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Folding Funnels and Free Energy Traps

Topographic features of the conformational energy landscape determine the proficiency with which proteins fold to their native conformation. Low energy minima away from the ground state or entropically favourable plateaus act as free energy traps by prohibiting occupation of the ground state minimum. Valleys and mountains acting collectively in place of a broad funnel slow folding kinetics by trapping in local minima before imposing slow uphill climbs.

The energy landscapegif of a random heteropolymer, shown in Figure gif, contains all of the ingredients detrimental to stable, fast folding. A hierarchy of valleys makes the ground state conformation only marginally lower in energy than quasi-degenerate local minima, which act as energetic traps by housing misfolded proteins. The absence of a steep gradient sloping toward the target slows navigation; like on a flat energy surface, proteins must meander through the landscape without guidance.

The more hospitable energy landscape shown in Figure gif contains a single deep minima above the ground state conformation separated by a large gap from the set of non-native structures. While this makes the target thermodynamically stable, it takes no measure to ensure that it is accessible kinetically. A significant fraction of an ensemble of proteins will, at equilibrium, reside in the target configuration, but the ensemble will take a very long time to equilibrate.

Stable folding not only requires a large energy gap -- conformational entropy may reduce stability as well. This is observed, for example, on the champagne glass landscape [8] in Figure gif. After traveling down the initially steep basin toward the ground state, proteins meander aimlessly along the shallow ridge before discovering the well above the target. At any time in equilibrium, most of the chains are found along the shallow plateau, where there are many more accessible conformations at a disproportionately small cost in energy.

  figure618

  figure625

An ideal folding landscape, drawn in Figure gif, is characterised by a deep, broad funnel centered about the ground state conformation. As proteins fall to lower energies, the conformational freedom is reduced such that between a near-native configuration 2 and a less near configuration 1,

  equation633

where tex2html_wrap_inline12917 , etc. This simply says that the funnel is everywhere sufficiently steep such that the loss in entropy is overcome by the decrease in energy.


next up previous contents
Next: LATTICE MODELS AND THERMODYNAMIC Up: PROTEIN FOLDINGINVERSE PROTEIN Previous: Smooth vs. Rugged Landscapes

Thomas Fink
Tue Jun 16 17:14:36 BST 1998