The Current-voltage Behavior of Ion Channels: Important Features of the Energy Profile of the Gramicidin Channel Deduced from the Conductance-voltage Characteristic in the Limit of Low Ion Concentration

Abstract

The conductance-voltage (G-V) c h a r a c t e r i s t i c of a s i n g l e -f i l i n g , m u l t ib a r r i e r , multi-occupancy channel depends i n t h e l i m i t of low i o n c o n c e n t r a t i o n upon only two parameters:t h e v o l t a g e dependence of t h e e n t r y s t e p and t h e r a t i o of t h e rate c o n s t a n t f o r l e a v i n g t h e channel t o t h a t f o r c r o s s i n g i t smiddle (14,17,20). W e show t h a t t h e G-V shape i n t h i s low c o n c e n t r a t i o n l i m i t can be measured a c c u r a t e l y u s i n g a t r i a n g u l a r wave, many-channel technique and demonstrate t h a t t h e observed shape i s incompatible w i t h t h a t expected i f t h e only important rate l i m i t i n g b a r r i e r a t low c o n c e n t r a t i o n w e r e a t t h e channel mouth. I n s t e a d t h e c e n t r a l b a r r i e r t u r n s o u t , s u r p r i s i n g l y , i n view of t h e markedly s u b l i n e a r I-V shape a t low c o n c e n t r a t i o n , t o b e even s l i g h t l y l a r g e r t h a n t h e e x i t b a r r i e r . A d d i t i o n a l l y , w e f i n d t h a t it i s n o t p o s s i b l e t o f i tboth t h e G-V shape and t h e c o n c e n t r a t i o n dependence of t h e zero-current conduct a n c e simultaneously w i t h a 3 -b a r r i e r 2 -s i t e model. However, by adding a d d it i o n a l sites t o y i e l d a 3 -b a r r i e r 4 -s i t e model e i t h e r of t h e t y p e 3B4S" where t h e e x t r a s i t e i n each channel h a l f i s e x t e r n a l t o t h e mouth of t h e channel o r of t h e t y p e 3B4S' where t h e e x t r a s i t e i s i n t e r n a l t o t h e mouth of t h e channel, w e o b t a i n good agreement.and Andersen (19) t o d i s c r i m i n a t e between 3B4S' and 3B4S" models, w e f i n d t h e 3B4S" model t o be t h e only s a t i s f a c t o r y one.

Multioccupancy models for single filing ionic channels: Theoretical behavior of a four-site channel with three barriers separating the sites

“…It is evident that each of the parameters is associated with a particular voltage and concentration dependent factor and that by measuring the current for an entire set of voltage and concentration values it is in principle possible to extract all the energy parameters of the system 9 Although the number of independent parameters is large, the uniqueness of a model can usually be established by examining the behavior in certain limits 9 The shape of the I-V curve at low concentrations, for instance, is a property which allows the shape and size of the barriers to be determined rather accurately for the empty channel (Eisenman et al, 1980Andersen, 1982a, b) and this information can then be used to fix a number of parameters in attempts to fit the entire model to experimental data.…”

“…At low concentrations all three models (3B2S, 3B4S', 3B4S') approach the same limiting behavior (Eisenman et al, 1980;H~igglund et al, 1982) cosh, dx = Cx" 2 sinh~q P~:…”

“…9A and B). In addition, certain complexities in the conductance-concentration behavior for T1, Ag and H as well as the details of the variation of permeability ratios for T1-K mixtures (Eisenman et al, 1978) and the /-V shape as a function of ion concentration (Eisenman, H~igglund, Sandblom & Enos, 1980; all suggest that it is necessary to consider the properties of channels occupiable by more than two cations in making an adequate model for the gramicidin channel. The present paper may therefore also be seen as an extension of the three-barrier two-site model (3B2S) (Hille & Schwarz, 1978; by the addition of outer sites in equilibrium with the aqueous solutions (3B4S") 1.…”

Gramicidin-mediated currents at very low permeant ion concentrations

“…These and other data suggest a first ion binding constant for Cs' in the region of 100 M'- (Neher et al, 1978;Hladky and Haydon, 1984) though they do not exclude higher values (Urban et al, 1980;Eisenman et al, 1983). Eisenman and co-workers Sandblom, 1983a, b, 1984;Eisenman et al, 1980Eisenman et al, , 1982Eisenman et al, , 1983 have recorded manychannel currents using a ramp protocol and report a significant change in shape of the current vs. voltage curve between 1.0 and 0.1 mM for Cs'. They conclude that this variation implies strong binding and have provided estimates for the first ion binding constant between 660 and 2,500 M ' (Eisenman et al, 1983).…”

“…Gramicidin A makes lipid bilayer membranes permeable to small monovalent cations and water (for reviews, see Finkelstein and Andersen, 1981;Hladky and Haydon, 1984). For sufficiently low permeant ion concentrations the rate of caesium ion movements across the membrane is limited by the rate of entry into the pores (Hladky and Haydon, 1972;Eisenman et al, 1980;Andersen, 1983c;Hladky and Haydon, 1984). Since the pores are then only rarely occupied, the conductance should increase linearly with concentration at all voltages, and thus the shape of the current-voltage relation should be independent of ion concentration.…”