Mathematics in Biology, Medicine and Pharmacology
Nov 26, 2017 · 7 min read

Everybody knows the saying «Mathematics is the queen of all sciences». Mathematical methods are applied in all spheres of human knowledge. Because of them, nowadays scientists can analyze vast arrays of data, predict or model various situations, improve the performance of different systems. Thus, while relatively simple forms of the phenomena are described quite fully (for example, in technology), research of more complicated processes causes problems. For instance, the development of symbolic notation, task solving algorithms, types of quantitative analysis of studied phenomena, etc. When we deal with large objects with complex organization, for example, in medicine, biology and pharmacology, the main difficulty of the research lays not only in development of mathematical theories and ways of research, but also in choosing raw data for the following mathematical processing, receiving detailed and well-grounded descriptions of processes and phenomena, complex calculations, and also in explication of the results received using this method.

For instance, let’s consider such a matter as the problem of the DNA deciphering. Why should we do this? Here are some spheres where this knowledge can be applied.

Scientists in Belgium, Croatia, France, Russia and Spain gathered ground samples and filtered them to separate out the human DNA samples. A single teaspoon of sand contained the traces of woolly rhinoceroses, mammoths, cave bears and ancient hyenas which made the search for human genes difficult. To remove the genetic “white noise”, the scientists developed a special method — they created some kind of a hook made of contemporary mitochondrial DNA. Because the hook belonged to the human kind, it was “catching” specifically the genes similar in some key properties from all the tangle of the samples. This molecular tool helped to discover the Neanderthal men’s DNA in the places where the archeologists hadn’t found neither the bodies, nor the relics belonged to this kind.

Putting to sleep a limped racing horse is a common practice, because it is too expansive to cure it and the results are not guaranteed. This problem was solved thanks to a simple injection. During the tests, the scientists separated out 2 genes and injected the medicine based on them into the limped horses’ legs. The results were astonishing! The injury wasn’t simply cured — in two weeks these horses were able to race again. Revolutionary VEGF164 and BMP2 genes were injected in the damaged ligaments and tendons, and the DNA molecules provoked the formation of new blood vessels, bone tissue, and the development of the new cartilaginous tissue. This ground-breaking therapy is not commonly used yet, but it obviously has its potential in curing both animals and people. The horses were in their peak form during the year after the injections. This gives us hope that people suffering from the injuries of ligaments and tendons, as well as spinal cord injuries, will be able to experience the joys of movement once again.

Photo: The Telegraph

The scientists from China recreated human embryos to learn how to cure a dangerous blood disease. For this project, they cloned the embryos and used biological material gathered from the patient suffering from beta-thalassemia. Just like many other genetic diseases, beta-thalassemia appears because of a malfunction in a person’s DNA. Our genetic code consists of 4 basic elements — adenine, cytosine, guanine and thymine (A, C, G, T). These nitrogenous bases contain a whole textbook on forming and functioning of a human body. The exchange of a single base for another one is called point mutation, which usually causes two-thirds of genetic diseases. To indicate the point mutation responsible for appearing of beta-thalassemia, the scientists checked 3 billion of these organic compounds in the patient’s genetic code. It turned out that it was all because the exchange of a single guanine. The method of the basic DNA editing allowed changing guanine for adenine and curing the disease on the genetic level for the first time. According to the experts, in the future the basic editing can prove to be useful for fighting many other genetic disorders.

The criminals, whose genetic information is already stored in the law enforcement services’ data bases, have all the grounds for hating their own DNA, traces of which they usually leave at the crime scene. Matching of these data will allow locking up whomever guilty. But an investigation usually reaches the dead-end when biological trails of criminals who commit their crime for the first time are discovered at the crime scene. Soon, even in this scenario the investigators will be able to identify the culprit. For instance, with the help from the technology, which allows recreating a person’s face using gathered genetic samples. The method was called the phenotype reconstruction using DNA and it can tell the investigators the color of the criminal’s eyes, hair and skin, their background and even whether or not they have freckles.

Therefore, in theory, knowing a person’s genotype one can predict many of their traits — not only the eye color and height, but also their underlying risk for the diseases (it is this what is of greatest interest for the scientists and doctors) and also for perilous habits! However the greatest difficulty here is the fact that the majority of such traits are identified by the sum of a large but finite number of “misprints” in the genome which have to be found. Results of appearing of a “misprint” are not always predictable and comprehensive. The effect of exchanging of a single letter is often too insignificant, and the researches don’t clearly understand how it can influence the phenotype.

But the DNA simply acts as a “flash-drive” which stores information on protides, while protides themselves are the “files”. Protides are the main biological molecules. They perform a number of various functions: catalytical, structural, transporting, receptor and many others. The life on Earth can be rightfully called protein-based. But how much do we know about the structure and functioning of this substance?

Protides are biopolymers which can be compared to a bead necklace, where each bead is represented by amino acids interconnected by peptide bonds. In a cell, the protides are synthesized on special molecular machines — Palades’s granules. Leaving the Palades’s granule, polypeptide chain congeals and the protide assumes a certain conformation, in other words, three-dimensional structure (Fig.1). It is vitally important for a living organism to contain the protide in a certain form, that is, conformation should be “proper” (native). The process of the protide congealing is called folding. The most curious thing here is that the information on the three-dimensional structure is “embedded” into the very sequence of the amino acids. In this fashion, protide needs only to “know”, what amino acids residues it contains and in what sequence, to assume the native structure. Comparison of amino acid sequences of protides (in this case — hemoglobins) of different organisms allow identifying the parts important for the functioning of the protides, as well as evolutionary history of the species being compared.

Fig.1 Native 3D conformation of protides

Apart from structural genomics, there is a field of research which deals with predicting the protide structure and seeks to develop the effective methods of creating of true-to-life protide models, the structures of which were determined experimentally. The main method of predicting the protide structure and protein-protein interaction is the simulation of the processes of protides congealing and fixating, using the methods of molecular dynamics. Knowledge concerning the protide structure can point towards the potential partners for the protein interaction, and thus push the researches towards the development or improving the new antibodies; explain the phenotype of the performed mutations; indirectly help in determining the place for performing the mutations, aiming at altering certain phenotypes.

Another important field of research of the modern molecular biology and genetic engineering is not only the studying of natural protides or their composing into the artificial ones, but also designing of brand new protides with required properties. (Fig.2)

Fig.2 Left: tips of protein spikes of many viral protides consist of 3 symmetrical parts, one of which is marked pink. Right: the new three-handed anti-influenza protide (on the left) ties the spike of the influenza virus

Some protides are connected with the diseases directly. The information on the protide structure is necessary to explain and determine its function and also to create a molecule which would attach this protide if the curing strategy will require doing so. The attachment is often used to predict the affinity and activity of a small molecule of the medicine in relation to the target protide. Therefore, the attachment of the molecules and other researches are of great importance for the development of medical preparations.

The creation of medical preparations we will discuss in our next article.

By Olesya Untevskaya, exclusively for the project

In Russian: Математика в биологии, медицине и фармокологии

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