Numerical Simulation Of Phase Separation In Binary Lipid Membrane Under Shear Flow

Along with the continuous development of biological science, researches in cell-membrane are becoming more and more broad and embedded. The study of cell-membrane's structure and function has been a hot subject concerning biology, chemistry and physics. Separating the cell's internal contents from the external environment, cell-membrane is playing an extremely important role in life activities. Veritable cell-membrane is a complicated system, the essential constitution of which is the bilayer formed spontaneously by amphiphilics in aqueous solution. Protein molecules studded in the bilayer actualize the exchange of materials and signals between the inside and outside of the cell, and also some other biological functions. Thus, via working on artificially synthesized binary or multi-component lipid membranes, many of cell-membrane's fundamental structural characters as well as its physiological functions and behaviors could be investigated.In cell-membrane, there are many peculiar domains enriched in cholesterol and sphingolipids, which are called"lipid rafts". Lipid rafts are representing very crucial roles in a large number of physiological processes, such as signal transfer, protein sorting, and viral budding, etc. The formation of lipid rafts is closely related to the phase separation of lipids in cell-membrane under special conditions (e.g. with suitable temperature). Mainly living in fluid environment, cells will certainly suffer the shear effect from flows, which is expected to bring about significant influence during the process of phase separation and raft formation. Due to the limitations of experimental researches, such as technique difficulties and high expenses, methods of numerical simulations have been constantly developed and perfected in recent years. With this, lots of valuable results which presently are not acquirable through experiments have been obtained.In the present work, we educed the systematic energy functional of the binary lipid membrane model. And based on the phase kinetics of continuous systems, we established the governing equations for the phase separation in binary lipid membrane under stationary shear flow. Then, by means of the cell dynamical system (CDS) approach, the equations were numerically solved, intuitively giving out the domain morphologies and membrane shapes. In order to more quantitatively describe this phase separation process, first of all we simulated the evolution of the small-angle scattering pattern. Subsequently, the time growth laws of the characteristic domain sizes in both directions parallel and perpendicular to the flow are discussed, and the variation of the membrane's rheological properties as well.Compared to the case of stationary shear flow, we then simulated and discussed how oscillatory shear flows with different frequencies and amplitudes would influence the phase separation in binary lipid membrane. Finally, so as to much more exactly reveal the actual situation in cell-membrane, we respectively constructed a continuum model and a particle model to simulate the phase separation in binary membrane containing protein inclusions. Comparing the results derived from the two models, we analyzed the coupling effect of the inclusion amount and the shear strength.