Abstract
It is known that many protein complexes are made of smaller identical subunits. The mechanism of assembly of those subunits to form a complete complex is still not well understood. In this work we use a Smoluchowski coagulation equation as a mean-field approximation, and study the efficiency of the process of formation of membrane protein complexes by considering both irreversible aggregation and fragmentation. Our objective is to analyze the possible ways biological organisms adapted to avoid wastage, and achieve a fast formation of the required number of complexes.
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Notes
- 1.
- 2.
- 3.
The primary structure of a protein is its amino acid sequence. The secondary structure the \(\alpha\)-helices and \(\beta\)-sheets. The tertiary represents the chain fold. The quaternary structure is the assembly of those folded polypeptide chains.
- 4.
In this notation C represents the cyclical symmetry of the protein and n the number of subunits that compose this protein. For example: \(C_6\) is a cyclic hexamer.
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The mechanosensitive channels are described in detail in this chapter.
- 6.
This operator corresponds to the Laplace operator on a curved surface.
- 7.
The maximum time that it takes for the particle to find the cap corresponds to the starting point \(\theta = \pi\) \(W(\pi) = {\frac{2R^2}{D}} \hbox{ln} \left({\frac{R}{r}}\right)\!.\)
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Guseva, K. (2012). The Role of Fragmentation on the Formation of Homomeric Protein Complexes. In: Formation and Cooperative Behaviour of Protein Complexes on the Cell Membrane. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23988-5_2
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