Energy Barrier Profiles Research Articles

Fluctuations and the Hofmeister Effect

The Hofmeister effect consists in changes of protein solubility triggered by neutral electrolyte cosolutes. Based on the assumption that salts cause stochastic fluctuations of the free energy barrier profiles, a kinetic theory of this phenomenon is proposed. An exponentially correlated noise, of amplitude proportional to the salt concentration, is added to each energy level, and the time-dependence of the mean protein concentration is calculated. It is found that the theory yields the well-known Setschenow equation if the noise correlation time is low in comparison to the aggregation time constant. Experimental data on salting-in agents are well fitted, whereas, in the case of salting-out cosolutes, two independent dichotomic fluctuations are needed to fit the data. This may result from the fact that, in both cases, the low-concentration regime is dominated by salting-in electrostatic contributions, whereas, at high salt concentrations, electron donor/acceptor interactions become important; these have opposite effects. The theory offers a novel way to metricate Hofmeister effects and also leads to thermodynamic quantities, which account for the influence of salts. The formalism may also be applied to describe kinetic phenomena in the presence of cosolutes.

2 Barrier–1 site pore: an interactive spreadsheet model for two permeating ions

An interactive ion channel permeation tutorial was developed using a Microsoft® Excel v5.0 spreadsheet to describe a two barrier, one site channel model by means of Eyring rate theory (ERT). The spreadsheet is inherently interactive so that the user receives immediate feedback about how changes in the energy barrier profile or ion concentrations affect current–voltage relations and single channel conductance. The spreadsheet model is easy to use, allows direct access to intermediate calculated values and all equations, contains graphical displays of parameters and lends itself to customization by a user having only a basic knowledge of spreadsheet operations.

Ion conduction in substates of the batrachotoxin-modified Na+ channel from toad skeletal muscle

Batrachotoxin-modified Na+ channels from toad muscle were inserted into planar lipid bilayers composed of neutral phospholipids. Single-channel conductances were measured for [Na+] ranging between 0.4 mM and 3 M. When membrane preparations were made in the absence of protease inhibitors, two open conductance states were identified: a fully open state (16.6 pS in 200 mM symmetrical NaCl) and a substate that was 71% of the full conductance. The substate was predominant at [Na+] > 65 mM, whereas the presence of the fully open state was predominant at [Na+] < 15 mM. Addition of protease inhibitors during membrane preparation stabilized the fully open state over the full range of [Na+] studied. In symmetrical Na+ solutions and in biionic conditions, the ratio of amplitudes remained constant and the two open states exhibited the same permeability ratios of PLi/PNa and PCs/PNa. The current-voltage relations for both states showed inward rectification only at [Na+] < 10 mM, suggesting the presence of asymmetric negative charge densities at both channel entrances, with higher charge density in the external side. An energy barrier profile that includes double ion occupancy and asymmetric charge densities at the channel entrances was required to fit the conductance-[Na+] relations and to account for the rectification seen at low [Na+]. Energy barrier profiles differing only in the energy peaks can give account of the differences between both conductance states. Estimation of the surface charge density at the channel entrances is very dependent on the ion occupancy used and the range of [Na+] tested. Independent evidence for the existence of a charged external vestibule was obtained at low external [Na+] by identical reduction of the outward current induced by micromolar additions of Mg2+ and Ba2+.

Modeling ion permeation through batrachotoxin-modified Na+ channels from rat skeletal muscle with a multi-ion pore

The mechanism of ion permeation through Na+ channels that have been modified by batrachotoxin (BTX) and inserted into planar bilayers has been generally described by models based on single-ion occupancy, with or without an influence of negative surface charge, depending on the tissue source. For native Na+ channels there is evidence suggestive of a multi-ion conduction mechanism. To explore the question of ion occupancy, we have reexamined permeation of Na+, Li+, and K+ through BTX-modified Na+ channels from rat skeletal muscle. Single-channel current-voltage (I-V) behavior was studied in neutral lipid bilayers in the presence of symmetrical Na+ concentrations ranging from 0.5 to 3,000 mM. The dependence of unitary current on the mole fraction of Na+ was also examined in symmetrical mixtures of Na(+)-Li+ and Na(+)-K+ at a constant total ionic strength of 206 and 2,006 mM. The dependence of unitary conductance on symmetrical Na+ concentration does not exhibit Michaelis-Menten behavior characteristic of single-ion occupancy but can be simulated by an Eyring-type model with three barriers and two sites (3B2S) that includes double occupancy and ion-ion repulsion. Best-fit energy barrier profiles for Na+, Li+, and K+ were obtained by nonlinear curve fitting of I-V data using the 3B2S model. The Na(+)-Li+ and Na(+)-K+ mole-fraction experiments do not exhibit an anomalous mole-fraction effect. However, the 3B2S model is able to account for the biphasic dependence of unitary conductance on symmetrical [Na+] that is suggestive of multiple occupancy and the monotonic dependence of unitary current on the mole fraction of Na+ that is compatible with single or multiple occupancy. The best-fit 3B2S barrier profiles also successfully predict bi-ionic reversal potentials for Na(+)-Li+ and Na(+)-K+ in both orientations across the channel. Our experimental and modeling results reconcile the dual personality of ion permeation through Na+ channels, which can display features of single or multiple occupancy under various conditions. To a first approximation, the 3B2S model developed for this channel does not require corrections for vestibule surface charge. However, if negative surface charges of the protein do influence conduction, the conductance behavior in the limit of low [Na+] does not correspond to a Gouy-Chapman model of planar surface charge.

Symmetry and asymmetry of permeation through toxin-modified Na+ channels

Single Na+ channels from rat skeletal muscle were inserted into planar lipid bilayers in the presence of either 200 nM batrachotoxin (BTX) or 50 microM veratridine (VT). These toxins, in addition to their ability to shift inactivation of voltage-gated Na+ channels, may be used as probes of ion conduction in these channels. Channels modified by either of the toxins have qualitatively similar selectivity for the alkali cations (Na+ approximately Li+ greater than K+ greater than Rb+ greater than Cs+). Biionic reversal potentials, for example, were concentration independent for all ions studied. Na+/K+ and Na+/Rb+ reversal potentials, however, were dependent on the orientation of the ionic species with respect to the intra- or extracellular face of the channel, whereas Na+/Li+ biionic reversal potentials were not orientation dependent. A simple, four-barrier, three-well, single-ion occupancy model was used to generate current-voltage relationships similar to those observed in symmetrical solutions of Na, K, or Li ions. The barrier profiles for Na and Li ions were symmetric, whereas that for K ions was asymmetric. This suggests the barrier to ion permeation for K ions may be different than that for Na and Li ions. With this model, these hypothetical energy barrier profiles could predict the orientation-dependent reversal potentials observed for Na+/K+ and Na+/Rb+. The energy barrier profiles, however, were not capable of describing biionic Na/Li ion permeation. Together these results support the hypothesis that Na ions have a different rate determining step for ion permeation than that of K and Rb ions.

Interactions of permeant cations with sodium channels of squid axon membranes

To determine how the permeant cations interact with the sodium channel, the instantaneous current-voltage (I-V) relationship, conductance-ion concentration relationship, and cation selectivity of sodium channels were studied with internally perfused, voltage clamped squid giant axons in the presence of different permeant cations in the external solution. In Na-containing media, the instantaneous I-V curve was almost linear between +60 and -20 mV, but deviated from the linearity in the direction to decrease the current at more negative potentials. The linearity of instantaneous I-V curve extended to more negative potentials with lowering the external Ca concentration. The I-V curve in Li solution was almost the same as that in Na solution. The linearity of the I-V curve improved in NH4 solution exhibiting only saturation at -100 mV with no sign of further decrease in current at more negative potentials. Guanidine and formamidine further linearized the instantaneous I-V curve. The conductance of the sodium channels as measured from the tail current saturated at high concentrations of permeant cations. The apparent dissociation constants determined from the conductance-ion concentration curve at -60 mV were as follows: Na, 378 mM; Li, 247 mM; NH4, 174 mM; guanidine, 111 mM; formamidine, 103 mM. The ratio of the test cation permeability to the sodium permeability as measured from the reversal potentials of tail currents varied with the test cation concentration and/or the membrane potential. These observations are incompatible with the independence principle, and can be explained on the basis of the Eyring's rate theory. It is suggested that the slope of the instantaneous I-V curve is determined by the relative affinity of permeant cations and blocking ions (Ca) for the binding site in the sodium channel. The ionic selectivity of the channel depends on the energy barrier profile of the channel.