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Energy profiles for sodium ion passage through the single‐filing gramicidin transmembrane channel
Author(s) -
Urry Dan W.,
Trapane Tina L.,
Venkatachalam C. M.,
Prasad Kari U.
Publication year - 2009
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560280703
Subject(s) - chemistry , ion , enthalpy , reaction rate constant , sodium channel , relaxation (psychology) , thermodynamics , analytical chemistry (journal) , atomic physics , sodium , physics , kinetics , quantum mechanics , psychology , social psychology , organic chemistry , chromatography
Abstract Sodium‐23 nuclear magnetic resonance longitudinal and transverse relaxation studies of sodium ion interaction with the Gramicidin A transmembrane channel are reported in the 30d̀ to 75d̀ temperature range to determine the temperature dependence of the off‐rate constant for the doubly occupied channel ( k w off ) of the binding constant for going from single to double ion occupancy ( K w b ), of the binding constant for going from empty to singly occupied channel ( K t b ), and of the off‐rate constant for the singly occupied channel, ( k k off ). With previous information for the temperature dependence of the intrachannel rate constant for an ion going from one ion binding site to the other ( k k ) for the singly occupied state of this two‐fold symmetric channel, the enthalpy (Δ H and the – TΔS energy profiles are plotted for ion passage through the channel. This provides energy profiles for comparison with theoretical calculations. Comparison of TΔS values defined by equilibrium theory (i.e. entropy changes on going from one minimum to another) with the TΔS values defined by Eyring rate theory (i.e. the entropy change between minima and activated state) shows that, even though Eyring rate theory has the very large pre‐exponential factor (kT/h), the changes in entropy obtained from the temperature dependence of equilibrium constants are very nearly the same as the changes in entropy obtained from the temperature dependence of the off‐rate constants. Thus application of Eyring rate theory to single filling channels, where the channel wall supplies lateral coordinations of the permeant ion and where the rate constants are of the order of 10 7 ions/sec, appears quite reasonable.