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.