Eigenvectors determination of the ribosome dynamics model during mRNA translation using the Kleene Star algorithm

Indonesian Operations Research Association - International Conference on Operations Research 2017

Ernawati^1 ; Carnia, E.^2 ; Supriatna, A.K.^2

Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia^1

Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Padjadjaran, Indonesia^2

关键词: Dynamics modeling;    Eigenvalues and eigenvectors;    Learning Activity;    Max-plus algebra;    Production system;    Protein production;    Protein translation;    Train systems;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/332/1/012019/pdf
DOI  :  10.1088/1757-899X/332/1/012019

来源: IOP

【 摘 要 】

Eigenvalues and eigenvectors in max-plus algebra have the same important role as eigenvalues and eigenvectors in conventional algebra. In max-plus algebra, eigenvalues and eigenvectors are useful for knowing dynamics of the system such as in train system scheduling, scheduling production systems and scheduling learning activities in moving classes. In the translation of proteins in which the ribosome move uni-directionally along the mRNA strand to recruit the amino acids that make up the protein, eigenvalues and eigenvectors are used to calculate protein production rates and density of ribosomes on the mRNA. Based on this, it is important to examine the eigenvalues and eigenvectors in the process of protein translation. In this paper an eigenvector formula is given for a ribosome dynamics during mRNA translation by using the Kleene star algorithm in which the resulting eigenvector formula is simpler and easier to apply to the system than that introduced elsewhere. This paper also discusses the properties of the matrix Bλ⊗nof model. Among the important properties, it always has the same elements in the first column for n =1, 2, if the eigenvalue is the time of initiation, λ =τin, and the column is the eigenvector of the model corresponding to λ.