A Global Warming Primer

The Discovery Channel has an interesting series of videos about the effects of global warming on: polar bears; the Antarctic Ice Sheets; the Amazon rainforest; and the Great Barrier Reef. They also have a nice bit on what goes into the average American carbon footprint.

Natural Selection and Polar vs. Grizzly Bears

What I end up seeing, in this quintessentially 21st century creature, is a glimpse of the future.

— Gamble (2012): One, two, three, er…many. in The Last Word on Nothing.

The effect of rapid Arctic warming on polar bears has been a theme this year in Environmental Science, so this article on the hybridization of polar bears and grizzly bears caught my eye.

As caribou migration routes have moved North, grizzlies have followed and started mating with polar bears. Not only have they produced hybrid young, but those young are fertile. Polar bears and grizzlies only diverged about 150,000 years ago and haven’t developed many genetic differences, despite quite dramatic visual dissimilarities. Second-generation hybrids have now been confirmed in the wild.

This article is also of note to my Middle School science class because we’ve talked about speciation — the divergent evolution of two populations into separate species — before when we looked at the phylogenetic tree and bison evolution in particular. This seems to be a re-convergence after separation. As the climate warms the grizzly bears are able to range further north, while the polar bears are more restricted to the shores by the melted sea ice, so the two populations encounter each other more and more. Thus polar bears, may eventually disappear as they are re-incorporated into the grizzly population.

The author, Jessa Gamble, thinks this is a glimpse of things to come.

↬ The Dish.

Warming of the West Antarctic Ice Sheet

… a breakup of the ice sheet, … could raise global sea levels by 10 feet, possibly more.

— Gillis (2012): Scientists Report Faster Warming in Antarctica in The New York Times.

In an excellent article, Justin Gillis highlights a new paper that shows the West Antarctic Ice sheet to be one of the fastest warming places on Earth.

The black star shows the Byrd Station. The colors show the number of melting days over Antarctica in January 2005. This number increases with warming temperatures (image from supplementary material in Bromwich et al., 2012).

Note to math students: The scientists use linear regression to get the rate of temperature increase.

The record reveals a linear increase in annual temperature between 1958 and 2010 by 2.4±1.2 °C, establishing central West Antarctica as one of the fastest-warming regions globally.

— Bromwich et al., (2012): Central West Antarctica among the most rapidly warming regions on Earth in Nature.

Anti-biotic Brass

Interesting research shows that brass and other copper metal alloy surfaces kill bacteria and degrade their DNA much better than stainless steel or plastic.

Plastic and stainless steel surfaces, which are now widely used in hospitals and public settings, allow bacteria to survive and spread when people touch them.

Even if the bacteria die, DNA that gives them resistance to antibiotics can survive and be passed on to other bacteria on these surfaces. Copper and brass, however, can kill the bacteria and also destroy this DNA.

— Grey (2012): Fit brass fixtures to cut superbugs, say scientists in The Telegraph.

Analyzing the 20th Century Carbon Dioxide Rise: A pre-calculus assignment

Carbon dioxide concentration (ppm) measured at the Mona Loa observatory in Hawaii shows exponential growth and a periodic annual variation.

The carbon dioxide concentration record from Mona Loa in Hawaii is an excellent data set to work with in high-school mathematics classes for two key reasons.

The first has to do with the spark-the-imagination excitement that comes from being able to work with a live, real, scientific record (updated every month) that is so easy to grab (from Scrippts), and is extremely relavant given all the issues we’re dealing with regarding global climate change.

The second is that the data is very clearly the sum of two different types of functions. The exponential growth of CO2 concentration in the atmosphere over the last 60 years dominates, but does not swamp, the annual sinusoidal variability as local plants respond to the seasons.

Assignment

So here’s the assignment using the dataset (mona-loa-2012.xls or plain text mona-loa-2012.csv):

1. Identify the exponential growth function:

Add an exponential curve trendline in a spreadsheet program or manual regression. If using the regression (which I’ve found gives the best match) your equation should have the form:

y = a b^{cx} + d

while the built-in exponential trendline will usually give something simpler like:

y = a e^{bx}

2. Subtract the exponential function.

Put the exponential function (model) into your spreadsheet program and subtract it from data set. The result should be just the annual sinusoidal function.

Dataset with the exponential curve subtracted.

If you look carefully you might also see what looks like a longer wavelength periodicity overlain on top of the annual cycle. You can attempt to extract if you wish.

3. Decipher the annual sinusoidal function

Try to match the stripped dataset with a sinusoidal function of the form:

y = a \sin (bx+c) + d

A good place to start at finding the best-fit coefficients is by recognizing that:

  • a = amplitude;
  • b = frequency (which is the inverse of the wavelength;
  • c = phase (to shift the curve left or right); and
  • d = vertical offset (this sets the baseline of the curve.

Wrap up

Now you have a model for carbon dioxide concentration, so you should be able to predict, for example, what the concentration will be for each month in the years 2020, 2050 and 2100 if the trends continue as they have for the last 60 years. This is the first step in predicting annual temperatures based on increasing CO2 concentrations.

DNA Extraction Labs

My middle school class tried DNA extractions from dried split peas and cheek cells for a lab this week, and the experiments went rather well.

Strands of DNA rising from the interface between crushed split pea “sludge” and rubbing alcohol. Bubbles trapped beneath the strands make for interesting convective-like patterns.

Split Pea DNA

For the split peas, we followed the Learn.Genetics lab. I blended the peas in some salty water at the front of the class (“Don’t you need a lid for that blender?”), and filtered it. This gave about 120 ml of filtrate. Then I added in 3 tablespoons of dish soap to the filtrate. The soap to breaks down the cell membranes and nuclear membranes because they are made of lipids (fats).

Split pea residue left behind after filtering.

I shared out the resulting green liquid to the four groups. Each student was able to get a fair amount into a test tube so they could complete the lab as individuals.

Disintegrating the cell and nuclear membranes with soap exposed the DNA, but the long DNA molecules tend to be coiled up around proteins. Each student added a pinch (highly quantified I know) of meat tenderizer to their test tube to break down the protein and allow the DNA to uncoil. Enzymes are biological catalysts, large complex molecules that accelerate chemical reactions, the breakdown of proteins in this case, without breaking down themselves, so only a little is needed.

Finally, each student carefully poured rubbing alcohol into the test tube. I had to demonstrate how to tilt the test tube while alcohol was being poured into it so that the alcohol would not mix in with the pea soup but, instead, form a layer at the top, since the alcohol is less dense than the suspension of split peas in salty water.

When the DNA is mixed in with the split pea filtrate (right) it becomes a little harder to distinguish. On the left you can see that the clear rubbing alcohol floats on top of the denser split pea/water/salt mixture.

If it was done carefully enough, the DNA would precipitate at the boundary between the two liquids. If not, the DNA would still precipitate, but it would be mixed in together with the green soup and be harder to distinguish.

Either way, however, students could see the long strands of DNA, and fish them out with glass rods.

Strands of DNA on a glass rod.

Human DNA

The human DNA extraction procedure is well demonstrated by the NOVA video. One student who missed the split pea lab did this experiment instead because it’s faster. It does not require blending to crush the cells, nor does it need the meat tenderizer enzyme.

Although this procedure produces a lot less DNA — after all, you’re only getting a few loose cells from the insides of your cheeks — the strands are still visible. And it’s YOUR DNA.

A few strands of human DNA (belonging to an individual who asked to be referred to as “Suzanne”) in a test tube. The rubbing alcohol is dyed blue for visual contrast.

Since I instructed the class on how to use the microscopes last month, one student wanted to see what his DNA looked like under the microscope. An individual DNA molecule is too small to see, but the strands we have are bunches molecules that are visible. They just don’t look like very much.

DNA strands under the microscope.