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Chemical Physics Letters 441 (2007) 148–151

Determination of the electrostatic potential difference betweenDNA and the solution containing it: A kinetic approach

Mario Carrasco, Raquel Coca, Isabel Cruz, Silvia Daza, Manuela Espina,Emilio Garcia-Fernandez, Francisco J. Guerra, Rafael Leon, Marıa J. Marchena,

Inmaculada Perez, Manuel Puente, Esteban Suarez, Inmaculada Valencia,Inmaculada Villalba, Rafael Jimenez *

Department of Physical Chemistry, Faculty of Chemistry, University of Seville, c/Profesor Garcıa Gonzalez s/n, 41012 Sevilla, Spain

Received 26 February 2007; in final form 14 April 2007Available online 29 April 2007

Abstract

A kinetic approach to determine the electrostatic potential difference in soft interfaces, when classical methods fail, is presented. Themethod is based on electrostatic and non-electrostatic separation of the binding constant of one reactant to one of the phases. Here themethod is applied to the DNA/water interface. Reliable results are obtained using as probes the reactions ½RuðNH3Þ5pz�2þ þ S2O2�

8 and[Co(NH3)5pz]3+ + [Fe(CN)6]4�.� 2007 Elsevier B.V. All rights reserved.

1. Introduction

In the last two decades, there has been a growing interestin the study of interactions of DNA with small ligands.This interest arises from the potential application of thesestudies to different fields, such as therapeutic effects ofthe ligands [1], molecular electronics [2], sensors fabrication[3], gene transfer [4] and reactivity under restricted geome-try conditions [5] , among others.

Fundamental to the design of new DNA binding agents,able to perform a desired function, is a detailed under-standing of the DNA binding properties of existing com-pounds [6]. A first step in this direction is the separationfor a given ligand of the different components of the bind-ing free energy. As a contribution to this field we presenthere a procedure for obtaining the electrostatic binding freeenergy of positively charged ligands to DNA. Obviously,these electrostatic interactions are the consequence of theelectrostatic potential difference existing between DNA

0009-2614/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.cplett.2007.04.090

* Corresponding author. Fax: +34 954 557174.E-mail address: gcjrv@us.es (R. Jimenez).

surface and the solution surrounding it, originated by thephosphate groups negative charges. Thus, measurementof this potential difference seems in order.

Unfortunately conventional methods used for measur-ing this kind of interfacial potential difference in manyother microheterogeneous systems producing soft surfacescannot be applied in the particular DNA case. Thus, themethod based on the use of indicators cannot be appliedin this case because this method would imply changes inthe pH of the solution containing the DNA [7]. It is clearthis would produce changes in the protonation of phos-phate groups, and consequently in the potential differenceto be measured. On the other hand, the method based onthe measurements of the wavelength changes correspond-ing to the maximum of some pyrene derivatives emissions[8], does not work in the case of DNA, because pyreneintercalates into DNA and this produces a change in theintensity of emission, instead of a change in its maximumwavelength, which cannot be related to the interfacialpotential difference.

For this reason we have considered a different approachto measure the electrostatic potential difference in the DNAcase.

Table 1Values of kobs · 102/s�1 at different DNA and NaCl concentrations for thereaction between [Ru(NH3)5pz]2+ + [S2O8]2�

[DNA]/10�3

mol dm�3[Na+]/mol dm�3

0.010 0.015 0.027 0.050

0 57 53 46 370.100 48 52 450.230 400.250 500.300 490.500 44 45 420.564 350.800 331.000 231.100 30 351.500 181.600 25 291.690 311.750 132.000 132.250 302.300 17 262.800 15 282.850 23

Table 2Values of kobs · 104/s�1 at different DNA and NaCl concentrations for thereaction between [Co(NH3)5pz]3+ + [Fe(CN)6]4�

[DNA]/10�3

mol dm�3[Na+]/mol dm�3

0.011 0.02 0.05 0.10

0 28 29 27 240.275 170.340 220.350 160.400 24 240.450 140.600 21 220.680 210.800 8 161.000 7 14 211.300 191.360 181.600 7 11 162.000 10 152.200 3 142.250 92.400 8 142.500 162.600 3 82.800 3 6 123.000 3 6 134.000 54.100 2

M. Carrasco et al. / Chemical Physics Letters 441 (2007) 148–151 149

This method, which of course can be applied to other softinterfaces when conventional methods do not work, is basedon the study of the kinetics of two reactions between ions ofopposite charge sign, in the present case the reactionsFeðCNÞ4�6 þ CoðNH3Þ5pz3þ and S2O2�

8 þRuðNH3Þ5pz2þ.These two reactions were selected for the following reasons:first of all, in each of them only the positively charged reac-tant binds to DNA thus simplifying calculations. Secondly,given the two cationic complex similarities, we expected thatthe non-electrostatic interaction of these complexes withDNA was the same. This point is an internal checking ofour method, which is based on a separation of the electro-static and non-electrostatic part of the binding free energy.

2. Experimental

2.1. Materials

[Ru(NH3)5pz]2+ and [Co(NH3)5pz]3+ (pz = pyrazine)were synthesised following the procedures in Refs. [9,10],respectively. Calf thymus DNA was purchased from Phar-macia and used without further purification. Preliminaryexperiments showed that purification does not produceany changes in the kinetic results. A buffer solution wasnot added to the solutions because as in the case of purifi-cation, the addition of a buffer (pH 7) does not modifykinetic results, provided that ionic strength of the solutionswas kept constant, as verified. NaCl, Na4[Fe(CN)6] andNa2S2O8 were commercial products (Merck P.A.) and wereused as received. Water was obtained from a MilliporeMilli-Q water system, its conductivity was less than10�6 S m�1, and was deoxygenated before use.

2.2. Kinetic measurements

The kinetic of the reactions were monitored employing astopped-flow spectrophotometer from Applied Photophys-ics. The oxidation of [Fe(CN)6]4� by [Co(NH3)5pz]3+ wasmonitored at 420 nm by following the appearance of[Fe(CN)6]3�. The oxidation of [Ru(NH3)5pz]2+ by S2O2�

8

was monitored at 407 nm, by following the disappearanceof the ruthenium complex. All the kinetic runs were carriedout under pseudofirst order conditions, in excess of thenegatively charged reagent ([Ru(NH3)5pz2+] = 2 · 10�4

mol dm�3, ½S2O2�8 � ¼ 2� 10�3 mol dm�3, [Co(NH3)5pz3+]

= 2 · 10�4 mol dm�3, ½FeðCNÞ4�6 � ¼ 2� 10�3 mol dm�3).DNA concentrations were determined spectrophotometri-cally [11], at 258 nm, using a value of molar absorptivitye = 6600 mol�1 dm3 cm�1 in such a way that the concentra-tions of DNA refer to nucleotides concentration.

3. Results

Kinetics runs were carried out at different concentra-tions of NaCl and, for each concentration of sodium chlo-ride, at different DNA concentrations. These results aregiven in Tables 1 and 2 for the two reactions studied here.

In the tables the results are given for the different [Na+].These Na+ concentrations include the Na+ ions from theanionic reactants.

4. Discussion

Under our working conditions, the cationic complexeswill be in two states, free of and bound to DNA, which will

[M(NH3)5 pzn+]f + DNA [M(NH3)5 pzn+]bK

kf kb

products

Scheme 1.

Table 3Values of K at different Na+ concentrations were obtained from the best fitto Eq. (2)

[Co(NH3)5pz]3+ [Ru(NH3)5pz]2+

[Na+]/mol dm�3 K/mol�1 dm3 [Na+]/mol dm�3 K/mol�1 dm3

0.011 2550 (2395) 0.010 1230 (1193)0.020 1099 (1318) 0.015 796 (809)0.050 394 (527) 0.027 332 (467)0.100 226 (264) 0.050 383 (271)

Data in parenthesis were obtained from the best fit of K values to Eq. (3).

[Na+] / mol·dm-3

0.00 0.02 0.04 0.06 0.08 0.10 0.12

K /

mol

-1dm

3

0

500

1000

1500

2000

2500

3000

Fig. 2. Plot of K vs. [Na+]/mol dm�3 for Co(NH3)5pz3+ in DNAsolutions. Solid line represents the best fit to equation K = (a + b[Na+])/(1 + c[Na+]).

150 M. Carrasco et al. / Chemical Physics Letters 441 (2007) 148–151

react at different rates. These two states are at equilibrium(Scheme 1).

It can be shown that under these circumstances, for asecond order process provided that, as here, only one ofthe reactants is bound to DNA, the measured rate con-stant, kobs, is given by [12]

kobs ¼kf þ kbK½DNA�

1þ K½DNA� ð1Þ

In the present case, as matter of fact, Eq. (1) can be simpli-fied to

kobs ¼kf

1þ K½DNA� ð2Þ

that is, kbK[DNA]� kf. Taking into account the negativecharge of S2O2�

8 and FeðCNÞ4�6 this is not an unexpected re-sult [13].

Fig. 1 is a plot of kobs vs. [DNA] for the reactionbetween FeðCNÞ4�6 þ CoðNH3Þ5pz3þ in DNA solutions at[NaCl]=0.011 mol dm�3. From this and similar plots thevalues of K corresponding to the different [Na+] can beobtained. These values are given in Table 3.

The values of K for both reactions can be fitted to

K ¼ aþ b½Naþ�1þ c½Naþ� ð3Þ

as shown in Fig. 2.

[DNA] / mol·dm-3

0.000 0.001 0.002 0.003 0.004 0.005

k obs

/ s-1

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

Fig. 1. Plot of kobs/s�1 vs. [DNA]/mol dm�3 for the reaction between

FeðCNÞ4�6 þ CoðNH3Þ5pz3þ in DNA solutions. Solid line represents bestfit to Eq. (2).

Obviously K contains contributions from the electro-static and non-electrostatic free energy of binding, in sucha way that can be written

DG ¼ �RT ln K ¼ DGel þ DGnel

¼ �RT ln Kel � RT ln Knel ð4Þ

In order to separate these contributions we used the Lipp-ard’s equation [14]

log K ¼ log Knel þ a log½Naþ� ð5ÞSo Knel can be obtained from the intercept of the plot of logK vs. log [Na+]. These plots are given in Fig. 3. It is worthpointing out that the points in Fig. 3 correspond to the fit-ted values of K, instead of the experimental ones.

It is satisfactory that, as expected, the values of Knel arepractically the same for the two cationic complexes (seeinsert in Fig. 3). Once the value of Knel (20 mol�1 dm3)has been obtained, Kel for each complex to each [Na+]can be obtained as Kel = K/Knel (see Eq. (4)). Kel can beexpressed as [15]

ln Kel ¼�nF DW

RTð6Þ

In this equation n represents the charge of the complexes(n = 2 for Ru(NH3)5pz2+ and n = 3 for Co(NH3)5pz3+)and DW is the electrostatic potential difference at theDNA interface. So, this parameter can be easily obtained

log ( [Na+] )-2.5 -2.0 -1.5 -1.0 -0.5 0.0

log

(K)

1.0

1.5

2.0

2.5

3.0

3.5

4.0

[Co(NH3)5pz]3+

[Ru(NH3)5pz]2+

y =1,3346 - 1,0580*xy =1,3278 - 0,8641*x

Fig. 3. Plot of log K vs. log [Na+] for the binding of Ruthenium andCobalt complexes. Solid and broken lines represent best fit to Lippard’sequation (Eq. (5)).

M. Carrasco et al. / Chemical Physics Letters 441 (2007) 148–151 151

from Eq. (6), once Kel have been obtained. The values ofDW at different [Na+] are given in Fig. 4. These DW valuesare given as matter of fact by DW = [�54/(1 + 16[Na+])] ±5 mV. It is interesting to note that the values of DW are ofthe same order of size as those existing at the interfaces ofmicelles.

It should be mentioned that the values of DW are slightlydifferent (in about ±5 mV) when they are calculated fromdata of Ru(NH3)5pz2+ or Co(NH3)5pz3+. These differencescould be due to dielectric saturation effects caused by thehigh electric field at the interface. This effect would pushboth probes towards the aqueous phase, but more so tothe ion with the higher charge. In other words, the locationof the cobalt complex would be different (closer to theaqueous pseudophase) from those of the ruthenium com-plex. However, data from both complexes are close enoughto be considered adequate. In some sense this is anexpected result, because the values of the electrostaticpotential differences that we have obtained are operational

[Na+] / mol·d m-3

0.00 0.02 0.04 0.06 0.08 0.10 0.12

ΔΨ /

Vol

ts

0.00

0.01

0.02

0.03

0.04

0.05

0.06

Fig. 4. Plot of DW/Volts vs. [Na+]. Solid line is the best fit to equation DW(mV) = (�54)/(1 + 16[Na+]). Full dots were obtained from cobalt com-plex data and empty dots were obtained from ruthenium complex data.

values, and for this reason are somewhat dependent on theprobe. In this regard, it is important to remember that thevalues of DW obtained from classical methods also areoperational values. These values, generally speaking, arebased on reasonable assumptions that relate the values ofmagnitudes, which cannot be measured and those of otherswhich can be measured. Here the reactivity of the com-plexes is related to the potential difference through a rea-sonable assumption, because the latter is intrinsicallyimmeasurable. However, the operational values of a mag-nitude can be considered reliable if different probes giveclose, although not identical, results. From this point ofview, the values presented here seem adequate.

It is also interesting to note that Knel corresponds to afree energy of 7.5 kJ/mol which is of the order of the freeenergy of a hydrogen bond. Thus, the formation of thiskind of bonds between the amino groups and the phos-phate groups seems to be the major contribution to Knel.Of course, other kinds of interactions such as hydrophobicinteractions can also contribute to Knel.

In conclusion we have obtained a separation of the non-electrostatic and electrostatic free energies separations ofcharged ligands binding to DNA. From the latter, we haveobtained the values of the electrostatic potential differencesat the DNA/solutions interface. Of course the method canbe applied to other charged interfaces in which the classicalmethods cannot be applied.

Acknowledgment

This work was financed by the D.G.I.C.Y.T. (CTQ2005– 01392/BQU) and the Conserjerıa de Educacion y Cienciade la Junta de Andalucıa.

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