Allostery in proteins involves, broadly speaking, ligand-induced conformational transitions that modulate function at active sites distal to where the ligand binds. In contrast, the concept of cooperativity (in the sense used in phase transition theory) is often invoked to understand protein folding and, therefore, function. The modern view on allostery is one based on dynamics and hinges on the time-dependent interactions between key residues in a complex network, interactions that determine the free-energy profile for the reaction at the distal site. Here, we merge allostery and cooperativity, and we discuss a joint model with features of both. In our model, the active-site reaction is replaced by the reaction pathway that leads to protein folding, and the presence or absence of the effector is replaced by mutant-vs-wild type changes in key residues. To this end, we employ our recently introduced time-lagged independent component analysis (tICA) correlation approach [Ray et al. Proc. Natl. Acad. Sci. 118(43) (2021), e2100943118] to identify the allosteric role of distant residues in the folded-state dynamics of a large protein. In this work, we apply the technique to identify key residues that have a significant role in the folding of a small, fast folding-protein, chignolin. Using extensive enhanced sampling simulations, we critically evaluate the accuracy of the predictions by mutating each residue one at a time and studying how the mutations change the underlying free energy landscape of the folding process. We observe that mutations in those residues whose associated backbone torsion angles have a high correlation score can indeed lead to loss of stability of the folded configuration. We also provide a rationale based on interaction energies between individual residues with the rest of the protein to explain this effect. From these observations, we conclude that the tICA correlation score metric is a useful tool for predicting the role of individual residues in the correlated dynamics of proteins and can find application to the problem of identifying regions of protein that are either most vulnerable to mutations or—mutatis mutandis—to binding events that affect their functionality.
REFERENCES
1.
Y.
Sugita
and Y.
Okamoto
, “Replica-exchange molecular dynamics method for protein folding
,” Chem. Phys. Lett.
314
, 141
–151
(1999
).2.
S.-H.
Ahn
, A. A.
Ojha
, R. E.
Amaro
, and J. A.
McCammon
, “Gaussian-accelerated molecular dynamics with the weighted ensemble method: A hybrid method improves thermodynamic and kinetic sampling
,” J. Chem. Theory Comput.
17
, 7938
–7951
(2021
).3.
D.
Ray
and I.
Andricioaei
, “Weighted ensemble milestoning (WEM): A combined approach for rare event simulations
,” J. Chem. Phys.
152
, 234114
(2020
).4.
A.
Laio
and M.
Parrinello
, “Escaping free-energy minima
,” Proc. Natl. Acad. Sci. U. S. A.
99
, 12562
–12566
(2002
).5.
G. M.
Torrie
and J. P.
Valleau
, “Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling
,” J. Comput. Phys.
23
, 187
–199
(1977
).6.
E.
Darve
, D.
Rodríguez-Gómez
, and A.
Pohorille
, “Adaptive biasing force method for scalar and vector free energy calculations
,” J. Chem. Phys.
128
, 144120
(2008
).7.
G. A.
Huber
and S.
Kim
, “Weighted-ensemble Brownian dynamics simulations for protein association reactions
,” Biophys. J.
70
, 97
–110
(1996
).8.
Q.
Chen
, W.
Cui
, Z.
Zhou
, and L.
Han
, “Exploration of key residues and conformational change of anti-terminator protein GlpP for ligand and RNA binding
,” Proteins: Struct., Funct., Bioinf.
89
, 623
–631
(2021
).9.
E. D.
Merkley
, B.
Bernard
, and V.
Daggett
, “Conformational changes below the Tm: Molecular dynamics studies of the thermal pretransition of ribonuclease A
,” Biochemistry
47
, 880
–892
(2008
).10.
J.
Holyoake
and M. S. P.
Sansom
, “Conformational change in an MFS protein: MD simulations of LacY
,” Structure
15
, 873
–884
(2007
).11.
D.
Ray
, L.
Le
, and I.
Andricioaei
, “Distant residues modulate conformational opening in SARS-CoV-2 spike protein
,” Proc. Natl. Acad. Sci. U. S. A.
118
, e2100943118
(2021
).12.
D.
Ray
, R. N.
Quijano
, and I.
Andricioaei
, “Point mutations in SARS-CoV-2 variants induce long-range dynamical perturbations in neutralizing antibodies
,” Chem. Sci.
13
, 7224
–7239
(2022
).13.
G.
Bouvignies
, P.
Vallurupalli
, D. F.
Hansen
, B. E.
Correia
, O.
Lange
, A.
Bah
, R. M.
Vernon
, F. W.
Dahlquist
, D.
Baker
, and L. E.
Kay
, “Solution structure of a minor and transiently formed state of a T4 lysozyme mutant
,” Nature
477
, 111
–114
(2011
).14.
Z.
Smith
, P.
Ravindra
, Y.
Wang
, R.
Cooley
, and P.
Tiwary
, “Discovering protein conformational flexibility through artificial-intelligence-aided molecular dynamics
,” J. Phys. Chem. B
124
, 8221
–8229
(2020
).15.
S.
Honda
, K.
Yamasaki
, Y.
Sawada
, and H.
Morii
, “10 residue folded peptide designed by segment statistics
,” Structure
12
, 1507
–1518
(2004
).16.
A.
Suenaga
, T.
Narumi
, N.
Futatsugi
, R.
Yanai
, Y.
Ohno
, N.
Okimoto
, and M.
Taiji
, “Folding dynamics of 10-residue β-hairpin peptide chignolin
,” Chem. -Asian J.
2
, 591
–598
(2007
).17.
T.
Sumi
and K.
Koga
, “Theoretical analysis on thermodynamic stability of chignolin
,” Sci. Rep.
9
, 5186
(2019
).18.
Y.
Maruyama
, S.
Koroku
, M.
Imai
, K.
Takeuchi
, and A.
Mitsutake
, “Mutation-induced change in chignolin stability from π-turn to α-turn
,” RSC Adv.
10
, 22797
–22808
(2020
).19.
S.
Honda
, T.
Akiba
, Y. S.
Kato
, Y.
Sawada
, M.
Sekijima
, M.
Ishimura
, A.
Ooishi
, H.
Watanabe
, T.
Odahara
, and K.
Harata
, “Crystal structure of a ten-amino acid protein
,” J. Am. Chem. Soc.
130
, 15327
–15331
(2008
).20.
C. M.
Davis
, S.
Xiao
, D. P.
Raleigh
, and R. B.
Dyer
, “Raising the speed limit for β-hairpin formation
,” J. Am. Chem. Soc.
134
, 14476
–14482
(2012
).21.
K. A.
McKiernan
, B. E.
Husic
, and V. S.
Pande
, “Modeling the mechanism of CLN025 beta-hairpin formation
,” J. Chem. Phys.
147
, 104107
(2017
).22.
K.
Lindorff-Larsen
, S.
Piana
, R. O.
Dror
, and D. E.
Shaw
, “How fast-folding proteins fold
,” Science
334
, 517
–520
(2011
).23.
L.
Molgedey
and H. G.
Schuster
, “Separation of a mixture of independent signals using time delayed correlations
,” Phys. Rev. Lett.
72
, 3634
–3637
(1994
).24.
S.
Schultze
and H.
Grubmüller
, “Time-lagged independent component analysis of random walks and protein dynamics
,” J. Chem. Theory Comput.
17
, 5766
–5776
(2021
).25.
G.
Pérez-Hernández
, F.
Paul
, T.
Giorgino
, G.
De Fabritiis
, and F.
Noé
, “Identification of slow molecular order parameters for Markov model construction
,” J. Chem. Phys.
139
, 015102
(2013
).26.
C. R.
Schwantes
and V. S.
Pande
, “Improvements in Markov state model construction reveal many non-native interactions in the folding of NTL9
,” J. Chem. Theory Comput.
9
, 2000
–2009
(2013
).27.
M. K.
Scherer
, B.
Trendelkamp-Schroer
, F.
Paul
, G.
Pérez-Hernández
, M.
Hoffmann
, N.
Plattner
, C.
Wehmeyer
, J.-H.
Prinz
, and F.
Noé
, “PyEMMA 2: A software package for estimation, validation, and analysis of Markov models
,” J. Chem. Theory Comput.
11
, 5525
–5542
(2015
).28.
K.
Tian
, X.
Zhao
, X.
Wan
, and S. S.-T.
Yau
, “Amino acid torsion angles enable prediction of protein fold classification
,” Sci. Rep.
10
, 21773
(2020
).29.
M.
Larocca
, F.
Foglia
, and A.
Cilibrizzi
, “Dihedral angle calculations to elucidate the folding of peptides through its main mechanical forces
,” Biochemistry
58
, 1032
–1037
(2019
).30.
O.
Valsson
, P.
Tiwary
, and M.
Parrinello
, “Enhancing important fluctuations: Rare events and metadynamics from a conceptual viewpoint
,” Annu. Rev. Phys. Chem.
67
, 159
–184
(2016
).31.
P.
Tiwary
and M.
Parrinello
, “From metadynamics to dynamics
,” Phys. Rev. Lett.
111
, 230602
(2013
).32.
M.
Karplus
and J. A.
McCammon
, “Molecular dynamics simulations of biomolecules
,” Nat. Struct. Biol.
9
, 646
–652
(2002
).33.
D. M.
Zuckerman
and L. T.
Chong
, “Weighted ensemble simulation: Review of methodology, applications, and software
,” Annu. Rev. Biophys.
46
, 43
–57
(2017
).34.
A.
Barducci
, G.
Bussi
, and M.
Parrinello
, “Well-tempered metadynamics: A smoothly converging and tunable free-energy method
,” Phys. Rev. Lett.
100
, 020603
(2008
).35.
J.
Lee
et al, “CHARMM-GUI input generator for NAMD, GROMACS, AMBER, OpenMM, and CHARMM/OpenMM simulations using the CHARMM36 additive force field
,” J. Chem. Theory Comput.
12
, 405
–413
(2016
).36.
B. R.
Brooks
et al, “CHARMM: The biomolecular simulation program
,” J. Comput. Chem.
30
, 1545
–1614
(2009
).37.
J. C.
Phillips
et al, “Scalable molecular dynamics on CPU and GPU architectures with NAMD
,” J. Chem. Phys.
153
, 044130
(2020
).38.
G.
Fiorin
, M. L.
Klein
, and J.
Hénin
, “Using collective variables to drive molecular dynamics simulations
,” Mol. Phys.
111
, 3345
–3362
(2013
).39.
X.
Daura
, K.
Gademann
, B.
Jaun
, D.
Seebach
, W. F.
van Gunsteren
, and A. E.
Mark
, “Peptide folding: When simulation meets experiment
,” Angew. Chem., Int. Ed.
38
, 236
–240
(1999
).40.
M. J.
Abraham
, T.
Murtola
, R.
Schulz
, S.
Páll
, J. C.
Smith
, B.
Hess
, and E.
Lindahl
, “GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers
,” SoftwareX
1–2
, 19
–25
(2015
).41.
S.
Jo
, X.
Cheng
, S. M.
Islam
, L.
Huang
, H.
Rui
, A.
Zhu
, H. S.
Lee
, Y.
Qi
, W.
Han
, K.
Vanommeslaeghe
, A. D.
MacKerell
, B.
Roux
, and W.
Im
, in Advances in Protein Chemistry and Structural Biology
, Biomolecular Modelling and Simulations, edited by T.
Karabencheva-Christova
(Academic Press
, 2014
), Vol. 96, pp. 235
–265
.42.
S.
Jo
, T.
Kim
, V. G.
Iyer
, and W.
Im
, “CHARMM-GUI: A web-based graphical user interface for CHARMM
,” J. Comput. Chem.
29
, 1859
–1865
(2008
).43.
M.
Bonomi
et al, “Promoting transparency and reproducibility in enhanced molecular simulations
,” Nat. Methods
16
, 670
–673
(2019
).44.
J. F.
Brandts
, H. R.
Halvorson
, and M.
Brennan
, “Consideration of the possibility that the slow step in protein denaturation reactions is due to cis–trans isomerism of proline residues
,” Biochemistry
14
, 4953
–4963
(1975
).45.
S.
Kawagoe
, H.
Nakagawa
, H.
Kumeta
, K.
Ishimori
, and T.
Saio
, “Structural insight into proline cis/trans isomerization of unfolded proteins catalyzed by the trigger factor chaperone
,” J. Biol. Chem.
293
, 15095
–15106
(2018
).46.
R. L.
Baldwin
, “The search for folding intermediates and the mechanism of protein folding
,” Annu. Rev. Biophys.
37
, 1
–21
(2008
).47.
M. T.
Fisher
, “Proline to the rescue
,” Proc. Natl. Acad. Sci. U. S. A.
103
, 13265
–13266
(2006
).48.
A. A.
Morgan
and E.
Rubenstein
, “Proline: The distribution, frequency, positioning, and common functional roles of proline and polyproline sequences in the human proteome
,” PLoS One
8
, e53785
(2013
).49.
W. J.
Wedemeyer
, E.
Welker
, and H. A.
Scheraga
, “Proline cis–trans isomerization and protein folding
,” Biochemistry
41
, 14637
–14644
(2002
).50.
T.-F.
Fu
, E. S.
Boja
, M. K.
Safo
, and V.
Schirch
, “Role of proline residues in the folding of serine hydroxymethyltransferase
,” J. Biol. Chem.
278
, 31088
–31094
(2003
).51.
F.
Krieger
, A.
Möglich
, and T.
Kiefhaber
, “Effect of proline and glycine residues on dynamics and barriers of loop formation in polypeptide chains
,” J. Am. Chem. Soc.
127
, 3346
–3352
(2005
).52.
B. X.
Yan
and Y. Q.
Sun
, “Glycine residues provide flexibility for enzyme active sites
,” J. Biol. Chem.
272
, 3190
–3194
(1997
).53.
S.
Enemark
, N. A.
Kurniawan
, and R.
Rajagopalan
, “β-hairpin forms by rolling up from C-terminal: Topological guidance of early folding dynamics
,” Sci. Rep.
2
, 649
(2012
).54.
T.
Terada
, D.
Satoh
, T.
Mikawa
, Y.
Ito
, and K.
Shimizu
, “Understanding the roles of amino acid residues in tertiary structure formation of chignolin by using molecular dynamics simulation
,” Proteins: Struct., Funct., Bioinf.
73
, 621
–631
(2008
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
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