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Protein Folding 183

the height of energy barriers between important species where X i is the mole fraction of each species i and S i is
on this pathway. In general, to perform either an equi- the intrinsic signal of species i. This relationship applies to
librium (thermodynamics) or time-dependent (kinetics) most solution optical spectroscopic methods. Clearly, for
study, one must be able to experimentally monitor a sig- a particular spectroscopic signal to be useful for tracking a
nal that tracks the population of the structural states of the N ↔ U transition, the signal of the N and U states must
protein. be sufficiently different. The native (X N ) and unfolded
There are a number of ways this can be done. The most (X U ) mole fractions are directly related to the equilibrium
convenient experimental methods involve solution-phase constant in Eq. (2), as:
spectroscopic measurements; among these methods are
X N = 1/(1 + K un ); X U = K un /(1 + K un ). (6)
absorption spectroscopy, fluorescence, circular dichroism,
and nuclear magnetic resonance. Other methods include The transition from the native state to the unfolded state,
differential scanning calorimetry, light scattering, elec- or vice versa, can be induced in several ways, essentially
trophoresis, and chromatography. This section gives a by varying the solution conditions in a way that changes
brief description of the advantages and disadvantages of the equilibrium between the native and unfolded state. The
some of the above methods. These methods are not equally transition may be induced by varying temperature, adding
applicable to equilibrium and time-dependent studies of chemical (chaotropic agent) denaturant, adding acid or
protein unfolding, as some methods have a rapid response base, or increasing pressure. In the case of multimeric
and some have a slow response. Methods also differ in proteins, subunit dissociation, which may be accompa-
their intrinsic sensitivity, which is related to the concen- nied by denaturation of the subunits, can be induced by
tration of protein necessary to perform the measurement, dilution of the protein. Before discussing the various spec-
their ease and economy of use, and whether they provide troscopic methods, some thermodynamic relationships are
auxiliary information about the structure of the protein in presented for describing the transitions induced in the
its native and denatured states. What is meant by the last above ways.
statement is that some of the spectroscopic signals can
provide information about the secondary or tertiary struc-
B. Basic Thermodynamic Relationships
ture of the protein species. For most types of spectroscopy,
the signal arises from particular amino acid residues (e.g., Table I gives some widely accepted relationships for
aromatic side chains or peptide bond), thus differences in describing the variation of G o for a two-state N ↔ U
un
the signals for the conformational states can be related transition with temperature, chemical denaturant, pH, or
to differences in the local environment of these amino pressure as the perturbations. One of the equations in
acid residues (e.g., tryptophan residue 140 in staphylo- Table I, when combined with those above and Eqs. (1–
coccal nuclease; see Fig. 1). If there are only a very few 3), can be used to describe data as a function of the de-
of such signal origination sites, then site-specific infor- naturing condition. The thermodynamic parameters re-
mation can be obtained. If there are many probe sites lated to the relationships in Table I are briefly described
and they are distributed throughout the protein’s struc- below.
ture, then the method yields global information (e.g., sig-
o
o
nal from the amide linkage in the peptide backbone; see 1. Thermal unfolding: H and S are the enthalpy
un un
Fig. 1). It goes without saying that the protein sample and entropy changes for a two-state unfolding reaction.
o
o
to be studied must be well defined with regard to purity, Both H un and S un may be temperature dependent,
and solution conditions must be selected and controlled when the heat capacity change, C p , has a nonzero value.
to be relevant to other functional studies and studies with In this case, Eq. (7b) in Table I (the Gibbs-Helmholtz
o
o
◦
other proteins. Neutral pH, 20 C, and an ionic strength equation) should be used, where the H o ,un and S o ,un
of 0.1 to 0.2 are the most commonly employed solution are values at some defined reference temperature, T o (e.g.,
◦ 6,7
conditions. 0 or 20 C). The heat capacity change for unfolding of
◦
A key to most of these methods and their use in protein proteins is typically found to be positive and to be related
unfolding studies is that the signal is a mole-fraction to the increase in solvent exposure of apolar side chains
weighted average of the signals of each protein species. upon unfolding. That is, a positive C p is a result of the
o
That is, for the simplest case of a thermodynamics study hydrophobic effect. A consequence is that the G (T )
un
of the transition between a native, N, and unfolded, U, forunfoldingofaproteinwillhaveaparabolicdependence
state of a protein, the observed signal, S, can be expre- on temperature and will show both high-temperature and
ssed as: low-temperature induced unfolding. 8
2. Denaturant-induced unfolding: The empirical re-

S = S i X i (5)
lationship in Table I for chemical denaturation includes