I teach and research in a university zoology department. When I first took up my job over 20 years ago, some of my students told me that they took zoology (or biology) because they would not have to “do any maths.” I found this attitude deeply shocking: in my view analysing biological phenomena in a quantitative manner gave insights into the beauty of biology that no other approach could match. Of course, I was biased; I had graduated with a bachelor’s degree in mathematics before studying for my postgraduate qualifications in biology.
In the intervening two decades, the role of mathematics in biology, especially in biological research, has grown enormously. The long-standing use of statistical analysis of experimental data has, of course, become more sophisticated and new-fangled concepts such as Bayesian analysis have become commonplace and not just in the fields, like ecology, that always had a statistical bent. Perhaps even more fundamentally, many parts of pure mathematics – algebra and calculus – are now fully in the mainstream of biologically relevant mathematics. Many areas of biology in which mathematical tools and models were absent or marginally important now rely on mathematics and its application for their most central questions.
For example, one area in which I carry out research is phylogenetics, the study of evolutionary trees that show how different species (or groups of species) are related to each other, rather like family trees show how people are related. Back in the dark ages (the 1960s and before) evolutionary biologists drew their trees freehand, according to how they personally interpreted the data (usually derived from morphology or fossils). Today, such an approach is just not scientifically acceptable. Like thousands of scientists worldwide, I use DNA-sequences as the data to feed into various computer programs that carry out several analyses. For example, once the sequences from the different species are matched to each other correctly (“aligned”), we need to have a way of searching through the unbelievably gargantuan number of possible trees to find those (or the one) that are (or is) best supported by the data. No amount of intuition or even hand calculation could achieve this goal and, indeed, such approaches would waste most of the information we have in the sequence data. In order to make the best use of our data and draw the most accurate conclusions, we need these computer programs, which are built on rather sophisticated algebra and algorithms.
In the fields of medical research, too, things have changed. Recently I was involved in a study of the consequences of dietary restriction on lifespan. Many scientists have wondered if restricting calories can extend life expectancy, especially in humans, but the experimental data (on various animal models) was not very clear. Our study, led by Gravida Investigator, Shinichi Nakagawa, carried out what is called a meta-analysis, discovering that the effect is more pronounced in females and in model species (laboratory mice, drosophila flies, etc.). Meta-analysis feeds the results of previous studies into a combined analysis to derive an overall conclusion. Meta-analytic results are often far more powerful than single studies because they make use of so much data, but they rely on some careful mathematics, to ensure that all the factors in different experiments are properly accounted for.
Of course, the fact that mathematics now pervades more and more of biology does not mean that we all have to become mathematicians any more than car drivers must become mechanics. But as biologists, we do need to be familiar with the basics of mathematical approaches and we must learn how to drive the mathematical programs that analyse our data. And researchers above all must have some facility for talking to mathematicians, who are the very people who will be inventing the next generation of mathematical tools to analyse the increasingly vast amounts of biological data being generated in laboratories around the world.
So, as biologists, we all need some quantitative skills, and it is never too early to think about developing those skills. High-school pupils contemplating a career in biology should ensure they take mathematics as far as possible. Those students wanting to go on to study biology at university should try to take both the statistics and calculus flavours. Such careful planning will open all sorts of options about the direction of study and possible jobs. But perhaps at least as satisfying will be a greater understanding of the majestic complexity inherent in so much of modern biology.
Ian Shaw is the Director of Biochemistry and Professor of Toxicology at the University of Canterbury in Christchurch, New Zealand. He is also a Principal Investigator of Gravida: National Centre for Growth & Development. His main research focus is the impact of environmental contaminants on humans. You might even remember seeing him in the media talking about bis-phenol A in plastic bottles. Professor Shaw won the NZ Association of Scientists Communicator Award in 2009, has written books, and is fairly frequently popping up on the television.
The Toxicology of DOHaD
The International Society for Developmental Origins of Health and Disease (DOHaD) is, as its name explains, concerned with the origins of health and disease in a developmental context. How do insults (by this I mean bad things that happen, e.g. the effects of mum smoking) during a child’s - or an animal’s for that matter – early stages in the womb affect its development and how do these developmental effects impact on its health later in life? These are huge questions with astoundingly inadequate answers, but our understanding is increasing…
Life begins in a moment of passion when a sperm meet an egg and fertilises it. From that point on the new being develops by a long and complex series of cell divisions that lead to organs and body anatomy; eventually a fully formed replica of its parents emerges at birth. Amazing! But think about the process more carefully; it all starts with a fertilised ovum – a single cell – that by myriad divisions forms an animal or a human. If that first cell was damaged this would probably lead to all of the cells derived from it also being damaged. If such damage was severe, it is likely that the cell would die or its division products would not be viable – this is an important safeguard against horrendous deformity. However, if the damage was seemingly slight – like a change in DNA for example – viable cells could be formed following division…each containing the replicated, damaged DNA. If this damaged DNA coded for a key protein the offspring would be biochemically compromised in some way. This might never come to light, but, on the other hand, it might lead to a change which compromises the adult’s life. This is where Toxicology and DOHaD meet.
The extreme example above relates to a very early effect on the developing embryo – the earlier the effect the greater the potential impact because the affected few cells will form the multitude of cells that make up the offspring’s body. Later effects will focus on the cells that are developing at the time of the impact. For example, the limbs begin to form in the middle of trimester 1 (about 2 months in a human pregnancy); so, if the embryo is impacted then it might affect the development of the limbs. This happened during the Thalidomide disaster in the late 1950s and early 1960s when many children were born with horrendous limb deformities which were traced back to their mothers being prescribed Thalidomide for morning sickness during the early stages of pregnancy. Thalidomide is now known to interfere with limb bud development and so if the embryo was exposed during mid-trimester 1 the resulting child was likely to have limb deformities. This illustrates well that if a particular toxic chemical exposure occurs during pregnancy it could adversely affect the cells actively dividing at the time of exposure. Trimester 1 exposures are by far the worst because this is a time of great embryological/fetal development.
Alcohol is another example of developmental toxin. Mothers who drink alcohol during pregnancy put their child at risk of fetal alcohol syndrome because of the effects of ethanol on cell development - particularly nerve cell development. This can lead, amongst many other things, to brain development abnormalities with all their serious ramifications for the child as it grows up and the adult that it grows into.
Thalidomide and alcohol are examples of well-established chemicals that interfere with growth and development and lead to impacts on the child’s health. They are termed teratogens (from the Greek, ‘teratos’ meaning monster). Their effects are obvious and devastating and easily avoidable by not exposing pregnant women to alcohol or Thalidomide. Easy!
As we explore developmental effects more and understand more, it is becoming clear that many every day exposures affect development and that these effects might have significant and complex impacts on later life. The seeds of adult health disorders can be set in the very early stages of pregnancy.
Diet during pregnancy is a key determinant of a child’s health, and, indeed the health of the adult it grows into. You are what your mother ate! If pregnant rats from non-obese family lines are fed large amounts of fat, their pups are more likely to become obese or over weight in later life. So, even if there is not a genetic determinant of obesity, the mother’s fat intake can determine whether her offspring become fat. With obesity comes an increased risk of type 2 diabetes. Therefore, too much fat in a pregnant mum’s diet might increase her child’s risk of contracting type 2 diabetes in later life. This research is in its infancy, but points to a whole new concept of health assurance – making sure the developing child in the womb is not exposed to chemicals (including normal dietary chemicals like fat) that might initiate a developmental change that might not manifest until much later in life. Watch this space…it’s getting exciting!
And it’s not only Mums that need to watch their exposures; it has been suggested that fathers’ exposures to chemicals that might affect their sperm can result in changes in their offspring, even if the exposure was a long time before the moment of passion that led to fertilisation. The male children of soldiers exposed to an insecticide (dibutyl phthalate (DBP)) have an increased incidence of genital developmental malformations. It has been suggested that this is because DBP affects the genes that code for key enzymes in the synthesis of the male hormone, testosterone. This means that the developing male embryo might not get the right signals for genital development. While these ideas are just the beginning of a new line of thinking – and a rather controversial line of thinking – it might be wise not to dismiss them just yet!
Kim JH & Scialli R (2011) Thalidomide: The tragedy of birth defect and the effective treatment of disease. Toxicological Sciences 122(1), 1-6
Howie GJ et al (2009) Maternal nutrition history predicts obesity in adult offspring independent of postnatal diet. Journal of Physiology 587(4), 905-915
Carran M & Shaw IC (2012) New Zealand Malayan war veterans’ exposure to dibutylphthalate is associated with an increased incidence of cryptorchidism, hypospadias and breast cancer in their children. New Zealand Medical Journal 125(1358), 52-63
Elwood M & Borman B (2012) Increases in disease in Malayan war veterans’ may be misleading. New Zealand Medical Journal 125(1367), Letter
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