Subcellular Systems - Molecular Theory of the Living Cell - page 289

Entropy ( Δ S)

Energy
( Δ E)

Conformational
substates of
Frauenfelder, each of
which may consists of
further ssubstates; also
called conformer
families (Kurakin 2009)

Native Structures

Fig. 11.1 The free energy landscape for protein folding (adopted from Brooks et al. 2009).
The vertical axis encodes the energy changes, D E, accompanying a protein folding process, and
the horizontal axis encodes the associated entropy changes, D S. The unfolded proteins have high
potential energy and high entropy content, whereas the folded proteins have low energy and low
entropy. Therefore the unfolded-to-folded transition leads to the so-called enthalpy-entropy
compensation (i.e., the mutual cancellation between D E and T D S) (Lumry 1974; Lumry and
Gregory 1986) due to the mathematics of the Gibbs free energy change i.e., D G ¼ D E T D S,
when volume changes, D V, are negligible (see Eq. 2.1 )

toward lower free energy conformers through several conformational states
(“molten globular states,” “transition state,” “glass transition,” “discrete folding
intermediates,” etc.) to the final native structure. The movement of protein
conformers down the folding funnel is accompanied by two kinds of thermody-
namic changes: (a) energy (i.e., Gibbs free energy under most conditions) decrease
due to downward movement and (b) entropy decrease due to the narrowing of
the funnel width, leading to increased conformational constraints (i.e., as
conformations of a protein become more compact to minimize energy, the confor-
mational motions of proteins become confined to an increasingly smaller volume,
leading to a decrease in entropy).
Since protein folding is ultimately driven by Gibbs free energy changes under
constant T and P conditions, D G ¼ D E+P D V T D S (see Eq. 2.1 in Sect. 2.1.1 ) ,

which becomes D G T D S, if the pressure-volume work is negligible in

protein folding, it would follow that, at some point along the vertical axis of the
folding funnel, the free energy decrease (

¼ D E

D G), due to energy decrease, D E,

should exactly cancel out the free energy gain (+ D G) due to entropy decrease, D S,

resulting in D G 0. At this point, spontaneous protein folding process would cease

(except thermal fluctuations) and an equilibrium state established (see Fig. 11.1 ).

¼