Nonlinear system lipid membrane

The phenomenological description of the excitability phenomenon given in Section 1.3 cannot claim to contain a final solution to the problem of the nature of transport systems of biological membranes responsible for nervous impuse generation. Where we stand, we can only conclude that the membrane as a whole is a nonlinear ion conductor whose properties are largely dependent upon the electrice field. For all that, the fact that the use of certain specific blocking compounds—tetrodotoxin and tetraethylammonium—allows the sodium and potassium ionic currents to be separated is alone sufficient to support the conception of selective transport systems located in the lipid matrix... 

At leading (quadratic) order in h, the three tension-like quantities, Tframe. Uuo and Fq, thus have identical values. Nevertheless, they might differ from each other due to nonlinear corrections [90, 164—167]. For instance, the bare tension Fq is expected to deviate from the frame tension Fframe due to the effect of fluctuations. The exact value of the correction depends on the ensemble and differs for systems with a fluctuating number of lipids (variable number of undulating modes) or a fixed number of lipids (fixed number of modes). The former case was analyzed by Cai et al. [165] and the latter case by Farago and Pincus [168] and subsequently by a number of other authors [169-171]. Interestingly, the correction has an additive component in both cases. Hence a stress-free membrane has a finite bare tension. 

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