between the globules, which is otherwise tightly packed against the
proximal histidine, His101, in the unliganded structure. Cooperativity depends on a number of residues at the interface in contact
with the tightly bound [82] cluster of water molecules [83–85],
and the Lys30-Asp89 salt bridge [86], which is farther from the
water cluster but crucial to the stability of the homodimer. Crystal
structures reveal differences between the hydrogen bonding
arrangement of the waters and side chains at the interface of the
unliganded and liganded states [87]. Modification of this arrangement by point mutation apparently influences cooperativity
[83, 85]. Overall the ligand-linked changes are mainly tertiary in
HbI. Quaternary changes that take place, among the last steps [88],
are much smaller than those in tetrameric human hemoglobin.
Having identified networks along which energy transport
occurs we model the flow of energy by master equation simulations.
Rate constants in the master equation can be obtained from local
energy diffusion coefficients or more directly by fitting results of
all-atom simulations of energy flow to a master equation. We
discuss here a recent comparison between results of a master equation simulation and results of all-atom nonequilibrium simulations
of energy flow in the villin headpiece subdomain HP36, where the
rate constants used in the master equation simulations were related
to the energy diffusion coefficients obtained by coarse-graining
thermal transport in the protein [17]. A more recent study on
HP36 by Stock and coworkers suggested that the rate constants
in the master equation simulations are related to dynamic fluctuations of the protein [23]. We consider that possibility here for the
hydrogen bonds of apomyoglobin. The hydrogen bond dynamics is
analyzed from results of molecular dynamics (MD) simulations,
and the rate constants for energy transfer along the bond are
obtained using the same trajectory in a calculation of the local
energy current, using the methodology developed by Yamato and
coworkers [13, 14].
In the following section we summarize a coarse-graining
approach to locate energy transport channels in proteins and discuss one application to the identification of energy transport networks in the homodimeric hemoglobin, HbI. We then review
results comparing the dynamics along protein energy transport
networks obtained by master equation simulations using rate constants obtained from a communication map with results of all-atom
simulations of the villin headpiece subdomain, HP36. Possible
scaling relations between rate constants in a master equation for
hydrogen bonds in a protein and the dynamics of that hydrogen
bond are then discussed. Concluding remarks are given in
Subheading 3.
Locating and Navigating Energy Transport Networks in Proteins
39
proximal histidine, His101, in the unliganded structure. Cooperativity depends on a number of residues at the interface in contact
with the tightly bound [82] cluster of water molecules [83–85],
and the Lys30-Asp89 salt bridge [86], which is farther from the
water cluster but crucial to the stability of the homodimer. Crystal
structures reveal differences between the hydrogen bonding
arrangement of the waters and side chains at the interface of the
unliganded and liganded states [87]. Modification of this arrangement by point mutation apparently influences cooperativity
[83, 85]. Overall the ligand-linked changes are mainly tertiary in
HbI. Quaternary changes that take place, among the last steps [88],
are much smaller than those in tetrameric human hemoglobin.
Having identified networks along which energy transport
occurs we model the flow of energy by master equation simulations.
Rate constants in the master equation can be obtained from local
energy diffusion coefficients or more directly by fitting results of
all-atom simulations of energy flow to a master equation. We
discuss here a recent comparison between results of a master equation simulation and results of all-atom nonequilibrium simulations
of energy flow in the villin headpiece subdomain HP36, where the
rate constants used in the master equation simulations were related
to the energy diffusion coefficients obtained by coarse-graining
thermal transport in the protein [17]. A more recent study on
HP36 by Stock and coworkers suggested that the rate constants
in the master equation simulations are related to dynamic fluctuations of the protein [23]. We consider that possibility here for the
hydrogen bonds of apomyoglobin. The hydrogen bond dynamics is
analyzed from results of molecular dynamics (MD) simulations,
and the rate constants for energy transfer along the bond are
obtained using the same trajectory in a calculation of the local
energy current, using the methodology developed by Yamato and
coworkers [13, 14].
In the following section we summarize a coarse-graining
approach to locate energy transport channels in proteins and discuss one application to the identification of energy transport networks in the homodimeric hemoglobin, HbI. We then review
results comparing the dynamics along protein energy transport
networks obtained by master equation simulations using rate constants obtained from a communication map with results of all-atom
simulations of the villin headpiece subdomain, HP36. Possible
scaling relations between rate constants in a master equation for
hydrogen bonds in a protein and the dynamics of that hydrogen
bond are then discussed. Concluding remarks are given in
Subheading 3.
Locating and Navigating Energy Transport Networks in Proteins
39