Communication Maps: Exploring Energy Transport through Proteins and Water

Abstract

Frequency‐resolved communication maps provide a coarse‐grained, global mapping of energy transport channels in a protein as a function of frequency of modes that carry energy. We illustrate the approach with a study of the homodimeric hemoglobin of Scapharca inaequivalvis, which exhibits cooperativity during ligand binding. We compare energy transport between the two hemes of the unliganded and oxygenated protein, which is mediated by water as well as residues forming a hydrogen‐bonding network at the interface between the globules, and lies along the pathway for allosteric transitions observed in time‐resolved X‐ray studies. Non‐equilibrium molecular simulations on energy transport from the heme corroborate the energy transport pathways identified by the communication maps.

Vibrational energy flow in the villin headpiece subdomain: Master equation simulations

“…One communication map suffices for many initial conditions. Communication maps have until now been calculated to locate energy transport networks in proteins and to examine the role of confined clusters of water molecules in energy transport, 19,71 as well as the role of hydrogen bonding. Comparison has been made with pathways obtained by other coarse-grained methods such as calculation of energy flux networks, 3 which includes effects of anharmonicity, where for photoactive yellow protein we found the same pathways to emerge from the two methods.…”

Mapping Energy Transport Networks in Proteins

“…Based on the linear response theory, irEC is defined in terms of the time correlation functions of irEF. 18-19, 29, 95 First, we consider the total energy of the system given by [23] where p i and R i are the momentum and position of atom i with mass m i , respectively. N is the total number of atoms, and V represents the potential energy term, which contains two-, three-, and four-body interactions in typical force-field models.…”

“…[12][13][14] Computational tools to locate energy transport pathways in proteins have also been advancing. 15 Energy transport pathways in proteins have since some time been identified by molecular dynamics (MD) simulations, [16][17] and more recent efforts have focused on the development of coarse graining approaches, [18][19][20][21][22][23][24][25][26][27][28][29] some of which have exploited analogies to thermal transport in other molecular materials. [30][31][32][33][34][35] With the identification of pathways in proteins and protein complexes, network analysis has been applied to locate residues that control protein dynamics and possibly allostery, [36][37][38] where chemical reactions at one binding site mediate reactions at distance sites of the protein.…”

Gregory S. Ezra

“…Included in the latter is Trp59, which has been probed by Mizutani coworkers by picosecond timeresolved anti-Stokes UVRR measurements [26]. In earlier work, we found vibrational energy transport pathways to be robust with respect to thermal motion of proteins around their native structure [81]. In earlier work, we found vibrational energy transport pathways to be robust with respect to thermal motion of proteins around their native structure [81].…”

“…, q n ) be coordinates in an n -dimensional Hamiltonian system and p = (p 1 , . ( 19 )] by the following consecutive Lie canonical transformations 2 Note that if the generating function F is real analytic, Q(q, p) and P(q, p) are also real analytic in Dom F [ 81 ]. .…”