Polymerization-induced enhancement of binding and binding-induced polymerization

Article abstract of DOI:10.1016/j.cplett.2003.12.026

We obtained the binding free energy of the complex [Co(C₂O ₄)₃]^3- to the peptide H-Lys-Gly-(Lys-Gly) ₉-Lys-NH₂, and to the monomers (aminoacids) forming the peptide, using the electron transfer reaction between [Ru(NH₃) ₅pz]²⁺ and [Co(C₂O₄) ₃]^3- as the probe. The polymerization of the monomers increases the negative free energy of binding and changes its character, non-cooperative for the monomers and anti-cooperative for the peptide. This increase in the negative free energy represents a driving force for the polymerization process that produces the peptide from the aminoacids (monomers) in such a way that the polymerization in the presence of the cobalt complex is more favourable, from a thermodynamic point of view, in 16.5 kJ/mol.

Full text of DOI:10.1016/j.cplett.2003.12.026

Chemical Physics Letters 384 (2004) 266–270
www.elsevier.com/locate/cplett
Polymerization-induced enhancement of binding
and binding-induced polymerization
a
J. Ortiz , J.F. Guichou , A. Chavanieu , F. Sanchez , R. Prado-Gotor
b
b
a
a,
*
ꢀ
a
Department of Physical Chemistry, Faculty of Chemistry, University of Sevilla, C/Profesor Garcꢀıa Gonzꢀalez s/N, Sevilla 41012, Spain
Centre de Biochemie Structurale, CNRS UMR 5048, INSERM UMR 554, Universitꢀe de Montpellier 1, 29, route de Navacelles,
Montpellier Cedex 34090, France
b
Received 3 October 2003; in final form 1 December 2003
Published online: 29 December 2003
Abstract
We obtained the binding free energy of the complex [Co(C2O4)3]3ꢀ to the peptide H–Lys–Gly–(Lys–Gly)9–Lys–NH2, and to the
monomers (aminoacids) forming the peptide, using the electron transfer reaction between [Ru(NH3)5pz]2þ and [Co(C2O4)3]3ꢀ as the
probe. The polymerization of the monomers increases the negative free energy of binding and changes its character, non-cooperative
for the monomers and anti-cooperative for the peptide. This increase in the negative free energy represents a driving force for the
polymerization process that produces the peptide from the aminoacids (monomers) in such a way that the polymerization in the
presence of the cobalt complex is more favourable, from a thermodynamic point of view, in 16.5 kJ/mol.
Ó 2003 Elsevier B.V. All rights reserved.
1. Introduction
of the oxidation of the complex [Ru(NH3)5pz]2þ
(pz ¼ pyrazine) by [Co(C2O4)3]3ꢀ (C2O42ꢀ ¼ oxalate an-
ion) in the presence of a peptide constituted by lysine
and glycine, as well as in the presence of the monomers
(aminoacids) constituent of the peptide. These results
indicate that polymerization produces an enhancement
of the binding (of the cobalt complex) as well as a
change in the character of the binding. The results
also show that in the presence of the cobalt complex
the polymerization becomes thermodynamically more
favourable.
The union of small ligands to substrates is of interest
from different points of view, encompassing phenomena
such as heterogeneous catalysis [1], enzymatic catalysis
[2], reactivity in micellar systems [3] and microemulsions
[4], molecular machines [5], molecular electronics [6],
trapping of substrates by polyelectrolytes [7], confor-
mational changes in DNA induced by the binding of
solutes [8], etc. In the field of chemical reactivity, these
unions can produce changes of several orders of mag-
nitude in the reaction rate constant. Examples from the
field of enzymatic catalysis are well known. But also in
other fields these drastic changes in reactivity are ob-
served. Thus, the rate of the electron transfer reaction
within the binuclear complex [(NH3)5RuIII–NC–
RuII(CN)5]ꢀ increases by a factor of 108 in going from
water to a 0.2 mol dmꢀ3 micellar solution of hexade-
cyltrimethylammonium chloride [9].
2. Experimental
The preparation of the reactants, [Ru(NH3)5pz]2þ
and [Co(C2O4)3]3ꢀ as well as the way of performing
kinetic experiments have been described in a previous
work [11].
As a continuation of our work in this field [10], we
present here the results corresponding to a kinetic study
The peptide consists of twenty one aminoacids with
the sequence H–Lys–Gly–Lys–Gly–Lys–Gly–Lys–Gly–
Lys–Gly–Lys–Gly–Lys–Gly–Lys–Gly–Lys–Gly–Lys–
Gly–Lys–NH2. It was prepared on a pioneer peptide
synthesis from Perspective Biosystems (SPPS) using
* Corresponding author. Fax: +34-954557174.
E-mail address: gcjrv@us.es (R. Prado-Gotor).
0009-2614/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved.
doi:10.1016/j.cplett.2003.12.026

J. Ortiz et al. / Chemical Physics Letters 384 (2004) 266–270
267
TBTU activation Fmoc-chemistry. (Fmoc-amino acids
for peptide synthesis were from Perspective Biosystems,
TBTU from Advenced Chemtech, di-iso-propylethyl-
amine from Perspective Biosystems, triisopropylsilane
and phenol from Fluka, TFA, DMF and acetonitrile
from SDS.) Coupling was carried out with a four-fold
excess of activated aminoacids for a minimum of 30
min. The peptide was synthetized on Pal-Peg-Ps resin
(Applied Biosystems). After synthesis the peptide was
treated with a mixture of TFA (88%), water (5%), phe-
nol (5%) and triisopropylsilane (2%) for cleavage from
the resin and side chain deprotection. The crude peptide
was purified using reversed-phase HPLC.
Kinetic runs were carried out in the presence of dif-
ferent peptide concentrations under pseudo-first order
conditions ([Co(C2O4)3]3ꢀ ¼ 3 ꢁ 10ꢀ4 mol dmꢀ3 and
[Ru(NH3)5pz]2þ ¼ 6 ꢁ 10ꢀ5 mol dmꢀ3) and in the pres-
ence of monomers at different concentrations, but al-
ways maintaining the same relation Lys/Gly as in the
peptide.
of monomers means that this mixture contains 10 ꢁ
10ꢀ3 ¼ 10ꢀ2 mol dmꢀ3 of glycine and 11 ꢁ 10ꢀ3 ¼ 1.1 ꢁ
10ꢀ2 mol dmꢀ3 of lysine.
The results in Fig. 1 are the pseudo-first order rate
constants (see Section 2) for the electron transfer reac-
tion:
Â
Ã
Â
Ã
3ꢀ
RuðNH3Þ pz 2þ þ CoðC2O4Þ
5
3
Â
Ã
Â
Ã
! RuðNH3Þ pz 3þ þ CoðC2O4Þ
ð1Þ
4ꢀ
5
3
which, as in other reductions of cobalt (III) complexes,
is followed by a rapid decomposition of the resultant
Co(II) complex [12]:
Â
Ã
4ꢀ
CoðC2O4Þ
! Co2aþq þ 3C2O2ꢀ
ð2Þ
3
4
This second process is rapid in relation to the redox step,
in such a way that the measured rate constants corre-
spond to the electron transfer process.
The results corresponding to the mixture of the
monomers will be considered first. These results can be
fitted to the equation:
kf þ Kkb½mꢂ
k ¼
ð3Þ
3. Results and discussion
1 þ K½mꢂ
This equation, in fact the Olson–Simonson equation
[13], corresponds to the behaviour expected for a two
state reactive system. The two states in the present case
are reactants free (f) and bound (b) to the aminoacid. It
is noteworthy that according to the charges of the re-
actants it is reasonable to assume that only the nega-
tively charged cobalt complex will associate with the
positively charged aminoacid. These two states are at
equilibrium:
Fig. 1 contains the results corresponding to the ex-
periments in the presence of the peptide and the mixture
of monomers. The concentrations in the case of the
mixtures of the aminoacids are given in such a way that
they can be directly compared with those of the peptide.
Thus, a concentration of 10ꢀ3 mol dmꢀ3 of the mixture
8
7
6
5
4
3
2
1
0
Â
Â
Ã
Â
Ã
Ã
kf
3ꢀ
RuðNH3Þ pz 2þ þ CoðC2O4Þ
! products
5
3
m m K
ð4Þ
Ã
Â
kb
RuðNH3Þ pz 2þ þ CoðC2O4Þ
! products
3ꢀ
5
3
and react at different rates ðkf and kbÞ. The observed rate
constant k is a weighed average of these rates, as is given
by Eq. (3). In the present case, the values of the equi-
librium and rate constants appearing in Eq. (3) are the
following: K ¼ 2:3 ꢁ 103 molꢀ1 dm3, kf ¼ 6:7 sꢀ1 and
kb ¼ 8:19 ꢁ 10ꢀ1
s
ꢀ1. The upper curve in Fig. 1 has been
drawn using Eq. (3) with these values of the parameters.
As can be seen, the agreement between the experimental
and the calculated values of the rate constant (given by
the curve) is satisfactory.
As to the results corresponding to the solutions
containing the peptide, these results cannot be fitted by
Eq. (3), unless allowance is made for a variation of K
with the ratio between the concentrations of the cobalt
complex and the peptide. However, since the concen-
tration of the reactant is a constant in our experiments
K depends only on the concentration of the peptide. At
first, this dependence is unknown. However, allowing
0.0000 0.0002 0.0004 0.0006 0.0008 0.0010 0.0012
[concentration]/mol dm-3
Fig. 1. Plot of the experimental rate constants of the reaction
[Ru(NH3)5pz ]2þ + [Co(C2O4)3]3ꢀ vs. concentration (see text for con-
centration of monomers). Symbols ((j) monomers and (d) peptide)
are experimental data and lines are the best fit using Eq. (3) and, in the
case of the peptide, this equation with K given by Eq. (6).

268
J. Ortiz et al. / Chemical Physics Letters 384 (2004) 266–270
for a quadratic dependence of K on the peptide con-
centration, [P],
According to this, the (apparent) quadratic dependence
of K on [P] comes from the fact that we are seeing only a
portion of the complete (sigmoidal) dependence of K.
Notice that, according to the value of kb, the reaction
of the cobalt complex bound to the peptide with the
ruthenium complex is insignificant, as expected, taking
into account that the peptide has a positive charge, like
the ruthenium complex, in such a way that the en-
counter between the peptide-bound cobalt complex and
the ruthenium complex is difficult.
2
K ¼ Koð1 þ a½Pꢂ þ b½Pꢂ Þ
Eq. (3) becomes:
ð5Þ
ð6Þ
2
3
kf þ kbKo½Pꢂ þ kba0½Pꢂ þ kbb0½Pꢂ
k ¼
2
3
1 þ Ko½Pꢂ þ a0½Pꢂ þ b0½Pꢂ
with a0 ¼ Koa and b0 ¼ Kob.
Eq. (6) fits well the results with the following values
of the parameters: kf ¼ 6:6 sꢀ1, kb ¼ 0:02 sꢀ1, Ko ¼ 9107
molꢀ1 dm3, a0 ¼ 0:39 molꢀ2 dm6 and b0 ¼ 1:31 ꢁ 1012
molꢀ3 dm9. The result of the fit is given in Fig. 2.
However, the quadratic dependence of K on the
peptide concentration cannot be accepted because it
produces an indefinite growing of K, which is mean-
ingless. To have physical meaning, K must reach a
constant value after a given concentration of the pep-
tide. There is a huge dependence of K on this variable
that can accomplish this requirement. However, in bio-
logical systems, a sigmoidal dependence is frequently
found [14]. Thus, using for K the following equation:
On the other hand, the fact that K increases as the
ratio [Co(C2O4)33ꢀ]/[P] decreases means that the union of
the ligand to the substrate not only changes its strength
in going from the monomer to the peptide but also its
character changes: it is non-cooperative in the case of
the monomers and anti-cooperative in the case of the
peptide [15]. This anti-cooperative character has also
been observed in the case of the binding of small ions to
DNA [11]. The anti-cooperative character of the binding
of the cobalt complex can be explained qualitatively as a
consequence of the possibility, in the case of the peptide,
of more than one bound cobalt complex. Obviously,
once one complex is bound, a second complex would
feel repulsion from the first bound ligand. However,
other causes of anti-cooperativity cannot be ruled out.
Thus, the binding of a ligand, with a charge sign op-
posite from the charges on the substrate, would produce
a screening between these charges, thus allowing a more
compact conformation of the substrate, with different
binding properties from the more extended conforma-
tion in the absence of ligand. In other words, anti-co-
operativity would be a consequence of a change in the
equilibrium between different conformations of the
peptide, in such a way that, after the union with the first
ligand, the polymer conformation less favourable for
binding would be favoured. It is also possible that the
anti-cooperative character of the binding of the cobalt
complex was, in some sense, a reflection of the cooper-
ativity of intramolecular peptide hydrogen bonds which,
as is well known, plays an important role in organiza-
tion, assembly and molecular recognition processes [16].
That is, the union of the cobalt complex to the peptide
through hydrogen bond would imply a reduction of the
number of intramolecular hydrogen bonds of the pep-
tide. This would produce a conformational change in
the peptide and thus a variation of the binding constant.
On the other hand, according to the previous results,
the free energy corresponding to the binding of the co-
balt complex to the peptide is more favourable than the
free energy of the binding to the monomers. In this
sense, it can be said that the polymerization of the
monomers induces an enhancement of binding. At the
same time it is clear that, because of this binding, po-
lymerization would be more favourable in the presence
of the ligand (see Fig. 3). According to Fig. 3 the rela-
tion between the free energies of polymerization in the
Kmaxet
1 þ et
K ¼
;
ð7Þ
where t ¼ ð½Pꢂ ꢀ hÞ=j, Kmax is the maximum (limiting)
value of K, h is the value of the concentration of the
peptide for which K ¼ ð1=2ÞKmax, and j is an adjustable
parameter, the data in the presence of the peptide can be
fitted, with the following values of the parameters:
kf ¼ 6:6 sꢀ1, kb ¼ 0:02 sꢀ1, Kmax ¼ 1:76 ꢁ 106 molꢀ1 dm3,
h ¼ 7:76 ꢁ 10ꢀ4 mol dmꢀ3 and j ¼ 1:57 ꢁ 10ꢀ4 mol
dmꢀ3. The results of the fit are displayed in Fig. 1.
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
kcalc/s-1
Fig. 2. Plot of the experimental rate constants, k, vs. the calculated rate
constants kcalc, (from Eq. (6)) in peptide solutions.

J. Ortiz et al. / Chemical Physics Letters 384 (2004) 266–270
269
Free
monomers
Energy
∆Gm
∆
monomers/complex
G polymerization
peptide
∆G`
∆
Gp
polymerization
peptide/complex
Fig. 3. Schematic diagram showing that polymerization is more favourable in the presence of the [Co(C2O4)]3ꢀ anion. DGm and DGp are, respectively,
the free energies corresponding to the binding of the anion to the monomer and polymer. DGpolymerization and DG0polymerization are the free energies of
the polymerization processes in the absence and in the presence of the anion, respectively.
presence and in the absence of the cobalt complex can be
established as follows; in the absence of the cobalt
complex the polymerization process is:
zation [17,18]. This point is important in relation to the
ion-promoted hierarchical formation of supramolecular
assemblies, as it is pointed out recently by Lehn and co-
workers [19], who have observed self-association of
monomers induced by cations. According to these au-
thors, ion-induced polymerizations could be relevant in
the promotion of transmembrane ion channels that
would not only conduct ions but would also be built up
only if suitable ions are present; thus, presenting a most
intriguing ability to perform an ion-selective self-regu-
lation of ion flow [20].
Finally, it is interesting to point out that, in some
sense, the induction of polymerization by the presence of
the ligand (the cobalt complex in the present case) is
reminiscent of some enhancement of aggregation phe-
nomena observed in other supramolecular aggregates.
Thus, in the case of the micellization process of ionic
surfactants an analogue phenomenon would be the en-
hancement of micellization in the presence of ions of
opposite sign from that of the surfactant, as indicated by
an increase in the aggregation number and a decrease in
the critical micellar concentration [21].
monomers ! peptide; DGpolymerization
and in the presence of this complex
;
ð8Þ
monomers=complex ! peptide=complex; DGp0 olymerization
;
ð9Þ
where monomers/complex and peptide/complex repre-
sent, respectively, the monomers, with one only of them
bound to the cobalt complex, and the peptide bound to
this complex. The difference in free energy of the species
on the left-hand side of Eqs. (8) and (9) is:
DGm ¼ ꢀRT ln K ðK ¼ 2:3 ꢁ 103 molꢀ1dm3Þ:
ð10Þ
On the other hand, the difference in free energy, for
the species on the right-hand side of Eqs. (8) and (9) is,
of course, dependent on the ratio [cobalt complex]/[P].
Using the maximum value of the equilibrium constant
for the binding cobalt complex/peptide, Kmax, we obtain:
DGm ¼ ꢀRT ln Kmax
ðKmax ¼ 1:76 ꢁ 106 molꢀ1dm3Þ:
ð11Þ
Acknowledgements
Now, according to the figure:
DG0polymerization þ DGm ¼ DGpolymerization þ DGp;
or
ð12Þ
This work was financed by the D.I.G.Y.T. (BQU-
ꢀ ꢀ
2002 01063) and the Consejerıa de Educacion y Ciencia
ꢀ
de la Junta de Andalucıa.
DG0polymerization ꢀ DGpolymerization ¼ DGp ꢀ DGm
¼ ꢀ16:5 kJ=mol:
ð13Þ
References
Thus, the polymerization in the presence of the cobalt
complex is more favourable, from a thermodynamic
point of view, in 16.5 kJ/mol. That is, the binding of the
cobalt complex to the monomers promotes polymeri-
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270
J. Ortiz et al. / Chemical Physics Letters 384 (2004) 266–270
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