J. Mol. Biol. (1991) 222, 423-433

Nature of Protamine-DNA

Complexes

A Special Type of Ligand Binding Co-operativity Dietmar Porschke Max

Plan&

Institut fiir biophysikalische 34 Giittingen, Germany

(Received 22 April

1991; accepted 19 July

Chemie

1991)

The mode of protamine binding to DNA double helices has been analyzed for the example of clupein Z from herring and DNA samples from bacteriophages i and PM2 by measurements of light-scattering intensities, ultracentrifugation and kinetics. The light-scattering intensity of DNA increases co-operatively at a threshold clupein concentration suggesting cooperative binding of clupein to double helices. These data are first analyzed in terms of a model with a transition at a threshold degree of binding. The parameters resulting from this analysis appear to be reasonable: but are shown to be in contrast with data on the absolute degree of clupein binding to DNA obtained by centrifugation experiments. ,4n analysis of the kinetics associated with clupein binding to DNA by measurements of the timedependence of light-scattering intensities in the time range of seconds demonstrates directly that clupein-induced intermolecular interactions of DNA molecules are essential. The rate constants of DNA association increase co-operatively at threshold clupein concentrations, which correspond to those observed in the equilibrium titrations. Above the threshold, the rate constants arrive at a level that is almost constant, but shows some decrease with increasing clupein concentrations. These results are described by a model with a monomer and a dimer state of DNA, which bind ligands with different affinities according to an excluded-site binding scheme. When the ligand binding constant is larger for the dimer than for the monomer state, as should be expected, binding of ligands drives the DNA from the monomer to the dimer state, even if the dimerization equilibrium in the absence of ligands is far in favor of the monomer. The transition from the monomer to the dimer state proves to be strongly co-operative. When the ligand concentration is increased to higher values, the dimers may be converted back to monomers due to an increased extent of ligand binding to the monomer state. The model is consistent with the available experimental data. The analysis of the data by the model indicates the existence of a reaction unit much below the DNA chain length, corresponding to about 80 nucleotide residues. The present model describes ligand driven intermolecular association; an analogous model is applicable to ligand driven intramolecular association. In summary, the co-operativity of clupein binding to DNA double helices is not due to nearest neighbor interactions, but results from thermodynamic coupling of clupein binding with clupein-induced DNA association. Krywords: clupein Z; dynamics of protamine-DNA interactions; models; transition of a limit degree of binding; ligand-induced

1. Introduction &lore than 100 years ago protamine-DNA complexes, prepared by F. Miescher from salmon sperm, were the first objects for scientific analysis of nucleic acids and of protein-nucleic acid complexes. Now it is known t)hat protamine-DNA complexes are specific to the male germ cell line, that protamines are relatively small basic proteins and that there are many different protamine species (Ando et al., 1973; Hecht, 1989; Kasinsky, 1989). The main reason for replacement of histones by protamines during spermatogenesis appears to be the fact that protamines convert DNA molecules into a very 0022-2X36/91

1220423-l

1 $03.00/O

DNA ligand binding DNA association

compact state. However, the mode of protamine binding to DNA has not been established yet. Due to the large number of positive charges associated with protamines at physiological pH values, it is expected that the main driving force for protamine binding to DNA comes from electrostatic interactions. This expectation is verified by a very strong dependence of the binding on the salt concentration. However, protamine binding to DNA also exhibits a distinct co-operativity, which cannot be explained on the basis of standard electrostatic interactions. Rather it should be expected that a binding process, which is mainly based on simple

423 0

1991 Academic

Press Limited

424

D. Porschke

electrostatic interactions, exhibits antico-operativity. According to a linear Ising model, with con-

sideration of excluded-site binding applied by Watanabe & Schwarz (1983), the co-operativity parameter is as high as approximately 1700. Similar results were obtained by Tobita et al. (1988) and by Nakano et al. (1989) using the same model (see Willmitzer & Wagner, 1980). Watanabe & Schwarz (1983)

tried

to explain

this

co-operativity

by

a

special electrostatic “screening”; however, there is no evidence for such special screening co-operativity from any quantitative analysis of related model systems (see Latt & Sober, 1967a,b; Mascotti B Lohman, 1990; Porschke, 1979, 1990). Apparently, the binding parameters obtained by application of a simple linear Tsing model, even with consideration of excluded-site binding, are without physical meaning. It seems that the model just happens to describe standard binding experiments, although is quite

the molecular binding process in solution different from that introduced into the

model. Thus, other models should be tested and more detailed experimental data should be collected for discrimination between potential binding models. Here some models are developed and special experiments are designed for discrimination. Due to the very similar structure of protamine species, it, may be expected that the choice of protamine does not affect the results in general. Clupein from herring sperm was selected because it can be purified to homogeneity relatively easily. In the literature, binding of protamine species has often been measured via spectroscopic labels attached to the protamine. This has been avoided here, at the expense of more laborious experiments, in order to obtain data that are susceptible to an unambiguous interpretation. By a combined analysis of equilibrium and kinetic parameters it is demonstrated that the co-operativity mainly results from protaBy a corremine-induced DNA interaciions. sponding model, with different, binding constants to “free” and associated DNA, the available experimental data can be explained to a very satisfactory level of accuracy and the resulting parameters are at’ the without problems in the assignment

the experiments. DNA concentrat,ionv arr given in rnolal units of nucleotide residues. Clupein Z was isolated from prot,amine sulfate gradr II1 from herring (Sigma Chemie GmbH, Deisenhofen. Germany) according to Ando &r Watanabe (1969). ThP samples were dialyzed extensively against wat,er. lyophilized and finally stored in, uacuo over P,O,. St,ock solutions werP prepared, according to weight, in the buffers used for the measurements. Light-scattering intensities were measured in various fluorimeters (Aminco SPF500. SLM800 and a, simple selfconstructed instrument). In all cases the samples were illuminated at a wavelength E, > 300 nm and the scattered light was collected at 90”. The time-dependence of tht light-scattering intensity was recorded &J personal computers: the data were transferred to thr facilities oi the Gesellschaft fiir wissenschaftliche Datenvrrarbeitung mbH, Giittingen, and evaluated by st,andard exponentialfit routines (Provencher, 1976). U.V. spectra were taken using a Lambda 17 spectraElmer. photometer from Perkin Bodenseewerk. oberlingen, Germany. Quantitative centrifugation experiments were performed with a Beckman TLlOO using a swing-out rotor.

3. Results (a) Il’mnsition

curve8 jrom measurem,ents scattering intensities

of light-

Addition of clupein to DNA induces a strong increase of the light-scattering intensity (Fig. 1). The clupein concentration required to induce t,his increase of the scat,tering intensity depends vrr? much on the ionic strength of the bufl’er used for the experiment. At ionic strengths below 200 rn,v and a DNA concentration of 2 PM, the change of the lightscattering intensity is complete at a clupein Concerl-tration of @I PM, corresponding to a stoichiometrl of about one clupein molecule per 20 nucleotidr residues. This stoichiometric ratio is consistent wit’h the number of 21 arginine residues in the sequencr of clupein Z (Iwai et al., 1971). Tt, is rxpec%ed t,hat

molecular level. 2. Materials

and Methods

DNA4 samples of high relative molecular mass from obtained from lambda were bacteriophage Boehringer-Mannheim and from Pharmacia. Freiburg (Germany). DNA from the bacteriophage PM2 (see Street & Gebhardt, 1979) was obtained from Boehringer-Mannheim. The samples were dialyzed exten1st against 1 M-NaC1, 10 mw-Na-cacodylat,e sively. (pH 7.0) 1 mM-EDTA and then either against 1 mM-NaCl, 1 mi%f-Na-cacodylate (pH 65) 50 PM-EDTA (buffer A) as a stock solution for measurements of light-scattering intensities or against 2 mM-K-phosphate (pH 6.5) (buffer B) as a stock solution for u.v.t absorbance measurements. Components were added as indicated in the description of t Abbreviations

used:

u.v..

ultraviolet,.

Figure 1. Light scattering intensity I of 4 ~M-IDKA in relative units as a function of the total clupein concentra(a) 0.6 M-NaCl and (0) tion ci at (x) @5 M-Nacl. 0.7 M-NaCl. The scattering intensity at ci = 0 has been subtracted and the high level has been normalized t,o 1 (buffer A. 20°C).

Protamine-DNA

the interaction with DNA is dominated by electrostatic contributions and that the other amino acid residues (3 Ala, 2 Pro, 3 Ser and 2 Val) do not contribute to the interactions directly. At ionic strengths I 2 600 mM the clupein concentration required to induce the increase of the lightscattering intensity is clearly larger than that expected from the stoichiometric ratio observed at I < 100 mM. Thus, the binding of clupein to DNA is essentially complete at I I 100 mM under the conditions of the titration experiments, whereas an excess concentration of clupein is required at I 2 600 mM. In the latter range the transition reflected by the change of the light-scattering intensity shows a distinct co-operativity. The strong ionic strength dependence of clupein binding to DNA is consistent with the expectation, whereas the nature of the strong co-operativity is not obvious. Measurements of transition curves at a given high level salt concentration of e.g. 700 mM shows a clear dependence of the transition midpoint on the DNA concentration: at DNA concentrations of 2, 4 and 8 FM the midpoints are observed at 2.05, 2.2 and 2.54 PM clupein. This dependence is analogous to that observed for the case of spermine-induced DNA condensation (Porschke, 1984). The condensation of DNA is known to be induced when the degree of spermine binding to DNA exceeds a threshold value (Wilson & Bloomfield, 1979; Widom & Baldwin, 1980). Because the binding of both spermine and clupein to DNA is mainly driven by electrostatic interactions, it is quite reasonable to assume a similar binding mechanism. A leastsquares fit of the data obtained at 700 mM-NaCl (see Porschke. 1984) provides a limit, degree of ligand binding 0, = 0.78 and a binding constant of I.9 x lo6 M-l. Application of the same binding mechanism to other titration data obtained at 800 mM and 1 M salt indicates a strong decrease of the binding constant with increasing salt concentration. An analysis of these data in terms of polyelectrolyte theory provides an approximate number of 11 ionic contacts. In view of the limits, both of the polyelectrolyte theory at high levels of salt concentrations and of the accuracy of the data, these results appear to be quite reasonable.

425

Complexes

According to these definitions the model involves two equilibrium constants; one for binding of ligands to the polymer (in its standard form) Kb and another for the intramolecular polymer transition K,. A further parameter of the model is the minimum degree of binding O,, which leads to a change of the polymer conformation. Of course, the transition implies an altered a%nity of the ligand to the polymer, but this need not be defined separately, as it is specified already by the intramolecular transition constant K,. Because most ligands of biological interest occupy more than a single lattice residue, the binding of these ligands has to be described by the excludedsite formalism (see McGhee & von Hippel, 1974). Usually the parameters for the binding of large ligands to polymers are evaluated by application of the excluded-site binding model derived for the limit case of infinitely long chains. According to this model all polymer chains arrive at a given degree of binding at a well-defined ligand concentration. Thus, the intramolecular transition of very long polymers induced by addition of ligands as defined above must appear infinitely sharp at a well-defined ligand concentration. In the present context it is of interest to study the influence of the polymer chain length on the transition. For this purpose a formalism for excluded-site binding has to be applied, which is without restriction on the length of the polymer chain. One approach is the combinatorial description of excluded-site binding, given first by Latt & Sober (1967a) and later by Epstein (1978). According to this model the number of different arrangements of n ligands, each of which covers k sites of the polymer, on a polymer chain with M sites is given by: P”(k’

(M-nk+k)! n, = (M-enk)! x k!’

The equilibrium concentration of polymers with n bound ligands c, can be calculated from the free ligand concentration c, and the free polymer concentration cp according to: c, = P,(k, n) x cp x (Kb

(b) Apparent transition

co-operativity resulting from a at a limit degree of binding

For a description of the shape of transition curves, the reaction model applied in the previous section has to be developed in some detail. According to this model, ligand binding itself is nonco-operative, in the sense that binding of a ligand to a site on the polymer lattice in its standard form is not influenced by the state of adjacent sites. However, the ligands are assumed to induce a transition of the polymer to a different state at a defined degree of ligand binding. This transition may correspond, for example, to folding of the polymer to a compact state.

x

cl)“.

(2)

When the number of ligands, n, bound to the polymer arrives at or exceeds the limit value 2, corresponding to a limit degree of binding O,, the altered state of the polymer is formed at a concentration: c*=Kxc ” t

“’

(3)

The equilibrium constant for the transition K, is assumed to be independent of n, provided that n 2 x. The degree of transition from the standard to the altered state of the polymer is then given by: (4)

426

D. Porschke

Figure 2. Degree of transition 0, according to the limit degree of binding model (eqn. S) as a fimction of’ the Jigand concentration for different polymer chain lengths = 100, 200. 400, 600 and 1000 (continuous lines from left, to right). K,, = IO4 M-‘. I(, = 10. = 20, 0, = 0% total polymer concentration 1 PM (in units of monomer residues): the broken line shows the degree of ligand binding 0, for M = 1000.

k

M

(c) Hinding data jiom centr@gation r.rperiment.s not support limit degree qf binding model

where c C” = i P,(/& n) x cp x (& x CJ n=l

(5)

and

cc; = i K(xP~(~,n)xc,x(~~xc,)”(6) “=X z is the maximal number of ligands, which can be bound to the polymer. The degree of ligand binding to the polymer can be evaluated from equations analogous to (4). All these model quantities hare been calculated by computer programs. As shown by the examples given in Figure 2, t,he degree of transition predicted by the model is relatively sharp, even though the binding of the ligands t,o the polymer itself is not co-operative. As expected, the steepness of the transition increases with increasing chain length. If the degree of transition is taken as a degree of binding and analyzed bp a fitting procedure based on the excluded-site binding model, very high values of co-operativit) are obtained. For example, the co-operativity parameber determined according to the excluded-site binding model is about 7000 for data simulated with an intramolecular transition constant) K, = 10. a polymer length M = 600 and a limit, degree of binding 0, = 0.80. Thus, a high co-operativity parameter need not, be due to nearest,-neighbor interactions. In many cases it is very difficult to decide which kind of co-operativity is valid for a given experimental system. This problem is usually connected with the quest)ion whether a given set of experimental data, obtained by spectroscopic measurements for example, reflects the degree of ligand binding or the degree of some intramolecular transition.

do

A decision on the mode of binding should be possible by experimental data that provide the absolute degree of binding without problems in interpretation. For the case of clupein binding to DNA. such dat,a can be obtained by quantit,ativc centrifugation experiments. provided that thca relative molecular mass of the DNA used in the experiments is suRicient,ly large. DEA from bat>teriophage i with a relative molecular mass of 32.3 x IO6 sediments much fast,er t’han clupein and thus can be easily separat’ed together with all> DNA-clupein complexes from free clupein 1)~s centrifugat#ion. Reaction mixtures of EDNA and clupein were prepared as usual and subjected to centrifugation in a Beckman TLIOO with a swingout rotor at an a,veraged value of 170,000 g for thrtxr hours. The concentrations remaining in the super natant were analyzed bv measurement,s of the U.V. absorbance. For a suf%entlv accurat,e determination of t,he clupein conrentrat’ions. the u.v. IllfYtSlIr( ments had t,o he conducted at 200 nm. Hecaust standard buffers contribute too much 10 t hcl II.\ absorbance at t’his wavelength. the crntrifugation experiments were performed in buffers containing phosphate and KF. which are transparent, into i hc deep u.v. range. Measurements of light-scattering intensities showed that the midpoint of the clnpein-inducoed DNA transition in the presence of a given KF concentration of e.g. @8 M is not identical with t)hat observed at, the same XaCl concentrat,ion. This is apparently due to a difference in the activity coeflicients for KF and i%aCI. For adjustment of th(t transition to given values of clupein and l>NA concentrations, higher concentrations of KF than of N&l have t,o be selected: t,hus, the affinity of

Yrotamine-DNA “d

Complexes

I” T

0.7-

(d) Kinetics of clupein-DNA that DNA association

T

-16

00 0 i0I

0.1 -,, 0 0000000 0 00 "T0

-2

t-o 0

I

2

3

4

5 6 c: [pLMI

7

8

9

IO

Figure 3. Degree of clupein binding 0, to iDNA from ( x ) centrifugation experiments and (0) the light-scat’tering intensity I as a function of the total clupein concentration c! (20 ~M-~DXA. 1.3 M-KF + buffer B. 20°C).

clupein to I)KA in the presence of a given concentration of KF is higher than that at an equivalent concentrat’ion of SaCI. However, the transition is very similar otherwise: the co-operativity and the general dependence on the concentrations of D1;A and clupein are virtually identical. For each experiment on a DEA-clupein mixture. separate DNA and clupein samples with concentrations identical to those in the mixture were centrifuged as controls. The data obtained from the controls were used to correct the result obtained for the mixture. Usually some minor contamination of the DNA samples remained in the supernatant, and a small decrease of the clupein absorbance corresponding to a few percent indicated some clupein sedimentation. After corrections. the decrease of the clupein concent,ration in the supernatant, of t’he mixt,ures was at’tributed to D?u’A-binding and the dat’a were converted into degrees of binding using the stoichiometric coefficient corresponding to one clupein molecule per 20 phosphate residues (see section (a)). The combina,tion of results obtained by centrifugation and by measurements of the light-scattering intensity (see Fig. 3) demonstrates that there is very little, if any, binding of clupein to DNA before the onset of the co-operative transition. whereas a rat’her high-degree of binding corresponding to approximately 70:/,, is found in the range beyond the transition. This result shows that the clupein-induced DEA transition is not really equivalent to the spermine-induced DXA condensation. In the lat’ter case a relatively high degree of spermine binding to DNA of approximately 80% is required to induce the co-operative condensation reaction.

complexation is essential

shows

During the clupein-DNA equilibrium titrations it was observed that the essential part of the transition indicat’ed by changes of t’he lightscattering intensity is rather slow. This is in contrast to the very high rate of the intramolecular condensation reaction of DNA induced by spermine binding (Porschke. 1984). Because knowledge of the kinetics of the reaction may be essential for understanding of the binding mode, a systematic analysis of the kinetics was initiated. The binding kinetrcs of large ligands t,o polymers is known t’o be very complex due to excluded-site effects. However, it is possible to select special conditions, where this complexit’y is without consequence and the observed reactions are very simple. The kinetics has been measured very simply by mixing clupein with DNA in a standard fluorescence cuvette and recording the light-scattering intensity in standard fluorimeters interfaced with personal computers. The light-scattering intensity measured as a function of time can be fitted by single exponent’ial time constants z (Fig. 4). Variation of the DNA concentration cDNA in the presence of a constant clupein excess reveals a clear linear dependence of the reciprocal time constant l/z on eDNA (Fig. 5). Because the total clupein concentration. 16 PM. used in the experiments represented in Figure 5. corresponds to a concentration of binding equivalents 20 x 16 PM = 320 PM, there was a huge excess of clupein reaction equivalentzs even at’ the

I 1

0.6-

427

J 6-

30

$ 0

500

1000

1500

Figure 4. Change of the light-scattering intensity Al of 1 FM-EDNA as a function of time f after addition of I~PM-clupein (09 M-Nacl + buffer A. ZO’C). The continuous line represents a fit by a single exponential with a time constant of 212 s; the lower part of the diagram shows the residuals AA1 as a function of time t.

428

-7 ‘v

0008-

1

0006-

D. Porschke

Figure 5. Reciprocal time constant l/z as a function of the lDNA concentration CL (in units of phosphate residues) at a constant total clupein concentration of 16 PM (0.8 M-Pu’aCl + buffer A, 20°C). The rate constants according to the dimerization model are k+ = 5.8 x 10’ M-~ s-l and k- = 2.0 x 10e3 s-l (k+ calculat’ed for molar DKA helix concentration units).

highest DNA concentration. Thus, the concentration dependence shown in Figure 5 cannot be due to the binding of clupein directly, but only indirectly. This concentration dependence reflects an association reaction between DNA strands, which is induced by clupein binding to the DNA. The most simple type of reaction consistent’ with the data shown in Figure 5 is a dimerization reaction according to: DNA,+DNA,

$ (DNA,),

(7)

where DNA, denotes some complex between DNA and clupein. For this reaction the concentration dependence of the reciprocal relaxation time constant is given by 11~ = 4xk+

xC&+k

(8)

CbNA denotes the concentration of the free DNA-clupein complex. The rate constants k+ and k- can be easily obtained from the slope and the of concentration depenintercept, respectively, dences like that shown in Figure 5. Because it is not clear whether the association of DNA is limited to dimerization, the other extreme, where association of DNA proceeds without limits, has to be considered as well. For this case it is reasonable to assume that the rate constants for subsequent’ steps are equivalent, corresponding to reaction scheme. The reciprocal an “isodesmic” relaxation time constant for the isodesmic reaction scheme is given by (Porschke & Eggers, 1972): l/z=2xkcxc&,+k-. ULNA denotes

the equilibrium

(9) concentration

of free

reaction sites. including those of associated DNA species. Tt should be noted that the evaluation of the present kinetic data by equations that, are valid for chemical relaxation processes represent’s an approximation. A more detailed evaluation should be based on equat’ions valid for second-order reactions without linearization. For a standard second-order reaction, however, it would not be possible t,o fib the experimental data b,v simple exponentials, unless t’he reaction is close to equilibrium. The unexpectedly simple reaction-progress curve may be due to several contributions. First of all, the initial part of the reaction occurs during mixing and t,hus has not been observed. Furthermore, the binding reaction is very complex: the association step reflected in Figure 1 is preceded by binding of clupein t,o DNA together with some intramolecular rearrangements and is followed by slow rearrangements including (partial) precipitation. These reactions also lead to changes of the light-scattering intensity and to some degree contribut,e t,o the measured reaction curves. Finally. the concentration of the reacting DNA-clupein complex is not exactly known. Due to these complications it, would be dangerous to interpret the data hy more than very simple models. Another observation that is not expect’ed for a standard second-order reaction is the rather high linear correlation of the reciprocal time constants with the total DNA concentration (Fig. 5). Fitting of the available experimental data sets to the “exact” versions of equations (8) and (9), wit’h implicit calculation of equilibrium concentrations by least-squares minimization, in general led t,o error sums larger than for the simplified evaluation described above. This result suggests that the concentration of free reaction sites is proportional to t,he total amount of DNA. In the present contribution it, will not, he attempted to describe t,hr complexity of the rea,ction in full detail. The emphasis is on the identification of major contributions to the binding reaction. Due to the approximations inherent in the present evaluat,ion. the magnitudes of the rate constants may be associat,ed with some systematic error. However, this does not affect’ general conclusions derived for the mechanism and obtained from comparison of rate constants that have been evaluated according to t,he same prot,hr infinite associat,ion model cedure. Although appears to be more appropriate, the rate c:onstant,s are given in terms of a simple dimerization model. in order to he comparable with the rest&s of the model calculations given in section (e). All rate constants are in concentration units of DNA double helices. The kinetics of clupein-induced DNA association has been studied for various fixed clupein concentrat’ions. The reaction is observed when the clupein concentration exceeds a threshold value. For a Na(ll concentration of 04 M. this threshold is at approximately 12.5 PM-clupein (at DNA concentrations of a few 11~). As shown in Figure 6, the association rate constants k+ measured just, above t,he threshold clupein concentration are much lower than t)hose

Protamine-DNA

429

Complexes

Jk 0

IO

1 20

I 30

I 40

I 50

u 60

t 70

I 80

8 90

8 loo

90 110

ct QLLMI

Figure 7. Rate constants k’ (0) and equilibrium (x ) for the association of constants K = k+/kFigure 6. Rate constants of association k+ measured for iDNA at various clupein concentrations ci in (0) 0.7 and ( x ) 0% M-NaCl

(buffer

A, 20°C. estimated

accuracy

PM2-DNA as a function of the total clupein concentration ci (0.7 M-NaCl + buffer A, 2O”C, estimated accuracy +20% for the k+ values and If: 3O”/b for the K values).

k20%).

observed at higher clupein concentrations ci. The increase of k+ with ci clearly reflects the co-operative transition observed by measurements of the light-scattering intensity. At high ci values, the rate constant k+ arrives at a plateau corresponding to approximately 1 x 108 M-I s-i, which appears to be the diffusion-controlled limit. These data demonstrate that the DNA association reaction requires a limit degree of clupein binding to the double helix. At low binding degrees the association rate seems to be reduced by electrostatic repulsion between DNA strands. When the negative phosphate charges are shielded by a sufficiently high degree of clupein binding, the DNA strands react at the diffusioncontrolled limit rate. increase of the association rate The co-operative constant lc’ observed at 98 M-NaCl is also found at 6.7 iv-NaCl. but’ is shifted at the lower salt concentration to lower clupein concentrations (Fig. 6). This is again consistent with the transition curves observed by measurements of the light-scattering intensity and demonstrates an increase of the clupein-DNA binding constant with decreasing ionic strength. Similar results have been obtained for PMB-DNA, which has about 9800 base-pairs (Streeck & Gebhardt, 1979). In this case the kinetics has been studied over an extended range of clupein concentrations and it has been possible to evaluate the rate constants of dissociation, which could not be derived at a sufficient accuracy for the much longer IDEA, because usually the intercepts were too close to the origin in the case of EDNA. The ratios k+/k- = K, corresponding to apparent equilibrium constants, are shown in Figure 7 together with the rate constants of association k+. Again there is a co-operative increase of the k+ value, when the clupein concentration is increased beyond a threshold value. A further increase of the clupein

concentration, however, leads to a decrease of k+; this effect is more clearly reflected in the apparent equilibrium constant K. A comparison of the parameters found for the two different DNA samples shows that the maximal rate constants k+ observed for the long EDNA are approximately a factor of 5 larger than those found for the relatively short PM2-DNA. This difference is probably due to an increased number of reaction contact sites available on the longer lDNA species, which evidently overcompensates the smaller diffusion coefficient of this DNA. (e) Ligand-driven

polymer association: of co-operativity

u source

The experimental data clearly show that clupein binding induces association of DNA strands and, thus, a model should be designed which describes both the co-operativity of clupein binding and the clupein-induced association process. Because clupein covers 20 nucleotide residues, the binding of ligands should be described in the framework of excluded-site binding. For simplicity t’he association of DNA strands is assumed to be limited t’o dimerization. It would be possible to extend the model to higher degrees of association, but this would require much more extensive computations. The ligand-induced dimerization model, in its most simple form, requires an equilibrium constant KM for the binding of ligands to the standard monomer form of double helices and another KD for the binding of ligands to the dimer form of double helices. Because the number of nucleotide residues k covered by the ligands is mainly determined by the number of positive net charges of the ligands, the value k may be assumed as equivalent for the monomer and the dimer state. Various models may be designed for the distribution of ligands in the associated state of DNA. In

430

,!J. Porschke

m +m+ m

Figure 8. Schematic representation of @and-driven association of DNA double helices (seetext).

with the thermodynamic. potential resulting from ligand binding. For this reason it, is sufficient t,o define a dimerization constant K,” at 0, = 0. The values K* at 0, > 0 are given implicitly by the paramet’ers of ligand binding. Trr complete analogy to equat,ion (2) the binding of ligands to the monomer form of DXA is described b) c”, zz t’M(k, n) x rm x (KM x Cl)”

t 10) the fee c-oncentrat,ions of the cm and f*, denotr monomer form of DXA and the ligand. respectively. fM(k. YI) are thr statistical factors defined by equation (1) and ci is t,hc c*oncent,ration of the monomer form of J)NA with n bound ligands. The corresponding equation for ligand binding to t’he dimrr form of DNA is: r; = t’,(k. n) x cd x (KD x e,)“.

the absence of experimental information an arrangement of ligands in the complex may be selected that’ can be described quantitatively without problems. For a particularly simple arrangement, represent,ed in Figure 8, it may be assumed that the ligands at the interface between two DNA strands are distributed exactly as predicted by the standard excluded-site binding model. In this case the distribution of ligands in the monomer and the dimer state are equivalent; however, the extent of binding to the dimer state is expected to be higher than that of t*he monomer state due to more extensive electrostatic interactions in the dimer. It may be argued that the capacity of the dimer for the uptake of ligands should be higher by a factor of 2 than that of the monomer. This factor may be introduced in the formalism of the excludedsite binding model by an increase of the effective chain length k, for t,he monomer, to 2/c for the dimer. Of course, it is also possible to define any other factor for the change of the binding capacity upon association. When the effective chain length in the associated state is 2k, the number of different individual dimer states is clearly larger than for a corresponding effective chain length k. Thus, it may be expected that for a given set of binding constants the DKA is driven into the associated state at a, lower ligand concentration, when the effective chain length is 2k. However, with respect to most other features the models are very similar. Thus. the description given below is restricted to the case with the effective chain length k for the associated state. The degree of DNA dimerization Od should increase with the degree of ligand binding 0, corresponding to a dimerization constant K,, which is a special function of 0,. At a first glance, it seems to be a particularly difficult task to design a relationship, which describes Ka as a reasonable function of 0,. However, it is neither necessary nor reasonable to design such a function, because this may be left to the driving force resulting from ligand binding. In fact, any function Kb =f(@,) must be consistent

ill)

The index d denotes that the corresponding paramet,ers refer to the dirnrr st,ate of J)NA: otherwise t,he definit#ions are exactly as before. The free (Y)IIcentration Td of the DNA dimer int>roduced into ryuation (I 1) is given by: Cd= K;l x (f&J”.

(Ii?)

ITsing equations (10) t)o (12). it is possible t#o compute t~he complet,e population of sJ>ecies. The degree of dimerization for any given population is: i

2 x r;

where z is the maximal number of ligands. which can be bound to a polymer with Jf residues (Z = integer(M/k)). Th e average degree of ligand binding is:

n=O The parameters of this model can be cbalculatrd relatively easily by appropriat’e computer programs: the distribution of species resulting at given equilibrium csonstants and concent,rations of polymer and ligand. which are not accessible in analytical form. have been evaluated by iteration routines. When the binding of ligands t)o strongly charged polymers like J)IVA double helices is mainly driven by electrostatic interact,ions, it is expected that t’he larger than KM. constant LCD is binding Furthermore. it is expected that h’z is very small. When the ligand concrnt,ration is increased from low values to the range of I/K,, the polymer may be converted to the dimer state. This expectation is verified by computations (Fig. 9) tha,t show a vet-) strong apparent co-operativity of the transition from the monomer to the dimer stat,e. At high ligand concentrations. exceeding the value I/KM. thca

Protamine-DNA

431

Complexes

a more detailed evaluation, the experimental results have to be given in a form that can be compared quantitatively. Using the kinetic parameters collected for PMB-DNA, apparent values of dimerization constants Kipp = k+/lc- are available for various clupein concentrations. These values may be compared with dimerization constants calculated from computed degrees of dimerization 0, according to: talc

Kd

I

0.1

IO c: QLLMI

Figure 9. Degree of transition Od according to the lignnd driven polymer association model as a function of the tot,al ligand concentration c! for polymer chain lengths 400. 500 and 600 and a ligand, which covers 20 residues (&, = 3 x IO4 M-‘. &, = 1 x lo6 M-I, K, = PO1 M-‘, total polymer concentration 601 PM (in units of monomer residues). The broken line shows the degree of ligand binding 0, for the chain length 500.

degree of ligand binding to the monomer state approaches the level of the dimer state. Then the driving force towards the dimer state is decreased again and finally 0, is reduced again to zero. The transition curves are also strongly affected by the polymer chain length. which is simply due to the increase

of the chemical

potential

caused by ligand

binding with increasing chain length (Fig. 9). As shown by the model curves, it is possible to represent experimental data on clupein-DNA interactions

by the new model, at least qualitatively.

For

_

- (I-c&)2

@Ii

x 2 xc;

where CLis the total polymer concentration. The experimental data could not be fitted using the chain length corresponding to the total number of base-pairs of PM2-DNA; at this chain length the steepness of the ligand-induced transition was much higher than the observed one. An optimal fit (Fig. 10) was observed for an effective chain length 80 together with the binding constants KM = and K,” = 1.06 x IO4 w-r, KD = 2.73 x IO8 M-’ 0.1 M-l. These values are without problem in the assignment at the molecular level. Obviously, the numerical values would be affected by the introduction of electrostatic repulsion, for example. 4. Discussion The widespread occurrence of protamines in sperm cells indicate an essential function for reproduction of most higher species. Tn spite of this, the principles of protamine function are still largely uncovered. As a first step towards understanding of the mechanisms associated with reproduction, it is necessary to characterize the mode of protamine-DNA binding. As described in the Introduction, the interpretation of protamine-DNA binding data by a standard

0

2.5E t IO i

0

I

I

I

20

I

40

60

SO

I 100

Figure 10. Apparent dimerization constants Ktp* measured for (0) PM2-DNA as a function of the clupein concentration c, (in 67 M-NaCl + buffer A, 20”; KBdPP = k+/k- as defined by equation (8)). The continuous line represents a least-squares fit according to the ligand driven polymer association model with KM = 196 x IO4 M-I. KD = 2.63x lO*M-I. Kg = 0.1 M-I? M = 80, k = 20.

432

D. Porschke

binding model with next,-nearest neighbor co-operativity leads to serious problems. The next obvious possibility for the explanation of the experimental data is given by a model with a ligand-induced intramolecular transition of the DNA. This model is consistent with a rather large amount of experimental data. However, a detailed experimental analysis reveals again some problems. First, the experiments ultracentrifuge described above provide evidence against a direct analogy of t,hr protamine-DNA binding with t,he DNA condensation reaction induced by simple positiveIT charged ligands. Second, the kinetics of the protamme-DNA reaction reveals that intermolecular DNA association is essential. It is remarkable that an important stimulus the mode of towards understanding of protamine-DNA binding comes from an analysis of the reaction mechanism. In the present case. a direct development of the results derived from t,he kinetics leads to a model which explains all the available experimental results without problems. Tn particular, the very high co-operativity resulting from the experiments can now be assigned to parameters that are very reasonable in terms of the molecular structure of the reactant’s, Some deviations remaining between the experimental data and bhe predictions of the model are very likely due to the simplifications inherent in the model. Obviously. a serious simplification is the neglection of electrc>,stat’ic repulsion between the ligands. It’ is very likely that, the difference between the measured and the calculated data at high ligand concentrations will be reduced considerably, when electrostatic repulsions are accounted for. More information is also required on the details of the reaction mechanism, which has been described at a rather simple level in the present communication. Indications on the significance of DNA-DNA interactions for protamine binding to DNA have been given in the literature. Direct) evidence for protamine-induced DNA interactions comes from investigations by electron microscopy (Bode B Lesemann, 1977). X-ray diffraction studies show a very compact packing of double helices and protafibers DKA-protaminr mine molecules in (Feughelman et al.. 1955; Suau & Subirana., 1977). but this should be expected anyway for crystalline structures. Details of intermolecular contacts have not been resolved yet at the limited resolution of fiber diffractions. Willmitzer & Wagner (1980) comment that they “would favour co-operativity to be due t,o the cross-linking ability of t,he protamines”. However, Willmitzer 8r Wagner have analyzed their experimental results only by the next,-nearest’ neighbor model assuming co-operativity. The present interpretation of the protamine-m DNA reaction is based entirely on the protamine induced intermolecular DNA association. The experimental data collected in the present investigation clearly support this interpretation. However. the protamine-DNA reaction may also be a ligand

induced intramolecular association reaction under certain experimental conditions. The binding rea(‘tion shown in Figure 9 may be easily modified from an inter- t,o an intramolecular association reaction. For the intramolecular reaction the source of cooperativit,J would be somewhat different, but should nevert,heless be sufficient for a strongly CC operative reaction. Some of the results obtained by the present model should be investigated in more detail. For example. bhr relat,ively low eflective chain length found for PM%DNA may partIF be due to simplifications inherent) in the model. However, the observed effecative chain length is close to the persistence length of DNA a,nd, thus. suggests that the react,ive unit maJ be determined by bhe persistence of the double helix. This may also be an explanation for tht, observation that the reciprocal relaxation time is linear with t,he total DNA concentration, c$, up to relatively high C; values. More information on the mechanism should be obtained by further measurements on various DNA samples with different chain lengths. Probably other observations present,ed in thSA double helioes should also not be a.tt,ribut,ed to nearest neighbor cbo-operativity. but t.o ligandinduced DSA association. A potential case appears to be bhe binding of hisbone HI to DNA, which has been reported to be highly co-operative (Triebel p.f nl., 1988: Clark & Thomas, 1988). Of course, the binding mode has to be characterized by detailed experiments in each case separately for an unambguous assignment. The author is nical assistance. wissenschaftjliche calculations and

indebted to ,Jiirgen Wawrzinek for tecllThe facilities of the Gesellschaft fiir Datrnverarbeitung were used for model fitt’ing of experimental data.

References Ando, T. & Watanahr. S. (1969). A new method for fractionation of protamines and the amino acid sequences of one component of salmine and t’hrer c*omponents of iridinr. Int. .I, Protein Rrs 1. 221-224. Ando, T.. Yamasaki, M. & Suzuki, K. (1973). t’rotami~tws, Springer-Verlag. Berlin. Bode. ,J. & Lesemann, 11. (1!)77). Thr anatomy of (‘(Ioperative binding between protaminrs and DNA. Hoppr-Xeyler’. .I. &, Thomas. *J. 0. (1988). Differences in the binding of Hl variants to DXA: co-oporativity and linker length related distribut,ion. JGur. .I. Hioch~em

178. 225233. Epstein. I. R. (1978). (‘o-operative and non-c,o-oyerativr binding of large ligands to a finite one-dimensional lattice. ;2 model for ligand-oligonucleotidr interactions. J3iophy.s. Chem. 8. 327-339. Feughelman. M.. Langridge, R.. Seeds. W. E.. Stokes. A, R.. Wilson, H. R., Hooper. C. W.. Wilkins. M. H. F.. Barclay, R. K. & Hamilton, L. D. (1955). Molecular structure of deoxyribosr nucleic acid and nucleoprotein. Naturr fbmdon), 175. 834-838.

Protamine-DNA Hecht, N. B. (1989). Mammalian protamines and their expression. In Histones and Other Basic Nuclear Proteins (Hnilica, L. S., Stein, G. S. & Stein, J. L.. eds), pp. 347-374, CRC Press, Boca Raton. Iwai. K., Nakahara, C. & Ando, T. (1971). Studies on protamines XV. The complete amino acid sequence of the Z component of clupeine. Application of N + 0 acyl rearrangement and selective hydrolysis in sequence determination. J. Biochem. 69, 493-509. Kasinsky, H. E. (1989). Specificity and distribution of sperm basic proteins. In Histones and, Other Basic Nuclear Proteins (Hnilica, L. S., Stein; G. S. & Stein. J. L., eds). pp. 73-164, CRC Press, Boca Raton. Latt. S. A. & Sober, H. A. (1967a). Protein-nucleic acid interactions. II. Oligopeptide-polyribonucleotide binding studies. Biochemistry, 6, 3293-3306. Latt, S. A. & Sober, H. A. (1967b). Protein-nucleic acid interactions. III. Cation effects on binding strength and specificity. Biochemistry, 6, 3307-3314. Mascotti, D. P. & Lohman, T. M. (1990). Thermodynamic extent of counterion release upon binding oligolysines to single stranded nucleic acids. Proc. Nat. Acad. Sci., I;.S.A. 87. 3142-3146. McGhee, J. D. & Von Hippel, P. H. (1974). Theoretical aspects of DNA-protein interactions: co-operative and non-co-operative binding of large ligands to a one-dimensional homogeneous lattice. J. ililoZ. Biol. 86, 469-489.

Nakano. M., Kasai, K., Yoshida. K., Tanimoto. T.. Tamaki, Y. & Tobita, T. (1989). Conformation of the fowl protamine, gailine, and its binding properties to DNA. J. Biochem. 105, 133-137. Porschke. D. (1979). The binding of Arg and Lys-peptides to single-stranded polyribonucleotides and its effect on the polymer conformation.. Biophys. Chem. 10. l-16. Porschke, D. (1984). Dynamics of DNA condensation. Riochemistry, 23. 4821-4828.

Complexes

Porschke, D. (1990). Model systems for the characterization of protein-nucleic acid interactions. In Landolt-Btirnstein, Neue Serie VII, 1dII (Saenger, W.. ed.), pp. 264-294, Springer-Verlag, Berlin. Porschke, D. & Eggers, F. (1972). Thermodynamics and kinetics of base-stacking interactions. Eur. J. Biochem.

26, 490-498.

Provencher. S. W. (1976). A Fourier method for the analysis of exponential decay curves. Biophys. J. 16, 27-41. Streeck, R. E. & Gebhardt, C. (1979). E’hysical map of PM2 DNA. Hoppe Seyler’s 2. Physiol. Chem. 360, 529-532.

Suau, P. & Subirana, J. A. (1977). X-ray diffraction studies of nucleo-protamine structure. J. Mol. Biol. 117. 909-926. Tobita, T.. Tanimoto, T. & Kakano. M. (1988). The binding mode of a mammalian (boar) protamine to DNA. Biochem. Znt. 16, 163-173. Triebel, H., von Mickwitz, C. U., Biir, H. 11:Burckhardt, G. (1988). Mg2 + -induced transition to strongly cooperative binding of histone Hl to linear DNA. Int. J. Biol. Macromol. 10, 322-328. Watanabe, F. & Schwarz, G. (1983). Thermodynamics and kinetics of co-operative protein-nucleic acid binding. II. Studies on the binding between protamine and calf thymus DNA. J. Mol. Hiol. 163, 485-498. Widom, J. & Baldwin, R. I,. (1980). Cation-induced toroidal condensation of DNA. Studies with Co’+(NH,),. J. Mol. Biol. 144, 431~-453. Willmitzer, L. & Wagner, K. G. (1980). The binding of protamines to DNA; role of protamine phosphorylation. Biophys. Struct. Mech. 6, 95-110. Wilson, R. W. & Bloomfield, V. A. (1979). Counterioninduced condensation of deoxyribonucleic acid. A light scattering study. Biochemistry. 18. 2192-2196.

Edited by R. Huber