Fluctuation pressure on a bio-membrane confined within a parabolic potential well

Abstract

A compliant bio-membrane with a nominally flat reference configuration is prone to random transverse deflections when placed in water, due primarily to the Brownian motion of the water molecules. On the average, these fluctuations result in a state of thermodynamic equilibrium between the entropic energy of the water and the total free energy of the membrane. When the membrane is in close proximity to a parallel surface, that surface restricts the fluctuations of the membrane which, in turn, results in an increase in its free energy. The amount of that increase depends on the degree of confinement, and the resulting gradient in free energy with degree of confinement implies the existence of a confining pressure. In the present study, we assume that the confinement is in the form of a continuous parabolic potential well resisting fluctuation. Analysis leads to a closed form expression for the mean pressure resulting from this confinement, and the results are discussed within the broader context of results in this area. In particular, the results provide insights into the roles of membrane stiffness, number of degrees of freedom in the model of the membrane and other system parameters.