In biochemistry, equilibrium unfolding is the process of unfolding a protein or RNA molecule by gradually changing its environment, such as by changing the temperature or pressure, pH, adding chemical denaturants, or applying force as with an atomic force microscope tip.
The molecule may transition between the native and unfolded states according to a simple kinetic model with rate constants
of a molecule with two-state folding is to measure its kinetic rate constants
However, since protein folding is typically completed in milliseconds, such measurements can be difficult to perform, usually requiring expensive stopped flow or (more recently) continuous-flow mixers to provoke folding with a high time resolution.
Dual polarisation interferometry is an emerging technique to directly measure conformational change and
, respectively) are measured as the solution conditions are gradually changed from those favoring the native state to those favoring the unfolded state, e.g., by adding a denaturant such as guanidinium hydrochloride or urea.
Given that the fractions must sum to one and their ratio must be given by the Boltzmann factor, we have Protein stabilities are typically found to vary linearly with the denaturant concentration.
In other words, the increased number of potential sites exposed in the unfolded state is seen as the reason for denaturation transitions.
The solvent exchange model (also called the ‘weak binding model’ or ‘selective solvation’) of Schellman invokes the idea of an equilibrium between the water molecules bound to independent sites on protein and the denaturant molecules in solution.
This model tries to answer the question of whether the denaturant molecules actually bind to the protein or they seem to be bound just because denaturants occupy about 20-30% of the total solution volume at high concentrations used in experiments, i.e. non-specific effects – and hence the term ‘weak binding’.
One common theme obtained from both these models is that the binding constants (in the molar scale) for urea and guanidinium hydrochloride are small: ~ 0.2
This forms the basis for the LEM which assumes a simple linear dependence of stability on the denaturant concentration.
The resulting slope of the plot of stability versus the denaturant concentration is called the m-value.
In pure mathematical terms, m-value is the derivative of the change in stabilization free energy upon the addition of denaturant.
However, a strong correlation between the accessible surface area (ASA) exposed upon unfolding, i.e. difference in the ASA between the unfolded and folded state of the studied protein (dASA), and the m-value has been documented by Pace and co-workers.
[5] In view of this observation, the m-values are typically interpreted as being proportional to the dASA.
There is no physical basis for the LEM and it is purely empirical, though it is widely used in interpreting solvent-denaturation data.
In practice, the observed experimental data at different denaturant concentrations are fit to a two-state model with this functional form for
Instead, we assay the relative population of folded molecules using various structural probes, e.g., absorbance at 287 nm (which reports on the solvent exposure of tryptophan and tyrosine), far-ultraviolet circular dichroism (180-250 nm, which reports on the secondary structure of the protein backbone), dual polarisation interferometry (which reports the molecular size and fold density) and near-ultraviolet fluorescence (which reports on changes in the environment of tryptophan and tyrosine).
However, nearly any probe of folded structure will work; since the measurement is taken at equilibrium, there is no need for high time resolution.
Thus, measurements can be made of NMR chemical shifts, intrinsic viscosity, solvent exposure (chemical reactivity) of side chains such as cysteine, backbone exposure to proteases, and various hydrodynamic measurements.
are sometimes allowed to vary linearly with the solution conditions, e.g., temperature or denaturant concentration, when the asymptotes of
indicate the enthalpy, entropy and Gibbs free energy of unfolding under a constant pH and pressure.
In principle one can calculate all the above thermodynamic observables from a single differential scanning calorimetry thermogram of the system assuming that the
which can be achieved from measurements with slight variations in pH or protein concentration.
can be calculated through computer programs such as Deepview (also known as swiss PDB viewer).
can be calculated from tabulated values of each amino acid through the semi-empirical equation: where the subscripts polar, non-polar and aromatic indicate the parts of the 20 naturally occurring amino acids.
This can be done with differential scanning calorimetry by comparing the calorimetric enthalpy of denaturation i.e. the area under the peak,
Using the above principles, equations that relate a global protein signal, corresponding to the folding states in equilibrium, and the variable value of a denaturing agent, either temperature or a chemical molecule, have been derived for homomeric and heteromeric proteins, from monomers to trimers and potentially tetramers.
[7] Such equations cannot be derived for pentamers of higher oligomers because of mathematical limitations (Abel–Ruffini theorem).