Although thermal transport is among the essential biophysical properties of proteins, its relationship with protein structures, dynamics, and functions is still elusive. The structures of folded proteins are highly inhomogeneous, giving rise to an anisotropic and non-uniform flow of thermal energy during conformational fluctuations. To illustrate the nature of proteins, we developed a theoretical framework for analyzing local thermal transport properties based on the autocorrelation function formalism, constructed a linear-homopolymer-like model, and applied it to a small α-helical protein, the villin headpiece subdomain (HP36), using equilibrium molecular dynamics simulations. As a result, the model reproduced the exact value of the protein’s thermal conductivity with an error of less than 1%. Interestingly, the site-selective analysis of the local, residue-wise, thermal conductivity demonstrated its distinct residue-type dependence, i.e., its magnitude decreased in the order of charged, polar, and hydrophobic residues. In addition, the local density dependence of the residue-wise thermal transport property was also discussed.
REFERENCES
1.
M.
Kashio
and M.
Tominaga
, “TRP channels in thermosensation
,” Curr. Opin. Neurobiol.
75
, 102591
(2022
).2.
M. C.
Thompson
, B. A.
Barad
, A. M.
Wolff
, H.
Sun Cho
, F.
Schotte
, D. M. C.
Schwarz
, P.
Anfinrud
, and J. S.
Fraser
, “Temperature-jump solution X-ray scattering reveals distinct motions in a dynamic enzyme
,” Nat. Chem.
11
(11
), 1058
–1066
(2019
).3.
C.
Riedel
, R.
Gabizon
, C. A. M.
Wilson
, K.
Hamadani
, K.
Tsekouras
, S.
Marqusee
, S.
Pressé
, and C.
Bustamante
, “The heat released during catalytic turnover enhances the diffusion of an enzyme
,” Nature
517
(7533
), 227
–230
(2015
).4.
S.
Kiyonaka
, T.
Kajimoto
, R.
Sakaguchi
, D.
Shinmi
, M.
Omatsu-Kanbe
, H.
Matsuura
, H.
Imamura
, T.
Yoshizaki
, I.
Hamachi
, T.
Morii
, and Y.
Mori
, “Genetically encoded fluorescent thermosensors visualize subcellular thermoregulation in living cells
,” Nat. Methods
10
(12
), 1232
–1238
(2013
).5.
M.
Weik
and J. P.
Colletier
, “Temperature-dependent macromolecular X-ray crystallography
,” Acta Crystallogr., Sect. D: Biol. Crystallogr.
66
, 437
–446
(2010
).6.
E.
Johnson
, A. G.
Palmer
III, and M.
Rance
, “Temperature dependence of the NMR generalized order parameter
,” Proteins: Struct., Funct., Bioinf.
66
(4
), 796
–803
(2007
).7.
E. M.
Adams
, S.
Pezzotti
, J.
Ahlers
, M.
Rüttermann
, M.
Levin
, A.
Goldenzweig
, Y.
Peleg
, S. J.
Fleishman
, I.
Sagi
, and M.
Havenith
, “Local mutations can serve as a game changer for global protein solvent interaction
,” JACS Au
1
(7
), 1076
–1085
(2021
).8.
S.
Tanimoto
, K.
Tamura
, S.
Hayashi
, N.
Yoshida
, and H.
Nakano
, “A computational method to simulate global conformational changes of proteins induced by cosolvent
,” J. Comput. Chem.
42
(8
), 552
–563
(2021
).9.
S.
Devineau
, K.-i.
Inoue
, R.
Kusaka
, S.-h.
Urashima
, S.
Nihonyanagi
, D.
Baigl
, A.
Tsuneshige
, and T.
Tahara
, “Change of the isoelectric point of hemoglobin at the air/water interface probed by the orientational flip-flop of water molecules
,” Phys. Chem. Chem. Phys.
19
(16
), 10292
–10300
(2017
).10.
T.
Oroguchi
and M.
Nakasako
, “Influences of lone-pair electrons on directionality of hydrogen bonds formed by hydrophilic amino acid side chains in molecular dynamics simulation
,” Sci. Rep.
7
(1
), 15859
(2017
).11.
V.
Conti Nibali
, G.
D’Angelo
, A.
Paciaroni
, D. J.
Tobias
, and M.
Tarek
, “On the coupling between the collective dynamics of proteins and their hydration water
,” J. Phys. Chem. Lett.
5
(7
), 1181
–1186
(2014
).12.
B. H.
McMahon
, H.
Frauenfelder
, and P. W.
Fenimore
, “The role of continuous and discrete water structures in protein function
,” Eur. Phys. J.: Spec. Top.
223
(5
), 915
–926
(2014
).13.
Y.
Mizutani
and M.
Mizuno
, “Time-resolved spectroscopic mapping of vibrational energy flow in proteins: Understanding thermal diffusion at the nanoscale
,” J. Chem. Phys.
157
(24
), 240901
(2022
).14.
S.
Yamashita
, M.
Mizuno
, D. P.
Tran
, H.
Dokainish
, A.
Kitao
, and Y.
Mizutani
, “Vibrational energy transfer from Heme through atomic contacts in proteins
,” J. Phys. Chem. B
122
(22
), 5877
–5884
(2018
).15.
V.
Botan
, E. H. G.
Backus
, R.
Pfister
, A.
Moretto
, M.
Crisma
, C.
Toniolo
, P. H.
Nguyen
, G.
Stock
, and P.
Hamm
, “Energy transport in peptide helices
,” Proc. Natl. Acad. Sci. U. S. A.
104
(31
), 12749
–12754
(2007
).16.
E.
Deniz
, L.
Valiño-Borau
, J. G.
Löffler
, K. B.
Eberl
, A.
Gulzar
, S.
Wolf
, P. M.
Durkin
, R.
Kaml
, N.
Budisa
, G.
Stock
, and J.
Bredenbeck
, “Through bonds or contacts? Mapping protein vibrational energy transfer using non-canonical amino acids
,” Nat. Commun.
12
(1
), 3284
(2021
).17.
Proteins: Energy, Heat and Signal Flow
, Computation in Chemistry
, edited by D. M.
Leitner
and J. E.
Straub
(CRC Press
, Boca Raton
, 2010
).18.
H.
Li
, S.
Wu
, and A.
Ma
, “Origin of protein quake: Energy waves conducted by a precise mechanical machine
,” J. Chem. Theory Comput.
18
(9
), 5692
–5702
(2022
).19.
L. M.
Thompson
, A.
Lasoroski
, P. M.
Champion
, J. T.
Sage
, M. J.
Frisch
, J. J.
van Thor
, and M. J.
Bearpark
, “Analytical harmonic vibrational frequencies for the green fluorescent protein computed with ONIOM: Chromophore mode character and its response to environment
,” J. Chem. Theory Comput.
10
(2
), 751
–766
(2014
).20.
H.
Fujisaki
and J. E.
Straub
, “Vibrational energy relaxation in proteins
,” Proc. Natl. Acad. Sci. U. S. A.
102
(19
), 6726
–6731
(2005
).21.
M.
Kobus
, P. H.
Nguyen
, and G.
Stock
, “Coherent vibrational energy transfer along a peptide helix
,” J. Chem. Phys.
134
(12
), 124518
(2011
).22.
S.
Buchenberg
, D. M.
Leitner
, and G.
Stock
, “Scaling rules for vibrational energy transport in globular proteins
,” J. Phys. Chem. Lett.
7
(1
), 25
–30
(2016
).23.
V.
Conti Nibali
, G.
Morra
, M.
Havenith
, and G.
Colombo
, “Role of terahertz (THz) fluctuations in the allosteric properties of the PDZ domains
,” J. Phys. Chem. B
121
(44
), 10200
–10208
(2017
).24.
A.
Kumawat
and S.
Chakrabarty
, “Hidden electrostatic basis of dynamic allostery in a PDZ domain
,” Proc. Natl. Acad. Sci. U. S. A.
114
(29
), E5825
(2017
).25.
G.
Miño
, R.
Barriga
, and G.
Gutierrez
, “Hydrogen bonds and heat diffusion in α-helices a computational study
,” J. Phys. Chem. B
118
(34
), 10025
–10034
(2014
).26.
I.
Kurisaki
, S.
Tanaka
, I.
Mori
, T.
Umegaki
, Y.
Mori
, and S.
Tanaka
, “Thermal conductivity and conductance of protein in aqueous solution: Effects of geometrical shape
,” J. Comput. Chem.
44
(7
), 857
–868
(2023
).27.
H. D.
Pandey
and D. M.
Leitner
, “Vibrational energy transport in molecules and the statistical properties of vibrational modes
,” Chem. Phys.
482
, 81
–85
(2017
).28.
T.
Ishikura
and T.
Yamato
, “Energy transfer pathways relevant for long-range intramolecular signaling of photosensory protein revealed by microscopic energy conductivity analysis
,” Chem. Phys. Lett.
432
(4–6
), 533
–537
(2006
).29.
K.
Ota
and T.
Yamato
, “Energy exchange network model demonstrates protein allosteric transition: An application to an oxygen sensor protein
,” J. Phys. Chem. B
123
(4
), 768
–775
(2019
).30.
K. M.
Reid
, T.
Yamato
, and D. M.
Leitner
, “Variation of energy transfer rates across protein–water contacts with equilibrium structural fluctuations of a homodimeric hemoglobin
,” J. Phys. Chem. B
124
(7
), 1148
–1159
(2020
).31.
H.
Poudel
and D. M.
Leitner
, “Locating dynamic contributions to allostery via determining rates of vibrational energy transfer
,” J. Chem. Phys.
158
(1
), 015101
(2023
).32.
K. M.
Reid
and D. M.
Leitner
, in Allostery: Methods and Protocols
, Methods in Molecular Biology
, edited by L.
Di Paola
and A.
Giuliani
(Springer
, New York
, 2021
), pp. 37
–59
.33.
L.
Valiño Borau
, A.
Gulzar
, and G.
Stock
, “Master equation model to predict energy transport pathways in proteins
,” J. Chem. Phys.
152
(4
), 045103
(2020
).34.
K. M.
Reid
, T.
Yamato
, and D. M.
Leitner
, “Scaling of rates of vibrational energy transfer in proteins with equilibrium dynamics and entropy
,” J. Phys. Chem. B
122
(40
), 9331
–9339
(2018
).35.
N.
Helmer
, S.
Wolf
, and G.
Stock
, “Energy transport and its function in heptahelical transmembrane proteins
,” J. Phys. Chem. B
126
(43
), 8735
–8746
(2022
).36.
J. K.
Agbo
, R.
Gnanasekaran
, and D. M.
Leitner
, “Communication maps: Exploring energy transport through proteins and water
,” Isr. J. Chem.
54
(8–9
), 1065
–1073
(2014
).37.
D. E.
Sagnella
and J. E.
Straub
, “Directed energy ‘funneling’ mechanism for heme cooling following ligand photolysis or direct excitation in solvated carbonmonoxy myoglobin
,” J. Phys. Chem. B
105
(29
), 7057
–7063
(2001
).38.
T.
Yamato
, T.
Wang
, W.
Sugiura
, O.
Laprévote
, and T.
Katagiri
, “Computational study on the thermal conductivity of a protein
,” J. Phys. Chem. B
126
(16
), 3029
–3036
(2022
).39.
D. A.
McQuarrie
, Statistical Mechanics
(University Science Books
, Sausalito, CA
, 2000
).40.
H.
Babaei
, P.
Keblinski
, and J. M.
Khodadadi
, “Equilibrium molecular dynamics determination of thermal conductivity for multi-component systems
,” J. Appl. Phys.
112
(5
), 054310
(2012
).41.
D. A.
Case
, I. Y.
Ben-Shalom
, S. R.
Brozell
et al, AMBER 19
, 2019
.42.
C. J.
McKnight
, P. T.
Matsudaira
, and P. S.
Kim
, “NMR structure of the 35-residue villin headpiece subdomain
,” Nat. Struct. Biol.
4
(3
), 180
–184
(1997
).43.
P.
Mark
and L.
Nilsson
, “Structure and dynamics of the TIP3P, SPC, and SPC/E water models at 298 K
,” J. Phys. Chem A
105
(43
), 9954
–9960
(2001
).44.
D. J.
Price
and C. L.
Brooks
, , “A modified TIP3P water potential for simulation with Ewald summation
,” J. Chem. Phys.
121
(20
), 10096
–10103
(2004
).45.
C.
Tian
, K.
Kasavajhala
, K. A. A.
Belfon
, L.
Raguette
, H.
Huang
, A. N.
Migues
, J.
Bickel
, Y.
Wang
, J.
Pincay
, Q.
Wu
, and C.
Simmerling
, “ff19SB: Amino-acid-specific protein backbone parameters trained against quantum mechanics energy surfaces in solution
,” J. Chem. Theory Comput.
16
(1
), 528
–552
(2020
).46.
W. D.
Cornell
, P.
Cieplak
, C. I.
Bayly
, I. R.
Gould
, K. M.
Merz
, D. M.
Ferguson
, D. C.
Spellmeyer
, T.
Fox
, J. W.
Caldwell
, and P. A.
Kollman
, “A second generation force field for the simulation of proteins, nucleic acids, and organic molecules
,” J. Am. Chem. Soc.
117
(19
), 5179
–5197
(1995
).47.
C.
Sagui
, L. G.
Pedersen
, and T. A.
Darden
, “Towards an accurate representation of electrostatics in classical force fields: Efficient implementation of multipolar interactions in biomolecular simulations
,” J. Chem. Phys.
120
(1
), 73
–87
(2004
).48.
J.
Esque
, S.
Léonard
, A. G.
de Brevern
, and C.
Oguey
, “VLDP web server: A powerful geometric tool for analysing protein structures in their environment
,” Nucleic Acids Res.
41
(W1
), W373
–W378
(2013
).49.
Fundamentals of Heat and Mass Transfer
, 7th ed.
, edited by T. L.
Bergman
and F. P.
Incropera
(Wiley
, Hoboken, NJ
, 2011
).50.
Y.
Xue
, S.
Lofland
, and X.
Hu
, “Thermal conductivity of protein-based materials: A review
,” Polymers
11
(3
), 456
(2019
).51.
H.
Fischer
, I.
Polikarpov
, and A. F.
Craievich
, “Average protein density is a molecular-weight-dependent function
,” Protein Sci.
13
(10
), 2825
–2828
(2004
).52.
Y.
Harpaz
, M.
Gerstein
, and C.
Chothia
, “Volume changes on protein folding
,” Structure
2
(7
), 641
–649
(1994
).53.
F.
Baud
and S.
Karlin
, “Measures of residue density in protein structures
,” Proc. Natl. Acad. Sci. U. S. A.
96
(22
), 12494
–12499
(1999
).54.
Y.
Mizutani
and T.
Kitagawa
, “Direct observation of cooling of heme upon photodissociation of carbonmonoxy myoglobin
,” Science
278
(5337
), 443
–446
(1997
).55.
A.
Lervik
, F.
Bresme
, S.
Kjelstrup
, D.
Bedeaux
, and J.
Miguel Rubi
, “Heat transfer in protein–water interfaces
,” Phys. Chem. Chem. Phys.
12
(7
), 1610
(2010
).56.
E. R.
Henry
, W. A.
Eaton
, and R. M.
Hochstrasser
, “Molecular dynamics simulations of cooling in laser-excited heme proteins
.” Proc. Natl. Acad. Sci. U. S. A.
83
(23
), 8982
–8986
(1986
).57.
L.
Bu
and J. E.
Straub
, “Simulating vibrational energy flow in proteins: Relaxation rate and mechanism for heme cooling in cytochrome c
,” J. Phys. Chem. B
107
(44
), 12339
–12345
(2003
).58.
P. H.
Nguyen
, S.-M.
Park
, and G.
Stock
, “Nonequilibrium molecular dynamics simulation of the energy transport through a peptide helix
,” J. Chem. Phys.
132
(2
), 025102
(2010
).59.
K.
Gekko
and H.
Noguchi
, “Compressibility of globular proteins in water at 25 °C
,” J. Chem. Phys.
83
(21
), 2706
–2714
(1979
).60.
Y.
Wu
, H. L.
Tepper
, and G. A.
Voth
, “Flexible simple point-charge water model with improved liquid-state properties
,” J. Chem. Phys.
124
(2
), 024503
(2006
).61.
K.
Takemura
and A.
Kitao
, “Effects of water model and simulation box size on protein diffusional motions
,” J. Phys. Chem. B
111
(41
), 11870
–11872
(2007
).62.
Y.
Xu
and D. M.
Leitner
, “Communication maps of vibrational energy transport through photoactive yellow protein
,” J. Phys. Chem. A
118
(35
), 7280
–7287
(2014
).63.
J. K.
Agbo
, Y.
Xu
, P.
Zhang
, J. E.
Straub
, and D. M.
Leitner
, “Vibrational energy flow across heme–cytochrome c and cytochrome c–water interfaces
,” Theor. Chem. Acc.
133
(7
), 1504
(2014
).64.
H.
Hamzi
, A.
Rajabpour
, E.
Roldán
, and A.
Hassanali
, “Learning the hydrophobic, hydrophilic, and aromatic character of amino acids from thermal relaxation and interfacial thermal conductance
,” J. Phys. Chem. B
126
(3
), 670
–678
(2022
).65.
Y.
Xu
and D. M.
Leitner
, “Vibrational energy flow through the green fluorescent protein–water interface: Communication maps and thermal boundary conductance
,” J. Phys. Chem. B
118
(28
), 7818
–7826
(2014
).66.
T.
Ishikura
, T.
Hatano
, and T.
Yamato
, “Atomic stress tensor analysis of proteins
,” Chem. Phys. Lett.
539–540
, 144
–150
(2012
).© 2023 Author(s). Published under an exclusive license by AIP Publishing.
2023
Author(s)
You do not currently have access to this content.
