V. M. Rotello et al.
more favorable entropy contribution, which is attenuated by
unfavorable enthalpy gain.
the “small” host–guest systems.[27,33] Thermodynamically, the
unit slope also reflects that the contribution of the enthalpic
gain by the system variation to the free energy change has
been fully eliminated by the accompanying entropic loss.
Moreover, it can be noted that nanoparticles bearing en-
antiomeric end-groups display completely different enthalpy
and entropy changes upon complexation with the same pro-
tein (i.e., DHd ¼DHl and TDSd ¼TDSl) (Table 1). An impor-
tant question arises: how do the thermodynamic quantities
contribute to the isomeric selectivity over NP–protein inter-
actions? The isomeric selectivity is defined as the differen-
tial Gibbs free energy changes for enantiomeric (or diaste-
reoisomeric) NPs; a thermodynamic relationship can be
readily established by using Equation (1):
Isomeric effects and enthalpy–entropy compensation: From
the above discussion, it is clear that a compensatory rela-
tionship between enthalpy and entropy exists, a common
phenomenon that has been found in various complexation
processes.[27,31] Although the basis of such extrathermody-
namic relationships is still under debate,[27] some efforts
have been devoted to clarifying their physical signifi-
cance.[32,33] In Figure 6a, the TDS values for the NP–protein
dðDGÞd=l ¼ DGdꢁDGl ¼ dðDHÞd=lꢁTdðDSÞd=l
ð1Þ
The physical meaning of isomeric selectivity is the exchange
efficiency of proteins from l isomer-functionalized NPs to
their d isomer counterparts, which can be expressed as
Equation (2):[34]
½NPl Á proteinþNPd Ð ½NPd Á proteinþNPl
ð2Þ
In this expression, structural features other than the chirality
of the NP functionalities are cancelled, leaving only the con-
tribution arising from structural (i.e., isomeric) differences.
According to Equation (1), the isomeric selectivity lies in
the compensation between d(DH)d/l and Td(DS)d/l. In the
case of a perfect compensation between these two parame-
ters, the value of d(DG)d/l would be equal to zero, resulting
in no isomeric discrimination. Figure 6b shows the compen-
sation plot for the enantiomeric exchange enthalpy (d(DH)d/l
)
and entropy (Td(DS)d/l). A linear correlation plot (Fig-
ure 6b) is obtained for these data points with a unit slope
and a small value of intercept (Td(DS)0 =0.5 kJmolꢁ1).
In comparison with the common enthalpy–entropy plot
(Figure 6a), an obviously more significant deviation from
linearity is observed for the first binding event of NP–CytC
interactions (Figure 6b), indicating that the large isomeric
effect for this interaction arises from the unmatched enthal-
py and entropy changes. In contrast, the smaller enthalpy–
entropy compensation for NP–ChT and the second binding
event of NP–CytC interactions lead to a reduced isomeric
effect. As we have proposed, the spatial arrangement of
CytC on the NP surface is different for the first and the
second binding events. Therefore, the orientations of the
proteins on the surface of NPs determine how the enantio-
meric thermodynamics are shaped. On the other hand, the
nanoparticles experience significant conformational changes,
as revealed by enthalpy–entropy compensation analysis. Ob-
viously, this process does not favor isomeric selectivity. In
this regard, appropriate reduction of ligand freedom either
by shortening the ligand length or by fastening the ligand
position should provide better isomeric selectivity, as well as
enhancement of the complex stability from the viewpoint of
enthalpy–entropy compensation.
Figure 6. a) Compensation plot of entropy (TDS) versus enthalpy (DH)
for NP–protein interactions. b) Compensation plot for the differential en-
tropy change (Td(DS)d/l) against the differential enthalpy change
(d(DH)d/l) upon complexation of NPs bearing enantiomeric (diastereo-
~
&
*
topic) end-groups with proteins. : NP-ChT, : NP-CytC (1); : NP-
CytC (2).
interactions have been plotted against the DH values. An
excellent linear correlation (r=0.998) was obtained, leading
to a slope of 1.04 and an intercept of 36.1 kJmolꢁ1, essential-
ly identical to the values observed with amino acid-function-
alized nanoparticles.[14] These coefficients can be taken as
quantitative measurements of conformational changes and
desolvation effects, respectively, during complex forma-
tion.[33] In our case, the near unit slope and the high value of
the intercept in enthalpy–entropy compensation indicate
that the system undergoes large conformational changes and
extensive desolvation, which is significantly different from
148
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Chem. Eur. J. 2008, 14, 143 –150