Abstract
The function of Chap. 14 has been to help the reader learn the details of how to use the EMT. The main body of the explanation has centered on the description of molecules moving in cell membranes. After a brief description of the physics of the field, we described an ordered model and then a disordered version of that model to understand observed phenomena. The ordered model consisted of periodically placed defects representing barriers for molecular motion arising from interaction with the cytoskeleton of the cell. It involved a standard application of the defect technique and was successful in explaining experiment. However, addressing static disorder in the barrier heights or barrier placements was beyond its reach. To describe that aspect we considered the disordered model in which we allowed the barrier heights to be random variables, then did the same with barrier placements and finally with both quantities. EMT methods were introduced and explained step by step. They led both to the calculation of time-independent and time-dependent effective quantities of relevance to the observations. Various probability distributions were used as input and the theory was worked out in detail. Mention was also made of the application of EMT to motion on networks. A careful examination of these examples should help the reader in learning the methods of the EMT.
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Notes
- 1.
Long before we decided to undertake the cell membrane analysis, I had some of the primary calculations for the ordered system ready. This was so because, decades earlier, I had worked them out for an unrelated physical system: Frenkel excitons supposedly rattling in cages whose walls were created by energy mismatch of ordinary and deuterated molecules in tetracholobenzene. I find myself always intrigued by Feynman’s well-known remark that “the same equations have the same solutions.” It is usually attributed to him as having expressed in Chap. 12 of volume II of his Lectures in Physics. I could make little out of the cage rattling in the Frenkel exciton context but it served us well (my collaborators Luca Giuggioli and Ziya Kalay, and me) when we turned to cell membranes!
- 2.
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Kenkre, V.M.(. (2021). Effective Medium Theory Application to Molecular Movement in Cell Membranes. In: Memory Functions, Projection Operators, and the Defect Technique. Lecture Notes in Physics, vol 982. Springer, Cham. https://doi.org/10.1007/978-3-030-68667-3_14
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