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Sunday, April 21, 2019

Hitting the Books: How calculus is helping unravel DNA's secrets | Medicine - Engadget

Welcome to Hitting the Books. With less than one in five Americans reading just for fun these days, we've done the hard work for you by scouring the internet for the most interesting, thought provoking books on science and technology we can find and delivering an easily digestible nugget of their stories.

It's not just for the hard sciences anymore! suggests Andrew Tarantola, Senior Editor at Engadget.

Photo: koto_feja via Getty Images
Calculus has provided humanity a window into the inner workings of the world around us since the fateful day Isaac Newton got conked by a falling apple. But we've only ever really applied these mathematical tools to our "hard" sciences, like physics or chemistry. Heck, we probably wouldn't have discovered Neptune if not for calculus. That's changed in recent years as the studies of between the discipline and big data, computer learning, AI, and quantum physics have increasingly overlapped.

In the excerpt from Infinite Powers: How Calculus Reveals the Secrets of the Universe below, author Steven Strogatz examines a novel application of calculus to the "soft" science of biology. Previously used to model how HIV spreads and overwhelms infected immune systems, calculus can now help researchers better understand the process by which nature manages to twist, fold and condense an entire double-helix strand of DNA into a package small enough to fit inside the nucleus of a cell.

Calculus has traditionally been applied in the "hard" sciences like physics, astronomy, and chemistry. But in recent decades, it has made inroads into biology and medicine, in fields like epidemiology, population biology, neuroscience, and medical imaging. We've seen examples of mathematical biology throughout our story, ranging from the use of calculus in predicting the outcome of facial surgery to the modeling of HIV as it battles the immune system...

In the early 1970s an American mathematician named Brock Fuller gave the first mathematical description of this three-dimensional contortion of DNA. He invented a quantity that he dubbed the writhing number of DNA. He derived formulas for it using integrals and derivatives and proved certain theorems about the writhing number that formalized the conservation law for twists and coils. The study of the geometry and topology of DNA has been a thriving industry ever since. Mathematicians have used knot theory and tangle calculus to elucidate the mechanisms of certain enzymes that can twist DNA or cut it or introduce knots and links into it. These enzymes alter the topology of DNA and hence are known as topoisomerases. They can break strands of DNA and reseal them, and they are essential for cells to divide and grow. They have proved to be effective targets for cancer-chemotherapy drugs. The mechanism of action is not completely clear, but it is thought that by blocking the action of topoisomerases, the drugs (known as topoisomerase inhibitors) can selectively damage the DNA of cancer cells, which causes them to commit cellular suicide. Good news for the patient, bad news for the tumor.
Read more... 

Recommended Reading

Infinite Powers:
How Calculus Reveals
the Secrets of the Universe
Source: Engadget