The foundations of protein folding began in the early 1960s when
Anfinsen et al. [3] showed that proteins can fold
reversibly. Under thermodynamic control, they observed the denaturation
(unfolding) of a compact protein
into a random coil of amino acids and the spontaneous assembly back to its
original configuration (see, e.g., Figure 
).
Two conclusions could be drawn: 1) proteins
organise themselves without assistant machinery into one of a myriad of
possible conformations; 2) the native conformation
of the heteropolymer is thermodynamically stable and,
accordingly, the global minimum of the free energy landscape.
Anfinsen's revelation was at odds with the common view at the time,
that proteins fold along a well-defined reaction pathway. Proteins were,
after all, the product of a chemical reaction and should be expected to
react accordingly. Pathway models dictate that the unfolded conformation
must sequentially traverse a series of intermediate configurations before
finally arriving at the folded conformation, in which intermediate
is in chemical equilibrium with intermediates
and 
.
Schematically, this is written as
where 
is the unfolded (denatured) state and
the fully folded state.
The classical view of pathways meant that proteins travel quickly downhill toward the local (and presumably global) minimum corresponding to the folded state along a set itinerary. The observation of thermodynamic reversibility implied that proteins seek out the global minimum along a path directed as much by thermal fluctuations as by the local gradient. These two views became known as kinetic and thermodynamic control.
The path-dependence of kinetic control and path-independence of
thermodynamic control are clearly incompatible.
The essential impediment to accepting the thermodynamic view is the
exponential size of the conformational landscape which the protein must
explore.
It would seem that a proportionally long search time would be necessary
for it to find its ground state structure.
If each additional amino acid can take on, say, two orientations with
respect to the polypeptide chain, then the number of conformations
available to
a 100 amino acid protein is 
. Assuming (conservatively)
the protein explores one conformation every picosecond [5],
the time necessary to find a particular conformation would take 
s.,
comparable to the age of the universe.
But proteins fold in times on the order of milliseconds, not years
(for a biological overview of protein folding, see [6]).
How can a protein navigate a vast landscape without a set path
yet still find its target quickly?
This apparent contradiction, posed by Cyrus Levinthal [15]
in the late 1960s
and since coined the `Levinthal paradox,' began the
extensive search for folding pathways via folding kinetics experiments.
Only recently has a new understanding of protein folding based on the
statistical mechanical interpretation of folding on an energy landscape come
to view.
The paradox rests on the assumption that
the unfolded state in () from which the reaction
begins is unique. But the denatured state is not a single conformation --
it is all conformations apart from the folded state.
Since the unfolded conformation is really a distribution over the entire
conformation space, an ensemble of
folding proteins requires an ensemble of independent folding pathways.
These pathways will converge and intertwine and eventually coalesce
as they approach the native conformation, all along traveling further downhill.
Of course, this picture has more to do with the thermodynamic exploration of an energy landscape funnel than with a well defined pathway. We are led to reject the view that proteins travel along a single deterministic pathway and instead consider the new statistical view of proteins scattered about the energy landscape making their way toward the funnel. Proteins navigate the landscape in ways that bring them downhill, all the while being buffeted by Brownian motion, occasionally knocking them uphill as well.
