Abstract
Do two-state proteins fold by pathways or funnels? Native-state
hydrogen exchange experiments show discrete normative structures in
equilibrium with the native state. These could be called hidden
intermediates (HI) because their populations are small at equilibrium,
and they are not detected in kinetic experiments. HIs have been invoked
as disproof of funnel models, because funnel pictures appear to
indicate (1) no specific sequences of events in folding; (2) a
continuum, rather than a discrete ladder, of structures; and (3) smooth
landscapes. In the present study, we solve the exact dynamics of a
simple model. We find, instead, that the present microscopic model is
indeed consistent with HIs and transition states, but such states occur
in parallel, rather than along the single pathway predicted by the
sequential stabilization model. At the microscopic level, we observe a
huge multiplicity of trajectories. But at the macroscopic level, we
observe two pathways of specific sequences of events that are
relatively traditional except that they are in parallel. so there is
not a single reaction coordinate. Using singular value decomposition,
we show an accurate representation of the shapes of the model energy
landscapes. They are highly complex funnels.
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