The effect is similar with the prior phase separation for the acceleration of crystal
nucleation in the concentrated phase, as described in Sect.11.3. Figure11.10shows
the snapshots of the single chains in the random coil state, the collapsed globule
state and the crystalline folding state, respectively, obtained in computer
simulations.
Such interplay of phase transitions in the single-chain system provides a logical
framework to the unified condensation-nucleation scheme for protein folding
(Daggett and Fersht 2003 ). If one describes the distributions of all the possible
states along the path of protein folding in analogy to a shape of funnel, the
intermediate molten globule states locate right in the vicinity of the small entrance
of the pipe: once the hydrophobic core forms, the speed for protein molecules to
reach their native states will be significantly accelerated (Wolynes et al. 1995 ). The
example shown here suggests that the complexity of protein folding may be
elucidated as the interplay of phase transitions.
Fig. 11.10Snapshots of single 512-mers obtained in Monte Carlo simulations. (a) The random
coil state atB/EP¼0.1,T¼2.174EP/k; (b) the collapsed globule state atB/EP¼0.1,
T¼3.289EP/k; (c) the crystalline folding state atB/EP¼0.1,T¼2.289EP/k (Hu and Frenkel
2006 ) (Reprinted with permission)
Fig. 11.9 (a) The free energy change versus the number of molten units (defined by the bonds
containing less than five parallel neighbors) for single 512-mers at equilibrium melting points with
various solvent qualities (B/Epvalues as denoted); (b) heights of free energy barriers at relative
mixing interactions, in comparison with the phase boundaries for collapse transitions (Tcol) and for
crystal nucleation (Tcry) (Hu and Frenkel 2006 ) (Reprinted with permission)
234 11 Interplay Between Phase Separation and Polymer Crystallization