Ever since its official conception in the 1970s, bioinformatics, the excellent combination of computer science and biology, has come a long way . From this interdisciplinary field sprang new fields of theoretical biology that we know of today .
However, bioinformatics is often confused with the now-broader field of computational biology.
As bioinformatics and computational biology grew from genomic research in the 1970s, the terms have been used interchangeably and (still) cause some degree of confusion — particularly among people unfamiliar with the fields. In 2000, the NIH Biomedical Information Science and Technology Initiative Consortium clarified the two by defining the fields as such :
Bioinformatics: Research, development, or application of computational tools and approaches for expanding the use of biological, medical, behavioral or health data, including those to acquire, store, organize, archive, analyze, or visualize such data.
Computational Biology: The development and application of data-analytical and theoretical methods, mathematical modeling and computational simulation techniques to the study of biological, behavioral, and social systems.
Bioinformatics: This is the most well-known field of computational biology. This field deals with the development and creation of databases or other methods of storing, retrieving, and analyzing biological data (originally starting with genes) through mathematical and computing algorithms. Bioinformatics employs both mathematics and an ever-increasing variety of computing languages to ease the storage and analysis of biological data. Databases themselves have made way for sprouting research fields such as data mining.
Computational Biology: Computational biology has become a broad term that refers to the application of mathematical models, computing algorithms and programs, and simulation tools to aid in various biological research such as genetics, molecular biology, biochemistry, ecology, and neuroscience among many others. Computational biology research encompasses many disciplines such as health informatics, comparative genomics and proteomics, protein modelling, neuroscience, etc.
Mathematical Biology: This field is an amalgamation of biology and a various fields of mathematics. Often times, some computational biology topics are more math-based (computing) than computer science-based. Various mathematics used in mathematical biology research include discrete mathematics, topology (also useful for computational modeling), Bayesian statistics (such as for biostatistics), Linear Algebra, Logic, Boolean algebra, and many other higher level mathematics. This field is also often called theoretical biology due to its focus on equations, algorithms, and theoretical models.
Systems Biology: This field deals with the interactions between various biological systems ranging from the cellular level to entire populations with the goal of discovering emergent properties. Systems biology usually involves networking cell signalling or metabolic pathways . Systems biology often employs computational techniques and biological modelling to study these complex interactions at cellular levels.
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 Bu Z & Callaway DJ (2011). Proteins move! Protein dynamics and long-range allostery in cell signaling. Advances in protein chemistry and structural biology. 83:163-221.
 Hogewag P (2011). The Roots of Bioinformatics in Theoretical Biology. PLoS Computational Biology. 7(3):e1002021.
 Huerta M et al. (2000). NIH Working Definition of Bioinformatics and Computational Biology. Biomedical Information Science and Technology Initiative.
 Johnson G & Wu TT (2000). Kabat Database and its applications: 30 years after the first variability plot. Nucleic Acids Research. 28(1)214-218.
bioinformatics.org this site contains more information on the Bioinformatics Organization.