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Categorical Abstractions of Molecular Structures of Biological Objects: A Case Study of Nucleic Acids

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Abstract

The type-level abstraction is a formal way to represent molecular structures in biological practice. Graphical representations of molecular structures of biological objects are also used to identify functional processes of things. This paper will reveal that category theory is a formal mathematical language not only to visualize molecular structures of biological objects as type-level abstraction formally but also to understand how to infer biological functions from the molecular structures of biological objects. Category theory is a toolkit to understand biological knowledge at the type-level formally, not individual token-level, as well as typical heuristic strategies in molecular biology.

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Notes

  1. Its reverse reaction is said to be hydrolysis which means the reverse chemical activity among molecules, called breaking.

  2. The linkages between amino acids are called peptide bonds.

  3. Sugars are of two types, ribose, and deoxyribose, within a nucleic acid. The prefix ‘deoxy’ indicates that the 2’-carbon atom of sugar lacks an oxygen atom linked to the 2’-carbon atom of ribose, containing both a hydrogen atom and an oxygen atom. The difference between the two sugars distinguishes the type of nucleic acid. It is well known that there are two constituents of nucleic acids, DNA-containing deoxyribose, and RNA-containing ribose. Nitrogenous bases are derivatives of two classes, purine, and pyrimidine. DNA and RNA contain two purine bases, adenine (A) and guanine (G), and two major pyrimidines. One of the pyrimidines in DNA and RNA is cytosine (C). However, the second common pyrimidine is thymine (T) in DNA or uracil (U) in RNA.

  4. Each polypeptide chain of proteins also has a structural feature, orientation from an amino (or N–terminal) end to a carboxyl (or C–terminal) end.

  5. Nucleosides are important because they individually indicate genetic information within DNA (and RNA). In particular, four bases within nucleosides determine the type of genetic information. However, individual nucleosides should be arranged within a certain frame or backbone to stabilize DNA and play a role in normal metabolic processes, such as DNA replication or transcription in protein synthesis. Nucleotides contribute to this requirement by attaching a phosphate to individual nucleosides. Therefore, nucleotides are new compounds at a higher level than nucleosides because of the additional bond by which a phosphate (represented by a circled ‘P’ in Fig. 4) links to a nucleoside.

  6. For individual nucleotides, depicted by the dashed lines Fig. 4, to be categories by definition, an individual phosphate molecule, a sugar molecule, and a base molecule must have their identity morphism. Those identity morphisms can be assigned by considering the chemical interactions of the three molecules with water in the condition of the solution. However, those precise descriptions are omitted here for simple illustrations.

  7. The structure proposed by Watson and Crick has two properties of central importance to the role of DNA as the hereditary material (Stryer et al. 2017). First, the structure is compatible with any sequence of bases. While the bases are distinct in structure, the base pairs have essentially the same shape and, thus, fit equally well into the center of the double-helical structure of any sequence. Without any constraints, the sequence of bases along a DNA strand can efficiently store information. Indeed, the sequence of bases along DNA strands is how genetic information is stored. The DNA sequence determines the sequences of the ribonucleic acid (RNA) and protein molecules that carry out most of the activities within cells. Second, because of base pairing, the sequence of bases along one strand ultimately determines the sequence along the other strand. As Watson and Crick so shortly wrote: “It has not escaped our notice that the specific pairing we have postulated immediately suggests a possible copying mechanism for the genetic material” (Watson and Crick 1953a, p.737). Thus, if the DNA double helix is separated into two single strands, each strand can act as a template for generating its partner strand through the specific base-pair formation. The three-dimensional structure of DNA beautifully illustrates the close connection between molecular structure and function.

  8. In the translational transition from mRNA to protein, for example, a small ribosomal subunit attaches itself to the 5’ end of a messenger RNA sequence and moves along the mRNA until it searches for a start codon within the mRNA. Before the large ribosomal subunit synthesizes a sequence of amino acids, aminoacyl tRNA synthetase attaches amino acids to their corresponding tRNA molecules in advance. As soon as the small ribosomal subunit finds out the start codon, the large ribosomal subunits join the first tRNA together. Subsequently, other tRNAs with anticodons matching the mRNA codons bind to the growing peptide chain of amino acids by the large ribosomal subunits. Until the ribosome reaches a stop codon, the synthesis continues repeatedly.

  9. See Machamer et al. (2000) and Darden (2006) ch. 3.

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  1. College of Liberal Studies, Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul, 08826, South Korea

    Jinyeong Gim

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Gim, J. Categorical Abstractions of Molecular Structures of Biological Objects: A Case Study of Nucleic Acids. glob. Philosophy 33, 43 (2023). https://doi.org/10.1007/s10516-023-09692-0

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