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The plasma membrane is second only to the genetic material as a signature of life. It is also the membrane that is wrapped around cellular organelles. Its role in both the shape and dynamics of cells cannot be overemphasized. At its simplest, it is a bilipid layer embedded with proteins and connected with an underlying cytoskeleton.
I shall start with a few general comments about application of mathematics to model natural phenomena at large length and slow time scales. Then I shall show how these general principles are used to build an increasingly complex model of the plasma membrane. Starting with elasticity of simple isotropic two dimensional surfaces embedded in three dimensions, I shall progressively complicate the problem by: (a) moving from plates to shells; (b) studying buckling (which is a key nonlinear effect); (c) adding active (non--equilibrium) processes; and (d) finally arrive at a model of plasma membrane which is simultaneously a (two--dimensional) fluid and solid. In summary, the plasma membrane is an active, heterogeneous, and nonlinear material. Its mathematical understanding must come from a general framework of soft active materials.
References :
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F Stridfeldt, et al Proceedings of the National Academy of Sciences 122 (16), e2414174122, 2025
[2] Measuring red blood cell deformability and its heterogeneity using a fast microfluidic device
S Kumari, et al Cell Reports Physical Science 5 (8), 2024
[3] Estimate of entropy production rate can spatiotemporally resolve the active nature of cell flickering
SK Manikandan, et al Physical Review Research 6 (2), 023310 2024
[4] Anomalous diffusion and effective shear modulus in a semi-solid membrane
V Pandey and D Mitra arXiv preprint arXiv:2404.12211
[5] Active buckling of pressurized spherical shells: Monte carlo simulation
V Agrawal, V Pandey, and D Mitra Physical Review E Letters 108 (3), L032601 2023 |