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The videos on this website provide a taste of how mathematical and biological ideas can be combined to obtain insight into different systems. How can you apply this kind of quantitative thinking to basic and clinical research? Browse the following links to identify experimental resources, additional examples of theoretical analysis, and interdisciplinary investigators with whom to collaborate.
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. . . the vast diversity of normal cell phenotypes in the metazoan body is generated by the same genome. This alone should prompt us to reason whether genetic mutation and selection are really necessary and sufficient to produce the sophisticated survival skills of invading and disseminated tumour cells. Who would question that the distinct phenotypes of a liver cell and a neuron are produced by the same genome? Yet, any subtle, incremental malignant trait that is acquired by a cancer cell, such as increased resistance to apoptosis, is usually explained by another genetic mutation -- a 'hit' in the multi-step process of tumorigenesis.-- Brock A, Chang H, and Huang S (2009) Non-genetic heterogeneity -- a mutation-independent driving force for the somatic evolution of tumours Nat. Rev. Genet. 10:336-342 PubMed ID: 19337290. Of relevance is a more recent perspective review: Lupski JR (2013) Genome mosaicism--One human, multiple genomes Science 341: 358-359 Pubmed ID: 23888031 (doi: 10.1126/science.1239503).
. . . Genome science will have a real impact on all our lives and even more on the lives of our children. It will revolutionize the diagnosis, prevention and treatment of most, if not all, human diseases. In coming years, doctors increasingly will be able to cure diseases like Alzheimer's, Parkinson's, diabetes and cancer by attacking their genetic roots.
Just to offer one example, patients with some forms of leukemia and breast cancer already are being treated in clinical trials, with sophisticated new drugs that precisely target the faulty genes and cancer cells, with little or not risk to healthy cells.
In fact, it is now conceivable that our children's children will know the term "cancer" only as a constellation of stars.--President Bill Clinton, 2000 June 26. This quotation can be placed next to the quotation from Brock, Chang, and Huang to depict variety in sentiment and opinion regarding the degrees to which and ways in which genetics are fundamental to cancer biology and treatment.
. . . in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense.--Charles Darwin (1887) The Autobiography of Charles Darwin: From the Life and Letters of Charles Darwin, edited by his son Francis Darwin
. . . with four parameters I can fit an elephant, and with five I can make him wiggle his trunk.--Attributed to John von Neumann by Enrico Fermi, as recounted in Dyson F (2004) Turning points: A meeting with Enrico Fermi Nature 427: 297 doi:10.1038/427297a
. . . the calculus was certainly invented by Newton specifically for a specific purpose in theoretical physics.
But still a large part of mathematics which became useful developed with absolutely no desire to be useful, and in a situation where nobody could possibly know in what area it would become useful; and there were no general indications that it ever would be so. By and large it is uniformly true in mathematics that there is a time lapse between a mathematical discovery and the moment when it is useful; and that this lapse of time can be anything from thirty to a hundred years, in some cases even more; and that the whole system seems to function without any direction, without any reference to usefulness, and without any desire to do the things whihc are useful. Of course, one must also consider that this is really true for the entire course of science; in other words, that you should consider whta processes a large part of science got into the place where impinges on society in everyday life: How most of physical science comes from mechanics, and how the original discoveries in mechanics were mainly connected with astronomy and were absolutely not connected to the places where the applications today lie.
This is true for all of science. Successes were largely due to forgetting completely about what one ultimately wanted, or whether one wanted anything ultimately; in refusing to investigate things which profit, and in relying solely on guidance by criteria of intellectual elegance; it was by following this rule that one actually got ahead in the long run, much better than any strictly utilitarian course would have permitted.-- John von Neumann (1995) The Neumann Compendium World Scientific. P. 652 is readable on Google Books.
This quotation can be used when illustrating that the relative roles of practical application and unguided discovery have been central considerations for scientific research for decades.
. . . Volterra's equations for the dynamics of a predator and prey species . . . [in] a sense . . . are manifestly false. . . . . Their merit is to show that even the simplest possible model of such an interaction leads to sustained oscillation -- a conclusion it would have been hard to reach by pure verbal reasoning.--John Maynard Smith (1982) Evolution and the Theory of Games, Cambridge University Press, p. 9
Recently, ideas about complexity, self-organization, and emergence--when the whole is greater than the sum of its parts--have come into fashion as alternatives for metaphors of control. But such explanations offer only smoke and mirrors, functioning merely to provide names for what we can't explain; they elicit for me the same dissatisfaction I feel when a physicist says that a particle's behavior is caused by the equivalence of two terms in an equation. . . .
The hope that general principles will explain the regulation of all the diverse complex dynamical systems that we find in nature can lead to ignoring anything that doesn't fit a pre-existing model. When we learn more abou the specifics of such systems, we will see where analogies between them are useful and where they break down.--Deborah Gordon (2007) Control without hierarchy. Nature 446: 143., manuscript available from author's research website.
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|© Copyright 2011-2015 David Liao. These videos and slides are open course ware made available under a Creative Commons license (CC BY-SA 4.0). The lightbox and social sharing effects are scripts by Stéphane Caron (CC BY 2.5).|