Energy function, potential channel model

The Markov model assumes that the channel protein can have only a few conformational states. The structure of a protein can be represented by a potential energy function. Stable conformational states correspond to local minima in that potential function. Thus, the well-defined discrete states of this model suggest that there are a few deep local minima in the potential that are well separated from other local minima. 

Calculations of the potential energy function of a large number of different globular proteins demonstrate that these proteins all have a very large number of shallow local energy minima (26). This analysis is consistent with the physical properties of ion channel proteins suggested by the fractal properties of the channel data and inconsistent with the few deep minima predicted by the Markov model. 

Thus, the biophysical studies demonstrate that globular proteins have (1) a very large number of conformational states corresponding to many shallow local minima in the potential energy function, (2) very broad continuous distributions of activation energies, and (3) time-dependent activation energy barriers. All these properties are consistent with the physical properties of ion channels derived from the fractal properties observed in the channel data and are inconsistent with the physical properties derived from the Markov model. 

In general, atomic-level computer simulations of channels in membranes or membrane-mimetic systems have proven to be quite useful in refining model structures, often postulated somewhat ad hoc. However, full assessments of channel stability from simulations on the currently accessible timescales is not nearly as reliable. Owing to the long relaxation times required to equilibrate membrane-bound systems, it is not currently feasible to arrive at the correct, equilibrium structure starting from an arbitrary initial conditions. Even if the potential energy functions used in simulations were accurate, correct results could be expected only if the initial and equilibrium structures were not too different. 

Fig. 6. Minimum interaction energies of K+ and Na+ with gramicidin A as a function of their position along the channel axis. The top two curves 1911 are calculated according to a model proposed by Gresh et.al. with blocked ethanolamine end chain. The more attractive curves 165-166> are determined using the pair potential method. The gramicidin A dimer ranges from about —14 A to +14 A...

With decay channel in the three excitation functions of Fig, 1(b) can be explained by finite llfetltne oscillator models (30-33) such as the "boomerang model (30-31)). Such an energy dependence on decay channel indicates that the lifetime of the resonance is comparable to the vibrational period. These findings suggest that the short-range part of the e -N2 potential well is not significantly modified in the solid and consequently, that the anion retains essentially the symmetry. 

Another system which has been treated in a rather complete manner is the dissociation of HOOH (Brouwer et al., 1987). The rates as well as the product energy distributions were calculated. As with the NO2 reaction, the interaction potential was assumed to have no barriers so that Ef for each HOOH reaction channel is assumed to be associated with the centrifugal barrier. In order to calculate this barrier, the reaction is treated as a triatomic dissociation, ABC AB + C. The effective rotational constant, at the centrifugal barrier is calculated according to formulas derived by Troe (1983). In addition, the model was simplified by replacing two adjustable parameters, a (from the interpolation function) and B (from the Morse potential), by their ratio, a/p. A value of 0.44 was found to adequately account for the data. Figure 7.25 shows the comparison of the SACM k E) curves with those obtained from experiments or trajectory calculations. 

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