Actin and amphiphilic polymers influence on channel formation by Syringomycin E in lipid bilayers

Abstract

The bacterial lipodepsipeptide syringomycin E (SRE) added to one (cis-) side of bilayer lipid membrane forms voltage dependent ion channels. It was found that G-actin increased the SRE-induced membrane conductance due to formation of additional SRE-channels only in the case when actin and SRE were applied to opposite sides of a lipid bilayer. The time course of conductance relaxation depended on the sequence of SRE and actin addition, suggesting that actin binds to the lipid bilayer and binding is a limiting step for SRE-channel formation. G-actin adsorption on the membrane was irreversible. The amphiphilic polymers, Konig’s polyanion (KP) and poly(Lys, Trp) (PLT) produced the actin-like effect. It was shown that the increase in the SRE membrane activity was due to hydrophobic interactions between the adsorbing molecules and membrane. Nevertheless, hydrophobic interactions were not sufficient for the increase of SRE channel-forming activity. The dependence of the number of SRE-channels on the concentration of adsorbing species gave an S-shaped curve indicating cooperative adsorption of the species. Kinetic analysis of SRE-channel number growth led to the conclusion that the actin, KP, and PLT molecules form aggregates (domains) on the trans-monolayer. It is suggested that an excess of SRE-channel formation occurs within the regions of the cis-monolayer adjacent to the domains of the adsorbed molecules, which increase the effective concentration of SRE-channel precursors.

Appendix

It is assumed that domain growth is a slow process that results from changes in the surface energy of a bilayer, Σ(t), with redistribution between areas AM(∞)S _s and S _m (domain occupied and unoccupied, respectively). The energy gained under such redistribution should be spent on a dissipative process of inclusion of actin- KP-or PLT-species into the domains. In other words, the sum of the surface and dissipated energies, W(t), is equal to zero at any time t of the process, as follows:

$$\Sigma (t) + W(t) = 0$$

(10)

This condition of the energy balance was first applied by Deryaguin to the consideration of capillary impregnation of grounds (Deryaguin 1946) and also to the cases of capillary rising, spreading of lenses, and black spot growth on lipid membranes (Malev and Matveeva 1981, 1983; Malev and Gribanova 1983), i.e. the processes of wetting, which are similar to what is being considered here. The surface energy of the membrane, containing AM(∞) domains of the same surface equal to S_s (see above) and S _m=A − AM(∞)S _s of unmodified surface, can be represented as follows:

$$ \Sigma (t) = \int\limits_0^t {[\sigma _{\text{m}} {\text{d}}S_{\text{m}} /{\text{d}}\tau ] + \sigma _{\text{s}} AM(\infty ){\text{d}}S_{\text{s}} /{\text{d}}\tau ]{\text{d}}\tau } + 2\pi AM(\infty )\gamma \int\limits_0^t {[{\text{d}}r(\tau )/{\text{d}}\tau ]{\text{d}}\tau } $$

(11)

If the domain growth only determines the dissipated energy, it can be written in the following form

$$ \begin{aligned} W(t) & = - AM(\infty )\kappa \int\limits_0^t {S_{\text{R}} U[(1/S_{\text{R}} ){\text{d}}N_{\text{a}} /{\text{d}}\tau ]{\text{d}}\tau } \\ & = - AM(\infty )\kappa P\int\limits_0^t {S_{\text{R}} [(1/S_{\text{R}} ){\text{d}}N_{\text{a}} /{\text{d}}\tau ]^2 {\text{d}}\tau } \\ \end{aligned} $$

(12)

Here, dN _a/dτ is the rate of changing the number of actin, KP or PLT species in a separate domain; U is an unknown moving force of inclusion of adsorbed species into the domain (with U=(P/S _R )dN _a/dτ if deviations from equilibrium are small); P is the resistance of the inclusion process; S _R=S _s=π r ²(t) in the case of inclusion of the species from aqueous solution, but S _R=2π r(t) in the alternative case of their inclusion from an adsorbed state (see above); κ is a factor of proportionality between the heat dissipated from a separate domain for unit time and the power S _R U[(1/S _R)dN _a/dτ] of the inclusion process. Substituting Eqs. 11, 12 into Eq. 10 and then differentiating the obtained equation with respect to time t, one obtains the following result:

$$\sigma _{\rm m} {\rm d}S_{\rm m} /{\rm d}t + \sigma _{\rm s} AM(\infty ){\rm d}S_{\rm s} /{\rm d}t + 2\pi AM(\infty )\gamma {\rm d} r(t)/{\rm d}t = AM(\infty )(\kappa P/S_{\rm R})[{\rm d}N_{\rm a} /{\rm d}t]^{2} $$

(13)

If area a ₀ occupied by an adsorbed particle is independent of the domain radius r(t), dN _a/dt=(1/a ₀)dS _s/dt=[2π r(t)/a ₀]dr(t)/dt. As a result, Eq. 13 reduces to

$$\sigma _{s} - \sigma _{m} + \gamma / r(t) = \mu {{\rm d}r(t)} / {{\rm d}t} \quad {\text{at}}\; S_{R} = 2\pi r(t),\;(\mu = \kappa P/a^{2}_{0})$$

(14)

and

$$\sigma _{\rm s} - \sigma _{\rm m} + \gamma /r(t) = {\left[ {\mu _{0} /r(t)} \right]}{\rm d}r(t)/{\rm d}(t)\quad {\text{at}}\;S_{R} = r^{2} (t),\;(\mu _{0} = 2\kappa P/a^{2}_{0})$$

(15)

In the general case, all tensions included in the above equations are dependent on the concentrations of adsorbing particles in the unmodified regions of the trans-side of the membrane. This is not the case if the rate of adsorption (on unmodified regions of the bilayer) is higher than that of domain growth. If so, the difference (σ_m − σ_s) can be replaced with γ/r(∞) in accordance with the equilibrium condition given by Eq. 6. As a result, Eqs. 14 and 15 take the forms of Eqs. 7 and 8, respectively. Note that, in the partial case of the black spot growth on colored lipid membranes (Malev and Matveeva 1983), the rate of the domain growth, dr(t)/dt, is constant and proportional to (σ_m–σ_s), since the value of this difference is high enough and cannot be compensated by linear tension γ at any macroscopic value of the spot radius, r(∞).

In Eq. 11 it is assumed that possible gradients in the concentration of separate adsorbing particles are absent within unmodified regions of trans-side of the membrane. This assumption is correct for absorption of particles into domains from aqueous solution, but may be invalid for inclusion from their adsorbed state. Eq. 11 can be written in a form that accounts for gradients of the adsorbing species, but a problem arises with such attempts. Unlike the previous considerations, an equation for the domain radius increase must be put in a concrete form, since resistance P (see the paragraph before Eq. 13) of the inclusion process should depend on the concentration of adsorbed particles at distance r(t) (i.e. the domain radius) from the domain centre. Parameters γ/μ r ²(∞)=γ a ²₀ /κ Pr ²(∞) and γ/μ₀ r(∞)=γ a ²₀ /2κ Pr(∞) of Eqs. 7a and 8a, respectively, might be dependent on the concentration of adsorbing particles, since the equilibrium radius r(∞) must obviously increase with increasing concentration C _a. In particular, r ²(∞) should be proportional to concentration C _a according to the phase theory of micelle formation (domain formation in our case). On the other hand, resistance P included in the above parameters is, most likely, in reverse proportion to concentration C _a, as is characteristic for heterogeneous process. If so, γ a ²₀ /κ Pr ²(∞) turns out independent of concentration C _a, while γ a ²₀ /2κ Pr(∞) ∼ C ^1/2_a . Taking into account the observed increase in the kinetic dependence of ln [1 − r(t)/r(∞)] vs. time t with increasing C _a (inset to Fig. 7a), it is speculated that a direct inclusion of actin molecules into domains from aqueous solution is more probable than the mechanism with participation of adsorbed actin species.