of the backbone.At present it is difficult to interpret unambiguously the reasons for the increaseI I in polypeptide chains during the transition from water to water+organicmixtures and organic solutions. It is possible, however, that an essential role isplayed here by the decrease of dielectric permeability of the solvent, which can leadto an increase in the role of dipole-dipole iiiteractions between the peptide groupsof the backbone.According to calculations by Flory et aZ.23 the increasing roleof these interactions leads to a shift of the energy minimum of monomer units fromthe region corresponding to the right a-helix into another region of angIes of internalrotation and thus can increase I I 0. R. PTITS’I” 75Ch. Tanford, J. Amer. Cheni. Sac,, 1964, 86, 2050.B. H. Zimni and S. A. Rice, &lo!. Phys., 1960, 3, 391.M. Nagasawa and A. M. Holtzer, J . Amer. Chem. Soc., 1964, 86, 538.0. B. Ptitsyn and T. M. Birshtein, Biopolynzers, 1969, 7, 435.T. M. Birshtein and 0. B. Ptitsyn, Mol. biologiya, 1969, 3, 121.P. L. Privalov, 0.B. Ptitsyn and T. M. Birshtein, Biopolymers, 1969, 8, 559.0. B. Ptitsyn, T. V. Barskaya and V. E. Bychkova, Bioptiysiku, 1971, in press.W. G. Miller and R. E. 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Ptitsyn, Mol. biologiya, 1968, 2,71021 R. L. Snipp, W. G. Miller and R. E. Nylund, J. Amer. Chern. SOC., 1965, 87,3547.22 J. A. Schellman, Compt. rend. trav. Lab. Carlsberg. Sir. chim., 1955, 29,223.23 P. J. Flory, Stutisficnl Mechanics of Chain Molecirles (Interscience Publishers, 1969), chap. VTT.’ P. L. Privalov, Mol. biologiya, 1969, 3,690