Bioinformatics is the application of informatics (computer science, information theory, statistics) to the discovery of biological knowledge.

Molecular biology systems (DNA, RNA, protein, cells) formed the first kind of information processing system on the planet. Bioinformatics applies the third kind of information processing system, computers, to biological problems.

The biological "dogma" is that DNA, specifically the coding part of a gene, is trancribed to messenger RNA (mRNA), and this mRNA is translated to a protein. Around 2000± it became apparent that much more DNA than just the coding DNA, perhaps most DNA, is transcribed to RNA and that much of this RNA is involved in regulating gene expression and who knows what else.

Some bioinformatics problems:

Sequence assembly is the piecing together of relatively short sequences, as output by a sequencing machine, into a longer sequence, e.g., a chromosome.

Compression techniques can assess the information content of sequences and other biological data. This can be used for pattern discovery [Kon21].

The alignment problem is to discover if all or part of two (or more) sequences are related and, if so, how [AWY90, AWY92, PAD04].

Multiple alignment [AW94] seeks to discover if several sequences are related and, if so, how.

A phylogenetic (evolutionary) tree shows how several sequences, and thus the species to which they belong, are thought to be related by evolutionary descent [AW94].

One place to start the search for a phylogenetic tree is from a multiple alignment, although the tree and the alignment are mutually dependent, like a chicken and an egg.

Protein structure, the three dimensional folding of a protein, determines a large part of the function of the protein and predicting protein structure is one of the grails of bioinformatics.

Systems biology includes the analysis of how the thousands of proteins in a complex organism interact in control networks (graphs [All18]) to make the products that the organism needs, in the right proportions, in the right places, at the right times.

References

[All18] L. Allison, 'Graphs', ch.11 of ''Coding Ockham's Razor', doi:10.1007/978-3-319-76433-7_11, 2018.

[AW94] L. Allison and C. S. Wallace, 'The Posterior Probability Distribution of Alignments and its Application to Parameter Estimation of Evolutionary Trees and to Optimisation of Multiple Alignments', Journal of Molecular Evolution, 39(4), pp.418-430, doi:10.1007/BF00160274, 1994.

[AWY90] L. Allison, C. S. Wallace and C. N. Yee, 'When is a string like a string?', Int. Symposium on Artificial Intelligence and Mathematics, Ft. Lauderdale, Florida, USA, [www], January 1990.

[AWY92] L. Allison, C. S. Wallace and C. N. Yee, 'Finite-State Models in the Alignment of Macro-Molecules', Journal of Molecular Evolution, 35(1), pp.77-89, doi:10.1007/BF00160262, 1992.

[Kon21] A. S. Konagurthu et al, 'Universal Architectural Concepts Underlying Protein Folding Patterns', Frontiers in Molecular Biosciences, special issue 'A Journey Through 50 Years of Structural Bioinformatics in Memoriam of Cyrus Chothia', doi:10.3389/fmolb.2020.612920, 2021

[PAD04] D. R. Powell, L. Allison and T. I. Dix, 'Modelling-Alignment for Non-Random Sequences', AI2004, Springer Verlag, LNCS vol.3339, pp.203-214, doi:10.1007/978-3-540-30549-1_19, 2004.

Also see publications.