-Mathematics and contemporary life sciences

Wujiarui

In the mid-20th century, with the analysis of protein's spatial structure and the discovery of DNA double helix, the era of molecular biology was formed, in which protein, the carrier of genetic information and the executor of life function, was the main research object. The birth of molecular biology has transformed traditional biological research into modern experimental science. However, compared with other experimental sciences such as experimental physics, experimental science in the field of life sciences pays more attention to experience rather than abstract theories or concepts. In addition, most of these biologists pay attention to qualitative research, the main goal is to find new genes or new protein, and pay little attention to quantitative research, such as molecular dynamics. Nevertheless, modern life sciences made great achievements in the second half of the 20th century. As molecular biologist B. Albert, president of the American Academy of Sciences, said, "In an era when gene cloning is dominant, many outstanding scientists today have made great achievements without any quantitative research ability." However, with the advent of the post-genome era, the quantitative research ability and knowledge of biological researchers are no longer dispensable.

As the trend of the times shows.

British biologist Paul? Paul nurse won the 200 1 Nobel Prize in Physiology or Medicine for his outstanding research on cell cycle. He once ended a summary of cell cycle research in the 20th century with the following words: "We need to enter a more abstract strange world, a world where cell activities are different from our daily imagination and can be effectively analyzed according to mathematics."

Perhaps based on the same consideration, R. Colwell, director of the National Science Foundation (NSF) of the United States, said in the report submitted to Congress in June, 5438 +2000 10 that mathematics is the foundation of all emerging disciplines and research fields at present, and requested that the funding for mathematics should be more than tripled next year, reaching $65,438+0.2/KLOC-0.0 billion. A large part of these increased budgets are used to support interdisciplinary research between mathematics and other disciplines, especially interdisciplinary research projects between mathematics and biology.

Although mathematics has always played a certain role in modern life sciences, such as quantitative genetics and biological mathematics. But it was biologists in the 1990s who really realized the importance of mathematics. Genomics is the main catalyst for this trend. With the rapid development of DNA sequencing technology, the number of DNA base sequences determined every year in the late 1990s increased at an alarming rate. Take GenBank of America as an example, the base sequence of 1997 is 1x 109, which doubled to 2x109 in the following year; ; By 2000, GenBank had nearly 8x 109 base sequence. Similarly, with the rapid development of protein group research and transcriptome research, all kinds of data are increasing rapidly. It is estimated that the amount of biological data can now reach 10 15 bytes per year. How to manage these "massive" data and how to extract useful knowledge from them has become a great challenge for biologists, mathematicians and computer experts. This leads to a new discipline: bioinformatics. In addition, the study of complex systems and networks such as cells and nerves led to the birth of mathematical biology. The National Science Foundation of the United States specially launched the project "Quantifying Environment and Integrated Biology" to encourage biologists to apply mathematics to biological research. Almost at the same time, the National Institutes of Health also set up a major project of "Computational Biology".

A new tool to understand life: model

The above discussion may give people an impression that the application of mathematics in modern life sciences is mainly in the processing of "massive" data. It can be said that there are indeed many biologists today who look at the role of mathematics in life science from the perspective of "calculation". However, calculation is far from enough to understand life phenomena. When we input thousands of experimental data obtained by gene chip into the computer and let the computer spit out piles of conclusions according to a certain running program, can we think that we have understood the biological problems to be studied? Not only that, we may need to be vigilant not to let computers take the place of our thinking.

For today's life science workers, the value of mathematics should be embodied in "modeling". Through the construction of the model, the seemingly chaotic experimental data are sorted into orderly mathematical problems; Through the construction of the model, the essence of the problem to be studied is clearly abstracted; Through the construction of the model, researchers' experiments are no longer random explorations, but rational experiments driven by "hypothesis-driven methods" like physicists' work.

Experimental biologists in the last century regarded life as a linear system and tried to explain life activities with simple causality. Usually, in the deep heart of researchers looking for new genes, most of them have a desire of "genetic determinism": once a gene is found, a biological problem can be solved. Cancer has an "oncogene", longevity has a "longevity gene", cleverness has a "smart gene", and even crimes are caused by a "crime gene". However, decades of research track has drawn more and more complex patterns. Take p53, the first tumor suppressor gene discovered by human beings, as an example. Since the discovery of 1979, nearly 25,000 articles have been related to it. There are dozens of protein that directly interact with p53, and new protein is still being discovered. Nowadays, people have regarded p53 as a rather complex regulatory network. Obviously, it is not easy to understand and analyze the function of p53 without the help of mathematical model. Not long ago, A. J. Levine, one of the biologists who discovered p53, established a mathematical model with mathematicians to explain the regulatory circuit of p53 [1].

Mathematics can not only help us abstract and explain models from existing biological experiments and data, but also be used to design and build biological models, which may not exist in the natural state. In this sense, biological experiments based on mathematical models and assumptions will be closer to the well-known physical and chemical experiments, more dependent on abstraction and rationality, and no longer an empirical science.

At the beginning of the new century, mathematics teaching experiment has become a reality. Not long ago, American scientists reported their artificial biological models in Nature. Scientists at Princeton University designed a network to control gene expression that does not exist in nature. This network can periodically regulate the expression of foreign genes in Escherichia coli [2]. In the same issue, biologists at Boston University also reported their similar work [3]. The common feature of these two works is that some differential equations (two laboratories use different differential equations) are used for derivation and design, and then biological experiments are carried out according to their designs, such as constructing gene expression plasmids and detecting gene expression. These scientists believe: "This kind of' rational design of network' can lead to new cell engineering and promote people's understanding of regulatory networks existing in nature." [2]

"Everything counts."

Mathematics is often regarded as a tool. This is also a very useful tool. However, as long as it is used as a tool, it can be replaced. All roads lead to Rome. Tools are roads. You can choose path A or path B as long as you can reach your destination. Of course, some may be shortcuts, and some may be detours. But they are not unique after all. Just like life science research in the past, we have achieved good results without mathematics. The application of mathematics will obviously be helpful to the present and future biological research, but can biologists do without mathematics?

Human beings' concern for nature and life is usually reflected in two aspects: what is the essence of everything in the world and how to understand and explore this essence. The former belongs to ontology and the latter belongs to epistemology. If we assume that the essence of life is ultimately embodied in the composition of mathematical laws. Then, obviously, without mathematics, we can't truly and thoroughly reveal the essence of life.

DNA and protein are the two most important biological macromolecules. They are usually long-chain molecules composed of many basic elements (bases and amino acids). However, their spatial shape is not a straight line, but a regular "spiral tube". Although DNA double helix and protein alpha helix were discovered in the middle of 20th century, it is still difficult to explain why nature chose "helix" as the structural basis of these biomacromolecules.

Not long ago, a group of scientists in the United States and Italy studied the "optimal packing" of dense lines by using the method of discrete geometry, and the answer was: the shape of the longest line that can be accommodated in a container of a certain volume is spiral [4]. Researchers realized that "naturally occurring protein is such a geometric shape" [4]. Obviously, we can get a glimpse of the mathematical reason why life chooses spiral as the basis of its spatial structure: to accommodate the longest molecule in the smallest space. Anyone familiar with molecular biology and cell biology knows that the packaging of biological macromolecules is an inevitable process of life. As the carrier of genetic material, the line of DNA is longer than the diameter of the nucleus containing it. For example, the length of DNA that constitutes human chromosomes is thousands of times the length of its nucleus. Therefore, it is usually necessary to fold and wrap the DNA chain many times to make the DNA double helix chain about 5 cm long into a compact chromosome about 5 microns long. It can be considered that life follows the mathematical principle of "maximum packaging" to construct its own biological macromolecules.

Cells are the basic constituent units and functional units of life. Cell division (also called cell proliferation) is the most basic and important activity of cells. The activity of completing a cell division is called cell cycle. The cell cycle length of different species is different, and there are strict regulations. So, what is the "clock" of the cell cycle made of? Recent studies have shown that for yeast cells, the degree of phosphorylation of cell cycle regulatory proteins can be used as a "clock" for cell cycle operation. There are nine sites on this protein called Sicl that can be phosphorylated by protein kinase CDK. When it was added to the 5th phosphate group together with the 1 phosphate gene, its molecular behavior did not change. However, once the sixth phosphate group is added, it can interact with a kind of protein called Cdc4, and then be degraded by protease, thus leading cells to enter the DNA synthesis phase (S phase) and finally completing cell division. The detailed and in-depth work of researchers revealed that every phosphorylation of Sicl protein contributed to the interaction with Cdc4, but only after the sixth or more times did its binding force reach a stable combination with Cdc4. In addition, if Sicl protein is artificially loaded with exogenous amino acid peptide, a phosphorylation can combine Sicl with Cdc4 and lead to its degradation, then the function of Sicl in controlling cell cycle time will be lost [5]. This research result typically reveals how cells realize their life activities through quantity control.

Pythagoras, a famous mathematician in ancient Greece, once left a view to future generations: "Everything has a number". If his view is correct, then life, as a masterpiece of nature, must also be designed in a mathematical way. Therefore, mathematics can not only promote the study of life science, make life science an abstract and quantitative science, but also be the only way to reveal the mystery of life.