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Alamethicin-induced conductances in lipid bilayers: I. Data analysis and simple steady-state model

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Summary

Conductance fluctuations induced by low concentrations of alamethicin in planar lipid bilayer membranes have been examined with a novel computer-aided analysis. A precise test is applied to show that the system is Markovian (except for the zeroth state) and an estimate is given for the (small) number of transitions between nonadjacent states: the system closely conforms to a birth-and-death process.

The complete set of rate parameters governing the steady-state distribution is derived, and it is shown that these parameters can be used to reconstruct exactly the experimental relative frequency distribution. It is also shown that the electrochemical free energies of the conductance states vary quadratically with state number for low-lying states; the free energies of activation of both the birth and death processes are linearly related to the free-energy differences between states but the transfer coefficient is close to unity. A detailed model based on the nucleation of a two-dimensional pore accounts for these observations provided both birth and death take place via an intermediate expansion of the pore lumen. This model requires two energy parameters, the “edge” and “bulk” energies of the pore, together with a trigger rate of the initial process which is a sufficient description for the steady-state behavior of this voltage-controlled system.

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Abbreviations

♯ j :

Thej th state of the system,j≧0.

P j (t) :

The probability of finding the system in ♯ j at timet

P s j :

The steady-state probability of finding the system in ♯ j , t=∞

P eq j :

The hypothetical equilibrium probability of finding the system in ♯ j

P j :

The observed relative frequency for the system being in ♯ j , an, average taken over the considered section of data

w j :

The reciprocal of the mean dwell-time in ♯ j , Eq. (3); (sec−1)

N j :

The calculated total number of dwell-times in ♯ j for the considered section of data, Eq. (3)

λ j :

The rate of birth for the transitionj»j+1, Eq (6a); (sec−1)

υ j :

The rate of death for the transitionj→j−1, Eq. (6b); (sec−1)

I :

The sampling rate, 20,000 for the data given in this paper; (sec−1)

I(t) :

The instantaneous current at timet; (A)

φ I (τ):

The current autocorrelation function, Eq. (11); (A 2)

G I (w):

The current power spectral density, Eq. (12); (A 2 Hz−1)

\(\bar g(j)\) :

The electrochemical free energy of ♯ j ; (J)

\(\Delta \bar g_j\) :

The change in electrochemical free energy for the transition ♯ j to ♯ j+1.

ℱ(j):

A frequency factor representing a multiplicity in transitions between states

k :

Boltzmann's constant; 1.38×10−23 JK −1

T :

Absolute temperature, 294K for the data given in this paper

K :

A constant

k λ :

A standard rate constant in the forwards direction of increasing state; (sec−1)

k μ :

A standard rate constant in the reverse direction of decreasing state; (sec−1)

N c :

Number concentration of alamethicin units at the bilayer/electrolyte interface; (dm −3)

k → :

A standard rate constant in the forwards direction of increasing state independent of the number concentrationN c ; (dm 3 sec −3)

α:

Linear fraction of the free-energy difference,\(\Delta \bar g_j\)

δ0,j :

Kroenecker delta: unity ifj=0 and zero elsewhere

ψ:

“Bulk” free-energy of replacing membrane lipid by electrolyte, Eq. (25) and Appendix 2; dimensionless

σ:

“Edge” free energy of interaction electrolyte/alamethicin/membrane lipid, Eq. (25) and Appendix 2; dimensionless

h :

The length of a cylindrical pore: thickness of the membrane; (m)

a :

The short dimension of an alamethicin molecule, at the interfacial perimeter; (m)

v :

The volume of a water molecule; (m3)

χ:

The free-energy for replacing membrane by water per unit molecule, Appendix 2; (J m−3)

ζ:

The free energy of the edge interaction in the sandwich electrolyte/alamethicin/membrane per unit area of pore exposed to membrane, Appendix 2; (J m−2)

n * :

Critical size of a nucleus

γ:

The surface energy of the water/lipid/water interphase; (J m−2)

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Author notes

  1. C. Gabrielli

    Present address: Groupe de Recherches No. 4 du C.N.R.S., Physique des Liquides et Electrochimie, associé à l'Université Pierre et Marie Curie, 4, Place Jussieu, 75230, Paris, Cedex 05, France

  2. T. H. Wilmshurst

    Present address: Department of Electronics, The University, S09 5NH, Southampton, England

Authors and Affiliations

  1. Department of Chemistry, The University, S09 5NH, Southampton, England

    M. Fleischmann, C. Gabrielli, M. T. G. Labram, A. I. McMullen & T. H. Wilmshurst

Authors
  1. M. Fleischmann
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  2. C. Gabrielli
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  3. M. T. G. Labram
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  4. A. I. McMullen
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  5. T. H. Wilmshurst
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Fleischmann, M., Gabrielli, C., Labram, M.T.G. et al. Alamethicin-induced conductances in lipid bilayers: I. Data analysis and simple steady-state model. J. Membrain Biol. 55, 9–27 (1980). https://doi.org/10.1007/BF01926367

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  • DOI: https://doi.org/10.1007/BF01926367

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