Influence of Alkali Cation Nature on Structural Transitions and

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Influence of Alkali Cation Nature on Structural Transitions and Reactions of Biopolyelectrolytes Nikolay Korolev* and Lars Nordenskio¨ld* Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S-106 91, Stockholm, Sweden Received May 15, 2000; Revised Manuscript Received July 17, 2000

A general thermodynamic analysis is presented, describing how counterion species of different nature, but the same valency, influence polyelectrolyte transformations and reactions of the general form: PA1‚B1M+ f PA2‚B2M+ + (B1 - B2)M+. Here PA1 and PA2 are two different states or structural forms of a polyanion, B1 and B2 are the number of M+ ions thermodynamically bound to the polyanions PA1 and PA2, respectively. The specific effects of the two counterions, M1+ and M2+, on this equilibrium can be simply related to the quotient of their selectivity constants, D2M2M1/D1M2M1, for the polyion states 1 and 2. We analyze how different monovalent counterions (particularly, sodium and potassium) affect polyelectrolyte reactions and transformations such as, e.g., the DNA helix-coil transition. Previous experimental results on the competition between DNA and the synthetic polyanion, poly(methacrylic acid), for binding to the synthetic polycation, poly(N-ethylvinylpyridinium), has been investigated with respect to sodium and potassium ion specificity, using our model. We also discuss the DNA-histone disassembly/assembly reaction modeled as a competition of two polyanions for binding to a polycation. Introduction

Li+ > Cs+ > Rb+ >K+ ≈ Na+

Two of the most important biological molecules, DNA and RNA, are highly charged polyanions. Many proteins contain oligo- and polyanion sequences enriched with aspartic and glutamic acid residues. Among them are actin, nucleoplasmins, high mobility group (HMG) proteins, tubulin, and others. Because of long-range Coulombic interactions, a considerable fraction of the fixed charges of these natural poly- and oligoanions will be effectively neutralized by electrostatically associated monovalent counterions that generally are present in the systems. In vivo, potassium and sodium are the principal monovalent ions. Structural transitions and reactions of DNA, RNA, and acidic polypeptides are generally dependent on temperature and solvent as well as on concentration, composition and nature of the neutralizing counterions. An ion specificity effect originates in a varying affinity of different counterions for binding to the polyanion. Numerous studies of DNA-ligand binding and DNA structural transitions have shown strong dependence on the monovalent electrolyte concentration.1-4 On the other hand, these reactions of DNA display only a weak sensitivity to the nature of the monovalent cation. This explains why the effect of specificity of monovalent counterions on biopolyelectrolyte transformations and reactions has not been systematically described in the literature. The selectivity of polyion-counterion binding is the result of a balance between counterion interactions with different functional groups of the polymer and with molecules of the solvent.5 For DNA in water, the selectivity series for alkalimetal cations is6-9

With the exception of Li+, the ions in this series are arranged in accordance with the increase of hydrated ionic radius. Differences in affinity for the listed ions are small and dependent on the concentrations and ratios of competing ions and also on the experimental techniques used.6-13 Synthetic carboxylic polyelectrolytes can to some extent serve as model for counterion preferences of Asp- and Glugroups in polypeptide acidic domains. The selectivity series for these polyanions is the reverse of that for DNA and corresponds to the increase of the crystallographic radius of the cations:5,14,15

* Correspondence may be addressed to either of the authors. Fax: (46 8) 15 21 87. E-mail: [email protected] (N.K.); [email protected] (L.N.).

Li+ > Na+ > K+ > Rb+ > Cs+ Most data on the selectivity of COO--containing polyelectrolytes report higher affinity for Na+ than for K+,14-16 or show site binding of Na+ to carboxylate groups.17-20 We are not aware of any literature data on the selectivity for real polypeptide systems, such as poly(L-glutamic acid). In the present work, we present a thermodynamic analysis on the effect of the nature of monovalent counterions on biopolyelectrolyte transformations and reactions, with particular emphasis on potassium and sodium. On the basis of existing thermodynamic descriptions, a new and simple relation describing this effect is obtained. Previous experimental results obtained for the helix-coil transition of DNA and anionic polypeptides, as well as for polyanion-ligand binding, are then interpreted and discussed with the use of this thermodynamic result. In addition, the competitive equilibrium reaction between two polyions of the same charge for binding to another polyion of opposite charge is analyzed. In light of these results, we also briefly discuss

10.1021/bm000042f CCC: $19.00 © 2000 American Chemical Society Published on Web 10/27/2000

Alkali Metal Ions and Biopolyelectrolytes

the DNA-histone disassembly/assembly reaction viewed as a competition of two polyanions for binding to a polycation. Largely, this is a theoretical paper, where we use a thermodynamically derived result to interpret literature data from a new and different angle that has not been performed previously. However, we have not found any experimental data on the selectivity of alkali ions for binding to any real polypeptide-based polyion with COO- as charged anionic group. To have a basis for discussion of the effect of K/Na specificity on polyelectrolyte equilibria involving charged carboxylic acid groups of proteins, such data are important. We have therefore also determined experimental selectivity coefficients for sodium and potassium binding to poly(Lglutamic acid). For comparison, using the same method, alkali ion selectivity data for poly(acrylic acid) and for DNA, have been obtained. Materials and Methods Poly(L-glutamic acid) (PGA) sodium salt from Sigma Chemical Co. (St. Louis, MO) (MW ≈ 71-75 kDa), poly(acrylic acid) (PAA) from Aldrich Chemical Co. (Milwaukee, WI) (MW ≈ 240 kDa, 25 wt % in water), and salmon testes NaDNA from Fluka BioChemika (Buchs, Switzerland) were used without further purification. Analytical grade NaCl and KCl from Merck KGaA (Darmstadt, Germany), KOH and NaOH from Kebo Lab AB (Spånga, Sweden), and Na2EDTA and K2EDTA from Fluka Chemie AG (Buchs, Switzerland) were used. Ultrapure KCl and specpure NaCl from Alfa, Johnson Matthey GmbH (Karlsruhe, Germany) were used in AAS analysis. Ethanol (99.5% v/v) was purchased from Kemetyl AB (Stockholm, Sweden). Stock solutions of polyelectrolytes (PGA, PAA, and DNA) were prepared by dissolution of weighed amounts of polymers in water eluent solution (0% EtOH, KCl + NaCl, 25 mM of each salt, 1 mM EDTA, pH 7.6). Eluents containing KCl + NaCl (25 mM of each salt), 1 mM EDTA, pH 7.6 and EtOH from 0 to 95% v/v were prepared by mixing stock solutions of the salts with EtOH and doubly distilled (dd) water aliquots. An ultrafiltration technique, described in detail in ref 21, was used for determination of, PGA, PAA, and DNA selectivity for Na+ relative to K+. Stock solutions of polyelectrolytes (4 mg/mL) were placed on centrifuge tube filters VectaSpin3 from Whatman International Ltd. (Kent, England) with polysulfone filter membrane (cutoff molecular weight 10 kDa). After the ion exchange and washing operations, an aliquot of ddwater was added to the filter tubes to dissolve and to extract the precipitated and membranebound polymer. The ionic composition of solution was then analyzed with a PU9100 AAS spectrometer (Phillips Scientific, Cambridge, Great Britain). Errors in the resulting selectivity coefficients, DM2M1, (see definition below) are generally 5% or less, except for one point for which error bars are included (see Figure 2 below). Results and Discussion Thermodynamic Analysis of the Effect of Counterion Selectivity on Transitions and Reactions of Polyelectrolytes. Polynucleotides such as single-stranded (ss) and

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double-stranded (ds) DNA are polyelectrolytes with high surface charge density, and thus a large fraction of the mobile counterions are closely associated with their charged groups. Polyelectrolyte theories3,22 and experimental data23 show that dsDNA attracts counterions to be within 6-8 Å from the phosphate groups, resulting in up to 80% neutralization of its negative charge. As a result of a structural transition or reaction, biopolyelectrolytes can change their degree of binding and/or the sensitivity to the nature of the counterion. Schematically, a polyelectrolyte transformation or reaction accompanied by a change of counterion binding can be written as PA1‚B1M+ f PA2‚B2M+ + (B1 - B2)M+

(1)

Here PA1 and PA2 represent two different states or structural forms of a polyanion. B1 and B2 are, respectively, the number of M+ ions thermodynamically bound to the PA1 and PA2. Thermodynamic binding includes all modes of interaction, i.e., not only diffuse electrostatic association of fully hydrated cations in the vicinity of the polyanion. Some polyelectrolyte reactions such as the helix coil transition of DNA or charged proteins are exactly represented by the scheme written in eq 1. We will use modifications of eq 1 to describe the stoichiometric details of more complex transformations of charged polymers, such as ligand binding or competition of two polyanions for binding to a polycation. These modifications, however, do not change the conclusions obtained in analysis of the general scheme presented as eq 1. The change in free energy for the process described by eq 1, ∆G, can be written as a sum of three terms: ∆G ) ∆GPA + ∆GPA‚M - ∆GM

(2)

Here ∆GPA is the difference in “internal” energies of the polyions PA1 and PA2. ∆GPA‚M is the change in the free energy for the process 1 due to the counterion-polyion interactions and is given by ∆GPA‚M ) ∆GPA2‚M - ∆GPA1‚M ) N2b2∆gPA2‚M - N1b1∆gPA1‚M (3) Here ∆gPA2‚M, ∆gPA1‚M and b2, b1 are respectively free energies and degrees of the M+-polyion binding determined per one charged group of the polyion; N2 and N1 are the numbers of monovalent charged groups of PA2 and PA1 involved in reaction 1. The third term ∆GM is the change in the free energy of the free M+ ions: ∆GM ) B2µM′′ - B1µM′

(4)

The experimentally measured apparent equilibrium constant of the process described by eq 1, K, can be derived from the three constants reflecting the corresponding energy terms: K ) KPA ‚ KPA‚M/KM

(5)

Consider now a change of monovalent cation from M1+ to M2+, keeping all other reaction variables intact. Then,

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the variation of the free energy change, δ∆G, resulting from the change of counterion nature can be expressed as δ∆G ) δ∆GPA + δ∆GPA‚M - δ∆GM|M2M1

(6)

To quantify the particular effect of the replacement of one kind of counterion by another, we now introduce a new parametersthe ratio of the reaction constants in the presence of M2+ and M1+, RKM2M1: RKM2M1 ≡ (KM2/KM1)T,p ) exp(-δ∆G/RT)

(7)

The abbreviation RKM2M1 is designed as an analogue to the SKobs parameter introduced by Anderson and Record to measure the salt-concentration dependence of a polyelectrolyte-charged ligand binding constant, Kobs.24,25 The replacement of M1+ by M2+ in binding to a polyanion, PA, can be written as a competitive ion exchange reaction: PA‚b′M1+ + b′′M2+ S PA‚b′′M2+ + b′M1+

(8)

A measure of the polyion’s selectivity for M2+ relative to M1+ is the ion-exchange selectivity coefficient, for which we assign the letter “D”, again in accordance with the work of Record and coauthors:10,12 DM2M1 ) (CM2,b/CM2,f)‚(CM1,f/CM1,b)

(9)

The indices b and f mark, respectively, concentrations of bound and free counterions M2+ and M1+. Combining eqs 5, 7, and 9, the parameter RKM2M1 can now readily be connected with the thermodynamic measure of counterion preference for the polyions, DRM2M1 (R ) 1,2): RKM2M1 ≈ (KPAM2/KPAM1)‚[(D2M2M1)b2N2/(D1M2M1)b1N1] ≈ (D2M2M1)b2N2/(D1M2M1)b1N1 (10a) In eq 10a, the value of RKM2M1 is calculated for the entire polyions, PA2 and PA1, taking part in reaction 1. Usually, however, the equilibrium constant is determined per unit of charged group on the polymer. The corresponding quotient of RKM2M1 for this case is RKuM2M1 ≈ (D2M2M1)b2/(D1M2M1)b1

(10b)

For a polyanion-ligand binding reaction, the equilibrium constant, KL, is determined per 1 mol of ligand bound to the polyion. Then, a measure of the sensitivity of the ligand binding reaction to the nature of monovalent cation is RKLM2M1 ≈ [(D2M2M1)b2/(D1M2M1)b1]Z

(10c)

The magnitude of Z (the charge of the ligand) has been set equal for PA1 and PA2. Two approximations have been made in the derivation of eq 10, parts a-c. It is assumed that b′ ) b′′ for respectively M1+ and M2+, bound either to PA1 or PA2 (eq 8). This simplification neglects the entropy component in the ion exchange substitution of M1+ by M2+ on either of the polyanions. However, for alkali-metal ions and for most common polyelectrolytes this difference between the values

of b′ and b′′ should be very small, due to the effect of mutual compensation between different modes of M+-polyion interactions, thus maintaining the thermodynamic degree of binding unchanged.7 In addition, it is implicitly assumed that the influence of the monovalent-counterion nature on the internal free energy of the polyanions is either negligible or equal for both PA1 and PA2; i.e., δ∆GPA ) 0. This simplification should be basically correct at least for DNA and RNA, because Raman spectroscopy data do not show any coordination binding of Li+, Na+, K+, Mg2+, or Ca2+ to subgroups of ds-26,27 or ssDNA.27 It may be noted that the selectivity effects for alkali-metal ions interacting with biopolyelectrolytes generally are relatively small. This has the effect that DM2M1 is only modestly larger than unity, and the effect of the coefficients b1 and b2, whose values usually do not differ much, will be small. Thus, a good estimate of RKuM2M1 is directly given by the value of the ratio D2M2M1/D1M2M1. Values of DM2M1 for different polyelectrolyte systems can be determined from experiments with direct competition of M2+ and M1+ for binding to the polyions PA1 and PA2.6,8,10,16-18,21 We would like to emphasize two important conclusions from the preceding analysis. First, a similar selectivity for M2+ (relative to M1+) of both PA1 and PA2, effectively reduce the influence of the kind of counterion. This is often the case for many polyelectrolyte reactions and transformations, where the nature of the fixed polyanion charges does not change, and as a result RKuM2M1 ≈ 1. Second, if D2M2M1/D1M2M1 in eq 10c is modestly larger than unity (in the range ∼1.3-2), there may still be a large influence of the counterion nature on a ligand binding reaction, if the charge Z of the ligand is reasonably large. This emphasizes an important point of our work, namely that even weak interactions such as those exhibited by monovalent counterions, can drive transformations of large scale when taken collectively. On the basis of the above thermodynamic description, we will now discuss and analyze the effects of monovalent counterion nature on structural transitions and reactions of biopolyelectrolytes. DNA Helix-Coil Transition. We first consider the thermally induced "melting” of double helical DNA. For this case PA1 and PA2 in eq 1, are respectively dsDNA and ssDNA. Several experimental studies of the thermal denaturation of DNA in aqueous solution have shown that the transition midpoint temperature, Tm, depends strongly on salt concentration, Cs.2,3,28,29 Among the alkali ions, only Li+ exhibits some specificity effect on the thermal stability of dsDNA, with Tm in the range 4-8 °C higher than Na+, K+, or Cs+.28,29 This implies that the equilibrium between ds helix and ss coil is shifted to dsDNA in the presence of lithium as compared to e.g. sodium or potassium. As a consequence, the ratio of experimental equilibrium constants for eq 1, i.e., the value of RKuLiNa, is less than unity. On the basis of the thermodynamic relationship in eq 10b, we can predict the value of RKuLiNa using experimental data on selectivity coefficients D1LiNa. For dsDNA immobilized in polyacrylamide gel (PAAG), the value of D1LiNa is


1.36 ( 0.08 at Cs ) 2 mM.8,9 The magnitude of the selectivity of ssDNA, D2LiNa, can be estimated from studies of immobilized synthetic poly(rA),30 resulting in a value of 1.15 ( 0.08. This gives RKuLiNa ≈ (D2LiNa)b2/(D1LiNa)b1 ≈ 0.85. Here values of b1 ) 0.88 and b2 ) 0.76 have been used.4,29 This is in qualitative agreement with the experimental fact that RKuLiNa, is smaller than unity. A quantitative estimation of the experimental value of RKuLiNa can be obtained from data on the variation of Tm as a function of DNA concentration in salt-free solutions of Li- and NaDNA.29 Under the assumption that the change of free energy of DNA melting depends only on the electrostatic component,31 an experimental estimate of the RKuLiNa value ≈ exp(-δ∆Gm/RT) ) 0.83 can be obtained. This is in excellent agreement with the value of 0.85 predicted from our model on the basis of selectivity coefficients.29 There are two reasons why the DNA melting temperature is not very sensitive to the nature of the counterion when comparing Na+, K+, and Cs+. First, neither ds-8 nor ssDNA30 is noticeably selective to any of these alkali ions. Second, the weak counterion preference of native and denatured DNA is similar, which cancels the selectivity effect in eq 10b. The correlation of ionic selectivity with double helix stability can also be observed in compact oriented fibers of DNA in equilibrium with ethanol/water/salt. Contrary to the water solutions, in ethanol-water mixtures the Li+ counterion destabilizes dsDNA fibers,32 with a decrease in Tm as compared to Na+, K+, and Cs+. This effect of Li+ on the DNA melting temperature correlates qualitatively well with an observed decrease in DNA selectivity for Li+ in water/ organic mixtures relative to the other alkali ions.13 Poly(L-glutamic acid): Coil-r-Helix Transition and Experimental Data on K/Na Selectivity. Another system for studying polyelectrolyte structural transitions is poly(Lglutamic acid) (PGA), which undergoes a coil to R-helix transition as a function of variations in pH, dielectric constant, and composition of the solvent, as well as temperature and other variables. In aqueous solution, this transition takes place only at high degrees of PGA protonation, i.e., when the charge of the polyion is considerably reduced. Under these conditions, alkali-metal cations interact with PGA only in a delocalized electrostatic manner, which is not counterion specific. The coil-R-helix transition of fully charged PGA is only possible in solvents with a decreased dielectric constant, for example in alcohol/water mixtures. It is precisely under those conditions that a decisive influence of the nature of the counterion on the structural transition of PGA has been found.33,34 Figure 1 illustrates the ethanol concentration dependence of coil-helix transition curves for salt-free Li-, Na-, K-, and Cs-PGA (data adapted from ref 33). A common feature of all systems studied by Satoh et al.33,34 is that NaPGA exhibits the highest ability to form the R-helix, and in a number of systems studied, KPGA never transforms into an R-helix (see Figure 1). The authors33,34 explain this phenomenon by the different abilities of the counterions to form stable ion pairs with the carboxylic groups of PGA. In this picture, the formation of COO-‚‚‚M+ pairs reduces the repulsion between the side groups of PGA and facilitates formation of the more compact R-helix.


Figure 1. Dependence of the R-helix content on ethanol concentration for salt-free solutions of alkali-metal salts of PGA. Reproduced with permission from ref 33. Copyright 1991 John Wiley & Sons.

Figure 2. Dependence of ion exchange selectivity constant, DNaK, on ethanol concentration for DNA, poly(L-glutamic) (PGA), and polyacrylic (PAA) acids. Eluent KCl + NaCl (25 mM each salt), 1 mM EDTA, pH 7.6.

The above data show that the equilibrium constant for the coil to R-helix transition for PGA is larger in the presence of Na+ as compared to K+ as counterion, i.e., RKuNaK > 1. Within our model, this behavior will be observed if the helix form of PGA has a higher specificity for Na+ than for K+. On the basis of eq 10b, this implies that the quotient of selectivity coefficients is larger than one, (D2NaK)b2/(D1NaK)b1 > 1 (here PA1 and PA2 are respectively coil and R-helical PGA). To check the validity of this interpretation, experimental results on ion specificity are needed. We have not found data in the literature, and therefore undertook a special study on the relative affinities of Na+ and K+ to PGA as a function of ethanol concentration. The results have been compared with similar data obtained for salts of poly(acrylic acid) (PAA) and DNA, using the same experimental method. The results are presented in Figure 2. It should be noted that this shows the effective ion equilibrium constant DNaK as a function of ethanol concentration, since it is not possible to separate these constants for coil and helix in a mixture containing both forms. Comparing Figures 1 and 2, one can see that the structural transition of NaPGA is accompanied by a parallel increase of DNaK.

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Two interpretations of the selectivity behavior may be discerned: (1) Selectivity of PGA for Na+ appears as a result of increasingly favorable ion-pairing with decreasing water activity, or (2) R-helix formation produces a structural form of PGA which has a higher affinity for Na+ in K/Na mixtures. We believe that the second factor prevails, although it is possible that these two effects are connected. The primary origin of the preference of the R-helix for Na+ over K+ may be due to the different binding sites on PGA for Na+ and K+. It is known that Na+ interacts selectively with COO- groups (both in PGA and in other carboxylic polyelectrolytes). This is clear from the dependencies of DNaK for PGA and PAA in Figure 2 and from other studies.18-20 Contrary to Na+, K+ has some affinity for the carbonyl group of the peptide bond. Formation of the R-helix makes the carbonyl group of PGA inaccessible for K+ binding. In ethanol-free solution PAA shows some selectivity toward Na+. The absence of such an affinity in PGA under similar conditions supports the explanation that the selectivity of the peptide bond carbonyl group for K+ in water is leveled by the higher affinity of the COO- anion for Na+ than for K+. At high ethanol concentration (75-85%), PGA is in the form of an R-helix with a charge density higher than that of the unstructured PAA and with carbonyl groups inaccessible for K+ binding. Combination of these factors results in higher DNaK values for PGA than for PAA in this region (Figure 2). The considerable drop of DNaK and the loss of data reproducibility for PGA, PAA, and DNA, observed at an ethanol concentration higher than 90%, can be explained by strong dehydration accompanied by a disruption of regular structures, replacement of water with ethanol in the hydration shells of the ions, and probably by cocrystallization of KCl and/or NaCl with the polymers. Competition of Monovalent Counterions with Charged Ligands. An example of a polyelectrolyte reaction that is potentially sensitive to the nature of monovalent counterions is the competition of monovalent cations with ions of higher valencies for binding to the polyanion. For this type of the polyelectrolyte transformation described by eq 1 can be explicitly written PA-N‚B1M+ + LZ+ S [PA‚L]Z-N‚B2M+ + (B1 - B2)M+ (11) Here N and Z are, respectively, the absolute values of the polyelectrolyte and ligand charges. The reaction shown as eq 11 is an example of the scheme given by eq 1 with PA1 ) PA and PA2 ) [PA‚L]. It can be assumed that the interaction with the multivalent ligand excludes Z singlecharged groups on the polyanion from binding with M+ and that this does not influence the M+ interaction with the rest of the polyanion.2,24 Equation 10c can then be rewritten as RKLM2M1 ≈ (D1M2M1)- b1Z

(12)

In eq 12, it is also assumed that the charged groups of the polyion, when associated with L+Z, do not possess any selectivity for M2+ or M1+ (D2M2M1 ) 1).

Reaction 11 has been extensively studied in the presence of either sodium or potassium salt for the case of DNA and RNA binding with different oligocations such as polyamines and oligolysines (see reviews 1, 2, and 4 and references therein). Generally, no significant counterion specificity effects have been observed. This is also the expected outcome on the basis of our model since DNaK in eq 12 is close to unity for DNA (refs 6-8 and 35; see also Figure 2). It must be noted, however, that no data for lithium salt, which is expected to show a clear selectivity effect, were obtained in these studies.4 On the other hand, a well-studied system that includes data for a range of counterions including lithium, is DNA binding with the lac repressor protein. It was found that about 9-11 monovalent cations are released upon formation of the lac repressor complex with both operator and nonoperator DNA, and the equilibrium constant is strongly dependent on monovalent electrolyte concentration.2 It follows from eq 12, with Z in the range 9-11, that a substantial influence of any counterion selectivity should be at hand. At pH ) 8.0, 20 °C, and CMCl ) 0.13 M, it was experimentally observed that the RKLMNa values decrease in the order Cs+ > K+ > Na+ > NH4+ > Li+.36 In this series, only the experimental value of RKLLiNa ) 0.12 shows a deviation from a value of unity that is beyond the uncertainty of the experiments. Using Z ) 9-11 and b1 ) 0.88, the theoretical value of the specificity RKLLiNa, can now be predicted from eq 12. For DNA we can use the value of DLiNa ≈ 1.2-1.4.8,9 The theoretically estimated value of RKLLiNa (eq 10c) thus obtained is in the range 0.05-0.23, in very good agreement with experiment. However, it should be noted that there are several variables influencing the DNA-lac repressor binding that is not considered in this simplified treatment. The interaction of the lac repressor with operator and nonoperator DNA includes numerous intra- and intermolecular structural transformations involving both positively and negatively charged amino acids (see ref 37 and references therein). The complexity of these interactions was noted by the authors36 who obtained an even stronger dependence on the nature of the anions than on the cations of monovalent salt. Competition of Polyanions for Binding to a Polycation. Another kind of polyelectrolyte reaction that may display sensitivity to the nature of monovalent counterion, is the competition between two polyanions for binding to a polycation: PA2‚PC + PA1‚B1M+ S PA1‚PC + PA2‚B2M+ + (B1 - B2)M+ (13) The sensitivity of this reaction to the kind of counterion originates in the different chemical nature of the two polyanions PA1 and PA2. In fact, eq 13 is a difference between two reactions of the kind described by eq 11. Thus, effects of mutual cancellation make the entropy driving force caused by the release of M+ during formation of the PAR‚ PC complex less important in this case as compared to eq 11. If there is an excess amount of the polyanions PA1 and


Figure 3. Dependence of the degree of conversion for polyanion competitive binding to a polycation (eq 13) on concentration of alkalimetal chlorides, CMCl, (M ) Li, Na, and K). The polycation, PC, is poly(N-ethyl-4-vinyl-pyridinium), PEVP; the polyanions are poly(methacrylic acid), PMA (PA1), and double- (ds) or single-stranded (ss) DNA (PA2). Reproduced with permission from ref 38. Copyright 1995 John Wiley & Sons.

PA2, a high charge on PC, and low or moderate concentration of low molecular salt in the system, it is expected that PC will be almost completely bound to either PA1 or PA2, and then the reaction is also independent of the concentration and nature of low molecular weight anions. An application of reaction 13 to a system of major interest is the assembly/disassembly reaction of natural DNAhistone or DNA-histone-like protein complexes with acidic nuclear proteins. To our knowledge, experimental data on assembly/disassembly reactions of DNA-histone complexes, which can be used for analysis by means of eq 13, are not available in the literature. On the other hand, a model system that can serve as a basis for further discussions is the competition of DNA with poly(methacrylic acid), PMA (labeled with a fluorescent tag), for binding to a model polycation, poly(N-ethylvinylpyridinium) (PEVP).38,39 The degree of conversion of PEVP from DNA-PEVP to PMA-PEVP complexes, as a function of the concentration of NaCl, KCl, and LiCl in water solution, is shown in Figure 3 for ds- and ssDNA (data adapted from ref 38). The specificity of the cation has a decisive influence on the equilibrium that can be analyzed on the basis of eq 13 identifying PMA ) PA1, DNA ) PA2, and PEVP ) PC. Qualitatively, the data can be explained by using eq 10c connecting the equilibrium of the polycation exchange reaction with the counterion preferences of the polyanions PA1 and PA2. Indeed, the specific binding of Li+ to dsDNA in water8,9,40 completely blocks PEVP transfer from PMA to dsDNA (though some transformation is possible for ssDNA). In turn, the somewhat higher selectivity of PMA carboxylates for Na+ than for K+ (D1NaK is on the order of 1.3-1.6),15 in combination with the lack of DNA selectivity for either to Na+ or K+ (D2NaK ≈ 1),8,9,13,41 results in a shift of the equilibrium of reaction 13 to the left. Thus, under “physiological” ionic strength, 100-250 mM, the amounts of polycation bound to DNA differ substantially depending on the presence of either NaCl or KCl. The observed difference between K+ and Na+ is due to a relatively small


Figure 4. Schematic presentation of the process of nucleosome disassembly, viewed as a competitive reaction (eq 13 in the text) between DNA (PA2) and acidic domains of proteins (PA1) for binding to the positively charged nucleosome histone core (PC). DNA binding domains of proteins and dissociation of the histone octamer are not shown. On the right side of the figure, an estimate of the free-energy difference between the decomposed nucleosome states in the presence of Na+ and K+ ions, δ∆GtotKNa, is shown to be proportional to the charge on the histone octamer (Ztot), degree of counterion binding on the acidic protein (b1), and difference in interaction energy of the protein COO- group with Na+ and K+, (δgCOO-)KNa. See text for details.

difference in free energies of Na+ and K+ binding to the polyanions. For the present system the charge of the ligand (PCZ+) is high with Z ≈ 30. This is the origin of the rather large effect on the equilibrium depending on the presence of either Na+ or K+. DNA-Histone Disassembly Viewed as a Competitive Polyion-Polyion Reaction. An elementary building block of the complex eukaryotic chromatin structure, the nucleosome, is a polyanion-polycation complex of DNA (146 base pairs of total charge -292) wrapped around the histone protein octamer core (with net charge of +146). A common feature of the nonhistone proteins in the cell nucleus that participate in the functioning of the chromatin structures, is the presence of negatively charged “acidic” domains, enriched with glutamic and aspartic amino acid residues. Examples include acidic tails of the HMG proteins, transcription regulators and nucleoplasmin.42 The release of DNA from the histone is an important precondition for function of DNA and RNA polymerases. Overcoming the repressive influence of DNA binding to histones is a rate-determining stage of DNA transcription and replication in vivo.43 Let us now make the simplifying assumption that the reactions involved in nucleosome disassembly and assembly can be modeled as a polycation exchange, written as eq 13. For this case, PC is histones of the nucleosome core (polycations), PA2 and PA1 are, respectively, DNA and acidic domains on proteins. This reaction is schematically illustrated in Figure 4. In the previous section, an analysis on the competition between two polyanions, DNA and PMA, for binding to a polycation, PEVP, was performed. In vivo, unlike this model reaction, the nucleosome disassembly/ assembly process, can only take place as a continuous chain of events, from the first to the last nucleotide (see Figure 4). Thus, the final equilibrium constant for this biological process is a product of elementary step constants, and our preceding analysis allows estimation of the influence of the Na+-K+ substitution on the resulting constant of the nucleosome disassembly reaction. The result is that total

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equilibrium constant, Ktot, is a product of elementary steps and the influence of substituting Na+ by K+ can be written as RKtotKNa ) RKL1KNa ‚...‚ RKLnKNa ≈ [(D2KNa)b2/(D1KNa)b1]Ztot (here Ztot ) Z1, + ... + Zn is the total charge due to all charges on the units L1, ..., Ln taking part in the elementary steps of reaction 13). Importantly, for the sequence of mutually dependent steps, the ultimate effect of counterion specificity does not depend on the mechanism of the ligand displacement. In terms of free energy, this cumulative effect may be related to δ∆GtotKNa, the change in free energy difference due to replacement of K+ by Na+ in the assembly/disassembly reaction. Using the experimentally established fact that to a good approximation for DNA (D2KNa)b2 ≈ 1, eqs 8 and 10 give δ∆GtotKNa ≈ -Ztotb1(δgCOO-)KNa

(14)

This is illustrated in Figure 4, which shows that, for the unwinding of DNA from one histone octamer according to eq 13, the free energy difference of replacing Na+ by K+ on one charged carboxylic residue of the protein, (δgCOO-)KNa, is amplified by the total charge on the histone octamer, Ztot. This means that within the present simplified analysis, the equilibrium is shifted toward stabilizing the assembled DNA-polycation (histone) complex in the presence of Na+, as compared to the presence of K+, which stabilizes the disassembled state. Thus, the presence of K+ makes the acidic protein capable of competing with DNA in binding to histones. The abundance of potassium ions in the cell nucleus may thus be important for nucleosome stability. Conclusions The thermodynamic analysis of the general polyelectrolyte transformation between two polyion states has shown that the effect of the specificity of two counterions, M1+ and M2+, on the equilibrium of the reaction, can be simply related to the quotient of selectivity constants for the two polyion states according to eq 10. Equation 10 in combination with experimental data was used to analyze the effects of the nature of monovalent counterion on the following polyion reactions/transformations: DNA helix-coil transition, coilR-helix transition of poly(L-glutamic acid), competition of monovalent counterions with charged ligands for polyion binding, and competition of polyanions for binding to a polycation. It is important to note that, although our discussion has been limited to effects of monovalent cations, the result is general and can be used as a starting point for an analysis of anion specificity effects, as well as for discussing the importance of the nature of divalent cations. In our view, interesting implications of the present work can be obtained from discussions based on an application of the polycation exchange reaction (eq 13) to the assembly/ disassembly processes in chromatin. K+ and Na+ are the dominant cations in living cells and in different surrounding media (seawater, blood serum, or the laboratory tube). On the basis of the discussion in the previous section, we put forward the hypothesis that a negative influence of Na+ on

the ability of protein acidic domains to strip DNA from polycations, and the consequent necessity to substitute Na+ by K+, could be an important reason for development of a mechanism (the Na+-K+ pumps) present in all living cells for creation and maintenance of an asymmetric Na/K distribution between the cytoplasm and the serum. Work is in progress to further develop this conjecture. This suggestion also has an important practical consequence, namely that for correct comparison of data obtained in vivo and in vitro it is strongly recommended to use potassium instead of sodium salt in such studies. Finally, we would like to emphasize that the ideas presented in this work are based on a considerably simplified model of the nucleosome assembly/disassembly. Despite this fact, the implications of the analysis are of such importance that further analysis and experimental studies aimed at corroborating our hypothesis are highly motivated. Abbreviations AAS: atomic absorption spectroscopy PA: polyanion PAA: poly(acrylic acid) PAAG: poly(acrylamide) gel PC: polycation PEVP: poly(N-ethyl-4-vinylpyridinium) PGA: poly(L-glutamic acid) PMA: poly(methacrylic acid).

Acknowledgment. This work was supported by the Swedish National Science Foundation (NFR), the Swedish Institute, and the foundation Wenner-Grenska Samfundet. References and Notes (1) Record, M. T., Jr.; Zhang, W.; Anderson, C. F. AdV. Protein Chem. 1998, 51, 281. (2) Record, M. T., Jr.; Anderson, C. F.; Lohman, T. M. Q. ReV. Biophys. 1978, 11, 103. (3) Anderson, C. F.; Record, M. T., Jr. Annu. ReV. Phys. Chem. 1982, 33, 191. (4) Lohman, T. M.; Mascotti, D. P. Methods Enzymol. 1992, 212, 400. (5) Eisenman, G. Biophys. J. 1962, 2 Suppl., 259. (6) Strauss, U. P.; Helfgott, C.; Pink, H. J. Phys. Chem. 1967, 71, 2550. (7) Manning, G. S. J. Phys. Chem. 1984, 88, 6654. (8) Kuznetsov, I. A.; Gorshkov, V. I.; Ivanov, V. A.; Kargov, S. I.; Korolev, N. I.; Filippov, S. M.; Khamisov, R. K. React. Polym. 1984, 3, 37. (9) Kuznetsov, I. A.; Kargov, S. I.; Kozlov, A. G. Mol. Biol. (Moscow) 1984, 18, 1583. (10) Bleam, M. L.; Anderson, C. F.; Record, M. T., Jr. Proc. Natl. Acad. Sci. U.S.A. 1980, 77, 3085. (11) Eichhorn, G. L.; Shin, Y. A. J. Am. Chem. Soc. 1968, 90, 7323. (12) Paulsen, M. D.; Anderson, C. F.; Record, M. T., Jr. Biopolymers 1988, 27, 1249. (13) Korolev, N.; Lyubartsev, A. P.; Rupprecht, A.; Nordenskio¨ld, L. J. Phys. Chem. B 1999, 103, 9008. (14) Reichenberg, D. In Ion-exchange; Marinsky, J. A., Ed.; Edward Arnold, Ltd., Marcel Dekker: London, 1966; p 227. (15) Gregor, H. P.; Hamilton, M. J.; Oza, R. J.; Bernstein, F. J. Phys. Chem. 1956, 60, 263. (16) Rinaudo, M.; Milas, M. In Charged and reactiVe polymers. V. 2. Polyelectrolytes and their applications; Rembaum, A., Selegny, E., Eds.; D. Reidel Publ. Co.: Dordrecht, The Netherlands, and Boston, MA, 1975; p 31. (17) Ferry, G. V.; Gill, S. J. J. Phys. Chem. 1962, 66, 999. (18) Noll, L.; Gill, S. J. J. Phys. Chem. 1963, 67, 498. (19) Zhang, H.; Dubin, P. L.; Kaplan, J.; Moorefield, C. N.; Newkome, G. R. J. Phys. Chem. B 1997, 101, 3494. (20) Miura, N.; Dubin, P. L.; Moorefield, C. N.; Newkome, G. R. Langmuir 1999, 15, 4245.

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