VECTOR SPACE AND LIE ALGEBRA OF GENETIC CODE

• Main Author: Ummi Safitri, Qonita
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/42343
• Institution: Institut Teknologi Bandung

This thesis examines the construction and utilization of vector space and Lie algebra on genetic code. The genetic code is a set of instructions in genes that express amino acids. Each genetic code represent an extention of the four- bases of Deoxyribonucleic Acid (DNA) or Ribonucleic Acid (RNA). The DNA bases are Adenine (A), Guanine (G), Cytosine (C) and Thymine (T). Whereas in RNA, the base Thymine (T) changes to Uracil (U). The study focused on RNA bases because RNA is single-stranded copy of DNA in protein synthesis and it can be used as a framework for building molecular machines. The main result of this thesis is the construction of the vector space of genetic code ensuring other structures can be dened. Structures that can be built from the genetic code vector space are the quotient space, Lie algebra and the linear transformation. Quotient space divides the genetic code based on its physicochemical proper- ties. This shows that the determination of the genetic code table is not done randomly. The Lie algebra divides the genetic code into collinear sets. The collinear set is related to the polarity of amino acids in the process of pro- tein interaction and the average contact of amino acid energy in the protein interior. Finally, linear transformation in vector space re ects the process of substitu- tion mutation in the genetic code. Further studies show that the substitution mutation process can be seen as a local diagonal automorphism in the gene- tic code vector space. This result is also shown by the transformation of the LK ITB5a lipase gene mutated with Polymerase Chain Reaction (PCR), whe- re the transformation matrix is a diagonal matrix with non-zero determinants. Furthermore, the local automorphism preserve the Lie algebraic structure in the genetic code.