Understanding the role of tilt-curvature coupling in lipid membrane elasticity
Understanding the role of tilt-curvature coupling in lipid membrane elasticity lead image
The elasticity of lipid membranes principally rests on two physical degrees of freedom: membrane curvature and lipid tilt. Nearly twenty years ago, researchers Hamm and Kozlov (“HK”) introduced a two-dimensional membrane Hamiltonian, or mechanical functional used to describe a dynamic system, that extended Helfrich’s seminal curvature-elastic Hamiltonian to account for both membrane curvature and lipid tilt within a unified elastic framework. Researchers at Carnegie Mellon University led by Markus Deserno have recognized a fundamental inconsistency in the prominent HK model and proposed a novel and more accurate theory in The Journal of Chemical Physics.
The authors explain that HK’s theory misses an important tilt-curvature coupling that influences functions of membrane shape and lipid tilt.
With the authors’ amended novel tilt-curvature coupling, they characterize two features. The first is the Gaussian curvature modulus as the Euler-Lagrange equation’s prefactor. The Gaussian curve modulus helps overcome the “Gauss-Bonnet irrelevance” and accommodates the extraction of the modulus in a manner suited to the power spectra of membrane shape, lipid tilt, and director fluctuations.
The second feature is the redefinition of an elastic monolayer ratio as a dimensionless parameter in the modified Euler-Lagrange equation, yielding a stronger coupling to the membrane curvature gradient within the tilt fields of both monolayers and bilayers when the value of the parameter lies between 1 and zero (HK’s theory sets this parameter to zero).
In this new theory, the monolayer Gaussian curvature modulus appears outside of its Gaussian curvature origin, creating an opportunity to measure this fundamental property by “more conventional means.”
Coauthor Markus Deserno says HK’s work remains “extremely fruitful,” enabling more precise understanding of membrane curvature and elasticity.
Source: “Novel tilt-curvature coupling in lipid membranes,” by M. Mert Terzi and Markus Deserno, The Journal of Chemical Physics (2017). The article can be accessed at https://doi.org/10.1063/1.4990404 .
