(742d) Irreversible Thermodynamics of Arbitrarily Curved Lipid Membranes: Effects of Osmosis and Permeability in Non-Electrolyte Solutions

Lipid membranes are the fundamental separation structures in all eukaryotic cells, forming the boundaries of both the cell itself and the vesicles that enter/exit the cell through endo/exo-cytosis. This broad gate-keeping role of the lipid bilayer membrane means that it is involved in a wide range of important biological processes including: cell-cell signaling, ATP synthesis, and neurotransmission. Osmotic forces are known to play a key role during many biological processes, as they can induce local membrane curvature while also facilitating the transport of chemical species to and from the bulk. We extend the framework of irreversible thermodynamics of lipid membranes previous developed in [1] to include the diffusion of species from a bulk fluid across the membrane. While still regarding the lipid bilayer as a two-dimensional membrane in three-dimensional space, we view the membrane as also being embedded in a bulk fluid where the membrane may act as a surface of discontinuity for scalar, vector, and tensorial quantities such as pressure, temperature, concentration, velocity, and stress. Using the mathematical techniques of surfaces of discontinuity and differential geometry, our irreversible thermodynamics formalism yields not only the equations governing the bulk fluid but also the dynamical equations governing the lipid membrane. Additionally, we obtain extensions of the well-known Kedem-Katchalsky equations [2] governing the driving forces for solvent and solute flow across fixed membranes to arbitrarily curved and deforming lipid interfaces. In particular, our formalism allows us to propose constitutive relations between the flux of chemical species across the membrane and the corresponding osmotic and hydrodynamic driving forces. The resulting membrane equations contain a number of “jump” terms that arise naturally out of modified Divergence and Reynolds Transport Theorems. We will also discuss the non-dimensionalization of the new membrane equations, including the extended Kedem-Katchalsky equations, and give physical interpretations of the jump quantities and the physical phenomena they enforce.

[1] A. Sahu, R. A. Sauer, and K. K. Mandadapu, “Irreversible thermodynamics of curved lipid membranes”, Phys. Rev. E (2017).

[2] O. Kedem and A. Katchalsky, “Thermodynamic analysis of the permeability of biological membranes to non-electrolytes”, Biochimica et Biophysica acta (1958).