Table 3 Coefficients of the Kamlet–Taft multi-parameter solvent
effect equation [eqn. (2)] for rate constants of diketopiperazine form-
ation from the trifluoroacetate salt of H-Ala-Pro-NH2 at 20 ЊCa
moderately basic pH. This step is catalysed by polyfunctional
acid catalysts, as often observed in cases where a proton switch
is involved.17
In organic solvents, peptide salts, as any salts obtained from
proton transfer from an acid (H–X) to a base (B), are present in
several forms in chemical equilibrium. A simplified description
of these equilibria, in which complexes higher than 1:1 and
specific solute–solvent interactions are not considered, is given
in eqn. (2), where the dashed lines represent hydrogen bonds.
log ko
s
a
b
h
Ϫ2.0 0.3 Ϫ4.5 0.4 Ϫ2.1 0.1 Ϫ1.4 0.2 0.0043 0.0006
a The ranges of the parameters π*, α, β and δH2 for the solvents used are
0.41–1.09, 0.00–1.96, 0.00–1.09 and 86–549, respectively.
XϪ ϩ H–Bϩ
XϪ ؒ ؒ ؒ H–Bϩ
X–H ؒ ؒ ؒ B
X–H ϩ B (2)
In buffered aqueous solution the fraction of the unproton-
ated peptide is determined by the pH value fixed by the buffer,
whereas in pure organic solvents it depends on the solvating
capacity of the surrounding medium. Solvents with a low
capability to stabilise ionic forms shift the equilibria to the
right. As regards the kinetic aspects of DKP formation, it is
worth noting that proton transfer between oxygen and nitrogen
atoms is usually much faster than the rate observed in the pres-
ent work,18 and then eqn. (2) represents equilibria that precede
the rate determining step (rds). In these cases the effects of
solvents on the reaction rate can be analysed in terms of the free
energy difference between the transition state of the rds and the
initial ionic substrate. The enhanced reactivity observed with
triethylammonium acetate suggests that a proton switch occurs
in the rds. Taking these facts into account, our experimental
results imply that the pathway proposed for the reaction in
water also holds in organic solvents, and that the rds is either
the transformation of InϩϪ to In or of In to the products
(Scheme 2). Both possibilities are consistent with the solvent
effect reported here. Solvents with a high ability to stabilise
charged and hydrogen donor or acceptor solutes (high values of
s, a and b coefficients) should stabilise the ionic form of the
substrate more effectively than the transition state of the pro-
posed limiting-step, that is expected to have a reduced ability to
form hydrogen bonds due to the delocalization of the charges.
Therefore, the net effect of polar and hydrogen donor and/or
acceptor solvents is an increase of the energy difference
between the ionic substrate and the transition state, hence a
decrease of the reaction rate. The coefficient h for the cavity
term, which reflects the energetic cost of disrupting the solvent–
solvent interaction to create or expand a cavity in the solvent,
also provides support for the proposed rds. The positive sign is
consistent with the expectation that the solvent shell contracts
as a consequence of the weakening of the ion–solute inter-
action, as the initial ionic substrate converts to the neutral
product. The cyclisation step to InϩϪ is ruled out as the rds
because no proton switch occurs in this step.
Fig. 2 First-order rate constants for diketopiperazine formation from
the trifluoroacetate salt of H-Ala-Pro-NH2 calculated by the Kamlet–
Taft equation with the constants reported in Table 3 against the rate
constants observed.
Discussion
The results of the multiple linear regression analysis of solvent
effects on the title reaction show that solvents with a high ability
to stabilise charged or dipolar solutes, by virtue of charge–
dipole or dipolar interactions (s = Ϫ4.5), and to stabilise hydro-
gen donor or acceptor solutes (a = Ϫ2.1 and b = Ϫ1.4) decrease
the reaction rate. Although it is not straightforward to draw
inferences about molecular processes from macroscopic proper-
ties, in our opinion the solvent effect reported here provides
some interesting indications of the reaction pathway.
Previous studies8 of DKP formation in aqueous solution
have shown that in this medium only the fraction of the peptide
with the deprotonated N-terminal amino group reacts at an
appreciable rate. The reaction involves the pre-equilibrium
attack of the N-terminal amino group on the carbonyl carbon
of the second residue, giving a zwitterionic cyclic intermediate16
in acid–base equilibrium with various forms characterised by
different grades of protonation. Breakdown to the product
occurs only from the neutral and anionic forms of the inter-
mediate by parallel steps.9 The step from the neutral form
(Scheme 2) is prevalent and rate-determining from acidic to
The mechanistic description reported above also gives a
sound explanation for the higher reactivity of salts from weak
acids (Table 2). In fact, according to our model, decreasing the
acidity of X–H [eqn. (2)] should result in a shift of the multi-
equilibrium toward the unprotonated form of the peptide,
which would reduce the free energy difference between the
reactant and the transition state. Finally, it is worth noting that,
because of the small size of the DKP ring, only peptides with
the first peptide bond in the cis conformation can react; hence
for most substrate molecules the first step of the overall reac-
tion is the trans→cis isomerization. However, from previous
studies on short Pro-containing peptides, it can be excluded
that the large solvent effect reported here is due to the solvent
influence on the isomerization step. First, the trans–cis equi-
librium is only slightly affected by solvents in comparison with
the effect reported here.19 Secondly, the trans→cis rate constant
is several orders of magnitude higher than the higher value
measured in this work20 and consequently cannot be rate
determining for the overall reaction of DKP formation.
Scheme 2
J. Chem. Soc., Perkin Trans. 2, 1999, 329–332
331