Equilibrium Unfolding - Theoretical Background

Theoretical Background

In its simplest form, equilibrium unfolding assumes that the molecule may belong to only two thermodynamic states, the folded state (typically denoted N for "native" state) and the unfolded state (typically denoted U). This "all-or-none" model of protein folding was first proposed by Tim Anson in 1945, but is believed to hold only for small, single structural domains of proteins (Jackson, 1998); larger domains and multi-domain proteins often exhibit intermediate states. As usual in statistical mechanics, these states correspond to ensembles of molecular conformations, not just one conformation.

The molecule may transition between the native and unfolded states according to a simple kinetic model

N U

with rate constants and for the folding and unfolding reactions, respectively. The dimensionless equilibrium constant can be used to determine the conformational stability by the equation

where is the gas constant and is the absolute temperature in kelvins. Thus, is positive if the unfolded state is less stable (i.e., disfavored) relative to the native state.

The most direct way to measure the conformational stability of a molecule with two-state folding is to measure its kinetic rate constants and under the solution conditions of interest. 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 .