Mathematics is valuable to our understanding of the living world around us. Throughout history mathematics has been used to solve biological problems. Recently mathematics has been utilised for interpreting biological sequence data. The field of bioinformatics which combines biology, mathematics and computer science identifies patterns in large datasets to extract meaning from DNA sequencing data. Susanna’s AMSI Vacation Research Project explores bioinformatics and uses mathematics to group protein sequences with similar biological functions.
Mathematics has a long history of solving biological problems. In the 13th century, the famous Fibonacci sequence was used to describe a growing population of rabbits. In the 1800s, Daniel Bernoulli used applied mathematics to describe the effects of smallpox on the human population and the physician John Snow used mathematics to prove that cholera and other pathogens are spread through contaminated water. These discoveries, as well as many others, have shaped our understanding of the living world around us. Since these discoveries, mathematics continues to play an important role in understanding biological processes.
Mathematical models allow researchers to build connections between biological observations and the underlying regulatory processes which govern them. These models can take several forms including game theoretic models, differential equations, and statistical models. By adjusting the model parameters and running simulations, modelling improves our understanding of how systems respond to changes in internal or external stimulus and environmental perturbations. Mathematical models are used to design novel experiments, assess the efficacy of certain molecules as therapeutic targets, and predict weather and climatic patterns.
Many challenging problems remain unanswered in biology. Exactly how and when did life on Earth originate? What metabolic pathways were used by early life forms? Future research may uncover answers to such questions by taking an interdisciplinary approach and paralleling biology and mathematics.
Bioinformatics in an emerging, interdisciplinary field combining biology, mathematics, statistics, and computer science. New technologies enabling DNA sequencing (genomics), protein sequencing (proteomics) and sequencing genetic material recovered from the environment (metagenomics) have allowed large volumes of biological sequence data to be obtained. The ‘big data’ produced from these technologies requires mathematical and statistical methods to identify patterns within sequence data, develop algorithms applicable to huge datasets and extract useful information from ‘noisy’ data collected from experiments. Recent advances in bioinformatics have allowed improved vaccine screening, protein structure prediction and enhanced crop production.
As a student with a background in molecular biology and mathematics I aim to build a career using bioinformatics and mathematical modelling to improve our understanding of biology. My AMSI Summer Research project utilises mathematics to hierarchically cluster bacterial protein sequences. As some protein sequences do not have known functions, grouping proteins with unknown functions presents an efficient approach to experimentally determining the function of unknown proteins. Advances in bioinformatics will allow to patterns hidden in the genetic code to be uncovered, advancing biomedical science and biotechnology.
To learn more about applications of mathematics in biology, Susanna’s report describes her project ‘Hierarchical Clustering of Bacterial Protein Sequences’.
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