The self-assembly of biological and synthetic nanostructures commonly proceeds via intermediate states. In living systems in particular, the intermediates have the capacity to tilt the balance between functional and potentially fatal behavior. This work develops a statistical mechanical treatment of conformational dynamics through an intermediate under a variable force. An analytical solution is derived for the key experimentally measurable quantity—the distribution of forces at which a conformational transition occurs. The solution reveals rich kinetics over a broad range of parameters and enables one to locate the intermediate and extract the activation barriers and rate constants.

1.
G. M.
Whitesides
,
J. P.
Mathias
, and
C. T.
Seto
,
Science
254
,
1312
(
1991
).
2.
B.
Alberts
 et al.,
Molecular Biology of the Cell
(
Garland Science
,
New York
,
2008
).
3.
M.
Vendruscolo
and
C. M.
Dobson
,
Nat. Chem. Biol.
9
,
216
(
2013
).
4.
P. E.
Marszalek
,
H.
Lu
,
H.
Li
,
M.
Carrion-Vazquez
,
A. F.
Oberhauser
,
K.
Schulten
, and
Julio M.
Fernandez
,
Nature (London)
402
,
100
(
1999
).
5.
C.
Cecconi
,
E. A.
Shank
,
C.
Bustamante
, and
S.
Marqusee
,
Science
309
,
2057
(
2005
).
6.
M. T.
Woodside
,
P. C.
Anthony
,
W. M.
Behnke-Parks
,
K.
Larizadeh
,
D.
Herschlag
, and
S. M.
Block
,
Science
314
,
1001
(
2006
).
7.
J.
Stigler
,
F.
Ziegler
,
A.
Gieseke
,
J. C. M.
Gebhardt
, and
M.
Rief
,
Science
334
,
512
(
2011
).
8.
R.
Merkel
,
P.
Nassoy
,
A.
Leung
,
K.
Ritchie
, and
E.
Evans
,
Nature (London)
397
,
50
(
1999
).
9.
A. R.
Fersht
,
Structure and Mechanism in Protein Science
(
W. H. Freeman
,
New York
,
1999
).
11.
O. K.
Dudko
,
G.
Hummer
, and
A.
Szabo
,
Phys. Rev. Lett.
96
,
108101
(
2006
).
12.
See supplementary material at http://dx.doi.org/10.1063/1.4869869 for details on the derivations and simulations.
13.
T.
Strunz
,
K.
Oroszlan
,
I.
Schumakovitch
,
H.-J.
Güntherodt
, and
M.
Hegner
,
Biophys. J.
79
,
1206
(
2000
).

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