Abstract
We discuss an example of self-organization in a biological system. It arises from long-range ion–ion interactions, and it leads us to propose a new kind of enhanced conduction in ion channels. The underlying mechanism involves charge fluctuations near the channel mouth, amplified by the mismatch between the relative permittivities of water and the protein of the channel walls. We use Brownian dynamics simulations to show that, as in conventional ‘knock on’ permeation, these interactions can strongly enhance the channel current; but unlike the conventional mechanism, the enhancement occurs without the instigating bath ion entering the channel. The transition between these two mechanisms is clearly demonstrated, emphasizing their distinction. A simple model accurately reproduces the observed phenomena. We point out that electrolyte plus protein of low relative permittivity are universal in living systems, so that long-range ion–ion correlations of the kind considered must be common.
Highlights
We have shown by semi-analytic analysis of the archetypal model, and by Brownian dynamics (BD) simulations, that a mechanism of enhanced conduction may exist in ion channels that differ from the standard knock on mechanism
For a value of the fixed protein charge Qf smaller than that required for standard knock on, this new mechanism can be dominant
Despite the highly simplified character of our archetypal model, both the current–concentration dependence shown in figure 3(a), and the dependence on the mouth charge shown in figure 4(b), are in semi-quantitative agreement with experimental observations [37] in the physiological range of parameters
Summary
The archetypal model [21, 22] of an ion channel views it as an open cylindrical pore of radius R and length L, through an impermeable membrane. A solution of the Poisson equation demonstrating this effect for an additional ion at the channel mouth (x = −15 Å) is shown by the dashed line in figure 2 (with the singularity at the mouth removed to simplify the figure) This strong modulation of the potential barrier is attributable to focusing of the electric field inside the channel [31, 32] leading to an almost linear decay of the potential along the channel axis. For the ion at the binding site with coordinate xi , the interaction term j=i φi j (xi , x j ) describes a random non-equilibrium modulation of the channel potential. We will show that the combination of this modulation with thermal agitation can result in a strong enhancement of the current through the channel even without the second ion entering the channel
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