Intrinsic reaction-cycle time scale of Na+,K+-ATPase manifests itself in the lipid-protein interactions of nonequilibrium membranes

Abstract

Interaction between integral membrane proteins and the lipid-bilayer component of biological membranes is expected to mutually influence the proteins and the membrane. We present quantitative evidence of a manifestation of the lipid-protein interactions in liposomal membranes, reconstituted with actively pumping Na(+),K(+)-ATPase, in terms of nonequilibrium shape fluctuations that contain a relaxation time, τ, which is robust and independent of the specific fluctuation modes of the membrane. In the case of pumping Na(+)-ions, analysis of the flicker-noise temporal correlation spectrum of the liposomes leads to τ ~/= 0.5 s, comparing favorably with an intrinsic reaction-cycle time of about 0.4 s from enzymology.

Fig. 1.

For a proteoGUV of DOPC/DOPS/Chol/ATPase, a radius of 12.97 μm in the presence of 1 mM of ATP is shown: (A) Experimental distribution of the Fourier amplitudes of the contour fluctuations; α⁵ or β⁵. (B) Plot of the normalized temporal cross-correlation function between modes 5 and 6. Mode 5 has been chosen randomly among the midrange modes (4–10), which have good statistics and are not limited by the video integration time. The solid curve in A is the best fit of the data to a Gaussian.

Fig. 2.

Normalized temporal correlation function for mode n = 5 for proteoGUVs of DOPC/DOPS/Chol/ATPase of similar reduced membrane tension. (A) Nonactive membranes in the absence of ATP conforming to a monoexponential form of the short-time decay (solid line). (B) Active membranes in the presence of ATP (1 mM) conforming to a double-exponential form for the full duration of the experiment. The double-exponential fit is illustrated by the solid line. The corresponding decay constants (relaxation times) for the first and second exponentials are depicted in Fig. 3.

Fig. 3.

Relaxation time as a function of mode number, n, for active membranes consisting of a proteoGUV of DOPC/DOPS/Chol/ATPase in the presence of ATP, (compare with Fig. 2B). (A) The initial relaxation time scales as τ₁ ∼ n^–3.1 for modes in the range of 2–12. (B) Second relaxation time, τ₂, is found to be independent of mode number for n ≳ 8. The error bars are calculated from the double-exponential fit for each exponential parameter and subsequently converted to an error bar for each relaxation time.