I have followed this discussion with interest. I hope I can impose on
the group to make an argument from a physicist’s perspective. I won’t
argue “kinetic” versus “thermodynamic” but will claim the process of
protein folding is indeed path dependent but that this path dependence
is not inconsistent with observations.
Given some initial unfolded protein state, the various components will
feel unbalanced electrical forces and dynamically respond, tracing out
some path in the multidimensional phase space whose coordinates
characterize the protein. As the protein system moves along this path,
individual components will be lose or gain kinetic energy in response to
the temporally changing forces they experience (alternatively, in
response to the steepness of the potential energy surfaces they are
traversing). When the protein finds a point in phase space about which
the variation of all its variables become periodic it can be said to be
metastable. Not only has the protein found a local energy minimum, but
each of its components is rocking or rotating back and forth in its own
potential well. I say metastable because such a system would
constitute a highly complex nonlinear oscillator in which resonances
could develop that would knock one or more components out of their
local well and thus destabilize the system. A complicated physical
system like a protein has many local energy minima and the particular
minimum (located at a point in phase space) in which the hypothetical
protein came to metastability represents the end point of the path it took
through phase space. A protein with different initial conditions might
well have followed a different path and metastabilized in a different local
minimum.
So what does this dynamical picture have to do with the observations
that most proteins (but, not all) fold to the same “native” state. To
explain these observations I would say that such proteins are
characterized by a minimum energy state (not necessarily global) with
two features - 1) much steeper walls than other local energy minima
(much more stable), and most important 2) a much greater basin of
attraction than the other local minima (much more accessible). By the
latter, I mean that the large majority of initial states follow phase space
trajectories that lead to this minimum. A two dimension example of such
a potential surface would be an empty swimming pool with a few pots
and pans scattered on the bottom. Where a given rain drop ends up
certainly depends on the path it takes, but most of them will go down
the drain at the bottom of the pool. For most proteins, then, the
“native” state corresponds to a local energy minimum with such a large
basin of attraction that almost any initial conditions will follow a path to
that minimum. Under such circumstances the native state appears to be
path independent.
I’m not sure what this picture means for a predictive theory of folding --
unless, perhaps, one could mathematically demonstrate that certain
sequences of amino acids are likely to lead to large phase space
attraction basins for certain secondary structures.
My two cents. I apologize if these arguments already exist in the literature.
N. T. Gladd
Berkeley Research Associates
ntgladd at langmuir.eecs.berkeley.edu
