- History of biomathematics
- Thomas Malthus
- Object of study of mathematical biology
- Applications
- References
The mathematical biology or biomathematics is a branch of science that is responsible for the development of numerical models that simulate different get natural phenomena related to living beings; that is, it involves the use of mathematical tools to study natural or biological systems.
As can be understood from its name, biomathematics is an interdisciplinary area, located at the intersection of knowledge between biology and mathematics. A simple example of this discipline could include the development of statistical methods to solve problems in the area of genetics or epidemiology, to name a few.
Lotka-Volterra law for the relationship between predators and prey (Source: Curtis Newton ↯ 10:55, 20. Apr. 2010 (CEST). The original uploader was Lämpel at German Wikipedia. Via Wikimedia Commons)
In this area of knowledge, it is normal that mathematical results arise from biological problems or are used to solve them, however, some researchers have managed to solve mathematical problems based on the observation of biological phenomena, so it is not a unidirectional relationship between both fields of science.
From the above it can be ensured that a mathematical problem is the purpose for which biological tools are used and vice versa; that a biological problem is the purpose for which the many different mathematical tools are used.
Today, the field of mathematical biology is growing rapidly and is considered one of the most modern and exciting applications of mathematics. It is very useful not only in biology, but in biomedical sciences and in the field of biotechnology.
History of biomathematics
Mathematics and biology are two sciences with a multiplicity of applications. Mathematics is perhaps as old as Western culture, its origin dates back to many years before Christ and its usefulness has since been demonstrated for a large number of applications.
Biology as a science, however, is much more recent, since its conceptualization did not occur until the early nineteenth century thanks to the intervention of Lamarck, in the 1800s.
The relationship of mathematical and biological knowledge is close since the earliest times of civilizations, since the settlement of nomadic peoples took place thanks to the discovery that nature could be systematically exploited, which necessarily had to have involved the first notions mathematical and biological.
In its beginnings, the biological sciences were considered "artisan", since they referred mainly to popular activities such as agriculture or livestock; meanwhile mathematics discovered abstraction and had somewhat distant immediate applications.
The confluence between biology and mathematics dates back, perhaps, to the 15th and 16th centuries, with the advent of physiology, which is a science that groups together knowledge, classifying, ordering and systematizing it, making use of mathematical tools when necessary.
Thomas Malthus
It was Thomas Malthus, an economist contemporary with Lamarck, who set the precedent for the beginning of mathematical biology, as he was the first to postulate a mathematical model to explain population dynamics as a function of natural resources.
Malthus' approaches were later further developed and elaborated, and today they are part of the foundation of ecological models that are used to explain the relationship between predators and their prey, for example.
Object of study of mathematical biology
Mathematical biology is an interdisciplinary scientific area. Source: Konstantin Kolosov - Pixabay
Mathematical biology is a science that results from the integration of different mathematical tools with biological data, experimental or not, which seeks to take advantage of the “power” of mathematical methods to better explain the world of living beings, their cells and of its molecules.
Regardless of the degree of technological complexity involved, mathematical biology consists of the “simple” consideration that there is an analogy between two processes, namely:
- The complex structure of a living being is the result of the application of simple operations of “copying” and “cutting and splicing” or “splicing” (for example) to an initial information that is contained in a DNA sequence (deoxyribonucleic acid).
- The result f (ω) of applying a computable function to an array w can be obtained by applying a combination of simple basic functions w.
The field of mathematical biology applies areas of mathematics such as calculus, probability theories, statistics, linear algebra, algebraic geometry, topology, differential equations, dynamical systems, combinatorics, and coding theory.
Recently this discipline has been widely exploited for the quantitative analysis of different types of data, since the biological sciences have been dedicated to producing large masses of data from which valuable information can be extracted.
In fact, many researchers consider that the great explosion of biological data "created" the need to develop new and more complex mathematical models for their analysis, as well as considerably more complex computational algorithms and statistical methods.
Applications
One of the most significant applications of mathematical biology has to do with the analysis of DNA sequences, but this science is also involved in the modeling of epidemics and in the study of the propagation of nerve signals.
It has been used to study neurological processes such as Parkinson's disease, Alzheimer's disease and amyotrophic lateral sclerosis, for example.
It is extremely useful for the study of evolutionary processes (theorizations) and for the development of models that explain the relationship of living beings with each other and with their environment, that is, for ecological approaches.
The modeling and simulation of different types of cancers is also a good example of the many applications that mathematical biology has today, especially with regard to the simulation of interactions between cell populations.
Example of the analysis of DNA sequences commonly used in genomics (Source: Radtk172 via Wikimedia Commons)
Biomathematics is also very advanced in the area of computational neuroscience, in studies of population dynamics and of phylogenomics and genomics in general.
In this last branch of genetics it has been of great relevance, since it is one of the areas with the highest growth in recent years, since the data collection rate is extremely high, which deserves new and better techniques for its processing and analysis.
References
- Andersson, S., Larsson, K., Larsson, M., & Jacob, M. (Eds.). (1999). Biomathematics: mathematics of biostructures and biodynamics. Elsevier.
- Elango, P. (2015). The role of Mathematics in Biology.
- Friedman, A. (2010). What is mathematical biology and how useful is it. Notices of the AMS, 57 (7), 851-857.
- Hofmeyr, JHS (2017). Mathematics and biology. South African Journal of Science, 113 (3-4), 1-3.
- Kari, L. (1997). DNA computing: arrival of biological mathematics. Mathematical Intelligencer, 19 (2), 9-22.
- Pacheco Castelao, JM (2000). What is mathematical biology?
- Reed, MC (2004). Why is mathematical biology so hard? Notices of the AMS, 51 (3), 338-342.
- Ulam, SM (1972). Some ideas and prospects in biomathematics. Annual review of biophysics and bioengineering, 1 (1), 277-292.