of the energy transport network reveals how a protein responds to
local structural changes, possibly pointing to pathways along which
allosteric transitions occur. In this chapter we review an approach to
calculate energy transport networks in proteins that is based on
calculation of local thermal transport in nanoscale materials. We
illustrate the method with the example of a homodimeric hemoglobin, where prominent energy transport channels were found to
lie along pathways important in allostery. In addition to locating
energy transport networks, the calculated local energy diffusion
coefficients can be used to model energy transport by master equation simulations, as we review here. We also examine the possibility
of relating the rate constants to dynamic fluctuations of hydrogen
bonds, where we present calculations exploring such a connection
in apomyoglobin.
That energy transport pathways exist, i.e., energy does not
simply flow isotropically through a globular protein, is an inherent
property of the geometry of a folded protein [52–60], which
resembles that of a percolation cluster at threshold. Some channels
are relatively long range, which may contribute to function such as
allostery [41, 51, 61–65], by which proteins regulate reactions that
occur in remote regions of the molecule [66–69]. In efforts to
elucidate protein dynamics, strategies have been adopted to identify
pathways or ensembles of pathways [64, 65, 70–75] along which
transitions between different states of the protein occur. Whether
or not vibrational energy transport channels point to pathways
involved in allosteric transitions, energy relaxation pathways regulate chemical reaction dynamics. Optical studies of energy relaxation in myoglobin have since some time produced a detailed picture
of events that follow excitation of the heme and ligand photolysis,
elucidating chemical dynamics of that protein [76, 77]. However,
the extent to which the relaxation pathways identified in myoglobin
play a role in allostery in hemoglobins remains unclear, due to the
diversity of orientations of the monomeric units of different hemoglobins [78]. It would thus be desirable to identify energy transport
in individual hemoglobins to examine the extent to which they
overlap pathways or ensembles of pathways along which allosteric
transitions take place.
Towards this goal, and as an illustrative example of the energy
transport networks that can be computed for a protein, we summarize recent computational work identifying networks of energy
transport channels in the allosteric homodimeric hemoglobin
from Scapharca inaequivalvis, HbI [79]. When HbI is in the unliganded state the crystallographic structure reveals a cluster of
17 water molecules at the interface between the two globules,
whereas 11 are found in the liganded state. The free energy of
ligand binding in HbI and the origin of cooperativity is mainly
entropic [80, 81]. Ligand-linked tertiary structural changes occur
upon ligand binding, including rotation of Phe97 into the interface
38
Korey M. Reid and David M. Leitner
local structural changes, possibly pointing to pathways along which
allosteric transitions occur. In this chapter we review an approach to
calculate energy transport networks in proteins that is based on
calculation of local thermal transport in nanoscale materials. We
illustrate the method with the example of a homodimeric hemoglobin, where prominent energy transport channels were found to
lie along pathways important in allostery. In addition to locating
energy transport networks, the calculated local energy diffusion
coefficients can be used to model energy transport by master equation simulations, as we review here. We also examine the possibility
of relating the rate constants to dynamic fluctuations of hydrogen
bonds, where we present calculations exploring such a connection
in apomyoglobin.
That energy transport pathways exist, i.e., energy does not
simply flow isotropically through a globular protein, is an inherent
property of the geometry of a folded protein [52–60], which
resembles that of a percolation cluster at threshold. Some channels
are relatively long range, which may contribute to function such as
allostery [41, 51, 61–65], by which proteins regulate reactions that
occur in remote regions of the molecule [66–69]. In efforts to
elucidate protein dynamics, strategies have been adopted to identify
pathways or ensembles of pathways [64, 65, 70–75] along which
transitions between different states of the protein occur. Whether
or not vibrational energy transport channels point to pathways
involved in allosteric transitions, energy relaxation pathways regulate chemical reaction dynamics. Optical studies of energy relaxation in myoglobin have since some time produced a detailed picture
of events that follow excitation of the heme and ligand photolysis,
elucidating chemical dynamics of that protein [76, 77]. However,
the extent to which the relaxation pathways identified in myoglobin
play a role in allostery in hemoglobins remains unclear, due to the
diversity of orientations of the monomeric units of different hemoglobins [78]. It would thus be desirable to identify energy transport
in individual hemoglobins to examine the extent to which they
overlap pathways or ensembles of pathways along which allosteric
transitions take place.
Towards this goal, and as an illustrative example of the energy
transport networks that can be computed for a protein, we summarize recent computational work identifying networks of energy
transport channels in the allosteric homodimeric hemoglobin
from Scapharca inaequivalvis, HbI [79]. When HbI is in the unliganded state the crystallographic structure reveals a cluster of
17 water molecules at the interface between the two globules,
whereas 11 are found in the liganded state. The free energy of
ligand binding in HbI and the origin of cooperativity is mainly
entropic [80, 81]. Ligand-linked tertiary structural changes occur
upon ligand binding, including rotation of Phe97 into the interface
38
Korey M. Reid and David M. Leitner