Numerical simulation of the stochastic dynamics of inclusions in biomembranes in the presence of surface tension

Abstract

The stochastic dynamics of inclusions in a randomly fluctuating biomembrane is simulated. These inclusions can represent the embedded proteins and the external particles arriving at a cell membrane. The energetics of the biomembrane is modelled via the Canham-Helfrich Hamiltonian. The contributions of both the bending elastic-curvature energy and the surface tension of the biomembrane are taken into account. The biomembrane is treated as a two-dimensional sheet whose height variations from a reference frame is treated as a stochastic Wiener process. The lateral diffusion parameter associated with this Wiener process coupled with the longitudinal diffusion parameter obtained from the standard Einsteinian diffusion theory completely determine the stochastic motion of the inclusions. It is shown that the presence of surface tension significantly affects the overall dynamics of the inclusions, particularly the rate of capture of the external inclusions, such as drug particles, at the site of the embedded inclusions, such as the embedded proteins.

Electric field effects on Nano-Scale bio-membrane of spherical cells

“…Also, thermal fluctuations of membranes are considerable, as has been studied and shown in Refs. [13,14].…”

Enhanced roughness of lipid membranes caused by external electric fields

“…Note that we use positive values for σ t to satisfy the nearly-flat assumption. Typical values for the intramembrane tension and bending rigidity of a fluctuating membrane at room temperature for different lipid materials are 10 −9 J m 2 ≤ σ 0 ≤ 10 −6 J m 2 [17] and κ 0 ∼ 10 −20 J (≃ 2.5k B T ) [20], respectively. These values correspond to the following range of values for the electric field, using equation ( 3) and ( 4), presented in Table I.…”

“…One may then proceed to obtain the height-height correlation function of the membrane in real space from which the roughness, associated with random changes in h, can be extracted. In the presence of an electric field and using the the Fourier representation of h, we arrived at the Hamiltonian [17] H = 1 2…”

“…In previous works [16,17], we computed the stochastic trajectories of objects (inclusions) existing within and on the surface of a membrane via the application of Langevin dynamics. Also, by introducing the height function as a stochastic Wiener process, a relation between random fluctuations of height and lateral diffusion of membranes was studied [17]. In this paper, we investigate the effects of electric fields on surface tension and bending rigidity and their influence on the roughness in lipid membranes.…”

On the dynamics of the interaction between triggered active inclusions

“…While these effects are rather well understood, the dynamics of elastically-mediated interactions remains a challenging subject. Mobile inclusions couple to the dynamics of the elastic medium, which produces non trivial effects [5,6,7,8], as in the dynamics of fluctuation-induced forces [9,10,11] Here, we investigate the dynamics of the force exchanged between two fixed but active inclusions, that are simultaneously triggered. For t < 0, the inclusions impose no deformation to the medium, either they are outside the medium, or they are in a state in which they do not couple with its elastic field.…”