Supplementary information
I. Theoretical considerations for the use of relative deglycosylation rate as a
measure of ligand-induced entropic change
The rate of enzymatic catalysis (kN) for a reaction is,
kN = kT/h exp(-∆G‡N/RT)
where k is Boltmann's constant, h is Planck's constant, R is the gas constant, T is the
temperature, and ∆G‡N is the standard free energy of activation for the reaction. For two
reactions, the difference in relative rate (RR) depends on the difference in activation
energy, ∆∆G‡. That is:
relative change in rate, RR = k1/k2
= kT/h exp(-∆G‡1/RT) / kT/h exp(-∆G‡2/RT)
= exp (-[∆G‡1-∆G‡2]/RT )
= exp (- ∆∆G‡/RT)
(eq. 1)
For degradative enzymatic reactions like proteolysis, accumulating evidence
indicates that the relative rate for two reactions, one on a well-ordered substrate and the
other on a flexible unfolded substrate, is dependent on the degree of substrate folding.
With proteases (reviewed in 1), experimental evidence ranges from correlation of
cleavage with crystallographic B-factor to correlation of rate of cleavage with degree of
urea-induced unfolding; with deglycosylation, experimental evidence is limited to the
demonstration that substrate denaturation greatly increases the rate of deglycosylation 2.
For the same substrate, in which the intrinsic rates are the same, ∆∆G‡ can be
assumed to be related to a function of the "degree of substrate folding". Therefore, the
relative rate comparing two reactions becomes:
RR = exp [ f ("degree of substrate folding")]
(eq. 2)
where f is a function relating ∆∆G‡ to "degree of substrate folding"
This relationship is consistent with analysis of enzymatic catalysis suggesting that the
standard free energy of activation relates to the ability of the enzyme to reorganize the
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reaction environment (see for example 3). Thus the ability of an enzyme to reorganize the
substrate (in this case, the protein being hydrolyzed) is influenced by the ease by which
the substrate can be brought into the appropriate conformation -- and this ease is
influenced by the degree that the substrate is folded.
In the present case, we have a panel of antibodies that bind to gp120 with
identical or very similar binding affinities (e.g. similar ∆G) but with vastly different
binding enthalpies and binding entropies. Furthermore, the bound complexes exhibit
different deglycosylation rates. Since the antibodies induce a structuring in gp120, the
retardation in the deglycosylation rates will be proportional to the degree of structuring or
substrate folding induced by antibody binding. The degree of structuring induced by the
antibodies studied in this paper is not proportional to the binding affinity since it is
similar for all of them.
How to discern the degree of folding induced by antibody binding? The free
energy of binding can be divided into two components. The intrinsic binding free energy,
∆Gbind, which is the one that would be observed if the bound conformations were the
same as the free conformations, and ∆Gconf, which includes the changes in free energy
associated with the conformational changes:
∆G = ∆Gbind + ∆Gconf
(eq. 3)
= ∆Hbind – T∆Sbind + ∆Hconf – T∆Sconf
= (∆Hbind + ∆Hconf ) – (T∆Sbind + T∆Sconf)
The enthalpies, ∆H, and entropies, -T∆S, measured by isothermal titration
calorimetry are given by the terms in parenthesis in eq. 3. That is: ∆H = (∆Hbind + ∆Hconf
) and -T∆S = – (T∆Sbind + T∆Sconf). It must be kept in mind that ∆Gconf measures the
difference in Gibbs energy between the free and bound conformations and does not
reflect how structured or unstructured those conformations are. The "degree of folding"
of the bound conformation relative to the free conformation is reflected in the magnitude
of the individual terms ∆Hconf or –T∆Sconf and, in principle, either one can be chosen for
the analysis. Since the entropic component is more easily linked conceptually to a
conformational change in gp120 (the degree of folding is related to the number of degrees
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of freedom), –T∆Sconf appears to be the most suitable parameter to correlate with the
experimental data:
“degree of substrate folding” = a( -T∆Sconf )
(eq. 4)
where a is a constant
According to eq. 2 and 4, the relative rate of deglycosylation can be written as:
RR = exp { f [ a( -T∆Sconf )] },
(eq. 5)
In general, -T∆Sconf cannot be experimentally separated from the overall entropy
change. In this case, however, an approximation can be made due to the large differences
in magnitude between –T∆Sbind and –T∆Sconf, and the availability of binding
thermodynamic data for pre-structured conformations of gp120. Thus for antibody
binding, -T∆Sbind is small in magnitude (e.g. binding of 17b to gp120 pre-bound to CD4
displays an entropy of 2 kcal/mol at 37°C; Fig. 2), whereas the overall -T∆S for gp120 can
be as high as 50 kcal/mol for the interaction with CD4 4. In general, for antibody binding
in the absence of a significant conformational change, the observed entropy is about 7±3
kcal/mol at 25° C 5. Thus one can conclude that the overall binding entropy is the sum of a
small term (the intrinsic binding term) and a large term (the conformational term):
-T∆S = s – T∆Sconf
(eq. 6)
According to eq. 5 and 6, the relative rate of deglycosylation can be written as:
RR = exp { f [ a( -T∆S –s ) ] },
or,
ln (RR) = f [ a( -T∆S –s )] = f [ - aT∆S + b ]
(eq. 7)
The last equation shows that, as long as the intrinsic entropy of ligand binding is much less
than the entropy of the ligand-induced folding, a theoretical relationship exists linking the
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entropy of the ligand binding and the effect of such binding on the relative rate of
deglycosylation. By fitting -T∆S, as determined experimentally by isothermal thermal
titration calorimetry, with the relative rate of deglycosylation, the function ( f ) relating
∆∆G‡ with "degree of folding" was found to be approximated well by a simple linear
relationship (see supplementary information II). Such a simple relationship indicates that
for the gp120 system under investigation the "degree of folding" is a primary determinant
of ∆∆G‡.
References:
1.
Hubbard, S. J. The structural aspects of limited proteolysis of native proteins.
Bioch. Biophy. Acta. 1382, 191-206 (1998).
2.
Chu, F. K. Requirements of cleavage of high mannose oligosaccharides in
glycoproteins by peptide N-glycosidase F. J. Biol. Chem. 261, 172-177 (1986).
3.
Cannon, W. R., Singleton, S. F. & Benkovic, S. J. A perspective on biological
catalysis. Nat. Struct. Biol. 3, 821-833 (1996).
4.
Myszka, D. G. et al. Energetics of the HIV gp120-CD4 binding reaction. Proc.
Natl. Acad. Sci. USA 97, 9026-9031 (2000).
5.
Stites, W. E. Protein-protein interactions: interface structure, binding
thermodynamics, and mutational analysis. Chem. Rev. 97, 1233-1250 (1997).
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