Biological membranes from the perspective of smart materials – A theoretical study

Abstract

a b s t r a c tThe unique properties and diverse functionality of biological membranes make them excellent candidates for nano-scale applications, such as sensors and actuators. Taking the view of biological membranes as smart bio-materials, we study the behavior of a simply supported beam made from a biological membrane-like material. Equilibrium configurations are derived by calculating the first variation of a generalized Helfrich energy, and their stability is examined by means of the second variation. Our numerical results demonstrate the richness of phenomena exhibited by these structures, in accordance with experimental observation of multi-component vesicles. Further, we demonstrate that the intriguing behavior of biological membrane beams, which is fundamentally different from standard beams and from standard Cahn Hilliard systems, can be utilized for actuation and sensing. For example, temperature and also pressure difference across the membrane can be indirectly measured by gauging the fluorescence intensity of the membrane components.

Curvature-Induced Spatial Ordering of Composition in Lipid Membranes

“…Typically, a value of n 1 = 100 was used to discretize a single length unit (or λ in dimensional length). We adopt a conservative second-order numerical scheme with adaptive time stepping [ 44 , 45 , 56 , 57 ]. Figure 2 shows snapshots of the composition field at different times, where a color scale is used to describe the level of local concentration.…”

“…Theoretical models have generalized uniform composition models [ 24 – 27 ] to account for multicomponent or multiphase membranes [ 28 – 35 ]. Features such as equilibrium configurations, stability [ 36 – 39 ], interaction with the cytoskeleton [ 40 – 42 ], formation of lipid rafts, anisotropy of the membrane constituents [ 43 ], and even using biomembranes as sensors or actuators [ 44 , 45 ] have been investigated. The complexity of the problem has forced the usage of sophisticated numerical methods, such as advanced phase field schemes, special nonlinear finite elements, and molecular dynamics simulations [ 17 , 46 – 50 ], while analytical derivations have commonly adopted simplifying assumptions, like small deformations, axisymmetry, and so forth.…”

A theoretical study of biological membrane response to temperature gradients at the single-cell level

“…In order to demonstrate the phenomena exhibited by (2.6) and (2.7), we set the following: the spontaneous curvature is linear with the composition, H 0 (c) ¼ K c (c 2 c 0 ) [23]; the free energy of mixture is assumed to behave according to the regular solution model [24] …”

“…with the four boundary conditions c ,x j x¼0,1 ¼ 0 and J m j x¼0,1 ¼ 0 [22]. The variation of the free energy with respect to the deflection dictates the following quasi-equilibrium deflection equation [23] k(w ,xx À H 0 (c)) ,xx À p ¼ 0, (2:6) with four boundary conditions wj x¼0,1 ¼ 0 and (w ,xx 2 H 0 (c))j x¼0,1 ¼ 0. We consider a particular case of a uniform load, p(x,t) ¼ p 0 ¼ const., and after some manipulation on (2.6), (2.5) takes the form…”

“…The variation of the free energy with respect to the deflection dictates the following quasi-equilibrium deflection equation [23] …”