Interpretation of Phase Boundary Fluctuation Spectra in Biological Membranes with Nanoscale Organization

In this work, we use support vector machine algorithm to detect simple and complex interfaces in atomistic and coarse-grained molecular simulation trajectories of phase-separating lipid bilayer systems. We show that the power spectral density of the interfacial height fluctuations and, in turn, the line tension of the lipid bilayer systems depends on the order parameter used to identify the intrinsic interface. To highlight the effect of artificial smoothing of the interface on the fluctuation spectra and the ensuing line tension calculations, we perform a convolution of the boundaries identified at molecular resolution with a 2D Gaussian function of variance ε² equal to the resolution limit, (1/2πε²)­exp­( – |r|²/2ε²). The convolution function is given by h ⊗ g where h is the instantaneous height fluctuation, and g is the Gaussian function. This is similar to the effect of point spread functions in experiments. We find that the region of fluctuation spectra that scales according to capillary wave theory formalism depends on the complexity of the interfacial geometry, which may not always be detected at experimental resolutions. We propose that the different k regimes in the fluctuation spectra can be used to characterize mode-dependent interfacial tensions to understand the interfaces beyond the linear line tension calculations.