The full characterization of protein folding is a remarkable long-standing challenge both for experiment and simulation. Working towards a complete understanding of this process, one needs to cover the full diversity of existing folds and identify the general principles driving the process. Here, we want to understand and quantify the diversity in folding routes for a large and representative set of protein topologies covering the full range from all alpha helical topologies towards beta barrels guided by the key question: Does the majority of the observed routes contribute to the folding process or only a particular route? We identified a set of two-state folders among non-homologous proteins with a sequence length of 40–120 residues. For each of these proteins, we ran native-structure based simulations both with homogeneous and heterogeneous contact potentials. For each protein, we simulated dozens of folding transitions in continuous uninterrupted simulations and constructed a large database of kinetic parameters. We investigate folding routes by tracking the formation of tertiary structure interfaces and discuss whether a single specific route exists for a topology or if all routes are equiprobable. These results permit us to characterize the complete folding space for small proteins in terms of folding barrier ΔG, number of routes, and the route specificity RT.

1.
J. N.
Onuchic
and
P. G.
Wolynes
, “
Theory of protein folding
,”
Curr. Opin. Struct. Biol.
14
,
70
75
(
2004
).
2.
S. S.
Plotkin
and
J. N.
Onuchic
, “
Understanding protein folding with energy landscape theory. Part I: Basic concepts
,”
Q. Rev. Biophys.
35
,
111
167
(
2002
).
3.
S. S.
Plotkin
and
J. N.
Onuchic
, “
Understanding protein folding with energy landscape theory. Part II: Quantitative aspects
,”
Q. Rev. Biophys.
35
,
205
286
(
2002
).
4.
J. D.
Bryngelson
,
J. N.
Onuchic
,
N. D.
Socci
, and
P. G.
Wolynes
, “
Funnels, pathways, and the energy landscape of protein folding: A synthesis
,”
Proteins
21
,
167
195
(
1995
).
5.
C.
Debès
,
M.
Wang
,
G.
Caetano-Anollés
, and
F.
Gräter
, “
Evolutionary optimization of protein folding
,”
PLoS Comput. Biol.
9
,
e1002861
(
2013
).
6.
F.
Morcos
,
N. P.
Schafer
,
R. R.
Cheng
,
J. N.
Onuchic
, and
P. G.
Wolynes
, “
Coevolutionary information, protein folding landscapes, and the thermodynamics of natural selection
,”
Proc. Natl. Acad. Sci. U. S. A.
111
,
12408
12413
(
2014
).
7.
C.
Clementi
,
H.
Nymeyer
, and
J. N.
Onuchic
, “
Topological and energetic factors: What determines the structural details of the transition state ensemble and ‘en-route’ intermediates for protein folding? An investigation for small globular proteins
,”
J. Mol. Biol.
298
,
937
953
(
2000
).
8.
A.
Schug
and
J. N.
Onuchic
, “
From protein folding to protein function and biomolecular binding by energy landscape theory
,”
Curr. Opin. Pharmacol.
10
,
709
714
(
2012
).
9.
P. C.
Whitford
 et al, “
An all-atom structure-based potential for proteins: Bridging minimal models with all-atom empirical forcefields
,”
Proteins
75
,
430
441
(
2009
).
10.
P. C.
Whitford
 et al, “
Accommodation of aminoacyl-tRNA into the ribosome involves reversible excursions along multiple pathways
,”
RNA
16
,
1196
1204
(
2010
).
11.
A.
Schug
,
M.
Weigt
,
J. N.
Onuchic
,
T.
Hwa
, and
H.
Szurmant
, “
High-resolution protein complexes from integrating genomic information with molecular simulation
,”
Proc. Natl. Acad. Sci. U. S. A.
106
,
22124
22129
(
2009
).
12.
P.
Casino
,
V.
Rubio
, and
A.
Marina
, “
Structural insight into partner specificity and phosphoryl transfer in two-component signal transduction
,”
Cell
139
,
325
336
(
2009
).
13.
A. E.
Dago
,
A.
Schug
,
A.
Procaccini
,
J. A.
Hoch
,
M.
Weigt
, and
H.
Szurmant
, “
The structural basis of histidine kinase autophosphorylation deduced by integrating genomics, molecular dynamics and mutagenesis
,”
Proc. Natl. Acad. Sci. U. S. A.
109
,
1733
1742
(
2012
).
14.
A.
Schug
,
P. C.
Whitford
,
Y.
Levy
, and
J. N.
Onuchic
, “
Mutations as trapdoors to two competing native conformations of the Rop-dimer
,”
Proc. Natl. Acad. Sci. U. S. A.
104
,
17674
17679
(
2007
).
15.
Y.
Gambin
 et al, “
Direct single-molecule observation of a protein living in two opposed native structures
,”
Proc. Natl. Acad. Sci. U. S. A.
106
,
10153
10158
(
2009
).
16.
C.
Hyeon
and
D.
Thirumalai
, “
Capturing the essence of folding and functions of biomolecules using coarse-grained models
,”
Nat. Commun.
2
,
487
(
2011
).
17.
C.
Sinner
 et al, “
Simulating biomolecular folding and function by native-structure-based/go-type models
,”
Isr. J. Chem.
54
,
1165
1175
(
2014
).
18.
P. C.
Whitford
 et al, “
Non-local helix formation is key to understanding SAM-1 riboswitch function
,”
Biophys. J.
96
,
7
9
(
2009
).
19.
B.
Lutz
 et al, “
Differences between co-transcriptional and free riboswitch folding
,”
Nucleic Acids Res.
42
,
2687
2696
(
2014
).
20.
P.
Anand
,
A.
Schug
, and
W.
Wenzel
, “
Structure-based design of protein linkers for zinc finger nuclease based gene manipulation
,”
FEBS Lett.
587
,
3231
3235
(
2013
).
21.
S. L.
Grage
 et al, “
Folding and self-assembly of the TatA translocation pore in the membrane via a novel charge zipper motif
,”
Cell
152
,
316
326
(
2013
).
22.
R. B.
Best
,
G.
Hummer
, and
W. A.
Eaton
, “
Native contacts determine protein folding mechanisms in atomistic simulations
,”
Proc. Natl. Acad. Sci. U. S. A.
110
,
17874
17879
(
2013
).
23.
K.
Lindorff-Larsen
,
S.
Piana
,
R. O.
Dror
, and
D. E.
Shaw
, “
How fast-folding proteins fold
,”
Science
334
,
517
520
(
2011
).
24.
G.
Hummer
, “
From transition paths to transition states and rate coefficients
,”
J. Chem. Phys.
120
,
516
523
(
2004
).
25.
J.
Wang
,
J.
Onuchic
, and
P.
Wolynes
, “
Statistics of kinetic pathways on biased rough energy landscapes with applications to protein folding
,”
Phys. Rev. Lett.
76
,
4861
4864
(
1996
).
26.
J.
Wang
,
K.
Zhang
,
H.
Lu
, and
E.
Wang
, “
Quantifying kinetic paths of protein folding
,”
Biophys. J.
89
,
1612
1620
(
2005
).
27.
H.
Lammert
,
J. K.
Noel
, and
J. N.
Onuchic
, “
The dominant folding route minimizes backbone distortion in SH3
,”
PLoS Comput. Biol.
8
,
e1002776
(
2012
).
28.
T.
Inanami
,
T. P.
Terada
, and
M.
Sasai
, “
Folding pathway of a multidomain protein depends on its topology of domain connectivity
,”
Proc. Natl. Acad. Sci. U. S. A.
111
,
15969
15974
(
2014
).
29.
H. M.
Berman
 et al, “
The protein data bank
,”
Nucleic Acids Res.
28
,
235
242
(
2000
).
30.
B.
Lutz
,
C.
Sinner
,
G.
Heuermann
,
A.
Verma
, and
A.
Schug
, “
eSBMTools 1.0: Enhanced native structure-based modeling tools
,”
Bioinformatics
29
,
2795
2796
(
2013
).
31.
E.
Shakhnovich
,
G.
Farztdinov
,
A. M.
Gutin
, and
M.
Karplus
, “
Protein folding bottlenecks: A lattice Monte Carlo simulation
,”
Phys. Rev. Lett.
67
,
1665
1668
(
1991
).
32.
S. S.
Cho
,
Y.
Levy
, and
P. G.
Wolynes
, “
P versus Q: Structural reaction coordinates capture protein folding on smooth landscapes
,”
Proc. Natl. Acad. Sci. U. S. A.
103
,
586
591
(
2006
).
33.
L. S.
Itzhaki
,
D. E.
Otzen
, and
A. R.
Fersht
, “
The structure of the transition-state for folding of chymotrypsin inhibitor-2 analyzed by protein engineering methods: Evidence for a nucleation-condensation mechanism for protein-folding
,”
J. Mol. Biol.
254
,
260
288
(
1995
).
34.
S. S.
Plotkin
and
J. N.
Onuchic
, “
Investigation of routes and funnels in protein folding by free energy functional methods
,”
Proc. Natl. Acad. Sci. U. S. A.
97
,
6509
6514
(
2000
).
35.
N.
Ferguson
,
A. P.
Capaldi
,
R.
James
,
C.
Kleanthous
, and
S. E.
Radford
, “
Rapid folding with and without populated intermediates in the homologous four-helix proteins Im7 and Im9
,”
J. Mol. Biol.
286
,
1597
1608
(
1999
).
36.
B.
Öztop
,
M. R.
Ejtehadi
, and
S. S.
Plotkin
, “
Protein folding rates correlate with heterogeneity of folding mechanism
,”
Phys. Rev. Lett.
93
,
1
4
(
2004
).
37.
Y.
Suzuki
and
J.
Onuchic
, “
Modeling the interplay between geometrical and energetic effects in protein folding
,”
J. Phys. Chem. B
34
(
109
),
16503
16510
(
2005
).
38.
S. S.
Cho
,
Y.
Levy
, and
P. G.
Wolynes
, “
Quantitative criteria for native energetic heterogeneity influences in the prediction of protein folding kinetics
,”
Proc. Natl. Acad. Sci. U. S. A.
106
,
434
439
(
2009
).
39.
S.
Miyazawa
and
R.
Jernigan
, “
Estimation of effective interresidue contact energies from protein crystal structures: Quasi-chemical approximation
,”
Macromolecules
534
552
(
1985
).
40.
S.
Miyazawa
and
R. L.
Jernigan
, “
Residue-residue potentials with a favorable contact pair term and an unfavorable high packing density term, for simulation and threading
,”
J. Mol. Biol.
256
,
623
644
(
1996
).
41.
T. R.
Weikl
and
K. A.
Dill
, “
Folding rates and low-entropy-loss routes of two-state proteins
,”
J. Mol. Biol.
329
,
585
598
(
2003
).
42.
S. S.
Cho
,
P.
Weinkam
, and
P. G.
Wolynes
, “
Origins of barriers and barrierless folding in BBL
,”
Proc. Natl. Acad. Sci. U. S. A.
105
,
118
123
(
2008
).
43.
M.
Sadqi
,
D.
Fushman
, and
V.
Muñoz
, “
Atom-by-atom analysis of global downhill protein folding
,”
Nature
442
,
317
321
(
2006
).
44.
L. L.
Chavez
,
J. N.
Onuchic
, and
C.
Clementi
, “
Quantifying the roughness on the free energy landscape: Entropic bottlenecks and protein folding rates
,”
J. Am. Chem. Soc.
126
,
8426
8432
(
2004
).
45.
K. W.
Plaxco
,
K. T.
Simons
, and
D.
Baker
, “
Contact order, transition state placement and the refolding rates of single domain proteins
,”
J. Mol. Biol.
277
,
985
994
(
1998
).
46.
R. P.
Joosten
 et al, “
A series of PDB related databases for everyday needs
,”
Nucleic Acids Res.
39
,
1
9
(
2011
).
47.
C.
Clementi
and
S.
Plotkin
, “
The effects of nonnative interactions on protein folding rates: Theory and simulation
,”
Protein Sci.
13
(
7
),
1750
1766
(
2004
).
48.
See supplementary material at http://dx.doi.org/10.1063/1.4938172 for (A) details on phylotopological tree construction with the distance matrix that we used in Table S1. (B) Details on the isoenergetic transformation between both models. (C) Table S2 with a list of multi-state folders. (D) Complete set of our mapped characteristics reported in Tables S3 and S4.
49.
L. C.
Packman
and
R. N.
Perham
, “
Chain folding in the dihydrolipoyl acyltransferase components of the 2-oxo-acid dehydrogenase complexes from Escherichia coli—Identification of a segment involved in binding the E3 subunit
,”
FEBS Lett
206
,
193
198
(
1986
).
50.
W.
Kabsch
and
C.
Sander
, “
Dictionary of protein secondary structure: pattern recognition of hydrogen-bonded and geometrical features
,”
Biopolymers
22
,
2577
2637
(
1983
).

Supplementary Material

You do not currently have access to this content.